UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

High performance silicon photonic filters for dense wavelength-division multiplexing applications Boeck, Robert 2016

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
24-ubc_2016_may_boeck_robert.pdf [ 16.61MB ]
Metadata
JSON: 24-1.0300138.json
JSON-LD: 24-1.0300138-ld.json
RDF/XML (Pretty): 24-1.0300138-rdf.xml
RDF/JSON: 24-1.0300138-rdf.json
Turtle: 24-1.0300138-turtle.txt
N-Triples: 24-1.0300138-rdf-ntriples.txt
Original Record: 24-1.0300138-source.json
Full Text
24-1.0300138-fulltext.txt
Citation
24-1.0300138.ris

Full Text

High Performance Silicon Photonic Filters for DenseWavelength-Division Multiplexing ApplicationsbyRobert BoeckB.A.Sc., The University of British Columbia, 2009M.A.Sc., The University of British Columbia, 2011A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Electrical and Computer Engineering)The University of British Columbia(Vancouver)April 2016c Robert Boeck, 2016AbstractThis dissertation presents theoretical and experimental results for silicon opticalring resonator filters that meet many of the typical commercial specifications fordense wavelength-division multiplexing (DWDM) filters. First, we theoreticallydemonstrate a silicon quadruple Vernier racetrack resonator that meets 4-port filtercommercial specifications for a clear window of 0.08 nm and a channel spacingof 0.8 nm while being tolerant to typical fabrication variations. Next, we exper-imentally demonstrate a silicon quadruple Vernier racetrack resonator that meetsmany 3-port filter commercial specifications for a clear window of 0.048 nm anda channel spacing of 0.8 nm. Then, enhanced resonant tuning range using theVernier effect is theoretically and experimentally demonstrated using a thermallytunable silicon quadruple Vernier racetrack resonator. Also, we sent 12.5 Gbpsdata through a thermally tunable silicon quadruple Vernier racetrack resonator andshow open eye diagrams in both the drop port and through port of the filter, evenwithin one of the minor through port notches. We then present theoretical andexperimental results on a high performance silicon double microring resonator fil-ter using Mach-Zhender interferometer-based coupling that meets numerous 3-portfilter commercial specifications for a clear window of 8 GHz and a channel spac-ing of 200 GHz as well as having an FSR larger than the span of the C-band andlow through port passband dispersion. Next, we present a FSR-eliminated siliconVernier racetrack resonator filter. We demonstrate the performance of this filterboth theoretically and experimentally. The FSR of this filter is eliminated by us-ing contra-directional grating couplers (contra-DCs) to suppress all but one of thenotches and peaks of the filter’s spectra. Lastly, a process calibration procedureis demonstrated that accurately determines the coupling coefficients of fabricatediicontra-DCs and is used to design a FSR-eliminated silicon Vernier racetrack res-onator filter that meets 3-port filter commercial specifications for a clear windowof 13 GHz and a channel spacing of 200 GHz. This filter also has low drop portdispersion and low dispersion within the passbands of the through port.iiiPrefaceThe content of this dissertation is mostly based on the following eight publicationsand I am first author on each of them. Additionally, Michael Caverley performedthe measurements shown in Figures 4.5(a) and 4.5(b), helped with Figures 1.3 and1.4, and provided valuable feedback regarding this dissertation.1. R. Boeck, L. Chrostowski, and N. A. F. Jaeger, “Sensitivity analysis of silicon-on-insulator quadruple Vernier racetrack resonators,”Optical Engineering, vol. 54,no. 11, p. 117102, Nov. 2015. Parts of this paper, verbatim and modified, can befound in Chapters 1.2, 1.3, 2.1, 2.2, 2.3, and was used in Chapters 1.3 and 7.2.cSPIE, 2015, by permission.I and Dr. Nicolas A. F. Jaeger came up with this idea to investigate whetherVernier ring resonators could meet commercial specifications under fabricationvariations. Dr. Lukas Chrostowski provided insight into fabrication variations andmethods for analyzing those devices taking into account such variations. I per-formed the modelling and analysis and I was the main contributor in writing themanuscript. Dr. Nicolas A. F. Jaeger helped me write the paper and helped deter-mine the technical content and direction of the research. Dr. Lukas Chrostowskihelped edit the drafts of the paper, provided additional insights, and aided with thenumerical modelling.Dr. Miguel A´ngel Guille´n Torres and Dr. Ives Maceˆdo provided useful dis-cussions and helped with initial simulation efforts regarding directional couplers.Also, Michael Caverley provided useful suggestions. In accordance with SPIE pol-icy, a majority of this paper was taken from an SPIE Proceedings. This Proceedingsis listed here as the fifth paper in the preface.iv2. R. Boeck, M. Caverley, L. Chrostowski, and N. A. F. Jaeger, “Process calibra-tion method for designing silicon-on-insulator contra-directional grating couplers,”Optics Express, vol. 23, no. 8, pp. 10573-10588, Apr. 2015. This paper, verbatimand modified, can be found in Chapter 6, Appendix C, Appendix D, and was usedin Chapter 1.3. cOptical Society of America, 2015, by permission.I came up with the idea for the project, was in charge of the theoretical analy-sis, created the mask layout of the devices, directed the measurements and was incharge of interpreting the measured results, and I was the main contributor in writ-ing the manuscript. Michael Caverley provided the idea and script for determiningthe group delay and dispersion of the contra-DC by using the Hilbert transform.Michael Caverley was in charge of the derivation of the minimum bandwidth equa-tion, helped with the derivation of the average propagation constant mismatch, wasin charge of doing the measurements, helped with MATLAB R coding and verifi-cation of my results, and helped with writing the paper. Dr. Nicolas A. F. Jaegerhelped me write the paper and helped determine the technical content and directionof the research. Dr. Lukas Chrostowski helped edit the final drafts of the paper,provided additional insights, aided with the numerical modelling, and coordinatedthe electron beam fabrication and developed the process design kit for this process.The devices were fabricated at the University of Washington by Richard Bojko.Han Yun provided a mask layout script for creating the contra-directional gratingcouplers. Yun Wang designed the fibre grating couplers. Some of the fabricateddevices were measured by Fan Zhang. Dr. Wei Shi provided help with regardsto contra-DC theory and modelling. Jonas Flueckiger provided useful discussionsand technical assistance with using the mask layout software, Pyxis, by MentorGraphics. Dr. Miguel A´ngel Guille´n Torres provided useful discussions.3. R. Boeck, M. Caverley, L. Chrostowski, and N. A. F. Jaeger, “Silicon quadrupleseries-coupled Vernier racetrack resonators: experimental signal quality,” in Op-tical Fiber Communication Conference, OSA Technical Digest (online) (OpticalSociety of America, 2015), paper W2A.8. This paper, verbatim and modified, canbe found in Chapter 3.2. cOptical Society of America, 2015, by permission.I came up with the idea for the project, created the mask layout of the device,directed the measurements, was in charge of thermally tuning the device, and wasvin charge of interpreting the measured results. I was the main contributor in writ-ing the manuscript. Michael Caverley performed the measurements, provided thescript for determining the group delay and dispersion of the device by using theHilbert transform, and helped with writing the paper. Dr. Nicolas A. F. Jaegerhelped me write the paper and helped with the technical content and direction ofthe research. Dr. Lukas Chrostowski provided useful discussions, design review,feedback on the layout, helped edit the final drafts of the paper and coordinated theIME fabrication and developed the process design kit for this process.The devices were fabricated at IME and Dr. Andy Knights provided the processspecification. Yun Wang designed the fiber grating couplers. Dr. Alina Kulpa tookthe microscope image of the device. Jonas Flueckiger provided technical assistancewith using the mask layout software, Pyxis, by Mentor Graphics.4. R. Boeck, M. Caverley, L. Chrostowski, and N. A. F. Jaeger, “Experimentaldemonstration of a silicon-on-insulator high-performance double microring filterusing MZI-based coupling,” Optics Letters, vol. 40, no. 2, pp. 276-279, Jan. 2015.This paper, verbatim and modified, can be found in Chapter 4 and was used inChapter 1.3. cOptical Society of America, 2015, by permission.I came up with the idea for the project, was in charge of the theoretical analy-sis, created the mask layout of the devices, directed the measurements and was incharge of interpreting the measured results, and I was the main contributor in writ-ing the manuscript. Michael Caverley was in charge of doing the measurements,helped verify my theoretical and experimental results, and helped with writing thepaper. Dr. Nicolas A. F. Jaeger helped me write the paper and helped determinethe technical content and direction of the research. Dr. Lukas Chrostowski helpededit the final drafts of the paper, provided additional insights, aided with the nu-merical modelling, and coordinated the electron beam fabrication and developedthe process design kit for this process.The devices were fabricated at the University of Washington by Richard Bo-jko. Jonas Flueckiger provided technical assistance with using the set-up and masklayout software, Pyxis, by Mentor Graphics. Dr. Wei Shi provided assistance withusing the mask layout software. Yun Wang designed the fibre grating couplers.vi5. R. Boeck, L. Chrostowski, and N. A. F. Jaeger, “Theoretical sensitivity analysisof quadruple Vernier racetrack resonators designed for fabrication on the silicon-on-insulator platform,” Proc. SPIE 9288, Photonics North 2014, pp. 928812, 2014.Parts of this paper, verbatim and modified, can be found in Chapters 1.2, 1.3, 2.1,2.2, 2.3, and was used in Chapters 1.3 and 7.2. cSPIE, 2014, by permission.I and Dr. Nicolas A. F. Jaeger came up with this idea to investigate whetherVernier ring resonators could meet commercial specifications under fabricationvariations. Dr. Lukas Chrostowski provided insight into fabrication variations andmethods for analyzing those devices taking into account such variations. I per-formed the modelling and analysis and I was the main contributor in writing themanuscript. Dr. Nicolas A. F. Jaeger helped me write the paper and helped deter-mine the technical content and direction of the research. Dr. Lukas Chrostowskihelped edit the drafts of the paper, provided additional insights, and aided with thenumerical modelling.Dr. Miguel A´ngel Guille´n Torres and Dr. Ives Maceˆdo provided useful discus-sions and helped with initial simulation efforts regarding directional couplers.6. R. Boeck, W. Shi, L. Chrostowski, and N. A. F. Jaeger, “FSR-eliminated Vernierracetrack resonators using grating-assisted couplers,” IEEE Photonics Journal, vol.5, no. 5, pp. 2202511, Oct. 2013. This paper, verbatim and modified, can be foundin Chapter 5. Also, the modelling methods in Chapter 6.3 are taken from this paper.cIEEE 2013, by permission.I came up with the idea for the project, performed the theoretical analysis,created the mask layout of the device, performed the measurements using an auto-mated fibre array setup, and I was the main contributor in writing the manuscript.Dr. Wei Shi provided insight into how to design contra-directional grating cou-plers and integrating them with racetrack resonators, provided MATLAB R codefor modelling a single racetrack resonator with contra-directional couplers whichI modified for my device, provided sentences for the paper with regards to anti-reflection gratings, and provided suggestions and helped edit the paper. Dr. NicolasA. F. Jaeger helped me write the paper and helped determine the technical contentand direction of the research. Dr. Nicolas A. F. Jaeger and Dr. Lukas Chros-towski suggested the original motivation of using contra-DCs in a ring resonator asviia means of eliminating the FSR. Dr. Lukas Chrostowski provided design review,feedback on the layout, helped edit the final drafts of the paper, provided additionalinsights, aided with the numerical modelling, and coordinated the electron beamwith metallization fabrication and developed the process design kit for this process.The device was fabricated at the University of Washington by Richard Bojkoand Dr. Edgar Huante-Ceron and Dr. Andy Knights did the metallization. YunWang designed the fibre grating couplers. Dr. Alina Kulpa took the microscopeimage of the device. Jonas Flueckiger provided technical assistance with usingthe mask layout software, Pyxis, by Mentor Graphics and using the measurementset-up. Han Yun provided a mask layout script for creating the contra-directionalgrating couplers. The automated fibre array setup was created by Jonas Flueckigerand Charlie Lin.7. R. Boeck, L. Chrostowski, and N. A. F. Jaeger, “Thermally tunable quadrupleVernier racetrack resonators, Optics Letters, vol. 38, no. 14, pp. 2440-2442,Jul. 2013. This paper, verbatim and modified, can be found in the Chapter 3.1,the introduction paragraph to Chapter 3, and was used in Chapter 1.3. cOpticalSociety of America, 2013, by permission.I came up with the idea for the project, performed the theoretical analysis,created the mask layout of the devices, measured the devices, and I was the maincontributor in writing the manuscript. Dr. Nicolas A. F. Jaeger helped me writethe paper and helped determine the technical content and direction of the research.Dr. Lukas Chrostowski provided design review, feedback on the layout, helped editthe final drafts of the paper, provided additional insights, aided with the numericalmodelling, and coordinated the electron beam with metallization fabrication anddeveloped the process design kit for this process.The device was fabricated at the University of Washington by Richard Bojkoand Dr. Edgar Huante-Ceron and Dr. Andy Knights did the metallization. JonasFlueckiger gave technical assistance with using the mask layout software. YunWang designed the fiber grating couplers. Jonas Flueckiger and Charlie Lin createdthe automated fibre array set-up used to measure the devices. Dr. Alina Kulpa tookthe microscope image of the device.viii8. R. Boeck, J. Flueckiger, L. Chrostowski, and N. A. F. Jaeger, “Experimentalperformance of DWDM quadruple Vernier racetrack resonators,” Optics Express,vol. 21, no. 7, pp. 9103-9112, Apr. 2013. This paper, verbatim and modified, canbe found in Chapter 2.4 and the introduction paragraph of Chapter 2 and AppendixA. cOptical Society of America, 2013, by permission.I came up with the idea for the project, performed the theoretical analysis,created the mask layout of the devices, directed the measurements, and I was themain contributor in writing the manuscript. Dr. Nicolas A. F. Jaeger helped mewrite the paper and helped determine the technical content and direction of theresearch. Dr. Lukas Chrostowski provided design review, feedback on the layout,helped edit the final drafts of the paper, provided additional insights, aided with thenumerical modelling, and coordinated the electron beam fabrication and developedthe process design kit for this process. Jonas Flueckiger was in charge of measuringthe device, giving technical assistance with using the mask layout software as wellas proofreading and providing suggestions for the paper.The device was fabricated at the University of Washington by Richard Bojkoand Yun Wang designed the fibre grating couplers. Jonas Flueckiger and CharlieLin created the automated fibre array set-up.ixTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Silicon Photonics: Potential Disruptor for Optical InterconnectsMarkets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Optical DWDM Filters . . . . . . . . . . . . . . . . . . . . . . . 61.2.1 Inter-Channel Cross-Talk and Intra-Channel Cross-Talk . 71.2.2 DWDM Filter Specifications . . . . . . . . . . . . . . . . 81.2.3 Optical Filter Dispersion . . . . . . . . . . . . . . . . . . 121.3 Methods to Extend the FSR of Ring Resonators . . . . . . . . . . 131.3.1 Ring Resonators Exhibiting the Vernier Effect . . . . . . . 171.3.2 Ring Resonators withMach-Zehnder Interferometer-BasedCoupling . . . . . . . . . . . . . . . . . . . . . . . . . . 241.3.3 Ring Resonators with Contra-Directional Grating Couplers 26x1.4 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 Silicon-On-Insulator Quadruple Vernier Racetrack Resonators . . . 312.1 Design of Silicon Quadruple Vernier Racetrack Resonators . . . . 322.2 Performance Optimization . . . . . . . . . . . . . . . . . . . . . 342.3 Fabrication Sensitivity . . . . . . . . . . . . . . . . . . . . . . . 392.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 493 Thermally Tunable Silicon-On-Insulator Vernier Racetrack Resonators 553.1 Thermally Tunable Silicon Quadruple Vernier Racetrack Resonators 563.2 Silicon-On-Insulator Quadruple Vernier Racetrack Resonators: Ex-perimental Signal Quality . . . . . . . . . . . . . . . . . . . . . . 614 High Performance Silicon-On-Insulator DoubleMicroring Filter Us-ing MZI-Based Coupling . . . . . . . . . . . . . . . . . . . . . . . . 664.1 Theory and Design . . . . . . . . . . . . . . . . . . . . . . . . . 674.2 Theoretical Results . . . . . . . . . . . . . . . . . . . . . . . . . 694.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 715 FSR-Eliminated Silicon-On-Insulator Vernier Racetrack ResonatorsUsing Grating-Assisted Couplers . . . . . . . . . . . . . . . . . . . . 755.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 876 Process CalibrationMethod for Designing Silicon-On-Insulator Contra-Directional Grating Couplers . . . . . . . . . . . . . . . . . . . . . . 926.1 Contra-DC Theory and Process Calibration Method . . . . . . . . 936.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 996.3 Example of Using the Process Calibration Method in the Filter De-sign Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1087 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . 1127.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1127.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115xiBibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172A Derivation of the Transfer Functions of a Quadruple Series-CoupledRacetrack Resonator Filter . . . . . . . . . . . . . . . . . . . . . . . 172B Derivation of the Transfer Functions of a Double Microring Res-onator Filter with MZI-Based Coupling . . . . . . . . . . . . . . . . 177C Derivation of the Average Propagation ConstantMismatch of a Contra-Directional Grating Coupler . . . . . . . . . . . . . . . . . . . . . . 181D Derivation of theMinimumBandwidth of a Contra-Directional Grat-ing Coupler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184xiiList of TablesTable 1.1 List of companies involved in silicon photonics [1, 7–73]. . . . 3Table 1.2 Target specifications for 3-port and 4-port filters with channelspacings of 100 GHz. . . . . . . . . . . . . . . . . . . . . . . 11Table 2.1 One of our device’s modelled results as compared to the targetspecifications. cSPIE, 2015, by permission [85]. . . . . . . . 37Table 2.2 Width tolerance for (gap 1, gap 2, gap 3) = (150 nm, 350 nm,390 nm). Bolded parameter values do not meet their commer-cial specifications. cSPIE, 2015, by permission [85]. . . . . . 44Table 2.3 Width tolerance for (gap 1, gap 2, gap 3) = (150 nm, 360 nm,410 nm). Bolded parameter values do not meet their commer-cial specifications. cSPIE, 2015, by permission [85]. . . . . . 45Table 2.4 Width tolerance for (gap 1, gap 2, gap 3) = (150 nm, 350 nm,390 nm). cSPIE, 2015, by permission [85]. . . . . . . . . . . 46Table 2.5 Height tolerance for (gap 1, gap 2, gap 3) = (150 nm, 350 nm,390 nm). cSPIE, 2015, by permission [85]. . . . . . . . . . . 47Table 2.6 Propagation loss tolerance for (gap 1, gap 2, gap 3) = (150 nm,350 nm, 390 nm). Bolded parameter value does not meet itscommercial specification. cSPIE, 2015, by permission [85]. . 48Table 2.7 Theoretical and target 3-port filter specifications [96]. . . . . . 50Table 2.8 Experimental and target 3-port filter specifications [96]. . . . . 54Table 4.1 Target specifications for 200 GHz optical filters [105]. . . . . . 69Table 4.2 Theoretical filter results [105]. . . . . . . . . . . . . . . . . . 71xiiiTable 4.3 Experimental filter results [105]. . . . . . . . . . . . . . . . . 73Table 5.1 Drop port and through port insertion loss for single racetrackresonators with gratings, cascaded Vernier racetrack resonatorswith and without gratings, and grating-coupled cascaded iden-tical racetrack resonators. c2013 IEEE, by permission [97]. . 85Table 5.2 Spectral characteristics for single racetrack resonators with grat-ings, cascaded Vernier racetrack resonators with and withoutgratings, and grating-coupled cascaded identical racetrack res-onators. c2013 IEEE, by permission [97]. . . . . . . . . . . . 86Table 5.3 Experimental results of grating-coupled cascaded Vernier race-track resonator. c2013 IEEE, by permission [97]. . . . . . . . 90Table 6.1 Modelled results and target specifications for 200 GHz 3-portfilters (table modified from [105]). . . . . . . . . . . . . . . . 111Table 7.1 Comparison of FSR extension methods as implemented in dis-sertation (the benefits are bolded). . . . . . . . . . . . . . . . . 114xivList of FiguresFigure 1.1 (a) The number of companies involved in silicon photonicsbased on market cap categories. . . . . . . . . . . . . . . . . 4Figure 1.2 Diagram of a commercial 4-port optical add-drop filter con-sisting of two 3-port optical filters [86, 87]. . . . . . . . . . . 7Figure 1.3 A diagram illustrating inter-channel cross-talk and intra-channelcross-talk using a 4-port optical add-after-drop filter. . . . . . 8Figure 1.4 Diagrams illustrating (a) a method to reduce inter-channel cross-talk by changing the filter’s drop port lineshape to have a fastertransition from passband to stopband and a smaller bandwidthand (b) a method to reduce intra-channel cross-talk by chang-ing the filter’s through port lineshape to have a larger differ-ence, in dB, between the passband and the stopband. . . . . . 12Figure 1.5 (a) Schematic diagram of a 4-port ring resonator optical add-drop filter and (b) example through port and drop port spectrawhen light is only injected into the input port. . . . . . . . . . 14Figure 1.6 Schematic diagram of two 3-port ring resonator filters cas-caded together to form a 4-port optical add-after-drop filter. . . 15Figure 1.7 Diagram that shows the 45 channels within the C-band thatare used in DWDM applications for a channel spacing of 100GHz (the location of each channel is taken from ITU-T Rec-ommendation G.694.1 [92, 110]). The FSR of a ring resonatorshould be larger than the wavelength span between channel 1and channel 45. . . . . . . . . . . . . . . . . . . . . . . . . . 16xvFigure 1.8 Schematic diagram of a double Vernier racetrack resonator (fig-ure adapted from [85]). . . . . . . . . . . . . . . . . . . . . . 17Figure 1.9 The number of publications from 1986 to 2015 which discussresonators that exhibit the Vernier effect [84, 85, 96, 97, 107,111–114, 126–429]. . . . . . . . . . . . . . . . . . . . . . . 19Figure 1.10 Schematic diagram of a Vernier device consisting of four race-track resonators (see Refs. 96, 126, 140–143, 149, 150 for re-sults on similar resonators). cSPIE, 2015, by permission [85]. 19Figure 1.11 (a) Schematic diagram of a Vernier filter consisting of tworacetrack resonators (figure adapted from [85]). . . . . . . . . 21Figure 1.12 (a) Drop port spectral responses for single silicon ring res-onators, “Ring 1” and “Ring 2”, that are not coupled together . 23Figure 1.13 (a) Schematic diagram of a series-coupled double ring res-onator, (b) schematic diagram of aMZI coupler, and (c) schematicdiagram of a double ring resonator filter that uses MZI-BC(modified from [105]). . . . . . . . . . . . . . . . . . . . . . 25Figure 1.14 (a) Example through port and drop port spectral response ofa series-coupled double ring resonator. (b) Example outputresponses of an MZI coupler when light is only injected intoinput port “In 1”. (c) Example through port and drop port spec-tral response of a double ring resonator filter that uses MZI-BC. 26Figure 1.15 (a) Schematic diagram of a typical design of a contra-DC and(b) a close-up view of a portion of a typical design of a contra-DC (modified version from [435]). . . . . . . . . . . . . . . . 27Figure 1.16 (a) Effective index versus wavelength where the red line is theeffective index of waveguide “b”, the green line is the effectiveindex of waveguide “a”, and the blue line is the average effec-tive index. (b) Example of a through port power transmissionfactor response (red line) and drop port power coupling factorresponse (green line) for a silicon contra-DC. . . . . . . . . . 29Figure 1.17 The number of publications from 2005 to 2015 which discusssilicon contra-DCs [97, 434–471]. . . . . . . . . . . . . . . . 29xviFigure 2.1 Schematic of a Vernier filter consisting of four racetrack res-onators (see Refs. 96, 126, 140–143, 149, 150 for results onsimilar resonators). cSPIE, 2015, by permission [85]. . . . . 34Figure 2.2 For light injected at the input port, (a) shows the theoreticaldrop port and through port responses (solid lines correspond toD1 and dashed lines correspond to D2) which show large IPSsand FSRs larger than the span of the C-band . . . . . . . . . . 35Figure 2.3 For light injected at the input port, (a) shows the drop port dis-persions within the region of the passband, and (b) the largestthrough port dispersions within one of through port passbandsfor devices D1 and D2. cSPIE, 2015, by permission [85]. . . 36Figure 2.4 (a) Spectral response at through port and drop port when lightis injected into the input port and the add port of the device,respectively. (b) shows that the major notch within the stop-band changes depending on whether the light is injected intothe input port or add port. (c) shows that the passband spec-trum changes depending on whether the light is injected intothe input port or add port. cSPIE, 2015, by permission [85]. . 38Figure 2.5 Dispersion at the through port and the drop port when lightis injected into the input port and the add port of the device,respectively. (b) A zoom-in of Figure 2.5(a) in the region ofone of the passbands. cSPIE, 2015, by permission [85]. . . . 38Figure 2.6 For light injected at the input port, (a) shows the sensitivity ofthe spectral response to changes in the waveguide width for aheight of 220 nm and a loss of 2.4 dB/cm . . . . . . . . . . . 43Figure 2.7 Schematic of our quadruple series-coupled racetrack resonatorsexhibiting the Vernier effect. cOptical Society of America,2013, by permission [96]. . . . . . . . . . . . . . . . . . . . 49Figure 2.8 (a) Theoretical spectral response. (b) A “zoom-in” of the majorresonance. cOptical Society of America, 2013, by permission[96]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Figure 2.9 (a) Measured through port and drop port spectral response. . . 53xviiFigure 3.1 (a) Shows the schematic of the quadruple Vernier racetrack res-onator and (b) shows the fabricated device. cOptical Societyof America, 2013, by permission [149]. . . . . . . . . . . . . 57Figure 3.2 (a) Shows the theoretical through port and drop port spectraand (b) shows a major peak in the drop port response and amajor notch in the through port response. cOptical Society ofAmerica, 2013, by permission [149]. . . . . . . . . . . . . . . 58Figure 3.3 (a) Shows the experimental through port and drop port spectraand (b) shows a major peak of the drop port response and amajor notch of the through port response. cOptical Societyof America, 2013, by permission [149]. . . . . . . . . . . . . 60Figure 3.4 (a) Shows the theoretical drop port spectral responses for var-ious temperature changes applied to racetrack resonators R3and R4 and (b) shows the experimental drop port spectral re-sponses for various changes in the voltage applied to the heaterson top of racetrack resonators R3 and R4. cOptical Societyof America, 2013, by permission [149]. . . . . . . . . . . . . 60Figure 3.5 (a) Schematic diagram of the Vernier filter (see [84, 96, 127,140–142, 149]) and (b) a microscope image of the fabricatedfilter showing the integrated heaters. cOptical Society of Amer-ica, 2015, by permission [150]. . . . . . . . . . . . . . . . . . 62Figure 3.6 (a) Measured spectra from the in port to the drop port as wellas the in port to the through port of our filter in the region ofthe major peak/notch before and after thermal tuning . . . . . 63Figure 3.7 (a) Eye diagram measured for data passing from the in portto the drop port at a wavelength of 1532.636 nm. Eye dia-grams for data passing from the in port to the through portat (b) 1543.018 nm, (c) 1545.153 nm, and (d) 1545.247 nm.cOptical Society of America, 2015, by permission [150]. . . 65Figure 4.1 Schematic of the device (either the add port or the drop port isused and the other is terminated when used as a 3-port device).cOptical Society of America, 2015, by permission [105]. . . 68xviiiFigure 4.2 (a) Theoretical drop port and through port response and (b)zoom-in of Figure 4.2(a). cOptical Society of America, 2015,by permission [105]. . . . . . . . . . . . . . . . . . . . . . . 70Figure 4.3 Dispersion of (a) the drop port within the passband region and(b) the region near the suppressed through port notch. cOpticalSociety of America, 2015, by permission. . . . . . . . . . . . 71Figure 4.4 (a) Experimental drop port and through port response and (b)zoom-in of Figure 4.4(a). cOptical Society of America, 2015,by permission [105]. . . . . . . . . . . . . . . . . . . . . . . 73Figure 4.5 (a) Experimental drop port dispersion (vertical dashed lines in-dicate width of clear window) and (b) experimental throughport dispersion within the through port passband. . . . . . . . 73Figure 5.1 (a) Schematic of a section of the contra-DC and (b) schematicof the grating-coupled cascaded Vernier racetrack resonator.c2013 IEEE, by permission [97]. . . . . . . . . . . . . . . . 78Figure 5.2 (a) |k|2 versus wavelength for the contra-directional (blue-solid)and co-directional (black-dash) couplers. (b) |t|2 versus wave-length for the contra-directional (red-solid) and co-directional(black-dash) couplers. c2013 IEEE, by permission [97]. . . . 80Figure 5.3 (a) Drop port spectral response comparison between single grating-coupled racetrack resonator with length La (green-solid) andLb (red-dash) . . . . . . . . . . . . . . . . . . . . . . . . . . 82Figure 5.4 (a) Drop port spectral response and phase and (b) group delayand dispersion of our grating-coupled cascaded Vernier race-track resonator. c2013 IEEE, by permission [97]. . . . . . . 83xixFigure 5.5 (a) Through port spectral response comparison between grating-coupled cascaded racetrack resonator (blue-solid) and cascadedracetrack resonator without gratings (black-dash), (b) a “zoom-in” of the major notch in Figure 5.5(a), (c) through port spec-tral response comparison between grating-coupled single (re-sponse same as cascaded configuration) racetrack resonatorwith lengths La and Lb, and (d) a “zoom-in” of the major notchin Figure 5.5(c). c2013 IEEE, by permission [97]. . . . . . . 83Figure 5.6 Optical microscope image of the fabricated device. c2013IEEE, by permission [97]. . . . . . . . . . . . . . . . . . . . 87Figure 5.7 (a) Experimental drop port (solid) and through port (dashed)responses when the voltage to the heater for racetrack res-onator “a” is 0 V (red), 4V (green), 5.8 V (black), and 7 V(blue). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Figure 6.1 (a) Diagram of a contra-DC. (b) A close-up view of a portion ofa contra-DC (figure was adapted from [97]). cOptical Societyof America, 2015, by permission [435]. . . . . . . . . . . . . 94Figure 6.2 (a) Diagram depicting some of the relevant contra-DC param-eters as functions of Db . (b) Experimental drop port spectrumof one of our devices as a function of Db . cOptical Societyof America, 2015, by permission [435]. . . . . . . . . . . . . 97Figure 6.3 Experimental drop port spectra for the devices from (a) “run1,” (c) “run 2,” and (e) “run 3” with gap distances equal to 140nm, 220 nm, 340 nm, and 400 nm. Experimental through portspectra for the devices from (b) “run 1,” (d) “run 2,” and (f)“run 3” with gap distances equal to 140 nm, 220 nm, 340 nm,and 400 nm. cOptical Society of America, 2015, by permis-sion [435]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 100xxFigure 6.4 (a) Experimental bandwidth at FWHM versus gap distance and(b) extracted coupling coefficient versus gap distance using theFWHM method. (c) Experimental bandwidth at FWHM ver-sus corrugation width and (d) extracted coupling coefficientversus corrugation width for devices from “run 1” with a fixedgap distance of 280 nm using the FWHM method. cOpticalSociety of America, 2015, by permission [435]. . . . . . . . . 102Figure 6.5 Comparison between the FWHMmethod, the null method, andthe curve-fit method to determine |k| for (a) “run 1,” (b) “run2,” and (c) “run 3.” (d) Drop port spectrum of a contra-DCwith a gap distance of 300 nm from “run 2,” which is chosento illustrate that there can be multiple possible choices for thelocation of the first null to the left of the main lobe (the reddots indicate possible choices for the null location). cOpticalSociety of America, 2015, by permission [435]. . . . . . . . . 103Figure 6.6 Theoretical predicted minimum bandwidth at FWHM versuscoupling length including experimental data points from thedevices with gap distances of 400 nm from the three fabricationruns. cOptical Society of America, 2015, by permission [435]. 104Figure 6.7 (a) Experimental and simulated (using the extracted |k| ob-tained using the FWHM method) drop port and through portspectra for a contra-DC (from “run 2”) with a gap distanceequal to 140 nm. . . . . . . . . . . . . . . . . . . . . . . . . 106Figure 6.8 Comparison between the experimental and the simulated (us-ing extracted |k|s determined from the FWHM method) (a)maximum power coupling factor and (b) minimum power trans-mission factor versus gap distance. cOptical Society of Amer-ica, 2015, by permission [435]. . . . . . . . . . . . . . . . . . 107xxiFigure 6.9 Comparison between the experimental through port (a) groupdelay response and (b) dispersion response that were deter-mined using the Hilbert transform method and the simulatedresults that were determined using the extracted |k| of 19882m-1 as well as the measured results using the OVA. cOpticalSociety of America, 2015, by permission [435]. . . . . . . . . 108Figure 6.10 Schematic diagram of an optimized 3-port grating-assisted Vernierfilter (figure has been adapted from [97]). . . . . . . . . . . . 109Figure 6.11 (a) Through port spectral response and drop port spectral re-sponse, (b) a zoom-in within the region of the major peak/notch,(c) drop port dispersion within the wavelength region of themajor peak, and (d) through port dispersion within the wave-length region corresponding to the passband to the left of themajor notch of an optimized 3-port grating-assisted Vernier filter.110Figure 7.1 (a) Through port passband and (b) drop port passband compar-ison, when light is injected into the input port and when lightis injected into the add port, respectively, of a 4-port quadru-ple Vernier racetrack resonator, for propagation losses of 2.4dB/cm and 0.5 dB/cm. . . . . . . . . . . . . . . . . . . . . . 116Figure C.1 Diagram depicting some of the relevant parameters used in ourderivation. cOptical Society of America, 2015, by permission[435]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183xxiiList of AbbreviationsWDM wavelength-division multiplexingcap capitalizationADR American depositary receiptUSD United States dollarCWDM coarse wavelength-division multiplexingMZI Mach-Zehnder interferometerDWDM dense wavelength-division multiplexingMUX multiplexerDEMUX demultiplexerITU International Telecommunication UnionAWG arrayed waveguide gratingFSR free spectral rangeIL insertion lossIPS interstitial peak suppressionEC express channelNRZ non-return-to-zeroSOI silicon-on-insulatorCMOS complementary metal-oxide-semiconductorMZI-BC Mach-Zehnder interferometer-based couplingFDTD finite-difference time-domainxxiiicontra-DC contra-directional grating couplerTE transverse electricTM transverse magneticCIFS coupling-induced frequency shiftBW bandwidthIME Institute of MicroelectronicsPRBS pseudorandom binary sequenceMRR microring resonatorOADM optical add-drop multiplexerFWHM full-width-at-half-maximumSEM scanning electron microscopeOVA Optical Vector AnalyzerxxivAcknowledgmentsI would like to thank my father, Max, for his support at every step of this journeyand, in memoriam, my mother, Ildiko, who inspired, encouraged, and taught me topursue excellence in all areas of my life.Additionally, I would like to thank Dr. Nicolas A. F. Jaeger and Dr. LukasChrostowski for their supervision. Specifically, I am incredibly grateful for theguidance and mentorship that Dr. Jaeger has provided me. I would also like tothank Michael Caverley, Dr. Wei Shi, Jonas Flueckiger, Dr. Miguel A´ngel Guille´nTorres, Yun Wang, Han Yun, Charlie Lin, Hasitha Jayatilleka, Dr. Xu Wang, KyleMurray, Dr. Alina Kulpa, Fan Zhang, and Dr. Ives Maceˆdo. Also, I would liketo thank Richard Bojko at the University of Washington for fabricating many ofthe devices that are presented within this dissertation as well as Dr. Edgar Huante-Ceron and Dr. Andy Knights at McMaster University for the metallization process.I would like to thank Dr. Edmond Cretu for being on my supervisory com-mittee as well as the other member of my qualifying and departmental examiningcommittees, Dr. Shahriar Mirabbasi as Heads Nominee and Drs. Konrad Walusand Alireza Nojeh for serving as the Chairs. Also, I thank the External Exam-iner, Dr. Vittorio Passaro, the University Examiners, Drs. William G. Dunford andAnasavarapu Srikantha Phani, and the Chair, Dr. Antony Hodgson, for serving asexamining committee members for my Final Doctoral Examination.Also, I acknowledge the Natural Sciences and Engineering Research Councilof Canada, the SiEPIC program, CMC Microsystems, Lumerical Solutions, Inc.,and Mentor Graphics. Part of this work was conducted at the University of Wash-ington Nanofabrication Facility, a member of the NSF National NanotechnologyInfrastructure Network.xxvChapter 1Introduction1.1 Silicon Photonics: Potential Disruptor for OpticalInterconnects MarketsSilicon photonics has emerged as an attractive alternative to on-chip copper in-terconnects as well as to currently used wavelength-division multiplexing (WDM)components (see [1]). In 2013, the application that had the largest market for sil-icon photonics was telecommunications [2] and in 2015 the largest market is datacommunications [1]. In 2014, WDM silicon photonic filters had the largest shareof the market as compared to other components, such as silicon modulators, andthe demand for these filters is expected to grow rapidly in the years to come [2].Yole De´veloppement has stated that the silicon photonics market sales are expectedto quadruple between 2010-2017 [3].Due to the enormous potential that silicon photonics has to be a technologydisruptor, numerous companies are involved in the design and/or manufacturing ofsilicon photonic devices and circuits, as well as selling software that can be used forthe modelling and layout of silicon photonic circuits for a variety of applicationsthat include telecommunications, data communications, and sensing, as listed inTable 1.1. Figure 1.1(a) provides a break-down of the 77 companies involved insilicon photonics that are listed in Table 1.1. The break-down is based on thenumber of companies that are not publicly traded (private) as well as based onthe market capitalization (cap) of publicly traded companies (all sectors of each1company). The market cap is categorized as micro cap, small cap, mid cap, andlarge cap [4]. Micro cap is defined as a market cap between 50 million dollarsand 300 million dollars, small cap is defined as a market cap between 300 milliondollars and 2 billion dollars, mid cap is defined as a market cap between 2 billiondollars and 10 billion dollars, and large cap is defined as a market cap greater than10 billion dollars [4]. Figure 1.1(a) shows that, currently, there are significantlymore private companies (52) involved in silicon photonics than publicly tradedcompanies (25). The market cap provides insight into the sentiment that investorshave with regards to a particular company [5, 6]. Figure 1.1(b) shows the marketcap of the 25 publicly traded companies involved in silicon photonics. The totalmarket cap of these companies, as of January 3, 2016, is about 1 trillion USD,which indicates the overall, positive sentiment that investors have towards thesecompanies [5, 6]. Furthermore, this positive investor sentiment [5, 6] translatesinto an advantageous situation with regard to the progress of this technology, asit is desirable to have companies with excellent track records involved in siliconphotonics research and development.2Table 1.1: List of companies involved in silicon photonics [1, 7–73].Acacia Communications, Inc. Fujitsu Ltd.e One Silicon Chip Photonics, Inc.Accelink Technologies Co., Ltd. Genalyte, Inc. Optic2Connect Pte. Ltd.Acorn Technologies Hamamatsu Photonics K. K. Optiwave Systems, Inc.AEPONYX, Inc. Hewlett-Packard Companyf Oracle Corp.Alcatel-Lucent S. A.a IBM PhoeniX B.V.Analog Photonics LLC Infinera Corp. Photline TechnologieshAPIC Corp. Inphi Corp. Photon Design, Inc.Apollo Photonics, Inc. Innolume GmbH PhotonIC Corp.Applied NanoTools, Inc. Intel PLCC2 LLCAurrion, Inc. JCMwave GmbH RANOVUS, Inc.Avago Technologies Kaiam Corp. Rockley PhotonicsAyar Labs Luceda Photonics Samsung Electronics Co., Ltd.BrPhotonics Produtos Optoeletroˆnicos LTDAb Lumerical Solutions, Inc. Samtec, Inc.Caliopac Luxmux Technology Corp. Sandia Corp.iCentera Photonics, Inc. Luxtera, Inc. Shanghai Industrial µTechnology Research Institute Co., Ltd.Chiral Photonics, Inc. M/A-COM Technology Solutions Holdings, Inc. Sicoya GmbHCisco Systems, Inc. Magic Leap, Inc. SiFiveCompass-EOS Maple Leaf Photonics LLC SiFotonics Technologies Co., Ltd.COMSOL, Inc. Mellanox Technologies Skorpios Technologies, Inc.Coriantd Mentor Graphics Corp. STMicroelectronicsDAS Photonics Morton Photonics, Inc. Synopsys, Inc.DermaLumics S.L. NEC Corp. TeraXion, Inc.EM Photonics, Inc. NeoPhotonics Corp. VLC Photonics S.L.Ericsson Novati Technologiesg VPIphotonics Inc.Etaphase, Inc. Oclaro, Inc. VTT Memsfab Ltd.Finisar Corp. Omega Optics, Inc.aOwns Bell Labs [50].bOwned by CPqD, 51%, and GigOptix, Inc., 49% [73].cOwned by Huawei Technologies Co. Ltd. [31].dFounded by Marlin Equity Partners [74].e Owns Fujitsu Laboratories Ltd. Fujitsu Laboratories of America, Inc., is owned by Fujitsu Laboratories Ltd. [18].f Has now split into two publicly traded companies: HP Inc. and Hewlett Packard Enterprise [75].gOwned by Tezzaron Semiconductor Corp. [76].h Now called iXBlue Photonics (originally two companies, Photline Technologies and iXFiber) and owned by iXBlue [77].iOwned by Lockheed Martin Corp. [33].367.53%1.30%6.49%10.39%14.29%a)privatemid capsmall capmicro caplarge cap1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25020406080100120140160180200Market cap (billion USD)Name of companyb)Figure 1.1: (a) The number of companies involved in silicon photonics basedon market cap categories. It should be noted that if a private companyis owned by a publicly traded company, only the publicly traded com-pany is included in this chart. We have included HP, Inc., and HewlettPackard Enterprise as a single large cap entity. (b) The market cap val-ues, as of January 3, 2016, for companies involved in silicon photonicswhere: 1 = Samsung Electronics Co., Ltd., 2 = Intel, 3 = Oracle Corp.,4 = Cisco Systems, Inc., 5 = IBM, 6 = Lockheed Martin Corp., 7 =the combined market caps for HP, Inc., and Hewlett Packard Enterprise,8 = Avago Technologies, 9 = Ericsson [American depositary receipt,ADR], 10 = Alcatel-Lucent S. A., [ADR], 11 = Fujitsu Ltd. [ADR], 12= NEC Corp., 13 = Synopsys, Inc., 14 = STMicroelectronics [ADR],15 = Hamamatsu Photonics K. K., 16 = Infinera Corp., 17 = M/A-COMTechnology Solutions Holdings, Inc., 18 = Mentor Graphics Corp., 19= Accelink Technologies Co., Ltd., 20 = Mellanox Technologies, 21 =Finisar Corp., 22 = Inphi Corp., 23 = NeoPhotonics Corp., 24 = Oclaro,Inc., and 25 = GigOptix, Inc. The market cap values were obtained fromhttps://www.google.com/finance and currency conversions to USD werecalculated using http://www.xe.com/currencyconverter/.4The on-chip integration of high-yield silicon photonics interconnect compo-nents such as lasers, modulators, WDM filters, and photodetectors is essentialfor the deployment of this technology in telecommunications and data commu-nications applications. Numerous companies have demonstrated integrated siliconphotonic chips, such as IBM [56], Intel [55], Oracle Corp. [78], Hewlett-PackardCompany [52], Luxtera, Inc. [65, 79], Aurrion, Inc. [56], and Acacia Communi-cations, Inc., [80]. For example, recently, IBM in collaboration with Aurrion, Inc.,have integrated tunable lasers, electro-absorption modulators, and multiplexers tocreate a four channel silicon photonic transmitter where each channel had a datarate of 28 Gbps [56]. Also, Hewlett-Packard Company in collaboration with Innol-ume GmbH have recently integrated silicon microring modulators with a quantumdot-based comb laser for the creation of a five channel silicon photonic transmit-ter [52]. Intel has recently demonstrated the integration of hybrid silicon lasers,modulators, multiplexer and demultiplexer filters, and SiGe photodetectors to cre-ate a coarse wavelength-division multiplexing (CWDM) four channel (12.5 Gbpsper channel) packaged silicon photonic transmitter and receiver [55]. Intel has alsodemonstrated a 1310 nm silicon photonic transceiver operating at a data rate of 25Gbps [55]. Oracle Corp. has demonstrated a packaged, eight channel (10 Gbpsper channel), WDM silicon photonic transceiver that included ring modulators,demultiplexer ring resonators, and Ge photodiodes [78]. In 2012, Luxtera, Inc.,announced that it had sold one million 10 Gbit channel silicon photonics products[65] and they have recently demonstrated a packaged silicon photonic transceiveroperating at an aggregate data rate of 104 Gbps [79]. Acacia Communications,Inc., have also demonstrated integrated silicon photonics by creating a 100 Gbpscoherent silicon photonic transceiver [80], and recently they announced their in-tention for an initial public offering in 2016 [81]. The fact that there are numerouscompanies involved in various aspects of silicon photonics technology providesclear evidence that silicon photonics is becoming widely accepted as the next tech-nology for data interconnects as well as for the WDM filters currently deployed intelecommunication applications.Multiplexer/demultiplexer filters and modulators have been utilized in a num-ber of the integrated silicon photonics chips mentioned above. There are a numberof waveguide-based structures that have been used by these companies to create5filters and/or modulators, such as ring resonators [52, 78] and Mach-Zehnder inter-ferometers (MZIs) [53, 80]. Specifically, there are numerous companies currentlyinvolved in research and development of ring resonator-based silicon photonics,see for example, Oracle Corp. [54, 78], Coriant [49], Ericsson [82], Hewlett-Packard Company [52], Samsung Electronics Co., Ltd. [8], Alcatel-Lucent S. A.[50], Sandia Corp. [33], RANOVUS [60], Chiral Photonics, Inc. [35], and Fu-jitsu Laboratories Ltd. [83]. The fact that numerous companies are involved insilicon photonic ring resonator research provides concrete evidence that ring res-onators are seen, from an industry perspective, as desirable components for nextgeneration data interconnects. Furthermore, the fact that WDM silicon photonicfilters had the largest share of the silicon photonics market in 2014 [2] providesadditional evidence that silicon photonic ring resonators are a promising area forresearch and development, since one of the main components that can be createdusing ring resonators are silicon photonic filters for WDM applications.The focus of this dissertation is the design and experimental demonstration ofsilicon photonic ring resonator-based filters for dense wavelength-division multi-plexing (DWDM) applications. Therefore, it is important to know what the typi-cal commercial filter specifications are to ensure that adequate filter operation inDWDM applications is achieved. In Chapter 1.2, I will present the typical com-mercial specifications for DWDM 3-port optical filters and 4-port optical add-dropfilters, as well as the definition for each specification.1.2 Optical DWDM Filters1 There are three main types of optical filters used in DWDM applications, whichare optical multiplexer filters (MUXs), optical demultiplexer filters (DEMUXs),and optical add-drop filters. The MUX consists of three ports which are the inputport, the add port, and the through port. The MUX allows signals to be mergedonto the same optical link by routing them from the add port to the through port.The DEMUX consists of three ports which are the input port, the drop port, and thethrough port. The DEMUX allows signals to be separated by routing them fromthe input port to the drop port. The optical add-drop filter consists of four ports1Parts of Chapter 1.2 are taken from [84, 85].6which are the input port, the drop port, the add port, and the through port. Opticaladd-drop filters function as both MUXs and as DEMUXs. It should be noted herethat some commercially available DWDM 4-port optical add-drop filters consist ofa 3-port DEMUX cascaded to a 3-port MUX to form a 4-port optical add-after-drop filter as shown in Figure 1.2 [86, 87]. In the example shown in Figure 1.2, theinput has three different signals at three different wavelengths, l1, l2, and l3. Thefirst 3-port filter passes the data at l2 and l3 to the through port and the data at l1is routed to the drop port. The input to the second 3-port filter is now l2 and l3.New data at l1 is then routed from the add port to the through port of the secondthree-port filter where it is combined with the data at l2 and l3.							DEMUX	THROUGH	λ1	 λ2	 λ1	ADD	λ1	 λ1	INPUT	 MUX	THROUGH	λ2	 λ3	 λ3	DROP	3-Port	Filter	 3-Port	Filter	λ2	 λ3	DEMUX	 MUX	Figure 1.2: Diagram of a commercial 4-port optical add-drop filter consistingof two 3-port optical filters [86, 87].1.2.1 Inter-Channel Cross-Talk and Intra-Channel Cross-TalkIdeally, a DEMUX will drop one of the input wavelengths and pass it to its dropport and a MUX will add a new wavelength and pass it to its through port (theDEMUX through port is the input port of the MUX). In Figure 1.2, the signals tobe removed and added are at l1. The rest of the signals pass through the filterswithout any distortion. However, in reality a filter has a wavelength-dependentspectral response which makes the selection of only one signal dependent on thefilter’s lineshape. In the following example shown in Figure 1.3, we use a 4-portoptical add-after-drop filter where each filter has a wavelength-dependent spectralresponse. Here, the input has 5 signals at wavelengths l1 to l5, and we wish to7separate out the signal at l3 and route it to the drop port of the filter. However,the filter will also route a small portion of the signals in the neighbouring channelsto the drop port, which will lead to inter-channel cross-talk at the photodetectorbetween the target signal at l3 and the small portions of the signals at l2 and l4[88–90]. The rest of the signals that are passed to the through port will be affectedby the filter’s wavelength dependent spectral response as well, which can lead tosignal distortion. Here, we can see that the intensities of the signals at l2 and l4are slightly reduced when they are passed to the DEMUX through port. Also, asmall portion of the signal at l3 will be routed to the DEMUX through port. If anew signal at l3 is required to be routed to the MUX through port, the partiallypassed signal at l3 will generate intra-channel cross-talk between it and the newsignal at l3 at the eventual photodetector [88–90].λ4 λ5 DROP!λ4 λ3 λ2 λ1 λ3 λ2 λ4 λ4 λ3 λ2 λ1 λ3 λ2 λ1 INPUT!DEMUX THROUGH!λ3 λ2 λ1 λ5 λ5 λ5 λ4 λ3 λ3 λ5 λ3 λ1 ADD!MUX!THROUGH!λ2 λ4 λ1 λ2 λ4 λ3 λ5 DEMUX! MUX!inter-channel cross-talk!intra-channel cross-talk!Figure 1.3: A diagram illustrating inter-channel cross-talk and intra-channelcross-talk using a 4-port optical add-after-drop filter.1.2.2 DWDM Filter SpecificationsFilters used in DWDM applications have performance specifications listed withintheir datasheets, which are provided by the telecommunication vendors. These8performance specifications provide businesses with the information needed to de-termine whether the filters are suitable for integration within their infrastructure.The performance specifications are determined within the clear windows of thechannels [91, 92]. Here, the clear window (which can be found in [91, 92]) is as-sumed to have the same definition as the channel wavelength range that is definedby the International Telecommunication Union (ITU) [93, 94]; the clear window isthe necessary wavelength span that is needed for the signal to go through a filtertaking into account everything that affects the signal’s frequency/spectrum such astransmitter temperature drift and data rate bandwidth [91, 94]. Since many filtershave a periodic spectral response, such as arrayed waveguide gratings, AWGs, [95]and ring resonator filters, the period, or free spectral range (FSR), should be largerthan the span of wavelengths to be covered. For example, in a typical telecom-munications application the C-band covers 35.09 nm from 1528.77 nm to 1563.86nm [96]. Hence, we have chosen the specification for the FSR to be greater thanor equal to the span of the C-band plus one adjacent channel [96]. Since there are45 channels within the C-band (100 GHz channel spacing), the number of chan-nels to both the left and right of the desired channel is chosen to be 44, unlessotherwise specified. Here, we have defined the centre wavelength value (this isthe wavelength at which the clear window is centred) of the major peak within thechannel of interest to be the arithmetic mean wavelength between the -3 dB points(referenced at the maximum transmission of the major peak).Next, the definitions for the drop port performance specifications are provided.The maximum drop port insertion loss, ILdrop, or maximum channel insertion loss,is defined as the the minimum transmission within the clear window (the channelwavelength range) of the desired channel with respect to 0 dB [92, 93, 97]. Theripple, Rdepth, is defined as the difference between the maximum and minimumdrop port transmission within the clear window of the desired channel [92, 93, 97].The adjacent channel isolation, Ai, is defined as the difference between the mini-mum and maximum drop port transmission within the clear window of the desiredchannel and the adjacent channels, respectively [93, 97]. The non-adjacent chan-nel isolation, nAi, is defined as the difference between the minimum and maximumdrop port transmission within the clear window of the desired channel and all non-adjacent channels (we have defined this for the 43 non-adjacent channels to the left9and right of the desired channel), respectively [93, 97]. The interstitial peak sup-pression (IPS) is defined as the difference between the minimum drop port trans-mission within the clear window of the desired channel and the maximum dropport transmission of the largest interstitial peak to the left and right of the majordrop port peak at which another channel might be located. Devices with larger Ai,nAi, and IPS will have less inter-channel cross-talk.Next, the definitions for the through port performance specifications are pro-vided. The express channel isolation, ECi, or channel extinction, of the throughport is defined as the difference between the minimum and maximum transmissionwithin the clear windows of the adjacent channels and the non-adjacent channelsand the clear window of the desired channel, respectively [93, 97]. Here, ECi willnot include non-adjacent channels (which is how Alliance Fiber Optic Products,Inc., [98] defined their specification that they named pass channel residual at ex-press port) [97]. Devices with larger ECi will have less intra-channel cross-talk.The minimum transmission within the adjacent and non-adjacent clear windows(44 channels to the left and right of the desired channel) of the through port withrespect to 0 dB is defined as the maximum through port insertion loss, ILthru [97].ILthru-m is the minimum through port transmission with respect to 0 dB at any wave-length within the passbands of the through port at which another channel might belocated.Table 1.2 shows the performance specifications that need to be met for DWDM3-port and 4-port optical filters with channel spacings of 100 GHz. The speci-fications used here are based on data sheets from telecom vendors for long-haulapplications. I have done this with the assumption that filters that can meet long-haul specifications will meet short-haul specifications.10Table 1.2: Target specifications for 3-port and 4-port filters with channelspacings of 100 GHz.Parameter 3-Port Target 4-Port TargetFSR (nm)  35.89 [96]  35.89 [96]Ai (dB)  25 [99, 100], 30 [101]  25 [87, 102]nAi (dB)  35 [101], 40 [99, 100]  40 [87, 102]IPS (dB)  35 [101], 40 [99, 100]  40 [87, 102]ILdrop (dB)  1.6 [101], 1.2 [99], 0.9 [100]  1.2 [87, 102]Rdepth (dB)  0.5 [99]  0.3 [102]ECi (dB)  10 [99], 12 [100]  25 [87, 102]ILthru (dB)  0.7 [101], 0.5 [99], 0.45 [100]  1.0 [87, 102]ILthru-m (dB)  0.7 [101], 0.5 [99], 0.45 [100]  1.0 [87, 102]As previously shown, the filter’s drop port spectral response leads to inter-channel cross-talk between the partially selected signals at l2 and l4 and the sig-nal at l3. However, a filter’s through port and drop port spectra can be designedto minimize intra-channel cross-talk and inter-channel cross-talk, respectively. Forexample, inter-channel cross-talk can be reduced if a filter’s drop port spectral re-sponse has a faster transition from passband to stopband and a smaller bandwidthas shown in Figure 1.4(a). Intra-channel cross-talk can be reduced if the differ-ence, in dB, between the passband and the stopband of the through port responseis increased as shown in Figure 1.4(b). For more information on cross-talk and itsmitigation, see Chapters 2 to 6 and Refs. 88–90.11λ4 λ5 λ2 λ3 λ4 λ1 λ5 λ1 λ2 λ3 λ1 λ2 λ3 λ4 λ5 λ1 λ2 λ3 λ4 λ5 less inter-channel cross-talk!a)!λ4 λ5 λ2 λ3 λ4 λ1 λ5 λ1 λ2 λ3 λ1 λ2 λ3 λ4 λ5 λ1 λ2 λ3 λ4 λ5 less intra-channel cross-talk!b)!λ3 + new signal !λ3 + new signal !Figure 1.4: Diagrams illustrating (a) a method to reduce inter-channel cross-talk by changing the filter’s drop port lineshape to have a faster transitionfrom passband to stopband and a smaller bandwidth and (b) a methodto reduce intra-channel cross-talk by changing the filter’s through portlineshape to have a larger difference, in dB, between the passband andthe stopband.1.2.3 Optical Filter DispersionFor a specific optical link, there is a maximum dispersion that is acceptable [103].For example, Ref. 103 states that for a 2.5 Gbps non-return-to-zero (NRZ) opticallink operating at 1550 nm with a power penalty of 1 dB the maximum dispersionthat can be tolerated is 18817 ps/nm [103]. If the data rate is increased to 10 Gbpsor 40 Gbps, then the maximum dispersion that can be tolerated is 1176 ps/nm or1273.5 ps/nm, respectively [103]. Also, for components used in an optical link, suchas an optical add-drop filter, there is an application-dependent maximum disper-sion, for example, ±30 ps/nm [104]. Since the through port dispersions of some ofour designed filters are much larger than ±30 ps/nm [104], this will cause a reduc-tion in the number of these devices that can be used in an optical link as well as areduction in the total length of the fibre that can be used. However, while some ofthe filters presented in this dissertation may not be useful for long haul, they shouldstill be suitable for metro and on-chip applications. For example, let’s say that anoptical add-drop filter has a dispersion of 500 ps/nm and the maximum allowabledispersion is 1176 ps/nm (for a data rate of 10 Gbps) [103] and the optical linkuses single-mode fibre with a dispersion coefficient of 17 ps/nm/km [103], then themaximum optical fibre length that can be used is almost 40 km (for an examplethat uses a filter dispersion of ±30 ps/nm, see Appendix II.2 in Ref. 104).References 92 and 91 define dispersion as the maximum dispersion within theclear window of any channel. Here, we will define the maximum drop port dis-persion, Ddrop, as the maximum positive or negative dispersion within the desiredchannel’s clear window [105]. The maximum through port dispersion, Dthru, is de-fined as the maximum positive or negative dispersion at the through port within anyof the clear windows of the adjacent and non-adjacent channels [105]. Dthru-m isdefined as the maximum positive or negative dispersion at any wavelength withinthe passbands of the through port at which another channel might be located.1.3 Methods to Extend the FSR of Ring Resonators2 Silicon-on-insulator (SOI) ring resonator DWDM optical filters offer advantagesas compared to commercially available DWDM optical filters; ring resonators arecompact and CMOS-compatible [106]. Thus, there has been substantial researchinto the design and fabrication of ring resonators, for example, see [8, 33, 35, 49,50, 52, 54, 60, 78, 82, 83]. When using ring resonators for DWDM applications,a single ring resonator can be used as a 4-port optical add-drop filter, as shown inFigure 1.5(a). An example through port spectral response and drop port spectralresponse are shown in Figure 1.5(b) for broadband illumination at the input port2Parts of Chapter 1.3 are taken from [84, 85].13with no other light injected into the device (total length of ring resonator is 45.416µm [85], bus-to-ring field coupling factor is 0.2, and propagation loss is 3 dB/cm).The transfer functions for a single ring resonator can be found in [107].	a) input port through port add port drop port 1530 1535 1540 1545 1550 1555 1560ï30ï20ï100Intensity (dB)Wavelength (nm)  ThroughDropFSRb)Figure 1.5: (a) Schematic diagram of a 4-port ring resonator optical add-dropfilter and (b) example through port and drop port spectra when light isonly injected into the input port.Alternatively, one can use two sets of ring resonators, as shown in Figure 1.6,to create a 4-port optical add-after-drop filter (see, for example, [108, 109]). Thebenefit of using the add-after-drop configuration is that the ECi specification foreach individual filter ( 10 dB [99], 12 dB [100]) is less than it would be if weused just one filter ( 25 dB [87, 102]) for the add-drop functionality. ECi isdefined within the clear window [85] and, therefore, it is possible to increase theclear window for the add-after-drop configuration since the ECi specification isless than for the 4-port add-drop filter (see Table 1.2). However, the add-after-dropconfiguration is more complex and less compact since more ring resonators areneeded.14!input port through port add port MUX !λ1! λ2! λ3!λ1!λ1! λ2! λ3!λ1!drop port Figure 1.6: Schematic diagram of two 3-port ring resonator filters cascadedtogether to form a 4-port optical add-after-drop filter.In DWDM applications that require 100 GHz channel spacings, the C-bandconsists of 45 channels (191.7 THz to 196.1 THz with 100 GHz channel spacing)that are utilized in data transmission [92, 96] and the centre frequency of each ofthese channels is determined by the ITU [92, 110], as shown in Figure 1.7. If theFSR of a ring resonator is smaller than or equal to the span of the C-band, then sig-nals that are operating at frequencies within the C-band may also correspond to thelocations of the filter’s resonances that are within the C-band and, thus, the signalswill be multiplexed or demultiplexed by the same device [111]. Thus, the FSR ofa ring resonator should be larger than the span of the C-band [111], see Figure 1.7.In Chapters 1.3.1 to 1.3.3, three methods to extend the FSRs of ring resonatorswill be presented, which provide a desirable alternative to the conventional way ofincreasing the FSR, i.e., the FSRs of ring resonators are inversely proportional tothe total lengths of the resonators [111].151530 1535 1540 1545 1550 1555 1560 15652 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 451Wavelength (nm)Span of the FSR Span of the Cïband (45 channels)Figure 1.7: Diagram that shows the 45 channels within the C-band that areused in DWDM applications for a channel spacing of 100 GHz (the lo-cation of each channel is taken from ITU-T Recommendation G.694.1[92, 110]). The FSR of a ring resonator should be larger than the wave-length span between channel 1 and channel 45.Some of the previous filters, such as [112–115], on the silicon photonics plat-form have met many of the current commercial telecom filter specifications that canbe found in vendor datasheets. However, no one has reported on fabricated siliconphotonic filters that meet all the specifications that can be found in current telecomvendor datasheets (including FSRs larger than the span of the C-band) for a givenclear window and channel spacing. Due to my prior experience with silicon pho-tonic resonators, I hypothesized that silicon photonic devices can meet commercialspecifications. In particular, my experience with extending the FSR by using mul-tiple rings and the Vernier effect inspired me to explore this area more fully. Thus,one of the main aspects of this dissertation is to theoretically demonstrate siliconphotonic filters that meet the current commercial specifications found in vendordatasheets as well as provide experimental evidence that such performance is re-alizable on the silicon photonics platform. The main design features that are in-vestigated in this dissertation to enable the creation of silicon photonics filters withdesirable performance are: FSR extension methods; resonant peak/notch suppres-sion; through port dispersion analysis; and wavelength tuning methods. Focusingon these design features as well as current fabrication technology constraints (e.g.,minimum feature sizes, propagation losses, etc.), silicon photonic filters have beenboth theoretically and experimentally demonstrated. The design methodology tocreate these filters consisted of using analytic models to gain insight into the fil-ters’ operation. This was followed by numerical design and optimization using16both compact models (MATLAB R) and commercial models (MODE Solutionsand FDTD Solutions by Lumerical Solutions, Inc.).1.3.1 Ring Resonators Exhibiting the Vernier EffectFilters should be designed to meet typical commercial specifications within theclear windows [91, 92] of the C-band channels. Popovic´ et al. experimentallydemonstrated a quadruple microring resonator filter, in silicon, that meets telecomspecifications [115]. However, the FSR was only 16 nm [115]. Others have experi-mentally demonstrated series-coupled silicon ring resonators [116–125] that do notexhibit the Vernier effect. The spectral response of a ring resonator filter is periodicand the distance between two resonant peaks is defined as the FSR [126, 127]. Ifwe wish to have a large FSR (i.e., greater than the span of the C-band), then verysmall microring resonators would be required [126–128]. The Vernier effect canbe used to extend the FSR to larger than the span of the C-band without needing touse very small microring resonators, i.e., radii of about less than 3 µm [107]. Theextended FSR is achieved by using two coupled ring resonators in which the opti-cal path lengths are not all the same, for example, in our Figure 1.8 “Ring 1” and“Ring 2” do not have the same optical path lengths [107, 126–129]. The extendedFSR, FSRextend, occurs when FSRextend = m1FSR1 = m2FSR2 where m1 and m2 areco-prime integers, FSR1 is the FSR of “Ring 1”, and FSR2 is the FSR of “Ring 2”[107, 129].	 	 	 	 		Add Drop t 1 In Through gap 1 Ring 1 Ring 2 gap 2 gap 1 Figure 1.8: Schematic diagram of a double Vernier racetrack resonator (fig-ure adapted from [85]).Figure 1.9 shows the approximate number of publications (theses, conferencepapers, journal papers, patents, and books) from 1986 to 2015 which discuss res-17onators exhibiting the Vernier effect, which clearly shows that research involvingthe Vernier effect and resonators has increased substantially over the years. Themain three areas of research from 1986 to 2015 regarding Vernier resonators havebeen filters for optical communications applications [96], tunable lasers [130], andsensors [131]. Vernier resonators have been demonstrated in a variety of materi-als such as single-mode fibre [132], Ta2O5-SiO2 [133], Hydex [134], SiON [135],Si3N4 [136], and Si [137]. Popovic´ demonstrated, theoretically, a high perfor-mance ring resonator-based filter exhibiting the Vernier effect [112, 138]. In 2008,researchers at Pirelli Labs presented theoretical and experimental results on sili-con Vernier microring resonators [113]. Socci et al. [114] have presented theo-retical results showing that silicon series-coupled double Vernier ring resonatorscascaded together can be used to create high performance filters. There have beentwo companies, Lambda Crossing [139] and Little Optics, Inc., [134, 139] thathave created Vernier filters using series-coupled double ring resonators cascadedtogether and series-coupled quintuple ring resonators cascaded together, respec-tively. To achieve large bandwidths and large IPSs, four coupled ring resonatorsin which the optical path lengths are not all the same can be used [96, 140–143]. For example, in our Figure 1.10 “Ring 1” and “Ring 2” do not have thesame optical path lengths as “Ring 3” and “Ring 4” have [126–128]. Series-coupled quadruple Vernier ring resonators have been demonstrated both theoreti-cally [84, 85, 96, 126, 140–149] and experimentally [96, 149, 150], which includesfive publications [84, 85, 96, 149, 150] that are presented within this dissertation.181985 1990 1995 2000 2005 2010 2015010203040YearPublicationsFigure 1.9: The number of publications from 1986 to 2015 which discussresonators that exhibit the Vernier effect [84, 85, 96, 97, 107, 111–114,126–429].! ! ! ! !!Add Drop t 1 In Through gap 1 Ring 1 Ring 2 Ring 3 Ring 4 gap 2 gap 3 gap 2 gap 1 Figure 1.10: Schematic diagram of a Vernier device consisting of four race-track resonators (see Refs. 96, 126, 140–143, 149, 150 for results onsimilar resonators). cSPIE, 2015, by permission [85].To explain how the Vernier effect works we will model a double Vernier race-track resonator. We chose “Ring 1” to have a total length, L1, of 45.416 µm [85]and “Ring 2” to have a total length, L2, of 60.555 µm [85], such that m2/m1 = L2/L1[107, 129] where m1 = 3 and m2 = 4. The propagation loss was chosen to be 3dB/cm, the bus-to-ring field coupling factor is 0.6, the ring-to-ring field couplingfactor is 0.2, the strip waveguides have widths of 500 nm and heights of 220 nm,and the waveguides have an oxide cladding. The transfer functions for a doubleseries-coupled ring resonator can be found in [107].19Figure 1.11(b) shows the drop port spectral response for single ring resonators“Ring 1” and “Ring 2” that are not coupled together in which we can see that, atcertain wavelengths, the peaks are aligned and at all other wavelengths the peaksare not aligned. If “Ring 1” and “Ring 2” are coupled together, as shown in Fig-ure 1.11(a), major peaks will occur where the individual peaks seen Figure 1.11(b)are aligned and all the other peaks, minor peaks, will be suppressed as shown inFigure 1.11(c). Also, the through port spectral response has an extended FSR dueto the suppressed minor notches located between the major notches, as shown inFigure 1.11(d). The drop port dispersion within the wavelength region of one ofthe major peaks is shown in Figure 1.11(e). Since within the through port pass-bands light will still resonate at certain wavelengths, as indicated by the minornotches in Figure 1.11(d), there will be wavelength-dependent dispersions withinthese locations [85], as shown in Figure 1.11(f).20! ! ! ! !!Add Drop t 1 In Through gap 1 Ring 1 Ring 2 gap 2 gap 1 a) 1500 1520 1540 1560 1580 1600ï10ï50Wavelength (nm)Intensity (dB)  R1R2b)1500 1520 1540 1560 1580 1600ï30ï20ï100Intensity (dB)Wavelength (nm)minor peaksextended FSR major peaksc)1500 1520 1540 1560 1580 1600ï20ï15ï10ï50Intensity (dB)Wavelength (nm)extended FSRmajor notchesminor notchesd)1542 1543 1544 1545 1546 1547ï505Dispersion (ps/nm)Wavelength (nm)e)1550 1555 1560 1565 1570 1575ï505Dispersion (ps/nm)Wavelength (nm)f)Figure 1.11: (a) Schematic diagram of a Vernier filter consisting of two race-track resonators (figure adapted from [85]). (b) Drop port spectral re-sponses for single silicon ring resonators, “Ring 1” and “Ring 2”, thatare not coupled together which show that their peaks are aligned atcertain wavelengths (indicated by the arrows) and at other wavelengthstheir peaks are not aligned. (c) The drop port spectral response and (d)the through port spectral response after serially coupling “Ring 1” and“Ring 2” together (light only injected into the input port), which clearlyshows that the FSR is extended. The wavelength-dependent dispersionat (e) the drop port within the wavelength region corresponding to thelocation of one of the major peaks and at (f) the through port withinthe wavelength region corresponding to the location of the through portpassband to the right of one of the major notches.21It is desirable to be able to thermally tune a ring resonator filter to any channelwithin the C-band [134, 430]. Such tuning can be achieved using ring resonatorsthat exhibit the Vernier effect and require smaller changes in temperature as com-pared to the temperature change required to tune across the C-band when using ringresonators that do not exhibit the Vernier effect [134, 149, 301, 430]. To explainhow the Vernier effect can be used to increase the tuning range of a ring resonatorfilter, the drop port spectral responses of single ring resonators “Ring 1” and “Ring2” (using the relevant parameters found in [85, 149]) that are not coupled togetherwill be compared to the spectral response when a temperature change of 46 C(dn/dT = 1.86⇥10-4 oC-1[431]) is applied to “Ring 2”. Figure 1.12(a) shows thedrop port spectral responses for “Ring 1” (solid blue line) and for “Ring 2” (solidred line) prior to changing the temperature of “Ring 2”. The resonances of the twodrop port spectral responses are aligned at l = 1544.824 nm. When a tempera-ture change, DT2, of 46 C is applied to “Ring 2”, the resonances of the two dropport spectral responses are now aligned at l = 1557.497 nm. If both resonatorswere tuned by 46 C the common peaks would only shift by about 3.2 nm whereasby tuning only one ring the common peaks have jumped by about 12.7 nm. Fig-ure 1.12(b) shows the drop port spectral responses when “Ring 1” and for “Ring2” are serially coupled together, now exhibiting the Vernier effect. The drop portspectral response prior to changing the temperature of “Ring 2” is shown by thesolid green line and the spectrum after changing the temperature of “Ring 2” by46 C is shown by the solid blue line. The location of the major peak (i.e., thecommon peak) is now centred at a new wavelength, which is about 12.7 nm awayfrom where the major peak was originally located. For comparison, the spectralresponse when the temperature change applied to both rings is 46 C is given bythe dashed black line. This demonstrates the benefit of using the Vernier effect.221530 1540 1550 1560 1570ï12ï10ï8ï6ï4ï20Wavelength (nm)Intensity (dB)  Ring 1 (6T1 = 0 oC)Ring 2 (6T2 = 0 oC)Ring 2 (6T2 = 46 oC)a)1530 1540 1550 1560 1570ï30ï20ï100Wavelength (nm)Intensity (dB)  6T1 = 0 oC, 6T2 = 0 oC6T1 = 0 oC, 6T2 = 46 oC6T1 = 46 oC, 6T2 = 46 oCb)Figure 1.12: (a) Drop port spectral responses for single silicon ring res-onators, “Ring 1” and “Ring 2”, that are not coupled together whenDT1 = 0 C (solid blue line) and DT2 = 0 C (solid red line) as well aswhen DT1 = 0 C and DT2 = 46 C (dashed blue line). The arrows in-dicate before and after changing the temperature applied to “Ring 2”.(b) The drop port spectral responses after serially coupling “Ring 1”and “Ring 2” together when DT1 = 0 C and DT2 = 0 C (solid greenline) as well as when DT1 = 0 C and DT2 = 46 C (solid blue line).Also, the drop port spectral response when DT1 = 46 C and DT2 =46 C (dashed black line) is provided, which clearly shows the limitedtuning range as compared to when the temperature change of 46 C isapplied to only “Ring 2”.231.3.2 Ring Resonators with Mach-Zehnder Interferometer-BasedCouplingAnother method to expand the FSR is to use identical series-coupled ring res-onators with Mach-Zehnder interferometer-based coupling (MZI-BC) [105, 432,433]. The amount of coupling from the bus waveguides to the ring resonators isdetermined by the periodic responses of the input MZI [105, 432, 433]. If the dif-ference in the branch lengths is equal to half the total length of the ring resonatorthen the MZI has an FSR that is twice the FSR of the ring resonator [105, 432, 433].Thus, it is possible to double the FSR of the ring resonator since the nulls of theMZI couplers’ responses are located at some of the wavelengths at which the ringsresonate [105, 432, 433].Next, an example is provided to show how an MZI coupler can be used to ex-tend the FSR of ring resonators. The transfer functions can be found in AppendixB. Figure 1.13(a) shows a schematic diagram of a series-coupled double ring res-onator without MZI-BC. Figure 1.13(b) shows a schematic diagram of an MZIcoupler and Figure 1.13(c) shows a schematic diagram of a double ring resonatorfilter that uses MZI-BC. In this example, the following parameters were used formodelling: the propagation loss was chosen to be 3 dB/cm; the power couplingfactors and power transmission factors at l = 1550 nm have been modelled in 3DFDTD and, thus, include coupling losses (the values were taken from [105]); thesilicon strip waveguide widths and heights are 500 nm and 220 nm, respectively,and the waveguides have a top oxide cladding; the lengths of the microring res-onators and branch lengths, Lmzi1 and Lmzi2, of the MZIs were taken from [105].In this example, the value of the bus-to-ring field coupling factor, kb, is equal tothe value of the MZI field coupling factor, kmzi.Figure 1.14(a) shows the through port and drop port spectral responses of theseries-coupled double ring resonator filter. Figure 1.14(b) shows the MZI couplerresponse from the input port, “In 1” to the output port, “Out 1”, as well as from theinput port, “In 1” to the output port “Out 2” [see Figure 1.13(b)] when no light isinjected into input port “In 2”. The responses are periodic and the MZI’s FSR istwice that of the FSR shown in Figure 1.14(a). Figure 1.14(c) shows the throughport and drop port spectral response of a double ring resonator filter that uses MZI-BC. The response has an extended FSR due to the suppression of the resonances24that align with the nulls of the MZI coupler’s response [105, 432, 433]. This typeof device has been demonstrated in silicon [105, 433] (including one of our ownpapers [105]) and silicon nitride [432]. These devices can be designed to alsohave minimal dispersion within the passbands of the through port [105, 432] whilemeeting numerous commercial 3-port filter specifications, as shown in Chapter 4.	 	Input Through Drop κr Add a) κb κb 	 	In 1 κmzi L mzi-1 L mzi-2 κmzi Out 2 Out 1 b) In 2 	 	Input Through κmzi Drop L mzi-1 L mzi-2 κmzi κr Add c) Figure 1.13: (a) Schematic diagram of a series-coupled double ring resonator,(b) schematic diagram of a MZI coupler, and (c) schematic diagram ofa double ring resonator filter that uses MZI-BC (modified from [105]).251500 1520 1540 1560 1580 1600ï60ï40ï200Wavelength (nm)Intensity (dB)  ThroughDropa)1500 1520 1540 1560 1580 1600ï80ï60ï40ï200Wavelength (nm)Intensity (dB)  Out 1Out 2b)1500 1520 1540 1560 1580 1600ï60ï40ï200Wavelength (nm)Intensity (dB)  ThroughDropc)Figure 1.14: (a) Example through port and drop port spectral response of aseries-coupled double ring resonator. (b) Example output responses ofan MZI coupler when light is only injected into input port “In 1”. (c)Example through port and drop port spectral response of a double ringresonator filter that uses MZI-BC.1.3.3 Ring Resonators with Contra-Directional Grating CouplersVernier ring resonators typically consist of very broadband wavelength-dependentdirectional couplers and, although MZI-BC directional couplers are highly wave-length dependent, both Vernier ring resonators and ring resonators with MZI-BCstill have (extended) FSRs [105]. However, there is another type of directionalcoupler that is highly wavelength dependent which is the contra-directional gratingcoupler (contra-DC) [97, 434]. A contra-DC can eliminate the FSR of a ring res-onator when the maximum reflectivity of the contra-DC occurs at the same wave-length as one of the resonances of the ring resonator [97, 434]. Furthermore, theextended FSRs of cascaded Vernier racetrack resonators can also be eliminated byusing contra-DCs [97], which will be presented in Chapter 5. However, a draw-back in using grating-assisted Vernier racetrack resonators is the enhanced resonantwavelength tuning range achievable by using the Vernier effect is not possible dueto the highly wavelength-dependent responses of contra-DCs.26Contra-DCs can be created by adding corrugations to the inner sidewalls oftwo waveguides that are in close proximity to one another [97, 434, 435], as shownin Figure 1.15, and can be used as either 3-port couplers (only light injected intothe input ports) or as 4-port couplers (light injected into both the input ports andthe add ports). The amount of light that is reflected from the input port to thedrop port is highly wavelength dependent due to the presence of the corrugations[97, 434, 435]. When the propagation constant mismatch equation equals zero,i.e., Db = ba+bbm 2pL = 0, where ba is the propagation constant of waveguide“a”, bb is the propagation constant of waveguide “b”, m is an integer (which here,equals 1), and L is the grating period, there is maximum reflectivity at lD at thedrop port of the contra-DC [434].Input Drop Through tc2κc2a)	Add κc2tc2	wa Λ wb b) Figure 1.15: (a) Schematic diagram of a typical design of a contra-DC and(b) a close-up view of a portion of a typical design of a contra-DC(modified version from [435]).27Besides the inter-waveguide reflections that occur using a contra-DC, each in-dividual waveguide has intra-waveguide reflections [97, 434]. The intra-waveguidereflections for waveguide “a” are centred at la which can be determined by solvingEq. 1.2 for l [434],ba(l )+ba(l ) 2pL = 0, (1.1)4pna(l )l 2pL= 0, (1.2)where na is the effective index of waveguide “a”. The intra-waveguide reflectionsfor waveguide “b” are centred at lb which can be determined by solving Eq. 1.4for l [434],bb(l )+bb(l ) 2pL = 0, (1.3)4pnb(l )l 2pL= 0, (1.4)where nb(l ) is the effective index of waveguide “b”. The inter-waveguide reflec-tions are centred at lD which can be determined by solving Eq. 1.6 for l [434],ba(l )+bb(l ) 2pL = 0, (1.5)2pna(l )l+2pnb(l )l 2pL= 0. (1.6)Figure 1.16(a) shows an example of how to determine the centre wavelength lo-cation of the intra-waveguide reflections and the inter-waveguide reflections [434]based on silicon dioxide cladded, silicon strip waveguides with heights of 220 nmand with widths of 450 nm for waveguide “a” and 550 nm for waveguide “b” [435].If light is only injected into the input port, the through port will see notches locatedat la and lD. If light is only injected into the add port, the drop port will see notcheslocated at lb and lD. Since in Figure 1.15 we added anti-reflection gratings to theexternal sidewalls of waveguides “a” and “b” [97, 435, 436], the intra-waveguidereflections, located at la and lb in Figure 1.16(a), are suppressed. Figure 1.16(b)shows the power coupling factor, |kc|2, and power transmission factor, |tc|2, versuswavelength, when light is only injected into the input port, in which we can clearly28see that the maximum intensity at the drop port occurs at the wavelength corre-sponding to lD in Figure 1.16(a). For the simulated spectra in Figure 1.16(b), thecoupling length is 159 µm, the propagation loss is 3 dB/cm, the period is 318 nm,the period number is 500, and the coupling coefficient is 10000 m-1. There havebeen numerous publications on silicon contra-DCs from 2005 to 2015, as shown inFigure 1.17, including theoretical and experimental demonstrations of integratingcontra-DCs into the coupling regions of ring resonators [97, 434, 437–441].1460 1480 1500 1520 1540 1560 1580 16002.32.42.52.6Wavelength (nm)Effective Index  [na(h) + nb(h)]/2nb(h)na(h)h/(2R)a)hahDhb1535 1540 1545 1550 1555 1560 1565ï50ï40ï30ï20ï100Wavelength (nm)|g c|2  / |t c|2  (dB)  ThroughDropb)Figure 1.16: (a) Effective index versus wavelength where the red line is theeffective index of waveguide “b”, the green line is the effective indexof waveguide “a”, and the blue line is the average effective index. (b)Example of a through port power transmission factor response (redline) and drop port power coupling factor response (green line) for asilicon contra-DC.2005 2007 2009 2011 2013 2015024681012YearPublicationsFigure 1.17: The number of publications from 2005 to 2015 which discusssilicon contra-DCs [97, 434–471].291.4 ObjectivesThe objective of this dissertation is to demonstrate high performance silicon pho-tonic filters that meet many typical commercial DWDM long-haul specificationsas well as demonstrate a new silicon photonic filter that has its FSR eliminated.Specifically, my research explores a variety of methods that increase the number ofchannels that can be multiplexed and/or demultiplexed for DWDM applications.In Chapter 1, I have presented an overview of the current state of silicon pho-tonics with regard to private and publicly-traded companies. I also provided anoverview of optical DWDM filters and their typical commercial specifications.Then, I provided an overview of three methods to extend the FSR, which areVernier ring resonators, ring resonators with MZI-BC, and ring resonators withcontra-DCs. In Chapter 2, I present theoretical results for silicon quadruple Vernierracetrack resonators that meet 4-port filter commercial specifications [84, 85]. Ialso present our theoretical results for a silicon quadruple Vernier racetrack res-onator that meets 4-port filter commercial specifications while being tolerant totypical fabrication variations [84, 85]. Next, I discuss our theoretical and experi-mental results on a silicon quadruple Vernier racetrack resonator that meets many3-port filter commercial specifications [96]. In Chapter 3, I present our results onthermally tunable silicon Vernier racetrack resonators. Specifically, I present ourtheoretical and experimental results on thermally tunable silicon quadruple Vernierracetrack resonators [149, 150]. In Chapter 4, I discuss our theoretical and experi-mental results for a high performance silicon double microring filter usingMZI-BCthat meets numerous 3-port filter commercial specifications and has an FSR largerthan the span of the C-band [105]. In Chapter 5, I discuss our theoretical and ex-perimental results on cascaded grating-assisted silicon Vernier racetrack resonatorsthat have no FSRs due to the use of contra-DCs [97]. In Chapter 6, I present a newprocess calibration technique to determine the coupling coefficients of fabricatedcontra-DCs [435]. In Chapter 7, I present conclusions and suggestions for futurework.30Chapter 2Silicon-On-Insulator QuadrupleVernier Racetrack Resonators1Ideally, one would like a box-like drop port spectral response, which can beachieved using series-coupled ring resonators [190]. Increasing the number ofseries-coupled rings, allows one to increase the clear window (channel bandwidth)and thus the data rate that the filter can handle. There have been a number of papersthat have discussed the benefits of increasing the number of ring resonators to fourto enable large IPSs, see, for example [140–143]. However, prior to our work, noone has experimentally demonstrated the Vernier effect in more than three series-coupled rings and no one has experimentally shown whether series-coupled Vernierring resonators can be used to meet many of the typical commercial DWDM fil-ter specifications that can be found in vendor datasheets. Timotijevic et al. [137]demonstrated double Vernier SOI series-coupled ring resonators which had an FSRlarger than the span of the C-band but minimal IPS. Fegadolli et al. [317] fabricatedthermally tunable double Vernier SOI series-coupled ring resonators exhibiting theVernier effect in the through port and drop port. Romagnoli et al. [113] exper-imentally demonstrated thermally tunable silicon double Vernier ring resonators,however, their IPS does not meet its typical commercial specification. Mancinelliet al. [290] used double Vernier SOI series-coupled resonators that had an extendedFSR of 20 nm. Prabhathan et al. [301] fabricated double SOI cascaded ring res-1A version of this paragraph has been published in [96].31onators exhibiting the Vernier effect at the drop port for use as a thermally tunablewavelength selective switch. The authors’ device had an FSR of approximately 50nm and a drop port out-of-band extinction greater than 15 dB [301]. However, ringresonators in cascaded configurations only exhibit the Vernier effect in the dropport response and not the through port response [415]. Yanagase et al. [190] haveshown triple-ring resonators exhibiting the Vernier effect, where the coupling wasdone vertically and the material used for the waveguides was Ta2O5-SiO2. How-ever, their devices showminimal IPS and their extended FSR was less than the spanof the C-band. Also, they do not show the through port responses. Previously pub-lished research, both experimental and theoretical, show the benefit (FSR expan-sion) of using the Vernier effect within series-coupled ring resonators, as comparedto the case where each resonator is identical. However, prior to our research results,there have been only a few publications regarding Vernier ring resonators meetingcommercial specifications as regards to the IPS (see [112–114, 134, 141–143]).Here, we theoretically and experimentally demonstrate that it is, in fact, possible tomeet many drop port and through port commercial filter specifications when usingsilicon quadruple series-coupled racetrack resonators exhibiting the Vernier effectincluding the necessary IPS and FSR.2.1 Design of Silicon Quadruple Vernier RacetrackResonators2The quadruple Vernier racetrack resonator has four racetrack resonators each witha radius, r, of 5 µm and a coupling length, Lc, of 7 µm. The two larger racetrackresonators, “Ring 3” and “Ring 4”, have additional straight segments, L, equal to7.5693 µm (see Figure 2.1). The ratio of the total length of the smaller racetrackresonator, “Ring 1” or “Ring 2”, to the total length of the larger racetrack resonator,“Ring 3” or “Ring 4” is 3/4 (this ratio can also be found in Refs. 97, 126). Thenominal widths and heights of the SOI strip waveguides are 500 nm and 220 nm,respectively. There is also a silicon dioxide cladding on top of the waveguides.The propagation loss was chosen to be 2.4 dB/cm (losses of 2.4±0.3 dB/cm forSOI channel waveguides are reported in Ref. 472). Also, some of these parameters2A version of Chapter 2.1 has been published in [84, 85].32were taken from Refs. 96 and 149 and the through port and drop port transferfunctions can be found in Appendix A.To determine the through port and drop port spectral responses of our mod-elled devices, we need to determine the real, wavelength dependent, point fieldcoupling factors, ks, and transmission factors, ts for each racetrack resonator’sdirectional couplers. To simplify our modelling of the directional coupler, weused straight waveguides to obtain k and t, on the assumption that changes ink and t due to changes in the waveguide widths, heights, and gap occur, predom-inantly, in the straight waveguide sections of the couplers and that, to fabricatethe devices studied herein that meet the commercial specifications one could mod-ify the gaps of the straight sections of the actual couplers to compensate for thecontributions of the bend regions. k and t were determined by calculating theeven and odd effective indices of the straight sections of the directional couplers[96, 97, 107, 111, 129, 149, 470, 473] using MODE Solutions by Lumerical Solu-tions, Inc. The even and odd effective indices were then curve-fitted to third-orderpolynomials in MATLAB R. Also, a third-order polynomial curve-fit was used forthe strip waveguide effective indices, which were calculated using MODE Solu-tions. Figure 2.1 shows the schematic of the Vernier filter.In our simulations, the waveguide effective indices used are for the fundamen-tal quasi-TE modes of the strip waveguides. If the polarization is changed, theperformance of the Vernier resonators will change. For quasi-TM polarization, themode is less confined within the waveguide core and, as a result, the effective in-dex will be smaller as compared to the effective index for a quasi-TE mode [470].Therefore, the resonance condition for a racetrack resonator will be polarization de-pendent. Since our Vernier filters consist of racetrack resonators, the wavelengthsat which the major and minor peaks and notches occur will be polarization de-pendent. With regards to the directional couplers, since quasi-TM modes are lessconfined within the waveguide cores, the field coupling factors will be larger thanthe field coupling factors for quasi-TE modes [474]. Since our Vernier filters in-clude directional couplers, the spectra of our filters will be further affected by thepolarization dependence of the field coupling factors.33! ! ! ! !!Add Drop t 1 Input Through gap 1 Ring 1 Ring 2 Ring 3 Ring 4 gap 2 gap 3 gap 2 gap 1 Lc Lc Lc Lc L L r r r r Figure 2.1: Schematic of a Vernier filter consisting of four racetrack res-onators (see Refs. 96, 126, 140–143, 149, 150 for results on similarresonators). cSPIE, 2015, by permission [85].2.2 Performance Optimization3We set “gap 1” to be 150 nm (we have assumed that the minimum fabrication gapdistance is 150 nm) and then varied “gap 2” and “gap 3”. The spectral responsesshown in Figure 2.2 (where we inject light into the input port) in solid lines cor-respond to the device, D1, which has gap distances “gap 1”, “gap 2”, and “gap 3”equal to 150 nm, 350 nm, and 390 nm, respectively. The spectral responses shownin Figure 2.2 (where we inject light into the input port) in dashed lines correspondto the device, D2, which has gap distances “gap 1”, “gap 2”, and “gap 3” equal to150 nm, 360 nm, and 410 nm, respectively. These devices meet all of the 4-portfilter specifications listed in Table 1.2. The field coupling factors at 1550 nm (here,to show the wavelength dependency of the field coupling factors we provide theslopes, dk/dl , at l = 1550 nm) for gap distances of 150 nm, 350 nm, 360 nm, 390nm, and 410 nm, are 0.44422 (dk/dl = 0.00158 nm-1), 0.07856 (dk/dl = 0.00047nm-1), 0.07209 (dk/dl = 0.00044 nm-1), 0.05570 (dk/dl = 0.00036 nm-1), and0.04692 (dk/dl = 0.00031 nm-1), respectively. Figure 2.2(a) shows that the FSR islarger than the span of the C-band and that the IPS for each device is greater than40 dB, which meets their performance specification. Figure 2.2(b) is a “zoom-in”of the major resonant peaks that are located within the C-band. Figure 2.2(c) is azoom-in of the through port spectral responses to the left of the major notches. Fig-3A version of Chapter 2.2 has been published in [84, 85].34ures 2.3(a) and 2.3(b) show the wavelength-dependent drop port dispersion withinthe drop port passband region and the largest wavelength dependent through portdispersion within one of the passbands, respectively, for D1 and D2. It is importantto note that the through port passbands have minor notches in their intensity spectra[96, 112, 114, 126, 127, 138, 149, 150] and large dispersions within the wavelengthregion where these minor notches are located [112, 138, 150, 231, 432]. Theseminor notches are the result of coupling of ring resonators with different opticallengths (i.e., the Vernier effect) [96, 112, 114, 126, 127, 138, 149, 150].1520 1540 1560 1580ï100ï80ï60ï40ï200Intensity (dB)Wavelength (nm)  Through portDrop porta)minor notches1544.4 1544.6 1544.8 1545 1545.2ï30ï20ï100Intensity (dB)Wavelength (nm)  Through portDrop portb)1520 1525 1530ï0.6ï0.4ï0.20Intensity (dB)Wavelength (nm)  Through portc)Figure 2.2: For light injected at the input port, (a) shows the theoreticaldrop port and through port responses (solid lines correspond to D1 anddashed lines correspond to D2) which show large IPSs and FSRs largerthan the span of the C-band, (b) shows flat drop port passbands and largenotches within the through port stopbands, and (c) shows minor notcheswithin the through port passbands. The two devices meet the 4-port fil-ter specifications listed in Table 1.2. cSPIE, 2015, by permission [85].351544.4 1544.6 1544.8 1545 1545.2ï2000200Wavelength (nm)Dispersion (ps/nm)  D1D2a)1520 1525 1530ï200ï1000100200Wavelength (nm)Dispersion (ps/nm)  D1D2b)Figure 2.3: For light injected at the input port, (a) shows the drop port dis-persions within the region of the passband, and (b) the largest throughport dispersions within one of through port passbands for devices D1and D2. cSPIE, 2015, by permission [85].For example, if we look at the device with gap distances “gap 1”, “gap 2”, and“gap 3” that are 150 nm, 350 nm, and 390 nm, respectively, the modelling resultslisted in Table 2.1 meet all of the 4-port filter specifications listed in Table 1.2. InTable 2.1, there are two different FSR values listed. The reason we give two valuesis that, provided that the group index of the waveguide forming a ring resonatoris constant, then the FSR is periodic in frequency but not in wavelength. Whenmeasured against wavelength, the FSR depends on which resonant peaks are cho-sen for measuring it [107]. Here, we have chosen a resonant peak and give theFSRs measured to both the adjacent shorter wavelength peak and to the adjacentlonger wavelength peak. It should be noted that, if we injected light into the addport of our Vernier resonator, the spectrum measured at the through port due to thislight will be the same as if we injected light into the input port and measured thespectrum at the drop port (see experimental results in Ref. 150). Therefore, the addport to through port parameters are defined in a similar way as the input port todrop port parameters (we will refer to both cases using the parameter symbols, Ai,nAi, IPS, ILdrop, Rdepth, and Ddrop). However, if we injected light into the add portof our Vernier resonator, the spectrum measured at the drop port due to this lightwill not be the same as if we injected light into the input port and measured thespectrum at the through port (see experimental results in Ref. 150). Thus, for lightinjected at the add port, the parameters, ECd, ILd, ILd-m, Dd, and Dd-m are definedin a similar way as ECi, ILthru, ILthru-m, Dthru, and Dthru-m are defined, respectively.36Also, Minoli stated that the clear window is typically 25% of the channel spacing[92]. However, in our modelling, the clear window (or channel wavelength range)was chosen to be 10% of the channel spacing. The channel spacing was chosento be 0.8 nm, and hence, the clear window was chosen to be 0.08 nm (similar tothe numbers given in Ref. 475). Figures 2.4 and 2.5, respectively, show that thespectral response and dispersion change depending on whether the light is injectedinto the input port or injected into the add port. For light injected at the input port,Dthru and Dthru-m are -150 ps/nm and -253 ps/nm, respectively. For light injectedat the add port, Dd and Dd-m are -247 ps/nm and +480 ps/nm, respectively. Ddropis ±26 ps/nm when light is injected into the input port as well as when light isinjected into the add port.Table 2.1: One of our device’s modelled results as compared to the targetspecifications. cSPIE, 2015, by permission [85].Parameter Modelling Result TargetFSR (nm) 36.85a/38.66b  35.89 [96]Ai (dB) 54.0  25 [87, 102]nAi (dB) 41.2  40 [87, 102]IPS (dB) 41.2  40 [87, 102]ILdrop (dB) 0.4  1.2 [87, 102]Rdepth (dB) 0.0  0.3 [102]ECi/ECd (dB) 28.0/29.1  25 [87, 102]ILthru/ILd (dB) 0.6/0.6  1.0 [87, 102]ILthru-m/ILd-m (dB) 0.6/0.8  1.0 [87, 102]aThe FSR to the left of the major peakbThe FSR to the right of the major peak371520 1530 1540 1550 1560 1570ï30ï20ï100Wavelength (nm)Intensity (dB)   input to through add to dropa)1544.6 1544.7 1544.8 1544.9 1545ï30ï20ï100Wavelength (nm)Intensity (dB)   input to through add to dropb)1515 1520 1525 1530 1535ï1ï0.8ï0.6ï0.4ï0.20Wavelength (nm)Intensity (dB)   input to through add to dropc)Figure 2.4: (a) Spectral response at through port and drop port when light isinjected into the input port and the add port of the device, respectively.(b) shows that the major notch within the stopband changes dependingon whether the light is injected into the input port or add port. (c) showsthat the passband spectrum changes depending on whether the light isinjected into the input port or add port. cSPIE, 2015, by permission[85].1520 1530 1540 1550 1560 1570ï200002000Wavelength (nm)Dispersion (ps/nm)  input to throughadd to dropa)1520 1525 1530 1535ï400ï2000200400600Wavelength (nm)Dispersion (ps/nm)  input to throughadd to dropb)Figure 2.5: Dispersion at the through port and the drop port when light isinjected into the input port and the add port of the device, respectively.(b) A zoom-in of Figure 2.5(a) in the region of one of the passbands.cSPIE, 2015, by permission [85].38It is also important to understand that there are many unknown variables withinthe fabrication process which make matching designed results to experimental re-sults difficult. These unknowns include the heights and the widths of the waveg-uides [129] and optical proximity effects in the coupling regions causing the waveg-uide widths to change [476]. In the next section we will analyze the effects ofchanging the waveguide widths and the corresponding gap distances for devicesD1 and D2. We will then analyze the effects of independently changing the waveg-uide height and the propagation loss for one of these quadruple Vernier racetrackresonators.2.3 Fabrication Sensitivity4The sensitivity to fabrication errors is important in determining whether the ac-tual device will, in fact, work as designed, given the inherent errors expected duringthe fabrication process. There are numerous publications regarding the fabricationsensitivities of silicon photonic devices [112, 472, 476–492]. Krishnamoorthy etal. has stated that the inter-wafer silicon thickness variation on a SOI wafer can beup to ±5 nm [481]. Recent advances in optical lithography have enabled improve-ments in the waveguide width variations by using 193 nm immersion lithography[488]. Selvaraja et al. [488] have demonstrated a “3s” silicon waveguide widthvariation of 7.95 nm. Hence, we have decided to vary the strip waveguide widths by±10 nm to capture virtually all possible variations for devices D1 and D2. MODESolutions by Lumerical Solutions, Inc., was used to determine the effective indexfor waveguide widths of 490 nm, 500 nm, and 510 nm with fixed heights of 220 nmas well as the even and odd supermode effective indices of the straight portions ofthe directional couplers. When calculating these supermode effective indices, weallowed for the changes in gap distances resulting from the changes in the waveg-uide widths (we assume that the centre-to-centre distance between the waveguidesof the coupler regions remain constant). Tables 2.2 and 2.3 show the results forwaveguide widths of 490 nm, 500 nm, and 510 nm for devices D1 and D2, re-spectively, when the waveguide height is fixed at 220 nm and the propagation lossis fixed at 2.4 dB/cm. The field coupling factors at 1550 nm (here, to show the4A version of Chapter 2.3 has been published in [84, 85].39wavelength dependency of the field coupling factors we provide the slopes, dk/dl ,at 1550 nm) for directional couplers with waveguide widths of 490 nm, heights of220 nm, and nominal gap distances (gap distances prior to varying the waveguidewidths) of 150 nm, 350 nm, 360 nm, 390 nm, and 410 nm, are 0.43906 (dk/dl= 0.00161 nm-1), 0.07939 (dk/dl = 0.00048 nm-1), 0.07290 (dk/dl = 0.00045nm-1), 0.05648 (dk/dl = 0.00037 nm-1), and 0.04766 (dk/dl = 0.00032 nm-1), re-spectively. The field coupling factors at 1550 nm (as well as their slopes, dk/dl , at1550 nm) for directional couplers with waveguide widths of 500 nm, heights of 220nm, and nominal gap distances of 150 nm, 350 nm, 360 nm, 390 nm, and 410 nm,are 0.44422 (dk/dl = 0.00158 nm-1), 0.07856 (dk/dl = 0.00047 nm-1), 0.07209(dk/dl = 0.00044 nm-1), 0.05570 (dk/dl = 0.00036 nm-1), and 0.04692 (dk/dl =0.00031 nm-1), respectively. The field coupling factors at 1550 nm (as well as theirslopes, dk/dl , at 1550 nm) for directional couplers with waveguide widths of 510nm, heights of 220 nm, and nominal gap distances of 150 nm, 350 nm, 360 nm, 390nm, and 410 nm, are 0.45162 (dk/dl = 0.00155 nm-1), 0.07813 (dk/dl = 0.00045nm-1), 0.07163 (dk/dl = 0.00042 nm-1), 0.05521 (dk/dl = 0.00034 nm-1), and0.04643 (dk/dl = 0.00030 nm-1), respectively. The ECi and ECd (indicated in thetables with bold values) for all of the devices with widths of 490 nm do not meetthe commercial specification of 25 dB. However, all of the other commercial 4-portfilter specifications listed in Table 1.2 are still met. By inspection of Tables 2.2 and2.3, we believe that Table 2.2 is the best choice since it shows the best combinationof ECi and ECd values for widths of 490 nm and 500 nm. Therefore, we believethat the device from Table 2.2 is the best one. Having chosen this device, we thenlooked to see what width variation it could tolerate. Table 2.4 shows the results forthis device when the waveguide widths are 494 nm, 502 nm, and 510 nm. The fieldcoupling factors at 1550 nm (as well as their slopes, dk/dl , at 1550 nm) for direc-tional couplers with waveguide widths of 494 nm, heights of 220 nm, and nominalgap distances of 150 nm, 350 nm, and 390 nm are 0.44081 (dk/dl = 0.00160nm-1), 0.07900 (dk/dl = 0.00048 nm-1), and 0.05613 (dk/dl = 0.00036 nm-1),respectively. The field coupling factors at 1550 nm (as well as their slopes, dk/dl ,at 1550 nm) for directional couplers with waveguide widths of 502 nm, heights of220 nm, and nominal gap distances of 150 nm, 350 nm, and 390 nm are 0.44546(dk/dl = 0.00157 nm-1), 0.07844 (dk/dl = 0.00046 nm-1), and 0.05558 (dk/dl =400.00035 nm-1), respectively. We can clearly see that all commercial specificationsare met for this device with a width tolerance of ±8 nm when designed for widthsof 502 nm (i.e., this is approximately twice the 3s variation given above). Hence,we chose waveguide widths of 502 nm for all subsequent modelling of this device.Figure 2.6(a) shows the spectral results (where light was injected only into the in-put port), for the chosen device, for waveguide widths of 494 nm, 502 nm, and 510nm. It can be clearly seen that a change in the waveguide width shifts the centralwavelength by a few nanometers due to the changes in the effective indices. Also,it is interesting to note that the FSR increases when the waveguide width increases.We now look at how the spectral characteristics are affected by changes in thewaveguide height. Table 2.5 shows the height variation analysis results for heightsof 210 nm, 220 nm, and 230 nm when the waveguide widths are 502 nm and thepropagation loss is 2.4 dB/cm. The field coupling factors at 1550 nm (as well astheir slopes, dk/dl , at 1550 nm) for directional couplers with waveguide widthsof 502 nm, heights of 210 nm, and nominal gap distances of 150 nm, 350 nm, and390 nm are 0.47215 (dk/dl = 0.00166 nm-1), 0.08669 (dk/dl = 0.00052 nm-1),and 0.06189 (dk/dl = 0.00040 nm-1), respectively. The field coupling factors at1550 nm (as well as their slopes, dk/dl , at 1550 nm) for directional couplers withwaveguide widths of 502 nm, heights of 230 nm, and nominal gap distances of 150nm, 350 nm, and 390 nm are 0.42229 (dk/dl = 0.00149 nm-1), 0.07160 (dk/dl= 0.00042 nm-1), and 0.05038 (dk/dl = 0.00032 nm-1), respectively. The resultsshow that, even with a variance in height of ±10 nm, all of the commercial filterspecifications are still met (which is twice the±5 nm variation given above). Closeinspection of Figures 2.6(a) and 2.6(b) shows that for the same change in heightor width, height changes cause greater shifts in the centre wavelength than widthchanges. However, ECi is relatively insensitive to the chosen changes in height.Upon analyzing the field coupling factor values presented in this chapter, thefield coupling factor is significantly more sensitive to a change in the waveguideheights of the directional coupler as compared to changes in the waveguide widthsof the directional coupler. For example, if we change the waveguide widths from490 nm to 510 nm for a directional coupler with a nominal gap distance of 150nm, the field coupling factor would increase by 2.86% at a wavelength of 1550nm. However, a change in the waveguide heights from 210 nm to 230 nm for a41directional coupler with waveguide widths of 502 nm and a nominal gap distanceof 150 nm would result in the field coupling factor decreasing by 10.56% at awavelength of 1550 nm.In the waveguide width and height analysis, we used a constant propagationloss of 2.4 dB/cm. To account for variations in the propagation loss, Table 2.6shows the propagation loss analysis results for losses of 1.4 dB/cm, 2.4 dB/cm,and 3.4 dB/cm for waveguide widths and heights of 502 nm and 220 nm, respec-tively. The maximum propagation loss considered is 3.4 dB/cm, due to ILd beingequal to 1.0 dB (which is the maximum value for meeting its commercial speci-fication). It should be noted, however, that ILd-m is 1.1 dB. If the spectrum wereto shift, it is possible that ILd might exceed the 1.0 dB specification as well werethe propagation loss to reach 3.4 dB/cm. Nevertheless, we note that reported lossvalues for SOI channel waveguides are 2.4±0.3 dB/cm and 2.35±0.33 dB/cm inRefs. 472 and 492, respectively, and that our calculations show that as long as thepropagation loss is less than or equal to 3.0 dB/cm, all the specifications will bemet. Figure 2.6(c) shows the sensitivity of ILthru-m to a change in propagation loss.421540 1545 1550 1555ï100ï80ï60ï40ï200Intensity (dB)Wavelength (nm)  width = 494 nmwidth = 502 nmwidth = 510 nma)1530 1540 1550 1560ï100ï80ï60ï40ï200Wavelength (nm)Intensity (dB)  height = 210 nmheight = 220 nmheight = 230 nmb)1520 1521 1522 1523ï1ï0.50Wavelength (nm)Intensity (dB)  loss = 1.4 dB/cmloss = 2.4 dB/cmloss = 3.4 dB/cmc)Figure 2.6: For light injected at the input port, (a) shows the sensitivity ofthe spectral response to changes in the waveguide width for a height of220 nm and a loss of 2.4 dB/cm, (b) shows the sensitivity of the spectralresponse to changes in the height for a width of 502 nm and a loss of 2.4dB/cm, and (c) shows the sensitivity of the spectral response to changesin loss for a width of 502 nm and a height of 220 nm. It should be notedthat some of these parameters were taken from Ref. 96 and Ref. 149.cSPIE, 2015, by permission [85].43Table 2.2: Width tolerance for (gap 1, gap 2, gap 3) = (150 nm, 350 nm, 390nm). Bolded parameter values do not meet their commercial specifica-tions. cSPIE, 2015, by permission [85].Parameter Width (nm) = 490 500 510FSR (nm) 36.43a/38.20b 36.85a/38.66b 37.26a/39.11bAi (dB) 55.7 54.0 52.2nAi (dB) 51.5 41.2 42.7IPS (dB) 41.9 41.2 40.3ILdrop (dB) 0.4 0.4 0.4Rdepth (dB) 0.0 0.0 0.0ECi/ECd (dB) 22.9/23.4 28.0/29.1 25.3/25.0ILthru/ILd (dB) 0.2/0.8 0.6/0.6 0.4/0.7ILthru-m/Ld-m (dB) 0.6/0.9 0.6/0.8 0.6/0.8Ddrop (ps/nm) ±32 ±26 -23Dthru/Dd (ps/nm) -119/+313 -150/-247 +177/-388Dthru-m/Dd-m (ps/nm) -297/+564 -253/+480 -215/+406aThe FSR to the left of the major peakbThe FSR to the right of the major peak44Table 2.3: Width tolerance for (gap 1, gap 2, gap 3) = (150 nm, 360 nm, 410nm). Bolded parameter values do not meet their commercial specifica-tions. cSPIE, 2015, by permission [85].Parameter Width (nm) = 490 500 510FSR (nm) 36.43a/38.20b 36.85a/38.66b 37.26a/39.11bAi (dB) 58.7 57.0 55.3nAi (dB) 54.6 42.7 44.2IPS (dB) 43.4 42.7 41.8ILdrop (dB) 0.4 0.4 0.4Rdepth (dB) 0.0 0.0 0.0ECi/ECd (dB) 22.4/23.4 25.3/25.7 25.9/25.0ILthru/ILd (dB) 0.2/0.8 0.6/0.6 0.5/0.7ILthru-m/ILd-m (dB) 0.7/0.9 0.6/0.8 0.6/0.8Ddrop (ps/nm) ±48 ±43 -41Dthru/Dd (ps/nm) -102/+255 -144/-261 +186/-409Dthru-m/Dd-m (ps/nm) -305/+578 -262/+496 -225/+425aThe FSR to the left of the major peakbThe FSR to the right of the major peak45Table 2.4: Width tolerance for (gap 1, gap 2, gap 3) = (150 nm, 350 nm, 390nm). cSPIE, 2015, by permission [85].Parameter Width (nm) = 494 502 510FSR (nm) 36.60a/38.38b 36.93a/38.75b 37.26a/39.11bAi (dB) 55.0 53.6 52.2nAi (dB) 45.8 41.1 42.7IPS (dB) 41.7 41.0 40.3ILdrop (dB) 0.4 0.4 0.4Rdepth (dB) 0.0 0.0 0.0ECi/ECd (dB) 25.4/26.1 28.0/28.7 25.3/25.0ILthru/ILd (dB) 0.4/0.8 0.5/0.7 0.4/0.7ILthru-m/ILd-m (dB) 0.6/0.8 0.6/0.8 0.6/0.8Ddrop (ps/nm) -30 -26 -23Dthru/Dd (ps/nm) +216/-443 +146/+465 +177/-388Dthru-m/Dd-m (ps/nm) -279/+530 -245/+465 -215/+406aThe FSR to the left of the major peakbThe FSR to the right of the major peak46Table 2.5: Height tolerance for (gap 1, gap 2, gap 3) = (150 nm, 350 nm, 390nm). cSPIE, 2015, by permission [85].Parameter Height (nm) = 210 220 230FSR (nm) 36.36a/38.16b 36.93a/38.75b 37.49a/39.33bAi (dB) 53.6 53.6 53.6nAi (dB) 50.8 41.1 43.7IPS (dB) 40.7 41.0 41.3ILdrop (dB) 0.4 0.4 0.4Rdepth (dB) 0.0 0.0 0.0ECi/ECd (dB) 27.9/28.4 28.0/28.7 28.1/28.9ILthru/ILd (dB) 0.2/0.7 0.5/0.7 0.5/0.7ILthru-m/ILd-m (dB) 0.6/0.8 0.6/0.8 0.6/0.8Ddrop (ps/nm) ±25 -26 ±26Dthru/Dd (ps/nm) -92/-219 +146/+465 +199/+280Dthru-m/Dd-m (ps/nm) -240/+456 -245/+465 -249/+472aThe FSR to the left of the major peakbThe FSR to the right of the major peak47Table 2.6: Propagation loss tolerance for (gap 1, gap 2, gap 3) = (150 nm,350 nm, 390 nm). Bolded parameter value does not meet its commercialspecification. cSPIE, 2015, by permission [85].Parameter Loss (dB/cm) = 1.4 2.4 3.4FSR (nm) 36.93a/38.75b 36.93a/38.75b 36.93a/38.75bAi (dB) 53.8 53.6 53.5nAi (dB) 41.1 41.1 41.0IPS (dB) 41.1 41.0 41.0ILdrop (dB) 0.2 0.4 0.5Rdepth (dB) 0.0 0.0 0.0ECi/ECd (dB) 28.0/ 28.4 28.0/28.7 28.0/29.0ILthru/ILd (dB) 0.3/0.4 0.5/0.7 0.7/1.0ILthru-m/ILd-m (dB) 0.3/0.5 0.6/0.8 0.8/1.1Ddrop (ps/nm) -26 -26 -26Dthru/Dd (ps/nm) +146/+464 +146/+465 +147/+466Dthru-m/Dd-m (ps/nm) -245/+464 -245/+465 -246/+466aThe FSR to the left of the major peakbThe FSR to the right of the major peakWe have presented silicon quadruple Vernier racetrack resonators designed tomeet typical 4-port filter commercial specifications. Also, we have shown that wecan design a device with a waveguide width of 502 nm and a height of 220 nmthat is tolerant to ±8 nm changes in the widths of the waveguides. This devicealso has a Ddrop of -26 ps/nm and a Dd-m of +465 ps/nm. Then, one at a time, wevaried the waveguide height and propagation loss. The device was also tolerantto a ±10 nm change in height as well as tolerant to changes in propagation loss.Next, theoretical and experimental results on a silicon quadruple Vernier racetrackresonator that meets numerous 3-port filter commercial specifications is presented.482.4 Experimental Results5A schematic of our quadruple series-coupled racetrack resonator exhibiting theVernier effect is shown in Figure 2.7 which is similar to that found in [126, 142,143] (same arrangement of the resonators but different resonator lengths, fieldtransmission and coupling factors, and propagation loss). Here, L1, L2, L3, andL4 are the total lengths of racetrack resonators R1, R2, R3, and R4, respectively.Lc is the length of the straight coupling regions, r is the radius of the racetrackresonators, and L is the length of the straight sections (other than those in the cou-pling regions) for racetrack resonators R3 and R4. k1, k2, k3, k4, and k5 are thesymmetric (real) point field coupling factors. t1, t2, t3, t4, and t5 are the straightthrough (real) point field transmission factors.	 	 	 	 		Add -jκ5 Drop -jκ4 -jκ3 -jκ2 -jκ1 t5 t4 t3 t2 t 1 In Through r g4 g3 g2 g1 g5 Lc R1 R2 R3 R4 t1 L r Lc L Lc Lc Lc r r r r Figure 2.7: Schematic of our quadruple series-coupled racetrack resonatorsexhibiting the Vernier effect. cOptical Society of America, 2013, bypermission [96].The following assumptions are made for the design: L1,2 = 2pr+2Lc and L3,4= (4/3)L1,2 = 2pr+2L+2Lc, where r = 5 µm, Lc = 7 µm and L = 7.569 µm. k1 =k5, k2 = k4, t1 = t5, and t2 = t4. The waveguides are SOI strip waveguides with atop silicon dioxide cladding having widths and heights of 502 nm and 220 nm, re-spectively. The propagation loss for each ring was assumed to be 2.4 dB/cm [492].The modelling and analysis of the quadruple Vernier racetrack resonator was doneusing a mixture of numeric and analytic methods. Specifically, the effective in-dex of the strip waveguides and the field coupling and transmission factors weredetermined using MODE Solutions by Lumerical Solutions, Inc., and everythingelse was done analytically. The gap distances are g1 = 125 nm, g2 = 350 nm, g35A version of Chapter 2.4 has been published in [96].49= 410 nm, g4 = 350 nm, and g5 = 125 nm, respectively. The value of their fieldcoupling and field transmission factors were determined by applying a third orderpolynomial curve-fit to the wavelength dependent even and odd effective indices.At 1550 nm, the field coupling factors are k1 = k5 = 0.5446, k2 = k4 = 0.0771, andk3 = 0.0460 and their slopes are dk1/dl = dk5/dl = 1.72⇥103 nm-1, dk2/dl =dk4/dl = 4.58⇥104 nm-1, dk3/dl = 3.03⇥104 nm-1. Also at 1550 nm, the ef-fective index is 2.4464 and the slope is -1.12⇥103 nm-1. The theoretical drop portand through port responses are shown in Figures 2.8(a) and 2.8(b). The derivationof the drop port and through port transfer functions can be found in Appendix A.We choose a 0.8 nm channel spacing and a 0.048 nm clear window centred at adesired wavelength. The spectral characteristics are determined within the clearwindows of the desired channel and the 44 clear windows to the left and right ofthe desired channel. The FSR should be greater than or equal to 35.89 nm (thespan of the C-band, 1528.77 nm to 1563.86 nm [92], plus one adjacent channel).The spectra (when light is only injected into the input port) shown in Figures 2.8(a)and 2.8(b) meet the typical commercial values for the target 3-port filter specifica-tions as shown in Table 2.7 (bolded values). It should be noted that there is somevariance in target values depending on the DWDM vendor. For example, [100]specifies an ECi value of 12 dB whereas [99] specifies a value of 10 dB.Table 2.7: Theoretical and target 3-port filter specifications [96].Parameter Theoretical TargetFSR (nm) 36.93  35.89Ai (dB) 52.7  25 [99, 100], 30 [101]nAi (dB) 40.4  35 [101], 40 [99, 100]IPS (dB) 38.5  35 [101], 40 [99, 100]Rdepth (dB) 0.1  0.5 [99]ECi (dB) 11.1  10 [99], 12 [100]501500 1520 1540 1560 1580ï100ï80ï60ï40ï200Intensity (dB)Wavelength (nm)  throughdropa)1545 1545.5 1546 1546.5 1547ï60ï40ï200Intensity (dB)Wavelength (nm)  throughdropb)Figure 2.8: (a) Theoretical spectral response. (b) A “zoom-in” of the majorresonance. cOptical Society of America, 2013, by permission [96].The device was fabricated at the University of Washington using electron beamlithography, as described in [493]. Figures 2.9(a) and 2.9(b) show the experimen-tal through port and drop port responses of one of our silicon quadruple Vernierracetrack resonators. Figure 2.9(a) clearly shows significant IPS. The maximumthrough port insertion loss [98] and the drop port insertion loss [92, 98, 494] havenot been included since we were unable to measure them accurately. The spec-tral characteristics meet numerous commercial 3-port filter specifications as shownin Table 2.8 (bolded values). The ECi, Rdepth, nAi, and IPS are within 1.6 dBof the theoretical results. The experimental Ai is 37.2 dB whereas the theoreti-cal Ai is 52.7 dB, which is likely due to the experimental filter line shape beingasymmetric and to increased field coupling factors due to the bend regions of thecouplers. To be able to simultaneously drop and add signals using just one in-stance of the device shown in Figure 2.7, the target values shown in Table 1.2 for4-port filters would be needed. Specifically, the ECi would need to be greater thanor equal to 25 dB [87, 102]. The much larger notches within the pass band ofthe through port as compared to the theoretical results are possibly due to fabri-cation variations and coupling-induced frequency shifts (CIFSs) [124, 495], whichcan be corrected by thermally tuning each racetrack resonator [124]. However,the notches are not located within any of the adjacent or non-adjacent channels asshown in Figures 2.9(c) and 2.9(d). The passband of the through port to the left ofthe major peak shows that there are actually 4 notches (two small notches and twolarge notches) as shown in Figure 5.7(c). However, our theoretical results showedthat there are only two small notches as shown in Figure 2.8(a). The likely rea-51sons for this difference between the theory and experimental results are fabricationvariations, in which the effective indices of the resonators are not all exactly thesame, and CIFS. For example, if the effective index of racetrack resonator R1 isdecreased by 0.003 [as shown in Figure 2.9(e)] each of the notches separates into2 notches (one small and one large), where the larger notch is located to the rightof the smaller notch [as shown in Figure 2.9(f)], which is in agreement with theexperimental results. In addition to the device presented here, we fabricated 48other devices in which the gap distances were varied. The device presented hereshowed the best performance. However, future designs based on this device can bemade to be thermally tunable to compensate for fabrication variations and effectssuch as CIFS.521520 1540 1560 1580ï70ï60ï50ï40ï30ï20Wavelength (nm)Power (dBm)  throughdropa)1556.5 1557 1557.5 1558 1558.5ï70ï60ï50ï40ï30ï20Wavelength (nm)Power (dBm)  throughdropb)1532 1534 1536 1538 1540 1542 1544ï70ï60ï50ï40ï30ï20Wavelength (nm)Power (dBm)  throughdropc)1572 1574 1576 1578 1580 1582 1584ï70ï60ï50ï40ï30Wavelength (nm)Power (dBm)  throughdropd)1532 1532.5 1533 1533.5ï2ï1.5ï1ï0.50Wavelength (nm)Intensity (dB)  6 nR1= 06 nR1= ï0.0016 nR1= ï0.0026 nR1= ï0.003e)1532 1532.5 1533 1533.5 1534ï10ï8ï6ï4ï20Wavelength (nm)Intensity (dB)  6 nR1= 06 nR1= ï0.0016 nR1= ï0.0026 nR1= ï0.003f)Figure 2.9: (a) Measured through port and drop port spectral response. (b)zoom-in of the measured major resonance. (c) Zoom-in of the mea-sured through port passband to the left of the major peak. (d) Zoom-inof the measured through port passband to the right of the major peak.(e) Zoom-in of the theoretical notch splitting when the effective indexof racetrack resonator R1 decreases and (f) zoom-out of Figure 2.9(e)(showing the increase in notch depth as the effective index of racetrackresonator R1 decreases). cOptical Society of America, 2013, by per-mission [96].53Table 2.8: Experimental and target 3-port filter specifications [96].Parameter Experimental TargetFSR (nm) 37.52  35.89Ai (dB) 37.2  25 [99, 100], 30 [101]nAi (dB) 39.7  35 [101], 40 [99, 100]IPS (dB) 36.9  35 [101], 40 [99, 100]Rdepth (dB) 0.2  0.5 [99]ECi (dB) 10.2  10 [99], 12 [100]In summary, we have experimentally shown that it is possible to meet numer-ous 3-port DWDM filter commercial requirements using silicon quadruple series-coupled racetrack resonators exhibiting the Vernier effect. We have demonstrateda Vernier filter having a FSR greater than the span of the C-band (37.52 nm), aripple of 0.2 dB, an adjacent channel isolation of 37.2 dB, a non-adjacent channelisolation of 39.7 dB, an interstitial peak suppression of 36.9 dB, and an expresschannel isolation of 10.2 dB. Next, I will discuss our work on thermally tunablesilicon quadruple Vernier racetrack resonators.54Chapter 3Thermally TunableSilicon-On-Insulator VernierRacetrack Resonators1 Thermal tuning of ring resonators is desirable since its effect on the effectiveindex is large [496] and there is no excess loss versus current [497]. Thermallytunable identical series-coupled ring resonators have been fabricated [115, 124],however, an increase in temperature tends to shift the resonant wavelength by ap-proximately 0.07 nm/oC, therefore, to tune the resonant wavelength by the span ofthe C-band (35.09 nm) would require a temperature change of several hundred de-grees Celsius. Fortunately, the Vernier effect enables one to significantly enhancethe resonant wavelength tuning range as compared to the range capable when usingidentical ring resonators [301]. Thermally tunable series [113, 212, 317] and cas-caded [134, 301] coupled double ring resonator filters exhibiting the Vernier effecthave been achieved previously. However, these devices show unacceptable spec-tral characteristics for typical DWDM applications such as low IPS [113, 301, 317],small extension of the FSR [212, 317], no extension of the FSR in the through port[134, 301], and many do not use the SOI platform [134, 212].In this chapter, I present our results on thermally tunable silicon quadruple1A version of this paragraph has been published in [149].55Vernier racetrack resonators that exhibit an increased resonant wavelength tuningrange as compared to resonators that do not utilize the Vernier effect. We also showthat it is possible to transmit data through a silicon quadruple Vernier racetrackresonator.3.1 Thermally Tunable Silicon Quadruple VernierRacetrack Resonators2 Here, we present theoretical and experimental results on a thermally tunable sil-icon quadruple Vernier racetrack resonator. For the modelling and analysis of ourVernier racetrack resonator, we have used SOI strip waveguides with heights of 220nm and widths of 502 nm, as well as a top SiO2 cladding. The Si refractive index iswavelength dependent and can be fitted to experimental data using a Lorentz model[470]. Since the wavelength dependency of the refractive index of SiO2 is mini-mal, we have assumed a constant refractive index of 1.4435. Also, we have used2.4 dB/cm propagation loss in our modelling. This is consistent with the valueof 2.35±0.33 dB/cm recently reported by [492], for SOI strip waveguides withtop SiO2 claddings. The schematic of the quadruple Vernier racetrack resonatoris shown in Figure 3.1(a), which has an asymmetric arrangement of resonators asdescribed in [96, 126, 142, 143]. The fabricated device is shown in Figure 3.1(b).2A version of Chapter 3.1 has been published in [149].56	 	 	 	 	 	-jκ2 t5 t4 t3 t2 t 1 r r L Lc Lc In Through g1 g2	 g3	 g4	 g5	 Add Drop R1 R2 -jκ1 -jκ3 -jκ4 -jκ5 t1 a) R3 R4 In/ThroughAdd/Dropb) Figure 3.1: (a) Shows the schematic of the quadruple Vernier racetrack res-onator and (b) shows the fabricated device. cOptical Society of Amer-ica, 2013, by permission [149].L1,2,3,4 are the total lengths of the racetrack resonators, k1 and k5 are the sym-metric (real) point field coupling factors to the bus waveguides, k2,3,4 are the inter-ring symmetric (real) point field coupling factors, and t1,2,3,4,5 are the respective(real) point field transmission factors. The derivations of the transfer functions canbe found in [96, 144] and Appendix A. The following simulations assume that L1= L2 = 2pr+2Lc (where r = 5 µm and Lc = 7 µm), L3 = L4 = (4/3)L1 = 2pr+2Lc+2L(where L = 7.569 µm), k1 = k5, k2 = k4, t1 = t5, and t2 = t4. The effective indexand field coupling and transmission factors are wavelength dependent and were de-termined using MODE Solutions software by Lumerical Solutions, Inc. The fieldcoupling and transmission factors were calculated by determining the even and oddeffective indices. At the major resonance wavelength (1545.96 nm), the effectiveindex for a single waveguide is 2.4509 and its slope is -0.0011 nm-1. The gapdistances g1, g2, g3, g4, and g5 were chosen to be 148 nm, 348 nm, 388 nm, 348nm, and 148 nm, respectively. At the major resonance wavelength, their respectivefield coupling factors (and slopes) are 0.4392 (0.0016 nm-1), 0.0766 (0.0005 nm-1),0.0542 (0.0003 nm-1), 0.0766 (0.0005 nm-1), and 0.4392 (0.0016 nm-1). We de-signed our device to have an ECi greater than or equal to 25 dB [87, 102] for a clear57window of 0.1 nm at a centre wavelength of 1545.94 nm and a channel spacing of0.8 nm, as shown in Figure 3.2(b), whereas our previous device had an ECi of 11.1dB for a clear window of 0.048 nm [96]. Also, minimal notches within the pass-bands of the through port and a large IPS is required, as shown in Figure 3.2(a).The 3-dB BW, IPS, FSR, and ECi are 0.34 nm, 41.0 dB, 36.93 nm, and 25.7 dB,respectively, when light is only injected into the input port.1520 1540 1560 1580ï100ï80ï60ï40ï200Wavelength (nm)Intensity (dB)  through portdrop porta)1545.2 1545.6 1546 1546.4 1546.8ï60ï40ï200Wavelength (nm)Intensity (dB)  through portdrop portb)Figure 3.2: (a) Shows the theoretical through port and drop port spectra and(b) shows a major peak in the drop port response and a major notchin the through port response. cOptical Society of America, 2013, bypermission [149].The device fabricated consisted of multiple e-beam lithography [493] and Cl2etch steps (to define the strip waveguides and shallow etch grating couplers), a 2micron oxide deposition, followed by a 300 nm deposition of Al for the electrodesand metal heaters (5 µm wide) above the waveguides. Figures 3.3(a) and 3.3(b)show the experimental through port and drop port responses of the device whenno voltage is applied (light is only injected into the input port). The FSR (37.09nm) is larger than the span of the C-band, the IPS is 24.5 dB for a clear windowof 0.1 nm centred at l = 1549.468 nm, and the 3-dB BW is 0.24 nm. It is alsoclear that the through port response shows suppression of the resonances withinthe passband. The minimum insertion loss (defined as the maximum transmissionat the through port) of the device is approximately 12 dB, which is mainly due tothe grating coupler loss (typically measured to be 10-12 dB), whereas other lossmechanisms are minimal such as mode-mismatch loss at the interfaces betweenstraight sections and 90 degree bends of the racetrack resonators which, based onour simulation results, is approximately 0.008 dB per interface. Also, one can58clearly see that the major peak is much lower than the through port transmissionand the major notch shows worse performance as compared to the theory which arelikely due to fabrication variations and CIFSs which can be corrected for by finelytuning each ring resonator [124]. However, here we have focussed on the discretewavelength tunability of our device (continuous tuning is possible as described in[301]). We applied the same voltage to racetrack resonators R3 and R4 to enablethe Vernier effect switching mechanism. Figure 3.4(a) shows the theoretical resultswhen the temperature difference between resonators R3 and R4, as compared tothe temperature of resonators R1 and R2, is increased from 0 oC to 46 oC (dn/dT= 1.86⇥10-4 oC-1[431]). We can clearly see the discrete switching of the majorpeak across a wavelength span of 12.70 nm, which corresponds to the FSR ofa single racetrack resonator with the dimensions of one of our small resonators(i.e., resonator R1 or R2). If we changed the temperatures of all of the racetrackresonators at the same time by 46 oC, the major peak would only shift by 3.17 nm.Thus, we can see one of the benefits of using the Vernier effect to tune the resonantwavelength. Figure 3.4(b) shows the experimental results in which we varied thevoltage applied to the heaters on top of both racetrack resonators R3 and R4 from 0V to 10.5 V. The major peak shifts discretely by 15.54 nm. When 10.5 V is applied,the major peak has an IPS of 32.7 dB for a clear window of 0.1 nm that is centredat l = 1565.062 nm, a 3-dB BW of 0.45 nm, and an FSR of 37.66 nm. Except fora 2.84 nm increase in the resonant shift, which is possibly due to thermal crosstalkbetween the racetrack resonators [301] (resonators R1 and R2 are likely also beingheated), the experimental Vernier switching mechanism seen here is in agreementwith the theoretical results.591520 1540 1560 1580ï80ï60ï40ï20Wavelength (nm)Power (dBm)  through portdrop porta)1548 1548.5 1549 1549.5 1550 1550.5ï70ï60ï50ï40ï30ï20Wavelength (nm)Power (dBm)  through portdrop portb)Figure 3.3: (a) Shows the experimental through port and drop port spectraand (b) shows a major peak of the drop port response and a major notchof the through port response. cOptical Society of America, 2013, bypermission [149].1545 1550 1555 1560ï60ï40ï2002040Wavelength (nm)Intensity (dB)  6T = 0 oC6T = 10 oC6T = 20 oC6T = 30 oC6T = 40 oC6T = 46 oC6 h = 12.70 nma)1550 1555 1560 1565ï70ï60ï50ï40ï30Wavelength (nm)Power (dBm)  voltage = 0 Vvoltage = 6 Vvoltage = 8 Vvoltage = 9 Vvoltage = 10.5 V6 h = 15.54 nmb)Figure 3.4: (a) Shows the theoretical drop port spectral responses for varioustemperature changes applied to racetrack resonators R3 and R4 and (b)shows the experimental drop port spectral responses for various changesin the voltage applied to the heaters on top of racetrack resonators R3and R4. cOptical Society of America, 2013, by permission [149].In summary, we have demonstrated a thermally tunable silicon quadruple Vernierracetrack resonator. This device has an IPS of 32.7 dB, a 3-dB BW of 0.45 nm,and an extended FSR of 37.66 nm when 10.5 V is applied to the heaters on topof the two larger racetrack resonators. We were also able to shift the major peakby 15.54 nm. Next, I discuss our experimental results that demonstrate that it ispossible to transmit data to the drop port of another one of our thermally tunablesilicon quadruple Vernier racetrack resonators as well as to the through port in thelocation of one of the minor notches at a data rate of 12.5 Gbps.603.2 Silicon-On-Insulator Quadruple Vernier RacetrackResonators: Experimental Signal Quality3One of the issues with using series-coupled Vernier ring resonators is that largedispersion can occur in the region of the suppressed notches of the through port[112, 231, 432]. Here, we experimentally demonstrate a thermally tunable siliconquadruple series-coupled Vernier racetrack resonator filter (similar to [149]) andshow data transmission at 12.5 Gbps through the filter. Our results show that thereis degradation of the signal quality through our filter in the region of a suppressednotch, however, the eye remained open.A thermally tunable silicon quadruple series-coupled Vernier racetrack res-onator filter was fabricated using optical lithography at the Institute of Microelec-tronics (IME) in Singapore. The filter had an oxide cladding and 3 µm wide TiNheaters were fabricated on top of the racetracks for the purpose of thermal tuning.The strip waveguides had widths of 500 nm and heights of 220 nm and the rest ofthe parameters can be seen in Figure 3.5(a) (some of these parameters can also befound in [84, 96, 149]). Figure 3.5(b) is an image of the fabricated filter. Fibregrating couplers were used for coupling light in/out of the device [498].3A version of Chapter 3.2 has been published in [150].617.569 µm 7 µm 5 µm In Through Drop Add a) Gap 1  = 190 nm Gap 2  = 380 nm Gap 3  = 410 nm Gap 4  = 380 nm Gap 5 = 190 nm Figure 3.5: (a) Schematic diagram of the Vernier filter (see [84, 96, 127, 140–142, 149]) and (b) a microscope image of the fabricated filter showingthe integrated heaters. cOptical Society of America, 2015, by permis-sion [150].Figure 3.6(a) shows the in-port-to-through-port and in-port-to-drop-port spec-tral responses before and after thermal tuning. For thermal tuning, we appliedvoltages of V1 = 0.631 V, V2 = 0.795 V, V3 = 0.37 V, and V4 = 1.07 V [see Fig-ure 3.5(b)]. The 3-dB BW after thermal tuning is 0.35 nm. Figure 3.6(b) shows azoom-out of the spectra after thermal tuning which exhibits a large FSR of 37.87nm and significant IPS. Figure 3.6(c) shows that the in-port-to-drop-port spectralresponse and the add-port-to-through-port spectral response are similar. In Fig-ure 3.6(d) we can see that there are two relatively suppressed notches (the otherthree notches are more suppressed and are not visible) within the passband of thethrough port (in-port-to-through-port) and three relatively suppressed notches (theother two notches are more suppressed and are not visible) within the passband ofthe drop port (add-port-to-drop-port) which is consistent with the theoretical re-sults in [84]. Figures 3.6(e) and 3.6(f) show the group delay and dispersion (see[112, 114, 140, 144]), respectively, from the in port to the drop port and from theadd port to the through port. The group delay and dispersion were determined62using the Hilbert transform method [112, 499] (we used the MATLAB R Hilberttransform function [500]) and averaging was used to smooth the results.1532 1532.5 1533 1533.5 1534 1534.5 1535ï70ï60ï50ï40ï30ï20Wavelength (nm)Power (dBm)  through: before tuningthrough: after tuningdrop: before tuningdrop: after tuninga)1530 1540 1550 1560 1570ï70ï60ï50ï40ï30ï20Wavelength (nm)Power (dBm)  through: after tuningdrop: after tuningb)suppressed notches1530 1540 1550 1560 1570ï70ï60ï50ï40ï30ï20Wavelength (nm)Power (dBm)  input: in port input: add portc)1530 1540 1550 1560 1570ï50ï40ï30ï20Wavelength (nm)Power (dBm)  input: in portinput: add portd)suppressed notches1532.4 1532.5 1532.6 1532.7 1532.8 1532.9010203040Wavelength (nm)Group Delay (ps)  input: in portinput: add porte)1532.4 1532.5 1532.6 1532.7 1532.8 1532.9ï5000500Wavelength (nm)Dispersion (ps/nm)  input: in portinput: add portf)Figure 3.6: (a) Measured spectra from the in port to the drop port as wellas the in port to the through port of our filter in the region of the ma-jor peak/notch before and after thermal tuning and (b) spectra of thefilter after thermal tuning. (c) Shows the measured in-port-to-drop-portspectrum as well as the measured add-port-to-through-port spectrum af-ter tuning. (d) Shows the measured in-port-to-through-port spectrum aswell as the measured add-port-to-drop-port spectrum after tuning. (e)and (f) show the group delay (zero set arbitrarily) and the dispersion,respectively, from the in port to the drop port as well as from the addport to the through port after tuning. cOptical Society of America,2015, by permission [150].63To determine if data can pass through our filter without significant distortion,we performed eye diagram measurements (see [501]). Electrical data was gener-ated using a bit pattern generator (data rate = 12.5 Gbps NRZ, PRBS 231-1, markratio = 1/4) which was then sent to a 10 GHz lithium niobate Mach-Zhender in-terferometer modulator and a polarization controller to modulate the light comingfrom the laser and to control the polarization, respectively. After the data waspassed through the quadruple Vernier racetrack resonator, an optical amplifier wasused to amplify the signal and a tunable grating filter was used to minimize thenoise. After the data was sent through a photodetector, a digital communicationanalyzer was used to measure the eye diagrams. The set-up is similar to the oneshown in [501]. Figure 3.7(a) shows an open eye diagram when data is passed fromthe in port to the drop port of our device at a wavelength of 1532.636 nm. For thethrough port spectral response, the most important wavelength regions of interestare at the suppressed notches within the through port passband [see Figure 3.6(b)]since large dispersion occurs here [112, 231, 432]. Figures 3.7(b)-3.7(d) show eyediagrams when data is passed from the in port to the through port at different wave-lengths within the through port passband. Figure 3.7(b) shows an open eye at awavelength of 1543.018 nm, which is to the left of one of the relatively suppressednotches. Next we measured the eye at two different wavelengths, 1545.153 nm and1545.247 nm, in the region of a relatively suppressed notch (i.e., near 1545.074nm which is in the middle of one of the notches). Both Figures 3.7(c) and 3.7(d)show signal degradation, as compared to Figure 3.7(b), however, both eyes are stillopen. Also, we can see that by changing the laser wavelength within the regionof the suppressed notch we are able to obtain a more open eye at 1545.153 nm ascompared to 1545.247 nm, which demonstrates that the signal quality can be tunedwithin the suppressed notch.64Figure 3.7: (a) Eye diagram measured for data passing from the in port tothe drop port at a wavelength of 1532.636 nm. Eye diagrams for datapassing from the in port to the through port at (b) 1543.018 nm, (c)1545.153 nm, and (d) 1545.247 nm. cOptical Society of America,2015, by permission [150].We have presented experimental results on a thermally tunable silicon quadru-ple series-coupled Vernier racetrack resonator filter. We have determined the groupdelay and dispersion of our filter and have shown successful data transmission at12.5 Gbps, with open eyes, at a through port suppressed notch. Also, we haveshown that the signal quality depends on where within the suppressed notch thedata is transmitted.In the next chapter, another method to extend the FSR using two identicalseries-coupled silicon microring resonators (MRRs) with MZI-BC will be pre-sented, including improved resonant suppression exhibited by our fabricated de-vice as compared to the suppression seen in [432]. The benefit of this approach toextending the FSR is that very low dispersion within the through port passbandscan be achieved [432].65Chapter 4High PerformanceSilicon-On-Insulator DoubleMicroring Filter UsingMZI-Based Coupling1One component of interest in optical interconnects is the optical add-drop filterfor multiplexing and demultiplexing signals, which can be created using ring res-onators [127]. Ring resonator-based filters have been shown to meet numerouscommercial specifications. For example, Popovic´ et al. showed that telecom spec-ifications can be met using four series-coupled silicon MRRs [115] and Boecket al. have shown that many key commercial specifications, for adding or droppingsignals, can be met using silicon quadruple series-coupled Vernier racetrack res-onators [96]. However, the challenge encountered when using ring resonators isthat they have FSRs which limit the number of channels that can be used, thus, itis desirable to have a large FSR in order to have a large number of usable chan-nels [127]. One method to increase the FSR is to use double MRRs with MZI-BC[432, 433] (see Figure 4.1).Various configurations of series-coupled ring resonators that use MZI-BC have1A version of Chapter 4 has been published in [105].66been studied [112, 141, 175, 432, 433]. Here, we are going to focus on doubleMRRs with MZI-BC. Watts et al. demonstrated such a device using silicon ni-tride [432]. Their device had an FSR and resonant suppression of 40.8 nm and19.5 dB, respectively [432]. Lira et al. experimentally demonstrated a thermallytunable SOI double MRR with MZI-BC which had an FSR of 19.2 nm and aresonant suppression of about 16 dB [433]. However, the suppressions demon-strated by [432] and [433] do not meet typical commercial specifications (e.g., 35 dB [101]). While the Vernier effect can also be used to increase the FSR[84, 96, 97, 107, 112, 127, 128, 141], a double MRR with MZI-BC also increasesthe FSR while providing low through port dispersion near the suppressed throughport notch [432]. Here we experimentally demonstrate a double MRR with MZI-BC for adding or dropping signals (i.e., a 3-port device) on SOI, which is a CMOScompatible technology that is of considerable commercial interest, while givinga similar FSR and an improved resonant suppression as compared to the siliconnitride based device presented in [432]. Also, we show that our device meetsmany 3-port filter commercial specifications. We also present theoretical resultson the maximum drop port dispersion, maximum drop port insertion loss, max-imum through port dispersion, and maximum through port insertion loss. Also,experimental drop port and through port dispersions are presented. While we fo-cus on 3-port filters, we can create a 4-port optical add-drop multiplexer (OADM)capable of simultaneously adding and dropping signals by cascading two 3-port fil-ters together [108]. Therefore, one should be able to cascade two double MRRwithMZI-BC filters at the through port (see [109]) to meet commercial specificationsfor adding and dropping signals.4.1 Theory and DesignOur SOI device consists of two series-coupled MRRs and two sets of MZI cou-plers, as shown in Figure 4.1. The field coupling factor versus wavelength of aco-directional coupler (such as the coupling between the two MRRs, kr, or thecoupling regions of the MZIs, kmzi) is relatively broadband. However, the MZIcoupler enables the overall coupling to the ring to be periodic due to the length dif-ference between the two MZI branches. It is possible to get resonant suppression67when the nulls and the peaks of the MZI are aligned, alternately, with the reso-nances of the rings, provided that the FSRs of the MZIs are twice that of the ringresonators’ (see [112, 432, 433]).Input Through r r r     mzi Drop L mzi-1 L mzi-2 mzi r Add Figure 4.1: Schematic of the device (either the add port or the drop portis used and the other is terminated when used as a 3-port device).cOptical Society of America, 2015, by permission [105].Using an initial design, we placed 17 devices on our mask in which the gap dis-tances were varied. In this initial design, the MZI-ring gap distances were chosento be 150 nm and the gap distance between the rings was chosen to be 290 nm. Wehave chosen a device that gave good experimental results, then, for the purpose ofcomparing the measurement and design, we put the as-designed gap distances forthe measured device into our model. In the modelling, we used the following: theSOI strip waveguide widths and heights are 500 nm and 220 nm, respectively, andthere is a silicon dioxide top cladding; the radius, r, to the centre of the waveguideof each MRR is 4.9 µm; the MZI-ring gap distance is 130 nm and the gap distancebetween the rings is 290 nm; the MZI-bus waveguide branch, Lmzi1, has a lengthof 26.2037 µm and the MZI-ring branch, Lmzi2 has a length of 10.8099 µm (theselengths were chosen such that their difference is equal to half the circumference ofthe MRR [112, 432, 433]); and the propagation loss is assumed to be 2.4 dB/cm[84, 96]. Since the radius of each of the microring resonators is 4.9 µm, their FSRsare larger than half the width of the C-band. Since every alternate peak/notch issuppressed by the use of MZI-BC, the resulting spectra have FSRs greater than thespan of the C-band. The power coupling and transmission factors were determinedusing 3-D FDTD and the effective indices were determined using a 2-D eigenmode68solver, both by Lumerical Solutions, Inc. The angles f and q for the MZI branches,which allow the device’s required gap distances, radii of the microring resonators,and lengths of the MZI branches to be achieved, were determined using Eqs. 1 - 3from [432] and are 18.2004 and 26.7996, respectively.The specifications of interest for the drop port response are ILdrop, Rdepth, Ai,nAi, IPS, and Ddrop. The specifications of interest for the through port response areECi, ILthru, ILthru-m, and Dthru. Also, our filter needs to have an FSR greater thanor equal to the width of the C-band plus one adjacent channel, i.e., 36.72 nm (see[92, 110]). Some of the specifications that need to be met for adding or droppingsignals, for a 200 GHz channel spacing, are listed in Table 4.1. The bolded valuesare the ones that the experimental results meet. The target specification for Ddrop is-30 ps/nm  Ddrop  +30 ps/nm, which is based on the example parameter valuefor a re-configurable OADM given in [104]. We have assumed that Dthru needs tomeet a target specification of -15 ps/nm  Dthru  +15 ps/nm, which is half of thetarget specification for Ddrop, since our device is for adding or dropping signals.Here, we chose a clear window of 8 GHz, based on our experimental results, andwe looked at the relevant channels when determining the nAi and ILthru in themeasured wavelength range (1520 nm to 1580 nm).Table 4.1: Target specifications for 200 GHz optical filters [105].Parameter Target valueFSR (nm)  36.72Ai (dB)  25 [502, 503], 30 [101]nAi (dB)  35 [101], 40 [502, 503]IPS (dB)  35 [101], 40 [502, 503]Rdepth (dB)  0.5 [502]ECi (dB)  10 [502], 12 [503]4.2 Theoretical ResultsThe simulated through port and drop port spectra were determined using trans-fer functions that were derived using Mason’s rule [128, 504] (see Appendix B).Figure 4.2(a) shows the theoretical spectra of the drop port and through port and69Figure 4.2(b) shows a zoom-in of the response in the location of the desired chan-nel. We have increased the effective indices by a constant value of 0.01787, ascompared to the effective indices obtained using the 2-D eigenmode solver assum-ing 25C, to align the theoretical drop port peak to that of the experimental dropport peak (at 1529.551 nm). Table 4.2 shows that, as modelled, this device meetsat least one of the specifications for each parameter listed in Table 4.1. Also, thisdevice has a theoretical 3-dB BW of 0.30 nm. The 3-dB BW is dependent on thethe choice of the gap distances, the propagation losses, and the optical path lengthsof each of the microring resonators [107], as well as the overall coupling due to theMZIs [433]. Figures 4.3(a) and 4.3(b) show the theoretical drop port dispersionwithin the clear window of the desired channel and the largest through port disper-sion located in the region of the suppressed notch near 1547.85 nm, respectively.Ddrop is -21 ps/nm, which meets its target specification of -30 ps/nmDdrop  +30ps/nm [104]. Dthru is±0 ps/nm which meets its target specification of -15 ps/nmDthru  +15 ps/nm (although there is no channel clear window in the region wherethe through port notch is suppressed [see Figure 4.3(b)], the maximum and min-imum dispersion is ±15 ps/nm). Our results are consistent with the statement in[432] that low through port dispersion near the suppressed notch can be achievedusing this type of device. Also, the modelled value for ILdrop is 1.0 dB, ILthru is 0.0dB, and ILthru-m is 0.0 dB which meets typical commercial specification of  1.2dB [101],  0.6 dB [101], and  0.6 dB [101], respectively.1520 1530 1540 1550 1560 1570 1580ï80ï60ï40ï200Wavelength (nm)Intensity (dB)  ThroughDropa)1528 1528.5 1529 1529.5 1530 1530.5 1531ï30ï20ï100Wavelength (nm)Intensity (dB)  ThroughDropadjacent channel clear windowsb)Figure 4.2: (a) Theoretical drop port and through port response and (b) zoom-in of Figure 4.2(a). cOptical Society of America, 2015, by permission[105].70Table 4.2: Theoretical filter results [105].Parameter Modelling resultFSR (nm) 37.10Ai (dB) 39.0nAi (dB) 38.3IPS (dB) 58.5Rdepth (dB) 0.0ECi (dB) 28.71529.52 1529.54 1529.56 1529.58ï20ï1001020Wavelength (nm)Dispersion (ps/nm)a)clear window1547.7 1547.8 1547.9 1548ï20ï1001020Wavelength (nm)Dispersion (ps/nm)b)Figure 4.3: Dispersion of (a) the drop port within the passband region and (b)the region near the suppressed through port notch. cOptical Society ofAmerica, 2015, by permission.4.3 Experimental Results17 devices were fabricated using e-beam lithography (see [493] for fabrication pro-cess) with the gap distances being varied. Figures 4.4(a) and 4.4(b) show the exper-imental drop port and through port responses for a good device. The FSR is 37.23nm due to the doubling of the FSR achieved by the MZIs which suppress interme-diate peaks and the 3-dB BW is 0.29 nm. Also, our device has an Ai, a nAi andan IPS of at least 41.0 dB, 38.6 dB, and 37.5 dB, respectively, since we are unableto distinguish the filter shape within the noise floor. The clear window is 8 GHzand the channel spacing is 200 GHz. The clear window is centred at 1529.490 nm.The location and the width of the clear window were chosen to ensure that Rdepth 0.5 dB [502] and ECi  10 dB [502]. The splitting of the major notch seen in71Figure 4.4(b) is likely due to variations in the coupling factors and variations inthe resonant wavelength of each of the microring resonators. Since we are usinggrating couplers to couple light into and out of our device [505], the shape of thegrating coupler response affects the measured filter spectrum. Therefore, some ofthe parameter values can be difficult to determine accurately. In particular ILdrop,ILthru, and ILthru-m are three such parameters and are not included in our experi-mental results for this reason. The maximum and minimum total device insertionloss measured at the through port, which includes two fibre grating couplers androuting waveguides, within the clear windows of the adjacent and non-adjacentchannels are 27.9 dB and 22.8 dB, respectively. The maximum total device inser-tion loss measured at the drop port within the clear window of the desired channelis 27.9 dB. We measured our device within the wavelength range 1520 nm to 1580nm, therefore, we looked at the 5 non-adjacent clear windows to the left of themajor peak and the 21 non-adjacent clear windows to the right of the major peakwhen measuring the nAi. Next, we measured the drop port dispersion (average of200 measurements) within the region of the major peak as well as the through portdispersion (average of 200 measurements) within the wavelength span correspond-ing to the through port passband to the right of the major notch as shown in Fig-ures 4.5(a) and 4.5(b), respectively. An Optical Vector AnalyzerTM STe by LunaInnovations, Inc., was used to measure the dispersion. The experimental throughport passband dispersion is minimal which is in agreement with the statementsmade in [432] that low through port dispersion is possible using double MRR withMZI-BC.721520 1530 1540 1550 1560 1570 1580ï70ï60ï50ï40ï30Wavelength (nm)Power (dBm)  ThroughDropa)1528 1528.5 1529 1529.5 1530 1530.5 1531ï70ï60ï50ï40ï30Wavelength (nm)Power (dBm)  ThroughDropadjacent channel clear windowsb)Figure 4.4: (a) Experimental drop port and through port response and (b)zoom-in of Figure 4.4(a). cOptical Society of America, 2015, by per-mission [105].1529.441529.461529.48 1529.5 1529.521529.5420406080100120Wavelength (nm)Dispersion (ps/nm)a)1544 1546 1548 1550 1552 1554 1556ï20ï1001020Dispersion (ps/nm)Wavelength (nm)b)Figure 4.5: (a) Experimental drop port dispersion (vertical dashed lines indi-cate width of clear window) and (b) experimental through port disper-sion within the through port passband.Table 4.3: Experimental filter results [105].Parameter Experimental resultFSR (nm) 37.23Ai (dB)  41.0nAi (dB)  38.6IPS (dB)  37.5Rdepth (dB) 0.5ECi (dB) 10.073As compared to [432] and [433], the IPS of our device meets its typical com-mercial specification. Also, our device’s FSR, 37.23 nm, is comparable to the FSRin [432], 40.8 nm, both larger than the C-band, and our device’s FSR is nearlydouble the FSR of [433]. We have provided the theoretical and experimental dis-persion of our device which [432] and [433] do not provide. Our device is morecompact (i.e., smaller radii) as compared to the devices in [432] and [433], andour device is fabricated in 220 nm SOI, whereas the device in [432] is fabricatedin silicon nitride. Although we have not included heaters on top of our device, aswas done in [433], we varied the temperature of the entire chip that contained ourdevice and determined that the spectral response shifts by 0.069 nm/C.In conclusion, we have experimentally demonstrated a high performance sili-con double MRR with MZI-BC that meets many key 3-port filter commercial spec-ifications for a 200 GHz channel spacing and a clear window of 8 GHz, which willbe useful in DWDM and sensor applications. Even though the FSR can be extendedusing MZI-BC, an FSR still exists. In the next chapter, I will discuss a method toincrease the IPS of cascaded Vernier ring resonators as well as eliminate the FSRby the use of contra-DCs instead of co-directional couplers (i.e., couplers withoutgratings).74Chapter 5FSR-EliminatedSilicon-On-Insulator VernierRacetrack Resonators UsingGrating-Assisted Couplers1Cascaded racetrack resonators exhibiting the Vernier effect have numerous ben-efits compared to single racetrack resonators, including an extended FSR in thedrop port [134, 137, 216, 287, 301, 343, 415]. However, the through port spectralresponse does not have an increased FSR [343, 415], which can be problematic forcertain DWDM applications. Fortunately, series-coupled racetrack resonators canexhibit the Vernier effect in both the drop port and the through port [96, 317, 415].Numerous papers have presented theoretical [126–128, 142–144] results as well asexperimental [96, 111, 129, 137, 157, 167, 190, 212, 290, 317] results for series-coupled Vernier resonators consisting of two [111, 127–129, 137, 142, 143, 157,167, 212, 290, 317], three [126–128, 143, 190], and four [96, 126, 142–144] rings.Also, combinations of cascaded and series-coupled Vernier ring resonators havebeen theoretically analyzed [114]. Recently, Yan et al. [331] presented a novelconfiguration of microring resonators exhibiting the Vernier effect in which one1A version of Chapter 5 has been published in [97]. c2013 IEEE, by permission.75ring resonator is directly coupled to four smaller ring resonators. Also, Vernier ringresonators have been used to create sensors [131, 286, 288, 416] and tunable lasers[203, 260]. Due to fabrication variations, the performance of the ring resonatorsmay be significantly degraded. Thermal tuning of each individual ring resonator isneeded to correct for the fabrication variations. A benefit of the cascaded config-uration of ring resonators, as compared to the series-coupled configuration, is thatthe thermal cross-talk between resonators is reduced due to the increased distancebetween the rings [301]. Recently, Shi et al. [439] designed and fabricated a newsingle silicon racetrack resonator with contra-DCs within the coupling regions tosuppress all but a single resonance in the drop port and the through port, whichis due to the small bandwidth of the coupler. The suppression of minor peaks isgreater than 8 dB [439]. Orlandi et al. [437] presented experimental results ona silicon racetrack resonator with gratings within the coupling regions but theirdevice showed minimal suppression of peaks in the drop port. Also, Orlandi etal. [437] discussed and presented theoretical results on a modified version of theirgrating coupled racetrack resonator in which the input coupler has gratings but theoutput coupler does not. In this chapter, we demonstrate both theoretically and ex-perimentally contra-directional grating-coupled cascaded racetrack resonators ex-hibiting the Vernier effect. The theoretical results show the elimination of the FSR(in both the drop port and the through port) as well as the improvement in the IPSat the drop port and the improvement in the through port insertion loss, ILthru, ascompared to the case in which no gratings were used. Our fabricated device showsan improvement in the suppression of minor peaks in the drop port as compared tothe suppression shown by [439] and [437]. Our experimental results show an IPSof 24.3 dB and the elimination of the FSR in the drop port and through port.5.1 TheoryWe have decided to use SOI strip waveguides with a top oxide cladding for theFSR-eliminated grating-coupled cascaded Vernier racetrack resonator, since pre-vious experimental results by Shi et al. [439] have shown promising results forindividual grating-coupled racetrack resonators. The waveguide heights are 220nm and the bus waveguide widths, wb, and the racetrack resonator widths, wr, are76450 nm and 550 nm, respectively. For the coupling regions that have co-directionalcoupling (no gratings), wb and wr are 550 nm and the gap distance is 280 nm. Thegratings within the coupling regions are formed by corrugating the sidewalls asshown in Figure 5.1(a). The corrugation depths, cb and cr, for waveguides withwidths of wb and wr, are defined as the extensions into the waveguides by cb/2and cr/2 and into the gap by cb/2 and cr/2. The number of grating periods, P, is110 and the perturbation period, L, is 311 nm, such that the drop port peak wave-length, lD, is very close to the resonance wavelength, lr, which corresponds tothe major peak within the drop port spectrum of the cascaded Vernier racetrackresonator. The contra-DC was designed so that the value of the contra-directionalpower coupling factor, |kc|2, and the contra-directional power transmission factor,|tc|2, would be very close to the value of the co-directional power coupling factor,|k|2, and power transmission factor, |t|2, at lD when the losses in the couplers aretaken into account. In order to suppress Bragg reflections back to the input port,an anti-reflection grating structure has been used, where additional gratings areformed on the external side-walls of the coupler [436] as shown in Figure 5.1(a).These external grating are out of phase with respective to the gratings inside thecoupler region, which can significantly suppress back reflections through destruc-tive interference [436].The schematic of the grating-coupled cascaded Vernier racetrack resonator isshown in Figure 5.1(b), where “a” is the first racetrack, “b” is the second (larger)racetrack, and “tr” is the tapered routing section between the resonators, Za,b,tr(l )=exp( jba,b,tr(l )La,b,traa,b,trLa,b,tr), ba,b,tr(l ) = 2pne f fa,b,tr(l )/l , ne f fa,b,tr(l )is the appropriate waveguide effective index, La and Lb are the total lengths of theracetrack resonators neglecting the lengths of the straight coupling regions, and aa[m-1] and ab [m-1] are the total field loss coefficients. Ltr and atr are the lengthand field loss coefficient of the tapered routing section between the two racetrackresonators. k1(l ) and k3(l ) are the symmetric complex field contra-directionalcoupling factors of the grating couplers of racetrack resonators “a” and “b”. t1(l )and t3(l ) are the straight-through racetrack waveguide complex field transmissionfactors of the grating couplers of racetrack resonators “a” and “b”. t1(l ) is thestraight-through bus waveguide complex field transmission factor of the gratingcoupler of racetrack resonator “a”. The propagation constant in the expression for77t1(l ) is different from that in the expression for t1(l ) since the bus waveguide andracetrack resonator widths are different. k2(l ) and k4(l ) are the symmetric com-plex field co-directional coupling factors of the waveguides. t2(l ) and t4(l ) arethe straight-through complex field transmission factors of the waveguides.!cb#cr#wb#wr#g a) Λ !!!!! !  κ2(λ) t4(λ) t3(λ) t2(λ) t1 Input Through r L g2"g1 b a t1(λ) r Lc g3"g4"Drop κ3(λ) Lc   κ4(λ) κ1(λ) κ1(λ) κ3(λ) Za (λ)1/2b) Za (λ)1/2Zb (λ)1/2 Zb (λ)1/2t1(λ) Ztr (λ)Ltr tr Figure 5.1: (a) Schematic of a section of the contra-DC and (b) schematicof the grating-coupled cascaded Vernier racetrack resonator. c2013IEEE, by permission [97].The drop port and through port intensity responses of the grating-coupled cas-caded Vernier racetrack resonator can be determined by multiplying Eq. 5.1 andEq. 5.2 by their respective complex conjugates,TFDrop(l ) =k1(l )k2(l )Za(l )1/21 t1(l )t2(l )Za(l ) ⇥Ztr(l )⇥k3(l )k4(l )Zb(l )1/21 t3(l )t4(l )Zb(l ) , (5.1)78TFThrough(l ) =k1(l )2t2(l )Za(l )+ t1(l )(1 t1(l )t2(l )Za(l ))1 t1(l )t2(l )Za(l ) (5.2)where,k1(l ) = k3(l ) = kc(l ), (5.3)t1(l ) = t3(l ) = tc(l )e jba,b(l )Lcaa,bLc , (5.4)t1(l ) = tc(l )e jba(l )LcaaLc , (5.5)k2(l ) = k4(l ) = j sin✓pLc2Lp(l )◆e jba,b(l )Lcaa,bLc , (5.6)t2(l ) = t4(l ) = cos✓pLc2Lp(l )◆e jba,b(l )Lcaa,bLc . (5.7)The following design was chosen for all simulations: La = 2pr (total length ofthe racetrack resonator not including the straight sections of the directional cou-plers), where r = 4.65 µm, and Lc = L⇥P where L and P are 311 nm and 110,respectively, Lb = 2pr+2L, where L = 16.27 µm, ba and bb are for waveguidewidths of 550 nm, ba is for a waveguide width of 450 nm, and Lp(l ) is the cross-over length. It should be noted that the ratio of the total length of resonator “b”to the total length of resonator “a” was chosen to be 4/3. Also, we assume thatthe propagation constants for the two racetrack resonators are identical (i.e., theeffective index is the same for all regions of each racetrack). The propagation lossseen from the input port to the through port, aa [m-1], is 7.4 dB/cm [506], sincethe waveguide width is 450 nm. Also, the propagation loss for each ring is as-sumed to be 2 dB/cm, since their waveguide widths are 550 nm. We assume theoptical attenuation due to the routing section between the two racetrack resonatorsis minimal and therefore the routing section is not included in our calculations.Finally, it is assumed that, since the waveguides within the coupling regions withgratings have different propagation constants, the co-directional coupling is mini-mal and is neglected in the model. In other words, only contra-directional couplingis considered within the regions with gratings.To determine the complex field contra-directional coupling factors and the79straight-through complex field transmission factors of the gratings, the modellingmethod presented by Shi et al. was used [439, 461]. Here, we have chosen thecoupling coefficient to be 12551 m-1 so that the contra-directional power couplingand power transmission factors are close to the values of the co-directional powercoupling and power transmission factors at lD, as shown in Figure 5.2. To de-termine the symmetric complex field co-directional coupling and transmission fac-tors, Lp(l )was determined using a numerical mode solver. The effective indices ofthe co-directional couplers and the waveguides were calculated at 11 wavelengthsbetween 1500 nm and 1600 nm and curve-fitted to third-order polynomials fromwhich all effective indices were obtained. Figures 5.2(a) and 5.2(b) show the wave-length dependent contra-directional and co-directional power coupling factors andthe straight-through power transmission factors for the coupler with and withoutgratings.1480 1500 1520 1540 1560 1580ï60ï40ï200Wavelength (nm)|g|2  (dB)   |g1|2, |g3|2: contraïdirectional|g2|2, |g4|2: coïdirectionala)1480 1500 1520 1540 1560 1580ï1.5ï1ï0.50Wavelength (nm)|t|2 (dB)  |t1|2, |t3|2: contraïdirectional|t2|2, |t4|2: coïdirectionalb)Figure 5.2: (a) |k|2 versus wavelength for the contra-directional (blue-solid)and co-directional (black-dash) couplers. (b) |t|2 versus wavelength forthe contra-directional (red-solid) and co-directional (black-dash) cou-plers. c2013 IEEE, by permission [97].Figure 5.3(a) shows the drop port responses for two independent single contra-directional grating-coupled racetrack resonators with lengths La (green-solid) andLb (red-dash). The limited suppression of the peaks to the left and to the right ofthe major peaks for the single racetrack resonators are due to the bandwidth of thecontra-DCs. Figure 5.3(b) shows the drop port responses for the cascaded configu-ration of these two racetrack resonators with (blue-solid) and without (black-dash)gratings. In the case where there are no gratings, we change the structure shownin Figure 5.1(b) such that the input port and the through port are exchanged with80each other as well as the drop port being placed at the spare output port. Wecan clearly see that the grating-coupled cascaded Vernier racetrack resonator spec-trum shows increased suppression of all minor peaks as compared to the spectraof the other three devices. However, we also need to compare the response of thegrating-coupled cascaded Vernier racetrack resonator to that of a grating-coupledcascaded identical racetrack resonator with lengths La as well as Lb. Figure 5.3(c)shows the drop port responses for grating-coupled cascaded Vernier (blue-solid)racetrack resonators as well as the response for identical (orange-dash) racetrackresonators with lengths La. Figure 5.3(d) shows the drop port responses for grating-coupled cascaded Vernier (blue-solid) racetrack resonators as well as the responsefor identical (light blue-dash) racetrack resonators with lengths Lb. In both cases,the Vernier effect causes an increase in suppression of all minor peaks as com-pared to the cases where identical racetrack resonators were used. The drop portspectrum and phase in the vicinity of the clear window of our grating-coupled cas-caded Vernier racetrack resonator are shown in Figure 5.4(a). The group delayand the dispersion of our grating-coupled cascaded Vernier racetrack resonator areshown in Figure 5.4(b). Next, we compare the through port response for cascadedVernier racetrack resonators with and without gratings, as shown in Figures 5.5(a)and 5.5(b). We can clearly see that using gratings is beneficial, since it significantlysuppresses all but one of the resonances. The through port response for the grating-coupled cascaded identical racetrack resonator has the same response as that of asingle contra-directional grating-coupled racetrack resonator when its dimensionsare the same as one of the racetrack resonators in the cascaded configuration. InFigures 5.5(c) and 5.5(d), the through port responses for grating-coupled cascaded(single) identical racetrack resonator with lengths La as well as Lb are shown. Itcan be clearly seen that the response for the device with lengths La has more sup-pression of its minor notches as compared to the device with lengths Lb.811480 1500 1520 1540 1560ï60ï40ï200Wavelength (nm)Intensity (dB)  single (La) with gratingssingle (Lb) with gratingsa)1480 1500 1520 1540 1560ï60ï40ï200Wavelength (nm)Intensity (dB)  Vernier (La, Lb) cascaded w/o gratingsVernier (La, Lb) cascaded with gratingsb)1480 1500 1520 1540 1560 1580ï100ï80ï60ï40ï200Wavelength (nm)Intensity (dB)  identical (La, La) cascaded with gratingsVernier (La, Lb) cascaded with gratingsc)1480 1500 1520 1540 1560 1580ï100ï80ï60ï40ï200Wavelength (nm)Intensity (dB)  identical (Lb, Lb) cascaded with gratingsVernier (La, Lb) cascaded with gratingsd)Figure 5.3: (a) Drop port spectral response comparison between singlegrating-coupled racetrack resonator with length La (green-solid) andLb (red-dash), (b) coupled racetrack resonators with (blue-solid) andwithout (black-dash) contra-DCs, (c) drop port spectral response com-parison between grating-coupled cascaded identical racetrack resonatorwith lengths La and grating-coupled cascaded Vernier racetrack res-onator, and (d) drop port spectral response comparison between grating-coupled cascaded identical racetrack resonator with lengths Lb andgrating-coupled cascaded Vernier racetrack resonator. c2013 IEEE,by permission [97].821527.74 1527.76 1527.78 1527.8 1527.82 1527.84ï6ï5ï4ï3ï2ï10Intensity (dB)Wavelength (nm)ï1.5ï1  ï0.50   0.5 1   1.5 Phase (rad)a)clear window1527.74 1527.76 1527.78 1527.8 1527.82 1527.84101112131415161718Group Delay (ps)Wavelength (nm)ï80ï60ï40ï20020406080Dispersion (ps/nm)b)clear windowFigure 5.4: (a) Drop port spectral response and phase and (b) group delay anddispersion of our grating-coupled cascaded Vernier racetrack resonator.c2013 IEEE, by permission [97].1500 1510 1520 1530 1540 1550 1560ï30ï20ï100Wavelength (nm)Intensity (dB)  Vernier (La, Lb) cascaded w/o gratingsVernier (La, Lb) cascaded with gratingsa)1515 1520 1525 1530 1535 1540ï8ï6ï4ï20Wavelength (nm)Intensity (dB)  Vernier (La, Lb) cascaded w/o gratingsVernier (La, Lb) cascaded with gratingsb)1500 1510 1520 1530 1540 1550 1560ï30ï20ï100Wavelength (nm)Intensity (dB)  single/cascaded (La) with gratingssingle/cascaded (Lb) with gratingsc)1515 1520 1525 1530 1535 1540ï8ï6ï4ï20Wavelength (nm)Intensity (dB)  single/cascaded (La) with gratingssingle/cascaded (Lb) with gratingsd)Figure 5.5: (a) Through port spectral response comparison between grating-coupled cascaded racetrack resonator (blue-solid) and cascaded race-track resonator without gratings (black-dash), (b) a “zoom-in” of themajor notch in Figure 5.5(a), (c) through port spectral response compar-ison between grating-coupled single (response same as cascaded config-uration) racetrack resonator with lengths La and Lb, and (d) a “zoom-in”of the major notch in Figure 5.5(c). c2013 IEEE, by permission [97].83All specifications are defined for a channel spacing of 0.8 nm, a clear windowof 0.048 nm, and within the clear window of the desired channel as well as the clearwindows of the 44 channels to the left and to the right of the desired channel (thenumber of channels within the ITU grid for the C-band is 45 [92]). Here, the clearwindow is centred at a wavelength value corresponding to the average wavelengthvalue of the major peak between its -3 dB points and -20 dB points (referenced atthe maximum intensity of the major peak) and of the major notch between its -3 dBpoints and -20 dB points (referenced at the maximum intensity of the major notch).Tables 5.1 and 5.2 show the spectral characteristics of the single grating-coupledracetrack resonators with lengths La and Lb, the cascaded Vernier racetrack res-onator with and without contra-directional gratings, and of the grating-coupled cas-caded identical racetrack resonators. We can clearly see that the cascaded Vernierracetrack resonator with gratings shows a significant improvement in its FSR (infact, there is no FSR), nAi, IPS, ILthru, and ILthru-m as compared to the response ofthe cascaded racetrack resonator without gratings. In the case of the cascaded con-figuration without gratings, the drop port shows an extended FSR of 17.30 nm and17.70 nm to the left and right of the major peak, respectively, whereas the throughport response only shows an FSR of 5.81 nm and 5.85 nm. However, the inclu-sion of the contra-directional gratings removes the FSR in both the drop port andthe through port. Also, the grating-coupled cascaded Vernier racetrack resonatorshows significant improvements in its Ai, nAi, and IPS as compared to both ofthe single contra-directional grating-coupled racetrack resonator responses. Also,the grating-coupled cascaded Vernier racetrack resonator shows an improvement inthe nAi and IPS as compared to the responses of grating-coupled cascaded identicalracetrack resonators. Thus, we can see the combined benefit of using contra-DCsand the Vernier effect within coupled racetrack resonators.84Table 5.1: Drop port and through port insertion loss for single racetrack resonators with gratings, cascaded Vernier race-track resonators with and without gratings, and grating-coupled cascaded identical racetrack resonators. c2013IEEE, by permission [97].Parameter single (La)with gratingssingle (Lb)with gratingscascadedVernier w/ogratingscascaded iden-tical (La) withgratingscascaded iden-tical (Lb) withgratingscascadedVernier withgratingsILdrop (dB) 0.3 0.5 1.0 0.4 0.6 1.0ILthru (dB) 0.3 0.3 8.8 0.3 0.2 0.3ILthru-m (dB) 2.5 7.0 40.9 2.5 7.0 2.585Table 5.2: Spectral characteristics for single racetrack resonators with gratings, cascaded Vernier racetrack resonatorswith and without gratings, and grating-coupled cascaded identical racetrack resonators. c2013 IEEE, by permis-sion [97].Parameter single (La)with gratingssingle (Lb)with gratingscascadedVernier w/ogratingscascaded iden-tical (La) withgratingscascaded iden-tical (Lb) withgratingscascadedVernier withgratingsFSR (nm) N/A N/A 5.81, 5.85 N/A N/A N/AAi (dB) 12.9 15.1 27.8 26.0 30.3 27.9nAi (dB) 11.3 12.5 0.1 23.6 25.8 33.9IPS (dB) 3.4 0.6 N/Aa 7.1 1.6 22.1Rdepth (dB) 0.2 0.3 0.6 0.2 0.3 0.6ECi (dB) 12.8 11.1 13.7 16.5 14.4 13.8aThere is no IPS since the wavelength range of the 44 channels to the left and right of the desired channel is larger than the filter’sextended FSR.865.2 Experimental ResultsThe device was fabricated using e-beam lithography [493] at the University ofWashington and aluminum (300 nm thick) metallization for the heaters (5 µmwide)and electrodes was done at McMaster University. Figure 5.6 shows a microscopeimage of our device. Heaters were placed on each contra-directional coupling re-gion to enable resonance tuning to correct for fabrication variations. The top oxideis 2 µm thick, the co-directional and contra-directional gap distances are 280 nmand 220 nm, wb and wr are 450 nm and 550 nm, the corrugation depths, cb andcr, for waveguides with widths of wb and wr are 30 nm and 40 nm, respectively.The tapered routing waveguide between the two racetrack resonators has a lengthof 74.912 µm.InputThroughDrop34.21 μmFigure 5.6: Optical microscope image of the fabricated device. c2013 IEEE,by permission [97].Figure 5.7(a) shows the experimental drop port and through port responses forapplied voltages of 0 V, 4 V, 5.8 V, and 7 V to the contra-directional couplingregion of racetrack resonator “a”. We can clearly see that applying a voltage of 5.8V significantly improves the major peak of the drop port response; the maximumdrop port peak intensity increases from -17.9 dB to -6.2 dB. Figure 5.7(b) shows thethrough port and drop port responses for this case. The drop port response has onemajor peak and all other peaks are suppressed and the through port response showsone major notch and all other notches have smaller notch depths (less than 2 dB) ascompared to the depth of the major notch (5.9 dB). Thus we have experimentallyconfirmed that it is possible to eliminate the FSR in the drop port and throughport. Next, we determine the Ai, nAi, IPS, Rdepth, and ECi for a clear window of0.048 nm centred at a wavelength of 1528.846 nm and a channel spacing of 0.887nm. It should be noted that the minimum wavelength we measured the spectrumfor is 1500 nm so only 36 channels to the left and 44 channels to the right of thedesired channel were used in calculating the nAi. Figure 5.7(c) shows a “zoom-in” of Figure 5.7(b) which includes vertical dashed lines that represent the clearwindow and channel spacing as well as labels for Ai, nAi, IPS, and ECi. Table 5.3shows the experimental spectral characteristics of the grating-coupled cascadedVernier racetrack resonator. The response of our device has no FSR in both thedrop port and through port, which is in agreement with the theoretical result shownin Table 5.2 (we were unable to accurately determine the values for ILdrop, ILthru,and ILthru-m). Also, the device has a large IPS of 24.3 dB. Our grating-coupledcascaded Vernier racetrack resonator needs further improvement to give a value ofthe ECi that is greater than or equal to 10 dB [99], of the Rdepth that is less than orequal to 0.5 dB [99], of the nAi that is greater than or equal to 35 dB [101], and ofthe IPS that is greater than or equal to 35 dB [101], so that this type of device canbe used in typical DWDM applications. It should be noted that our device has anAi of 30.5 dB (which is better than the 25 dB that can be found in data sheets forsome commercial products [99]).881525 1530 1535ï50ï40ï30ï20ï100Wavelength (nm)Insertion loss (dB)  a)1500 1520 1540 1560 1580 1600ï50ï40ï30ï20ï100Wavelength (nm)Insertion loss (dB)  drop portthrough portb)1524 1526 1528 1530ï40ï30ï20ï10Wavelength (nm)Insertion loss (dB)  drop portthrough portc) ECiAinAiIPSFigure 5.7: (a) Experimental drop port (solid) and through port (dashed) re-sponses when the voltage to the heater for racetrack resonator “a” is 0V (red), 4V (green), 5.8 V (black), and 7 V (blue). (b) the experimentaldrop port (black) and through port (light blue) spectra when a voltage of5.8 V is applied to the heater of racetrack resonator “a”. (c) a zoom-in ofFigure 5.7(b) with a 0.048 nm clear window and 0.8 nm channel spac-ing indicated by the dashed vertical lines. c2013 IEEE, by permission[97].89Table 5.3: Experimental results of grating-coupled cascaded Vernier race-track resonator. c2013 IEEE, by permission [97].Parameter Measured valueFSR (nm) N/AAi (dB) 30.5nAi (dB) 29.3IPS (dB) 24.3Rdepth (dB) 1.2ECi (dB) 5.2In summary, we have shown that using contra-DCs in cascaded racetrack res-onators exhibiting the Vernier effect provides numerous advantages as compared tothe responses of cascaded racetrack resonators exhibiting the Vernier effect with-out contra-DCs. The grating-coupled cascaded Vernier racetrack resonator studiedhere has a theoretical IPS of 22.1 dB whereas without the gratings there is no IPSsince the wavelength range of the 44 channels to the left and right of the desiredchannel is larger than the filter’s extended FSR. Also, the grating-coupled cascadedVernier racetrack resonator has a theoretical ILthru-m of 2.5 dB whereas without thegratings ILthru-m is 40.9 dB. The reason why the ILthru-m is substantially improvedis due to the suppression of all but one of the resonances in the through port, whichis the result of the small bandwidth of the contra-DC. Also, there is no FSR in boththe drop port and through port for the grating-coupled cascaded Vernier racetrackresonator whereas there is a 17.3 nm/17.7 nm extended FSR at the drop port andan FSR of 5.8 nm at the through port for the case without gratings. Also, we havepresented experimental results which show that it is in fact possible to eliminate theFSR in the drop port as well as the through port. Our fabricated device also showsa large IPS of 24.3 dB. Thus, we are now able to use the cascaded configuration ofthe Vernier effect and not be limited to applications that only require a large FSRin the drop port.The coupling coefficients of the contra-DCs are very important design param-90eters since they will have a major impact on the performance of the filter. Thus, itis essential that the contra-DC-based filter designs are based on accurate modellingwhich takes into account the impact of the fabrication process. In the next chapter,I will present a process calibration method that can be used to extract the couplingcoefficients from fabricated contra-DCs, which can then be fed back into futuredesigns.91Chapter 6Process Calibration Method forDesigning Silicon-On-InsulatorContra-Directional GratingCouplers1In communication applications that involve multiplexing and/or demultiplexingoptical signals, maximizing the number of usable channels is essential for creat-ing high data-rate interconnects [106, 111, 129]. Silicon contra-DCs are partic-ularly useful in optical filtering applications because they do not have periodicspectral responses like ring resonator-based filters [97, 436, 439, 460–462, 466].Silicon contra-DCs have been experimentally demonstrated in numerous publica-tions [97, 434, 436–439, 459–468]. Although previous demonstrations of siliconcontra-DCs have shown good results, it remains challenging to design a contra-DC’s bandwidth and have the “as-fabricated” device’s bandwidth, maximum powercoupling factor, and minimum power transmission factor correspond to the designvalues, in the presence of lithography smoothing [470, 507]. Using a calibrationprocedure for the design process, a filter designer would be able to design a contra-DC such that the “as-designed” spectra closely matches the as-fabricated spectra.1A version of Chapter 6 has been published in [435].92In this chapter, we present a process calibration method which can be used to deter-mine the absolute value of the coupling coefficient, |k|, of a fabricated contra-DCby measuring its full-width-at-half-maximum (FWHM) bandwidth, Dlbw. Once|k| is known, the through port and drop port spectra can be simulated. We demon-strate the effectiveness of our FWHM method (similar to [457, 508]) by extractingthe |k|s of contra-DCs that were fabricated using electron beam lithography [493]on three fabrication runs. Our FWHM method for extracting |k| provides moreconsistent results as compared to using the null bandwidth (see [470, 507, 509–511]) due to the fact that Dlbw can be more easily determined. Also, as comparedto using the null method, the |k|s extracted using our FWHMmethod are in generalagreement with the values extracted by curve-fitting the drop port spectra. We thenshow that, using our FWHMmethod to extract |k|, the simulated spectra agree wellwith the experimental spectra. Also, the simulated through port group delay anddispersion responses of a particular device are calculated using the extracted |k|,which agree well with the Hilbert transform-determined and the measured groupdelay and dispersion responses. Using the process calibration method, we thendesign a 3-port grating-assisted Vernier filter that meets 3-port filter commercialspecifications for a clear window of 13 GHz and a channel spacing of 200 GHz.6.1 Contra-DC Theory and Process Calibration MethodFirst, we will discuss the theoretical aspects of contra-DCs and the contra-DC de-sign we used in this chapter. The contra-DC design [Figures 6.1(a) and 6.1(b)]has two strip waveguides, waveguide “a” and waveguide “b,” which have differentaverage waveguide widths, wa and wb, respectively [97]. The waveguides havethe same height and are separated from each other by an average gap distance, g[97]. Each waveguide has periodic grating corrugations, with a grating period, L,defined in Figure 6.1(b), on the sidewalls located within the gap region [97]. Thecorrugation widths are labelled ca and cb for waveguide “a” and waveguide “b,” re-spectively [97]. The corrugations allow the coupler to act as a Bragg reflector withthe strength of the inter-waveguide coupling determined by the inter-waveguidecoupling coefficient, k [97, 434, 436]. We have also included anti-reflection grat-ings on the external sidewalls of the waveguides to suppress the intra-waveguideBragg reflections [97, 434, 436, 512].93InputDropThrough Ltc2c2A1(0)A2 (0)A1(L)a)wawbgb) cacacbcbFigure 6.1: (a) Diagram of a contra-DC. (b) A close-up view of a portionof a contra-DC (figure was adapted from [97]). cOptical Society ofAmerica, 2015, by permission [435].The power transferred from the input port to the drop port of a contra-DC isgiven by the power coupling factor, |kc|2, and the amount of power transferredto the through port is given by the power transmission factor, |tc|2, which can becalculated using the following equations,|kc|2 =A2(0)A1(0)2 = |k|2 sinh2(sL)s2 cosh2(sL)+⇣Db2⌘2sinh2(sL)(6.1)|tc|2 =A1(L)A1(0)2 = s2s2 cosh2(sL)+⇣Db2⌘2sinh2(sL)(6.2)where s2 = |k|2⇣Db2⌘2, Db = ba+bbm 2pL , ba and bb are the propagation con-stants of waveguide “a” and waveguide “b” without corrugations with widths equalto wa and wb, respectively, L is the length of the coupler, and m is the grating orderwhich equals 1 since we are using first-order gratings [513]. Equation 6.1 is thesame as Eq. 13.5-19 in [513] and Eq. 1 in [461] and Eq. 6.2 can be determined fromEq. 13.5-16 in [513]. In this chapter, ba and bb are calculated by numerically deter-mining the wavelength dependent effective indices of the waveguides using MODESolutions by Lumerical Solutions, Inc., and curve-fitting them to third-order poly-94nomials [97]. The material model that was used for silicon included dispersionand was lossless [97, 111, 149, 470] and the refractive index for silicon dioxidewas fixed at 1.4435 [97, 111, 149]. The inter-waveguide coupling coefficient, k , isdefined as the strength of the coupling of light from waveguide “a” to waveguide“b” within the contra-DC and traditionally has been calculated using the followingequation [434, 459, 461, 465, 467, 512, 513],k = w4ZZx ⇤a (x,y) · em(x,y)xb(x,y)dxdy (6.3)where w is the angular frequency, xa(x,y) is the transverse mode of waveguide “a,”xb(x,y) is the transverse mode of waveguide “b,” and em(x,y) is the mth compo-nent of the Fourier series expansion of the dielectric perturbation. However, thisexpression is appropriate for the weakly-guiding approximation and is not neces-sarily accurate for high-contrast nanophotonic waveguides. Using this equation,two different methods have been used to calculate |k| [434, 512]. The first methodinvolves treating each waveguide as isolated [434, 461, 512–515]. In this method,xa(x,y) and xb(x,y), correspond to the modes of the isolated unperturbed waveg-uides [434, 461, 512–515]. The second method involves calculating the first andsecond-order transverse modes of the coupler (i.e., supermode theory) [434, 465–467, 512, 514]. [507] and [470] have demonstrated that there is a large differencebetween the modelled results and experimental results for SOI Bragg gratings (seeFigure 2.35 in [507] and Figure 4.43 in [470]). [461] showed good agreement be-tween experimental results and simulated results for contra-DCs by using Eq. 6.3.However, cross-sectional SEM images were needed for calibration. Recently, [511]demonstrated a method to model Bragg gratings using 3-D FDTD simulations andBloch boundary conditions which showed good agreement between theoretical andexperimental results. However, the above-mentioned methods require knowledgeof the effects of the lithography on the shape of the grating. One method to sig-nificantly reduce the difference between the modelled results and the experimen-tal results is to take into account how the fabrication process affects the designof the device (e.g., lithography smoothing) by using lithography simulation soft-ware, such as Mentor Graphics Calibre, and then simulating the structure using 3-DFDTD simulation software, such as FDTD Solutions by Lumerical Solutions, Inc.,95[470, 507]. However, this process is more complex since knowledge of fabricationprocess parameters are needed. In this chapter, we will demonstrate an experimen-tal method to determine |k| by using Dlbw. With our experimental method, wecan extract |k| without having to measure the effects of lithography directly, norwithout resorting to the approximations in Equation 6.3.There are three steps to extract |k|. The first step is to determine Dlbw, whichcan be measured directly from the drop port spectrum. The second step is to deter-mine the average propagation constant mismatch, dbavg. To obtain dbavg, we usethe propagation constant differences, dbH and dbL, where dbH is measured fromthe frequency that corresponds to the centre of the main lobe to the high-frequencyhalf-maximum point and dbL is measured from the frequency that corresponds tothe centre of the main lobe to the low-frequency half-maximum point (for a com-plete mathematical description see Appendix C). The magnitude of dbH and themagnitude of dbL are given in Eqs. 6.4 and 6.5, respectively, and defined graphi-cally in Figure 6.2(a),|dbH |=✓2pD fHc◆ng,a( f0)+ng,b( f0)=✓2pDlLlLl0◆ng,a(l0)+ng,b(l0)(6.4)|dbL|=✓2pD fLc◆ng,a( f0)+ng,b( f0)=✓2pDlHlHl0◆ng,a(l0)+ng,b(l0)(6.5)where D fH = fH  f0, D fL = f0  fL, DlL = l0  lL, DlH = lH  l0, f0 andl0 are the frequency and wavelength corresponding to the centre frequency andcentre wavelength (middle point between the FWHM points), respectively, fH andlL correspond to the higher frequency FWHM point and the lower wavelengthFWHM point, respectively, fL and lH correspond to the lower frequency FWHMpoint and the higher wavelength FWHM point, respectively, ng,a and ng,b are thegroup indices of waveguide “a” and waveguide “b,” respectively, and c is the speedof light in a vacuum. Equations 6.4 and 6.5 are similar to Eq. 13.5-22 in [513] buthere we include the effects of dispersion and use the group indices, since dispersion96affects the spectral response of contra-DCs (see [516]). To determine dbavg, wetake the average of Eqs. 6.4 and 6.5,dbavg =|dbH |+ |dbL|2=pDlbwlLlHng,a(l0)+ng,b(l0)(6.6)where Dlbw= lHlL. Here, for convenience, the wavelength dependent group in-dices are numerically determined using MODE Solutions by Lumerical Solutions,Inc., and curve-fitted to third-order polynomials. Equation 6.6 is similar to Eq. 31in [508] but here we include the effects of dispersion and use the group indices.Figure 6.2(b) shows the experimental drop port spectrum of one of our fabricatedcontra-DCs, with a gap distance of 140 nm, as a function of Db . The FWHM be-comes 2dbavg when the spectrum is plotted as a function of Db . By plotting ourspectral response as a function of Db , we are able to directly measure dbavg fromthe spectral response without having to use Eq. 6.6. One may use either of thesemethods to determine dbavg but we will focus on the method that utilizes Eq. 6.6.Intensity (dB) |L| |H| 2avg3 dB a) ( fL ) ( f0 ) ( fH ) ï5 0 5x 104ï15ï10ï506` (mï1)Insertion Loss (dB)b)2b`avgFigure 6.2: (a) Diagram depicting some of the relevant contra-DC parametersas functions of Db . (b) Experimental drop port spectrum of one of ourdevices as a function of Db . cOptical Society of America, 2015, bypermission [435].The third step is to extract |k| by using Eq. 6.1 and Eq. 6.6. We replace Db inEq. 6.1 with Eq. 6.6 as shown in the left-hand side of Eq. 6.7 where s2 = |k|2(dbavg/2)2. Since Eq. 6.1 reduces to tanh2(|k|L) for Db = 0 [513], we can find theFWHM intensity by dividing tanh2(|k|L) by 2 and finding the value of |k| that will97satisfy Eq. 6.7 for our value of dbavg. [457, 508] use a similar method to extractthe bandwidths of contra-DCs.|k|2 sinh2(sL)s2 cosh2(sL)+⇣dbavg2⌘2sinh2(sL)=12tanh2(|k|L) (6.7)It should be noted that there can be multiple solutions to Eq. 6.7 when the sidebandsare greater than or equal to the half maximum intensity. The correct solution is thevalue of |k| that is largest.An alternative method, using the nulls to determine |k|, is to measure the band-width at the first nulls to the left and to the right of the main lobe and to use Eq. 6.8(similar to [470, 507, 509, 517] and is a re-arrangement of the equation found in[510, 513]),|k|="db 2avg4 p2L2# 12, (6.8)where dbavg is calculated using Eq. 6.6 but using the first null points instead ofthe FWHM points. [470, 511] have also used the null bandwidth to extract |k|but for SOI Bragg gratings. Also, another method to extract |k| is to curve-fit thedrop port spectrum of the contra-DC using a nonlinear least-squares method. Aswe will show in the next section, the extracted |k|s from the curve-fit method andfrom the FWHM method are in general agreement with each other as comparedto the values determined using the null method. However, the curve-fit methodrelies on an accurate normalization of the measured drop port spectrum (an issuewhich others have previously mentioned [518]) whereas the FWHM method doesnot require that the measured data be normalized. Both the FWHM method andthe curve-fit method provide more consistent results than the null method does.Also, provided that dbavg can be accurately obtained, our FWHM method shouldbe applicable to devices fabricated in other material platforms because the methodis not platform dependent.986.2 Experimental ResultsElectron beam lithography was used to fabricate the SOI contra-DCs [493] and asilicon dioxide cladding layer was deposited on top of the devices. The siliconstrip waveguide heights were all chosen to be 220 nm. The width of waveguide“a” was 450 nm and the width of waveguide “b” was 550 nm. The corrugationwidths for waveguide “a” and “b” were 30 nm and 40 nm, respectively. Thesedimensions were taken from [97]. The grating period was chosen to be 312 nmand the number of periods was chosen to be 500. Therefore, the total length ofeach contra-DC was 156 µm. The gap distances were varied between 120 nm and400 nm in 20 nm increments for a total of 15 devices. Fibre grating couplers wereused for coupling light into and out of the devices [498, 505]. The contra-DCswere fabricated on three separate fabrication runs, “run 1,” “run 2,” and “run 3” atdifferent times. Fully-etched fibre grating couplers [505] were used in “run 1” and“run 3” and shallow-etched fibre grating couplers [498] were used in “run 2.” Theexperimental drop port spectra of four of the devices from “run 1,” “run 2,” and “run3” with gap distances equal to 140 nm, 220 nm, 340 nm, and 400 nm are shownin Figures 6.3(a), 6.3(c), and 6.3(e), respectively. The experimental through portspectra of four of the devices from “run 1,” “run 2,” and “run 3” with gap distancesequal to 140 nm, 220 nm, 340 nm, and 400 nm are shown in Figures 6.3(b), 6.3(d),and 6.3(f), respectively. The fibre grating coupler response was removed from boththe through port and drop port spectral responses by normalizing the spectra to thefibre grating response envelope in the through port spectral response.991520 1530 1540 1550 1560ï60ï40ï200Insertion Loss (dB)Wavelength (nm)  gap = 140 nmgap = 220 nmgap = 340 nmgap = 400 nma)1520 1530 1540 1550 1560ï20ï15ï10ï50Insertion Loss (dB)Wavelength (nm)  gap = 140 nmgap = 220 nmgap = 340 nmgap = 400 nmb)1520 1530 1540 1550 1560ï60ï40ï200Insertion Loss (dB)Wavelength (nm)  gap = 140 nmgap = 220 nmgap = 340 nmgap = 400 nmc)1520 1530 1540 1550 1560ï20ï15ï10ï50Insertion Loss (dB)Wavelength (nm)  gap = 140 nmgap = 220 nmgap = 340 nmgap = 400 nmd)1520 1530 1540 1550 1560ï60ï40ï200Insertion Loss (dB)Wavelength (nm)  gap = 140 nmgap = 220 nmgap = 340 nmgap = 400 nme)1520 1530 1540 1550 1560ï20ï15ï10ï50Insertion Loss (dB)Wavelength (nm)  gap = 140 nmgap = 220 nmgap = 340 nmgap = 400 nmf)Figure 6.3: Experimental drop port spectra for the devices from (a) “run 1,”(c) “run 2,” and (e) “run 3” with gap distances equal to 140 nm, 220 nm,340 nm, and 400 nm. Experimental through port spectra for the devicesfrom (b) “run 1,” (d) “run 2,” and (f) “run 3” with gap distances equal to140 nm, 220 nm, 340 nm, and 400 nm. cOptical Society of America,2015, by permission [435].The relationship between the bandwidths of contra-DCs and their gap distanceshas been theoretically [459, 461] and experimentally [460, 461] demonstrated, andshows that, as the gap distance increases, the bandwidth decreases. Also, the rela-tionship between |k| and the gap distance has been theoretically demonstrated, andshows that, as the gap distance increases, |k| exponentially decreases [466]. Here,we also experimentally demonstrate the relationship between Dlbw and the gap100distance, which is in agreement with previously published results. Also, we exper-imentally demonstrate the relationship between |k| and the gap distance, which isin agreement with the theoretical results in [466]. Figures 6.4(a) and 6.4(b) showDlbw and the extracted |k| (extracted using our FWHM method) versus gap dis-tance, respectively, for the contra-DCs fabricated on “run 1,” “run 2,” and “run 3.”As the gap distance increases, Dlbw and |k| tend to decrease and Dlbw reaches aminimum and for one of our devices, the device from “run 3” with a gap distanceof 400 nm, we are not able to obtain a value for |k| since it goes to zero. We alsofabricated contra-DCs on “run 1” with a fixed gap distance of 280 nm and variedthe corrugation widths of waveguide “a” and waveguide “b.” Figures 6.4(c) and6.4(d) show Dlbw and the extracted |k| versus corrugation width, respectively, forcorrugation widths of 30 nm to 150 nm in 20 nm increments for waveguide “a” andcorrugation widths of 40 nm to 160 nm in 20 nm increments for waveguide “b.” Asthe corrugation width increases, Dlbw [459, 461, 462] and |k| [466] increase.101100 150 200 250 300 350 400100101Gap Distance (nm)6hbw (nm)  run 1run 2run 3a)100 150 200 250 300 350 400103104Gap Distance (nm)|g| (mï1)  run 1run 2run 3b)30/40 50/60 70/80 90/100 110/120 130/140 150/1601001016hbw (nm)Ca/Cb (nm)  run 1c)30/40 50/60 70/80 90/100 110/120 130/140 150/160103104105|g| (mï1)Ca/Cb (nm)  run 1d)Figure 6.4: (a) Experimental bandwidth at FWHM versus gap distance and(b) extracted coupling coefficient versus gap distance using the FWHMmethod. (c) Experimental bandwidth at FWHM versus corrugationwidth and (d) extracted coupling coefficient versus corrugation widthfor devices from “run 1” with a fixed gap distance of 280 nm using theFWHM method. cOptical Society of America, 2015, by permission[435].Next, we provide a comparison between the |k|s extracted using the FWHMmethod [using Eqs. 6.6 and 6.7], the null method [using Eqs. 6.6 and 6.8], and thecurve-fit method (using the lsqcurvefit function from MATLAB R [519]) from thedevices made in three fabrication runs. Figures 6.5(a), 6.5(b), and 6.5(c) show theextracted |k|s using the three methods for “run 1,” “run 2,” and “run 3,” respec-tively. Upon inspection of Figures 6.5(a)-6.5(c), it is clear that the |k|s that weredetermined using the FWHM method and the curve-fit method exhibit nearly ex-ponential trends, as expected. The |k|s extracted using the FWHMmethod and thecurve-fit method are relatively close to each other as compared to the |k|s deter-mined using the null method. The discrepancies seen in Figures 6.5(a)-6.5(c) usingthe null method are due to the difficulty in determining the locations of the nulls[e.g., see Figure 6.5(d)]. Also, we were unable to determine the |k|s for five of thedevices using the null method since there are no valid solutions to Eq. 6.8. For one102of the devices using the FWHM method we could only extract a zero solution for|k|. With the curve-fit method, we were able to extract a non-zero value for |k| foreach of the devices.150 200 250 300 350 400103104Gap Distance (nm)|g| (mï1)  null method: run 1FWHM method: run 1curveïfit method: run 1a)150 200 250 300 350 400103104Gap Distance (nm)|g| (mï1)  null method: run 2FWHM method: run 2curveïfit method: run 2b)150 200 250 300 350 400103104Gap Distance (nm)|g| (mï1)  null method: run 3FWHM method: run 3curveïfit method: run 3c)1525 1530 1535 1540 1545 1550ï60ï50ï40ï30ï20ï100Wavelength (nm)Insertion Loss (dB)d)Figure 6.5: Comparison between the FWHM method, the null method, andthe curve-fit method to determine |k| for (a) “run 1,” (b) “run 2,” and(c) “run 3.” (d) Drop port spectrum of a contra-DC with a gap distanceof 300 nm from “run 2,” which is chosen to illustrate that there can bemultiple possible choices for the location of the first null to the left of themain lobe (the red dots indicate possible choices for the null location).cOptical Society of America, 2015, by permission [435].Next, we demonstrate, for a given contra-DC with a fixed coupling length, thatDlbw reaches a minimum value as |k| approaches zero ([517] also demonstratedthis trend in Bragg gratings). To determine the theoretical minimum bandwidth,Dlbwmin, the following equation can be used (see Appendix D for the derivation),Dlbwmin ⇡ 2.783115l20pL⇥ng,a(l0)+ng,b(l0)⇤ (6.9)which is similar to the minimum bandwidth equation in [520] except that theirequation is for a distributed Bragg reflector and does not account for dispersion.103Figure 6.6 shows how Dlbwmin changes as the coupling length increases (the groupindices were evaluated at 1535.33 nm). Dlbwmin can be reduced by increasing thecoupling length [520]. The device from “run 3” with a gap distance of 400 nmhas a measured bandwidth below Dlbwmin (due to the experimental results havingripples likely caused by the grating couplers), which could be the reason that thereis no |k| solution other than zero for this device using the FWHM method.0 200 400 600 800 1000100101102Coupling Length (µm)6hbwïmin (nm)  run 1run 2run 3Figure 6.6: Theoretical predicted minimum bandwidth at FWHM versus cou-pling length including experimental data points from the devices withgap distances of 400 nm from the three fabrication runs. cOptical So-ciety of America, 2015, by permission [435].Next, we show an example of using the extracted |k| (using the FWHMmethod)to closely match the simulated spectra to the experimental spectra of one of ourcontra-DCs. We have chosen one of our devices that showed a highly symmetricspectral response to the left and right of the centre of the main lobe for the com-parison between the simulated results (using the extracted |k| determined from theFWHM method) and the experimental results. The device has a gap distance of140 nm and is from “run 2.” The simulated spectra were plotted using Eqs. 6.1 and6.2 and we have added 0.0147 to the modelled values of the effective indices forspectral alignment purposes. Figure 6.7(a) shows that the simulated through portand drop port spectra using the extracted |k| of 19882 m-1 from “run 2” closelymatch the experimental spectra. Figure 6.7(b) shows a comparison between thesimulated spectra using the extracted |k| of 18466 m-1 from “run 1” and the ex-perimental spectra from “run 2.” The results in Figure 6.7(b) show that, since thereis close agreement between the two fabrication runs, using a previously extracted104|k| can be used to predict the spectral response of future fabricated devices withthe same as-designed dimensions. Figures 6.7(c) and 6.7(d) show a comparisonbetween the drop port spectra and through port spectra, respectively, from “run1,” “run 2,” and “run 3” and the simulated spectra (we have aligned the measuredspectra from “run 1,” “run 2,” “run 3,” and the simulated spectra to their respec-tive centre wavelengths) using the average |k| of 18856 m-1, calculated using theextracted |k|s from the three runs (i.e., 18466 m-1, 19882 m-1, and 18219 m-1).Our method can also be used to predict the maximum power coupling factors,MAX|kc|2s, and the minimum power transmission factors, MIN|tc|2s, of contra-DCs. In Figures 6.8(a) and 6.8(b) we show a comparison between the experimen-tal and simulated (using the extracted |k|s determined from the FWHM method)MAX|kc|2s and MIN|tc|2s versus gap distance, respectively, for the devices from“run 1,” “run 2,” and “run 3.” Experimental MIN|tc|2s for the devices from “run1” with gap distances of 320 nm, 380 nm, and 400 nm and for the devices from“run 3” with gap distances of 380 nm and 400 nm are not shown in Figure 6.8(b)since the main notches within their through port spectra were not visible. Simu-lated MAX|kc|2 and MIN|tc|2 for the device from “run 3” with a gap distance of400 nm is not shown since we were unable to extract a value for |k| other thanzero. Also, the MAX|kc|2s determined using the curve-fit method are closer to thenormalized measured results as compared to the MAX|kc|2s determined using theFWHMmethod. However, using the |k|s extracted by the FWHMmethod result inmany of the simulated MIN|tc|2s being closer to the measured results as comparedto the MIN|tc|2s determined using the curve-fit method. The likely reason that theFWHM method gives better results for MIN|tc|2, as compared to the values deter-mined using the curve-fit method, is that the curve-fit method relies on an accuratenormalization of the drop port spectrum.1051525 1530 1535 1540 1545 1550ï40ï30ï20ï100Wavelength (nm)Insertion Loss (dB)  drop: experimental (run 2)through: experimental (run 2)drop: simulated (run 2 |g|)through: simulated (run 2 |g|)a)1525 1530 1535 1540 1545 1550ï40ï30ï20ï100Wavelength (nm)Insertion Loss (dB)  drop: experimental (run 2)through: experimental (run 2)drop: simulated (run 1 |g|)through: simulated (run 1 |g|)b)ï5 0 5ï30ï25ï20ï15ï10ï506h (nm)Insertion Loss (dB)  drop (run 1)drop (run 2)drop (run 3)simulated (average |g|)c)ï5 0 5ï40ï30ï20ï1006h (nm)Insertion Loss (dB)  through (run 1)through (run 2)through (run 3)simulated (average |g|)d)Figure 6.7: (a) Experimental and simulated (using the extracted |k| obtainedusing the FWHM method) drop port and through port spectra for acontra-DC (from “run 2”) with a gap distance equal to 140 nm. (b)Comparison between the experimental spectra from “run 2” and thesimulated spectra using the extracted |k| of 18466 m-1 from “run 1”for contra-DCs with gap distances of 140 nm. Comparison between theexperimental (c) drop port spectra and (d) through port spectra from“run 1,” “run 2,” and “run 3” and the simulated spectra using the av-erage extracted |k| of 18856 m-1 from the three runs for contra-DCswith gap distances of 140 nm. cOptical Society of America, 2015, bypermission [435].106100 150 200 250 300 350 400ï15ï10ï50Gap Distance (nm)MAX|g c|2  (dB)  experimental (run 1)simulated (run 1)experimental (run 2)simulated (run 2)experimental (run 3)simulated (run 3)a)100 150 200 250 300 350 400ï50ï40ï30ï20ï100Gap Distance (nm)MIN|t c|2  (dB)  experimental (run 1)simulated (run 1)experimental (run 2)simulated (run 2)experimental (run 3)simulated (run 3)b)Figure 6.8: Comparison between the experimental and the simulated (us-ing extracted |k|s determined from the FWHM method) (a) maximumpower coupling factor and (b) minimum power transmission factor ver-sus gap distance. cOptical Society of America, 2015, by permission[435].The group delay and the dispersion of a contra-DC is of interest because theygive us an indication of the effect the contra-DC will have on a signal. Previously,it has been shown that the phase (and, therefore, the group delay and dispersion) offibre Bragg gratings [499, 521, 522] and ring resonators [112, 501, 523, 524] can bedetermined using the Hilbert transform method. Specifically, the Hilbert transformmethod can be used to determine through port phase responses of Bragg gratingsbecause the through port response is minimum phase [499, 521, 522]. Here, weuse the Hilbert transform method [499] to determine the through port phase of acontra-DC from “run 2” with a gap distance of 140 nm (we use the hilbert functionfrom MATLAB R [500]). Once the phase response is determined, the group delay[97, 525] and dispersion [97, 525, 526] can be calculated. Figures 6.9(a) and 6.9(b)show the group delay and dispersion responses, respectively, using the Hilberttransform method on the experimental through port spectrum from Figure 6.7(a)(the results shown were smoothed using moving averages) and are compared to thesimulated responses that were determined for the |k| extracted using the FWHMmethod and the measured results (the average of 300 measurements) using an Op-tical Vector AnalyzerTM STe by Luna Innovations, Inc., (OVA). For the simulatedresults, we added an additional phase to account for the transit time of the device.The effective indices for this additional phase were calculated for a waveguidewidth of 450 nm using MODE Solutions by Lumerical Solutions, Inc. Similarly,we have added a 2.22 ps group delay offset to the Hilbert transform-determined107group delay. Also, a constant group delay offset was subtracted from the mea-sured group delay for alignment to the simulated result. The Hilbert transform-determined through port group delay and dispersion results are in close agreementwith the simulated results using the extracted |k| and the measured results usingthe OVA. Therefore, our FWHM method can also be used to predict the throughport group delay response and the dispersion response of contra-DCs.1530 1535 1540 1545246Wavelength (nm)Group Delay (ps)  simulatedHilbert transformmeasureda)1530 1535 1540 1545ï5051015Wavelength (nm)Dispersion (ps/nm)  simulatedHilbert transformmeasuredb)Figure 6.9: Comparison between the experimental through port (a) group de-lay response and (b) dispersion response that were determined usingthe Hilbert transform method and the simulated results that were de-termined using the extracted |k| of 19882 m-1 as well as the measuredresults using the OVA. cOptical Society of America, 2015, by permis-sion [435].6.3 Example of Using the Process Calibration Method inthe Filter Design ProcessHere, a 3-port Vernier filter consisting of four silicon grating-assisted racetrackresonators (similar to the filter in [97]), as shown in Figure 6.10, is demonstratedtheoretically. The arrangement of the racetrack resonators is similar to those foundin [85, 126, 142], however, the racetrack resonators presented here are cascaded.The Vernier filter meets typical 3-port filter commercial specifications as well aslow drop port and through port dispersions. The process calibration method pre-sented in this chapter can be used to accurately determine the coupling coefficientsof fabricated contra-DCs, and this method will be used to determine the gap dis-tance that corresponds to the coupling coefficient of the contra-DC that is requiredfor the filter to operate as desired.108					 	  κ2(λ) t2(λ) Input Through g2	g1 a t1(λ) r Lc Drop κ1(λ) κ1(λ) Za (λ)1/2Za (λ)1/2t1(λ) r L b Lc Zb (λ)1/2Zb (λ)1/2  κ2(λ) t2(λ) g2	g1 a r Lc κ1(λ) Za (λ)1/2 Za (λ)1/2t1(λ) t1(λ) r L b Zb (λ)1/2Zb (λ)1/2g1 t1(λ) t1(λ) g2	Lc   κ2(λ) t2(λ)g1 t1(λ) t1(λ)   κ2(λ) t2(λ) g2	κ1(λ) κ1(λ) κ1(λ) κ1(λ) κ1(λ) Figure 6.10: Schematic diagram of an optimized 3-port grating-assistedVernier filter (figure has been adapted from [97]).Simulation results for an optimized 3-port silicon grating-assisted Vernier race-track resonator filter are presented. Figure 6.11(a) shows the theoretical spectraat the drop port and at the through port of an optimized 3-port grating-assistedVernier filter that has the configuration shown in Figure 6.10. Figure 6.11(b) showsa zoom-in within the wavelength region of the major peak/notch where the clearwindow (indicated by the dashed vertical lines) is 13 GHz and the channel spacingis 200 GHz. This filter meets the target specifications that are bolded in Table 6.1.The drop port dispersion within the wavelength region near the desired channel’sclear window is shown in Figure 6.11(c) and the through port dispersion withinthe wavelength region corresponding to the through port passband to the left of themajor notch is shown in Figure 6.11(d). Ddrop is +15 ps/nm and Dthru-m is -4 ps/nm,which meet their typical requirements of -30 ps/nmDdrop  +30 ps/nm [105] and-15 ps/nm  Dthru-m  +15 ps/nm [105], respectively. The method to model thisgrating-assisted Vernier racetrack resonator filter was based on [97]. The follow-ing parameter values were used in the simulation of the filter: the grating periodwas 312 nm [440]; the grating number was 182 [440]; the radius was 3 µm [440];L = 22.07 µm; the routing length between each cascaded racetrack resonator was20 µm; the propagation loss was set to 3 dB/cm; k was chosen to be 13000 m-1;the co-directional couplers without gratings consisted of silicon strip waveguideswith widths of 550 nm and heights of 220 nm, a top oxide cladding, and gap dis-tances of 280 nm [97]; the bend regions of the racetrack resonators had widths of109550 nm, heights of 220 nm, and were not included in the calculations of the fieldcoupling factors and field transmission factors [97]; and the contra-DCs consistedof strip waveguides with average widths of 450 nm and 550 nm and heights of220 nm [97]. Based on the extracted |k|s, using the FWHM method, shown inFigures 6.5(a)-6.5(c), the chosen k of 13000 m-1 corresponds to a gap distance ofabout 170 nm.1500 1510 1520 1530 1540 1550 1560ï150ï100ï500Intensity (dB)  Wavelength (nm)ThroughDropa)1529.5 1530 1530.5 1531 1531.5 1532 1532.5ï50ï40ï30ï20ï100Intensity (dB)  Wavelength (nm)ThroughDropb)1530.6 1530.8 1531 1531.2ï30ï20ï100102030Wavelength (nm)Dispersion (ps/nm)c)1505 1510 1515 1520 1525ï4ï202Dispersion (ps/nm)Wavelength (nm)d)Figure 6.11: (a) Through port spectral response and drop port spectral re-sponse, (b) a zoom-in within the region of the major peak/notch, (c)drop port dispersion within the wavelength region of the major peak,and (d) through port dispersion within the wavelength region corre-sponding to the passband to the left of the major notch of an optimized3-port grating-assisted Vernier filter.110Table 6.1: Modelled results and target specifications for 200 GHz 3-port fil-ters (table modified from [105]).Parameter Modelled result Target valueFSR (nm) N/A  36.72Rdepth (dB) 0.5  0.5 [502]Ai (dB) 47.9  25 [502, 503], 30 [101]nAi (dB) 38.9  35 [101], 40 [502, 503]IPS (dB) 35.4  35 [101], 40 [502, 503]ILdrop (dB) 0.9  0.8 [503], 1.0 [502], 1.2 [101]ECi (dB) 17.0  10 [502], 12 [503]ILthru (dB) 0.3  0.4 [503], 0.5 [502], 0.6 [101]ILthru-m (dB) 0.5  0.4 [503], 0.5 [502], 0.6 [101]In the filter design process, the ability to predict the performance of contra-DCs is invaluable. We have presented a method, the FWHM method, for deter-mining the coupling coefficients of contra-DCs. To demonstrate the usefulness ofour method, we fabricated SOI contra-DCs on three separate fabrication runs. OurFWHM method of extracting the coupling coefficient of contra-DCs can be usedto predict the spectral response, group delay, and dispersion of subsequently fab-ricated devices. The FWHM method provides more consistent extracted couplingcoefficient values as compared to the values extracted using the null method. Also,the FWHMmethod provides extracted coupling coefficient values of fabricated de-vices that are relatively close, as compared to using the null method, to the valuesextracted by curve-fitting the drop port spectra. However, the curve-fit method re-lies on the accurate normalization of the drop port spectrum whereas our FWHMmethod does not require normalization of the data, and our method is generallyeasier to implement. We have also shown that there is a minimum bandwidth thatcan be obtained by reducing the coupling coefficient, which needs to be consid-ered when designing a contra-DC-based filter. We have presented an equation forthis minimum bandwidth as a function of the length of the coupler. The methodpresented in this chapter can be used to calibrate the design process, enabling de-signers to accurately predict the as-fabricated contra-DC response.111Chapter 7Conclusion and Future Work7.1 ConclusionThe design of a variety of silicon photonic ring resonator filters for DWDM appli-cations that allow for a large number of channels to be multiplexed and/or demul-tiplexed have been theoretically and experimentally demonstrated. Specifically,three methods to increase the FSR and, thus, increase the channel count, have beenpresented.The first method utilized the Vernier effect to increase the FSR by couplingnon-identical ring resonators together. First, silicon quadruple series-coupled ringresonators exhibiting the Vernier effect were theoretically shown to be able to meettypical 4-port filter commercial specifications as well as have FSRs larger than thespan of the C-band. Also, experimental results on silicon quadruple series-coupledring resonators exhibiting the Vernier effect have shown that it is possible to meetnumerous 3-port commercial specifications, enhance the resonant tuning range, aswell as the ability to transmit data through the device at 12.5 Gbps. The nextmethod to increase the channel count is to use MZI-BC. Theoretical and experi-mental results on silicon series-coupled microring resonators with MZI-BC havebeen presented which showed that it is possible to meet numerous 3-port filtercommercial specifications, have an FSR greater than the span of the C-band, andhave low dispersion within the through port passbands. Although the FSR canbe increased by using these two methods, ideally one would like to eliminate the112FSR. The third method utilized contra-DCs, which are highly wavelength selectivecouplers. Theoretical and experimental results on silicon cascaded Vernier race-track resonators with integrated contra-DCs in the coupling regions have shownthat it is possible to not only eliminate the FSR but also to increase the IPS ascompared to the case in which co-directional couplers without gratings are usedwithin all the coupling regions of the cascaded racetrack resonator filter. Whenusing contra-DCs in the design of filters, it is important to accurately determinethe coupling coefficients and, thus, we presented a process calibration method todetermine the coupling coefficients of fabricated contra-DCs by measuring theirFWHM bandwidths. Then, this process calibration method was used to designa silicon cascaded Vernier racetrack resonator with integrated contra-DCs, whichmet 3-port filter commercial specifications.The three methods used to extend the FSRs of ring resonators (series-coupledVernier ring resonators, MRRs with MZI-BCs, and cascaded Vernier ring res-onators with contra-DCs) each have benefits and drawbacks, which are shownin Table 7.1. The comparison shown in Table 7.1 is based on the following fea-tures: FSR, wavelength tunability, thermal cross-talk, minor notch dispersion, fil-ter shape, and filter application [fixed wavelength filter applications, limited wave-length tuning range filter applications (i.e., less than C-band span), and C-band tun-ing range filter applications]. The benefits of series-coupled Vernier ring resonatorsare extend FSRs, enhanced wavelength tuning ranges, and flat-topped responses[149, 150]. However, series-coupled Vernier ring resonators typically have largedispersions within their through port minor notches [105, 112, 432]. Fortunately,low dispersion can be achieved using MRRs with MZI-BCs while extending theFSR and providing a flat-topped response [105, 432]. However, the current designwithin this dissertation cannot exhibit an enhanced wavelength tuning range. Thelast method, cascaded Vernier ring resonators with contra-DCs, has the desirablefeatures that the FSRs are eliminated in the drop port and through port, reducedthermal cross-talks due to the cascaded configurations [97], and low minor notchdispersions. However, the drawbacks to this method are that the filters have noenhanced wavelength tuning ranges, and the filter responses are not flat-topped.With regard to the MZI-BC method, it may be possible to achieve the enhancedwavelength tuning range feature by reducing the FSRs of the MZIs, and, thus, the113Table 7.1: Comparison of FSR extension methods as implemented in dissertation (the benefits are bolded).Method FSR WavelengthtunabilityThermalcross-talkMinor notchdispersionFlat-toppedresponseApplicationVernier rings (series)[105, 149, 150]extended enhanced standard large yes fixed, C-band tuningMRRs with MZI-BC[105]extended standard* standard minimal yes fixed, limited tuning*Vernier rings (cas-cade) with contra-DCs [97]eliminated standard reduced minimal no fixed, limited tuning* Potential for enhanced wavelength tuning range.114MZI-BC method would be the most desirable method, since it would be the onlymethod with, both, enhanced wavelength tuning ranges and minimal minor notchdispersions.Overall, I have shown a variety of silicon photonic filters that meet commercialspecifications including: first commercial specification-dependent sensitivity anal-ysis of silicon Vernier ring resonators; first experimental demonstration of a siliconquadruple series-coupled Vernier racetrack resonator; first experimental demon-stration of thermally tunable silicon quadruple series-coupled Vernier racetrackresonators; first experimental demonstration of a silicon MRR filter with MZI-BCthat meets many of the typical commercial specifications; and the first demonstra-tion of silicon cascaded Vernier racetrack resonators with integrated contra-DCs.Lastly, a superior process calibration method for contra-DC filter designs was pre-sented.7.2 Future WorkExperimental validation that silicon series-coupled Vernier racetrack resonatorscan meet all of the 4-port filter specifications, especially the express channel isola-tion, is still needed and the starting point would be to take the 4-port Vernier filterdesigns presented in Chapter 2 and model the directional couplers in 3-D FDTD;the bend regions of the couplers will increase the values of the coupling factorsas compared to when the coupling factors are calculated using just the straightsections of the couplers, and, thus, the gap distances will have to be modified toachieve devices that exhibit similar performance to those presented in Chapter 2.Also, waveguide offsets can be introduced between the bent and straight regions ofthe racetrack resonators to reduce mode-mismatch losses [470]. The use of a fabri-cation process that results in lower waveguide losses would enable improvementsin the performance of Vernier resonators. For example, the minor through portnotches would be smaller since propagation losses can be dramatically reduced toas low as 0.5 dB/cm [527]. If we take the 4-port Vernier filter design from Chapter2 with nominal gap distances, “gap 1”, “gap 2”, and “gap 3” equal to 150 nm, 350nm, and 390 nm and reduce the propagation loss from 2.4 dB/cm to 0.5 dB/cm,then ILthru-m would reduce from 0.6 dB to 0.1 dB when light is injected into the115input port and ILthru-m would reduce from 0.8 dB to 0.2 dB when light is injectedinto the add port, as shown in Figures 7.1(a) and 7.1(b), respectively. An automatedtuning and optimization method, such as the ones presented in [430, 528], can beused to create an automatically tunable silicon quadruple series-coupled Vernierracetrack resonator.1515 1520 1525 1530 1535 1540ï1ï0.8ï0.6ï0.4ï0.20Wavelength (nm)Intensity (dB)   loss = 2.4 dB/cm loss = 0.5 dB/cma)1515 1520 1525 1530 1535 1540ï1ï0.8ï0.6ï0.4ï0.20Wavelength (nm)Intensity (dB)   loss = 2.4 dB/cm  loss = 0.5 dB/cmb)Figure 7.1: (a) Through port passband and (b) drop port passband compari-son, when light is injected into the input port and when light is injectedinto the add port, respectively, of a 4-port quadruple Vernier racetrackresonator, for propagation losses of 2.4 dB/cm and 0.5 dB/cm.With regard to the silicon double microring resonator with MZI-BC, addingheaters on top of the MZI-bus branches, as well as to each microring resonator,will enable it to operate as a wavelength tunable filter (as previously demonstratedin [433]) while meeting numerous commercial specifications. The integration ofheaters will also help improve the performance of the device by enabling the abil-ity to correct for fabrication variations. An automated tuning and optimizationmethod, such as the ones presented in [430, 528], could be used with the silicondouble microring resonator with MZI-BC.With regard to the cascaded Vernier racetrack resonator that uses grating-assistedcouplers, experimentally demonstrating the improved filter design that was pre-sented in Chapter 6.3 is needed since such a device would be a desirable componentin silicon photonic systems that require DWDM filters. To correct for fabricationvariations, heaters can be placed on top of the contra-DCs as well as the portions ofeach of the racetrack resonators that are not within the coupling regions. Waveg-uide offsets can be introduced between the bent and straight regions of each race-track resonator to reduce mode-mismatch losses [470]. Also, an automated tuning116and optimization method, such as the ones presented in [430, 528], could be usedwith the grating-assisted cascaded Vernier racetrack resonator.Many of the filters presented in this dissertation have met numerous commer-cial filter specifications based on telecommunications vendor data sheets and, withever-increasing improvements in the fabrication process, such filters could be com-mercializable. Thus, the silicon photonic DWDM filters presented in this disser-tation have provided additional evidence that silicon photonics has the real poten-tial to be a disruptive technology that transforms the telecommunications and datacommunications industries.117Bibliography[1] Future Market Insights, “Silicon Photonics Market: Global IndustryAnalysis and Opportunity Assessment 2015-2025,” [Online]. Available:http://www.futuremarketinsights.com/reports/silicon-photonics-market,(Jan. 15, 2016).[2] Markets and Markets, “Silicon Phonics Market by Product (PhotonicWavelength, Optical Modulators, Optical Interconnects, WDMF, LED, andOthers), by Application (Telecommunication, Data Communication, andOthers), and by Geography - Global Trends and Forecasts to 2014 - 2020,”[Online]. Available: http://www.marketsandmarkets.com/Market-Reports/silicon-photonics-116.html, (Jan. 15, 2016).[3] Yole De´veloppement, “Silicon Photonics Market & Technologies2011-2017: Big Investments, Small Business,” [Online]. Available:http://www.yole.fr/iso upload/News/2012/PR Silicon%20Photonics%20 Big%20Investments%20Small%20Business YOLE%20DEVELOPPEMENT October%202012.pdf, (Jan. 15, 2016).[4] P. P. Drake and F. J. Fabozzi, The Basics of Finance: An Introduction toFinancial Markets, Business Finance, and Portfolio Management. JohnWiley & Sons, Inc., 2010.[5] M. S. Fridson and F. Alvarez, Financial Statement Analysis: APractitioner’s Guide, 4th Edition. John Wiley & Sons, Inc., 2011.[6] iMinds, Market Capitalisation: Money. iMinds Pty Ltd., 2009.[7] Etaphase, Inc., “Etaphase successfully demonstrates fabrication of HUDSin silicon CMOS chip,” [Online]. Available:http://etaphase.com/2012/10/huds silicon cmos/, (Jan. 15, 2016).[8] H. Byun, J. Bok, K. Cho, K. Cho, H. Choi, J. Choi, S. Choi, S. Han,S. Hong, S. Hyun, T. J. Jeong, H.-C. Ji, I.-S. Joe, B. Kim, D. Kim, J. Kim,118J.-K. Kim, K. Kim, S.-G. Kim, D. Kong, B. Kuh, H. Kwon, B. Lee, H. Lee,K. Lee, S. Lee, K. Na, J. Nam, A. Nejadmalayeri, Y. Park, S. Parmar,J. Pyo, D. Shin, J. Shin, Y. hwack Shin, S.-D. Suh, H. Yoon, Y. Park,J. Choi, K.-H. Ha, and G. Jeong, “Bulk-Si photonics technology forDRAM interface [Invited],” Photonics Research, vol. 2, no. 3, pp.A25–A33, Jun. 2014.[9] Morton Photonics, Inc., [Online]. Available: http://mortonphotonics.com,(Jan. 15, 2016).[10] Kaiam Corp., “Kaiam Corporation Introduces a 40GB/S QSFP+ LR4Transceiver with Integrated Optical Engines for Use in High VolumeApplications at OFC 2014,” [Online]. Available:http://kaiamcorp.com/?page id=7994, (Jan. 15, 2016).[11] Centera Photonics, Inc., [Online]. Available:http://www.centera-photonics.com/pages/page company en, (Jan. 15,2016).[12] VLC Photonics S.L., [Online]. Available:http://www.vlcphotonics.com/technology-2/, (Jan. 15, 2016).[13] Compass-EOS, “Silicon Photonics and the Future of Core Routing,”[Online]. Available: http://compassnetworks.com/wp-content/uploads/Compass-EOS-Technology-White-Paper.pdf, (Jan. 15, 2016).[14] APIC Corp., [Online]. Available: http://www.apichip.com/next.html, (Jan.15, 2016).[15] PhotonIC Corp., [Online]. Available: http://www.photonic-corp.com, (Jan.15, 2016).[16] photonics.com, “Samtec Joins French Silicon Photonics DevelopmentProject,” [Online]. Available:http://www.photonics.com/Article.aspx?AID=57434, (Jan. 15, 2016).[17] AEPONYX, Inc., [Online]. Available: http://www.aeponyx.com/OCS,(Jan. 15, 2016).[18] Fujitsu Ltd., “Fujitsu, PETRA, and NEDO Achieve World’s Lowest EnergyRequirements of 5 mW per 1 Gbps for High-Speed Inter-Processor DataTransmissions,” [Online]. Available: http://www.fujitsu.com/global/about/resources/news/press-releases/2015/0223-02.html, (Jan. 15, 2016).119[19] Optic2Connect Pte. Ltd., [Online]. Available:http://www.optic2connect.com, (Jan. 15, 2016).[20] COMSOL, Inc., “Optical ring resonator notch filter,” [Online]. Available:http://www.comsol.com/model/optical-ring-resonator-notch-filter-22221,(Jan. 15, 2016).[21] Optiwave Systems, Inc., [Online]. Available: http://optiwave.com, (Jan. 15,2016).[22] PhoeniX B.V., [Online]. Available: http://www.phoenixbv.com/index.php,(Jan. 15, 2016).[23] Photon Design, Inc., [Online]. Available: http://www.photond.com, (Jan.15, 2016).[24] EM Photonics, Inc., [Online]. Available:http://www.emphotonics.com/projects/electromagnetics/, (Jan. 15, 2016).[25] Apollo Photonics, Inc., [Online]. Available:http://www.apollophoton.com/apollo/, (Jan. 15, 2016).[26] Luceda Photonics, [Online]. Available:http://www.lucedaphotonics.com/en, (Jan. 15, 2016).[27] Synopsys, Inc., [Online]. Available:https://optics.synopsys.com/rsoft/rsoft-product-applications.html, (Jan. 15,2016).[28] Mentor Graphics Corp., “Mentor Graphics and Lumerical Unify OpticalDesign and Simulation Flow,” [Online]. Available:http://www.mentor.com/company/news/mentor-lumerical-optical-design,(Jan. 15, 2016).[29] Maple Leaf Photonics LLC, [Online]. Available:http://mapleleafphotonics.com;http://www.sos.wa.gov/corps/search detail.aspx?ubi=603483503, (Apr. 14,2016).[30] Inphi Corp., “Inphi Collaborates to Announce Industry’s First 100G CloudPlatform at IDF 2014,” [Online]. Available: http://www.inphi.com/media-center/press-room/press-releases-and-media-alerts/inphi-collaborates-to-announce-industryrsquos-first-100g-cloud-platform-at-idf-2014.php, (Jan. 15, 2016).120[31] Caliopa, [Online]. Available: http://www.caliopa.com, (Jan. 15, 2016).[32] Novati Technologies, [Online]. Available:http://www.novati-tech.com/silicon-photonics, (Jan. 15, 2016).[33] Sandia National Laboratories, [Online]. Available:http://www.sandia.gov/mstc/IPIMI/, (Jan. 15, 2016).[34] F. Boeuf, S. Cremer, E. Temporiti, M. Fere’, M. Shaw, N. Vulliet,B. Orlando, D. Ristoiu, A. Farcy, T. Pinguet, A. Mekis, G. Masini, P. Sun,Y. Chi, H. Petiton, S. Jan, J.-R. Manouvrier, C. Baudot, P. Le-Maitre, J. F.Carpentier, L. Salager, M. Traldi, L. Maggi, D. Rigamonti, C. Zaccherini,C. Elemi, B. Sautreuil, and L. Verga, “Recent progress in silicon photonicsR&D and manufacturing on 300mm wafer platform,” in Optical FiberCommunication Conference. Optical Society of America, 2015, p.W3A.1.[35] P. Liao, M. Sakib, F. Lou, J. Park, M. Wlodawski, V. Kopp, D. Neugroschl,and O. Liboiron-Ladouceur, “Ultradense silicon photonic interface foroptical interconnection,” IEEE Photonics Technology Letters, vol. 27,no. 7, pp. 725–728, Apr. 2015.[36] M/A-COM Technology Solutions Holdings, Inc., [Online]. Available:http://www.macom.com/technologies/siph, (Jan. 15, 2016).[37] One Silicon Chip Photonics, Inc., [Online]. Available:http://onesiliconchipphotonics.com/technology, (Jan. 15, 2016).[38] Applied NanoTools, Inc., [Online]. Available: http://www.appliednt.com,(Jan. 15, 2016).[39] Acacia Communications, Inc., [Online]. Available:http://acacia-inc.com/acacia-advantage/silicon-photonics-integration/,(Jan. 15, 2016).[40] NEC Corp., “NEC develops silicon integrated optical switch technologywith port count extendability according to network size,” [Online].Available: http://www.nec.com/en/press/201503/global 20150319 02.html,(Jan. 15, 2016).[41] VTT Memsfab Ltd., [Online]. Available:http://www.vttmemsfab.fi/services, (Jan. 15, 2016).121[42] Markets and Markets, “Silicon Photonics Market by Product, Applicationand by Geography - Global Trends and Forecasts to 2014 - 2020,” [Online].Available:http://www.researchandmarkets.com/research/n42dsl/silicon photonics,(Jan. 15, 2016).[43] Omega Optics, Inc., [Online]. Available: http://www.omegaoptics.com,(Jan. 15, 2016).[44] Rockley Photonics, [Online]. Available: http://rockleyphotonics.com, (Jan.15, 2016).[45] Luxmux Technology Corp., [Online]. Available: http://www.luxmux.com,(Jan. 15, 2016).[46] Lumerical Solutions, Inc., “Unified Design Flow for Silicon Photonics,”[Online]. Available:https://www.lumerical.com/solutions/partners/eda/mentor graphics/, (Jan.15, 2016).[47] Mellanox Technologies, “Mellanox Introduces Next Generation 100Gb/sSilicon Photonics Transceivers,” [Online]. Available:http://www.mellanox.com/page/press release item?id=1504, (Jan. 15,2016).[48] Y. Painchaud, M. Poulin, F. Pelletier, C. Latrasse, J.-F. Gagne, S. Savard,G. Robidoux, M. Picard, S. Paquet, C. Davidson, M. Pelletier, M. Cyr,C. Paquet, M. Guy, M. Morsy-Osman, M. Chagnon, and D. V. Plant,“Silicon-based products and solutions,” Proc. SPIE, vol. 8988, p. 89880L,2014.[49] D. M. Calhoun, Q. Li, C. Browning, N. C. Abrams, Y. Liu, R. Ding, L. P.Barry, T. Baehr-Jones, M. Hochberg, and K. Bergman, “Programmablewavelength locking and routing in a silicon-photonic interconnectionnetwork implementation,” in Optical Fiber Communication Conference.Optical Society of America, 2015, p. Tu2H.3.[50] P. Dong, Y.-K. Chen, and L. L. Buhl, “Reconfigurable four-channelpolarization diversity silicon photonic WDM receiver,” in Optical FiberCommunication Conference. Optical Society of America, 2015, p.W3A.2.122[51] D. Mahgerefteh and C. Thompson, “Techno-economic comparison ofsilicon photonics and multimode VCSELs,” in Optical FiberCommunication Conference. Optical Society of America, 2015, p. M3B.2.[52] C.-H. J. Chen, T.-C. Huang, D. Livshit, A. Gubenko, S. Mikhrin,V. Mikhrin, M. Fiorentino, and R. Beausoleil, “A comb laser-drivenDWDM silicon photonic transmitter with microring modulator for opticalinterconnect,” in CLEO: 2015. Optical Society of America, 2015, p.STu4F.1.[53] M. Mazzini, M. Traverso, M. Webster, C. Muzio, S. Anderson, P. Sun,D. Siadat, D. Conti, A. Cervasio, S. Pfnuer, J. Stayt, M. Nyland, C. Togami,K. Yanushefski, and T. Daugherty, “25GBaud PAM-4 error freetransmission over both single mode fiber and multimode fiber in a QSFPform factor based on silicon photonics,” in Optical Fiber CommunicationConference Post Deadline Papers. Optical Society of America, 2015, p.Th5B.3.[54] X. Zheng and A. V. Krishnamoorthy, “A WDM CMOS photonic platformfor chip-to-chip optical interconnects,” in CLEO: 2014. Optical Societyof America, 2014, p. SM4O.3.[55] H.-F. Liu, “Integrated silicon photonics links for high bandwidth datatransportation,” in Optical Fiber Communication Conference. OpticalSociety of America, 2014, p. Th1D.1.[56] A. Ramaswamy, J. E. Roth, E. J. Norberg, R. S. Guzzon, J. H. Shin, J. T.Imamura, B. R. Koch, D. K. Sparacin, G. A. Fish, B. G. Lee,R. Rimolo-Donadio, C. W. Baks, A. Rylyakov, J. Proesel, M. Meghelli, andC. L. Schow, “A WDM 4x28Gbps integrated silicon photonic transmitterdriven by 32nm CMOS driver ICs,” in Optical Fiber CommunicationConference Post Deadline Papers. Optical Society of America, 2015, p.Th5B.5.[57] Ericsson, “Ericsson-backed research project breaks new ground in siliconphotonic integration,” [Online]. Available:http://www.ericsson.com/news/1948557, (Jan. 15, 2016).[58] Analog Photonics LLC, [Online]. Available:http://www.analogphotonics.com, (Jan. 15, 2016).[59] BrPhotonics Produtos Optoeletroˆnicos LTDA., [Online]. Available:http://brphotonics.com/en/, (Jan. 15, 2016).123[60] RANOVUS, Inc., [Online]. Available: http://ranovus.com/technology/,(Jan. 15, 2016).[61] Iris Dorbian, “Target Partners backs Sicoya,” [Online]. Available:https://www.pehub.com/2015/11/target-partners-backs-sicoya/, (Jan. 15,2016).[62] SiFotonics Technologies Co., Ltd., [Online]. Available:http://sifotonics.com/en/, (Jan. 15, 2016).[63] Katherine Bourzac, “Magic Leap needs to engineer a miracle,” [Online].Available: http://www.technologyreview.com/news/538146/magic-leap-needs-to-engineer-a-miracle/, (Jan. 15, 2016).[64] Acorn Technologies, [Online]. Available:http://acorntech.com/applications/semiconductor/, (Jan. 15, 2016).[65] Luxtera, Inc., “Luxtera Ships One-Millionth Silicon CMOS PhotonicsEnabled 10Gbit Channel,” [Online]. Available:http://www.luxtera.com/luxtera/201221LuxteraOneMillionthCMOS.pdf,(Jan. 15, 2016).[66] VPIphotonics Inc., [Online]. Available:http://www.vpiphotonics.com/Tools/PhotonicCircuits/Applications/, (Jan.15, 2016).[67] PLCC2 LLC, [Online]. Available:http://www.plcconnections.com/silicon.html, (Jan. 15, 2016).[68] Genalyte, Inc., [Online]. Available:http://www.genalyte.com/about-us/our-technology/, (Jan. 15, 2016).[69] P. Brown, “Optoelectronics Deal Struck Between Two Chinese Firms,”[Online]. Available: http://electronics360.globalspec.com/article/6132/optoelectronics-deal-struck-between-two-chinese-firms, (Jan. 15, 2016).[70] photonics.com, “Microprocessor Integrates Silicon Photonics,” [Online].Available: http://www.photonics.com/Article.aspx?AID=58119, (Jan. 15,2016).[71] DermaLumics S.L., [Online]. Available:http://www.dermalumics.com/integrated-optics/, (Jan. 15, 2016).124[72] JCMwave GmbH, “Simulation of an integrated optical (de)multiplexer /SOI ring resonator,” [Online]. Available:http://www.jcmwave.com/applications/287-add-drop-multiplexers, (Jan.15, 2016).[73] GigOptix, Inc., “GigOptix, Inc. and CPqD Announce Signing of DefinitiveAgreements to Incept BrPhotonics Produtos Optoeletroˆnicos LTDA., aNew Joint Venture Company in Brazil,” [Online]. Available:http://ir.gigoptix.com/phoenix.zhtml?c=225697&p=irol-newsArticle&ID=1899101, (Jan. 15, 2016).[74] Coriant, “Coriant Begins Independent Path, Starts with Leadership Positionin Optical Networking Market,” [Online]. Available: https://www.coriant.com/company/press-releases/Coriant-Begins-Independent-Path-Starts.asp,(Jan. 15, 2016).[75] HP Inc., “HP Inc. and Hewlett Packard Enterprise to jointly present liveaudio webcast of Hewlett-Packards fourth quarter earnings conferencecall,” [Online]. Available: http://h30261.www3.hp.com/news-and-events/news-library/2015/11-10-2015.aspx, (Jan. 15, 2016).[76] Novati Technologies, “Company profile,” [Online]. Available:http://www.novati-tech.com/company-profile, (Jan. 15, 2016).[77] iXBlue Photonics, [Online]. Available:http://www.photonics.ixblue.com/about-us/overview, (Jan. 15, 2016).[78] I. Shubin, X. Zheng, H. Thacker, S. S. Djordjevic, S. Lin, P. Amberg,J. Yao, J. Lexau, E. Chang, F. Liu, N. Park, K. Raj, R. Ho, J. E.Cunningham, and A. V. Krishnamoorthy, “Microring-based multi-chipWDM photonic module,” Optics Express, vol. 23, no. 10, pp.13 172–13 184, May 2015.[79] A. Mekis, G. Armijo, J. Balardeta, S. Barabas, B. Chase, Y. Chi, A. Dahl,Y. De Koninck, S. Denton, M. Eker, S. Fathpour, D. Foltz, F. Gholami,S. Gloeckner, K. Hon, S. Hovey, S. Jackson, W. Li, Y. Liang, M. Mack,G. Masini, G. McGee, S. Pang, M. Peterson, T. Pinguet, L. Planchon,K. Roberson, S. Sahni, J. Schramm, M. Sharp, C. Sohn, K. Stechschulte,P. Sun, G. Vastola, S. Wang, G. Wong, K. Xu, K. Yokoyama, S. Yu,R. Zhou, and P. De Dobbelaere, “High-speed silicon photonics opticaltransceivers,” in IEEE Summer Topicals Meeting Series (SUM), 2015, Jul.2015, pp. 23–24.125[80] C. R. Doerr, L. Chen, D. Vermeulen, T. Nielsen, S. Azemati, S. Stulz,G. McBrien, X.-M. Xu, B. Mikkelsen, M. Givehchi, C. Rasmussen, andS. Y. Park, “Single-chip silicon photonics 100-Gb/s coherent transceiver,”in Optical Fiber Communication Conference: Postdeadline Papers.Optical Society of America, 2014, p. Th5C.1.[81] S. Hardy, “Acacia Communications IPO a referendum on opticalsubsystems space?” [Online]. Available:http://www.lightwaveonline.com/articles/2016/01/acacia-communications-ipo-a-referendum-on-optical-subsystems-space.html, (Jan. 15, 2016).[82] IRIS Project Consortium, “IRIS Project Deliverable 8.1 First ScientificReport,” [Online]. Available:http://www.ict-iris.eu/IRIS 619194 Deliverable 8.1, (Jan. 15, 2016).[83] Fujitsu Ltd., “Fujitsu Laboratories Develops 4-Wavelength IntegratedSilicon Laser for Inter-Processor Data Transmission,” [Online]. Available:http://www.fujitsu.com/global/about/resources/news/press-releases/2013/0321-03.html, (Jan. 15, 2016).[84] R. Boeck, L. Chrostowski, and N. A. F. Jaeger, “Theoretical sensitivityanalysis of quadruple Vernier racetrack resonators designed for fabricationon the silicon-on-insulator platform,” Proc. SPIE, vol. 9288, p. 928812,2014.[85] R. Boeck, L. Chrostowski, and N. A. F. Jaeger, “Sensitivity analysis ofsilicon-on-insulator quadruple Vernier racetrack resonators,” OpticalEngineering, vol. 54, no. 11, p. 117102, Nov. 2015.[86] B. Peng, Alliance Fiber Optic Products, Inc. personal communication, May8, 2012.[87] Alliance Fiber Optic Products, Inc., “High isolation OADM (100 GHz),”REV. G, Feb. 23, 2006.[88] R. Papannareddy, Lightwave Communication Systems : A PracticalPerspective. Penram International Publishing (India) Pvt. Ltd., 2004.[89] H. Simos, C. Mesaritakis, D. Alexandropoulos, and D. Syvridis, “Dynamicanalysis of crosstalk performance in microring-based add/drop filters,”Journal of Lightwave Technology, vol. 27, no. 12, pp. 2027–2034, Jun.2009.126[90] H. Jayatilleka, K. Murray, M. Caverley, N. A. F. Jaeger, L. Chrostowski,and S. Shekhar, “Crosstalk in SOI microring resonator-based filters,”Journal of Lightwave Technology, vol. PP, no. 99, pp. 1–1, Sep. 2015.[91] V. Tandon, M. Volanthen, M. van der Vliet, and J. Bonar, “Standardizedparameters for AWGs would ease system design,” Lightwave Online, 2001.[92] D. Minoli, Telecommunications Technology Handbook. Norwood: ArtechHouse, Inc., 2003.[93] ITU Telecommunication Standardization Sector, “Recommendation ITU-TG.671, Transmission characteristics of optical components andsubsystems,” 2012.[94] ITU Telecommunication Standardization Sector., “Recommendation ITU-TG.692, Optical interfaces for multichannel systems with optical amplifiers,”1998.[95] “APSS Apollo Application Note on Array Waveguide Grating (AWG),”[Online]. Available:http://www.apollophoton.com/apollo/APNT/APN-APSS-AWG.pdf,Apollo Photonics, Inc. 2003., (Jan. 15, 2016).[96] R. Boeck, J. Flueckiger, L. Chrostowski, and N. A. F. Jaeger,“Experimental performance of DWDM quadruple Vernier racetrackresonators,” Optics Express, vol. 21, no. 7, pp. 9103–9112, Apr. 2013.[97] R. Boeck, W. Shi, L. Chrostowski, and N. A. F. Jaeger, “FSR-eliminatedVernier racetrack resonators using grating-assisted couplers,” IEEEPhotonics Journal, vol. 5, no. 5, p. 2202511, Oct. 2013.[98] Alliance Fiber Optic Products, Inc., “DWDM and CWDM three port deviceoptical parameter definition and test requirements,” REV. C, Feb. 24 2005.[99] Photonics-USA, “Optical Add/Drop Multiplexers 100 GHz OADM (1x2),”(Jan. 15, 2016).[100] Alliance Fiber Optic Products, Inc., “Single Channel DWDM (100 GHz),”REV. G, Mar. 4 2009.[101] AOXC Technologies, “Fiber Optic DWDM Single Add/Drop Device,”DWDM-100/200-N1.[102] AC Photonics, Inc., “100GHz single channel OADM(2x2),” Apr. 11, 2005.127[103] B. Collings, F. Heismann, and G. Lietaert, “Reference Guide to Fiber OpticTesting: Volume 2,” JDS Uniphase Corporation, 2010.[104] ITU Telecommunication Standardization Sector, “ITU-T RecommendationG.680, Physical transfer functions of optical network elements,” 2007.[105] R. Boeck, M. Caverley, L. Chrostowski, and N. A. F. Jaeger, “Experimentaldemonstration of a silicon-on-insulator high-performance double microringfilter using MZI-based coupling,” Optics Letters, vol. 40, no. 2, pp.276–279, Jan. 2015.[106] K. Bergman, L. P. Carloni, A. Biberman, J. Chan, and G. Hendry, PhotonicNetwork-on-Chip Design. Springer, 2014.[107] R. Boeck, “Silicon ring resonator add-drop multiplexers,” Master’s thesis,University of British Columbia, Oct. 2011.[108] M. Popovic´, T. Barwicz, M. R. Watts, P. T. Rakich, L. Socci, E. P. Ippen,F. X. Ka¨rtner, and H. I. Smith, “Multistage high-order microring-resonatorfilters with relaxed tolerances for high through-port extinction,” in CLEO:2005. Optical Society of America, 2005, p. CMP2.[109] M. A. Popovı´c, T. Barwicz, M. R. Watts, P. T. Rakich, L. Socci, E. P. Ippen,F. X. Ka¨rtner, and H. I. Smith, “Multistage high-order microring-resonatoradd-drop filters,” Optics Letters, vol. 31, no. 17, pp. 2571–2573, Sep. 2006.[110] ITU Telecommunication Standardization Sector, “ITU-T RecommendationG.694.1, Spectral grids for WDM applications: DWDM frequency grid,”Feb. 2012.[111] R. Boeck, J. Flueckiger, H. Yun, L. Chrostowski, and N. A. F. Jaeger,“High performance Vernier racetrack resonators,” Optics Letters, vol. 37,no. 24, pp. 5199–5201, Dec. 2012.[112] M. Popovic´, “Theory and design of high-index-contrast microphotoniccircuits,” PhD thesis, Massachusetts Institute of Technology, Feb. 2008.[113] M. Romagnoli, L. Socci, L. Bolla, S. Ghidini, P. Galli, C. Rampinini,G. Mutinati, A. Nottola, A. Cabas, S. Doneda, M. Di Muri, R. Morson,T. Tomasi, G. Zuliani, S. Lorenzotti, D. Chacon, S. Marinoni, R. Corsini,F. Giacometti, S. Sardo, M. Gentili, and G. Grasso, “Silicon photonics inPirelli,” Proc. SPIE, vol. 6996, p. 699611, 2008.128[114] L. Socci, S. Ghidini, P. Galli, L. Bolla, and F. Boffi, “Method anddevice.for tunable optical filtering using Vernier effect,” European UnionPatent EP 2 181 348 B1, Jan. 18, 2012.[115] M. A. Popovic´, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T.Rakich, H. I. Smith, E. P. Ippen, and F. X. Ka¨rtner, “Tunable, fourth-ordersilicon microring-resonator add-drop filters,” 33rd European Conferenceand Exhibition of Optical Communication (ECOC), pp. 1–2, 2007.[116] C. Ferrari, A. Canciamilla, F. Morichetti, M. Sorel, and A. Melloni,“Penalty-free transmission in a silicon coupled resonator optical waveguideover the full C-band,” Optics Letters, vol. 36, no. 19, pp. 3948–3950, Sep.2011.[117] P. Chen, S. Chen, X. Guan, Y. Shi, and D. Dai, “High-order microringresonators with bent couplers for a box-like filter response,” Optics Letters,vol. 39, no. 21, pp. 6304–6307, Oct. 2014.[118] F. Xia, L. Sekaric, M. O’Boyle, and Y. Vlasov, “Coupled resonator opticalwaveguides based on silicon-on-insulator photonic wires,” Applied PhysicsLetters, vol. 89, no. 4, p. 041122, Jul. 2006.[119] J. R. Ong, R. Kumar, and S. Mookherjea, “Ultra-high-contrast andtunable-bandwidth filter using cascaded high-order silicon microringfilters,” IEEE Photonics Technology Letters, vol. 25, no. 16, pp.1543–1546, Aug. 2013.[120] F. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, “Ultra-compact silicon WDMoptical filters with flat-top response for on-chip optical interconnects,”2007 Conference on Lasers and Electro-Optics, p. CTuG3, May 2007.[121] S. H. Tao, J. Song, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “50thorder series-coupled micro-ring resonator,” PhotonicsGlobal@Singapore,pp. 1–3, Dec. 2008.[122] Q. Li, M. Soltani, S. Yegnanarayanan, and A. Adibi, “Design anddemonstration of compact, wide bandwidth coupled-resonator filters on asilicon-on-insulator platform,” Optics Express, vol. 17, no. 4, pp.2247–2254, Apr. 2009.[123] A. Rohit, R. Stabile, and K. A. Williams, “Dynamic routing in a fifth-orderring resonator switch array,” 2012 38th European Conference andExhibition on Optical Communications (ECOC), p. Tu.1.E.1, Sep. 2012.129[124] P. Prabhathan, V. M. Murukeshan, and J. Zhang, “Optimal detuningcombinations in a series coupled silicon micro ring resonator thermooptic-wavelength selective switch,” Optical Engineering, vol. 51, no. 4, p.044604, Apr. 2012.[125] M. L. Cooper, G. Gupta, M. A. Schneider, W. M. J. Green, S. Assefa,F. Xia, Y. A. Vlasov, and S. Mookherjea, “Statistics of light transport in235-ring silicon coupled-resonator optical waveguides,” Optics Express,vol. 18, no. 25, pp. 26 505–26 516, Dec. 2010.[126] O. Schwelb and I. Frigyes, “Vernier operation of series-coupled opticalmicroring resonator filters,”Microwave Optical Technology Letters,vol. 39, no. 4, pp. 257–261, Nov. 2003.[127] O. Schwelb, “The nature of spurious mode suppression in extended FSRmicroring multiplexers,” Optics Communications, vol. 271, no. 2, pp.424–429, Mar. 2007.[128] C. Chaichuay, P. P. Yupapin, and P. Saeung, “The serially coupled multiplering resonator filters and Vernier effect,” Optica Applicata, vol. 39, no. 1,pp. 175–194, 2009.[129] R. Boeck, N. A. F. Jaeger, N. Rouger, and L. Chrostowski, “Series-coupledsilicon racetrack resonators and the Vernier effect: theory andmeasurement,” Optics Express, vol. 18, no. 24, pp. 25 151–25 157, Nov.2010.[130] S. Srinivasan, M. Davenport, T. Komljenovic, J. Hulme, D. T. Spencer, andJ. E. Bowers, “Coupled-ring-resonator-mirror-based heterogeneous III-Vsilicon tunable laser,” IEEE Photonics Journal, vol. 7, no. 3, p. 2700908,Jun. 2015.[131] T. Claes, W. Bogaerts, and P. Bienstman, “Experimental characterization ofa silicon photonic biosensor consisting of two cascaded ring resonatorsbased on the Vernier-effect and introduction of a curve fitting method foran improved detection limit,” Optics Express, vol. 18, no. 22, pp.22 747–22 761, Oct. 2010.[132] J. A. Thorsveen and K. Blotekjaer, “High-resolution fringe-counting sensorutilizing the Vernier effect,” Proc. SPIE, vol. 3483, pp. 169–173, 1998.[133] Y. Yanagase, S. Suzuki, Y. Kokubun, and S. T. Chu, “Vertical tripleseries-coupled microring resonator filter for passband flattening and130expansion of free spectral range,” Japanese Journal of Applied Physics,vol. 41, no. 2A, pp. L141–L143, Feb. 2002.[134] S. T. Chu, B. E. Little, V. Van, J. V. Hryniewicz, P. P. Absil, F. G. Johnson,D. Gill, O. King, F. Seiferth, M. Trakalo, and J. Shanton, “Compact fullC-band tunable filters for 50 GHz channel spacing based on high ordermicro-ring resonators,” Optical Fiber Communication Conference, p. PD9,2004.[135] L. Zhu, M. Li, J. Ye, and J.-J. He, “Highly-sensitive optical waveguidesensor based on SiON using two cascaded-microring resonators,” in 2012Asia Communications and Photonics Conference (ACP), Nov. 2012, pp.1–3.[136] S. A. Miller, Y. Okawachi, S. Ramelow, K. Luke, A. Dutt, A. Farsi, A. L.Gaeta, and M. Lipson, “Tunable frequency combs based on dual microringresonators,” Optics Express, vol. 23, no. 16, pp. 21 527–21 540, Aug. 2015.[137] B. Timotijevic, G. Mashanovich, A. Michaeli, O. Cohen, V. M. N. Passaro,J. Crnjanski, and G. T. Reed, “Tailoring the spectral response of add/dropsingle and multiple resonators in silicon-on-insulator,” Chinese OpticsLetters, vol. 7, no. 4, pp. 291–295, Apr. 2009.[138] M. Popovic´, “Wide free-spectral-range, widely tunable andhitless-switchable optical channel add-drop filters,” U.S. PatentUS8 032 027 B2, Oct. 4, 2011.[139] K. Vahala, Optical Microcavities. Singapore: World Scientific PublishingCo. Pte. Ltd., 2004.[140] Y. Kokubun and T. Kato, “Series-coupled and parallel-coupled add/dropfilters and FSR extension,” in Photonic Microresonator Research andApplications, ser. Springer Series in Optical Sciences, I. Chremmos,O. Schwelb, and N. Uzunoglu, Eds. Springer US, 2010, no. 156, pp.87–113.[141] A. Sayarath, “Silicon microring resonator-based devices forwavelength-division-multiplexing optical communications,” Master’sthesis, The Hong Kong University of Science and Technology, Dec. 2011.[142] D. Zhang, Y. Huang, X. Ren, X. Duan, B. Shen, Q. Wang, X. Zhang, andS. Cai, “Add-drop filters based on asymmetric high-order microringresonators,” Proc. SPIE, vol. 8555, p. 85550U, 2012.131[143] Y. Goebuchi, T. Kato, and Y. Kokubun, “Optimum arrangement ofhigh-order series-coupled microring resonator for crosstalk reduction,”Japanese Journal of Applied Physics, vol. 45, no. 7, pp. 5769–5774, Jul.2006.[144] S. Dey and S. Mandal, “Modeling and analysis of quadruple optical ringresonator performance as optical filter using Vernier principle,” OpticsCommunications, vol. 285, no. 4, pp. 439–446, Feb. 2012.[145] I. Bhar, T. Jha, P. Priya, and S. Dey, “Design and simulation of integratedoptic ring resonator based devices,” 2012 International Conference onCommunications, Devices and Intelligent Systems (CODIS), pp. 453–456,2012.[146] S. Ghosh, T. Bandyopadhyay, S. Ghosh, A. Bondyopadhyay, and S. Dey,“Comparartive analysis of quadruple optical ring resonator based filterusing SOI waveguides,” 2012 National Conference on Computing andCommunication Systems (NCCCS), pp. 1–5, 2012.[147] S. B. Dey, S. Mandal, and N. N. Jana, “Optical signal processing usinglinear system theory,” 2nd International Conference on Power, Control andEmbedded Systems (ICPCES), pp. 1–6, 2012.[148] S. B. Dey, S. Mandal, and N. N. Jana, “Quadruple optical ring resonatorbased filter on silicon-on-insulator,” Optik, vol. 124, no. 17, pp.2920–2927, Sep. 2013.[149] R. Boeck, L. Chrostowski, and N. A. F. Jaeger, “Thermally tunablequadruple Vernier racetrack resonators,” Optics Letters, vol. 38, no. 14, pp.2440–2442, Jul. 2013.[150] R. Boeck, M. Caverley, L. Chrostowski, and N. A. F. Jaeger, “Siliconquadruple series-coupled Vernier racetrack resonators: experimental signalquality,” in Optical Fiber Communication Conference. Optical Society ofAmerica, 2015, p. W2A.8.[151] I. P. Kaminow, P. P. Iannone, J. Stone, and L. W. Stulz, “FDM-FSK starnetwork with a tunable optical filter demultiplexer,” Electronics Letters,vol. 23, no. 21, pp. 1102–1103, Oct. 1987.[152] P. Urquhart, “Compound optical-fiber-based resonators,” Journal of theOptical Society of America A, vol. 5, no. 6, pp. 803–812, Jun. 1988.132[153] I. P. Kaminow, P. P. Iannone, J. Stone, and L. W. Stulz, “FDMA-FSK starnetwork with a tunable optical filter demultiplexer,” Journal of LightwaveTechnology, vol. 6, no. 9, pp. 1406–1414, Sep. 1988.[154] P. Barnsley, P. Urquhart, C. Millar, and M. Brierley, “Fiber Fox-Smithresonators: application to single-longitudinal-mode operation of fiberlasers,” Journal of the Optical Society of America A, vol. 5, no. 8, pp.1339–1346, Aug. 1988.[155] I. P. Kaminow, P. P. Iannone, J. Stone, and L. W. Stulz, “A tunable Vernierfiber Fabry-Perot filter for FDM demultiplexing and detection,” IEEEPhotonics Technology Letters, vol. 1, no. 1, pp. 24–26, Jan. 1989.[156] A. Frenkel and C. Lin, “Angle-tuned etalon filters for optical channelselection in high density wavelength division multiplexed systems,”Journal of Lightwave Technology, vol. 7, no. 4, pp. 615–624, Apr. 1989.[157] K. Oda, N. Takato, and H. Toba, “A wide-FSR waveguide double-ringresonator for optical FDM transmission systems,” Journal of LightwaveTechnology, vol. 9, no. 6, pp. 728–736, Jun. 1991.[158] Y. H. Ja, “A Vernier fiber double-ring resonator with a 3*3 fiber couplerand degenerate two-wave mixing,” IEEE Photonics Technology Letters,vol. 4, no. 7, pp. 743–745, Jul. 1992.[159] H. Okamura and K. Iwatsuki, “Proposal of ultra-high finesse, bi-directionalVernier based on Er-doped fiber ring resonator,” in Optical Fiber Sensors,ser. Collected Papers of the International Conferences on Optical FiberSensors 1983-1997. Optical Society of America, Jan. 1992, p. TH35.[160] Y. H. Ja, “Vernier fiber double-ring resonator using degenerate two-wavemixing,” Microwave and Optical Technology Letters, vol. 5, no. 4, pp.181–183, Apr. 1992.[161] Y. H. Ja, “A Vernier S-shaped fiber double-loop resonator with doublecouplers and degenerate two-wave mixing,” Journal of LightwaveTechnology, vol. 11, no. 2, pp. 258–264, Feb. 1993.[162] G. Barbarossa, M. N. Armenise, and A. M. Matteo, “Novel architecture forwide free-spectral range optical resonator for frequency divisionmultiplexing transmission systems,” Proc. SPIE, vol. 2150, pp. 211–219,1994.133[163] J. Zhang and J. W. Y. Lit, “All-fiber compound ring resonator with a ringfilter,” Journal of Lightwave Technology, vol. 12, no. 7, pp. 1256–1262, Jul.1994.[164] J. Capmany, “Amplified double recirculating delay line using a 3x3coupler,” Journal of Lightwave Technology, vol. 12, no. 7, pp. 1136–1143,Jul. 1994.[165] K. Oda, S. Suzuki, H. Takahashi, and H. Toba, “An optical FDMdistribution experiment using a high finesse waveguide-type double ringresonator,” IEEE Photonics Technology Letters, vol. 6, no. 8, pp.1031–1034, Aug. 1994.[166] Y. H. Ja, “Optical vernier filter with two single 3x3 planar coupler fiber ringresonators in tandem,” Applied optics, vol. 33, no. 27, pp. 6409–6411, Sep.1994.[167] S. Suzuki, K. Oda, and Y. Hibino, “Integrated-optic double-ring resonatorswith a wide free spectral range of 100 GHz,” Journal of LightwaveTechnology, vol. 13, no. 8, pp. 1766–1771, Aug. 1995.[168] Y. H. Ja, “Optical vernier filter with fiber grating Fabry-Perot resonators,”Applied Optics, vol. 34, no. 27, pp. 6164–6167, Sep. 1995.[169] G. Barbarossa, A. M. Matteo, and M. N. Armenise, “Theoretical analysisof triple-coupler ring-based optical guided-wave resonator,” Journal ofLightwave Technology, vol. 13, no. 2, pp. 148–157, Feb. 1995.[170] S. Shimada, Coherent Lightwave Communications Technology.Springer-Science+Business Media, B.V., 1995.[171] W. Weiershausen and R. Zengerle, “Photonic highway switches based onring resonators used as frequency-selective components,” Applied Optics,vol. 35, no. 30, pp. 5967–5978, Oct. 1996.[172] J. Zhang, C.-Y. Yue, G. Schinn, W. R. L. Clements, and J. W. Y. Lit,“Stable single-mode compound-ring erbium-doped fiber laser,” Journal ofLightwave Technology, vol. 14, no. 1, pp. 104–109, Jan. 1996.[173] J. Martin and J. Capmany, “Transfer functions of double- andmultiple-cavity Fabry-Perot filters driven by Lorentzian sources,” AppliedOptics, vol. 35, no. 36, pp. 7108–7111, Dec. 1996.134[174] Y. Zhao and C. Shu, “Multi-wavelength lasing oscillation of a Vernier-typeunidirectional Er3+-doped fiber compound ring,” Applied Physics Letters,vol. 70, no. 25, pp. 3344–3346, Jun. 1997.[175] G. Barbarossa and A. M. Matteo, “Novel double-ring optical-guided-waveVernier resonator,” IEE Proceedings - Optoelectronics, vol. 144, no. 4, pp.203–208, Aug. 1997.[176] K. Blotekjaer, “Theoretical concepts of a novel Vernier-basedfringe-counting fibre optic sensor,” IEE Proceedings - Optoelectronics, vol.144, no. 3, pp. 126–129, Jun. 1997.[177] O. Schwelb, “Generalized analysis for a class of linear interferometricnetworks. part II: simulations,” IEEE Transactions on Microwave Theoryand Techniques, vol. 46, no. 10, pp. 1409–1418, Oct. 1998.[178] H. A. Haus, “Microwaves and photonics,” in Symposium on Electro-Optics:Present and Future, ser. OSA Trends in Optics and Photonics, T. Li, Ed.,vol. 23. Optical Society of America, Apr. 1998, p. CB1.[179] C.-C. Lee, Y.-K. Chen, and S.-K. Liaw, “Single-longitudinal-mode fiberlaser with a passive multiple-ring cavity and its application for videotransmission,” Optics Letters, vol. 23, no. 5, pp. 358–360, Mar. 1998.[180] S.-T. Chu, B. E. Little, W. Pan, T. Kaneko, and Y. Kokubun, “Cascadedmicroring resonators for crosstalk reduction and spectrum cleanup inadd-drop filters,” IEEE Photonics Technology Letters, vol. 11, no. 11, pp.1423–1425, Nov. 1999.[181] G. Lenz and C. K. Madsen, “General optical all-pass filter structures fordispersion control in WDM systems,” Journal of Lightwave Technology,vol. 17, no. 7, pp. 1248–1254, Jul. 1999.[182] M. Sorel, S. Gluck, and P. J. R. Laybourn, “Semiconductor double ringwaveguide resonators,” Electronics Letters, vol. 35, no. 18, pp. 1551–1552,Sep. 1999.[183] B. Ortega, J. Capmany, and J. L. Cruz, “Wavelength division multiplexingall-fiber hybrid devices based on Fabry-Perot’s and gratings,” Journal ofLightwave Technology, vol. 17, no. 7, pp. 1241–1247, Jul. 1999.[184] Z. Hu, L. Zheng, Y. Zhang, and Q. Tang, “Composite cavity semiconductorfiber ring laser,” Optics Letters, vol. 25, no. 7, pp. 469–471, Apr. 2000.135[185] I. Ribet, A. Godard, C. Ventalon, C. Simonneau, E. Rosencher, andM. Lefebvre, “Pulsed single-mode doubly resonant optical parametricoscillator based on the Vernier effect,” in 2000 Conference on Lasers andElectro-Optics Europe. Conference Digest, Sep. 2000, p. CThH4.[186] Y. Yanagase, S. Suzuki, Y. Kokubun, and S.-T. Chu, “Box-like filterresponse by vertically series coupled microring resonator filter,” in 27thEuropean Conference on Optical Communication, 2001. ECOC ’01, vol. 4,2001, pp. 634–635.[187] O. Schwelb, “Interferometric circuits: analysis, configurations,applications,” Proc. SPIE, vol. 4417, pp. 131–141, 2001.[188] D. H. Geuzebroek, E. J. Klein, H. Kelderman, F. S. Tan, D. J. W. Klunder,and A. Driessen, “Thermally tuneable, wide FSR switch based onmicro-ring resonators,” Proc. Symp. IEEE/LEOS Benelux Chapter, pp.155–158, 2002.[189] I. S. Hidayat, Y. Toyota, O. Torigoe, O. Wada, and R. Koga, “Application oftransfer matrix method with signal flow-chart to analyze optical multi-pathring-resonator,”Memoirs of the Faculty of Engineering, OkayamaUniversity, vol. 36, no. 2, pp. 73–82, Mar. 2002.[190] Y. Yanagase, S. Suzuki, Y. Kokubun, and S. T. Chu, “Box-like filterresponse and expansion of FSR by a vertically triple coupled microringresonator filter,” Journal of Lightwave Technology, vol. 20, no. 8, pp.1525–1529, Aug. 2002.[191] F. Rana, C. Manolatou, and R. J. Ram, “Microring resonator based widelytunable semiconductor lasers,” in Integrated Photonics Research, ser. OSATrends in Optics and Photonics, A. Sawchuk, Ed., vol. 78. OpticalSociety of America, Jul. 2002, p. IFH3.[192] Y. Meng, Z. Huang, and L. Wang, “Multifunction double-ring resonantoptical comb filter,” Proc. SPIE, vol. 4906, pp. 81–89, 2002.[193] S. T. Chu, T. Kaneko, Y. Kokubun, B. E. Little, W. Pan, and S. Sato,“Optical waveguide wavelength filter with ring resonator and 1xN opticalwaveguide wavelength filter,” European Patent Application EP1 176 438A1, Jan. 30, 2002.[194] B. Liu, A. Shakouri, and J. E. Bowers, “Wide tunable double ring resonatorcoupled lasers,” IEEE Photonics Technology Letters, vol. 14, no. 5, pp.600–602, May 2002.136[195] D. G. Rabus, “Realization of optical filters using ring resonators withintegrated semiconductor optical amplifiers in GaInAsP / InP,” Ph.D.dissertation, Technical University Berlin, 2002.[196] L. R. Dalton, B. H. Robinson, R. Nielsen, A. K. Jen, D. Casmier, P. Rabiei,and W. H. Steier, “Organic electro-optics: exploiting the best of electronicsand photonics,” Proc. SPIE, vol. 4991, pp. 508–519, 2003.[197] Y. Kokubun, “Three-dimensional integration of vertically coupledmicroring resonator filters: fabrication and wavelength trimmingtechnologies,” Proc. SPIE, vol. 4944, pp. 1–14, 2003.[198] O. Schwelb and I. Frigyes, “A design for a high finesse parallel-coupledmicroring resonator filter,”Microwave and Optical Technology Letters,vol. 38, no. 2, pp. 125–129, Jul. 2003.[199] B. Little, “Advances in microring resonators,” in Integrated PhotonicsResearch, ser. OSA Trends in Optics and Photonics, A. Sawchuk, Ed.,vol. 91. Optical Society of America, Jun. 2003, p. ITuE6.[200] W. H. Steier, H.-C. Song, Y.-H. Kuo, P. Rabiei, S.-W. Ahn, M.-C. Oh, H. R.Fetterman, C. Zhang, L. R. Dalton, and A. K. Y. Jen, “Advances in polymerwaveguide devices,” in The 16th Annual Meeting of the IEEE Lasers andElectro-Optics Society, 2003. LEOS 2003, vol. 2, Oct. 2003, pp. 748–749.[201] P. Rabiei and W. H. Steier, “Tunable double micro-ring (DMR) filters forwidely tunable lasers,” 11th European Conference on Integrated Optics, p.FrB3.1, 2003.[202] I. S. Hidayat, Y. Toyota, O. Torigoe, O. Wada, and R. Koga, “Multipathstructure for FSR expansion in waveguide-based optical ring resonator,”Electronics Letters, vol. 39, no. 4, pp. 366–367, Feb. 2003.[203] P. Rabiei and W. H. Steier, “Tunable polymer double micro-ring filters,”IEEE Photonics Technology Letters, vol. 15, no. 9, pp. 1255–1257, Sep.2003.[204] L. Bach, J. P. Reithmaier, A. Forchel, J.-L. Gentner, and L. Goldstein,“Wavelength stabilized single-mode lasers by coupled micro-squareresonators,” IEEE Photonics Technology Letters, vol. 15, no. 3, pp.377–379, Mar. 2003.137[205] S.-J. Choi, Z. Peng, Q. Yang, S.-J. Choi, and P. D. Dapkus, “All-buriedactive microring resonators using vernier effects for free spectral rangeexpansion and optical channel configuration,” in 2004 Digest of the LEOSSummer Topical Meetings Biophotonics/Optical Interconnects and VLSIPhotonics/WBM Microcavities, Jun. 2004, p. 2.[206] B. Liu and A. Shakouri, “Narrow linewidth, low frequency chirping andbroad wavelength tunable ring resonator coupled lasers,” U.S. PatentUS6 680 962 B2, Jan. 20, 2004.[207] J. K. S. Poon, J. Scheuer, and A. Yariv, “Wavelength-selective reflectorbased on a circular array of coupled microring resonators,” IEEE PhotonicsTechnology Letters, vol. 16, no. 5, pp. 1331–1333, May 2004.[208] S. Srivastava and K. Srinivasan, “Signal flow graphs in the analysis anddesign of fiber optical resonating structures,” 2004.[209] L. Binh, “A Venier double ring shape-8 optically amplified resonator,”Department of Electrical and Computer Systems Engineering TechnicalReport MECSE-33-2004, 2004.[210] S. T. Chu, B. E. Little, J. V. Hryniewicz, F. G. Johnson, O. King, D. Gill,W. Chen, and W. Chen, “High index contrast photonics platform,” Proc.SPIE, vol. 6014, p. 60140E, 2005.[211] S.-J. Choi, Z. Peng, Q. Yang, E. H. Hwang, and P. D. Dapkus, “Asemiconductor tunable laser using a wavelength selective reflector based onring resonators,” in Optical Fiber Communication Conference andExposition and The National Fiber Optic Engineers Conference, ser.Technical Digest (CD). Optical Society of America, Mar. 2005, p. PDP20.[212] Y. Goebuchi, T. Kato, and Y. Kokubun, “Expansion of tuning range ofwavelength selective switch using Vernier effect of series coupledmicroring resonator,” The 18th Annual Meeting of the IEEE Lasers andElectro-Optics Society (LEOS), pp. 734–735, 2005.[213] A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki,“High-order tunable filters based on a chain of coupled crystallinewhispering gallery-mode resonators,” IEEE Photonics Technology Letters,vol. 17, no. 1, pp. 136–138, Jan. 2005.[214] S. June, Choi, P. D. Dapkus, Q. Yang, Z. Peng, S.-J. Choi, and E. H.Hwang, “High-Q buried heterostructure resonators for photonic integrated138circuits,” in Conference on Lasers and Electro-Optics, 2005. (CLEO),vol. 1, May 2005, pp. 553–555.[215] A. Driessen, R. Dekker, M. B. J. Diemeer, D. H. Geuzebroek, H. J. W. M.Hoekstra, E. J. Klein, and A. Leinse, “Microresonators as promisingbuilding blocks for VLSI photonics,” Proc. SPIE, vol. 5956, p. 59560Q,2005.[216] S. J. Choi, Z. Peng, Q. Yang, S. J. Choi, and P. D. Dapkus, “Tunable narrowlinewidth all-buried heterostructure ring resonator filters using Verniereffects,” IEEE Photonics Technology Letters, vol. 17, no. 1, pp. 106–108,Jan. 2005.[217] T. Barwicz, “Accurate Nanofabrication Techniques forHigh-Index-Contrast Microphotonic Devices,” PhD thesis, MassachusettsInstitute of Technology, 2005.[218] L. Kolodziejski and G. S. Petrich, “Tunable optical add/drop multiplexerwith multi-function optical amplifiers,” U.S. Patent US6 888 973 B2, May3, 2005.[219] Y. Kokubun, “Vertically coupled microring resonator filter for integratedadd/drop node,” IEICE TRANSACTIONS on Electronics, vol. E88-C, no. 3,pp. 349–362, Mar. 2005.[220] G. T. Reed, W. R. Headley, F. Y. Gardes, B. D. Timotijevic, S. P. Chan, andG. Z. Mashanovich, “Characteristics of rib waveguide racetrack resonatorsin SOI,” Proc. SPIE, vol. 6183, p. 61830G, 2006.[221] O. Schwelb, “Phase-matched lossy microring resonator add/dropmultiplexers,” Proc. SPIE, vol. 6343, p. 63433P, 2006.[222] P. Koonath, T. Indukuri, and B. Jalali, “3-D integrated Vernier filters insilicon,” in Integrated Photonics Research andApplications/Nanophotonics, ser. Technical Digest (CD). Optical Societyof America, Apr. 2006, p. IMG1.[223] S. Mandal, K. Dasgupta, T. K. Basak, and S. K. Ghosh, “A generalizedapproach for modeling and analysis of ring-resonator performance asoptical filter,” Optics Communications, vol. 264, no. 1, pp. 97–104, Aug.2006.139[224] Z. Bian, W. J. He, D. G. Rabus, and A. Shakouri, “A wavelength-tunablemonolithically integrated double ring resonator coupled laser,” inConference on Lasers and Electro-Optics, 2006 and 2006 QuantumElectronics and Laser Science Conference. CLEO/QELS 2006, May 2006,pp. 1–2.[225] Y. Goebuchi, T. Kato, and Y. Kokubun, “Fast and stablewavelength-selective switch using double-series coupled dielectricmicroring resonator,” IEEE Photonics Technology Letters, vol. 18, no. 3,pp. 538–540, Feb. 2006.[226] Y. Kokubun, “Integrated microring resonator circuits for large-scale opticalcross-connects,” Proc. SPIE, vol. 6352, p. 635201, 2006.[227] B. D. Timotijevic, G. T. Reed, R. Jones, A. Liu, A. Michaeli, and G. Z.Mashanovich, “Optical filters in silicon-on-insulator: design considerationsfor devices based upon strip and rib waveguides,” Proc. SPIE, vol. 6350, p.63500K, 2006.[228] J. Scheuer, M. Margalit, and D. Bortman-Arbiv, “Integrated optical filtersutilizing resonators,” U.S. Patent US7 065 276 B2, Jun. 20, 2006.[229] M. Margalit, M. Yasin, and M. Orenstein, “Optical filtering device andmethod,” U.S. Patent US7 149 381 B2, Dec. 12, 2006.[230] Y. Chung, D.-G. Kim, and N. Dagli, “Reflection properties of coupled-ringreflectors,” Journal of Lightwave Technology, vol. 24, no. 4, pp.1865–1874, Apr. 2006.[231] M. A. Popovic´, E. P. Ippen, and F. X. Ka¨rtner, “Universally balancedphotonic interferometers,” Optics Letters, vol. 31, no. 18, pp. 2713–2715,Aug. 2006.[232] M. Ishizaka and H. Yamazaki, “Wavelength tunable laser using silicadouble ring resonators,” Electronics and Communications in Japan (PartII: Electronics), vol. 89, no. 3, pp. 34–41, Mar. 2006.[233] B. D. Timotijevic, G. T. Reed, R. Jones, A. Michaeli, A. Liu, and G. Z.Mashanovich, “Small optical filters in silicon-on-insulator,” in 3rd IEEEInternational Conference on Group IV Photonics, 2006, Sept 2006, pp.25–27.140[234] B. D. Timotijevic, D. Thomson, F. Y. Gardes, S. Howe, A. Michaeli, J. V.Crnjanski, V. M. N. Passaro, G. Z. Mashanovich, G. T. Reed, andD. Ikuesan, “Tailoring the response and temperature characteristics ofmultiple serial-coupled resonators in silicon on insulator,” Proc. SPIE, vol.6477, p. 64770B, 2007.[235] O. Schwelb, “An overview of recent developments in microring resonatorbased photonic circuits,”Mikrotalasna revija, vol. 13, no. 2, pp. 26–33,Dec. 2007.[236] Y. Kokubun, “High index contrast optical waveguides and theirapplications to microring filter circuit and wavelength selective switch,”IEICE TRANSACTIONS on Electronics, vol. E90-C, no. 5, pp. 1037–1045,May 2007.[237] D. G. Rabus, Integrated Ring Resonators - The Compendium. BerlinHeidelberg: Springer-Verlag, 2007.[238] O. Schwelb, “Invariant resonance splitting in stand-alone multiringresonators,” in Integrated Photonics and Nanophotonics Research andApplications / Slow and Fast Light, ser. OSA Technical Digest (CD).Optical Society of America, Jul. 2007, p. ITuA5.[239] T. T. Le and L. W. Cahill, “Photonic signal processing using MMIcoupler-based microring resonators,” in The 20th Annual Meeting of theIEEE Lasers and Electro-Optics Society, 2007. LEOS 2007, 2007, pp.395–396.[240] O. Schwelb, “Resonance splitting and its invariance in coupled opticalmicroring resonators,” Proc. SPIE, vol. 6796, p. 67962P, 2007.[241] T. Kakitsuka, S. Matsuo, T. Segawa, and H. Suzuki, “Semiconductortunable lasers based on integrated waveguide filters for wavelength routingapplications,” in Integrated Photonics and Nanophotonics Research andApplications / Slow and Fast Light, ser. OSA Technical Digest (CD).Optical Society of America, Jul. 2007, p. IMA1.[242] Z. Peng, “Coupled multiple micro-resonators design and activesemiconductor micro-resonator fabrication,” PhD thesis, University ofSouthern California, 2007.[243] R. Todt, S. Watanabe, Y. Deki, M. Takahashi, T. Takeuchi, S. Takaesu,T. Miyazaki, M. Horie, H. Yamazaki, and H. Yamazaki, “Widely tunable141resonated-ring-reflector lasers covering C- and L-bands,” in 2007 33rdEuropean Conference and Exhibition of Optical Communication -Post-Deadline Papers (published 2008), Sep. 2007, pp. 1–2.[244] G. Sun, D. S. Moon, and Y. Chung, “Theoretical analysis of feedback highbirefringence fiber loop mirror with dramatically enhanced free spectralrange,” Proc. SPIE, vol. 6781, p. 678131, 2007.[245] T. Segawa, S. Matsuo, T. Kakitsuka, T. Sato, Y. Kondo, and H. Suzuki,“Tunable double-ring-resonator-coupled laser over full C-band with lowtuning current,” in IEEE 19th International Conference on IndiumPhosphide Related Materials, 2007. IPRM ’07, May 2007, pp. 598–601.[246] M. Takahashi, T. Takeuchi, Y. Deki, S. Takaesu, M. Horie, T. Miyazaki,M. Kurihara, S. Watanabe, K. Suzuki, N. Sakuma, A. Kawauchi, andH. Yamazaki, “Tunable lasers based on silica waveguide ring resonators,” inConference on Optical Fiber Communication and the National Fiber OpticEngineers Conference, 2007. OFC/NFOEC 2007, Mar. 2007, pp. 1–3.[247] P. Saeung and P. P. Yupapin, “Vernier effect of multiple-ring resonatorfilters modeling by a graphical approach,” Optical Engineering, vol. 46,no. 7, p. 075005, Jul. 2007.[248] Y. Deki, T. Hatanaka, M. Takahashi, T. Takeuchi, S. Watanabe, S. Takaesu,T. Miyazaki, M. Horie, and H. Yamazaki, “Wide-wavelength tunable laserswith 100 ghz fsr ring resonators,” Electronics Letters, vol. 43, no. 4, pp.225–226, Feb. 2007.[249] H. Lee, G.-W. Kim, J.-O. Park, S.-H. Kim, and Y.-C. Chung, “Widelytunable wavelength-selective reflector using polymer waveguidedouble-ring-resonator add/drop filter and loop-back mirror,” Journal of theOptical Society of Korea, vol. 12, no. 3, pp. 157–161, Sept. 2008.[250] L. Zhang, M. Song, T. Wu, L. Zou, R. G. Beausoleil, and A. E. Willner,“Embedded ring resonators for microphotonic applications,” Optics Letters,vol. 33, no. 17, pp. 1978–1980, Sep. 2008.[251] L. Y. M. Tobing, D. C. S. Lim, P. Dumon, R. Baets, and M.-K. Chin,“Experimental verification of finesse enhancement scheme in two-ringresonator system,” Proc. SPIE, vol. 6996, p. 69960B, 2008.[252] L. Y. M. Tobing, D. C. S. Lim, P. Dumon, R. Baets, and M.-K. Chin,“Finesse enhancement in silicon-on-insulator two-ring resonator system,”Applied Physics Letters, vol. 92, no. 10, p. 101122, Mar. 2008.142[253] J. E. Heebner, R. Grover, and T. Ibrahim, Optical microresonators: theory,fabrication, and applications. Springer, 2008.[254] Y.-W. Choi and D.-G. Kim, “Micro resonator sensor,” U.S. PatentApplication US 2008/0 266 573 A1, Oct. 30, 2008.[255] T. Segawa, S. Matsuo, T. Kakitsuka, Y. Shibata, T. Sato, Y. Kondo, andR. Takahashi, “Monolithically integrated filter-free wavelength converterwith widely tunable double-ring resonator coupled laser,” in 20thInternational Conference on Indium Phosphide and Related Materials,2008. IPRM 2008, May 2008, pp. 1–4.[256] L. Y. M. A. L. Tobing and M.-K. Chin, “Optical buffering scheme based ontwo-ring resonator system,” Proc. SPIE, vol. 6996, p. 69961G, 2008.[257] L. Y. Mario, S. Darmawan, P. Dumon, R. Baets, and M.-K. Chin,“Transmission properties and application of a two-ring one-bus buildingblock,” in 2nd IEEE International Nanoelectronics Conference, 2008.INEC 2008., Mar. 2008, pp. 217–221.[258] J. Park, T. Lee, D. Lee, S. Kim, W. Hwang, and Y. Chung, “Widely tunablecoupled-ring-reflector filter based on planar polymer waveguide,” IEEEPhotonics Technology Letters, vol. 20, no. 12, pp. 988–990, Jun. 2008.[259] T. Chu, N. Fujioka, S. Nakamura, M. Tokushima, and M. Ishizaka,“Compact, low power consumption wavelength tunable laser with siliconphotonic-wire waveguide micro-ring resonators,” in 35th EuropeanConference on Optical Communication, 2009. ECOC ’09, Sep. 2009, pp.1–2.[260] T. Chu, N. Fujioka, and M. Ishizaka, “Compact, lower-power-consumptionwavelength tunable laser fabricated with silicon photonic-wire waveguidemicro-ring resonators,” Optics Express, vol. 17, no. 16, pp. 14 063–14 068,Jul. 2009.[261] T. Segawa, S. Matsuo, T. Kakitsuka, Y. Shibata, T. Sato, Y. Kawaguchi,Y. Kondo, and R. Takahashi, “Dynamic operation of a monolithicwavelength-routing switch using double-ring-resonator-coupled tunablelaser diodes,” in International Conference on Photonics in Switching, 2009.PS ’09, Sep. 2009, pp. 1–2.[262] D. Dai, “Highly sensitive digital optical sensor based on cascaded high-Qring-resonators,” Optics Express, vol. 17, no. 26, pp. 23 817–23 822, Dec.2009.143[263] L. Jin, M. Li, and J.-J. He, “Highly-sensitive optical sensor using twocascaded-microring resonators with Vernier effect,” in 2009 AsiaCommunications and Photonics Conference and Exhibition (ACP), Nov.2009, p. AS4E.2.[264] S. Matsuo and T. Segawa, “Microring-resonator-based widely tunablelasers,” IEEE Journal of Selected Topics in Quantum Electronics, vol. 15,no. 3, pp. 545–554, May 2009.[265] H. Lee, G. Kim, S. Kim, and Y. Chung, “Widely tunable PLC-basedpolymer double-ring-resonator add/drop reflection filter,” in Conference onLasers Electro Optics The Pacific Rim Conference on Lasers andElectro-Optics, 2009. CLEO/PACIFIC RIM ’09., Aug. 2009, pp. 1–2.[266] T. Segawa, S. Matsuo, T. Kakitsuka, T. Sato, Y. Kondo, and R. Takahashi,“Semiconductor double-ring-resonator-coupled tunable laser forwavelength routing,” IEEE Journal of Quantum Electronics, vol. 45, no. 7,pp. 892–899, Jul. 2009.[267] A. Kapsalis, D. Syvridis, M. Hamacher, and H. Heidrich, “Broadly tunablelaser using double-rings vertically coupled to a passive waveguide,” IEEEJournal of Quantum Electronics, vol. 46, no. 3, pp. 306–312, Mar. 2010.[268] T. Chu, N. Fujioka, M. Tokushima, S. Nakamura, and M. Ishizaka, “C andL bands wavelength tunable laser with silicon photonic-wire waveguidemicro-ring resonators,” in Integrated Photonics Research, Silicon andNanophotonics and Photonics in Switching, ser. OSA Technical Digest(CD). Optical Society of America, Jul. 2010, p. IME1.[269] N. Fujioka, T. Chu, and M. Ishizaka, “Compact and low powerconsumption hybrid integrated wavelength tunable laser module usingsilicon waveguide resonators,” Journal of Lightwave Technology, vol. 28,no. 21, pp. 3115–3120, Nov. 2010.[270] R. Boeck, N. A. F. Jaeger, and L. Chrostowski, “Experimentaldemonstration of the Vernier effect using series-coupled racetrackresonators,” 2010 International Conference on Optical MEMS andNanophotonics (OPT MEMS), pp. 1–2, 2010.[271] L. Jin, M. Li, and J.-J. He, “Experimental investigation of waveguidesensor based on cascaded-microring resonators with Vernier effect,” inConference on Lasers and Electro-Optics 2010, ser. OSA Technical Digest(CD). Optical Society of America, May 2010, p. JWA84.144[272] T. Chu, N. Fujioka, M. Tokushima, S. Nakamura, and M. Ishizaka, “Full Cand L bands wavelength tunable laser module with silicon micro-ringresonators,” in 2010 15th OptoElectronics and CommunicationsConference (OECC), July 2010, pp. 866–867.[273] M. Popovic and M. R. Watts, “Hitless tuning and switching of opticalresonator amplitude and phase responses,” U.S. Patent ApplicationUS20 100 209 038 A1, Aug. 19, 2010.[274] T. Okamoto, K. Mizutani, K. Tsuruoka, S. Sudo, M. Sato, K. Kudo,T. Kato, and K. Sato, “Monolithic integration of a 10 Gb/s Mach-Zehndermodulator and a widely tunable laser based on a 2-ring loop-filter,” in 2010International Conference on Indium Phosphide Related Materials (IPRM),May 2010, pp. 1–4.[275] T. Segawa and S. Matsuo, “Monolithically integrated wavelength-routingswitch with double-ring-resonator-coupled tunable lasers,” in IntegratedPhotonics Research, Silicon and Nanophotonics and Photonics inSwitching, ser. OSA Technical Digest (CD). Optical Society of America,Jul. 2010, p. ITuC2.[276] T. Matsumoto, A. Suzuki, M. Takahashi, S. Watanabe, S. Ishii, K. Suzuki,T. Kaneko, H. Yamazaki, and N. Sakuma, “Narrow spectral linewidth fullband tunable laser based on waveguide ring resonators with low powerconsumption,” in Optical Fiber Communication Conference, ser. OSATechnical Digest (CD). Optical Society of America, Mar. 2010, p.OThQ5.[277] K. Lee, S. D. Lim, C. H. Kim, J. H. Lee, Y.-G. Han, and S. B. Lee, “Noisereduction in multiwavelength SOA-based ring laser by coupled dualcavities for WDM applications,” Journal of Lightwave Technology, vol. 28,no. 5, pp. 739–745, Mar. 2010.[278] W. Li and J. Sun, “Optical vernier filter with cascaded double-couplercompound fiber loop resonators,” Optik - International Journal for Lightand Electron Optics, vol. 121, no. 15, pp. 1370–1375, Sep. 2010.[279] K. S. Hyun, “Single mode lasing in MMI coupled square semiconductorring resonators,” in 2010 12th International Conference on TransparentOptical Networks (ICTON), Jun. 2010, pp. 1–4.[280] G. Sun, Y. Zhou, Y. Hu, and Y. Chung, “Theoretical analysis of Sagnacloop mirror with an inline high birefringence fiber ring resonator:145Application in single-frequency fiber lasers,” Optical Fiber Technology,vol. 16, no. 2, pp. 86–89, Mar. 2010.[281] H. Yamazaki, “Tunable laser with multiple ring resonator and mode filter,”European Patent EP1 708 323 B1, Jan. 6, 2010.[282] K. Suzuki and H. Yamazaki, “Tunable resonator, tunable light source usingthe same, and method for tuning wavelength of multiple resonator,” U.S.Patent US7 701 983 B2, Apr. 20, 2010.[283] H. Lee, Y. Lee, G. Kim, S. Kim, and Y. Chung, “Widely tunabledouble-ring resonator add/drop reflection filter based on polymer PLC,”Microwave and Optical Technology Letters, vol. 52, no. 4, pp. 852–855,Apr. 2010.[284] A. Sayarath and A. W. Poon, “Proposed high-speed electro-optical hitlessreconfigurable demultiplexer using feedback-waveguides coupled tomicroring resonators,” The 12th IEEE Photonics Society Hong KongChapter Postgraduate Conference, pp. 1–3, 2011.[285] K. Kasai, M. Nakazawa, and H. Yamazaki, “Absolute frequencystabilization of a laser diode based on triple ring resonators to an C2H2absorption line,” in 17th Microopics Conference (MOC), Oct. 2011, pp.1–2.[286] J. Hu and D. Dai, “Cascaded-ring optical sensor with enhanced sensitivityby using suspended Si-nanowires,” IEEE Photonics Technology Letters,vol. 23, no. 13, pp. 842–844, Jul. 2011.[287] G. Ren, T. Cao, and S. Chen, “Design and analysis of a cascaded microringresonator-based thermo-optical tunable filter with ultralarge free spectrumrange and low power consumption,” Optical Engineering, vol. 50, no. 7, p.074601, Jul. 2011.[288] L. Jin, M. Li, and J.-J. He, “Highly-sensitive silicon-on-insulator sensorbased on two cascaded micro-ring resonators with vernier effect,” OpticsCommunications, vol. 284, no. 1, pp. 156–159, Jan. 2011.[289] L. S. Stewart and P. D. Dapkus, “In-plane thermally tuned silicon oninsulator wavelength selective reflector,” in 2011 IEEE Winter Topicals(WTM), Jan. 2011, pp. 123–124.146[290] M. Mancinelli, R. Guider, P. Bettotti, M. Masi, M. R. Vanacharla, J. Fedeli,D. V. Thourhout, and L. Pavesi, “Optical characterization ofsilicon-on-insulator-based single and coupled racetrack resonators,”Journal of Nanophotonics, vol. 5, no. 1, p. 051705, Jun. 2011.[291] L. Jin, M. Li, and J.-J. He, “Optical waveguide double-ring sensor usingintensity interrogation with a low-cost broadband source,” Optics Letters,vol. 36, no. 7, pp. 1128–1130, Mar. 2011.[292] J.-J. He, L. Jin, and M. Li, “The ‘Lord of the Rings’ of optical biosensors,”SPIE Newsroom, Sep. 2011.[293] T. Claes, W. Bogaerts, and P. Bienstman, “Vernier-cascade silicon photoniclabel-free biosensor with very large sensitivity and low-cost interrogation,”Proc. SPIE, vol. 8099, p. 80990R, 2011.[294] Y. Lee, H. Lee, G. Kim, S. Lee, and Y. Chung, “Widely tunable opticalsource hybrid-integrated with wavelength-selective double-ring-resonatorreflector,” Microwave and Optical Technology Letters, vol. 53, no. 4, pp.924–927, Apr. 2011.[295] Y. Li and A. W. Poon, “Analytical methods of strong-coupled microringcoupled-resonator optical waveguides,” The 12th IEEE Photonics SocietyHong Kong Chapter Postgraduate Conference, pp. 1–2, 2011.[296] V. M. N. Passaro, B. Troia, and F. De Leonardis, “A generalized approachfor design of photonic gas sensors based on Vernier-effect in mid-IR,”Sensors and Actuators B: Chemical, vol. 168, pp. 402–420, Jun. 2012.[297] T. Segawa, T. Sato, R. Iga, S. Matsuo, and R. Takahashi, “A novel tunablelaser with flat-output wideband tuning based on parallel ring resonators,” in2012 International Conference on Photonics in Switching (PS), Sep. 2012,pp. 1–3.[298] L. Jin, M. Li, and J.-J. He, “Analysis of wavelength and intensityinterrogation methods in cascaded double-ring sensors,” Journal ofLightwave Technology, vol. 30, no. 12, pp. 1994–2002, Jun. 2012.[299] C. Sirawattananon, M. Bahadoran, J. Ali, S. Mitatha, and P. P. Yupapin,“Analytical Vernier effects of a PANDA ring resonator for microforcesensing application,” IEEE Transactions on Nanotechnology, vol. 11, no. 4,pp. 707–712, Jul. 2012.147[300] B. Troia, V. M. N. Passaro, F. D. Leonardis, and A. V. Tsarev, “Design ofefficient photonic sensors based on vernier effect in near-IR,” 16thEuropean Conference on Integrated Optics (ECIO 2012), 2012.[301] P. Prabhathan, Z. Jing, V. M. Murukeshan, Z. Huijuan, and C. Shiyi,“Discrete and fine wavelength tunable thermo-optic WSS for low powerconsumption C+L band tunability,” IEEE Photonics Technology Letters,vol. 24, no. 2, pp. 152–154, Jan. 2012.[302] S. B. Dey, S. Mandal, and N. N. Jana, “Enhancement of free spectral rangeusing pentuple microresonator,” Applied Optics, vol. 51, no. 29, pp.6901–6912, Oct. 2012.[303] R. Xu, S. Liu, Q. Sun, P. Lu, and D. Liu, “Experimental characterization ofa Vernier strain sensor using cascaded fiber rings,” IEEE PhotonicsTechnology Letters, vol. 24, no. 23, pp. 2125–2128, Dec. 2012.[304] K. Kulrod, C. Sirawattananon, S. Mitatha, K. Srinuanjan, and P. P. Yupapin,“Force sensing device design using a modified add-drop filter,” ProcediaEngineering, vol. 32, pp. 291–298, Mar. 2012.[305] S. Dey and S. Mandal, “Enhancement of free spectral range in optical triplering resonator: A Vernier principle approach,” 1st International Conferenceon Recent Advances in Information Technology (RAIT), pp. 246–250, 2012.[306] X. Jiang, J. Song, L. Jin, and J.-J. He, “High-sensitivity silicon photonicbiosensors based on cascaded resonators,” Proc. SPIE, vol. 8564, p.85640Y, 2012.[307] J.-J. He, “Intensity interrogated planar waveguide biosensors,” inInternational Photonics and Optoelectronics Meetings, ser. OSA TechnicalDigest (online). Optical Society of America, Nov. 2012, p. IF3B.1.[308] J. Song, L. Wang, L. Jin, X. Xia, Q. Kou, S. Bouchoule, and J.-J. He,“Intensity-interrogated sensor based on cascaded Fabry Perot laser andmicroring resonator,” Journal of Lightwave Technology, vol. 30, no. 17, pp.2901–2906, Sep. 2012.[309] B. Troia, V. M. N. Passaro, and F. D. Leonardis, “Investigation ofwide-FSR SOI optical filters operating in C and L bands,” Telfor Journal,vol. 4, no. 1, pp. 37–42, 2012.148[310] B. Troia, F. D. Leonardis, and V. M. N. Passaro, “Design of integratedphotonic sensor based on Vernier effect for very sensitive chemical surfacesensing,” in Proceedings of the 2012 Annual Symposium of the IEEEPhotonics Society Benelux Chapter, Nov. 2012, pp. 1–4.[311] S. Mandal and S. Dey, “Modeling and analysis of multiple ring resonatorperformance as optical filter,” Proc. SPIE, vol. 8264, p. 82640J, 2012.[312] K. Nemoto, T. Kita, and H. Yamada, “Narrow spectral linewidthwavelength tunable laser with Si photonic-wire waveguide ring resonators,”in 2012 IEEE 9th International Conference on Group IV Photonics (GFP),Aug. 2012, pp. 216–218.[313] J.-J. He, L. Jin, and M. Li, “Optical sensor based on a broadband lightsource and cascaded waveguide filters,” U.S. Patent ApplicationUS2012/0 298 849 A1, Nov. 29, 2012.[314] L. Qin, L. Wang, M. Li, and J.-J. He, “Optical sensor based onVernier-cascade of ring resonator and echelle diffraction grating,” IEEEPhotonics Technology Letters, vol. 24, no. 11, pp. 954–956, Jun. 2012.[315] T. Segawa, W. Kobayashi, S. Matsuo, T. Sato, R. Iga, and R. Takahashi,“Parallel-ring-resonator tunable laser integrated with electroabsorptionmodulator for 100-Gb/s (25-Gb/s x 4) optical packet switching,” inEuropean Conference and Exhibition on Optical Communication, ser. OSATechnical Digest (online). Optical Society of America, Sep. 2012, p.Mo.1.E.1.[316] I. Khan, “Design consideration analysis of optical filters based on multiplering resonator,” International Journal of Electronics & Informatics, vol. 1,no. 1, pp. 8–13, Aug. 2012.[317] W. S. Fegadolli, G. Vargas, X. Wang, F. Valini, L. A. M. Barea, J. E. B.Oliveira, N. Frateschi, A. Scherer, V. R. Almeida, and R. R. Panepucci,“Reconfigurable silicon thermo-optical ring resonator switch based onVernier effect control,” Optics Express, vol. 20, no. 13, pp. 14 722–14 733,Jun. 2012.[318] Y. Lu, C. Hao, B. Lu, X. Huang, B. Wu, and J. Yao, “Transmission andgroup delay in a double microring resonator reflector,” OpticsCommunications, vol. 285, no. 21-22, pp. 4567–4570, Oct. 2012.149[319] R. D. Mansoor, H. Sasse, and A. P. Duffy, “Analysis of optical ringresonator add/drop filters,” Proc. of the 62nd IWCS Conference, pp.471–475, 2013.[320] V. Zamora, P. Lutzow, M. Weiland, and D. Pergande, “A highly sensitiverefractometric sensor based on cascaded SiN microring resonators,”Sensors, vol. 13, no. 11, pp. 14 601–14 610, Oct. 2013.[321] V. Zamora, P. Lutzow, D. Pergande, and H. Heidrich, “Cascaded microringresonators for biomedical applications: improved sensitivity at large tuningrange,” Proc. SPIE, vol. 8570, p. 857002, 2013.[322] X. Jiang, J. Ye, J. Zou, M. Li, and J.-J. He, “Cascaded silicon-on-insulatordouble-ring sensors operating in high-sensitivity transverse-magneticmode,” Optics Letters, vol. 38, no. 8, pp. 1349–1351, Apr. 2013.[323] V. Raghunathan, “Athermal Photonic Devices and Circuits on a SiliconPlatform,” PhD thesis, Massachusetts Institute of Technology, 2013.[324] J. C. Hulme, J. K. Doylend, and J. E. Bowers, “Widely tunable Vernier ringlaser on hybrid silicon,” Optics Express, vol. 21, no. 17, pp. 19 718–19 722,2013.[325] J. Dong, L. Liu, D. Gao, Y. Yu, A. Zheng, T. Yang, and X. Zhang,“Compact notch microwave photonic filters using on-chip integratedmicroring resonators,” IEEE Photonics Journal, vol. 5, no. 2, p. 5500307,Apr. 2013.[326] H. Yan, X. Feng, D. Zhang, K. Cui, F. Liu, and Y. Huang, “Compact opticaladd-drop multiplexers with parent-sub ring resonators on SOI substrates,”IEEE Photonics Technology Letters, vol. 25, no. 15, pp. 1462–1465, Aug.2013.[327] C. Gentry and M. Popovic, “Dark state lasers,” in CLEO: 2013, ser. OSATechnical Digest (online). Optical Society of America, Jun. 2013, p.CM3F.1.[328] R. Dey, J. Doylend, J. Ackert, A. Evans, P. Jessop, and A. Knights,“Demonstration of a wavelength monitor comprised of racetrack-ringresonators with defect mediated photodiodes operating in the C-band,”Optics Express, vol. 21, no. 20, pp. 23 450–23 458, Sep. 2013.150[329] M. Bahadoran, J. Ali, and P. P. Yupapin, “Graphical approach for nonlinearoptical switching by PANDA Vernier filter,” IEEE Photonics TechnologyLetters, vol. 25, no. 15, pp. 1470–1473, Aug. 2013.[330] S. Tan, L. Xiang, J. Zou, Q. Zhang, Z. Wu, Y. Yu, J. Dong, and X. Zhang,“High-order all-optical differential equation solver based on microringresonators,” Optics Letters, vol. 38, no. 19, pp. 3735–3738, Oct. 2013.[331] H. Yan, X. Feng, D. Zhang, and Y. Huang, “Integrated optical add-dropmultiplexer based on a compact parent-sub microring-resonator structure,”Optics Communications, vol. 289, pp. 53–59, Feb. 2013.[332] V. Zamora, P. Lutzow, M. Weiland, and D. Pergande, “Investigation ofcascaded SiN microring resonators at 1.3 µm and 1.5 µm,” Optics Express,vol. 21, no. 23, pp. 27 550–27 557, Nov. 2013.[333] S. Qin, P. Cho, D. H. Park, V. Yun, Y. Leng, P.-T. Ho, J. Goldhar, W. N.Herman, and J. T. Fourkas, “MAP-fabricated acrylic double ring resonators(DRRs) with expanded free spectral range (FSR),” 2013 Conference onLasers and Electro-Optics (CLEO), p. CF2I.3, 2013.[334] T. Kita, K. Nemoto, and H. Yamada, “Narrow spectral linewidth and highoutput power Si photonic wavelength tunable laser diode,” in 2013 IEEE10th International Conference on Group IV Photonics (GFP), Aug. 2013,pp. 152–153.[335] E. H. W. Chan, “Noise investigation of a large free spectral rangehigh-resolution microwave photonic signal processor,” IEEE PhotonicsJournal, vol. 5, no. 6, pp. 5 502 109–5 502 109, 2013.[336] D. Bachman, Z. Chen, R. Fedosejevs, Y. Y. Tsui, and V. Van, “Permanentfine tuning of silicon microring devices by femtosecond laser surfaceamorphization and ablation,” Optics Express, vol. 21, no. 9, pp.11 048–11 056, Apr. 2013.[337] D. Bachman, Z. Chen, R. Fedosejevs, Y. Y. Tsui, and V. Van, “Permanenttuning of high-Q silicon microring resonators by Fs laser surfacemodification,” in 2013 Conference on Lasers and Electro-Optics PacificRim (CLEO-PR), Jun. 2013, pp. TuPM–8.[338] M. H. M. Salleh, A. Glidle, M. Sorel, J. Reboud, and J. M. Cooper,“Polymer dual ring resonators for label-free optical biosensing usingmicrofluidics,” Chemical Communications, vol. 49, no. 30, pp. 3095–3097,Apr. 2013.151[339] Z. Huang and Y. Wang, “Selectable heterogeneous integrated III-V /SOIsingle mode laser based on Vernier effect,” in 2013 Conference on Lasersand Electro-Optics Pacific Rim (CLEO-PR), Jun. 2013, pp. TuPM–3.[340] T. Kita, K. Nemoto, K. Watanabe, H. Yamazaki, and H. Yamada, “Siphotonic wavelength tunable laser diode for digital coherent opticalcommunication,” in 2013 18th OptoElectronics and CommunicationsConference held jointly with 2013 International Conference on Photonicsin Switching (OECC/PS), Jun. 2013, pp. WM1–3.[341] C. Ciminelli, C. E. Campanella, F. Dell’Olio, C. M. Campanella, and M. N.Armenise, “Theoretical investigation on the scale factor of a triple ringcavity to be used in frequency sensitive resonant gyroscopes,” Journal ofthe European Optical Society Rapid Publications, vol. 8, p. 13050, Jul.2013.[342] L. Ding, X. Jiang, C. Yang, and J.-J. He, “Thermally-tuned silicon doublering resonator for external cavity tunable laser,” in PIERS Proceedings,Aug. 2014, pp. 822–825.[343] X. Zhang, L. Zhou, L. Lu, J. Xie, X. Sun, X. Li, and J. Chen, “TunableVernier microring optical filters using p-i-p resistor-based micro-heaters,”Optical Fiber Communication Conference/National Fiber Optic EngineersConference, p. OTu3C.7, 2013.[344] L. Zhou, X. Zhang, L. Lu, and J. Chen, “Tunable Vernier microring opticalfilters with p-i-p-type microheaters,” IEEE Photonics Journal, vol. 5, no. 4,p. 6601211, Aug. 2013.[345] M. La Notte and V. M. N. Passaro, “Ultra high sensitivity chemicalphotonic sensing by Mach-Zehnder interferometer enhancedVernier-effect,” Sensors and Actuators B: Chemical, vol. 176, pp.994–1007, Jan. 2013.[346] “Vernier effect based dual-micro-ring resonator optical biochemical sensingchip,” Patent Application CN103 308 476 A, Sep. 18, 2013. [Online].Available: http://www.google.com/patents/CN103308476A?cl=en[347] S. Chiangga, S. Pitakwongsaporn, T. D. Frank, and P. P. Yupapin, “Opticalbistability investigation in a nonlinear silicon microring circuit,” Journal ofLightwave Technology, vol. 31, no. 7, pp. 1101–1105, Apr. 2013.152[348] P. Bienstman, T. Claes, and W. Bogaerts, “Vernier photonic sensordata-analysis,” U.S. Patent Application US20 130 094 029 A1, Apr. 18,2013.[349] X. Zhang, Z. quan Li, and K. Tong, “A compact cascaded microring filterwith two master rings and two slave rings for sensing application,”Optoelectronics Letters, vol. 10, no. 1, pp. 16–20, Jan. 2014.[350] M. Ren, H. Cai, Y. D. Gu, P. Kropelnicki, A. B. Randles, and A. Q. Liu, “Atunable laser based on nano-opto-mechanical system,” in 2014 IEEE 27thInternational Conference on Micro Electro Mechanical Systems (MEMS),Jan. 2014, pp. 1143–1146.[351] L. Liu, J. Dong, T. Yang, X. Zhang, and D. Gao, “Comparison analysis ofmicrowave photonic filter using SOI microring and microdisk resonators,”Proc. SPIE, vol. 8985, p. 898515, 2014.[352] C. M. Gentry and M. A. Popovic´, “Dark state lasers,” Optics Letters,vol. 39, no. 14, pp. 4136–4139, Jul. 2014.[353] V. D. Ta, R. Chen, and H. Sun, “Flexible microresonators: lasing andsensing,” Proc. SPIE, vol. 8960, p. 89600E, 2014.[354] T. Kita, K. Nemoto, and H. Yamada, “Silicon photonic wavelength-tunablelaser diode with asymmetric Mach-Zehnder interferometer,” IEEE Journalof Selected Topics in Quantum Electronics, vol. 20, no. 4, pp. 344–349, Jul.2014.[355] V. Zamora, P. Lutzow, M. Weiland, D. Pergande, and H. Schroder, “Highlysensitive integrated optical biosensors,” Proc. SPIE, vol. 8933, p. 893307,2014.[356] B. Troia and V. M. N. Passaro, “Investigation of a novelsilicon-on-insulator rib-slot photonic sensor based on the vernier effect andoperating at 3.8 µm,” Journal of the European Optical Society RapidPublications, vol. 9, p. 14005, Jan. 2014.[357] S. Lakra and S. Mandal, “Modeling and performance analysis of verticallycoupled triple microring resonator in the Z domain,” Applied Optics,vol. 53, no. 36, pp. 8381–8388, Dec. 2014.[358] D. Dai and J. E. Bowers, “Silicon-based on-chip multiplexing technologiesand devices for peta-bit optical interconnects,” Nanophotonics, vol. 3, no.4-5, pp. 283–311, Aug. 2014.153[359] K. Sato, N. Kobayashi, M. Namiwaka, K. Yamamoto, T. Kita, H. Yamada,and H. Yamazaki, “High output power and narrow linewidth siliconphotonic hybrid ring-filter external cavity wavelength tunable lasers,” in2014 European Conference on Optical Communication (ECOC), Sept.2014, p. PD.2.3.[360] B. Troia, V. M. N. Passaro, A. Z. Khokhar, M. Nedeljkovic, J. S. Penades,and G. Z. Mashanovich, “Design and fabrication of silicon cascade-coupledring resonators operating in mid infrared,” in 2014 Fotonica AEIT ItalianConference on Photonics Technologies, May 2014, pp. 1–4.[361] H. Debregeas, C. Ferrari, M. A. Cappuzzo, F. Klemens, R. Keller, F. Pardo,C. Bolle, C. Xie, and M. P. Earnshaw, “2kHz Linewidth C-Band TunableLaser by Hybrid Integration of Reflective SOA and SiO2 PLC ExternalCavity,” in 2014 International Semiconductor Laser Conference (ISLC),Sept. 2014, pp. 50–51.[362] G. Fan, Y. Li, C. Hu, L. Lei, D. Zhao, H. Li, Y. Luo, and Z. Zhen, “Modelof Vernier devices in silicon-on-insulator technology,” Infrared Physics &Technology, vol. 65, pp. 83–86, 2014.[363] M. Ren, H. Cai, J. F. Tao, Y. D. Gu, K. Radhakrishnan, Z. C. Yang, D. L.Kwong, and A. Q. Liu, “An integrated tunable laser usingnano-silicon-photonic circuits,” in 2014 IEEE International ElectronDevices Meeting (IEDM), Dec. 2014, pp. 15.6.1–15.6.4.[364] R. Tang, T. Kita, and H. Yamada, “Narrow spectral linewidth Si photonicwavelength tunable laser diode for digital coherent opticalcommunication,” in 2014 International Semiconductor Laser Conference(ISLC), Sept. 2014, pp. 96–97.[365] T. Segawa, W. Kobayashi, T. Nakahara, and R. Takahashi,“Wavelength-Routed Switching for 25-Gbit/s Optical Packets Using aCompact Transmitter Integrating a Parallel-Ring-Resonator Tunable Laserand an InGaAlAs EAM,” IEICE TRANSACTIONS on Electronics, vol.E97-C, no. 7, pp. 719–724, Jul. 2014.[366] T. Kita, R. Tang, and H. Yamada, “Wide-band wavelength tunable laserdiode with Si photonic filter,” in 2014 International Semiconductor LaserConference (ISLC), Sept. 2014, pp. 149–150.154[367] T. Kita, K. Nemoto, and H. Yamada, “Long external cavity Si photonicwavelength tunable laser diode,” Japanese Journal of Applied Physics,vol. 53, no. 4S, p. 04EG04, Jan. 2014.[368] M. La Notte, B. Troia, T. Muciaccia, C. E. Campanella, F. De Leonardis,and V. M. N. Passaro, “Recent advances in gas and chemical detection byVernier effect-based photonic sensors,” Sensors, vol. 14, no. 3, pp.4831–4855, Mar. 2014.[369] J. Xie, L. Zhou, X. Sun, Z. Zou, L. Lu, H. Zhu, X. Li, and J. Chen,“Selective excitation of microring resonances using a pulley-couplingstructure,” Applied Optics, vol. 53, no. 5, pp. 878–884, Feb. 2014.[370] Y. Liu, J.-L. Yu, W.-R. Wang, H.-G. Pan, and E.-Z. Yang, “Singlelongitudinal mode Brillouin fiber laser with cascaded ring Fabry-Perotresonator,” IEEE Photonics Technology Letters, vol. 26, no. 2, pp. 169–172,2014.[371] T. Kita, R. Tang, and H. Yamada, “Compact silicon photonicwavelength-tunable laser diode with ultra-wide wavelength tuning range,”Applied Physics Letters, vol. 106, no. 11, p. 111104, Mar. 2015.[372] S. Mandal and S. Lakra, “Z-domain modeling and analysis of verticallycoupled triple asymmetrical optical micro ring resonator (VCTAOMRR),”Proc. SPIE, vol. 9598, p. 95980F, 2015.[373] M. Sun, L. Wu, X. Xiong, X. Liao, and J.-J. He, “Doublehalf-wave-coupled rectangular ring-FP semiconductor laser with 19-nmquasi-continuous tuning range,” in CLEO: 2015. Optical Society ofAmerica, 2015, p. SF1I.5.[374] A. Ouariach, K. Ghoumid, R. Malek, A. E. Moussati, A. Nougaoui, andT. Gharbi, “Multiband filter at adjustable free spectral range by convolutionof transfer functions according to the Vernier effect,” IET Optoelectronics,Sep. 2015.[375] H. Gevorgyan, K. A. Qubaisi, M. Dahlem, and A. Khilo,“Time-wavelength pulse interleaver on a silicon platform,” in AdvancedPhotonics 2015. Optical Society of America, 2015, p. IM2A.2.[376] M. Bahadoran, A. F. A. Noorden, K. Chaudhary, M. S. Aziz, J. Ali, andP. Yupapin, “Nano force sensing using symmetric double stage microresonator,” Measurement, vol. 58, pp. 215–220, Dec. 2014.155[377] R. Tang, T. Kita, and H. Yamada, “Narrow-spectral-linewidth siliconphotonic wavelength-tunable laser with highly asymmetric Mach-Zehnderinterferometer,” Optics Letters, vol. 40, no. 7, pp. 1504–1507, Apr. 2015.[378] Y. Chen, F. Yu, C. Yang, J. Song, L. Tang, M. Li, and J.-J. He, “Label-freebiosensing using cascaded double-microring resonators integrated withmicrofluidic channels,” Optics Communications, vol. 344, pp. 129–133,Jun. 2015.[379] T.-R. Kim, H.-S. Kim, J. Li, G.-Y. Oh, D.-G. Kim, and Y.-W. Choi,“Ultra-high sensitivity optical biosensor based on Vernier effect intriangular ring resonators (TRRs) with SPR,” Proc. SPIE, vol. 9357, p.93571A, 2015.[380] G. Z. Mashanovich, M. Nedeljkovic, J. Soler Penades, C. J. Mitchell, A. Z.Khokhar, C. J. Littlejohns, S. Stankovic, B. Troia, Y. Wang, S. Reynolds,V. M. N. Passaro, L. Shen, N. Healy, A. C. Peacock, C. Alonso-Ramos,A. Ortega-Monux, G. Wanguemert-Perez, I. Molina-Fernandez, D. J.Rowe, J. S. Wilkinson, P. Cheben, J. J. Ackert, A. P. Knights, D. J.Thomson, and F. Y. Gardes, “Group IV mid-infrared photonics,” Proc.SPIE, vol. 9367, p. 93670Q, 2015.[381] G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li,M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell,S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N.Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T.Reed, “Silicon photonic waveguides and devices for near- and mid-IRapplications,” IEEE Journal of Selected Topics in Quantum Electronics,vol. 21, no. 4, pp. 407–418, Jul. 2015.[382] X. Xiao, X. Li, X. Feng, K. Cui, F. Liu, and Y. Huang, “Eight-channeloptical add-drop multiplexer with cascaded parent-sub microringresonators,” IEEE Photonics Journal, vol. 7, no. 4, p. 7801307, Aug. 2015.[383] X. Gu, D. Zhu, S. Li, Y. Zhao, and S. Pan, “Photonic RF channelizationbased on series-coupled asymmetric double-ring resonator filter,” in 2014IEEE 7th International Conference on Advanced Infocomm Technology(ICAIT), Nov. 2014, pp. 240–244.[384] M. Ren, H. Cai, L. K. Chin, K. Radhakrishnan, Y. Gu, G.-Q. Lo, D. L.Kwong, and A. Q. Liu, “Coupled-ring reflector in an external-cavitytunable laser,” Optica, vol. 2, no. 11, pp. 940–943, Nov. 2015.156[385] C. Errando-Herranz, F. Niklaus, G. Stemme, and K. B. Gylfason,“Low-power microelectromechanically tunable silicon photonic ringresonator add–drop filter,” Optics Letters, vol. 40, no. 15, pp. 3556–3559,Aug. 2015.[386] G. de Valicourt, G. Levaufre, Y. Pointurier, A. Le Liepvre, J.-C. Antona,C. Jany, A. Accard, F. Lelarge, D. Make, and G.-H. Duan, “Directmodulation of hybrid-integrated InP/Si transmitters for short and longreach access network,” Journal of Lightwave Technology, vol. 33, no. 8, pp.1608–1616, Apr. 2015.[387] Y. Li, Q. Li, Y. Liu, T. Baehr-Jones, M. Hochberg, and K. Bergman,“Integrated on-chip C-band optical spectrum analyzer using dual-ringresonators,” in CLEO: 2015. Optical Society of America, 2015, p.SM1I.4.[388] B. Dong, H. Cai, M. Tang, Y. D. Gu, Z. C. Yang, Y. F. Jin, Y. L. Hao, D. L.Kwong, and A. Q. Liu, “NEMS integrated photonic system usingnano-silicon-photonic circuits,” in 2015 Transducers - 2015 18thInternational Conference on Solid-State Sensors, Actuators andMicrosystems (TRANSDUCERS), Jun. 2015, pp. 997–1000.[389] J. C. Hulme, J. K. Doylend, M. J. R. Heck, J. D. Peters, M. L. Davenport,J. T. Bovington, L. A. Coldren, and J. E. Bowers, “Fully integrated hybridsilicon two dimensional beam scanner,” Optics Express, vol. 23, no. 5, pp.5861–5874, Mar. 2015.[390] G.-M. Parsanasab, M. Moshkani, and A. Gharavi, “Femtosecond laserdirect writing of single mode polymer micro ring laser with high stabilityand low pumping threshold,” Optics Express, vol. 23, no. 7, pp.8310–8316, Apr. 2015.[391] R. Bruck, B. Mills, D. J. Thomson, B. Troia, V. M. N. Passaro, G. Z.Mashanovich, G. T. Reed, and O. L. Muskens, “Picosecond opticallyreconfigurable filters exploiting full free spectral range tuning of single ringand Vernier effect resonators,” Optics Express, vol. 23, no. 9, pp.12 468–12 477, May 2015.[392] L. Liu, J. Dong, and X. Zhang, “Chip-integrated all-optical 4-bit Gray codegeneration based on silicon microring resonators,” Optics Express, vol. 23,no. 16, pp. 21 414–21 423, Aug. 2015.157[393] B. Troia, A. Z. Khokhar, M. Nedeljkovic, S. A. Reynolds, Y. Hu, G. Z.Mashanovich, and V. M. N. Passaro, “Design procedure and fabrication ofreproducible silicon Vernier devices for high-performance refractive indexsensing,” Sensors, vol. 15, no. 6, p. 13548, 2015.[394] L. Liu, J. Dong, D. Gao, A. Zheng, and X. Zhang, “On-chip passivethree-port circuit of all-optical ordered-route transmission,” ScientificReports, vol. 5, p. 10190, 2015.[395] T. Baehr-Jones, Y. Liu, R. Ding, and M. J. Hochberg, “Operation andstabilization of mod-mux WDM transmitters based on silicon microrings,”U.S. Patent Application US 2015/0 104 176 A1, Apr. 16, 2015.[396] T. Komljenovic, M. Davenport, S. Srinivasan, J. Hulme, and J. E. Bowers,“Narrow linewidth tunable laser using coupled resonator mirrors,” inOptical Fiber Communication Conference. Optical Society of America,2015, p. W2A.52.[397] S. Dey, “Microring resonator for WDM filter applications,” in 2015International Conference on Industrial Instrumentation and Control(ICIC), May 2015, pp. 133–138.[398] K. R. Oh, “Resonator, variable wavelength optical filter, and variablewavelength laser diode,” U.S. Patent US 9 008 134 B2, Apr. 14, 2015.[399] S. Addya and S. Dey, “Design and analysis of optical filter using seriescoupled racetrack resonator,” in 2015 IEEE 2nd International Conferenceon Recent Trends in Information Systems (ReTIS), Jul. 2015, pp. 76–80.[400] T. Komljenovic and J. Bowers, “Monolithically integrated high-Q rings fornarrow linewidth widely tunable lasers,” IEEE Journal of QuantumElectronics, vol. 51, no. 11, pp. 1–10, Nov. 2015.[401] R. Mansoor and A. Duffy, “Review of progress in optical ring resonatorswith crosstalk modelling in OADMS,” 2015 IWCS Conference, 2015.[402] J. W. Hicks, Jr., “Adscititious resonator,” U.S. Patent US4 676 583 A, Jun.30, 1987.[403] D. R. Huber and J. B. Carroll, “Time domain response of an opticallyfrequency swept Fabry-Perot interferometer,” Applied Optics, vol. 25,no. 14, pp. 2386–2390, Jul. 1986.158[404] K. L. Belsley, J. B. Carroll, L. A. Hess, D. R. Huber, and D. Schmadel,“Optically multiplexed interferometric fiber optic sensor system,” Proc.SPIE, vol. 0566, pp. 257–264, 1986.[405] R. Mock, B. Hillebrands, and R. Sandercock, “Construction andperformance of a Brillouin scattering set-up using a triple-pass tandemFabry-Perot interferometer,” Journal of Physics E: Scientific Instruments,vol. 20, no. 6, p. 656, Jan. 1987.[406] L. W. Bin, “Signal Flow Graph Theory and Its Applications in the Analysisof Optical Ring Resonator,” PhD thesis, Huazhong University of Scienceand Technology, 2009.[407] L. Zhuang, M. Hoekman, W. Beeker, A. Leinse, R. Heideman, P. van Dijk,and C. Roeloffzen, “Novel low-loss waveguide delay lines using Vernierring resonators for on-chip multi-l microwave photonic signal processors,”Laser & Photonics Reviews, vol. 7, no. 6, pp. 994–1002, Nov. 2013.[408] J. T. Kindt and R. C. Bailey, “Biomolecular analysis with microringresonators: applications in multiplexed diagnostics and interactionscreening,” Current Opinion in Chemical Biology, vol. 17, no. 5, pp. 818 –826, Oct. 2013.[409] R. Bruck, B. Mills, B. Troia, D. J. Thomson, F. Y. Gardes, Y. Hu, G. Z.Mashanovich, V. M. N. Passaro, G. T. Reed, and O. L. Muskens,“Device-level characterization of the flow of light in integrated photoniccircuits using ultrafast photomodulation spectroscopy,” Nature Photonics,vol. 9, no. 1, pp. 54–60, Jan. 2015.[410] O. A. Mrayat and M. S. Rasras, “A digital-like on-chip photonics sensor,”in Frontiers in Optics 2015. Optical Society of America, 2015, p.JW2A.78.[411] L. Wu, X. Liao, Z. Hu, and J.-J. He, “Double half-wave-coupledrectangular ring-FP laser with 35 x 100 GHz wavelength tuning,” IEEEPhotonics Technology Letters, vol. 27, no. 10, pp. 1076–1079, May 2015.[412] D. V. Orden, A. Mizrahi, T. Creazzo, and S. B. Krasulick, “Tunablereflectors based on multi-cavity interference,” U.S. Patent Application US2015/0 331 184 A1, Nov. 19, 2015.[413] H. Chandrahalim and X. Fan, “Reconfigurable solid-state dye-dopedpolymer ring resonator lasers,” Scientific Reports, vol. 5, p. 18310, 2015.159[414] Y. Liu, Y. Hsu, C.-W. Hsu, L.-G. Yang, C.-W. Chow, C.-H. Yeh, Y.-C. Lai,and H.-K. Tsang, “Narrow line-width single-longitudinal-mode fiber laserusing silicon-on-insulator based micro-ring-resonator,” Laser PhysicsLetters, vol. 13, no. 2, p. 025102, 2015.[415] E. J. Klein, “Densely integrated microring-resonator based components forfiber-to-the-home applications,” PhD thesis, University of Twente, 2007.[416] X. Jiang, “Silicon nanowire waveguide sensor based on two cascaded ringresonators,” in Asia Communications and Photonics Conference, ser. OSATechnical Digest (online). Optical Society of America, Nov. 2012, p.AS4E.3.[417] B. Troia, A. Z. Khokhar, M. Nedeljkovic, J. S. Penades, V. M. N. Passaro,and G. Z. Mashanovich, “Cascade-coupled racetrack resonators based onthe Vernier effect in the mid-infrared,” Optics Express, vol. 22, no. 20, pp.23 990–24 003, Oct. 2014.[418] J. H. Lee, I. Shubin, J. Yao, J. Bickford, Y. Luo, S. Lin, S. S. Djordjevic,H. D. Thacker, J. E. Cunningham, K. Raj, X. Zheng, and A. V.Krishnamoorthy, “High power and widely tunable Si hybrid external-cavitylaser for power efficient Si photonics WDM links,” Optics Express, vol. 22,no. 7, pp. 7678–7685, Apr. 2014.[419] X. Gu, D. Zhu, Y. Zhao, and S. Pan, “Series-coupled double-ringresonators with asymmetric radii for use in channelizer,” Proc. SPIE, vol.9270, p. 927010, 2014.[420] N. Feng, X. Sun, and D. Zheng, “Tunable optical system with hybridintegrated laser,” U.S. Patent US 8,831,049 B2, Sept. 9, 2014.[421] A. V. Krishnamoorthy, X. Zheng, G. Li, and J. E. Cunningham, “Opticaldevice with reduced thermal tuning energy,” U.S. Patent US 8,768,170 B2,Jul. 1, 2014.[422] H. Tanaka, T. Ishikawa, and T. Machida, “Method for tuningsemiconductor laser,” U.S. Patent US 8,681,826 B2, Mar. 25, 2014.[423] M. Bahadoran, J. Ali, and P. Yupapin, Vernier effect for optical microringresonator. Lap Lambert Academic Publishing GmbH KG, 2013.[424] L. Vivien and L. Pavesi, Handbook of Silicon Photonics. CRC Press,2013.160[425] P. Yupapin and J. Ali, Small Scale Optics. CRC Press, 2013.[426] P. Yupapin, C. Teeka, and J. Ali, Nanoscale Nonlinear PANDA RingResonator. CRC Press, 2012.[427] L. A. Coldren, S. W. Corzine, and M. L. Masanovic, Diode Lasers andPhotonic Integrated Circuits. John Wiley & Sons, Inc., 2012.[428] D. Mahmudin, T. T. Estu, P. Daud, I. D. P. Hermida, G. Sugandi, Y. N.Wijayanto, P. S. Menon, and S. Shaari, “Sensitivity improvement ofmultipath optical ring resonators using silicon-on-insulator technology,” in2015 IEEE Regional Symposium on Micro and Nanoelectronics (RSM),Aug 2015, pp. 1–4.[429] C.-C. Lee, Y. K. Chen, S.-K. Liaw, F. Tsai, C. S. Wang, and Y. K. Tu,“Single-longitudinal-mode fiber laser using passive multiple-ring-cavitytechnique,” Proc. SPIE, vol. 3420, pp. 253–257, 1998.[430] H. Jayatilleka, R. Boeck, K. Murray, J. Flueckiger, L. Chrostowski, N. A. F.Jaeger, and S. Shekhar, “Automatic wavelength tuning of series-coupledVernier racetrack resonators on SOI,” in Optical Fiber CommunicationConference. Optical Society of America, 2016, p. Th3J.5.[431] P. Dong, W. Qian, H. Liang, R. Shafiiha, N.-N. Feng, D. Feng, X. Zheng,A. V. Krishnamoorthy, and M. Asghari, “Low power and compactreconfigurable multiplexing devices based on silicon microring resonators,”Optics Express, vol. 18, no. 10, pp. 9852–9858, May 2010.[432] M. R. Watts, T. Barwicz, M. A. Popovic´, P. T. Rakich, L. Socci, E. P. Ippen,H. I. Smith, and F. Kaertner, “Microring-resonator filter with doubledfree-spectral-range by two-point coupling,” Conference on Lasers andElectro-Optics/Quantum Electronics and Laser Science and PhotonicApplications Systems Technologies, p. CMP3, 2005.[433] H. L. R. Lira, C. B. Poitras, and M. Lipson, “CMOS compatiblereconfigurable filter for high bandwidth non-blocking operation,” OpticsExpress, vol. 19, no. 21, pp. 20 115–20 121, Oct. 2011.[434] W. Shi, “Silicon photonic filters for wavelength-division multiplexing andsensing applications,” PhD thesis, University of British Columbia, Aug.2012.161[435] R. Boeck, M. Caverley, L. Chrostowski, and N. A. F. Jaeger, “Processcalibration method for designing silicon-on-insulator contra-directionalgrating couplers,” Optics Express, vol. 23, no. 8, pp. 10 573–10 588, Apr.2015.[436] W. Shi, H. Yun, C. Lin, M. Greenberg, X. Wang, Y. Wang, S. T. Fard,J. Flueckiger, N. A. F. Jaeger, and L. Chrostowski, “Ultra-compact, flat-topdemultiplexer using anti-reflection contra-directional couplers for CWDMnetworks on silicon,” Optics Express, vol. 21, no. 6, pp. 6733–6738, Mar.2013.[437] P. Orlandi, P. Velha, M. Gnan, P. Bassi, A. Samarelli, M. Sorel, M. J.Strain, and R. D. L. Rue, “Microring resonator with wavelength selectivecoupling in SOI,” 8th IEEE International Conference on Group IVPhotonics, pp. 281–283, 2011.[438] W. Shi, X. Wang, W. Zhang, H. Yun, N. A. F. Jaeger, and L. Chrostowski,“Integrated microring add-drop filters with contradirectional couplers,” inConference on Lasers and Electro-Optics 2012. Optical Society ofAmerica, 2012, p. JW4A.91.[439] W. Shi, X. Wang, W. Zhang, H. Yun, C. Lin, L. Chrostowski, and N. A. F.Jaeger, “Grating-coupled silicon microring resonators,” Applied PhysicsLetters, vol. 100, no. 12, p. 121118, Mar. 2012.[440] R. Boeck, M. Caverley, L. Chrostowski, and N. A. F. Jaeger,“Grating-assisted silicon-on-insulator racetrack resonator reflector,” OpticsExpress, vol. 23, no. 20, pp. 25 509–25 522, Oct. 2015.[441] R. Boeck, M. Caverley, L. Chrostowski, and N. A. F. Jaeger, “An FSR-freesilicon resonator reflector using a contra-directional coupler and a Braggreflector,” in Photonics North, 2015, June 2015, p. 1.[442] N. Zhang, “Forward and Backward Grating-Assisted Directional Couplersin Silicon for Wavelength Multiplexing Tunable Add-Drop Applications,”Master’s thesis, University of Cincinnati, Sep. 2005.[443] D. T. Tan, K. Ikeda, and Y. Fainman, “On-chip group velocity dispersioncompensation using coupled chirped vertical gratings,” in Advances inOptical Sciences Congress. Optical Society of America, 2009, p. JTuB12.[444] D. T. H. Tan, K. Ikeda, and Y. Fainman, “Coupled chirped vertical gratingsfor on-chip group velocity dispersion engineering,” Applied PhysicsLetters, vol. 95, no. 14, p. 141109, Oct. 2009.162[445] D. T. H. Tan, K. Ikeda, A. Mizrahi, M. Nezhad, and Y. Fainman, “Coupledvertical gratings on silicon for applications in wavelength divisionmultiplexing,” Proc. SPIE, vol. 7607, p. 760705, 2010.[446] D. T. H. Tan, K. Ikeda, S. Zamek, A. Mizrahi, M. Nezhad, and Y. Fainman,“Wavelength selective coupler on silicon for applications in wavelengthdivision multiplexing,” in 2010 IEEE Photonics Society Summer TopicalMeeting Series, Jul. 2010, pp. 203–204.[447] W. Shi, X. Wang, C. Lin, H. Yun, Y. Liu, T. Baehr-Jones, M. Hochberg,N. A. F. Jaeger, and L. Chrostowski, “Electrically tunable resonant filters inphase-shifted contra-directional couplers,” in 2012 IEEE 9th InternationalConference on Group IV Photonics (GFP), Aug. 2012, pp. 78–80.[448] W. Shi, V. Veerasubramanian, D. V. Plant, N. A. F. Jaeger, andL. Chrostowski, “Silicon photonic bragg-grating couplers for opticalcommunications,” Proc. SPIE, vol. 9010, p. 90100F, 2014.[449] W. Shi, V. Veerasubramanian, D. Patel, and D. V. Plant, “Tunablenanophotonic delay lines using linearly chirped contradirectional couplerswith uniform Bragg gratings,” Optics Letters, vol. 39, no. 3, pp. 701–703,Feb. 2014.[450] D. T. H. Tan, A. Grieco, and Y. Fainman, “Silicon-based opticalinterconnects for dense wavelength division multiplexing with 100GHzSpacing,” in Advanced Photonics for Communications. Optical Society ofAmerica, 2014, p. PT4B.3.[451] H. Qiu, T. Hu, P. Yu, Y. Wang, and X. Jiang, “A nonreciprocal add-dropmultiplexer based on grating assisted couplers,” Optik - InternationalJournal for Light and Electron Optics, vol. 126, no. 23, pp. 3959 – 3961,Dec. 2015.[452] G. F. R. Chen, T. Wang, K. J. A. Ooi, A. K. L. Chee, L. K. Ang, andD. T. H. Tan, “Wavelength selective mode division multiplexing on asilicon chip,” Optics Express, vol. 23, no. 6, pp. 8095–8103, Mar. 2015.[453] H. Qiu, Y. Su, P. Yu, T. Hu, J. Yang, and X. Jiang, “Compact polarizationsplitter based on silicon grating-assisted couplers,” Optics Letters, vol. 40,no. 9, pp. 1885–1887, Apr. 2015.[454] J. St-Yves, H. Bahrami, S. LaRochelle, and W. Shi, “Widelybandwidth-tunable broadband optical filter on silicon,” in Optical Fiber163Communication Conference. Optical Society of America, 2015, p.Th1F.2.[455] M. Caverley, “Silicon photonic modulators and filters for opticalinterconnects,” Master’s thesis, University of British Columbia, Aug. 2015.[456] L. Chrostowski and K. Iniewski, High-Speed Photonics Interconnects.CRC Press, 2013.[457] N. Zhang and J. T. Boyd, “Forward and backward grating-assisteddirectional couplers in silicon for wavelength-division multiplexing tunableadd-drop applications,” Optical Engineering, vol. 45, no. 5, p. 054603,2006.[458] K. Ikeda, H. C. Kim, M. Nezhad, A. Krishnamoorthy, J. Cunningham, andY. Fainman, “Wavelength selective coupler with vertical gratings on siliconchip,” in Frontiers in Optics 2007/Laser Science XXIII/Organic Materialsand Devices for Displays and Energy Conversion. Optical Society ofAmerica, 2007, p. FTuB2.[459] K. Ikeda, M. Nezhad, and Y. Fainman, “Wavelength selective coupler withvertical gratings on silicon chip,” Applied Physics Letters, vol. 92, no. 20,p. 201111, May 2008.[460] D. T. H. Tan, K. Ikeda, S. Zamek, A. Mizrahi, M. P. Nezhad, A. V.Krishnamoorthy, K. Raj, J. E. Cunningham, X. Zheng, I. Shubin, Y. Luo,and Y. Fainman, “Wide bandwidth, low loss 1 by 4 wavelength divisionmultiplexer on silicon for optical interconnects,” Optics Express, vol. 19,no. 3, pp. 2401–2409, Jan. 2011.[461] W. Shi, X. Wang, W. Zhang, L. Chrostowski, and N. A. F. Jaeger,“Contradirectional couplers in silicon-on-insulator rib waveguides,” OpticsLetters, vol. 36, no. 20, pp. 3999–4001, Oct. 2011.[462] W. Shi, X. Wang, H. Yun, W. Zhang, L. Chrowtowski, and N. A. F. Jaeger,“Add-drop filters in silicon grating-assisted asymmetric couplers,” inOptical Fiber Communication Conference. Optical Society of America,2012, p. OTh3D.3.[463] Q. Huiye, T. Hu, P. Yu, J. Yang, and X. Jiang, “Add-drop filter withasymmetric vertical gratings in silicon-on-insulator rib waveguides,” inAsia Communications and Photonics Conference. Optical Society ofAmerica, 2012, p. AF4A.10.164[464] W. Shi, H. Yun, C. Lin, X. Wang, J. Flueckiger, N. A. F. Jaeger, andL. Chrostowski, “Silicon CWDM demultiplexers using contra-directionalcouplers,” in CLEO: 2013. Optical Society of America, 2013, p. CTu3F.5.[465] W. Shi, X. Wang, C. Lin, H. Yun, Y. Liu, T. Baehr-Jones, M. Hochberg,N. A. F. Jaeger, and L. Chrostowski, “Silicon photonic grating-assisted,contra-directional couplers,” Optics Express, vol. 21, no. 3, pp. 3633–3650,Feb. 2013.[466] H. Qiu, G. Jiang, T. Hu, H. Shao, P. Yu, J. Yang, and X. Jiang, “FSR-freeadd-drop filter based on silicon grating-assisted contradirectional couplers,”Optics Letters, vol. 38, no. 1, pp. 1–3, Jan. 2013.[467] W. Shi, H. Yun, C. Lin, J. Flueckiger, N. A. F. Jaeger, and L. Chrostowski,“Coupler-apodized Bragg-grating add-drop filter,” Optics Letters, vol. 38,no. 16, pp. 3068–3070, Aug. 2013.[468] D. T. H. Tan, A. Grieco, and Y. Fainman, “Towards 100 channel densewavelength division multiplexing with 100GHz spacing on silicon,” OpticsExpress, vol. 22, no. 9, pp. 10 408–10 415, May 2014.[469] M. Caverley, R. Boeck, L. Chrostowski, and N. A. F. Jaeger, “High-speeddata transmission through silicon contra-directional grating coupler opticaladd-drop multiplexers,” in CLEO: 2015. Optical Society of America,2015, p. JTh2A.41.[470] L. Chrostowski and M. Hochberg, Silicon Photonics Design: From Devicesto Systems. Cambridge University Press, 2015.[471] J. St-Yves, H. Bahrami, P. Jean, S. LaRochelle, and W. Shi, “Widelybandwidth-tunable silicon filter with an unlimited free-spectral range,”Optics Letters, vol. 40, no. 23, pp. 5471–5474, Dec. 2015.[472] T. Baehr-Jones, R. Ding, A. Ayazi, T. Pinguet, M. Streshinsky, N. Harris,J. Li, L. He, M. Gould, Y. Zhang, A. E.-J. Lim, T.-Y. Liow, S. H.-G. Teo,G.-Q. Lo, and M. Hochberg, “A 25 Gb/s silicon photonics platform,”arXiv:1203.0767 [physics.optics], 2012.[473] N. Rouger, L. Chrostowski, and R. Vafaei, “Temperature effects onsilicon-on-insulator (SOI) racetrack resonators: a coupled analytic and 2-Dfinite difference approach,” Journal of Lightwave Technology, vol. 28,no. 9, pp. 1380–1391, May 2010.165[474] H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, andS. ichi Itabashi, “Ultrasmall polarization splitter based on silicon wirewaveguides,” Optics Express, vol. 14, no. 25, pp. 12 401–12 408, Dec.2006.[475] S. Bandyopadhyay, Dissemination of Information in Optical Networks:From Technology to Algorithms. Springer, 2008.[476] P. Dumon, “Ultra-compact integrated optical filters in silicon-on-insulatorby means of wafer-scale technology,” PhD thesis, Universiteit Gent, 2007.[477] F. Dell’Olio, V. M. N. Passaro, G. Z. Mashanovich, and F. De Leonardis,“Micro-racetrack coupled-resonator optical waveguides in silicon photonicwires,” Journal of Optics A: Pure and Applied Optics, vol. 10, no. 6, p.064003, Apr. 2008.[478] X. Wang, W. Shi, H. Yun, S. Grist, N. A. F. Jaeger, and L. Chrostowski,“Narrow-band waveguide Bragg gratings on SOI wafers withCMOS-compatible fabrication process,” Optics Express, vol. 20, no. 14,pp. 15 547–15 558, Jun. 2012.[479] A. V. Krishnamoorthy, R. Ho, X. Zheng, H. Schwetman, J. Lexau, P. Koka,G. Li, I. Shubin, and J. E. Cunningham, “Computer systems based onsilicon photonic interconnects,” Proc. IEEE, vol. 97, no. 7, pp. 1337 –1361,2009.[480] P. Matavulj and T. Kecˇa, “Influence of geometric parameters on the SOIracetrack resonator properties,” PIERS Proc. Moscow, pp. 13–17, 2012.[481] A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis,H. Thacker, I. Shubin, Y. Luo, K. Raj, and J. E. Cunningham, “ExploitingCMOS manufacturing to reduce tuning requirements for resonant opticaldevices,” IEEE Photonics Journal, vol. 3, no. 3, pp. 567–579, Jun. 2011.[482] D. Dai and S. He, “Proposal of a coupled-microring-basedwavelength-selective 1⇥N power splitter,” IEEE Photonics TechnologyLetters, vol. 21, no. 21, pp. 1630–1632, Nov. 2009.[483] J. D. Dome´nech, P. Mun˜oz, and J. Capmany, “The longitudinal offsettechnique for apodization of coupled resonator optical waveguide devices:concept and fabrication tolerance analysis,” Optics Express, vol. 17, no. 23,pp. 21 050–21 059, Nov. 2009.166[484] L. Chrostowski, X. Wang, J. Flueckiger, Y. Wu, Y. Wang, andS. Talebi Fard, “Impact of fabrication non-uniformity on chip-scale siliconphotonic integrated circuits,” Optical Fiber Communication Conference, p.Th2A.37, 2014.[485] A. Prinzen, J. Bolten, M. Waldow, and H. Kurz, “Study on fabricationtolerances of SOI based directional couplers and ring resonators,”Microelectronic Engineering, vol. 121, pp. 51–54, Jun. 2014.[486] J. C. Mikkelsen, W. D. Sacher, and J. K. S. Poon, “Dimensional variationtolerant silicon-on-insulator directional couplers,” Optics Express, vol. 22,no. 3, pp. 3145–3150, Feb. 2014.[487] A. Prinzen, M. Waldow, and H. Kurz, “Fabrication tolerances of SOI baseddirectional couplers and ring resonators,” Optics Express, vol. 21, no. 14,pp. 17 212–17 220, Jul. 2013.[488] S. K. Selvaraja, G. Winroth, S. Locorotondo, G. Murdoch, A. Milenin,C. Delvaux, P. Ong, S. Pathak, W. Xie, G. Sterckx, G. Lepage,D. Van Thourhout, W. Bogaerts, J. Van Campenhout, and P. Absil, “193nmimmersion lithography for high-performance silicon photonic circuits,”Proc. SPIE, vol. 9052, p. 90520F, 2014.[489] T. Kecˇa, P. Matavulj, W. Headley, and G. Mashanovich, “Free spectralrange adjustment of a silicon rib racetrack resonator,” Physica Scripta, vol.2012, no. T149, p. 014031, Apr. 2012.[490] D.-X. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson,M. Nedeljkovic, X. Chen, D. Van Thourhout, S. Keyvaninia, and S. K.Selvaraja, “Silicon photonic integration platform - have we found the sweetspot?” IEEE Journal of Selected Topics in Quantum Electronics, vol. 20,no. 4, pp. 1–17, Jul. - Aug. 2014.[491] F. Boeuf, S. Cre´mer, N. Vulliet, T. Pinguet, A. Mekis, G. Masini,L. Verslegers, P. Sun, A. Ayazi, N. K. Hon, S. Sahni, Y. Chi, B. Orlando,D. Ristoiu, A. Farcy, F. Leverd, L. Broussous, D. Pelissier-Tanon,C. Richard, L. Pinzelli, R. Beneyton, O. Gourhant, E. Gourvest,Y. Le-Friec, D. Monnier, P. Brun, M. Guillermet, D. Benoit, K. Haxaire,J. R. Manouvrier, S. Jan, H. Petiton, J. F. Carpentier, T. Que´merais,C. Durand, D. Gloria, M. Fourel, F. Battegay, Y. Sanchez, E. Batail,F. Baron, P. Delpech, L. Salager, P. De Dobbelaere, and B. Sautreuil, “Amulti-wavelength 3D-compatible silicon photonics platform on 300mm167SOI wafers for 25Gb/s applications,” IEEE International Electron DevicesMeeting (IEDM), pp. 13.3.1–13.3.4, 2013.[492] R. Ding, T. Baehr-Jones, T. Pinguet, J. Li, N. C. Harris, M. Streshinsky,L. He, A. Novack, E.-J. Lim, T.-Y. Liow, H.-G. Teo, G.-Q. Lo, andM. Hochberg, “A silicon platform for high-speed photonics systems,”Optical Fiber Communication Conference, p. OM2E.6, 2012.[493] R. J. Bojko, J. Li, L. He, T. Baehr-Jones, M. Hochberg, and Y. Aida,“Electron beam lithography writing strategies for low loss, highconfinement silicon optical waveguides,” Journal of Vacuum Science &Technology B, vol. 29, no. 6, p. 06F309, Nov. 2011.[494] R. S. Romaniuk, “Optical fiber transmission with wavelength multiplexing:faster or denser?” Proc. SPIE, vol. 5484, pp. 19–28, Jul. 2004.[495] C. Manolatou, M. A. Popovic, P. T. Rakich, T. Barwicz, H. A. Haus, andE. P. Ippen, “Spectral anomalies due to coupling-induced frequency shiftsin dielectric coupled-resonator filters,” in Optical Fiber CommunicationConference, ser. Technical Digest (CD). Optical Society of America, Feb.2004, p. TuD5.[496] N. Sherwood-Droz, H. Wang, L. Chen, B. G. Lee, A. Biberman,K. Bergman, and M. Lipson, “Optical 4x4 hitless slicon router for opticalnetworks-on-chip (NoC),” Optics Express, vol. 16, no. 20, pp.15 915–15 922, Sep. 2008.[497] M. Geng, L. Jia, L. Zhang, L. Yang, P. Chen, T. Wang, and Y. Liu,“Four-channel reconfigurable optical add-drop multiplexer based onphotonic wire waveguide,” Optics Express, vol. 17, no. 7, pp. 5502–5516,Mar. 2009.[498] Y. Wang, J. Flueckiger, C. Lin, and L. Chrostowski, “Universal gratingcoupler design,” Proc. SPIE, vol. 8915, p. 89150Y, 2013.[499] M.-C. N. Dicaire, J. Upham, I. D. Leon, S. A. Schulz, and R. W. Boyd,“Group delay measurement of fiber Bragg grating resonances intransmission: Fourier transform interferometry versus Hilbert transform,”Journal of the Optical Society of America B, vol. 31, no. 5, pp. 1006–1010,May 2014.[500] The MathWorks, Inc., “Discrete-time analytic signal using Hilberttransform - MATLAB hilbert,” [Online]. Available:http://www.mathworks.com/help/signal/ref/hilbert.html, (Jan. 15, 2016).168[501] A. Melloni, M. Martinelli, G. Cusmai, and R. Siano, “Experimentalevaluation of ring resonator filters impact on the bit error rate in non returnto zero transmission systems,” Optics Communications, vol. 234, no. 1-6,pp. 211 – 216, Apr. 2004.[502] Photonics-USA, “Optical Add/Drop Multiplexers 200 GHz OADM (1x2).”[503] Alliance Fiber Optic Products, Inc., “Single Channel DWDM (200 GHz),”REV. H, Mar. 4, 2009.[504] S. Mason, “Feedback theory-further properties of signal flow graphs,”Proc. IRE, vol. 44, pp. 920–926, 1956.[505] Y. Wang, X. Wang, J. Flueckiger, H. Yun, W. Shi, R. Bojko, N. A. F. Jaeger,and L. Chrostowski, “Focusing sub-wavelength grating couplers with lowback reflections for rapid prototyping of silicon photonic circuits,” OpticsExpress, vol. 22, no. 17, pp. 20 652–20 662, Aug. 2014.[506] W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert,B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout,“Nanophotonic waveguides in silicon-on-insulator fabricated with CMOStechnology,” Journal of Lightwave Technology, vol. 23, no. 1, pp. 401–412, Jan. 2005.[507] X. Wang, “Silicon photonic waveguide Bragg gratings,” PhD thesis,University of British Columbia, Dec. 2013.[508] D. Marcuse, “Bandwidth of forward and backward coupling directionalcouplers,” Journal of Lightwave Technology,, vol. 5, no. 12, pp. 1773–1777,Dec. 1987.[509] M. R. Shenoy, K. Thyagarajan, V. Priye, and N. S. Madhavan, “Estimationof the characteristic parameters of fiber Bragg gratings from spectralmeasurements,” Proc. SPIE, vol. 3666, pp. 94–99, 1999.[510] R. Kashyap, Fiber Bragg Gratings. Academic, 1999.[511] X. Wang, Y. Wang, J. Flueckiger, R. Bojko, A. Liu, A. Reid, J. Pond,N. A. F. Jaeger, and L. Chrostowski, “Precise control of the couplingcoefficient through destructive interference in silicon waveguide Bragggratings,” Optics Letters, vol. 39, no. 19, pp. 5519–5522, Oct. 2014.[512] J. P. Weber, “Spectral characteristics of coupled-waveguideBragg-reflection tunable optical filter,” IEE Proceedings J. Optoelectronics,vol. 140, no. 5, pp. 275–284, Oct. 1993.169[513] A. Yariv and P. Yeh, Photonics: optical electronics in moderncommunications. Oxford University Press, 2007.[514] D. Marcuse, “Directional couplers made of nonidentical asymmetric slabs.Part II: Grating-assisted couplers,” Journal of Lightwave Technology,vol. 5, no. 2, pp. 268–273, Feb. 1987.[515] R. Marz and H. P. Nolting, “Spectral properties of asymmetrical opticaldirectional couplers with periodic structures,” Optical and QuantumElectronics, vol. 19, no. 5, pp. 273–287, Sep. 1987.[516] S. Nacer, A. Aissat, K. Ferdjani, and M. Bensebti, “Influence of dispersionon spectral characteristics of GADC optical filters,” Optical and QuantumElectronics, vol. 38, no. 8, pp. 701–710, Jun. 2006.[517] D. T. H. Tan, K. Ikeda, and Y. Fainman, “Cladding-modulated Bragggratings in silicon waveguides,” Optics Letters, vol. 34, no. 9, pp.1357–1359, May 2009.[518] S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Modeling and measurement oflosses in silicon-on-insulator resonators and bends,” Optics Express,vol. 15, no. 17, pp. 10 553–10 561, Aug. 2007.[519] The MathWorks, Inc., “Solve nonlinear curve-fitting (data-fitting) problemsin least-squares sense - MATLAB lsqcurvefit,” [Online]. Available:http://www.mathworks.com/help/optim/ug/lsqcurvefit.html, (Jan. 15,2016).[520] J. Willems, K. David, G. Morthier, and R. Baets, “Filter characteristics ofDBR amplifier with index and gain coupling,” Electronics Letters, vol. 27,no. 10, pp. 831–833, May 1991.[521] L. Poladian, “Group-delay reconstruction for fiber Bragg gratings inreflection and transmission,” Optics Letters, vol. 22, no. 20, pp. 1571–1573,Oct. 1997.[522] J. Skaar and H. E. Engan, “Phase reconstruction from reflectivity in fiberBragg gratings,” Optics Letters, vol. 24, no. 3, pp. 136–138, Feb. 1999.[523] A. Melloni, R. Costa, P. Monguzzi, and M. Martinelli, “Ring-resonatorfilters in silicon oxynitride technology for dense wavelength-divisionmultiplexing systems,” Optics Letters, vol. 28, no. 17, pp. 1567–1569, Sep.2003.170[524] A. Canciamilla, F. Morichetti, and A. Melloni, “Full characterization ofintegrated optical ring-resonators by phase-sensitive time-domaininterferometry,” Proc. SPIE, vol. 7138, p. 71381L, 2008.[525] O. Schwelb, “Transmission, group delay, and dispersion in single-ringoptical resonators and add/drop filters - a tutorial overview,” Journal ofLightwave Technology, vol. 22, no. 5, pp. 1380–1394, May 2004.[526] P. Pintus, P. Contu, N. Andriolli, A. D’Errico, F. Di Pasquale, and F. Testa,“Analysis and design of microring-based switching elements in a siliconphotonic integrated transponder aggregator,” Journal of LightwaveTechnology, vol. 31, no. 24, pp. 3943–3955, Dec. 2013.[527] S. K. Selvaraja, P. D. Heyn, G. Winroth, P. Ong, G. Lepage, C. Cailler,A. Rigny, K. Bourdelle, W. Bogaerts, D. VanThourhout, J. V. Campenhout,and P. Absil, “Highly uniform and low-loss passive silicon photonicsdevices using a 300mm CMOS platform,” in Optical Fiber CommunicationConference. Optical Society of America, 2014, p. Th2A.33.[528] H. Jayatilleka, K. Murray, M. A´ngel Guille´n-Torres, M. Caverley, R. Hu,N. A. F. Jaeger, L. Chrostowski, and S. Shekhar, “Wavelength tuning andstabilization of microring-based filters using silicon in-resonatorphotoconductive heaters,” Optics Express, vol. 23, no. 19, pp.25 084–25 097, Sep. 2015.171Appendix ADerivation of the TransferFunctions of a QuadrupleSeries-Coupled RacetrackResonator Filter1Here, we will derive the drop port and through port transfer functions of quadrupleseries-coupled racetrack resonators using Mason’s rule [504]. In [144], Dey etal. derived the drop port transfer function using Mason’s rule [504] but did notderive nor present the through port transfer function. For completeness, here wehave re-derived the drop port transfer function as well as derived the through porttransfer function. Since in our configuration, there are four racetrack resonatorscoupled in series, there are 33 loop gains. There are 10 loop gains of the 10 possible1A version of Appendix A has been published in [96].172combinations of 1 non-touching loop,P11 = t1t2Xa, (A.1)P21 = t2t3Xb, (A.2)P31 = t3t4Xc, (A.3)P41 = t4t5Xd , (A.4)P51 = k22k23 t1t4XaXbXc, (A.5)P61 = k23k24 t2t5XbXcXd , (A.6)P71 =k23 t2t4XbXc, (A.7)P81 =k24 t3t5XcXd , (A.8)P91 =k22k23k24 t1t5XaXbXcXd , (A.9)P101 =k22 t1t3XaXb (A.10)where Xa,b,c,d = exp( jba,b,c,dLa,b,c,daa,b,c,dLa,b,c,d), where the field loss coef-ficients and propagations constants for the racetrack resonators are represented byaa,b,c,d , and ba,b,c,d , respectively. k1, k2, k3, k4, and k5 are the symmetric (real)point field coupling factors. t1, t2, t3, t4, and t5 are the straight through (real) pointfield transmission factors. There are 15 loop gains of the 15 possible combinationsof 2 non-touching loops,173P12 = P11P21, (A.11)P22 = P21P31, (A.12)P32 = P31P41, (A.13)P42 = P11P31, (A.14)P52 = P11P41, (A.15)P62 = P21P41, (A.16)P72 = P41P51, (A.17)P82 = P11P71, (A.18)P92 = P41P71, (A.19)P102 = P81P101, (A.20)P112 = P31P101, (A.21)P122 = P41P101, (A.22)P132 = P11P81, (A.23)P142 = P21P81, (A.24)P152 = P11P61. (A.25)There are 7 loop gains of the 7 possible combinations of 3 non-touching loops,P13 = P11P21P31, (A.26)P23 = P21P31P41, (A.27)P33 = P31P41P101, (A.28)P43 = P11P41P71, (A.29)P53 = P11P21P81, (A.30)P63 = P11P21P41, (A.31)P73 = P11P31P41. (A.32)174There is 1 loop gain of the 1 possible combination of 4 non-touching loops,P14 = P11P21P31P41. (A.33)The gain and co-factor of the first forward path that is used to determine the dropport transfer function is,G1 = jk1k2k3k4k5pXaXbXcXd , (A.34)D1 = 1. (A.35)The determinant for the entire system is given by,D= 1(P11+P21+P31+P41+P51+P61+P71+P81+P91+P101)+(P12+P22+P32+P42+P52+P62+P72+P82+P92+P102+P112+P122+P132+P142+P152)(P13+P23+P33+P43+P53+P63+P73)+P14. (A.36)Thus, the transfer function for the drop port is given by [144],TFdrop =G1D1D. (A.37)The gains of the second to sixth forward path that are used to determine the throughport transfer function are,G2 = t1, (A.38)G3 =k21 t2Xa, (A.39)G4 = k21k22 t3XaXb, (A.40)G5 =k21k22k23 t4XaXbXc, (A.41)G6 = k21k22k23k24 t5XaXbXcXd , (A.42)175and the corresponding co-factors are,D2 = D, (A.43)D3 = 1 (P21+P31+P41+P61+P71+P81)+(P22+P32+P62+P92+P142)P23, (A.44)D4 = 1 (P31+P41+P81)+P32, (A.45)D5 = 1P41, (A.46)D6 = 1. (A.47)Thus, the transfer function for the through port is given by,TFthrough =G2D2+G3D3+G4D4+G5D5+G6D6D. (A.48)176Appendix BDerivation of the TransferFunctions of a Double MicroringResonator Filter with MZI-BasedCouplingThe drop port and through port transfer functions of a double microring resonatorfilter with MZI-based coupling (which are used in [105]) are determined using thesame method used in Appendix A, which is Mason’s rule [96, 107, 504]. There are8 loop gains of the 8 possible combinations of 1 non-touching loops,P11 = t2mzitrXrXmzi2, (B.1)P21 = t2mzitrXrXmzi2, (B.2)P31 =t4mzik2r X2r X2mzi2, (B.3)P41 =trk2mziXrXmzi1, (B.4)P51 =trk2mziXrXmzi1, (B.5)P61 = k2mzit2mzik2r Xmzi1X2r Xmzi2, (B.6)P71 = t2mzik2r k2mziXmzi2X2r Xmzi1, (B.7)P81 =k4mzik2r X2r X2mzi1, (B.8)177whereXr = e jbrLraLr , (B.9)Xmzi2 = e jbrLmzi2aLmzi2 , (B.10)Xmzi1 = e jbrLmzi1aLmzi1 , (B.11)a is the field propagation loss coefficient, Lr is the length of the microring resonatorthat does not include the portion within the MZI section. br is the propagationconstant of the microring resonator and the MZI-bus waveguide branch. The lengthLmzi2 is the MZI-ring waveguide branch length [105]. The length Lmzi1 is thetotal length of the MZI-bus waveguide branch [105]. kr and tr are the inter-ringreal point field coupling factor and transmission factor, respectively, kmzi and tmziare the real point field coupling factor and transmission factor for the MZI regions,respectively [105]. There are 4 loop gains of the 4 possible combinations of 2non-touching loops,P12 = P11P21, (B.12)P22 = P41P21, (B.13)P32 = P41P51, (B.14)P42 = P51P11, (B.15)The determinant, D, for the filter is,D= 1 (P11+P21+P31+P41+P51+P61+P71+P81)+(P12+P22+P32+P42).(B.16)178The forward path gains and their, respective, co-factors for the drop port transferfunction are,G1 = jkrk2mzit2mziXrXmzi1Xmzi2, (B.17)D1 = 1, (B.18)G2 = jkrk2mzit2mziXrXmzi1Xmzi2, (B.19)D2 = 1, (B.20)G3 = jkrk2mzit2mziXrX2mzi2, (B.21)D3 = 1, (B.22)G4 = jkrk2mzit2mziXrX2mzi1, (B.23)D4 = 1. (B.24)Therefore, the drop port transfer function is,TFdrop =G1D1+G2D2+G3D3+G4D4D. (B.25)179The forward path gains and their, respective, co-factors for the through port transferfunction are,G5 = t2mziXmzi1, (B.26)D5 = 1 (P11+P21+P31+P41+P61)+(P12+P22), (B.27)G6 =k2mziXmzi2, (B.28)D6 = 1 (P11+P41+P51+P71+P81)+(P32+P42), (B.29)G7 = k2r k2mzit4mziX2r Xmzi1X2mzi2, (B.30)D7 = 1, (B.31)G8 =k2mzitrt2mziXrXmzi1Xmzi2, (B.32)D8 = 1 (P11+P41), (B.33)G9 =k2mzitrt2mziXrXmzi1Xmzi2, (B.34)D9 = 1 (P11+P41), (B.35)G10 =k2r k4mzit2mziX2r X2mzi1Xmzi2, (B.36)D10 = 1, (B.37)G11 =k2r k4mzit2mziX2r X2mzi1Xmzi2, (B.38)D11 = 1, (B.39)G12 = k2r k2mzit4mziX2r Xmzi1X2mzi2, (B.40)D12 = 1. (B.41)Therefore, the through port transfer function is,TFthrough =G5D5+G6D6+G7D7+G8D8+G9D9+G10D10+G11D11+G12D12D.(B.42)180Appendix CDerivation of the AveragePropagation Constant Mismatchof a Contra-Directional GratingCoupler1Here, we will derive the equation for the average propagation constant mismatch,dbavg. The first step in determining dbavg is to calculate the propagation constantdifference, dbH , which is defined as the difference between the propagation con-stant mismatch, Db ( fH), at the frequency, fH , corresponding to the intensity atFWHM at the higher frequency and the propagation constant mismatch, Db ( f0), atthe centre frequency, f0, (see Figure C.1) as shown in Eq. C.1.dbH = Db ( fH)Db ( f0) (C.1)Next, we substitute into Eq. C.1 the propagation constant mismatch equation, Db =ba+ bbm 2pL , where ba and bb are the propagation constants of waveguide “a”and waveguide “b” in isolation, respectively, m is the grating order which is equalto 1 for our first-order contra-DCs, and L is the grating period [513] as shown in1A version of Appendix C has been published in [435].181Eq. C.2.dbH = ba( fH)+bb( fH) 2pL ba( f0)bb( f0)+2pL(C.2)The next steps involve simplifying Eq. C.2, substitutions for the propagation con-stants, and rearrangements of the terms,dbH = ba( fH)+bb( fH)ba( f0)bb( f0) (C.3)=✓2pc◆(na( fH) fH +nb( fH) fH na( f0) f0nb( f0) f0) (C.4)=✓2pc◆(na( fH) fH na( f0) f0+nb( fH) fH nb( f0) f0) (C.5)where na and nb are the effective indices of waveguide “a” and waveguide “b”,respectively, and c is the speed of light in a vacuum. Since the effective indicesare frequency dependent due to dispersion, we will express na( fH) as na( f0) +D fH dnad ff0and nb( fH) as nb( f0)+D fH dnbd ff0where D fH = fH  f0 [107]. Aftersimplification by grouping terms, dbH becomes,dbH =✓2pD fHc◆ na( f0)+ fHdnad ff0+nb( f0)+ fHdnbd ff0!. (C.6)In Eq. C.6, the terms, na( f0)+ fH dnad ff0and nb( f0)+ fH dnbd ff0correspond approx-imately to the group indices of waveguide “a” and waveguide “b,” respectively,since D fH << f0 [107]. Therefore, the final equation for dbH is,dbH =✓2pD fHc◆ng,a( f0)+ng,b( f0)(C.7)where ng,a and ng,b are the group indices of waveguide “a” and waveguide “b”,respectively.Next, we show the equation for the propagation constant difference, dbL, [seeEq. C.8 where D fL = f0 fL] which is defined as the difference between the prop-agation constant mismatch, Db ( fL), at the frequency, fL, corresponding to the in-tensity at FWHM at the lower frequency and the propagation constant mismatch,182Db ( f0), at the center frequency, f0 (see Figure C.1). dbL was derived using thesame procedure as used to derive dbH .dbL =✓2pD fLc◆ng,a( f0)+ng,b( f0)(C.8)We are now able to determine dbavg,dbavg =|dbH |+ |dbL|2(C.9)dbavg =✓2p2c◆ng,a( f0)+ng,b( f0)(D fH +D fL) (C.10)dbavg =⇣pc⌘ng,a( f0)+ng,b( f0)( fH  fL) (C.11)dbavg =⇣pc⌘ng,a( f0)+ng,b( f0)✓ clL clH◆(C.12)dbavg =pDlbwlLlHng,a(l0)+ng,b(l0)(C.13)where the wavelengths l0, lL, and lH correspond to the frequencies f0, fH , and fL,respectively, and Dlbw = lH lL. Equations C.7 and C.8 are similar to Eq. 13.5-22 in [513] and Eq. C.13 is similar to Eq. 31 in [508] except that we have takendispersion into account.Intensity (dB) |L| |H| 2avg3 dB ( fL ) ( f0 ) ( fH ) Figure C.1: Diagram depicting some of the relevant parameters used in ourderivation. cOptical Society of America, 2015, by permission [435].183Appendix DDerivation of the MinimumBandwidth of aContra-Directional GratingCoupler1Here, we present the derivation for the minimum bandwidth of a contra-DC,Dlbwmin as |k| goes to zero. First, we rearrange the terms in Eq. 6.7 as shownbelow,2|k|2 sinh2(sL)tanh2(|k|L) = s2 cosh2(sL)+✓dbavg2◆2sinh2(sL). (D.1)1A version of Appendix D has been published in [435].184Next, we take the limit of the left side and the right side of Eq. D.1,limk!02|k|2 sinh2(sL)tanh2(|k|L) = limk!0"s2 cosh2(sL)+✓dbavg2◆2sinh2(sL)#(D.2)cos(dbavgL)1L2=db2avg4(D.3)cos(dbavgL)+(dbavgL)241= 0. (D.4)The numerically determined solution to Eq. D.4 is dbavgL = 2.783115 (we ne-glect the trivial solution which is zero). Therefore, for a contra-DC with a givenL, dbavgL needs to be greater than 2.783115. Therefore, substituting dbavgL =2.783115 into Eq. C.13, we get (similar to [520]),Dlbwmin =2.783115lLlHpL⇥ng,a(l0)+ng,b(l0)⇤ (D.5)which is approximately equal to,Dlbwmin ⇡ 2.783115l20pL⇥ng,a(l0)+ng,b(l0)⇤ . (D.6)185

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.24.1-0300138/manifest

Comment

Related Items