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Silicon-on-insulator microring resonator based filters with bent couplers Eid, Nourhan 2016

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Silicon-on-Insulator Microring Resonator BasedFilters with Bent CouplersbyNourhan EidB.A.Sc, The University of Ottawa, 2014A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of Applied ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Electrical and Computer Engineering)The University of British Columbia(Vancouver)October 2016c© Nourhan Eid, 2016AbstractIn this thesis, we present and study the use of bent couplers in silicon-on-insulator(SOI) microring resonator (MRR) based filters. MRR based filters are attractivecandidates in wavelength division-multiplexing (WDM) transceivers because oftheir compactness and low power consumptions. However, they suffer from draw-backs that include a limited free spectral range (FSR) which limit the number ofchannels that can be simultaneously multiplexed and/or demultiplexed. Our workinvestigates SOI single-ring MRR filters with bent couplers that have extendedFSRs, enhanced filter performance (such as bandwidth, out-of-band rejection ra-tio, side-mode suppression, extinction ratio, and insertion loss) while maintainingcompact footprints. Our aim is to make these filters attractive candidates to thecurrent state-of-the-art WDM transceivers.We first demonstrated a 2.75 µm radius MRR filter that employs bent direc-tional couplers in its coupling regions. This MRR filter was fabricated using a 248nm photolithography process. Our filter has a 33.4 nm FSR and a 3-dB bandwidthof 25 GHz. Also, our MRR achieved an out-of-band-rejection ratio of 42 dB, anextinction ratio of 19 dB, and a drop-port insertion loss that is less than 1 dB.Lastly, our MRR filter has a tuning efficiency of 12 mW/FSR. Then, we theoreti-cally and experimentally demonstrated an MRR filter with bent contra-directionalcouplers that exhibits an FSR-free response, at both the drop and through ports,while achieving a compact footprint. Also, using bent contra-directional couplersin the coupling regions of MRRs allows us to achieve larger side-mode suppres-sions than MRRs with straight CDCs. The fabricated MRR filter has a minimumiisuppression ratio of more than 15 dB, a 3dB-bandwidth of ∼23 GHz, a through-port extinction ratio of ∼18 dB, and a drop-port insertion loss of ∼1 dB. High-speed data transmission through the MRR filter is demonstrated at data rates of12.5 Gbps, 20 Gbps, and 28 Gbps.iiiPrefaceThis thesis is based on two publications on which I am the main author. The con-tent of Chapter 2 is based on the following publication, which has been accepted,[1]:1. N. Eid, H. Jayatilleka, M. Caverley, S. Shekhar, L. Chrostowski, andN. A. F. Jaeger, ”Wide FSR silicon-on-insulator microring resonator withbent couplers,” in IEEE 12th International Conference on Group IV Pho-tonics, 2015. c©2015 IEEE. Material including text and figures used withpermission.H. Jayatilleka and I conceived the idea. H. Jayatilleka created the mask layout. Idid the design and simulations for the device, and performed the measurementsfor the fabricated device and the data analysis. M. Caverley helped me in perform-ing the parameter extraction for the fabricated device. L. Chrostowski providedaccess to the fabrication technology used. I wrote the first draft of the manuscript,and N. A. F. Jaeger and M. Caverley worked with me to determine the final con-tent and to edit the manuscript. S. Shekhar, L. Chrostowski, and N. A. F. Jaegerprovided insights during the design process and S. Shekhar and L. Chrostowskifeedback on the manuscript.ivThe content of Chapter 3 is based on the following publication which has beenaccepted:2. N. Eid, R. Boeck, H. Jayatilleka, L. Chrostowski, W. Shi, and N. A. F. Jaeger,”A Silicon-on-Insulator Microring Resonator Filter with Bent Contradirec-tional Couplers,” in IEEE Photonics Conference, 2016. c©2016 IEEE. Ma-terial including text and figures used with permission.N. A. F. Jaeger and W. Shi conceived the idea. R. Boeck provided guidance andinsights at the early stages of the design process. L. Chrostowski obtained accessto the fabrication used in this project. I designed and simulated the device, andcreated the mask layout of the device. I also did measurements on the fabricateddevice and the data analysis. H. Jayatilleka created the setup for the high-speedtesting. I wrote the first draft of the manuscript and N. A. F. Jaeger worked withme to determine the technical content and to revise and edit the manuscript. Allthe co-authors provided feedback on the manuscript.Also, the content Chapter 3 is mainly based on the following publication whichhas been submitted to a journal:3. N. Eid, R. Boeck, H. Jayatilleka, L. Chrostowski, W. Shi, and N. A. F. Jaeger,”FSR-Free Silicon-on-Insulator Microring Resonator Based Filter with BentContra-Directional Couplers,” [submitted in 2016].N. A. F. Jaeger and W. Shi conceived the idea. R. Boeck provided guidance andinsights at the early stages of the design process. L. Chrostowski obtained accessto the fabrication used in this project. I designed and simulated the device, andcreated the mask layout of the device. I also did measurements on the fabricateddevice and the data analysis. H. Jayatilleka created the setup for the high-speedtesting. I wrote the first draft of the manuscript and N. A. F. Jaeger worked withme to determine the technical content and to help in writing the final version ofthe manuscript. All the co-authors provided feedback on the manuscript.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Silicon Photonics . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 WDM Systems and Transceivers . . . . . . . . . . . . . . . . . . 21.3 Filters in WDM Links . . . . . . . . . . . . . . . . . . . . . . . . 41.3.1 Common Types of WDM Filter . . . . . . . . . . . . . . . 51.3.1.1 Echelle gratings . . . . . . . . . . . . . . . . . 51.3.1.2 Arrayed Waveguide Gratings (AWGs) . . . . . . 61.3.1.3 Mach-Zehnder interferometer (MZI) Lattices . . 71.3.1.4 Contra-directional couplers (CDCs) . . . . . . . 81.3.2 MRR Based Filters . . . . . . . . . . . . . . . . . . . . . 9vi1.4 Thesis Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.5 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Wide FSR Silicon-on-InsulatorMicroring Resonator Filter with BentDirectional Couplers . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.1 Bent Directional Couplers . . . . . . . . . . . . . . . . . . . . . . 132.1.1 Analysis of Bent Waveguides . . . . . . . . . . . . . . . . 152.2 Microring Resonators . . . . . . . . . . . . . . . . . . . . . . . . 182.3 Device Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.4 Layout and Fabrication . . . . . . . . . . . . . . . . . . . . . . . 292.5 Measurement Results and Discussion . . . . . . . . . . . . . . . . 302.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 FSR-Free Silicon-on-Insulator Microring Resonator Based Filterwith Bent Contra-Directional Couplers . . . . . . . . . . . . . . . . 373.1 Contra-directional Couplers . . . . . . . . . . . . . . . . . . . . . 383.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 383.1.2 Bent CDCs . . . . . . . . . . . . . . . . . . . . . . . . . 433.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.3 Device Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.4 MRR with Bent CDCs Transfer Function . . . . . . . . . . . . . . 543.5 Theoretical Results . . . . . . . . . . . . . . . . . . . . . . . . . 573.6 Device Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . 593.7 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . 603.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.9 High-Speed Testing . . . . . . . . . . . . . . . . . . . . . . . . . 653.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694 Summary, Conclusions, and Suggestions for Future Work . . . . . . 714.1 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . 714.2 Suggestions for Future Work . . . . . . . . . . . . . . . . . . . . 73viiBibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76viiiList of TablesTable 2.1 MRR with bent couplers filter design parameter variations. . . . 30Table 2.2 Summary of the theoretical and measured results of our MRRfilter with bent couplers. . . . . . . . . . . . . . . . . . . . . . 32Table 2.3 Comparison of our MRR filter with other single-ring MRR filters. 35Table 3.1 Our MRR with bent CDCs filter design parameters. . . . . . . 54Table 3.2 Summary of the as-designed, measured, and fitted results ofour MRR filter with bent CDCs and its comparison with theresults of a previously demonstrated MRR with straight CDCs. 63Table 3.3 List of equipment used in our setup to measure the eye dia-grams and BERs of our MRR filter. . . . . . . . . . . . . . . . 66ixList of FiguresFigure 1.1 A block diagram of a wavelength-division multiplexing (WDM)transceiver, which is composed of a four-channel transmitterand a four-channel receiver. The block diagram shows theoptical components of the transceiver, but not the electricalcomponents. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Figure 1.2 A schematic of an echelle gratings filter that is used as a DE-MUX. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Figure 1.3 A schematic of an AWG filter that is used as a DEMUX. . . . 7Figure 1.4 A schematic of an MZI lattice filter. . . . . . . . . . . . . . . 8Figure 1.5 A schematic of a CDC coupler that is used as a filter. . . . . . 9Figure 2.1 A schematic of a bent directional coupler. . . . . . . . . . . . 14Figure 2.2 A plot of (a) nBRB versus WB and (b) |κ|2 versus WB for a bentcoupler with R = 5 µm, WR = 500 nm, and g = 200 nm. Theplot of the fitted data in (b) is done using the shape-preservingfit in MATLAB R©. . . . . . . . . . . . . . . . . . . . . . . . 16Figure 2.3 The electric field profile of the fundamental quasi-TE modein (a) a straight waveguide, (b) a bent waveguide with a bendradius, R, of 3 µm, and (c) a bent waveguide with R = 1.5 µm.The waveguides have widths of 650 nm and heights of 220nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16xFigure 2.4 Plots of (a) the effective index, (b) the group index, (c) theradiation loss in dB/µm, and (d) the power coupling loss indB at various values of bend radius, R. . . . . . . . . . . . . . 17Figure 2.5 Schematics of (a) a racetrack resonator and (b) a point-coupledMRR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Figure 2.6 A plot showing the drop-port and through-port responses of anMRR. An inset shows zoomed-in responses around the reso-nant wavelength. . . . . . . . . . . . . . . . . . . . . . . . . 21Figure 2.7 A schematic of our MRR with bent couplers. . . . . . . . . . 26Figure 2.8 A plot of nBRB versus WB of our MRR filter. This plot is usedto design the bent couplers, in our filter, for the phase-matchcondition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Figure 2.9 Plots of (a) the 3dB-BW, (b) the OBRR, (c) the ILdrop, and (d)the ER of a symmetric add-drop MRR filter (R = 2.75 µm) atvarious |κ|2 values. . . . . . . . . . . . . . . . . . . . . . . . 27Figure 2.10 A plot of |κ|2 at various θ values of the simulated bent couplers. 28Figure 2.11 Theoretical responses of our MRR filter, at the drop port andat the through port, when |κ|2 = 0.02. . . . . . . . . . . . . . 29Figure 2.12 (a) Measured spectral responses of the through and drop portsover the wavelength range 1510 nm to 1560 nm. (b) Normal-ized spectral responses, in GHz, at the through and drop portsfor the resonance at 1549.6 nm. . . . . . . . . . . . . . . . . . 31Figure 2.13 (a) Drop-port responses at various total tuning powers. (b)Plot of the total tuning power versus wavelength shift. . . . . . 33Figure 2.14 (a) The power coupling coefficient, |κ|2, from measurementdata and FDTD simulations, versus θ . . . . . . . . . . . . . . 34Figure 2.15 Measured spectral responses, in GHz, at the through (dashedlines) and drop ports (solid lines) for θ = 5◦ (blue), θ = 10◦(red), and θ = 20◦ (green). . . . . . . . . . . . . . . . . . . . 34xiFigure 3.1 A schematic of a straight CDC that has a coupling length ofLc. The inset shows a zoomed-in section of the CDC withdesign parameters illustrated on it. . . . . . . . . . . . . . . . 39Figure 3.2 Plot illustrating the phase-match conditions of a straight CDCfor wavelengths λD, λB, and λR. . . . . . . . . . . . . . . . . 41Figure 3.3 Plots of the magnitude-squared responses of a CDC at thedrop port (|κc|2) and at the through port (|tc|2). . . . . . . . . 42Figure 3.4 A schematic of a bent CDC that has a coupling length of Lc.The inset shows a zoomed-in section of the CDC on which thedesign parameters and the bend angle, θΛ, are illustrated. . . . 44Figure 3.5 (a) A schematic of an MRR with straight CDCs and (b) aschematic of an MRR with bent CDCs. The dark waveguidesections in both of the schematics are the CDCs. . . . . . . . . 46Figure 3.6 A CDC’s spectral response (dashed trace) and an MRR’s re-sponse (solid trace) when ∆λnull = 2FSR. . . . . . . . . . . . 46Figure 3.7 Plots of the required MRR’s coverage with the CDCs (γ) toachieve maximum suppression versus Lrt for MRRs with straightCDCs and MRRs with bent CDCs. . . . . . . . . . . . . . . . 48Figure 3.8 Plots of Kc, in dB, versus Lrt for MRRs with straight CDC andMRRs with bent CDCs at γ = 87%. . . . . . . . . . . . . . . 49Figure 3.9 (a) A CDC’s spectral response and an MRR’s response when∆λnull > 2FSR. . . . . . . . . . . . . . . . . . . . . . . . . . 50Figure 3.10 Schematic of an MRR with bent CDCs, as well as an insetshowing a zoom-in of a section of a bent CDC. The dark bluetraces are the corrugated waveguides (gratings) of the CDCs. . 51Figure 3.11 Plots of the MRR’s coverage with the CDCs (Lc/piR) versusR at various κo values. . . . . . . . . . . . . . . . . . . . . . 52Figure 3.12 Plot of Kc, in dB, versus R at κo = 8000 m−1. . . . . . . . . . 52xiiFigure 3.13 Theoretical spectral responses, for the simulated bent CDC(using FDTD), of the power transmission (|tc|2) at the throughport, the power coupling (|κc|2) at the drop port, as well as thefitted CDC response at the drop port. . . . . . . . . . . . . . . 53Figure 3.14 Diagrams illustrating the gains of (a) loop L1, (b) path FD1,(c) path FT 1, and (d) path FT 2. . . . . . . . . . . . . . . . . . 55Figure 3.15 Theoretical spectral responses of our MRR filter with bentCDCs at the drop port, Tdrop, and at through port, Tthru. . . . . 57Figure 3.16 The (a) group delay (GD) and (b) chromatic dispersion (CD)at the drop-port around 1537.2 nm. . . . . . . . . . . . . . . . 58Figure 3.17 A microscopic image of our MRR filter with metal heaters;the inset shows a scanning electron microscope (SEM) imageof a portion of a bent CDC. . . . . . . . . . . . . . . . . . . . 59Figure 3.18 (a) Spectral responses of our MRR filter at the drop and throughports; the illustrated SMSR is 15.3 dB. (b) The responses rel-ative to 1540.3 nm, after normalizing them with respect to thegrating couplers’ responses. . . . . . . . . . . . . . . . . . . 60Figure 3.19 (a) Drop-port responses at various total tuning powers. (b)Plot of the total tuning power versus wavelength shift. . . . . . 61Figure 3.20 Chromatic dispersion at the drop port in a 25 GHz windowrelative to 1540.3 nm. . . . . . . . . . . . . . . . . . . . . . . 62Figure 3.21 Drop-port spectral responses from the measured data and fromEdrop calculated using fitted κo and α values relative to 1540.3nm, as well as the theoretical drop-port response obtained insection 3.5 relative to 1537.2 nm. . . . . . . . . . . . . . . . . 64Figure 3.22 Block diagram showing the experimental setup used to mea-sure the eye diagrams of our filter . . . . . . . . . . . . . . . 65xiiiFigure 3.23 Eye diagrams of NRZ data at the input of our filter at 1540.3nm for data rates of (a) 12.5 Gbps, (b) 20 Gbps, and (c) 28Gbps as well as at the drop port (output) for data rates of (d)12.5 Gbps, (e) 20 Gbps, and (f) 28 Gbps. Eye diagrams ofNRZ data at 1533.1 nm at the input of our filter for data ratesof (g) 12.5 Gbps, (h) 20 Gbps, and (i) 28 Gbps as well as atthe through port (output) for data rates of (j) 12.5 Gbps, (k)20 Gbps, and (l) 28 Gbps. . . . . . . . . . . . . . . . . . . . . 67Figure 3.24 Diagram showing the experimental setup used to measure theBER of our filter. . . . . . . . . . . . . . . . . . . . . . . . . 68Figure 3.25 Measured BERs versus received optical power at the PD atdata rates of 12.5 Gb/s, 20 Gb/s, and 25 Gb/s at the drop port,at 1540.3 nm, and at the through port, at 1533.1 nm. . . . . . . 69Figure 4.1 (a) A schematic of a proposed two series-coupled Vernier ringfilter with bent directional couplers in their bus to ring cou-pling regions and adiabatic tapering of the widths of the waveg-uides of the microrings. (b) A schematic of a proposed twoseries-coupled Vernier ring filter with bent directional cou-plers in all of its coupling regions. . . . . . . . . . . . . . . . 74Figure 4.2 A schematic of an MRR with bent CDC in one of its couplingregions and a tunable directional coupler in the other couplingregion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75xivList of AcronymsSOI silicon-on-insulatorPIC photonic integrated circuitWDM wavelength-division multiplexingDWDM dense WDMDWDM dense wavelength-division multiplexingSFP small form-factor pluggableQSFP quad small form-factor pluggableCFP C form-factor pluggableMUX multiplexerDEMUX demultiplexerOADM optical add-drop multiplexerFSR free spectral rangeAWG arrayed waveguide gratingMZI Mach-Zehnder interferometerMRR microring resonatorxvCDC contra-directional couplerPD photodetectorMZM Mach-Zehnder modulatorGC grating coupler3dB-BW 3dB-bandwidthER extinction ratioOBRR out-of-band rejection ratioSMSR side-mode suppression ratioBER bit error rateBERT bit error rate testerVOA variable optical attenuatorPPG pulse pattern generatorEDFA erbium-doped fiber amplifierOTF optical tunable filterDCA digital communication analyzerTLS tunable laser sourcexviAcknowledgmentsI would like to begin by expressing my profound gratitude to my parents andto my spouse for providing me with the support and continuous encouragementthroughout my studiesI also express my sincere gratitude to my supervisor Dr. Nicolas A. F. Jaegerfor the guidance and mentorship that he has provided me. I am especially gratefulfor his continuous support and patience during my studies. I would also like tothank Dr. Lukas Chrostowski for all the opportunities and useful feedback thathas assisted me during this work.I would also like to thank all my colleagues, that I have worked with, for theirhelp and collaboration, and especially Hasitha Jayatilleka, Robert Boeck, MichaelCaverley, Han Yun, Kyle Murray and Minglei Ma.I acknowledge Ranovus Inc. for providing an internship opportunity duringmy studies. I also acknowledge CMC Microsystems for the provision of ser-vices that facilitated this research as well as Lumerical Solutions, Inc., and Men-tor Graphics, Corp., for the design tools. Additionally, I acknowledge the NaturalSciences and Engineering Research Council of Canada as well as the SiEPIC pro-gram for financial support. Part of this work was conducted at the University ofWashington Nanofabrication Facility, a member of the NSF National Nanotech-nology Infrastructure Network..xviiChapter 1Introduction1.1 Silicon PhotonicsSilicon-on-insulator (SOI) is an attractive platform for photonic integrated circuits(PICs) used in telecommunication applications as well as in high-performancecomputing systems [2, 3]. Thus, tremendous research efforts have been targetedtoward silicon photonics by the research community in academia and industry.An advantage of SOI is that on it devices can be fabricated using complementarymetal-oxide-semiconductor (CMOS) compatible processes which are mature andreliable, are low cost, and allow for monolithic integration of the photonics de-vices with the electrical circuits [4]. In addition, the high refractive index contrastbetween the silicon waveguides and the oxide cladding allow for the creation ofcompact devices and small waveguide bends. This facilitates dense integration ofthe optical components in order to realize photonic chips with small footprints.There are numerous optical components that are demonstrated on SOI platforms,such as detectors [5, 6], modulators [7], filters [8], edge couplers [9], grating cou-plers [10], and polarization splitters-rotators [11].11.2 WDM Systems and TransceiversWavelength-division multiplexing (WDM) is widely used in the optical intercon-nects of data centers and high-performance computing systems [12–15]. In WDMsystems, multiple channels of optical signals (each channel having a different cen-ter wavelength) are simultaneously transmitted over the same fiber. As a result,WDM systems provide means for increasing the aggregate bandwidths of the op-tical links; namely, if a WDM system has N channels and each channel trans-mits at data rate R, then the aggregate data rate of the link is NxR. In fact, someWDM based links can transmit several terabits per second [16, 17]. WDM sys-tems can either be coarse WDM (CWDM) systems, which can transmit up to 16channels per fiber, or dense WDM (DWDM) systems, where channels are moreclosely spaced and can transmit up to 80 channels per fiber (at a 50 GHz channelspacing) [18]. While, DWDM based links can transmit a larger number of chan-nels per fiber and have higher aggregate bandwidths than CWDM links, each ofthe channels in a CWDM system has a wider bandwidth and a flat-top response.Thus, CWDM systems have more tolerance to laser wavelength drift [19]. As aresult, CWDM systems are used in short-range communications as stable lasersources (which are expensive) are not required, and hence such systems are morecost-effective. On the other hand, DWDM systems are predominantly used inlong-haul communications. This is because in long-haul communications, it ismore desirable to transmit a large number of channels in a single fiber, as well asthe costs associated with having stable laser sources can be tolerated in long-haulcommunications.WDM transceivers are important components for optical interconnects. Fig-ure 1.1 shows the block diagram of a typical architecture of a four-channel WDMtransceiver. At the transmitter end, various lasers, each having a unique wave-length, are modulated by the input data; the most common implementations of themodulators include Mach-Zehnder modulators [20, 21], electro-absorption modu-lators [22, 23], and microring modulators [24–27]. The modulated optical signalsare then multiplexed into the fiber channel via a multiplexer (MUX) that is made2cModulatorcModulatorcModulatorcModulatorDetectorcDetectorcDetectorcDetectorcOptical Fiber4:1 MUX 1:4 DEMUXCW Laser λ1λ2λ3λ4λ1 λ3λ2 λ4CW LaserCW LaserCW LaserRx Out 4Data In 2Data In 3Data In 4Data In 1Rx Out 2Rx Out 3Rx Out 1Transmitter Receiver (Rx) Figure 1.1: A block diagram of a WDM transceiver, which is composed ofa four-channel transmitter and a four-channel receiver. The block di-agram shows the optical components of the transceiver, but not theelectrical components.from several optical add-drop multiplexers (OADMs). At the receiver end, theoptical signals are demultiplexed via a demultiplexer (DEMUX), also made fromseveral OADMs. The de-multiplexed optical signals are then converted to elec-trical signals via photodetectors (PDs). Such detectors can be Germanium PINphotodetectors [28] or avalanche photodiodes [29].Several companies are developing WDM transceivers that use the SOI plat-form for optical interconnects. Intel, for instance, demonstrated a 40 Gbps siliconphotonics CWDM link; the link is made of four channels and each channel carriesa data rate of 10 Gbps (4 x 10 Gbps) [30]. Luxtera has also developed a 4 x 10Gbps monolithically integrated transceiver [31], and has recently announced its 4x 26 Gbps transceiver for data centers [32]. In addition, IBM has demonstratedits fully integrated silicon photonics chip for 100 Gbps WDM transceivers [33].Skorpios Technologies has demonstrated a 100 Gbps WDM transceiver that usesan SOI platform [34]. Lastly, Inphi and M/A-COM have each recently announcedtheir silicon photonics transceiver chips for 100G WDM data center applications[35, 36]. A large number of the WDM transceivers developed commercially are3small form-factor pluggable (SFP) transceivers. There are two common types ofSFP transceivers: quad small form-factor pluggable (QSFP) transceivers, whichsupport four WDM channels and speeds up to 100 Gbps [37], and C form-factorpluggable (CFP) transceivers, which support 40G and 100G Ethernet [38]. Hence,there is a trend toward developing compact and pluggable transceiver modulesthat can support high-speed data signals of up to 100 Gbps and 400 Gbps [39].QSFP28 transceivers, which are QSFP transceivers that support four channelseach with data rates of 28 Gbps, are an example of the demand to increase theaggregate bandwidths supported by WDM transceivers, by increasing the numberof transmit channels, while maintaining the small footprints of SFP chips [40].The transceivers discussed above that are offered by Luxtera, Skorpios Technolo-gies, Inphi, and M/A-COM are QSFP28 transceivers.1.3 Filters in WDM LinksFilters are important building blocks of WDM transceivers where they are used asOADMs on both the transmitter and receiver sides. There are some design param-eters that a proposed filter design should have in order to be used in commercialWDM transceivers [41, 42]. One of the design requirements is that a WDM filtershould have a compact footprint so that it can be used in SFP transceiver chips.This design requirement becomes especially important in QSFP transceivers wherethe circuits of these transceivers can have up to four filters (for the four trans-mit channels), and these circuits should be within the space requirements of SFPchips. As a result, it is important to keep these filters as compact as possibleand densely integrate the components of SFP transceivers. Another filter designrequirement is that a transceiver should have a large channel capacity, and accord-ingly a filter should have a wide free spectral range (FSR) to increase the numberof channels that can be MUXed/DEMUXed in a particular band. Furthermore,a filter should have a wide bandwidth per channel which contributes to increas-ing the aggregate bandwidth of the link. For instance, the filters used in QSFP28transceivers should have bandwidths that support at least 28 Gbps. Additionally,4a filter is required to have good thermal efficiency to reduce the amount of powerrequired to tune the center wavelengths. Additionally, a filter should have lowchannel cross-talk [43], have low insertion loss, have a tolerance to fabricationerrors and temperature changes, and be fully reconfigurable (for instance in band-width [44]) .1.3.1 Common Types of WDM FilterSome of the most common types of filter used in WDM transceivers includeechelle gratings [45], arrayed waveguide gratings (AWGs) [46], Mach-Zehnderinterferometer (MZI) lattices [47], and contra-directional couplers (CDCs) [48].In this section, we will describe the principle of operation of each of these filtersand present some of their strengths and weaknesses.1.3.1.1 Echelle gratingsA schematic of an echelle grating filter is shown in Figure 1.2. In echelle gratingfilters, when used as DEMUXs, light from the input waveguide enters the freepropagation region where it diverges and propagates to the diffraction grating.The etched facets (teeth) of the diffraction grating cause the light to diffract atangles which are wavelength dependent. Also, the angle of diffraction at eachincident wavelength depends on where on the grating it impinges. The diffractedlight is focused onto a series of output waveguides bu the grating, such that thelight focused on each of the waveguides has a unique wavelength. This operationis reversed when echelle grating filters are used as MUXs. Because the designsof echelle gratings require careful placement of the input and output waveguides,the filter performance is sensitive to fabrication errors [49]. Furthermore, echellegrating filters occupy relatively large footprints and have relatively large insertionlosses.5Inputλ1λ1 , λ2 , λ3λ2λ3 Free Propagation RegionDiffraction GratingsOutputInput WaveguideOutput WaveguidesFigure 1.2: A schematic of an echelle gratings filter that is used as a DE-MUX.1.3.1.2 Arrayed Waveguide Gratings (AWGs)A schematic of an AWG is shown in Figure 1.3. The AWG is similar in principleto the echelle grating. In AWGs, when used as DEMUXs, the input light is split,via a coupler (such as a star coupler), into multiple paths which then propagatethrough an array of waveguides. Each waveguide has a constant increment (plusor minus) in length with respect to its adjacent waveguides. The linearly increas-ing lengths of the array of waveguides cause linearly varying phase shifts at theoutputs across the waveguides. These phase shifts are wavelength-dependent suchthat the wavefront for a particular wavelength, at the end of the waveguide array,is tilted at a certain angle such that the light is directed towards a particular outputwaveguide. As a result, the light propagating in each of the output waveguideswill have a unique wavelength.AWG filters occupy relatively large footprints and have large insertion losses.However, in an AWG, its design can allow for independently tuning each of thewaveguides to control the wavelengths of each of the output channels, which isnot possible in echelle grating filters. However, the different waveguides are proneto thermal crosstalk.6λ1  , λ2λ3  , λ4InputWaveguideOutput Waveguidesλ1 λ2 λ3 λ4CouplersArray of WaveguidesFigure 1.3: A schematic of an AWG filter that is used as a DEMUX.1.3.1.3 MZI LatticesAn MZI lattice filter is made from multiple cascaded stages of unbalanced MZIsas shown in the schematic in Figure 1.4. In an unbalanced MZI, one of the arms ofthe MZI has a different length with respect to the other arm; this causes construc-tive interference at certain wavelengths, at the output, because of the wavelength-dependent phase delay. As a result, such an MZI will have a sinusoidal responsewith peaks at equally spaced wavelengths. In this filter, a series of cascaded unbal-anced MZIs are used so that each of the stages filters out some of the wavelengthpeaks and passes the remaining wavelengths, see Figure 1.4. Accordingly, theresulting output response of this filter will have a single wavelength peak at aparticular band.In order to use such a filter as a MUX/DEMUX, the first MZI stage should bebranched into a tree of MZIs, each of the branches selecting a unique wavelength.As apposed to echelle gratings and AWG filters, MZI lattice filters can achievelower insertion losses. However, active tuning is required to align all of the MZIstages, which increases the power consumed by the filter. Also, MZI lattice filters(especially when used as a MUX/DEMUX) can have large footprints.7Inputλ1  , λ2λ3  , λ4λ1 , λ2  , λ4 λ2  , λ4 λ2  OutputMZI Stage 1 MZI Stage 2 MZI Stage 3Unbalanced MZIFigure 1.4: A schematic of an MZI lattice filter.1.3.1.4 Contra-directional couplers (CDCs)CDCs are another type of add-drop filter that can be used in WDM based links[48]. The contra-directional coupling occurs due to the corrugations (gratings) onthe inner sidewalls of the waveguides which cause coupling between the forwardpropagating mode of one waveguide and the backward propagating mode of theother waveguide (see Figure 1.5) [50]. The contra-directional coupling occursat the wavelength at which the phase-match condition is satisfied, and thus theyare used as filters. CDCs have flat-top responses with wide bandwidths, that canexceed 3 nm. These wide bandwidths allow for error-free transmission withina range of operating temperature drift of the laser and the filter, and thus CDCshave higher temperature tolerance than other types of filters. Nevertheless, CDCsare not appropriate for DWDM systems, where a spacing as low as 50 GHz isrequired. This is because a CDC, with a typical coupling length, will have abandwidth that exceeds a typical DWDM channel spacing (50 GHz to 200 GHz).Moreover, CDCs have feature sizes that are small and comparable, or less than,photolithography wavelengths (193 nm or 248 nm). This makes it difficult tofabricate CDCs using conventional optical lithography processes. In other words,the gratings in the walls of a CDC, fabricated using optical lithography, will besmoothed by the lithography and fabrication errors are more likely to occur.8InputDropThroughGratingsλ1  , λ2λ3  , λ4λ2λ1  , λ3  , λ4Figure 1.5: A schematic of a CDC coupler that is used as a filter.1.3.2 MRR Based FiltersSilicon microring resonator (MRR) based filters are attractive candidates in WDMtransceivers because of their compact sizes and low power consumptions [17]. Onthe other hand, due to the relatively high sensitivity of MRRs, wavelength stabi-lization is typically needed to offset the effect of fabrication errors and changesin the external environment on the resonant wavelengths of MRRs. Although,there are several stabilization techniques that have been demonstrated, especiallyfor single-ring MRRs [51], MRR stabilization, in general, is a disadvantage forMRRs as power is needed to stabilize them.In addition, MRRs have limited FSRs which limits the number of transmitchannels in a particular band, and hence the aggregate bandwidth of the link. Asa result, several MRR designs have been demonstrated that extended the MRR’sFSR [41]. One technique uses the Vernier effect in which multiple series-coupledMRRs are used to extend the FSR [52]. Another method proposed is to use two-point coupling to an MRR in which an MZI is used as the coupler to act as afilter to the MRR side modes [53]. Although the previously mentioned techniqueshave been effective in increasing the MRRs’ FSRs and in demonstrating MRRfilters with improved performance (in some cases the demonstrated filters met theDWDM commercial specifications [54]), they have complex designs. As a re-sult, designing the MRRs that use these techniques is relatively complicated andstabilizing them using automatic control algorithms can be difficult. Also, thesedesigns were not compact and required tuning several MRRs which increased thepower consumption of the filter. In conclusion, because of some of the aforemen-9tioned drawbacks of MRR filters, they are not widely used in commercial WDMtransceivers. Accordingly, more research effort needs to be invested to improvethe designs of MRR filters and mitigate their weaknesses.1.4 Thesis ObjectiveThe goal of the research presented in this thesis is to design MRR based fil-ters and solve some of the weaknesses discussed above (in section 1.3.2). Thiswork is aimed at making MRRs more appealing as filters in commercial WDMtransceivers. Specifically, we used bent couplers in our MRR filters to improvetheir designs. One of our objectives is to use single-ring MRR filters, with ex-tended FSRs, as they can be more compact and energy-efficient solutions as com-pared to multiple-coupled MRR filters. Thus, we proposed a wide FSR, single-ring MRR filter with bent directional couplers. Bent directional couplers allow forfabrication of small radii MRRs using 248 nm optical lithography, while achiev-ing wide FSRs and enhanced performance. Thus, our demonstrated MRR filterwith bent couplers has an FSR of ∼ 34 nm and also has sufficient coupling coeffi-cient to achieve a wide 3dB-bandwidth (3dB-BW) of 25 GHz and an out-of-bandrejection ratio (OBRR) of 42 dB. Such results were previously difficult to achieveusing MRRs fabricated using typical optical lithography processes.CDCs are another kind of coupler that are used to extend the FSRs of single-ring MRR filters. Since CDCs are wavelength selective couplers, they have beenused in the coupling regions of MRRs to eliminate the FSRs (within the wave-length range over which silicon is transparent) [55]. Thus, an ”FSR-free” re-sponse can be achieved using MRR filters consisting of a single ring. In thisthesis, we propose and demonstrate an MRR filter that uses bent CDCs in the cou-pling regions, instead of straight CDCs, and thus obtain a more compact filter ascompared to a previously demonstrated single-ring MRR filter that used straightCDCs (three-fold decrease in the filter’s footprint) [55]. Also, our design achievesimproved performance and side-mode suppression as compared to the previouslydemonstrated filter [55].101.5 Thesis OverviewThis thesis is divided into four chapters. In this chapter, we give a brief in-troduction to silicon photonics, as well as an overview of WDM systems andtransceivers. Then, we discuss the various kinds of filter used in WDM transceiversas well as the current challenges in using MRR based filters in current commercialWDM transceivers. Also, various implementations of MRR filters are presentedand the thesis objective is outlined. In the next two chapters, we present and ex-perimentally demonstrate, two kinds of MRR based filter that use bent couplersin their coupling regions. Chapter 2 presents an MRR filter with bent directionalcouplers that is compact, has a wide FSR, and a wide bandwidth. Chapter 3presents an MRR filter with bent CDCs that is more compact than a previouslydemonstrated MRR filter with straight CDCs, has an FSR free response at boththe drop port and the through port, has a relatively large side-mode suppression,and has a wide bandwidth. Finally, in Chapter 4, a summary of the thesis, as wellas conclusions and suggestions for future work are provided.11Chapter 2Wide FSR Silicon-on-InsulatorMicroring Resonator Filter withBent Directional CouplersMRR based filters are attractive for use in PICs due to their compact footprints. Inapplications such as WDM, a wide FSR, that is greater than the C-band, is desir-able in order to add or drop only a single channel in the band. As a consequence,many SOI MRR based designs have been proposed and demonstrated to achievethis goal, such as using MRRs with two-point coupling [53] or the Vernier effect[56]. However, these schemes use mutually coupled rings, which require tuningof the resonance wavelength of each ring. Alternatively, single-ring MRRs areattractive because they have smaller footprints and there are techniques availablefor stabilizing their resonance wavelengths [51, 57]. Hence, significant effort hasgone into creating MRRs with radii below 3 µm in order to widen their FSRs [58–60]. Such small radius MRRs are typically point coupled [58–60]. When usingpoint coupled MRRs, small gaps are usually used to achieve the coupling neededto obtain wide bandwidths. These small gaps have usually been realized on SOIusing electron-beam lithography.Here, in this chapter, using bent directional couplers, that are wrapped around12a portion of the ring, [61, 62] are explored. By using bent directional couplers, theMRR’s coupling coefficient can be increased because the couplers have longercoupling lengths and, therefore, allowing the use of coupler gaps large enoughfor fabrication using optical lithography. Optical lithography is preferable overelectron-beam lithography because it is low cost and it allows for mass productionof PICs. The MRRs presented here are also designed with optimal phase-matchingin the couplers to maximize the MRRs’ coupling coefficients and to increase theirbandwidths. We will describe below (in section 2.1) how to achieve the optimalphase-matching in bent directional couplers, as well as give a brief introduction tobent directional couplers. Also, we will derive (in section 2.2) the equations usedto optimize an MRR design for a target 3dB-BW, OBRR, ILdrop, and extinctionratio (ER). Last but not least, we will describe the design procedure and presentexperimental results for an MRR using bent couplers that has a 2.75 µm radius, a33.4 nm FSR, and a 3dB-BW of 25 GHz.2.1 Bent Directional CouplersBent directional couplers are made of two waveguides in which one of the waveg-uides, the bus waveguide in this case, is partially curved around another waveg-uide, the ring waveguide, as shown in Figure 2.1. Bent couplers have been pre-viously demonstrated to be more broadband (less wavelength sensitive) and tobe more reliable and tolerant to fabrication errors than conventional directionalcouplers [63]. Thus, they have been used as broadband 50/50 splitters (or cou-plers) [64], as well having been proposed as short, broadband polarization split-ters [65, 66]. Additionally, 50/50 splitters based on bent couplers have been usedin MZIs to form compact, low insertion loss, high extinction ratio MZI switches[67]. Bent couplers were also used in the coupling regions of all-pass MRRs [62]and fourth-order (i.e., using four series-coupled MRRs) MRR filters [61] to in-crease the coupling coefficients of these MRRs. Although these bent couplerswere proposed as broadband couplers, we intend to use them in our MRR filtersfor the purpose of increasing their couplings and not to make use of their broad-13RWBgInputCrossThroughRBWRWaveguide RWaveguide BFigure 2.1: A schematic of a bent directional coupler.band operation.In a bent directional coupler, the bend radius of the bus waveguide is differentthan the bend radius of the ring waveguide. Thus, the ring and bus waveguideshave different coupling lengths. In the case that the ring and bus waveguides areidentical (i.e., have the same widths and propagation constants), the local normalmodes of the bus and ring waveguides at any point along the coupler will havedifferent phases and will not be phase-matched. Here, we assume that each ofthe waveguides will support one local normal mode and that the waveguides areisolated. As a result, a full exchange of power between the waveguides (whenused in a bent coupler) will not be possible and the cross coupling coefficientswill be lower than what could be achieved in conventional directional couplers.Hence, in order to optimize the coupling coefficients in bent couplers, the busand ring waveguides should be asymmetric (i.e., have different widths) so that thephase-match condition is satisfied; the phase-match condition is given bynBRB = nRR (2.1)where nB and nR are the effective indices of the fundamental local normal modesin the bus waveguide (waveguide B) and the ring waveguide (waveguide R), re-spectively. R is the bend radius of waveguide R, and RB is the bend radius of14waveguide B and is given byRB = R+WR2+g+WB2(2.2)where WR and WB are the widths of waveguides R and B, respectively, and g isthe coupler’s gap width. Here, nB and nR depend on WB and WR. Accordingly, todesign a bent coupler, our desired values for R, WR, and g are first chosen. WB isthen designed to satisfy the phase-match condition for these chosen values. Thisis done by plotting nBRB at various values of WB, and choosing WB at the pointat which our curve intersects our nRR value; this is illustrated in Figure 2.2(a).Here, R = 5 µm, WR = 500 nm, and g = 200 nm and, according to the plot, WBis 380.8 nm (at the point nBRB = nRR = 12.2 µm). In order to verify the phase-match condition, the demonstrated bent coupler is simulated in Lumerical FDTDSolutions by Lumerical Solutions, Inc. Here, the bent coupler is simulated atvarious values of WB (including WB = 380.8 nm), and the resulting cross powercoupling coefficient, |κ|2, is plotted for these WB values as shown in Figure 2.2(b).In the plot, the maximum |κ|2 value occurs at WB = 380.8 nm, which is clearlyclose to the maximum attainable |κ|2 for the simulated coupler.2.1.1 Analysis of Bent WaveguidesGiven that bent waveguides form an important part of bent couplers and MRRs,the effects of bending on the effective indicies, group indicies, and losses of bentwaveguides are presented in this section. The bent waveguides are simulated atdifferent bend radii using Lumerical MODE Solutions by Lumerical Solutions,Inc. Here, the simulated waveguides are strip waveguides with widths of 650 nmand heights of 220 nm, and are surrounded by oxide cladding. The electric fieldprofile of the fundamental quasi-TE mode in a straight waveguide is shown inFigure 2.3(a), and the field profiles of the fundamental quasi-TE mode in bentwaveguides with radii of 3 µm and 1.5 µm are shown in Figure 2.3(b) and 2.3(c),respectively. Clearly, in the straight waveguide, the mode is positioned in the15WB = 380.8 nm (b)(a)WB = 380.8 nm nBRB = nRR = 12.2 μmFigure 2.2: A plot of (a) nBRB versus WB and (b) |κ|2 versus WB for a bentcoupler with R = 5 µm, WR = 500 nm, and g = 200 nm. The plot of thefitted data in (b) is done using the shape-preserving fit in MATLAB R©.(b)(a) (c)Straight Waveguide Bent WaveguideR = 1.5 μmBent WaveguideR = 3 μmFigure 2.3: The electric field profile of the fundamental quasi-TE mode in(a) a straight waveguide, (b) a bent waveguide with a bend radius, R,of 3 µm, and (c) a bent waveguide with R = 1.5 µm. The waveguideshave widths of 650 nm and heights of 220 nm.waveguide such that its peak power coincides with the center of the core of thewaveguide. As the waveguide is bent, the mode is displaced toward the outside ofthe bend; the more the waveguide is bent (i.e., the more the bend radius decreases),the more the mode is pushed toward the outside of the bend.Moreover, the effective indicies, group indicies, and losses (commonly re-ferred to as bending losses) are plotted at various values of bend radii, see Figure16(b)(a)(c) (d)Figure 2.4: Plots of (a) the effective index, (b) the group index, (c) the radi-ation loss in dB/µm, and (d) the power coupling loss in dB at variousvalues of bend radius, R.2.4. The effective index decreases as the bend radius of the waveguide increases asshown in Figure 2.4(a). In addition, the group index decreases as the bend radiusincreases because of the decrease in the effective index, see Figure 2.4(b). Thelosses in bent waveguides are caused by the radiation losses and, predominantly,by the power coupling losses. In Figure 2.4(c), the radiation loss decreases asthe bend radius increases. The power coupling loss arises from mode mismatchesbetween the fields in the straight waveguide section and the bent waveguide sec-tion. The power coupling loss decreases as the bend radius increases as shown in17Figure 2.4(d). This is because, as the bend radius decreases, the mode is pushedfurther out of the waveguide, and the mode mismatch between the straight andbent waveguides increases. In the plot of coupling losses in Figure 2.4(d), there isno offset between the center of the core of the straight waveguide and the center ofthe core of the bent waveguide coupling losses. However, the coupling losses canbe decreased by introducing the necessary offset between the center of the core ofthe straight waveguide and the center of the core of the bent waveguide. In con-clusion, bent waveguides, typically, have larger effective indicies, group indicies,and losses than straight waveguides.2.2 Microring ResonatorsMRRs are commonly used in WDM transceivers as filters and as modulators[17, 68–71]. MRRs can be used in optical delay lines when used as coupledresonator optical waveguides (CROWs) [72], in sensing applications [73], and inexternal cavity lasers as reflectors [74]. MRRs are resonating devices which areformed by having a waveguide in a closed loop (i.e., forming a ring or a race-track) that is coupled to external bus waveguides. The microrings can be coupledto the bus waveguides via directional couplers that have coupling lengths, Lc, asshown in Figure 2.5(a). The MRR shown in Figure 2.5(a) is known as a race-track resonator. The MRR can be also be point coupled, with Lc = 0, as shown inFigure 2.5(b). The MRR shown in Figure 2.5(b) is a classical (round) microringresonator. At the resonant wavelengths, the optical signal in the microring un-dergoes an integer multiple of 2pi phase change when it propagates once aroundthe microring; this leads to the optical signal constructively interfering withinthe resonator and resonance occurs. As a result, there can be multiple resonantwavelengths. The resonances are evenly spaced in frequency and the spacing be-tween them is characterized by the FSR. Here, we use the FSR as the spacing,in wavelength, between the resonances around 1550 nm and is calculated as FSR≈ λ 2r /ngLrt , where λr is the resonant wavelength and ng is the group index. TheFSR is usually controlled by the roundtrip length of the MRR, Lrt , in which the18InputDropThroughAddAddThroughInputDropRjκ2jκ1t2t1Lc(b)(a)jκ1t1jκ2t2LcRLc= 0Lc= 0Figure 2.5: Schematics of (a) a racetrack resonator and (b) a point-coupledMRR.19FSR is inversely proportional to Lrt . Lrt is determined using R and Lc and is givenas Lrt = 2piR+ 2Lc for racetrack resonators and as Lrt = 2piR for point coupledMRRs.Other design parameters are the couplers’ gap widths between the ring andbus waveguides. These gap widths, together with Lc, control the field couplingcoefficients of the couplers. These coupling coefficients are essential in definingthe MRR’s response and, consequently, in determining some of the filter perfor-mance parameters such as the Q-factor, the 3dB-BW, the drop-port insertion loss(ILdrop), the OBRR, and the ER [75]. The MRR’s electric field transfer functionsat the drop port, Gdrop, and the through port, Gthru, are given byGdrop =−κ1κ2√χ1− t1t2χ (2.3)andGthru =t1− t2χ1− t1t2χ , (2.4)respectively, whereχ = a e− j2pinRλ Lrt , (2.5)a = e−α2 Lrt , (2.6)and where nR is the effective index of the ring waveguide and α/2 is the waveg-uide propagation field loss in nepers per meter (i.e., α is the power loss). Also,κ1 and κ2 are the magnitudes of the field coupling coefficients of the couplers asillustrated in Figures 2.5(a) and 2.5(b). t1 and t2 are the magnitudes of the fieldtransmission coefficients and are calculated as (assuming lossless couplers),t1 =√1−κ21 and t2 =√1−κ22 (2.7)Here, we assume that the equations presented, in this section, apply equally toboth of the MRRs in Figures 2.5(a) and 2.5(b), and that both MRRs are asym-metric add-drop MRRs. In asymmetric MRRs, the directional couplers each have203dB-BWILdropOBRRER Tthru(max)Tdrop(min)Tthru(min)Tdrop(max)FSRFigure 2.6: A plot showing the drop-port and through-port responses of anMRR. An inset shows zoomed-in responses around the resonant wave-length.different gap sizes and/or the bus waveguides each have different widths. Fromequations 2.3 and 2.4, the magnitude-squared responses of an MRR at the dropport, Tdrop, and at the through port, Tthru, are given byTdrop = |Gdrop|2 = κ21κ22 a1+(t1t2a)2−2t1t2a cos(φrt) (2.8)andTthru = |Gthru|2 = t21 +(t2a)2−2t1t2a cos(φrt)1+(t1t2a)2−2t1t2a cos(φrt) , (2.9)respectively, where φrt is the phase change (of the electric field) after a roundtripof the micororing and φrt =−2pinR(λo)λo Lrt .The magnitude responses, in equations 2.8 and 2.9, are then used to deriveanalytical equations for the ILdrop, the OBRR, the ER, and the 3dB-BW. The21equations that determine these parameters will be important in our MRR designprocedure; as we shall see, these equations will be used in order to optimize thecoupling coefficients to improve the filter performance. First, we define the peaksand minima of an MRR’s drop-port response and through-port response. Namely,we derive Tdrop(max), which is the maximum power level of the drop-port responsethat occurs at the resonant wavelengths at φrt=-2pim (m = 0,1,2,...) and Tdrop(min),which is the minimum power level of the drop-port response that occurs betweenthe resonant wavelengths at φrt=-2pi(m±0.5). Furthermore, we derive Tthru(max),which is the maximum power level of the through-port response that occurs be-tween the resonant wavelengths (at φrt=-2pi(m±0.5)) and Tthru(min), which is theminimum power level of the through-port response that occurs at the resonantwavelengths (at φrt=-2pim), see Figure 2.6. Accordingly, Tdrop(max), Tdrop(min),Tthru(max), and Tthru(min) are given byTdrop(max) = Tdrop|φrt=−2pim =κ21κ22 a(1− t1t2a)2 , (2.10)Tdrop(min) = Tdrop|φrt=−2pi(m±0.5) =κ21κ22 a(1+ t1t2a)2, (2.11)Tthru(max) = Tthru|φrt=−2pi(m±0.5) =(t1 + t2a)2(1+ t1t2a)2, (2.12)andTthru(min) = Tthru|φrt=−2pim =(t1− t2a)2(1− t1t2a)2 (2.13)ILdrop is defined as the drop-port insertion loss, in dB, at the resonant wavelengths,see Figure 2.6, and is given byILdrop =−10 log10(Tdrop(max)) =−10 log10[κ21κ22 a(1− t1t2a)2](2.14)OBRR is the ratio, in dB, of the power level at the drop port at resonance to the22minimum power level, see Figure 2.6. The OBRR is given byOBRR = 10 log10(Tdrop(max)Tdrop(min))= 20 log10(1+ t1t2a1− t1t2a)(2.15)ER is defined as the ratio, in dB, of the maximum power level at the through-portresponse to the magnitude of the through-port notch at resonance, see Figure 2.6.ER is given byER = 10 log10(Tthru(max)Tthru(min))= 20 log10[(t1 + t2at1− t2a)(1− t1t2a1+ t1t2a)](2.16)Lastly, we will derive an analytical equation for the 3dB-BW of an MRR de-sign. The 3dB-BW is defined as the full-width-at-half maximum power levels. Inother words, the 3dB-BW is the difference between the frequencies, fL and fH ,which occur at the points at which the power levels are equal to half of the peakpower level (i.e., when Tdrop( fL) = Tdrop( fH) = Tdrop(max)/2). This criterion givesκ21κ22 a1+(t1t2a)2−2t1t2a cos(φL) =κ21κ22 a1+(t1t2a)2−2t1t2a cos(φH)=κ21κ22 a2(1− t1t2a)2(2.17)where φL is the phase at frequency fL and is given by φL = 2pinR( fL) fLc Lrt (c isthe speed of light), and φH is the phase at frequency fH and is given by φH =−2pinR( fH) fHc Lrt . Here, we assume that if the maximum power level occurs at theresonant frequency, fr, then fL occurs at fr− 3dB-BW/2 and fH occurs at fr+3dB-BW/2. After simplifying equation 2.17 and solving for φL and φH , we getφH =−φL = arccos[1− (1− t1t2a)22t1t2a](2.18)23We know that arccos(1− x22 )' x for small values of x (x 1). Here, x = 1−t1t2a√t1t2a ,and x is often close to 0, in our MRR designs, given that t1t2a ≈ 1. Thus, φL andφH can be approximated to beφL ' 1− t1t2a√t1t2aandφH '−1− t1t2a√t1t2a ,(2.19)respectively. The 3dB-BW can be obtained by equatingφL−φH = 2pinR( fH) fHc Lrt −2pinR( fL) fLcLrt (2.20)Clearly, φH =−φL. Equation 2.20 can be then rewritten as2φL =2piLrtngc( fH− fL) (2.21)where ng is the group index, which takes into account the effect of dispersionon the effective indicies. After substituting equation 2.19 into equation 2.21 andgiven that 3dB-BW = fH− fL, the 3dB-BW is given by3dB-BW =cpingLrt(1− t1t2a√t1t2a)(2.22)Also, from equation 2.22, the bandwidth as the difference in wavelengths, ∆λ3dB,can be given by∆λ3dB ≈ λ2rpingLrt(1− t1t2a√t1t2a)(2.23)Equation 2.23 is similar to the equation given in [75] for the bandwidth. The Q-factor measures the ability of an MRR to store energy and is commonly definedas24Q-factor = 2pi frenergy stored in the MRRpower dissipated in the MRR(2.24)The Q-factor can also be defined as the sharpness of the resonance relative to itscenter frequency in which case it is given byQ-factor≡ fr3dB-BW(2.25)or, in terms of wavelength, is given byQ-factor≡ λr∆λ3dB(2.26)Using equations 2.23 and 2.26, the Q-factor can be calculated using the followingequationQ-factor≈ pingLrtλr( √t1t2a1− t1t2a)(2.27)2.3 Device DesignA schematic of our proposed MRR with bent couplers is shown in Figure 2.7. OurMRR is composed of two identical bent directional couplers in both of the MRR’scoupling regions to form a symmetric add-drop MRR filter. In this section, theprocedure to design an MRR with bent directional couplers is described. TheMRR has a radius, R, and the bus waveguides have bends in them of radius, 2R,to connect the couplers to external components. The height of the waveguidesis 220 nm and the width of the ring waveguide, WR, is chosen to be 650 nm.Additionally, the gap width of each of the couplers, g, is chosen to be 200 nm.The MRR is designed with a radius, R, of 2.75 µm so as to obtain an FSR of'35 nm (nearly equal to the width of the C-band). For example, taking the groupindex of a 650 nm wide waveguide to be 4, the FSR of our 2.75 µm MRR would be34.8 nm at a wavelength of 1550 nm. The width of the bus waveguide, WB, is thendesigned according to the phase-match condition for bent waveguides [62]. Here,25θRWRWB gθ 2RInputDropThroughFigure 2.7: A schematic of our MRR with bent couplers.7.17 μmWB = 357 nmFigure 2.8: A plot of nBRB versus WB of our MRR filter. This plot is used todesign the bent couplers, in our filter, for the phase-match condition.the effective indicies of the ring and bus waveguides, nR and nB, are obtained usingthe eigenmode solver in Lumerical MODE Solutions. Using the plot in Figure 2.8,and given that WR = 650 nm, g = 200 nm, and R = 2.75 µm, WB is designed to be357 nm (at nBRB = nRR = 7.17 µm in the plot).263dB-BW = 29.6 dBOBRR =  39.5 dBILdrop =  0.5 dBER =  25.07 dB(b)(a)(d)(c)Figure 2.9: Plots of (a) the 3dB-BW, (b) the OBRR, (c) the ILdrop, and (d)the ER of a symmetric add-drop MRR filter (R = 2.75 µm) at various|κ|2 values.Lastly, the bend angle, θ , of our MRR couplers is designed. θ is defined asthe angle from the vertical to the inflection point of the bent coupler, as illus-trated in Figure 2.7. An increase in θ will lead to an increase in the effectivecoupling length and, consequently, an increase in the power coupling coefficient,|κ|2. Thus, in our design procedure the choice of θ depends on our chosen |κ|2value; |κ|2 is chosen to obtain the desired 3dB-BW, OBRR, through-port ER, andILdrop. Accordingly, the 3dB-BW, the OBRR, the ILdrop, and the ER of a sym-27θ = 5 ̊Figure 2.10: A plot of |κ|2 at various θ values of the simulated bent cou-plers.metric MRR are plotted at various |κ|2 values and are shown in Figures 2.9(a),2.9(b), 2.9(c), and 2.9(d), respectively. In these plots, the ILdrop, the OBRR, theER, and the 3dB-BW are calculated using equations 2.14, 2.15, 2.16, and 2.22,respectively. Here κ1 = κ2 = κ , and the ring loss is assumed to be 6 dB/cm; thisloss is chosen to account for the bending losses in a 2.75 µm radius microring.To obtain a target bandwidth of ∼30 GHz, a |κ|2 value of 0.02 is chosen for ourMRR design, see Figure 2.9(a). In addition, at our chosen |κ|2 value of 0.02, theOBRR ' 40 dB (see Figure 2.9(b)), the ILdrop = 0.5 dB (see Figure 2.9(c)), andthe ER ' 25 dB (see Figure 2.9(d)). Accordingly, our chosen MRR filter designshould follow most of the target specifications presented in [76]. Our bent direc-tional coupler is then simulated, in 3D, using Lumerical FDTD Solutions. In thesesimulations, θ is swept (from 0◦ to 20◦) and the resulting |κ|2 values are collectedfor each of the θ values. A plot of |κ|2 at various θ values for our simulated bentcouplers (using FDTD Solutions) is shown in Figure 2.10. The simulations indi-cate that a θ of 5◦ be chosen for our design as it will result in the desired coupling(|κ|2 = 0.02) as seen in Figure 2.10. Using equations 2.8 and 2.9, the responses atthe drop and through ports of our designed MRR filter are shown in Figure 2.11.28From these responses, our MRR filter achieved an FSR of ∼35 nm, which willspan most of the C-band.FSR ≈ 35 nm Figure 2.11: Theoretical responses of our MRR filter, at the drop port and atthe through port, when |κ|2 = 0.02..2.4 Layout and FabricationIn order to account for fabrication variations, MRRs with various values of θ andWB were fabricated. For all variations, g and WR are kept constant at 200 nm and650 nm, respectively. Table 2.1 summarizes the design variations for our MRRfilter. Our filter was fabricated using 248 nm deep-UV photolithography at theIME A*STAR foundry. The waveguides are 220 nm in height and have a topoxide cladding. Metal TiN heaters are also used on top of the waveguides forthermal tuning; the metal heaters are 2 µm wide. Additionally, deep trenches inthe oxide and silicon undercuts, similar to the ones described in [77], are used.The deep trenches are 10 µm wide and are placed ∼2.3 µm away from the MRRs’waveguides. The air trenches surround each of our MRRs for thermal isolation.Also, some of the underlying silicon beneath the MRRs’ waveguides and betweenthe trenches is removed to form silicon undercuts. The air trenches and the under-cuts are intended to improve the tuning efficiency. Also, a total of three grating29couplers (GCs) are used for each of our MRRs; one GC is connected to the inputport of the MRR to couple light into the filter and the other two GCs are eachconnected to the drop port and the through port to couple light out of the filter.The GCs are optimized to couple TE-polarized light and to operate around a laserwavelength of 1550 nm.Table 2.1: MRR with bent couplers filter design parameter variations.Design Parameter VariationsR 2.75 µmWB 340 nm, 350 nm, 357 nm, 370 nmWR 650 nmg 200 nmθ 5◦, 10◦, 20◦2.5 Measurement Results and DiscussionThe spectral responses of our fabricated MRR filters are measured and their |κ|2values are extracted using a method similar to the one presented in [78]. Theextracted |κ|2 for the MRR with WB = 370 nm and θ = 5◦ was 0.017 and wasthe closest to the desired value of 0.02. The MRR with the next closest |κ|2 of0.012 was the one with WB = 357 nm and θ = 5◦. Therefore, the MRR with WB =370 nm has results that are closest to the theoretical results shown in Figure 2.11.Hence, the results for the MRR with WB = 370 nm, θ = 5◦, WR = 650 nm, g =200 nm, and R = 2.75 µm are presented.Figures 2.12(a) and 2.12(b) show the spectral responses of our MRR filter.The MRR has an FSR of 33.4 nm, which is close to the designed value of 35 nm.Figure 2.12(b) shows a zoomed-in plot of the normalized (with respect to the30(b)(a)Figure 2.12: (a) Measured spectral responses of the through and drop portsover the wavelength range 1510 nm to 1560 nm. (b) Normalizedspectral responses, in GHz, at the through and drop ports for the res-onance at 1549.6 nm.31GCs responses) through and drop port spectral responses around the resonance at1549.6 nm. The 3dB-BW of the MRR is 25 GHz, which is also close to the designvalue. This MRR also has an ER of 19 dB, an OBRR of 42 dB, and an ILdrop ofless than 1 dB. These measured results are summarized in Table 2.2; also, the the-oretical results calculated in section 2.3 are included in the table for comparisonpurposes. From Table 2.2, the measured results (3dB-BW, OBRR, ILdrop, andER) are all smaller than the theoretical results. This could be because |κ|2 of thefabricated device is less than that of the simulated device. Also, the measured FSRof our device is smaller than the expected (theoretical) value. The measured FSRmay be smaller because the theoretical FSR value is calculated using the group in-dex of a straight waveguide despite the ring waveguide of our MRR being bent. Ina bent waveguide with R = 2.75 µm the group index is larger than that of a straightwaveguide, see Figure 2.4(b). As a result, the group index of the fabricated de-vice (of a 2.75 µm bent waveguide) will be larger than the group index used (ofa straight waveguide) to theoretically calculate the FSR of our MRR; hence, themeasured FSR is smaller than the theoretical one. The drop-port responses of ourMRR are measured at various total tuning powers, and the responses are shown inFigure 2.13(a). In each of these measurements, power is applied to the TiN heaterTable 2.2: Summary of the theoretical and measured results of our MRR fil-ter with bent couplers.Parameter Theoretical MeasuredFSR (nm) 35 33.43dB-BW (GHz) 30 25OBRR (dB) 40 42ILdrop (dB) 0.5 < 1ER (dB) 25 19|κ|2 0.02 0.01732to shift the drop-port peak wavelength, and the wavelength shift is plotted versusthe tuning power in Figure 2.13(b). Our MRR filter with bent couplers has a tun-ing efficiency, η , of∼12 mW/FSR; the improved tuning efficiency is attributed tothe deep trenches and the silicon undercuts.FSR = 33.4 nm (b)(a)Figure 2.13: (a) Drop-port responses at various total tuning powers. (b) Plotof the total tuning power versus wavelength shift.The extracted |κ|2s of the MRRs with WB = 370 nm and various values of θare compared to the |κ|2 values obtained from FDTD simulations. A point cou-pler is also simulated and is designated as the θ = 0◦ coupler. These results areshown in Figure 2.14. The θ = 0◦ coupler has the lowest |κ|2 value, and, therefore,the point-coupled MRR would have the smallest bandwidth. |κ|2 increases as θincreases due to the longer effective coupling lengths. This, in turn, leads to anincrease in the MRR’s 3dB-BW and the ER. This is demonstrated in Figure 2.15,which shows the normalized measured spectral responses of the through and dropports for three MRRs with different θ values. The through and drop responseswere normalized to the grating couplers’ responses. The drop port responses werefurther normalized to their peak values. The bandwidths of the MRRs increasefrom 25 GHz at θ = 5◦ to 37 GHz at θ = 10◦ to 71 GHz at θ = 20◦. This demon-strates that, by using bent couplers, MRRs with ultra-wide bandwidths and largeFSRs can be realized.33Figure 2.14: (a) The power coupling coefficient, |κ|2, from measurementdata and FDTD simulations, versus θ .-200 -100 0 100 200-30-20-100Relative Frequency (GHz)Normalized Transmission (dB)  =5 (through)=5 (drop)=10 (through)=10 (drop)=20 (through)=20 (drop)Figure 2.15: Measured spectral responses, in GHz, at the through (dashedlines) and drop ports (solid lines) for θ = 5◦ (blue), θ = 10◦ (red),and θ = 20◦ (green).34Lastly, our MRR performance is compared to other state-of-the-art single-ringMRR filters; the compared results are shown in Table 2.3. The footprints providedin the table are estimated based on the R and Lc values of the MRRs as piR2+2RLc.The MRR demonstrated in [79] was thermally tuned using TiN heaters and had airtrenches around the MRR and the MRR demonstrated in [80] was also tuned usingTiN heaters and had both air trenches and silicon undercuts. However, the MRRdemonstrated in [81] was electrically tuned using PiN doping in the waveguidesand achieved an OBRR of 28 dB, an ILdrop of 1.3 dB, and an ER greater than15 dB. Clearly, the OBRR and the ER of the MRR in [81] are less than thoseof our MRR and its ILdrop is greater than that of our MRR. From Table 2.3, ourdevice has the smallest footprint because it has the smallest R and it is a ring nota racetrack (i.e., Lc = 0). In addition, our MRR has the smallest η as compared tothe other devices. Finally, our device has one of the widest FSRs because it hasthe shortest roundtrip length.Table 2.3: Comparison of our MRR filter with other single-ring MRR filters.Parameter Our device P. Dong, et al. P. Dong, et al. Z. Su, et al.[79] [80] [81]R (µm) 2.75 4 4 3Lc (µm) 0 2 11 0FSR (nm) 33.4 19 11.5 343dB-BW (GHz) 25 25 25 59.5η (mW/FSR) 12 21 2.4 31Footprint (µm2) 24 66 138 28352.6 SummaryA compact MRR based filter with a radius of 2.75 µm, that uses bent directionalcouplers to increase the power coupling coefficient, has been studied. Bent direc-tional couplers allow for gaps that are large enough to be fabricated using opticallithography, thereby making compact MRR filters with large FSRs amenable tomass-production in CMOS-compatible processes. In this chapter, a brief overviewof bent directional couplers and the MRRs that use them has been presented, aswell as the design procedure used to design MRRs with bent directional couplers.Measurements show that our filter exhibits a wide FSR of 33.4 nm, while achiev-ing a 3dB-bandwidth of 25 GHz, a through-port extinction ratio of 19 dB, and alow drop-port insertion loss. Finally, it is shown that by using bent couplers, θcan be used to control a small radius MRR’s bandwidth while maintaining a largeFSR.36Chapter 3FSR-Free Silicon-on-InsulatorMicroring Resonator Based Filterwith Bent Contra-DirectionalCouplersHigh-speed optical interconnects drive the need for compact MRR filters withwide FSRs and with wide bandwidths [17, 41]. MRR based filters that integratestraight CDCs (contra-directional couplers) in the coupling regions of racetrackresonators have been previously demonstrated [55, 82, 83]. By proper design,integrating CDCs in an MRR’s coupling regions can suppress the undesired lon-gitudinal modes of the MRR and eliminate the FSR. In other words, all of theMRRs longitudinal modes, except for the one that aligns with the CDCs mainlobes are suppressed. As a result, FSR-free responses can be obtained. In thesedesigns, the CDCs increase the footprints of the filters as compared to standardmicroring and racetrack resonators. However, by partially wrapping the CDCsaround the MRR, we demonstrate that MRRs with CDCs can be smaller thanthose previously demonstrated. Additionally, MRRs with bent CDCs allow forfilter designs that can have large side-mode suppressions; this can be difficult to37achieve using MRRs with straight CDCs. Hence, by utilizing bent CDCs in anMRR design, a filter is realized that has a more compact footprint, has a relativelylarge side-mode suppression, and has a wide bandwidth while having ”FSR-free”responses at both the drop and through ports. Here, by ”FSR-free” we mean thatour filter significantly suppresses the MRR side modes; achieving an amplituderesponse that appears as though it has no FSR. In this chapter, we will first givea brief introduction to CDCs: both straight CDCs and bent CDCs. Then, we willdescribe the design procedure and present the experimental results of our MRRbased filter with bent CDCs.3.1 Contra-directional Couplers3.1.1 OverviewCDCs have been proposed as add-drop filters due to their wavelength selectivenatures [84]. CDCs are composed of two asymmetric waveguides with corruga-tions on each of the waveguides’ side-walls as shown in the schematic in Figure3.1. Here, the corrugations are achieved by applying periodic perturbations tothe widths of the waveguides; the perturbations have corrugations depths of ∆WBand ∆WR for waveguides B and R, respectively. The gratings on the inner side-walls cause contra-directional coupling between the forward propagating mode inone waveguide (waveguide B) and the backward propagating mode in the otherwaveguide (waveguide R). In order to suppress the CDCs’ Bragg reflections, anti-reflection gratings are used at the external side-walls of the waveguides, in whichthe gratings are out-of-phase with the gratings used at the inner side-walls [85].Contra-directional coupling occurs when the forward propagating mode inwaveguide B is in-phase with the backward propagating mode in waveguide R(this causes constructive interference between these modes) [86]. In other words,contra-directional coupling occur when the difference between the phases of theforward local normal mode and of the backward local normal mode, after each38A1(Lc)A2(Lc)A1(0)A2(0)κctcInputDropThroughWaveguide B Waveguide R ΛgWRWB ΔWRΔWBFigure 3.1: A schematic of a straight CDC that has a coupling length of Lc.The inset shows a zoomed-in section of the CDC with design parame-ters illustrated on it.perturbation, is 2pi; this givesβBΛ+βRΛ= 2pi (3.1)where Λ is the perturbation period, βB and βR are the propagation constants inwaveguides B and R, respectively, andβB =2pinB(λo)λo(3.2)andβR =2pinR(λo)λo(3.3)39where λo is the wavelength in free space, and nB and nR are the effective indiciesof waveguides B and R, respectively. Because βB and βR change with wavelength,equation 3.1 is only satisfied at a wavelength λD. λD is the wavelength at whichcontra-directional coupling occurs. Accordingly, the phase-match condition for aCDC becomesΛ=λDnB(λD)+nR(λD)(3.4)Clearly, λD depends on Λ, nB, and nR; the effective indicies, nB, and nR, dependon the widths of waveguides B and R, WB and WR, respectively. Thus, one of thedesign procedures for CDCs is to determine Λ for a target λD and for the chosenwaveguide widths. This is done by solving the phase-match condition given inequation 3.4.Besides contra-directional coupling, there are Bragg reflections in each of thewaveguides, B and R, [50]. The reflections in waveguide B occur at wavelength,λB, which is determined by the phase-match condition, 2βBΛ = 2pi . Also, thereflections in waveguide R occur at λR, which is determined by the phase-matchcondition, 2βRΛ = 2pi . Figure 3.2 summarizes the three phase-match conditionsfor the wavelengths: λD, λB, and λR. Here, nB and nR are obtained by simulat-ing each of the waveguides B and R using Lumerical MODE Solutions. In thissimulation, each of the waveguides is simulated individually for simplicity. Theparameters of the waveguides of the CDC are: WB = 450 nm, WR = 550 nm, andΛ = 318 nm.The responses of a CDC at the drop port and at the through port are deter-mined using coupled-mode theory [87]. The coupled equations (shown below)relate the forward propagating mode in waveguide B (A1) to the backward propa-gating mode in waveguide R (A2) and vice versa. In these equations co-directionalcoupling is assumed to be negligible. In the case of contra-directional coupling,the coupled equations are given byddzA1 =− jκoA2(z)e j∆β z (3.5)40λBλRλD nBnR λ2Λ𝑛𝑅 + 𝑛𝐵2Figure 3.2: Plot illustrating the phase-match conditions of a straight CDCfor wavelengths λD, λB, and λR.andddzA2 = jκoA1(z)e− j∆β z (3.6)where ∆β is the phase mismatch between the modes, and κo is the magnitude ofthe distributed coupling coefficient. Also, in these equation the forward propagat-ing mode is assumed to be propagating in the +z direction. Solving equations 3.5and 3.6 we getA1(z) = e j∆β2 zs cosh(s(Lc− z))+ j∆β2 sinh(s(Lc− z))s cosh(sLc)+ j∆β2 sinh(sLc)A1(0) (3.7)andA2(z) = e− j∆β2 z− jκo sinh(s(Lc− z))s cosh(sLc)+ j∆β2 sinh(sLc)A1(0) (3.8)where Lc is the coupling length of the CDC. As a result, the electric field transferfunctions of a CDC at the drop port, κc, and at through port, tc, are given by41κc =A2(0)A1(0)=− jκo sinh(sLc)s cosh(sLc)+ j∆β2 sinh(sLc)(3.9)andtc =A1(Lc)A1(0)=s e j∆β2 Lcs cosh(sLc)+ j∆β2 sinh(sLc), (3.10)respectively, where, s2 = κ2o − (∆β2 )2 and ∆β = 2pinBλ + 2pinRλ − 2piΛ .κo is the coupling coefficient per unit length and is a representation of the couplingstrength of a CDC. κo increases as the coupler’s gap between waveguide B andwaveguide R decreases, and as ∆WB or ∆WR increases. The magnitude responses,in dB, of equations 3.9 and 3.10 are shown in Figure 3.3. The CDC, for whichwe have plotted the responses, has the following parameters: WB = 450 nm, WR =550 nm, Λ = 318 nm, Lc = 200 µm, and κo ' 10000 m−1.Figure 3.3: Plots of the magnitude-squared responses of a CDC at the dropport (|κc|2) and at the through port (|tc|2).423.1.2 Bent CDCsIn bent CDCs one of the waveguides (waveguide B) is partially wrapped aroundthe other waveguide (waveguide R) as shown in Figure 3.4. This is a similar de-sign to a bent directional coupler (discussed in chapter 2), but with periodic per-turbations being used on the side-walls of the waveguides. The design parameters,illustrated in Figure 3.4, for the CDCs include: the widths of the waveguides, WBand WR, the corrugation depths, ∆WB and ∆WR, the couplers’ gap widths, g, andΛ. In bent CDCs, Λ is measured at the center of the coupler’s gap as shown inFigure 3.4. Clearly, the design parameters of bent CDCs are the same as those ofstraight CDCs. Also, equations 3.9 and 3.10, for the drop port and the throughport responses, are the same as in bent CDCs.However, the phase-match conditions for straight CDCs are modified for bentCDCs to account for the changes in the perturbation period as we move awayand/or towards the side-walls of waveguides B and R. Specifically, in bent CDCswaveguides B and R have different bend radii, RB and R, respectively. This causesthe perturbation period measured at the center of waveguide B (ΛB) to be differentfrom the perturbation period measured at the center of waveguide R (ΛR); whichis not the case in straight CDCs. Here, we assume that the phase-match condi-tions approximately depend on ΛB and ΛR, which are measured at the centersof the waveguides. Takings these facts into account, we will modify the phase-match condition for contra-directional coupling. Accordingly, the condition forconstructive interference between the forward and backward propagating modesin bent CDCs becomesβBθΛRB +βRθΛR∼= 2pi (3.11)where, θΛ, illustrated in Figure 3.4, is the bend angle of each perturbation and isgiven byθΛ =ΛR+ WR2 +g2(3.12)Also, RB is given by RB = R+ WR2 + g+WB2 . Substituting equations 3.2 and 3.343A1(0)A2(0) A2(Lc)A1(Lc)InputDropThroughR RBWaveguide RWaveguide BWRWBΔWBΔWRΛgθΛAddFigure 3.4: A schematic of a bent CDC that has a coupling length of Lc.The inset shows a zoomed-in section of the CDC on which the designparameters and the bend angle, θΛ, are illustrated.into equation 3.11 we get2pinB(λD)λDθΛRB +2pinR(λD)λDθΛR∼= 2pi (3.13)Rearranging equation 3.13 we getλD ∼= θΛ(nBRB +nRR) (3.14)44We can now solve for Λ and our phase-match condition, for contra-directionalcoupling, for bent CDCs becomesΛ=λD(R+ Wr2 +g2)nb(R+Wb2 +g+Wr2 )+nrR(3.15)Additionally, the phase-match conditions for the wavelengths of the Bragg reflec-tions, λB and λR, will be different in bent CDCs as compared to straight CDCs.Here, we assume that λB and λR are approximately determined by ΛB and ΛR,respectively. Accordingly, in bent CDCs, λB is given by λB ≈ 2nBRBθΛ and λR isgiven by λR ≈ 2nRRθΛ. We will then study an MRR filter that uses bent CDCs inits coupling regions.3.2 MotivationUntil now there has only been one type of MRR with CDCs integrated in thecoupling regions and that is MRRs with straight CDCs. Here we are introducinganother type of MRR with CDCs: the MRR with bent CDCs. Typically, in anMRR with straight CDCs, two identical straight CDCs are used as the couplersof a racetrack resonator with the CDCs having coupling lengths, Lc, and with thebend radii of the racetrack being Rst , see Figure 3.5(a). In our MRR with bentCDCs, two identical bent CDCs are used as the couplers to a microring with theCDCs having coupling lengths, Lc, and with the radius of the MRR being, R, seeFigure 3.5(b). In this chapter, we show that MRRs with bent CDCs can achievelarger side-mode suppressions than similar MRRs with straight CDCs.In order for an MRR with CDCs to attain maximum side-mode suppressions,the MRR’s side modes should coincide with the nulls of the CDCs, as shownin Figure 3.6, and therefore, the spacings between the first CDCs’ nulls, ∆λnull ,should be equal to twice the MRR’s FSR. The spacing ∆λnull of a CDC and the45(a) (b)RLcLcRstLcLcRstInputDropThroughInputDropThroughFigure 3.5: (a) A schematic of an MRR with straight CDCs and (b) aschematic of an MRR with bent CDCs. The dark waveguide sectionsin both of the schematics are the CDCs.Δλnull = 2FSRMRR side modes FSRFigure 3.6: A CDC’s spectral response (dashed trace) and an MRR’s re-sponse (solid trace) when ∆λnull = 2FSR.FSR of an MRR are given by∆λnull =2λ 2pi(ngR +ngB)√κ2o +(piLc)2 (3.16)andFSR =λ 2LrtngR, (3.17)respectively, and where κo is the distributed coupling coefficient for a CDC (Lc46and κo are the same for each of the two CDCs), and ngR and ngB are the ring andbus waveguides’ group indicies, respectively. Also, Lrt is the roundtrip length ofan MRR; in an MRR with straight CDCs, Lrt = 2piRst +2Lc, and in an MRR withbent CDCs, Lrt = 2piR. Consequently, for an MRR with straight CDCs to achieve∆λnull =2FSR, Rst of the racetrack should satisfy the following relation,Rst =ngR+ngBngR2√κ2o +( piLc )2− Lcpi(3.18)In addition, for an MRR with bent CDCs to achieve ∆λnull =2FSR, Lc of each ofthe CDCs should satisfy the relation,Lc =2pi√(ngR+ngBngRR)2− (2κo)2(3.19)Using equation 3.18, the Rst required to satisfy ∆λnull =2FSR is calculatedat various values of Lc. Also, using equation 3.19, the Lc required to satisfy∆λnull =2FSR, is calculated at various values of R. Using the Rst and Lc values ob-tained from equations 3.18 and 3.19, we then calculate γ = (2Lc/Lrt)∗100, whereγ is the percentage of coverage of the roundtrip length of the MRR by the CDCs.γ is plotted versus various Lrt values in Figure 3.7 for MRRs with straight CDCsand for MRRs with bent CDCs each for κo = 2000 m−1 and κo = 8000 m−1. Here,in these plots, we chose the widths of the ring waveguides of the bent CDCs andthe straight CDCs to be the same and to be 550 nm, as well as we chose the widthsof the bus waveguides of the bent CDCs and the straight CDCs to be the same andto be 450 nm. Clearly, in the MRRs with bent CDCs, we can fit both of the CDCson the microrings’ circumference (γ < 100%) for all of our plotted Lrt values.Accordingly, an MRR with bent CDCs can be designed so that the MRR’s longi-tudinal modes are aligned with the CDCs’ nulls, and hence maximum side-modesuppressions can be achieved. On the other hand, in the MRR with straight CDCs,γ > 100% for all of our plotted Lrt values. In other words, there is no physical47κo= 8000 m-1 κo= 2000 m-1 κo= 8000 m-1 κo= 2000 m-1 MRR with straight CDCsMRR with bent CDCsFigure 3.7: Plots of the required MRR’s coverage with the CDCs (γ) toachieve maximum suppression versus Lrt for MRRs with straightCDCs and MRRs with bent CDCs.MRR design that exists that can satisfy ∆λnull =2FSR and achieves maximumsuppression. This is because the group indicies of the waveguides of a straightCDC are typically smaller than the group indicies of the waveguides of a bentCDC with the same waveguide widths; this causes ∆λnull of a straight CDC to belarger than ∆λnull of a bent CDC. As a result, the Lc value required for an MRRwith bent CDCs to achieve ∆λnull = 2FSR will be less than that of an MRR withstraight CDCs with the same κo and Lrt values.Furthermore, an MRR with bent CDCs and with a large γ value will typicallyhave a larger side-mode suppressions than an MRR with straight CDCs with thesame γ value. This is because, in an MRR with straight CDCs, as the couplinglengths of the CDCs are increased, to decrease ∆λnull , the roundtrip length of theracetrack resonator decreases and the FSR of the MRR increases. Hence, this cancause the FSR to increase at a greater rate than the decrease in ∆λnull , which leadsto decreased suppression. However, in an MRR with bent CDCs increasing thecoupling lengths of the CDCs will not effect the roundtrip length of the microring.As a result, ∆λnull can be decreased without changing the FSR of the MRR which48κo= 8000 m-1 κo= 2000 m-1 κo= 8000 m-1 κo= 2000 m-1 MRR with straight CDCsMRR with bent CDCsFigure 3.8: Plots of Kc, in dB, versus Lrt for MRRs with straight CDC andMRRs with bent CDCs at γ = 87%.leads to an increase in suppression. For illustration purposes, a measure of side-mode suppression, Kc, is plotted at various Lrt values (ranging from 18 µm to207 µm) for MRRs with both straight and bent CDCs each for κo = 2000 m−1 andκo = 8000 m−1. Plots of Kc versus Lrt at γ = 87% are shown in Figure 3.8; γ =87% is used to allow for bends in the bus waveguides needed to connect to externalcomponents, and to have enough space to place heaters on top of the sections ofthe microring that are not covered by CDCs for thermal tuning (see section 3.3 forfurther discussion on the device design). For our analysis, Kc is used as a metricthat is directly proportional to the to the side-mode suppression ratio (SMSR) atthe MRR resonances immediately adjacent to the resonant wavelength of the filter,SMSRad j. Specifically, Kc is the normalized contra-directional power couplingfactor of a CDC evaluated at λD±1FSR assuming that λD coincides with oneof the longitudinal modes of the MRR, see Figure 3.9. In other words, Kc =|κc(λD±1FSR)|2/|κc(λD)|2 where κc(λD) is the field coupling factor of a CDC.From the plots in Figure 3.8, the MRRs with bent CDCs achieve larger Kc values(i.e., larger suppressions) than the MRR with straight CDCs for all plotted Lrt and49κo values. In the following section we will describe the design procedure of anMRR filter with bent CDCs.Δλnull > 2FSRKcFSRFigure 3.9: (a) A CDC’s spectral response and an MRR’s response when∆λnull > 2FSR.3.3 Device DesignFigure 3.10 shows a schematic of our proposed MRR filter with two, identical,bent CDCs. The parameters to be designed for the CDCs include WB, WR, ∆WB,∆WR, g, andΛ, as well as the number of periods, N. The CDCs are designed so thatthe widths of the waveguides, WB and WR, are 450 nm and 550 nm, respectively;also, a ∆WB of 30 nm and a ∆WR of 40 nm are used [88]. Also, g = 280 nm. Thewidths, WR and WB, are asymmetric so that the wavelengths of the reflections dueto the CDCs are far from the drop-port peak wavelength, λD, [50, 55]. λD is thecenter wavelength of the main lobes of the CDCs’ drop-port spectra, and is chosento coincide with one of the MRR’s longitudinal modes in the C-band. The bentCDCs are designed using previously proposed bent coupler designs [1, 62, 89].In order to design an MRR with bent CDCs that achieves maximum side-mode suppression, Lc of each of the CDCs, should be chosen so that it satisfiesthe relation in equation 3.19. Clearly, this chosen Lc value should be less than halfthe microring’s circumference (i.e., Lc< piR) to accommodate both of the CDCs50RInputDropThroughGwgRwgLcAddFigure 3.10: Schematic of an MRR with bent CDCs, as well as an insetshowing a zoom-in of a section of a bent CDC. The dark blue tracesare the corrugated waveguides (gratings) of the CDCs.on a microring. Accordingly, R should be less than or equal to ∼34 µm for κovalues up to 8000 m−1 (see Figure 3.11; here we used WB = 450 nm and WR =550 nm). Also, it is shown in Figure 3.11 that the least possible coverage, Lc/piR,to satisfy equation 3.19 is approximately 0.964. However, such a large coveragewill not allow for filter to be connected to other components (for example, thebus waveguides need bends in them of radius, Rwg, and to be separated from eachother by Gwg, as illustrated in Figure 3.10). Hence, it is difficult to realize a designfor which the MRR’s side modes coincide exactly with the CDCs’ nulls. Here, inorder to minimize radiation losses in the bends we use Rwg = 5 µm and to minimizecross-coupling between the buses we use Gwg = 2.5 µm. Accordingly, Lc is chosento accommodate our chosen Rwg and Gwg for various R values. In Figure 3.12, wehave plotted the theoretical Kc, in dB, for κo values up to 8000 m−1. As can beseen from Figure 3.12, the minimum Kc for κo ≤ 8000 m−1 and R = 34 µm is∼18 dB. Nevertheless, the minimum Kc for an MRR with R = 25 µm is also ∼18dB at κo = 8000 m−1. Given that the actual fabricated κo will typically be less than51the simulated value, the Kc in the actual device should be greater than 18 dB forany κo < 8000 m−1 and for R values between 25 µm and 34 µm. However, sincethe footprint of our device almost doubles as R changes from 25 µm to 34 µm, wehave picked the smaller radius for our device.κo= 8000 m-1 κo= 6000 m-1 κo= 4000 m-1 κo= 2000 m-1 R ≈ 34 μmFigure 3.11: Plots of the MRR’s coverage with the CDCs (Lc/piR) versus Rat various κo values.κo< 8000 m-1 κo> 8000 m-1 34μm25μmFigure 3.12: Plot of Kc, in dB, versus R at κo = 8000 m−1.52After designing R, Λ is designed for a target λD value that will satisfy thephase-match condition for bent CDCs represented by equation 3.15. Hence, ac-cording to our phase-match condition, Λ = 318 nm for λD ' 1537 nm. N is chosento be 216 to obtain maximum coverage by the CDCs, as previously discussed. Ta-ble 3.1 summarizes the design parameters for our MRR with bent CDCs. Ourbent CDCs are simulated using Lumerical FDTD Solutions. Consequently, thecontra-directional field coupling factor for a CDC, κc, and the field transmissionfactor, tc, are obtained and their power factors, in dB, are shown in Figure 3.13.Also, the power coupling factor, |κc|2, is fitted to equations 3.9 and 3.10 usinglsqcurvefit function in MATLAB R©; as a result, κo is found to be ∼6800 m−1.The co-directional power coupling factor of the simulated bent CDC is ∼0.015 at1537.2 nm (λD). From the CDC transmission in Figure 3.13, two notches are ob-served: a notch at 1537.2 nm (λD), due to the contra-directional coupling betweenthe bus and ring waveguides, and a notch at ∼1522 nm, from intra-waveguideBragg reflections at the input port [50].Figure 3.13: Theoretical spectral responses, for the simulated bent CDC (us-ing FDTD), of the power transmission (|tc|2) at the through port, thepower coupling (|κc|2) at the drop port, as well as the fitted CDCresponse at the drop port.53Table 3.1: Our MRR with bent CDCs filter design parameters.Design Parameter ValueWB 450 nmWR 550 nm∆B 30 nm∆R 40 nmg 280 nmΛ 318 nmN 216R 25 µmRwg 5 µmGwg 2.5 µm3.4 MRR with Bent CDCs Transfer FunctionFor the contra-directional coupling, the electric field transfer function of the MRRfilter with bent CDCs at the drop port, Edrop, and at the through port, Ethru, arederived using Mason’s rule, similar to the approach presented in [90]. Mason’srule (also known as Mason’s gain formula) provides a method to evaluate thetransfer function between the input and output of a given system [91]. The transferfunction of a system is represented byG =∑ni=1 Fi∆i∆(3.20)where Fi is the gain of the ith path given that the system has n paths, and ∆=1 -(sum of all non-touching loop gains) + (sum of the products of the gains of allpossible two loops that are not touching) - (sum of the products of the gains of all54InputDropThroughtc χR√χtc χR√χLoop : L1κcκc√χPath : FD1InputDropThroughκc√χPath : FT2κc√χtc χRInputDropThroughPath : FT1tc χBInputDropThrough(c)(a) (b)(d)Figure 3.14: Diagrams illustrating the gains of (a) loop L1, (b) path FD1, (c)path FT 1, and (d) path FT 2.possible three loops that that are not touching) + ... so forth. Also, ∆i is the ∆ ofthe loops that are not touching the ith path. Accordingly, the gain of the loop, L1,(the loop is illustrated in Figure 3.14(a)) is given byL1 = tc2χR2χ (3.21)The gain of the path for the drop-port transfer function, FD1, (the path is illustratedin Figure 3.14(b)) is given byFD1 = κc2√χ (3.22)the gains of the first and seconds paths for the through port transfer function, FT 155and FT 2 respectively, (the paths are illustrated in Figures 3.14(c) and 3.14(d)) andare given byFT 1 = tc2χB (3.23)andFT 1 = κc2tcχRχ (3.24)where χ , χB, and χR are the gains of the sections of the MRR that is not coveredby the CDC, the bus waveguide of each of the CDCs, and the ring waveguide ofeach of the CDCs, respectively (their equations will be given below). Given thegain of the loops and paths of this system and following Mason’s rule in equation3.20, Edrop and Ethru are represented asEdrop =FD11−L1 (3.25)andEthru =FT 1(1−L1) + FT 21−L1 (3.26)After substituting equations 3.21 to 3.24 into equations 3.25 and 3.26, the resultingequations for Edrop and Ethru of our MRR becomeEdrop =κc2√χ1− tc2χR2χ(3.27)andEthru =tcχB(1− tc2χR2χ)+κc2tcχRχ1− tc2χR2χ(3.28)where χ = exp(−α2 L− j 2pinRλ L), χR = exp(−α2 Lc− j 2pinRλ Lc), χB = exp(−α2 Lc−j 2pinBλ Lc), Lc = N×Λ, L = 2piR−2Lc, and α/2 is the waveguide propagation fieldloss in nepers per meter (i.e., α is the power loss).563.5 Theoretical ResultsUsing equations 3.27 and 3.28, and assuming a propagation loss of 3 dB/cm (α' 69 m−1), the power transmission to the drop port, Tdrop, and to the throughport, Tthru, can be calculated. Our MRR power transmissions are calculated as,Tdrop = |Edrop|2 and Tthru = |Ethru|2. In order to characterize the side-mode sup-pression of our filter using the drop-port response, we determine two side-modesuppression ratios: SMSRmin and SMSRad j, both of these measures are illustratedin Figure 3.15. SMSRmin is the minimum side-mode suppression ratio within thewavelength span for which the response is measured. We use SMSRmin to typi-cally mean the overall SMSR of the filter. SMSRad j is the suppression ratio ofthe side modes occurring at λD±1FSR; if the suppression ratio of the side modeat λD+1FSR is not equal to the suppression ratio of the side mode at λD-1FSR,the smaller ratio is chosen to be SMSRad j. From Tdrop, in Figure 3.15, SMSRad jBragg reflection at 1522 nm SMSRmin SMSRadjFigure 3.15: Theoretical spectral responses of our MRR filter with bentCDCs at the drop port, Tdrop, and at through port, Tthru.57is 17.5 dB, which is expected given our choice of R =25 µm to achieve Kc >18 dB (as discussed above). Additionally, SMSRmin is ∼15 dB, the 3dB-BW is∼35 GHz, and the insertion loss is 1.6 dB. From Tthru, in Figure 3.15, the ERis 16.5 dB. Furthermore, the phase of the drop-port response, φdrop, is evaluatedfrom Edrop in equation 3.27. The group delay (GD) and the chromatic dispersion(CD) are then calculated using the following equations.GD =φdrop2pi f(3.29)andCD =GDλ(3.30)The resulting group delay and chromatic dispersion of our MRR filter are shown inFigures 3.16(a) and 3.16(b). The drop-port chromatic dispersion within a 25 GHzwindow around 1537.2 nm, is ±42 ps/nm.(a) (b)0.2 nmFigure 3.16: The (a) group delay (GD) and (b) chromatic dispersion (CD) atthe drop-port around 1537.2 nm.583.6 Device FabricationThe MRR filter with bent CDCs was fabricated using electron beam lithographyat the University of Washington [92]. The fabricated device has strip waveguideswith 220 nm heights and a top oxide cladding. Metal heaters are used on top of theMRR waveguides for thermal tuning. A total of three sections of micro-heatersare used: two sections on top of the CDCs and another section on top of portionsof the microring that don’t contain gratings, and each of the heater sections istuned separately. A microscopic image of our fabricated MRR filter is shown inFigure 3.17. GC structures are also used to couple TE modes into and out of thedevice for measurements purposes [93].microring heaterCDC heaterCDC heaterFigure 3.17: A microscopic image of our MRR filter with metal heaters; theinset shows a scanning electron microscope (SEM) image of a portionof a bent CDC.593.7 Measurement ResultsThe spectral responses at both the drop and through ports are shown in Fig-ure 3.18(a) for wavelengths between 1520 nm and 1580 nm. These responsesinclude the responses of the GCs at the input (input port) and the outputs (dropport and/or through port). The setup used to measure the optical spectra of ourfilter include an Agilent 81682A sweepable laser source and an Agilent 81635Aoptical power meter; both of these are used in an an Agilent 8164A mainframe. Inthese measurements, the laser source, with a 0 dBm optical power, sweeps the out-put wavelength between 1520 nm and 1580 nm at equally spaced wavelength stepsand the optical power meter measures the output power at each of the wavelengthsteps. A Python script is then used to plot the relative output power versus the laserwavelengths to get the responses shown in Figure 3.18(a). The drop-port spectralresponse shows a single resonant peak at∼1540.3 nm in a 60 nm wavelength span,which contains the C-band. In addition, the SMSRad j is 20.7 dB and the SMSRminis more than 15 dB. Additionally, from the normalized responses (i.e., where the3 dB-BW ER(b)(a)SMSRminSMSRadjFigure 3.18: (a) Spectral responses of our MRR filter at the drop and throughports; the illustrated SMSR is 15.3 dB. (b) The responses relative to1540.3 nm, after normalizing them with respect to the grating cou-plers’ responses.60grating couplers’ responses have been de-embedded) in Figure 3.18(b), the ER is∼18 dB, the 3dB-BW is ∼23 GHz, and the drop-port insertion loss (ILdrop) is∼1 dB. Furthermore, the suppressed notch at the through port, at 1533.1 nm, hasa magnitude of 2.9 dB. The drop-port response is measured at various total tuningpowers for both heater sections, and the responses are shown in Figure 3.19(a).In these measurements, power is applied to the CDC heaters to shift the drop-portpeak wavelength, while power is applied to the microring heater to align the mi-croring’s response with the CDCs’ responses. Our MRR filter with bent CDCsdemonstrates tunability with a tuning efficiency, η , of ∼56 mW/nm, as shownin Figure 3.19(b). The chromatic dispersion at the filter’s drop-port is measuredusing a Luna Optical Vector AnalyzerTM. From Figure 3.20, the chromatic dis-persion within a 25 GHz window centered on 1540.3 nm is ±90 ps/nm.η ≈ 56 mW/nm(b)(a)Figure 3.19: (a) Drop-port responses at various total tuning powers. (b) Plotof the total tuning power versus wavelength shift.3.8 DiscussionTable 3.2 gives a comparison between the as-designed results (obtained in section3.5) and the measured results of our filter. Clearly, the measured dispersion islarger than the as-designed value because the κo of the fabricated device is less61Figure 3.20: Chromatic dispersion at the drop port in a 25 GHz window rel-ative to 1540.3 nm.than that of the simulated device. This would be consistent with the reduction inthe 3dB-BW and the increase in SMSRad j from the design value. The measureddrop-port response is thus fitted to obtain κo and α of our fabricated filter. Ourobjective is to verify the model that we use to obtain the theoretical responsesfor MRRs with bent CDCs and to verify that κo of the fabricated device is lessthan our design value of 6800 m−1. Here, we fit the measured drop-port responseto the magnitude-squared of equation 3.27, and κc and tc are obtained using theCDC’s coupled-mode equations described in section 3.1. From our fit, κo is foundto be 5530 m−1 and α is found to be ∼161 m−1 (i.e., a power propagation lossof 7 dB/cm). Clearly, κo of the fabricated device is smaller than the design valueand α of the fabricated device is larger than the design value. Edrop and Ethruare then recalculated using equations 3.27 and 3.28 and using the fitted κo and αvalues. The magnitude-squared response of the calculated Edrop (fitted response),and the measured and theoretical (designed) drop-port responses are shown in Fig-ure 3.21; the fitted response shows a closer agreement to the measured responseas compared to the designed response. The following are the extracted results62Table 3.2: Summary of the as-designed, measured, and fitted results of ourMRR filter with bent CDCs and its comparison with the results of apreviously demonstrated MRR with straight CDCs.Parameter This device This device This device Shi et al.(Designed) (Measured) (Fitted) [55]Footprint (µm2) 1963 1963 1963 6880λr (nm) 1 1537.2 1540.3 1540.3 1504.6κo (m−1) 6800 5530 5530 2000SMSRmin (dB) 15 >15 19.2 > 8SMSRad j (dB) 17.5 >20.7 19.2 > 8ER (dB) 16.5 ∼18 22.8 > 103dB-BW (nm) 0.28 0.18 0.19 0.06ILdrop (dB) 1.6 ∼1 0.7 N/ADispersion (ps/nm) ±42 ±90 ±90 N/A1 λr is the MRR filter’s resonant wavelengthfrom the calculated Edrop and Ethru responses: SMSRad j = 19.2 dB, ILdrop =0.7 dB, 3dB-BW = 24 GHz (0.19 nm), and ER = 22.8‘dB. These results closelyagree with the measured results, see Table 3.2. Also, the chromatic dispersionwithin a 25 GHz window centered on 1540.3 nm is ±90 ps/nm; this dispersionmatches the measured dispersion, see Table 3.2. We can thus safely conclude thatour model closely approximates the fabricated device and that the assumptions wemade during our design procedure (such as co-directional coupling is negligible)are valid.Table 3.2 also gives a comparison between the measured results of our filter63Figure 3.21: Drop-port spectral responses from the measured data and fromEdrop calculated using fitted κo and α values relative to 1540.3 nm,as well as the theoretical drop-port response obtained in section 3.5relative to 1537.2 nm.and previously reported values for a single-ring MRR with straight CDCs [55].Our MRR filter achieves larger SMSRad j and SMSRmin than those of the previ-ously demonstrated MRR filter with straight CDCs even though κo of our filter islarger. In addition, our MRR filter with bent CDCs has a footprint of ∼1963 µm2,which is significantly more compact, less than one-third the area, as compared tothe previously demonstrated MRR with straight CDCs. In section 3.2, we haveshown that an MRR with bent CDCs will achieve larger side-mode suppressionsthan an equivalent MRR with straight CDCs, see Figure 3.8. As a result, wedesigned our proof-of-concept MRR with bent CDCs so as to achieve higher side-mode suppressions and to be more compact than other demonstrated MRRs withstraight CDCs. Our proof-of-concept filter achieved our predicted design resultsand demonstrated a more attractive alternative to MRRs with straight CDCs thathas higher suppressions and is more space-efficient while still having the advan-tages of integrating CDCs in the coupling regions.643.9 High-Speed TestingIn order to characterize the demonstrated filter for high-speed data transmission,an experimental setup is used similar to the one proposed in [94]. Our experimen-tal setup is shown in Figure 3.22 and Table 3.3 lists the equipment used in thesetup. Our setup is composed of a tunable laser source (TLS), a pulse pattern gen-erator (PPG), a Mach-Zehnder modulator (MZM), an erbium-doped fiber ampli-fier (EDFA), a variable optical attenuator (VOA), an optical tunable filter (OTF),a photo-detector (PD), and a digital communication analyzer (DCA). The EDFAand the attenuator together provide variable gain at the output of our filter. Thetotal gain of this stage is set so that the peak power of the data at the PD is 0 dBm.The MZM has polarization maintaining input and output fibers. The OTF wave-length is set to be the same as the TLS wavelength, and the bandwidth of theOTF is set to be 2 nm. NRZ signals with 231−1 PRBS patterns and data rates of12.5 Gbps, 20 Gbps, and 28 Gbps are used in our characterizations.TLSOTFPPGcMZM DUT EDFA VOAPDDCAFigure 3.22: Block diagram showing the experimental setup used to measurethe eye diagrams of our filterEye diagrams of the modulated NRZ data are measured at the input and atthe drop port of our filter at 1540.3 nm for data rates of 12.5 Gbps, 20 Gbps, and28 Gbps, see Figures 3.23(a)-3.23(f). A wavelength of 1540.3 nm correspondsto the center wavelength of our filter. Here, the signal at the input to our filter is65Table 3.3: List of equipment used in our setup to measure the eye diagramsand BERs of our MRR filter.Instrument Equipment ModelTLS Keysight N7714APPG Anritsu MP1800A BERT (PPG module)MZM LiNb03 Lucent X2623YEDFA Fiberprime EDFA-C-26G-SVOA HP 8156AOTF Santec OTF-950PD Lab Buddy DSC-R411DCA Agilent 86100ABERT Anritsu MP1800Athe signal from the MZM. As can be seen from Figures 3.23(a)-3.23(f), the eyesexhibit small reductions in the signal quality at the drop port of our filter. We arealso interested in the data transmitted at the through port for wavelengths that arenot being filtered. Specifically, eye diagrams are measured at the input and at thethrough port of our filter at 1533.1 nm, which corresponds to the major suppressednotch. The major suppressed notch was chosen because it is the point at which thelargest deterioration of the signal is expected [95]. The eye diagrams are shownin Figures. 3.23(g)-3.23(i) at the input to our filter and in Figures 3.23(j)-3.23(l)at the through port of our filter. The patterns maintain open eyes at the throughport’s notch at 1533.1 nm for data rates up to 28 Gbps with minimal reduction inthe signal quality.Our filter is further characterized for high-speed data transmission by measur-ing its bit error rate (BER). The experimental setup used to measure the BER is6612.5 Gbps 20 Gbps 28 GbpsInput 1533.1 nm(d) (e) (f)(g) (h) (i)(a) (b) (c)(j) (k) (l)1540.3 nmInput Drop PortThrough PortFigure 3.23: Eye diagrams of NRZ data at the input of our filter at 1540.3nm for data rates of (a) 12.5 Gbps, (b) 20 Gbps, and (c) 28 Gbps aswell as at the drop port (output) for data rates of (d) 12.5 Gbps, (e)20 Gbps, and (f) 28 Gbps. Eye diagrams of NRZ data at 1533.1 nmat the input of our filter for data rates of (g) 12.5 Gbps, (h) 20 Gbps,and (i) 28 Gbps as well as at the through port (output) for data ratesof (j) 12.5 Gbps, (k) 20 Gbps, and (l) 28 Gbps.67shown in Figure 3.24. The setup is similar to the one used to measure the eyediagram. However, in this setup (to measure the BER) the output of the PD is fedto the error detection (ED) module of the bit error rate tester (BERT). Also, thereceived power is varied at the PD by varying the attenuation setting of the VOA.BERs of the modulated NRZ data (231-1 PRBS pattern) are measured at the dropport of our filter at 1540.3 nm for data rates of 12.5 Gbps, 20 Gbps, and 25 Gbps.Also, BERs are measured at the through port of our filter at 1533.1 nm for datarates of 12.5 Gbps, 20 Gbps, and 25 Gbps. The BER plots versus the receivedoptical power at the PD are shown in Figure 3.25. A BER below 10−12 is takento mean than the transmission of the data is essentially error free. Accordingly,at a received optical power of 1.5 dBm, error-free transmission is achieved at thethrough port for data rates up to 25 Gbps and at the drop port for data rates upto 20 Gbps. However, at a received power of 4 dBm, error-free transmission isachieved for the drop and through ports for data rates up to 25 Gbps. In general,the data at the through port has lower BERs, at the various received powers, ascompared to data at the drop port, and both ports can have error-free transmissionfor data rates up to 25 Gbps.TLSOTFBERTcMZM DUT EDFA VOAPDPPGEDFigure 3.24: Diagram showing the experimental setup used to measure theBER of our filter.68Figure 3.25: Measured BERs versus received optical power at the PD at datarates of 12.5 Gb/s, 20 Gb/s, and 25 Gb/s at the drop port, at 1540.3nm, and at the through port, at 1533.1 nm.3.10 SummaryIn conclusion, we study the design of an SOI MRR based filter with bent CDCs inwhich the CDCs are partially wrapped around the MRR. With the aid of bendingthe CDCs, a relatively compact filter design with an FSR-free response, a rela-tively high SMSR, and a large 3dB-BW is achieved. Our design facilitates the useof MRR based multiplexers/de-multiplexers for densely integrated optical inter-connects in WDM systems, where large channel capacities and small chip foot-prints are desired. The fabricated MRR filter with bent CDCs is experimentallydemonstrated showing an FSR-free response at both the drop port and the throughport. Moreover, the measurements show an SMSRmin of more than 15 dB; suchan SMSR would be difficult to obtain using MRRs with straight CDCs. Also, our69filter has a 3dB-BW of ∼23 GHz and has an ER of ∼18 dB. The eye diagrams ofNRZ 231−1 PRBS patterns, for data rates up to 28 Gbps, exhibit small reductionsin the signal quality at the drop port and the through port of our filter.70Chapter 4Summary, Conclusions, andSuggestions for Future Work4.1 Summary and ConclusionsIn this research, we demonstrated MRR filters that used bent couplers in theircoupling regions. We first studied and experimentally demonstrated an MRR fil-ter that used bent directional couplers in Chapter 2. By using bent directionalcouplers, we were able to fabricate a 2.75 um radius MRR filter using a 248 nmphotolithography process and to achieve our desired performance. Because of thebent couplers, our MRR filter had a wide FSR of 33.4 nm (covering most of theC-band) and sufficient coupling to achieve a wide 3dB-BW of 25 GHz, a largeOBRR of 42 dB, a large ER of 19 dB, and an ILdrop of less than 1 dB. Addi-tionally, our MRR had metal heaters on top of it for thermal tuning as well asair trenches around it and silicon undercuts to achieve an improved thermal ef-ficiency of 12 mW/FSR. In Chapter 3, we experimentally demonstrated a noveldesign of an MRR filter with bent CDCs. By using CDCs in the coupling re-gions of an MRR filter, FSR-free responses at the drop port and the through portare achieved. In addition, by bending the CDCs around the MRR, a large side-mode suppression can be achieved. Also, our MRR with bent CDCs achieved71a more compact filter design as compared to the previously demonstrated MRRwith straight CDCs. Our MRR filter achieved a larger SMSRmin of more than15 dB, a 3dB-BW of ∼23 GHz, and an ER of ∼18 dB. Our MRR filter was alsodemonstrated for high-speed transmission of NRZ data, 231− 1 PRBS patterns.This high-speed testing was performed by measuring the eye diagrams at the inputport, the drop port, and the through port of our filter for data rates up to 28 Gbps,and by measuring the BER at the drop port and the through port for data rates upto 25 Gbps. The drop-port measurements were performed at the resonant wave-length, and the through-port measurements were performed at the wavelength ofthe major (in magnitude) suppressed notch. From these measurements, open eyeswere achieved for the transmissions with minimal reductions in the signal qualitybetween the input and the drop ports, as well as between the input and the throughports. Error-free (BER < 10−12) transmissions were also observed, for the dropand the through ports, at a received optical power (after amplification) of 0 dBm.Additionally, in Chapter 3 we showed that it is not possible to realize designsfor MRR filters with straight CDCs such that the microrings’ side modes coin-cide with the nulls of the CDCs’ responses, and, as a result, MRR filters withstraight CDCs cannot achieve maximum (i.e., complete) side-mode suppressions,see Figure 3.7. Nevertheless, in MRR filters with bent CDCs, it is possible torealize designs for which maximum side-mode suppressions can be achieved, seeFigure 3.7. In our proof-of-concept MRR with bent CDCs we were not able toattain a design that had the γ (CDC coverage of the microring) value required toachieve maximum suppression. While there were additional considerations re-lated to attaching the bus waveguides to the CDCs, the primarily reason we couldnot achieve the required γ value was that we used two identical CDCs (in both ofthe coupling regions) in our design. This was because we wanted to keep our de-sign similar to the MRR filter with straight CDC for comparison purposes. Afterobtaining the additional insights into this issue as a result of our work, we con-clude that it should be possible to achieve maximum suppressions if a CDC wasused in one of the coupling regions while the other coupling region used a direc-72tional coupler. In this case, the CDC coverage requirements will be lessened, γwill be halved. When we were trying to obtain maximum suppression for an MRRhaving two identical CDCs in its coupling regions, γ values between∼96% (for κo= 2000 m−1) and∼98% (for κo = 8000 m−1) were required for R = 25 um. There-fore, if an otherwise identical MRR had one CDC in one of its coupling regionsthen the γ values would be reduced to ∼48% (for κo = 2000 m−1) and ∼49% (forκo = 8000 m−1). These new γ values, when a CDC is used in one of the MRR’scoupling regions, are less than 50% and, thus, can be achieved while having suffi-cient room to attach the bus waveguides to the filter. In addition to achieving themaximum possible suppression, such a design will have better tuning efficiency.This is because, in this proposed design, only one CDC needs tuning and the por-tion of the microring that is not covered by the CDC is increased. This means thatone CDC heater is used, which decreases power consumption, and that a largermicroring heater can be used, which increases thermal efficiency. In the next sec-tion, we will discuss, and give some suggested designs that use a CDC in onlyone of the MRR’s coupling regions, as well as give some suggested designs thatutilize bent directional couplers.4.2 Suggestions for Future WorkIn this thesis, we demonstrate two MRR filter designs in which bent couplers areused to improve their performance. Another possible application of utilizing bentcouplers in MRR filters could be by using them in the coupling regions of series-coupled Vernier ring filters. By doing this one can realize MRR filters that haveFSRs exceeding the span of the C-band and have compact footprints. Addition-ally, bent couplers allow for the MRRs to have the desired coupling coefficientsto achieve wide bandwidths and large ERs. As a result, these Vernier ring filterswith bent couplers can have wide FSRs, have wide 3dB-BWs, and have smallfootprints. In Figures 4.1(a) and 4.1(b) we show two possible designs for Vernierring filters with bent directional couplers. In the design shown in Figure 4.1(a),the ring waveguide’ widths are adiabatically tapered such that the widths of the73ring waveguides at gap2 are smaller than the widths of the ring waveguides atgap1 and gap3. This is done to increase the coupling coefficient of the coupler atgap2 to achieve the desired performance. In the design shown in Figure 4.1(b),which uses a bent directional coupler at the coupler between the microrings (atgap2), one of the microrings is slightly deformed from the typical ring shape toallow for the bent directional coupler. Such a design has a more compact footprintas compared to the design shown in Figure 4.1(a).(b)(a)ThroughInputDropgap2450 nm650 nm450 nm650 nmgap1gap3ThroughInputDropgap2gap1gap3Figure 4.1: (a) A schematic of a proposed two series-coupled Vernier ringfilter with bent directional couplers in their bus to ring coupling re-gions and adiabatic tapering of the widths of the waveguides of themicrorings. (b) A schematic of a proposed two series-coupled Vernierring filter with bent directional couplers in all of its coupling regions.In our proof-of-concept MRR with bent CDCs, the measured SMSR at theside modes adjacent to the filter’s resonance was ∼20 dB. Although this SMSRwas sufficient to obtain an FSR-free response, a larger SMSR can be achieved ifchanges are made to the design that make the microring longitudinal side modesalign with the CDC’s nulls. As has been discussed in section 4.1, the MRR filtercan be designed such that it uses bent CDCs in one of its coupling regions and a di-rectional coupler at the other coupling region. However, in order to achieve a lowILdrop, a wide 3dB-BW, and a large ER, as in our demonstrated proof-of-conceptMRR filter with bent CDCs, the coupling coefficients of both couplers should be74matched at the filter’s resonance. Because of fabrication errors, the coupling co-efficient of the fabricated coupler will likely be different from the simulated oneand, thus, the coupling coefficients of both couplers of the fabricated filter will,typically, not be matched. This issue can be solved by using a tunable MZI as thedirectional coupler, see Figure 4.2; this will allow one to tune the coupling coef-ficient so that it matches the CDC’s coupling and, thus, provide extra flexibility.Tuning of the MZI and the CDC are typically done using metal heaters.Tunable CouplerTunable CDCThroughInputDropFigure 4.2: A schematic of an MRR with bent CDC in one of its couplingregions and a tunable directional coupler in the other coupling region.75Bibliography[1] N. Eid, H. Jayatilleka, M. Caverley, S. Shekhar, L. Chrostowski, andN. A. F. Jaeger, “Wide FSR silicon-on-insulator microring resonator withbent couplers,” in IEEE 12th International Conference on Group IVPhotonics. IEEE, Aug. 2015, pp. 96–97.[2] S. J. B. 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