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Silicon-on-insulator, free-spectral-range-free devices for wavelength-division multiplexing applications Mistry, Ajay 2020

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Silicon-on-Insulator, Free-Spectral-Range-Free Devicesfor Wavelength-Division Multiplexing ApplicationsbyAjay MistryB.A.Sc., The University of British Columbia, 2017A 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)March 2020c© Ajay Mistry, 2020The following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled:Silicon-on-Insulator, Free-Spectral-Range-Free Devices for Wavelength-Division Multiplexing Applicationssubmitted by Ajay Mistry in partial fulfillment of the requirements for the degreeof Master of Applied Science in Electrical and Computer Engineering.Examining Committee:Dr. Nicolas A. F. Jaeger, The Department of Electrical and Computer EngineeringSupervisorDr. Lukas Chrostowski, The Department of Electrical and Computer EngineeringSupervisory Committee MemberDr. Shahriah Mirabassi, The Department of Electrical and Computer EngineeringAdditional ExamineriiAbstractSilicon-on-insulator (SOI) microring resonator (MRR)-based modulators and fil-ters have been researched extensively for use in wavelength-division multiplexing(WDM) systems due to their attractive spectral characteristics and small devicefootprints. However, an inherent drawback of using MRRs in WDM systems istheir free-spectral-ranges (FSR). The FSR limits the aggregate data rate of the sys-tem, as it limits the number of channels that can be selectively modulated in aWDM transmitter, or simultaneously de-multiplexed in a WDM receiver. The goalof this thesis is to present and demonstrate SOI, MRR-based modulators and filterswith FSR-free responses.We first experimentally demonstrate an SOI, FSR-free, MRR-based filter witha reconfigurable bandwidth. The device uses a grating-assisted coupler integratedinto the MRR cavity to achieve an FSR-free response. Here, we demonstrate a non-adjacent channel isolation, for 400-GHz WDM, greater than 26.7 dB. A thermallytunable coupling scheme is utilized to compensate for fabrication variations and todemonstrate the reconfigurable filter bandwidth. We then demonstrate how lithog-raphy effects affect the performance of SOI devices, which include grating-basedcomponents. Using lithography models developed for deep ultraviolet lithogra-phy processes, we analyze the effects of lithography on the performance of anMRR with an integrated, grating-assisted coupler. We show that, if the effects oflithography are not taken in account during device design flow, large discrepan-cies result between the predicted “as-fabricated” and “as-designed” device perfor-mance. We also demonstrate how to use the lithography models to compensate forlithographic-effects in future device designs. Lastly, we experimentally demon-strate an FSR-free, MRR-based, coupling modulator. We demonstrate open eyeiiidiagrams at 2.5 Gbps and discuss how the effects of DUV lithography limited theelectro-optic bandwidth of the fabricated modulator to 2.6 GHz. We also discussthe effects of lithography on the modulation crosstalk of the device and how tosignificantly improve the electro-optic bandwidth and how to minimize crosstalkin future implementations of the device.ivLay SummaryWavelength-division multiplexing (WDM) technology has become one of the mostwidely used technologies to meet current demands for data transmission in opti-cal communication networks. Due to their attractive spectral characteristics andsmall device footprints, silicon-on-insulator (SOI) microring resonator (MRR)-based modulators and filters have been researched extensively for use in WDMsystems. However, the aggregate data rate of MRR-based, WDM systems is in-herently limited by the spacing between the MRR resonances, also known as theMRR’s free-spectral-range (FSR). The goal of this thesis is to present and exper-imentally demonstrate SOI, MRR-based modulators and filters that overcome thecurrent limitations. In particular, we focus on the integration of grating-assistedcouplers into MRR cavities in order to achieve FSR-free responses and also ana-lyze the effects of deep ultra violet lithography on device performance.vPrefaceThe content of this thesis is based on three publications, listed below, in which I amthe principal author. Most of Chapter 2 is based on the following publication [1]:1. A. Mistry, M. Hammood, H. Shoman, L. Chrostowski, and N. A. F. Jaeger,“Bandwidth-tunable, FSR-free, microring-based, SOI filter with integratedcontra-directional couplers,” Optics Letters, 2018. c©2018 The Optical So-ciety of America. Material including text and figures used with permission.N. A. F. Jaeger conceived the idea. I designed and modelled the device. Themask layout was created by myself and M. Hammood. I performed the measure-ments of the fabricated device, with assistance from M. Hammood and H. Shoman.L. Chrostowski obtained access to the fabrication technology used for this project. Iwrote the first draft of the manuscript, and N. A. F. Jaeger and M. Hammood helpeddetermine the final content and to edit the manuscript. H. Shoman and L. Chros-towski provided feedback during the design process and on the manuscript.Chapter 3 is based on the following publication [2]:2. A. Mistry, M. Hammood, S. Lin, L. Chrostowski, and N. A. F. Jaeger, “Ef-fect of lithography on SOI, grating-based devices for sensor and telecom-munications applications,” in 2019 IEEE 10th Annual Information Technol-ogy, Electronics and Mobile Communication Conference (IEMCON), 2019.c©2019 IEEE. Material including text and figures used with permission.I, together with Lukas Chrostowski and M. Hammood, conceived the idea for thepaper. I performed the device simulations and analysis. The mask layout for thevifabricated test structures was created by M. Hammood and S. Lin. The lithographymodel used for the analysis and modelling was developed by S. Lin. M. Hammoodand I performed the measurements of the fabricated test structures. L. Chrostowskiobtained access to the fabrication technology used for this project. M. Hammoodand I wrote the first draft of the manuscript, and N. A. F. Jaeger and S. Lin helpeddetermine the final content and to edit the manuscript. L. Chrostowski also gavefeedback on the manuscript.Chapter 4 is based on the following publication (which has been accepted) [3]:3. A. Mistry, M. Hammood, H. Shoman, S. Lin, L. Chrostowski, and N. A. F.Jaeger, “Free-spectral-range-free microring-based coupling modulator withintegrated contra-directional couplers,” presented at SPIE Photonics West,2020. c©2020 SPIE. Material including text and figures used with permis-sion.I, together with N. A. F. Jaeger and M. Hammood, conceived the idea for theproject. I designed the device and performed the device simulations. The masklayout was created by myself and M. Hammood. I performed the measurementsof the fabricated device, with assistance from M. Hammood and H. Shoman. L.Chrostowski and N. A. F. Jaeger obtained access to the fabrication technology usedfor this project. The lithography model used for analysis was developed by S. Lin.I wrote the first draft of the manuscript, and N. A. F. Jaeger and M. Hammoodhelped determine the final content and to edit the manuscript. H. Shoman providedinsights during the design process and gave feedback on the manuscript.viiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Silicon Photonics . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 WDM Optical Communication Systems . . . . . . . . . . . . . . 21.3 OADMs in WDM Links . . . . . . . . . . . . . . . . . . . . . . 41.4 Modulators in WDM Links . . . . . . . . . . . . . . . . . . . . . 61.5 Thesis Objective . . . . . . . . . . . . . . . . . . . . . . . . . . 91.6 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . 102 Bandwidth-Tunable, FSR-free, Microring-Based, SOI Filter with In-tegrated Contra-Directional Couplers . . . . . . . . . . . . . . . . . 11viii2.1 Contra-Directional Couplers . . . . . . . . . . . . . . . . . . . . 122.1.1 Overview and Theory . . . . . . . . . . . . . . . . . . . . 122.1.2 Calculation of the Distributed Coupling Coefficient . . . . 152.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.1 Bent Contra-DCs . . . . . . . . . . . . . . . . . . . . . . 222.2.2 MZI-Based Couplers . . . . . . . . . . . . . . . . . . . . 232.3 Device Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.4 Device Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.5 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 312.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 Effect of Lithography on SOI, Grating-Based Devices for Sensor andTelecommunications Applications . . . . . . . . . . . . . . . . . . . 393.1 Device Behaviour and Modelling . . . . . . . . . . . . . . . . . . 403.2 Effect of Lithography on Filter Performance . . . . . . . . . . . . 443.3 Compensating for Lithographic-Effects . . . . . . . . . . . . . . 493.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514 Free-Spectral-Range-Free, Microring-Based Coupling Modulator withIntegrated Contra-Directional Couplers . . . . . . . . . . . . . . . . 524.1 Device Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.2 DUV Lithography . . . . . . . . . . . . . . . . . . . . . . . . . . 564.3 Device Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 574.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 584.4.1 DC Device Characterization . . . . . . . . . . . . . . . . 594.4.2 High-Speed Characterization and Testing . . . . . . . . . 634.4.3 Adjacent and Non-Adjacent Resonance Suppression . . . 664.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 Summary, Conclusions, and Suggestions for Future Work . . . . . . 715.1 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . 715.2 Suggestions for Future Work . . . . . . . . . . . . . . . . . . . . 72Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75ixList of TablesTable 2.1 κ0 values of various bent contra-DC designs. . . . . . . . . . . 28Table 2.2 Design parameters for the bent contra-DC in the filter. . . . . . 28xList of FiguresFigure 1.1 A block diagram of a WDM link. . . . . . . . . . . . . . . . 2Figure 1.2 Schematic of a) a conventional Mach-Zehnder modulator andb) a conventional microring resonator-based modulator. . . . . 7Figure 1.3 A block diagram of a 4-channel, single-bus, MRR-based WDMtransmitter architecture. . . . . . . . . . . . . . . . . . . . . 8Figure 2.1 a) Diagram of a straight contra-DC. b) Zoom-in of the structureillustrating device design parameters. . . . . . . . . . . . . . 12Figure 2.2 Graphical solution for the phase match conditions of a contra-DC with WB = 450 nm, WR = 550 nm, and Λ = 318 nm. Thesolid arrow shows the wavelength at which contra-directionalcoupling occurs and the dashed arrows show the wavelengthsat which intra-Bragg reflections can occur. . . . . . . . . . . . 14Figure 2.3 Theoretical through-port (|tc|2) and drop-port (|kc|2) amplituderesponses of a contra-DC. . . . . . . . . . . . . . . . . . . . 15Figure 2.4 Band diagram of a contra-DC. The spacing between the ar-rows is the bandgap (∆λbg) of the contra-DC and represents thewavelengths at which light is reflected and, hence, the wave-lengths at which contra-directional coupling occurs. . . . . . . 16Figure 2.5 Band diagram of a contra-DC withWB = 450 nm,WR = 550 nm,∆WB = 50 nm, ∆WR = 60 nm, Λ = 318 nm, and g = 280 nm. . . 18Figure 2.6 Comparison between contra-DC k0 values determined via band-structure calculations and k0 values extracted from measuredtest structures fabricated at UW and ANT. . . . . . . . . . . . 19xiFigure 2.7 Spectral responses (arbitrary linear scales) of a) the contra-DC drop-port response, b) the MRR response, and c) the MZIcross-state response when ∆λnull = 2FSRring = FSRMZI . TheBW of the filter is tuned as the MZI response is redshifted(green arrow). Reprinted with permission from [1] c© The Op-tical Society of America. . . . . . . . . . . . . . . . . . . . . 21Figure 2.8 A schematic of our tunable filter. Inset shows the design pa-rameters of the bent contra-DC. Reprinted with permissionfrom [1] c© The Optical Society of America. . . . . . . . . . 22Figure 2.9 Diagram of filter illustrating the coupling coefficients of thebent contra-DC and MZI-coupler. The coupling coefficients,te f f and ke f f (not shown in figure), of the MZI-coupler can bereadily controlled by tuning φarm. . . . . . . . . . . . . . . . 25Figure 2.10 Graphical solution to Equation 2.12, for select κ0 values, todetermine Lc required to satisfy 2FSRring = ∆λnull . . . . . . . 27Figure 2.11 a) Simulated through- and drop-port responses of the filter,with the nulls of the MZI-coupler cross-port response alignedwith the contra-DC nulls. b) Zoom-in around the operatingwavelength. Dotted lines represent the wavelengths of sup-pressed resonant modes. . . . . . . . . . . . . . . . . . . . . 29Figure 2.12 a) Filter drop-port response (blue) with the MZI-coupler cross-port response (grey-dotted) shifted by a quarter cycle (φarm =−pi/2), and b) by a half cycle (φarm = ±pi). The contra-DCresponse (red-dotted) is static and does not shift as a functionof φarm. Adapted with permission from [1] c© The OpticalSociety of America. . . . . . . . . . . . . . . . . . . . . . . . 30Figure 2.13 Filter a) 3-dB BW and |te f f |2 versus φarm and b) SMSR and ILversus φarm. . . . . . . . . . . . . . . . . . . . . . . . . . . . 30xiiFigure 2.14 The through- (blue) and drop-port (red) responses of the filter;a) before alignment-tuning, b) aligned to the operating wave-length (1548.2 nm) and tuned to the maximum BW (60 GHz),and c) aligned to the operating wavelength (1548.2 nm) andtuned to the minimum BW (25 GHz). Dotted lines show possi-ble channel locations on a 400-GHz grid. The simulated drop-port responses, based on extracted fit parameters, are overlayedonto the measured drop-port response. Reprinted with permis-sion from [1] c© The Optical Society of America. . . . . . . . 32Figure 2.15 Spectral responses of the fabricated, point-coupled referencedevices with a) complete suppression of the adjacent MRR sidemodes and b) one adjacent side mode not fully suppressed dueto 2FSRring > ∆λnull , due to fabrication variations. Reprintedwith permission from [1] c© The Optical Society of America. 35Figure 2.16 a) Drop-port BW and extracted effective MZI-coupler powercoupling coefficient as a function of control-arm heater cur-rent. b) Ai and nAi of the filter for a 400-GHz grid WDM, andSMSR as a function of control-arm heater current. Reprintedwith permission from [1] c© The Optical Society of America. 36Figure 2.17 Group delay at the through-port of the filter (when operatedin the overcoupled region) and of a grating coupler test struc-ture (zero set arbitrarily). A single spike in the filter’s groupdelay is observed at the resonant wavelength. Reprinted withpermission from [1] c© The Optical Society of America. . . . 37Figure 3.1 Schematic of an MRR with an integrated contra-directionalcoupler. c©2019 IEEE. . . . . . . . . . . . . . . . . . . . . . 41Figure 3.2 Graphical solutions for the phase match condition of a contra-DC with Λ = 318 nm and 1) WB = 450 nm and WR = 550 nm(blue line) and 2) WB = 429 nm and WR = 528 nm (red line). . 42xiiiFigure 3.3 Simulated spectral response of our MRR drop-port (blue). Dot-ted grey lines show the locations of the suppressed MRR sidesmodes (adjacent to the operating wavelength), due to null-coupling to the cavity via the contra-DC (red). c©2019 IEEE. . 43Figure 3.4 (a) Mask layout of a section of our as-designed contra-DC. (b)The predicted outcome of our lithography model. Smoothingand proximity effects can be clearly seen on the corrugations.(c) A scanning electron microscope image of our as-fabricatedcontra-DC. c©2019 IEEE. . . . . . . . . . . . . . . . . . . . 45Figure 3.5 Drop-port response of an as-fabricated contra-DC test structure(red), simulated prediction-model (black) and simulated as-designed (blue) contra-DC test structures (detuned to the cen-tral wavelength of the drop-port response of the as-fabricatedtest structure, 1534 nm). Lithographic-effects reduce the cou-pling strength, κ0, from the simulated/expected value of 9,350 m-1to approximately 1,900 m-1. c©2019 IEEE. . . . . . . . . . . 47Figure 3.6 a) Simulated spectral drop-port response after applying the lithog-raphy model to the contra-DC test structure (solid). Simulatedas-designed response detuned to the central wavelength of thepost-lithography response (dashed), shown for reference. TheMRR side mode adjacent to the right of the operating wave-length is not fully suppressed due to a reduced κ0 and thechange in the cavity resonance condition. The insertion lossof the MRR increases and the 3-dB bandwidth of the MRRdecreases. b) Zoom-in of the un-suppressed adjacent MRRmode. The adjacent channel SMSR is reduced to 26 dB since∆λnull < 2FSRring. c©2019 IEEE. . . . . . . . . . . . . . . . 48Figure 3.7 a) Mask layout of a section of our re-designed contra-DC. (b)The predicted outcome of our lithography model. The κ0 ofthe prediction-model of the re-designed device matches that ofthe as-designed contra-DC (see Figure 3.4a). c©2019 IEEE. . 49xivFigure 3.8 Simulated drop-port spectra of the as-design contra-DC (red)and lithography prediction-model of the re-designed device(blue). c©2019 IEEE. . . . . . . . . . . . . . . . . . . . . . . 50Figure 4.1 Schematic of the modulator. Inset shows the design parametersof the bent contra-DC. . . . . . . . . . . . . . . . . . . . . . 54Figure 4.2 Cross-section of the p-n junction segment integrated in themodulation-arm (not shown to scale). . . . . . . . . . . . . . 55Figure 4.3 a) Theoretical through-port response of the modulator withthe static phase of the modulation-arm set to 0. An FSR-free response is observed across the C-band with a single res-onance mode located near 1550 nm. The contra-DC drop-port response (dotted-red) and locations of the suppressed res-onant wavelengths are shown for reference (dotted-black). b)Through-port response of the modulator for various reversebias voltages applied to the modulation-arm p-n junction withthe static phase shift set to 4.25 radians. . . . . . . . . . . . . 58Figure 4.4 Micrograph of the fabricated modulator showing DC (left-side)and RF (right-side) signal pads. The contra-DC test structureis also shown, located close to the modulator. . . . . . . . . . 59Figure 4.5 a) Measured through-port spectral response, with the modulation-arm tuned close to critical coupling, overlayed with the the-oretical response generated using device parameters obtainedby curve-fitting the measured response to analytical equations.b) Zoom-in on the operating resonance mode. c) Analyticalcavity linewidth and Q-factor of an add-drop ring resonator atcritical coupling, as a function of κ0, assuming a contra-DCthrough-port coupler. The calculated loaded Q-factor factor(63,000) and cavity linewidth (3.11 GHz) closely match themeasured values. . . . . . . . . . . . . . . . . . . . . . . . . 61xvFigure 4.6 a) ER of the modulator as functions of voltage applied to themodulation-arm heater. b) Measured through-port spectra forvarious reverse-bias voltages applied to a p-n junction segmentin the modulation-arm. c) Static modulation depth as functionsof wavelength for a bias voltage of -2 V and Vpp swings of 2 Vand 4 V. Dotted line shows the operating wavelength (1529.56nm) where the static modulation depths are 3.75 dB and 6 dBfor 2 Vpp and 4 Vpp, respectively. . . . . . . . . . . . . . . . 62Figure 4.7 Block diagrams of the experimental setups used a) to measurethe modulator EOBW and b) to generate eye-diagrams. . . . 64Figure 4.8 a) Measured EOBW of the modulator. The EOBW for a 1.0 GHzdetuning from resonance was 2.6 GHz. b) Optical eye diagramat the modulator through-port for a 2.488 Gbps, 2 Vpp drivesignal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Figure 4.9 Contra-DC response for our κ0 design value of 6,900 m-1 (solid-red) and ring response of the cavity (dotted-black). The in-tersection of the two curves (blue circles) is the amount ofcoupling to the cavity when the contra-DC nulls are optimallyaligned to the resonance modes. The coupling to the cavitysaturates at wavelengths far from the operating mode (less than-38 dB, shown by the shaded blue area). . . . . . . . . . . . . 67Figure 4.10 a) Measured through-port spectra at the left adjacent resonancemode for various reverse-bias voltages (with the right adjacentmode suppressed). b) Static modulation depth as functions ofwavelength for a bias voltage of -2 V and a Vpp swing of 2 V. 69Figure 4.11 Measured response of an as-fabricated contra-DC test struc-ture and predicted response of the as-designed contra-DC afterapplying lithography models. The responses are detuned to thecentral wavelength of the as-fabricated test structure response(1530 nm). . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Figure 5.1 Schematic of the proposed filter; an FSR-free MRR filter cas-caded with a two-stage, series-cascaded contra-DC. . . . . . 73xviList of AcronymsAWG Arrayed waveguide gratingBER Bit error rateBPF Bandpass optical tunable filterBW 3-dB bandwidthCMOS Complementary metal-oxide-semiconductorCW Continuous waveCWDM Coarse wavelength-division multiplexingDCA Digital communications analyzerDEMUX De-multiplexerDUV Deep-ultra-violetDWDM Dense wavelength-division multiplexingEDFA Erbium-doped fiber amplifiersEOBW Electro-optic bandwidthFDTD Finite-difference time-domainFSR Free-spectral-rangeFWHM Full width at half maximumxviiGC Grating couplerIL Insertion lossLIDAR Light detection and rangingMRR Microring resonatorMUX MultiplexerMZI Mach-Zehnder interferometerOADM Optical add-drop multiplexerOBRR Out-of-band rejection ratioOOK On-off-keyingPAM Pulse-amplitude modulationPIC Photonic-integrated circuitPPG Pulse pattern generatorPRBS Pseudo-random binary sequenceQSFP Quad small form-factor pluggableSEM Scanning electron microscopeSLSR Side lobe suppression ratioSMSR Side mode suppression ratioSOI Silicon-on-insulatorWDM Wavelength-division multiplexingVNA Vector network analyzerxviiiAcknowledgmentsI would like to first express my gratitude to my supervisor, Dr. Nicolas A. F. Jaeger,for providing me guidance and mentorship over the past years. I want to especiallythank him for being so passionate and supporting when it came to our work, and forhis outright commitment to his students and willingness to be patient with them.I would also like to thank Dr. Lukas Chrostowski for all the opportunities that heprovided during my time at UBC, as well as the time he took to discuss and providefeedback on my research.I would also like to thank all my colleagues who I got to work with and becomefriends with at UBC. I especially want to thank Mustafa Hammood and HossamShoman, for supporting and collaborating on projects with me, as well as Han Yun,Stephen Lin, Jaspreet Jhoja, Enxiao Luan, Rui Cheng, Minglei Ma, and Abdelrah-man Afifi. I would also like to thank all the collaborators from other institutionsthat I was able to work with over the past years, as well as Elenion Technologies,for providing me with the opportunity to continue my studies while working as aphotonics engineer.I also acknowledge the Natural Sciences and Engineering Research Council ofCanada (NSERC) and the SiEPIC program and for financial support. Additionally,I acknowledge CMC Microsystems, The University of Washington Nanofabrica-tion Facility, and Applied Nanotools Inc. for their assistance in fabricating devices,and Lumerical Inc. for providing simulation software and technical support.Lastly, I would like to thank my family for teaching me importance of workinghard and prioritizing my education and for always providing me with unconditionalsupport in all my endeavours. I am also grateful for my friends for their friendship,encouragement, and for always motivating me to strive for success.xixChapter 1Introduction1.1 Silicon PhotonicsSilicon photonic (SiPh) platforms, such as silicon-on-insulator (SOI), have shownenormous potential to meet demands in fields such as telecommunications and datacommunications, quantum computing, light detection and ranging (LIDAR), andoptical sensing technologies. The SOI platform is particularly attractive as it lever-ages the already mature and reliable complementary metal-oxide-semiconductor(CMOS) technology, enabling eventual monolithic integration of photonic devicesand CMOS electronics [4–7]. On the SOI platform, due to the high index contrastbetween the silicon (core) layer and the oxide cladding layers, light is primarilyconfined to the core allowing for the realization of compact nanowires with tightbend radii and components with small feature sizes. As a result, densely integratedphotonic integrated circuits (PICs) with small footprints can be made [8–11]. Var-ious components for use in PICs on the SOI platform have been demonstrated inthe literature, including lasers [12–15], photodetectors [16–19], splitters [20–24],polarization rotators [25–29], and variable optical attenuators [30–32].Silicon photonics has demonstrated the capability to meet the increasing de-mand for higher data transmission capacity in optical communication systems,such as short-reach optical interconnects and long-haul telecommunications sys-tems [33–35]. Due to the current availability and cost effectiveness of 100 Gbpsand 400 Gbps devices, the global optical transceiver market is projected to be worth1at least 20 billion dollars by 2023 [36], with the total market for SiPh PIC-basedtransceivers expected to grow to around 4 billion dollars in 2024 [37]. Major play-ers in the SiPh-based transceiver market include companies such as Luxtera/Cisco,Intel, Acacia Communications, InPhi, Ciena, and Elenion Technologies [38], withhyperscale networking companies like Alibaba Cloud, Amazon, Apple, Facebook,Google, and Microsoft motivating the future development and deployment of SiPh-based technologies and transceivers. Intel, for example, has developed a 100 Gbpsquad small form-factor pluggable 28 (QSFP-28) transceiver, with four channels,each capable of supporting data rates up to 28 Gbps [39]. Alibaba Group alsorecently launched a 400 Gbps optical transceiver through joint technology devel-opment with Elenion Technologies [40].1.2 WDM Optical Communication SystemsCW LaserCW LaserN-Channel DEMUXN-Channel MUXCW LaserModulatorModulatorModulatorλ1λ2λNData In NData In 2Data In 1λ1, λ2, ... , λNOptical FiberTransmitter (Tx)DetectorDetectorDetectorλ1λ2λNRx Out 1Rx Out 2Rx Out NReceiver (Rx)Figure 1.1: A block diagram of a WDM link.One of the most widely used technologies for high-capacity optical communi-cation systems is wavelength-division multiplexing (WDM) [41–46]. Figure 1.1shows a schematic of a typical WDM transceiver. In a WDM transceiver, at thetransmitter side, several electro-optic modulators are used to encode optical car-riers with data. Here, we show external modulators in which light from severalcontinuous-wave (CW) laser sources is modulated. The encoded data is then com-2bined onto a single communications link using a multiplexer (MUX). This is anadvantage of a WDM system, in which separate data streams can be encoded ontooptical carriers operating at different wavelengths, in parallel, and then combinedand transmitted simultaneously down a single communication medium. Transmit-ting multiple frequencies over the single link results in a higher aggregate datarate for the link; i.e., for a system with N channels, each transmitting at a datarate R, the aggregate data rate becomes NR. While On-Off-Keying (OOK), orpulse-amplitude modulation (PAM)-2, is the simplest encoding scheme and one ofthe most common modulation formats employed in short reach optical intercon-nects [47, 48], different encoding schemes may be used in order to further increasethe data rate of the link. In OOK, the digital data (0s and 1s) are represented inthe form of absence or presence of light. By employing higher-order modulationformats, i.e., PAM-4 and PAM-8, where four and eight levels of optical amplitudeare used to represent data, respectively, the bits per symbol (bits/sym) increasesfrom 1 bit/sym for PAM-2, to 2 bits/sym and 3 bits/sym for PAM-4 and PAM-8, respectively. The communications medium used is typically an optical fiber(shown in Figure 1.1), but in short-reach or on-chip integrated photonics applica-tions, the medium may be a waveguide. On the receiver side of the transceiver, ade-multiplexer (DEMUX) is used to separate the signals encoded on each opticalcarrier. The optical signals are then converted to electrical signals using photode-tectors, and the data can then be further processed.WDM systems typically fall into two categories; dense-WDM (DWDM) andcoarse-WDM (CWDM). DWDM systems have higher aggregate data rates, aschannels are closely spaced (in wavelength) and a large number of channels perfiber are transmitted. For example, in the C- and L-bands, with 100-GHz frequencyspacing (≈ 0.8 nm), a total of 115 wavelength channels can be transmitted in onefiber. DWDM systems are predominantly used in long-haul communications dueto the optical fiber amplifiers required to compensate for optical fiber losses [45,49]. DWDM is advantageous because a large number of tightly spaced channelscan utilize the limited gain bandwidths of typical erbium-doped fiber amplifiers(EDFAs). CWDM is typically used for short-range communications and uses awider-range of frequencies with the operating wavelengths spaced further apart(typically around 20 nm). This standardized channel spacing allows for levels of3laser wavelength drift during operation which would not be acceptable in DWDM[50]. As a result, CWDM can be used as a cost-effective solution when spectralefficiency can be sacrificed (i.e., in short-reach applications), as expensive stablelaser source and EDFAs are not required [50, 51].1.3 OADMs in WDM LinksOptical add-drop multiplexers (OADM) are important components on both thetransmitter and receiver side of a WDM link. On the transmitter side, an OADMis used to multiplex the individual wavelength channels, while on the receiver sidean OADM is used to de-multiplex or filter the channels. The performance of anoptical filter can be defined by several figures-of-merit (FOMs), including, inser-tion loss (IL), 3-dB bandwidth (BW), group delay and out-of-band rejection ratios(OBRRs). The required performance metrics vary based on the application of theOADM. For example, filters in CWDM de-multiplexers require wide bandwidthsand flat-top responses, in order to compensate for laser wavelength drift, while fil-ters in DWDM de-multiplexer would require a narrow bandwidth due to the densechannel spacing, as described in the previous section. One of the most importantOADM FOMs is the free-spectral-range (FSR) of the device. Devices with widerFSRs enable WDM receivers in which a larger number channels can be selectivelymultiplexed or de-multiplexed within a particular communication band. In this sec-tion, we present an overview of some OADMs on the SOI platform demonstratedin the literature, including lattice filters [52–54], echelle gratings [55–57], arrayedwaveguide gratings (AWGs) [58–61], grating-assisted couplers [62–65], and mi-croring resonator (MRR)-based filters [66–69].Lattice filters consist of multiple cascaded stages of unbalanced Mach-Zehnderinterferometers (MZIs). Each MZI-stage introduces a constant phase delay in onearm, resulting in either constructive (or destructive) interference at certain wave-lengths at the output of each stage. By controlling the number of stages, the cou-pling coefficient of the directional couplers, and the phase delays in each stage, thespectral response of the lattice filter can be designed to achieve low-loss and flat-toppass bands. However, the shape of the lattice filter spectral response is susceptibleto fabrication variations, as fabrication-induced deviations from the “as-designed”4optical phase delays and coupling coefficients will deteriorate the filter response.As a result, precise control of the waveguide phase delays and the coupling coef-ficients are required to produce filters that meet the required design targets. Whilethermal tuners can be used to actively tune the phase delays of each lattice stage,this significantly increases the overall power consumption of the filter. Also, dueto the periodic nature of the MZI response, the device cannot be FSR-free.Echelle gratings and AWGs have similar operating principles and are based onmulti-path interference [70]. In an echelle grating, the input signal, consisting ofmultiple wavelength channels, enters a free-propagation region, where the light di-verges and impinges upon a grating reflector, creating interference patterns in thereflection. Based on the angle of the grating reflector and the phase delays intro-duced in the propagation region, light of a particular wavelength will be focusedonto/coupled into its corresponding output waveguide. Similarly, in an AWG, theincoming (multi-wavelength channel) signal is split into multiple paths which thenpropagate through a waveguide array. Here, the incoming beam is split using aninput star coupler. Based on the optical phase delays introduced in each path, inter-ference between the light from each path leads to light of a particular wavelengthbeing refocused onto a particular output in an output star-coupler. As a result,in both echelle gratings and AWGs, the wavelength channel coupled into each ofthe output waveguides will be de-multiplexed from the other wavelength channels.While both echelle gratings and AWGs have been demonstrated to have flat-top re-sponses [71] with large FSRs, both typically have large footprints, relatively largeinsertion losses, and are also susceptible to fabrication variations.Grating-assisted couplers, such as contra-directional couplers (contra-DCs),have also been demonstrated in the literature as OADMs [72–74]. The contra-DCconsists of two parallel Bragg grating waveguides. Each Bragg grating waveguideis a structure with a periodic modulation of the effective refractive index in thepropagation direction. In a single Bragg grating, the modulation of the effectiveindex causes multiple distributed reflections, resulting in constructive interferencearound a narrow wavelength band in which light is strongly reflected [75]. In thecontra-DC, contra-directional coupling occurs when the two grating waveguidesare bought close to together and the forward propagating mode of one waveguideis in phase with the backward propagating mode of the second waveguide. As a5result, light from the input waveguide is coupled backwards into the second outputwaveguide, instead of the same input waveguide like in a standalone Bragg grat-ing. Contra-DC based filters are particularly attractive for CWDM applications,as devices with wide bandwidths, flat-top responses, large OBRRs, and low inser-tion losses have been demonstrated in the literature [65, 76]. While the spectralresponse of contra-DCs can easily be tailored by modulating the grating couplingcoefficient along the length of the device, a major drawback of grating-assistedfilters is their small device features which are sensitive to fabrication variations,namely lithographic-effects including smoothing and proximity effects [77].SOI-based MRR filters for OADMs have been researched extensively, namelyfor DWDM applications due to their relatively narrow linewidths. Moreover, dif-ferent methods, such as two-point coupling [78], can be used to make the devicereconfigurable (in terms of bandwidth, extinction ratio, etc.) [79–81]. While MRRfilters have demonstrated good performance as regards narrow and reconfigurablebandwidths, large OBRRs, and low insertion losses, the device performance is of-ten sensitive to fabrication and temperature variations [82]. Moreover, single-ringMRRs have limited FSRs, reducing the number of channels that can be selectivelyfiltered in an OADM. For example, if the spacing between two adjacent MRRmodes (the FSR) is smaller than the communication band, two or more signals cor-responding to separate wavelength channels would be de-multiplexed by a singlefilter, leading to interchannel crosstalk [83]. In order to extend the FSR or elim-inate the FSR in MRR filters (and enable increased channel capacities for WDMsystems), multiple methods have been demonstrated in the literature. These meth-ods include higher-order MRRs and the Vernier effect [69], MZI-based coupling[84, 85], and grating-assisted coupling [86–88]. The work in [86], [87], and [88]demonstrated that by integrating contra-DCs within the coupling regions of single-or higher-order MRRs, suppression of all but one MRR mode could be achieved,resulting in effectively FSR-free responses.1.4 Modulators in WDM LinksThe optical modulator is an essential component of the WDM link, setting im-portant link metrics such as the data rate [89]. Typically, modulators on the SOI6platform integrate a p-n junction into a waveguide section and use the free-carrierplasma dispersion effect to change the refractive index of silicon [89, 90]. Whena voltage is applied across the junction, free carriers are either depleted or injectedinto the junction, changing the effective index of the waveguide. The effective in-dex change results in a phase shift, which translates to optical signal modulationin interferometric or resonant modulators. In this section, we discuss the two mostprominent modulator types researched and developed; the Mach-Zehnder modu-lator (MZM) [91–94] and the MRR modulator [95–100]. Schematics of a con-ventional MZM and MRR modulator are shown in Figure 1.2a and Figure 1.2b,respectively.Input OutputV1V2 OutputInputa) b)kVFigure 1.2: Schematic of a) a conventional Mach-Zehnder modulator and b)a conventional microring resonator-based modulator.In an MZM, a phase shift is applied to either one (single-ended drive) or both(push-pull drive) of the MZM arms, changing the interference conditions and theamount of light that exits at the output of the modulator. Typically, MZMs re-quire multi-millimeter long p-n junction segments due to the small refractive indexchanges that result when carrier-depletion mode phase shifters are used. As a re-sult, travelling-wave electrodes are required in order to minimize the RF signal andoptical velocity mismatch which enables high electro-optic bandwidths (EOBWs).While travelling-wave MZMs with large bandwidths have been demonstrated inthe literature [101–103], these devices typically have higher energy consumption,greater design complexity and occupy a larger footprint as compared to their MRRmodulator counterparts.Two types of MRR modulation schemes have been demonstrated; intracavity7modulation and coupling modulation. Typically, intracavity modulation has beendominant, where applying a phase shift to the microring cavity results in a shift inthe resonant wavelength of the cavity and, hence, a change in the output power.In coupling modulation, the resonant wavelength remains constant, while the cou-pling coefficients (t and k) of the resonator are modulated, changing the extinc-tion ratio of the modulator and, hence, power at the output port (see Figure 1.2b).MRR intracavity modulators presented in the literature have demonstrated largeEOBWs while occupying very small footprints and achieving very high power perbit efficiencies [104–106]. Coupling modulators that have been demonstrated haveshown the ability to achieve data rates that exceed the cavity linewidth limit thattypically restricts the maximum data rate of intracavity-modulated MRRs [107–109]. It should be noted that MRR modulators (like, MRR filters) are also sen-sitive to temperature variations and fabrication imperfections and also require theuse of resonance wavelength tuning and/or stabilization schemes, which increasesthe overall power consumption of the modulator.DATA1 DATA2 DATA3λ1 λ2 λ3DATA4λ4Figure 1.3: A block diagram of a 4-channel, single-bus, MRR-based WDMtransmitter architecture.MRR-based modulators are particularly appealing in WDM transmitter appli-cations in which a series of ring modulators are coupled to a common bus waveg-uide and each modulator only modulates at a single wavelength [110, 111]. A sim-plified 4-channel example of this single-bus architecture is shown in Figure 1.3.This type of transmitter configuration simplifies the WDM architecture, as all ofthe channels can be combined onto a single output without the need for an addi-tional wavelength multiplexer (i.e., which would be needed if MZMs were used).8However, as previously mentioned, an inherent drawback of using MRRs is theirFSRs. In this particular application, the FSRs would limit the aggregate data rate ofthe system, as it restricts the number of channels that can be selectively modulatedwithin a particular communication band [1, 110, 112, 113].1.5 Thesis ObjectiveThe research presented in this thesis focuses on SOI, FSR-free, MRR-based fil-ters and modulators for WDM transceiver applications. Specifically, we focuson the use of contra-DCs integrated into MRR cavities in order to achieve FSR-free responses. Our first objective is to demonstrate a truly FSR-free, microring-based filter, with integrated contra-DCs, in which the adjacent MRR side modesare completely suppressed. While there have been previous demonstrations ofFSR-free, single-ring MRR-based filters with integrated contra-DCs in the litera-ture ([86, 88]), these designs did not achieve full suppression of the adjacent MRRside modes. Moreover, these designs were not robust to fabrication variations.Here, in this work, we demonstrate a filter with improved MRR side mode suppres-sion ratios (SMSRs), and with an integrated, thermally-tunable, two-point couplingscheme to compensate for fabrication variations and to provide post-fabricationcontrol of the filter performance (such as a reconfigurable filter bandwidth).While we show that contra-DCs have many advantages when used as wave-length selective couplers in SOI devices, due to their small feature sizes, contra-DCs fabricated using deep-ultra-violet (DUV) lithography are susceptible to smooth-ing and proximity effects. As a result, if lithography effects are not compensatedfor when designing devices that use contra-DCs, large discrepancies arise betweenthe “as-designed” and “as-fabricated” device performance. In this work, usinglithography models developed for DUV processes, we simulate and analyze the ef-fects of lithography on the performance of an MRR with an integrated contra-DC.We establish that it is possible to use the lithography models to compensate forlithographic effects during device design flow and layout. Using this approach, wethen design a contra-DC in which the as-fabricated spectral response matches thetarget/expected as-designed spectral response.Finally, our last objective is to demonstrate a proof-of-concept, MRR-based9modulator with an FSR-free response at its through-port for single-bus, WDMtransmitter architectures. While an extended FSR MRR modulator was recentlydemonstrated in the literature ([113]), it would be difficult to design an MRR mod-ulator based on this design with an FSR greater than the C-band. Here, in thiswork, by integrating a contra-DC into an MRR cavity, we demonstrate a mod-ulator with an FSR-free response. We demonstrate open eyes at a data rate of2.5 Gbps. We discuss how the effects of DUV lithography on the contra-DC intro-duced non-fully-suppressed resonance modes in the modulator response and alsohow the effects limited the EOBW of the fabricated modulator to 2.6 GHz. Wealso provide suggestions on how to significantly improve the EOBW and minimizechannel crosstalk in future designs of the modulator.1.6 Thesis OrganizationThis thesis is divided into five chapters. In this chapter, first we presented an intro-duction to silicon photonics and WDM communication systems. Then we providedan overview of SOI OADMs and optical modulators that have been demonstratedin the literature and, finally, the thesis objectives were outlined. In Chapter 2,first we present an overview of contra-directional couplers and the related theory.Then we present an FSR-free, MRR-based filter with a reconfigurable bandwidthand large SMSRs. In Chapter 3, we discuss the effects of lithography on SOI de-vices that integrate contra-DCs and demonstrate methods to compensate for theseeffects during device design flow. In Chapter 4, we experimentally demonstratea proof-of-concept, FSR-free, MRR-based coupling modulator for use in single-bus WDM transmitter applications and discuss methods to improve the modulatorperformance in future designs. Finally, in Chapter 5, a summary of this work,conclusions drawn, and suggestions for future work are provided.10Chapter 2Bandwidth-Tunable, FSR-free,Microring-Based, SOI Filter withIntegrated Contra-DirectionalCouplersIn this chapter, we experimentally demonstrate a bandwidth tunable, FSR-freeMRR filter with integrated bent contra-DCs. A thermally tunable MZI-coupler isused to compensate for fabrication variations, allowing the fabricated filter to havea reconfigurable bandwidth, as compared to non-tunable filters which have fixedbandwidths and which lack post-fabrication control of their performance. For ex-ample, we show that one can achieve a desired operating point by easily tuning thefilter (regardless of system losses) while maintaining a large non-adjacent channelisolation for a 400-GHz grid WDM system. Our device also has larger SMSRsthan similar designs previously reported in [86] and [88]. We also show that theamplitude and phase responses at the through-port of our filter are truly FSR-freeby presenting the measured group delay response of our filter. In this chapter, wefirst present an overview of contra-DC theory and design. We then discuss the mo-tivation behind our filter design and provide device theory and design parameters.Lastly, we present and discuss the measurement results of the fabricated filter.112.1 Contra-Directional Couplers2.1.1 Overview and TheoryInputDropThrough𝒕𝒄𝒌𝒄𝒈𝑾𝑩𝑾𝑹𝚲𝚫𝑾𝑩𝚫𝑾𝑹a)b)Waveguide BWaveguide RFigure 2.1: a) Diagram of a straight contra-DC. b) Zoom-in of the structureillustrating device design parameters.A contra-DC, like a Bragg grating, is a grating-assisted waveguide structurein which a periodic modulation of the effective refractive index along the struc-ture creates a Bragg reflector. In a contra-DC, the forward propagating mode in awaveguide couples to the backward propagating mode in a second, parallel waveg-uide [62, 63]. This is in contrast to a waveguide Bragg grating, in which the forwardpropagating mode of a waveguide couples to the backward propagating mode in thesame waveguide [114]. A schematic of a contra-DC is shown in Figure 2.1. Thecontra-DC consists of two parallel waveguides (waveguide B and waveguide R)with average waveguide widths, WB and WR, separated by an average gap distance,g. Typically, in a contra-DC, the two waveguides have dissimilar widths in orderto reduce forward cross-coupling [72]. In the contra-DC, the periodic modulationof the effective refractive index is achieved by creating corrugation profiles alongthe side-walls of waveguide B and waveguide R, with corrugations depths ∆WBand ∆WR, respectively. While the corrugations shown in Figure 2.1 are rectangular,other corrugation profiles, such as sinusoidal and trapezoidal profiles, can also be12used. Contra-directional coupling will occur when the forward propagating modeof waveguide B is in phase with the backward propagating mode of waveguide R.The phase match condition is given by,βBΛ+βRΛ= 2pi (2.1)where Λ is the grating period and βB and βR are the propagation constants forwaveguide B and waveguide R, respectively. The propagation constants are givenby,βB =2pine f f ,B(λ0)λ0(2.2)and,βR =2pine f f ,R(λ0)λ0(2.3)where λ0 is the free space wavelength and ne f f ,B and ne f f ,R are the wavelength-dependent effective indices of waveguide B and waveguide R, respectively. Solvingfor the wavelength at which contra-directional coupling occurs, the phase matchcondition of the contra-DC becomes:λ0 = Λ[ne f f ,B(λ0)+ne f f ,R(λ0)] (2.4)Within each waveguide, intra-waveguide Bragg reflections can also occur. Thephase match conditions for the Bragg reflections are βBΛ = 2pi for waveguide Band βRΛ = 2pi for waveguide R. These intra-waveguide Bragg reflections can besuppressed by using an “anti-reflection” grating, where the outer corrugations ofeach waveguide are out-of-phase with the inner corrugations [73]. This misalign-ment is shown in Figure 2.1. Figure 2.2 shows a graphical solution to the threephase match conditions of the contra-DC. In this plot, 220 nm thick strip waveg-uides (surrounded by a silicon dioxide cladding) are assumed, with WB = 450 nm,WR = 550 nm, and Λ = 318 nm. The waveguide effective indices were simulated inMODE Solutions, by Lumerical Inc.The transfer functions for the through-port and drop-port of the contra-DC canbe derived using coupled-mode theory [115]. The through-port and drop-port trans-13neff,Rneff,B𝜆2ΛnavgFigure 2.2: Graphical solution for the phase match conditions of a contra-DC with WB = 450 nm, WR = 550 nm, and Λ = 318 nm. The solid arrowshows the wavelength at which contra-directional coupling occurs andthe dashed arrows show the wavelengths at which intra-Bragg reflec-tions can occur.fer functions, tc and kc, respectively, are given by [116],tc =EthroughEinput=− jκ0 sinh(sLc)scosh(sLc)+ j∆β2 sinh(sLc)(2.5)andkc =EdropEinput=se j∆β2 Lcscosh(sLc)+ j∆β2 sinh(sLc)(2.6)where s =√κ20 − ∆β24 , ∆β = βR+βB− 2piΛ , and Lc is the length of contra-DC (Lcis given by NΛ, where N is the number of corrugations used). κ0 is the distributedfield coupling coefficient per unit length of the contra-DC and is effectively a mea-sure of coupling strength between the forward coupling mode in one waveguide14and the backward coupling mode in the other waveguide. In Figure 2.3, we plot thethrough-port and drop-port amplitude responses for a contra-DC withWB = 450 nm,WR = 550 nm, Λ = 318 nm, N = 470, and κ0 = 12,000 m-1.1530 1535 1540 1545 1550 1555 1560 1565 1570Wavelength (nm)-30-25-20-15-10-50Transmission (dB)10log10|tc|210log10|kc|2Figure 2.3: Theoretical through-port (|tc|2) and drop-port (|kc|2) amplituderesponses of a contra-DC.2.1.2 Calculation of the Distributed Coupling Coefficientκ0 is commonly defined analytically via the following equation [62, 72, 117, 118]:κ0 =ω4∫∫E∗1 (x,y) ·∆ε1(x,y)E2(x,y)dxdy (2.7)where ω is the angular frequency, E1 and E2 are the normalized transverse modesof the unperturbed waveguides (waveguides without side-wall corrugations), and∆ε1(x,y) is the first-order Fourier-expansion coefficient of the dielectric perturba-tion (due to the side-wall corrugation profile). Intuitively, Equation 2.7 shows thatstronger coupling (a larger κ0) is achieved when there is a large mode overlap be-tween the two waveguides and/or when the dielectric perturbation is large. This15λ0ΔλbgFigure 2.4: Band diagram of a contra-DC. The spacing between the arrowsis the bandgap (∆λbg) of the contra-DC and represents the wavelengthsat which light is reflected and, hence, the wavelengths at which contra-directional coupling occurs.translates to a contra-DC with a smaller average gap between the two waveguides(g) and/or large corrugation depths (∆WB and ∆WR).When designing contra-DCs, there are various methods that have been demon-strated in the literature to determine κ0. One method is to solve for κ0 usingEquation 2.7, by simulating the mode distributions of the two-waveguide systemvia eigenmode simulations, either treating each waveguide as an isolated, unper-turbed waveguide, or by using a super-mode analysis [62, 63, 72, 117, 118]. An-other method, which was originally proposed to obtain the coupling coefficient ofBragg gratings, involves determining the photonic band structure of a contra-DCunit-cell via three-dimensional (3-D) finite-difference-time-domain (FDTD) simu-lations and extracting κ0 from the band diagram [119]. Recently, this method wasalso used to calculate the band structure of a sub-wavelength contra-DC [120]. Weadopted this approach in our contra-DC design flow, and present it here.16The photonic band diagram, or ω-k dispersion relation, is a plot of the propa-gating solutions to the wave equation in a dielectric medium at angular frequencies,ω , for various values of the wavevector, kz, as shown in Figure 2.4. Similar to one-dimensional (1-D) photonic crystals, Bragg gratings and contra-DCs can be effec-tively described as structures with periodic perturbations of the dielectric mediumin the direction of the propagating optical mode. These periodic perturbations giverise to photonics bandgaps (∆λbg); ranges of wavelengths or frequencies in whichthere are no propagating solutions to Maxwell’s equations for any wavevector, kz(see Figure 2.4) [121]. Within this range of wavelengths, light will be reflected.The band diagram of a contra-DC can be used to extract its ∆λbg and central wave-length, λ0 [119, 120, 122]. The ∆λbg of the contra-DC band diagram, in fact,corresponds to ∆λnull of an infinitely long contra-DC, in which ∆λnull is the spac-ing between the first nulls of the contra-DC drop-port response (see Figure 2.3)[120]. ∆λnull for an infinitely long contra-DC is given by [116],∆λnull(Lc→ ∞) = 2λ20 κ0pi[ng,R(λ0)+ng,B(λ0)](2.8)where ng,B and ng,R are the wavelength-dependent group indices of waveguide Band waveguide R, respectively. Thus, κ0 for a contra-DC can be determined viaEquation 2.8. To plot the ω-k dispersion relation of a contra-DC, we performFDTD bandstructure calculations using FDTD Solutions, by Lumerical Inc. In thesimulations, we consider an infinitely long contra-DC as a single contra-DC unit-cell (single grating period) with Bloch boundary conditions. By sweeping kz, andperforming a Fourier transform on the time-domain signals in the simulation, ωnfor the nth propagating Bloch mode in a given frequency range, can be determined[119, 120, 122]. The ω-k dispersion diagram can then be constructed and ∆λbg andλ0 can be extracted to determine κ0 of the contra-DC.Figure 2.5 shows the calculated band diagram for a contra-DC with the param-eters WB = 450 nm, WR = 550 nm, ∆WB = 50 nm, ∆WR = 60 nm, Λ = 318 nm, andg = 280 nm. In the plot, ω was converted to wavelength and kz was normalized by afactor of Λ/2pi . In the band diagram, the blue and red dotted lines represent the in-dividual dispersion relations for waveguide B and waveguide R, respectively. Theband diagram shows that at wavelengths far from the bandgap, optical modes prop-17λBragg,RλBragg,BΔλbgFigure 2.5: Band diagram of a contra-DC with WB = 450 nm, WR = 550 nm,∆WB = 50 nm, ∆WR = 60 nm, Λ = 318 nm, and g = 280 nm.agate through the perturbed waveguides as if the waveguides were unperturbed.However, at wavelengths near the band gap, where there is an effective crossingbetween the waveguide modes, light is reflected, and contra-directional couplingoccurs. The spacing between the arrows in Figure 2.5 denotes the bandgap of thisparticular contra-DC. The bandgap is 2.2 nm, centered around 1550 nm, corre-sponding to a κ0 value of 12,000 m-1. (This is the same κ0 value that was usedto simulate the contra-DC through- and drop-port responses in Figure 2.1). Theband diagram can also be used to determine the strength of the intra-waveguideBragg reflections from each waveguide, which occur at a normalized kz value of0.5 (corresponding to the edge of the first Brillouin zone) [119]. Here, becauseanti-reflection grating waveguides were simulated, no bandgap is visible at kz =0.5, and the effect of the intra-Bragg reflections can be considered negligible.Similar to [119] and [123], we demonstrate how κ0 values extracted from band-structure calculations compare with experimental results of fabricated contra-DCs.Here, we present measurement results of fabricated contra-DC test structures from1810/20 30/40 50/60 70/80 90/100 110/120 130/140WB/ WR (nm)01234560 (m-1 )104Rect. SimulatedSinu. SimulatedRect. UWSinu. UWRect. ANTSinu. ANTFigure 2.6: Comparison between contra-DC k0 values determined via band-structure calculations and k0 values extracted from measured test struc-tures fabricated at UW and ANT.two different fabrication facilities: The University of Washington Microfabrica-tion/Nanotechnology User Facility (UW) and Applied Nanotools, Inc. (ANT).Both sets of test structures were fabricated using electron-beam (e-beam) lithogra-phy. The devices had a 220 nm silicon thickness with a target 3 µm silicon dioxidecladding layer deposited over top. The test structure parameters wereWB = 450 nm,WR = 550 nm, Λ = 318 nm, and g = 280 nm. The contra-DCs were 159 µm long(N = 500). ∆WR was varied from 20 nm to 140 nm in 20 nm steps and ∆WB foreach structure was 10 nm less than ∆WR. Test structures with rectangular and si-nusoidal corrugation profiles were simulated and fabricated. The κ0 values of thefabricated test structures from both UW and ANT were extracted from the mea-sured drop-port spectra using the full width at half maximum (FWHM) methodpresented in [123]. The κ0 values of the simulated and fabricated test structuresare plotted in Figure 2.6. The κ0 values extracted from our bandstructure calcula-tions (which have been fitted to a 4th order polynomial) show good agreement with19the measured test structures for both rectangular and sinusoidal contra-DCs fromboth fabrication runs. Having plots like Figure 2.6 is advantageous during devicedesign flow, as they can be used as look-up tables to determine which values of thecontra-DC parameters are required to achieve a desired κ0 value.2.2 MotivationGrating-assisted filters have typically been demonstrated as coarse-WDM filters.This is due to such filters having wide-bandwidths and FSR-free responses withhigh side lobe suppression ratios (SLSRs) [72]. Used solely as couplers, as com-pared to conventional broadband directional couplers used in MRR filters, contra-DCs effectively filter selected wavelengths at the drop-port of the device. Thistype of coupler can be used in MRR devices to prevent certain wavelengths fromcoupling to, and resonating in, the cavity, as compared to conventional directionalcouplers in which light at all wavelengths couples to the cavity. As a result, ifwavelengths that are not filtered to the drop-port coincide with the resonant wave-lengths of the MRR cavity, light will not enter the cavity and, thus, the selectivesuppression of those MRR resonant modes occur [88]. An FSR-free response isachieved when the contra-DC suppresses all MRR modes except the one at or nearthe contra-DC central wavelength (λ0). Maximum suppression of the amplitude re-sponses at all other undesired resonant wavelengths (side modes) will be achievedprovided that the spacing between the first nulls of the contra-DC, ∆λnull , is equal totwice the FSR of the MRR (2FSRring = ∆λnull), as shown in Figures 2.7a and 2.7b.A schematic of the proposed filter is given in Figure 2.8. The filter consistsof an add-drop (AD) MRR with a bent contra-DC integrated into the through-portcoupling region and an MZI-coupler as the drop-port coupler. The design differsfrom that presented in [88], as we only integrate a contra-DC into the through-portcoupling region rather than both the through- and drop-port coupling regions. Asdemonstrated in [88], in order to meet the maximum suppression condition, eachcontra-DC should cover approximately 50% of the cavity. Bent contra-DCs are,thus, used to achieve this condition, as compared to cavities with straight contra-DCs [86] in racetrack resonator configurations in which the maximum suppressioncondition cannot be met. However, devices that use two bent contra-DCs, that20Ring MZIContra-DCΔλnull = 2FSRringFSRringFSRMZI(a)(b)(c)Figure 2.7: Spectral responses (arbitrary linear scales) of a) the contra-DCdrop-port response, b) the MRR response, and c) the MZI cross-stateresponse when ∆λnull = 2FSRring = FSRMZI . The BW of the filter istuned as the MZI response is redshifted (green arrow). Reprinted withpermission from [1] c© The Optical Society of America.combined cover approximately 100% of the cavity, are susceptible to fabricationvariations and are not practical as they do not allow adequate space to connect buswaveguides to route the filter to external components (optical input/output, otherdevices, etc.) [88]. As the suppression of the MRR side modes is primarily de-pendent on the through-port coupler, we have replaced the drop-port contra-DC in[88] with a tunable MZI-coupler, such that the through-port contra-DC can coverapproximately 50% of the cavity to enable larger side mode suppression ratios(SMSRs) as compared to filters presented in [86] and [88]. Moreover, the tunablecoupler itself allows for the post-fabrication control of the drop-port couplers cou-pling coefficient (this is shown as the MZI response in Figure 2.7c) and enables thebandwidth reconfigurability of the device.21Input ThroughL1L2DropRTiN HeaterWBWRΛΔWBΔWR gFigure 2.8: A schematic of our tunable filter. Inset shows the design parame-ters of the bent contra-DC. Reprinted with permission from [1] c© TheOptical Society of America.2.2.1 Bent Contra-DCsAs shown in Figure 2.8, the bent contra-DC is integrated into the through-portcoupling region of the MRR cavity. In a bent contra-DC, the outer waveguide iswrapped around the inner waveguide, which as a radius of curvature, R. Here, wedenote the upper waveguide of the bent contra-DC as the bus (grating) waveguide(WB) and the inner waveguide as the ring (grating) waveguide (WR), where the ringwaveguide also forms part of the MRR cavity. The bent contra-DC shares the samedesign parameters as a straight contra-DC, however, Λ of the bent contra-DC ismeasured in the center of the coupler’s gap. By defining Λ this way, the phasematch condition of a bent contra-DC becomes [116],λ0 = Λne f f ,B(λ0)[R+ WB2 +g+WR2 ]+ne f f ,R(λ0)RR+g+ WB2(2.9)For large R, Equation 2.4 and Equation 2.9 yield approximately the same solu-tion. The equations for tc (Equation 2.5) and kc (Equation 2.6) of a straight contra-22DC also hold for a bent contra-DC. ∆λnull of a contra-DC with a finite length, Lc isgiven by [116],∆λnull =2λ 20pi[ng,R(λ0)+ng,B(λ0)]√κ20 +(piLc)2 (2.10)where ng,B and ng,R are the group indices of the bus and ring waveguides, respec-tively. The FSR of the MRR is given by,FSRring =λ 202piRng,R(λ0).(2.11)Hence, to achieve the 2FSRring = ∆λnull , the length of the contra-DC integratedinto the MRR cavity, Lc, should satisfy the following relation, which can be deter-mined from Equation 2.10 and Equation 2.11:Lc =2pi√(ng,R(λ0)+ng,B(λ0)ng,R(λ0)R )2−4κ20(2.12)2.2.2 MZI-Based CouplersMZI-based coupling schemes have been used to double the FSR of single- [78]and double-ring AD MRR filters [84, 85]. Here, in this paper, we use an MZI-coupling scheme in the drop-coupler of our MRR (see Figure 2.8) for two pur-poses. Firstly, we show that, if the nulls of the MZI-coupler cross state align withthe contra-DC nulls, then the directly adjacent side mode of the MRR response canbe further suppressed at the drop-port regardless of any fabrication induced mis-alignment between the contra-DC and ring responses. This requires that the FSRof the MZI matches ∆λnull of the contra-DC (Figures 2.7a and 2.7c). Secondly, theMZI-coupler can provide independent control of the drop-port coupler couplingcoefficients by introducing a phase shift (φarm) in the lower (control)-arm of thecoupler (see Figure 2.8). A phase shift induces a redshift of the MZI response anda change in the effective coupling coefficients of the drop-port coupler at the op-erating wavelength, resulting in an adjustable drop-port BW. (The phase shift canbe induced via the thermo-optic effect by placing resistive metal heaters over thewaveguide, or via the plasma-dispersion effect by integrating p-n junctions into the23control-arm waveguide.) This effect can be understood by analyzing the equationfor the BW of an AD MRR. The BW is given by [124],BW3dB =(1− t1t2a)λ 20ping,RLrt√t1t2a(2.13)where t1 is the self-coupling coefficient of the through-port coupler, t2 is the self-coupling coefficient of the drop-port coupler, a is the attenuation factor of theMRR, and Lrt is the roundtrip length of the cavity. Clearly, if all other resonatorparameters are static, the MRR BW can be adjusted dynamically by varying t2.In our device, by using an MZI-coupler, t2 becomes of function of φarm and thus,the BW becomes a function of φarm. The BW tunability allows one to compensatefor fabrication variations (i.e., variations in the directional coupler coupling coef-ficients, variations in the roundtrip cavity losses, etc.), enabling post-fabricationcontrol of the device to achieve the “as-designed” or desired device performance.2.3 Device TheoryThe through-port and drop-port transfer functions of our device are determinedfollowing the Mason’s rule [125] based approach presented in [116] and [126].The equations of our device differ from those presented in [88] and [116], as inour device, the drop-port coupler is an MZI-coupler. The MZI-coupler consists oftwo directional couplers, K1 and K2, with the top arm of the coupler (of length L1)sharing part of the microring cavity (see Figure 2.9). The transfer matrix of theMZI-coupler, H, is given by,H =[t2 − jk2− jk2 t2][X1 00 X2] [t1 − jk1− jk1 t1](2.14)where,X1 = e− jβRL1e−αR2 L1 , (2.15)X2 = e− jβRL2− jφarme−αR2 L2 , (2.16)ki is the field cross-coupling coefficient of Ki, ti =√1− k2i (and assuming lossless24K1 K2L1L2 + φarm𝒕𝒄,𝑹𝒕𝒄,B𝒌𝒄 𝒌𝒄𝒕𝒆𝒇𝒇(𝝋𝒂𝒓𝒎)Figure 2.9: Diagram of filter illustrating the coupling coefficients of the bentcontra-DC and MZI-coupler. The coupling coefficients, te f f and ke f f(not shown in figure), of the MZI-coupler can be readily controlled bytuning φarm.couplers), L1 is the length of the MZI-coupler arm that is shared with the microringcavity, L2 is the length of the control-arm, and αR is the field loss coefficient of thewaveguides (which have the same width as the ring waveguide). If we assume thatthe directional couplers are the same (K1 = K2), then the effective through-port(te f f ) and cross-port (ke f f ) coupling coefficients of the MZI-coupler are given byEquation 2.17 and Equation 2.18, respectively. As can be seen from their respectiveequations, te f f and ke f f are both functions of φarm.te f f = H11 = t21e− αR2 L1e− jβRL1− k21e−αR2 L2e− j(βRL2+φarm) (2.17)ke f f = H12 =− jk1t1[e−αR2 L1e− jβRL1 + e−αR2 L2e− j(βRL2+φarm)] (2.18)Following a similar derivation for the device presented in [116], the resulting25through-port and drop-port transfer functions of our device are given by,Ethru =te f f k2cX+ tc,B[1− te f f tc,RX ]1− te f f tc,RX (2.19)Edrop =ke f f kc√X1− te f f tc,RX (2.20)where,tc,B = tce− jβBLce−αB2 Lc , (2.21)tc,R = tce− jβRLce−αR2 Lc , (2.22)X = e− jβRLRe−αR2 LR , (2.23)LR is the residual cavity path length that is not shared with the contra-DC ringwaveguide or the top arm of the MZI-coupler (LR = 2piR−Lc−L1) and αB is thefield loss coefficient of the bus waveguide. The equations for tc,B and tc,R differfrom Equation 2.5 in order to account for the difference in phase accumulation inthe contra-DC bus and ring waveguides (see Figure 2.9).2.4 Device DesignThe devices were designed assuming a 220 nm silicon thickness and a top oxidecladding layer. WB and WR of the bent contra-DC were chosen to be 450 nm and550 nm, respectively, and Λ was set to 318 nm to place the filter operating wave-length close to 1550 nm. The large asymmetry between the waveguide widths re-duced forward cross-coupling. To determine the length of the contra-DC requiredto achieve 2FSR = ∆λnull , we plotted Lc as a function of R for various κ0 valuesbased on Equation 2.12. (The group indices used to solve for Lc for unperturbedwaveguides, waveguide B and waveguide R, were 4.11 and 4.33, respectively, de-termined using MODE Solutions). To compare our design to that presented in[88], we chose R to be also be equal to 34 µm. From Figure 2.10, we see that themaximum suppression condition for a 34 µm ring is met when κ0 = 4,700 m-1 andLc = 105.3 µm. This length corresponds to N = 330 and thus, the contra-DC cover-26age of the ring was 48.44%. The corresponding contra-DC design parameters forthe κ0 values plotted in Figure 2.10, are listed in Table 2.1. These values were de-termined from the bandstructure simulation results which we plotted in Figure 2.6.Because the radius of curvature of the ring was relatively large, we assumed thatthe κ0 values of the bent contra-DCs were approximately equal for straight contra-DCs with similar design parameters. This assumption was verified by simulatingthe full bent contra-DC structures in FDTD and comparing the extracted κ0 fromthose simulations to the bandstructure results. From Table 2.1, a contra-DC withκ0 = 4,700 m-1 is achieved by setting ∆WB equal to 20 nm, ∆WR equal to 30 nm,and g equal to 280 nm. A summary of the chosen design parameters for the bentcontra-DC used in the filter is presented in Table 2.2.30 31 32 33 34 35 36 37 38R (µm)9095100105110115120125L c (µm)2900 m-14700 m-16900 m-19350 m-1Figure 2.10: Graphical solution to Equation 2.12, for select κ0 values, to de-termine Lc required to satisfy 2FSRring = ∆λnull .To set the FSR of the MZI-coupler to be equal to ∆λnull , the length of the MZI-coupler control-arm, L2, was chosen such that L2 = L1+piR (L1 was 50 µm long)and the width of the coupler arm waveguide was also 550 nm. The gap width for27Table 2.1: κ0 values of various bent contra-DC designs.κ0 g ∆WB ∆WR2,900 m-1 280 nm 10 nm 20 nm4,700 m-1 280 nm 20 nm 30 nm6,900 m-1 280 nm 30 nm 40 nm9,350 m-1 280 nm 40 nm 50 nmTable 2.2: Design parameters for the bent contra-DC in the filter.Design Parameters ValueWB 450 nm∆WB 20 nmWR 550 nm∆WR 30 nmΛ 318 nmg 280 nmN 330R 34 µmeach directional coupler used in the MZI-coupler was set to 60 nm to maximize|ke f f |2 of the MZI-coupler (60 nm was the minimum resolvable gap width guaran-teed by the fabrication process). The coupling coefficient of the directional couplerat 1550 nm was 15% based on FDTD simulations. A 160 µm long TiN heaterwas placed above the MZI-coupler control arm in order to thermally induce thephase shift used to tune the coupling coefficients of the drop-port coupler (via thethermo-optic effect). A second 105 µm long TiN heater was also placed above thecontra-DC to allow us to align the contra-DC and ring responses. A third 80 µmlong TiN heater was placed across the section of the ring not covered by the contra-DC or MZI-coupler to allow us to tune the operating wavelength of the filter. TheTiN heaters were 3 µm wide, 200 nm in thickness and had a target bulk resistivityof 0.8 µΩ-m. We also designed a reference device with a conventional directionalcoupler in the drop-port coupling region in order to compare the effect of fabrica-tion variations on the contra-DC and filter SMSR. The device was also designed toachieve a wide target BW of 46 GHz (0.375 nm). The coupler had a gap of 60 nm28SMSR SMSRΔλnullFigure 2.11: a) Simulated through- and drop-port responses of the filter, withthe nulls of the MZI-coupler cross-port response aligned with thecontra-DC nulls. b) Zoom-in around the operating wavelength. Dottedlines represent the wavelengths of suppressed resonant modes.and a power coupling coefficient of 25% at 1550 nm.The through-port and drop-port responses of our designed filter are shownin Figure 2.11a. The responses are simulated in MATLAB R©, based on the de-vice transfer functions (Equation 2.19 and Equation 2.20). In our simulations, weassume the waveguide propagation loss for all waveguides to be 3 dB/cm. Fig-ure 2.11a shows the response of the filter when the nulls of the MZI-coupler cross-state align with the contra-DC nulls. Across the 80 nm wavelength range shownin Figure 2.11a, the resonant modes of the MRR are suppressed at all wavelengthsother than the operating wavelength (1547.8 nm). The insertion loss is 1.3 dBand the 3-dB BW is approximately 60 GHz. Figure 2.11b shows a zoom-in ofthe responses near the operating wavelength, where the dotted lines represent the(wavelength) locations of the first two left adjacent and first two right adjacentsuppressed MRR side modes. The directly adjacent side modes are suppresseddue to both the MZI-coupler and the contra-DC, while the second adjacent sidemodes are suppressed solely by the contra-DC. Interstitial peaks are also visiblein the drop-port transmission spectra. While these peaks at not located directlyat suppressed resonant wavelengths, the peaks can potentially lead to interchannelcrosstalk. Here, we define the SMSR of the filter to be the minimum difference29between the drop-port transmission at the operating wavelength and the maximumdrop-port transmission of the largest interstitial peak on either side of the drop-portoperating wavelength (within the C-band). The SMSR of the simulated device is26.5 dB.Figure 2.12: a) Filter drop-port response (blue) with the MZI-coupler cross-port response (grey-dotted) shifted by a quarter cycle (φarm =−pi/2),and b) by a half cycle (φarm = ±pi). The contra-DC response (red-dotted) is static and does not shift as a function of φarm. Adapted withpermission from [1] c© The Optical Society of America.Figure 2.13: Filter a) 3-dB BW and |te f f |2 versus φarm and b) SMSR and ILversus φarm.30Figure 2.12 shows how the drop-port spectrum changes when a phase shiftis applied to the MZI-coupler control-arm. In Figure 2.12a, φarm = −pi/2, andthe MZI-coupler cross-state is shifted by a quarter cycle. The phase shift altersthe coupling conditions around the operating wavelength and, hence, results in achange in the 3-dB BW of the filter (as per Equation 2.13). The BW is reduced to26 GHz. The simulated filter BW as a function of φarm is plotted in Figure 2.13a.The MZI-coupler through-port power coupling coefficient (|te f f |2) is also plottedas a function of φarm in Figure 2.13a. When a phase shift is applied to the control-arm, because the contra-DC response remains static, the MRR side modes are stillsuppressed. However, the interstitial peaks become larger due to the change in|ke f f |2 at wavelengths near a suppressed mode. This effect decreases the SMSR ofthe filter, as demonstrated in Figure 2.12a. In Figure 2.13b, we plot the SMSR ofthe filter as a function φarm. Over the pi/2 phase shift range, the SMSR remainsgreater than 22.5 dB. The insertion loss of the filter is also a function of φarm.As the phase shift approaches pi , destructive interference occurs at the cross-portof the MZI-coupler and no light will be transmitted to the drop-port of the filter,as demonstrated in Figure 2.12b. For phase shifts ranging from −pi/2 to 0, theinsertion loss of the filter is less than 1.4 dB, as shown in Figure 2.13b.2.5 Experimental ResultsOur devices were fabricated by Applied Nanotools, Inc., using their electron-beamlithography process. Sub-wavelength fiber grating couplers (GCs) were used forthe optical input and output. The devices were measured using an Agilent 81600Btunable laser source and two Agilent 81635A optical power sensors. First, one ofthe cavity heaters was used to align the contra-DC nulls with the cavity resonantmodes. The MZI-coupler was then tuned to achieve a desired operating BW. Lastly,a common signal was applied to both the cavity heaters to obtain the target operat-ing wavelength of the filter (1548.2 nm). The operating wavelength was set last inorder to compensate for the parasitic wavelength shift that accompanies the tuningof the control-arm [127]. Figures 2.14a and 2.14b show the measured through-and drop-port responses of a fabricated filter before and after this alignment-tuningprocess, respectively. The responses were normalized to remove the spectral re-31Ai3.2 nmSMSRnAiAiSMSRnAia)b)c)Figure 2.14: The through- (blue) and drop-port (red) responses of the fil-ter; a) before alignment-tuning, b) aligned to the operating wavelength(1548.2 nm) and tuned to the maximum BW (60 GHz), and c) alignedto the operating wavelength (1548.2 nm) and tuned to the minimumBW (25 GHz). Dotted lines show possible channel locations on a400-GHz grid. The simulated drop-port responses, based on extractedfit parameters, are overlayed onto the measured drop-port response.Reprinted with permission from [1] c© The Optical Society of Amer-ica.32sponses from the input and output (through/drop-port) GCs. Due to high lossesof the fabricated GCs, it should be noted that our measurements of the drop-portspectrum was limited by the noise floor of the power sensors.A single resonant mode is observed within the C-band. The drop-port responseshows a large 3-dB BW of approximately 60 GHz (0.48 nm) and an insertion lossof less than 3 dB. As seen in Figure 2.14b, the MRR side modes adjacent to theoperating wavelength are completely suppressed. Moreover, all suppressed modesat the through-port notches have magnitudes of less than 0.75 dB. The measuredSMSR was 20.8 dB, which is larger than the values reported in both [86] and [88].Figure 2.14c (to be discussed in further detail below) shows the same filter whenthe MZI-coupler was tuned to achieve a BW of 25 GHz.Here, we also characterize the filters adjacent channel isolation, Ai, and non-adjacent channel isolation, nAi, as defined in [87], for a channel spacing of 400 GHz(3.2 nm). Ai is defined as the minimum difference (in dB) between the transmis-sion of the filter at the operating wavelength and its transmission at the locationof the directly adjacent channels. nAi is the minimum difference (in dB) betweenthe transmission of the filter at the operating wavelength and its transmission atall non-adjacent channels within the C-band (1528.77 nm to 1563.86 nm [69]). Inother words, here we only considered the 11 possible channels in the C-band (6 tothe left and 4 to the right of the operating wavelength) when calculating Ai and nAi.Ideally, one would like the nAi to be greater than the Ai to minimize interchannelcrosstalk in a WDM system [83, 85]. Adjusting the control-arm phase of our filterto have a 60 GHz BW, the Ai of our filter was 35.5 dB and the nAi was 26.7 dB.In order to extract the filter parameters of the “as-fabricated” device, we fit themeasured drop-port response to the device transfer function (Equation 2.20). Thedesign parameters of interest were the waveguide loss, power coupling coefficientof the MZI-coupler directional couplers (|k1|2) and κ0 of the contra-DC. These pa-rameters were most likely to vary from the as-designed values. In our fitting, we as-sumed that the waveguide dimensions of the fabricated device did not deviate fromthe as-designed dimensions, and, hence, the waveguide effective index models usedfor fitting were the same as those used in the device simulations. From the fitting,it was determined that κ0 of the fabricated filter was 4,100 m-1, the waveguide losswas 18 dB/cm and |k1|2 was 14.1%. The simulated drop-port responses based on33the extract fit parameters show good agreement with the measured drop-port re-sponses in Figures 2.14b and 2.14c. We also extracted κ0 from the measurementresults of an on-chip, bent contra-DC test structure that was located close to thefilter (using the method presented in [123]). The κ0 value extracted from the teststructure agreed well with the value determined from the fitting. The waveguideloss determined from the fitting was also close to the value that we extracted fromon-chip waveguide loop-back calibration structures, validating our extracted fit pa-rameters. Due to the small feature sizes of the contra-DC, κ0 is very sensitive tofabrication variations. Hence, the reduction in κ0 from the design value was likelydue to fabrication variations which reduced the corrugation depths and/or increasedthe average gap between the grating waveguides. FSRring of the fabricated devicewas also extracted by measuring the spacing between the major through-port notchand the suppressed through-port notch left adjacent to the major notch. The mea-sured FSR was 2.74 nm. Based this value, the group index of the ring waveguidewas solved for using Equation 2.11. The measured group index near 1550 nm was4.1, which closely matched the simulated value of 4.11. Based on the extractedparameters, clearly ∆λnull of the fabricated device was less than 2FSRring and themaximum suppression condition was not met. However, for the filter state wherethe first contra-DC nulls align with the MZI-coupler cross-state nulls, the adjacentMRR side modes were still completely suppressed due to the MZI-coupler.We also compared the suppression of the adjacent MRR side modes for thereference devices with drop-port point couplers (instead of an MZI-coupler). Fig-ure 2.15 shows the measured drop-port spectra (after alignment) of the two de-vices, which were spaced 460 µm apart on the chip. Compared to the tunable filter,both reference devices had smaller SMSRs (approximately 17 dB). While the ad-jacent side modes of the first reference device appear to be completely suppressed(Figure 2.15a), the right adjacent side mode of the second device is not fully sup-pressed (Figure 2.15b). For the second device 2FSRring was greater than ∆λnulland, hence, the contra-DC nulls could not be aligned to the ring resonant wave-lengths. Moreover, this misalignment resulted in minor notches in the through-port response. This result illustrates the versatility of using an MZI-coupler, inwhich large suppressions of the adjacent MRR side modes can still be achieved,regardless of variations between the as-designed and as-fabricated κ0 values (due34SMSRSMSRFigure 2.15: Spectral responses of the fabricated, point-coupled referencedevices with a) complete suppression of the adjacent MRR sidemodes and b) one adjacent side mode not fully suppressed due to2FSRring > ∆λnull , due to fabrication variations. Reprinted with per-mission from [1] c© The Optical Society of America.to fabrication variations, wafer thickness variations, etc.).Besides having contra-DC and ring responses that could not be aligned, themeasured drop-port BWs of the reference devices (33.8 GHz and 31.3 GHz) werealso lower than their target design value of 46 GHz. While these devices could notachieve their target BWs, with our tunable device, we demonstrate that independentcontrol of the filter’s drop-port coupling coefficient allows us to achieve a range ofBWs from a maximum of approximately 60 GHz to a minimum of 25 GHz. Fig-ure 2.16a demonstrates how the device BW changes when a current is applied tothe MZI-coupler control-arm heater. We also plot |ke f f |2 as a function of heatercurrent, which was determined using the extracted fit parameters. At a heater cur-rent of approximately 20 mA, the maximum BW of the filter was achieved whenthe effective cross-coupling coefficient of the drop-port coupler was at a maximumand the MZI coupler cross-state nulls and the contra-DC nulls were aligned (asshow in Figure 2.14a). For these coupling conditions, the MRR was undercoupled,as the light that was effectively lost to the MRR (due to waveguide loss and lightcoupled to the drop-port) was greater than that which was coupled to the MRR[124]. As the heater current was reduced, the |ke f f |2 decreased, the MRR became35less undercoupled and the BW decreased. Figure 2.14c shows the through- anddrop-port responses of the filter, where the BW was reduced to 25 GHz for a heatercurrent of 15 mA. Smaller bandwidths were achievable at the expense of higherinsertion losses. Over the demonstrated tuning range, the device maintained anSMSR greater than 15.25 dB, an Ai greater than 23.5 dB, and an nAi greater than26.7 dB, as shown in Figure 2.16b. When tuning the MZI-coupler, this reductionin Ai was due to the redshift of the MZI-nulls and the increase of the effectivecoupling coefficients at wavelengths near resonant wavelengths, as demonstratedin device simulations. The Ai was at its minimum across the tuning range whenthe filter was tuned to the 25 GHz BW operating point (Figure 2.14c).Figure 2.16: a) Drop-port BW and extracted effective MZI-coupler powercoupling coefficient as a function of control-arm heater current. b) Aiand nAi of the filter for a 400-GHz grid WDM, and SMSR as a func-tion of control-arm heater current. Reprinted with permission from [1]c© The Optical Society of America.Here, we also show that resonance-induced through-port phase responses atsuppressed resonant modes are virtually non-existent, as compared to Vernier ef-fect filter designs. This because the contra-DC effectively prevents light from cou-pling to the ring at these all wavelengths other than at the operating wavelength,as compared to conventional broadband directional couplers used in Vernier de-vices. As a result, low dispersions and group delays occur when the contra-DC andring responses are aligned, reducing signal distortion in the passband and the need36for dispersion compensation [128]. To illustrate this, we show the group delay ofour filter when the control-arm is tuned to operate the filter in the over-coupledregime close to critical coupling, where the largest MRR group delays occur [124](it should be noted that we actually operated our filter in the under-coupled regimewhere the group delays near resonance are typically much smaller). As shown inFigure 2.17, a large group delay at through-port is observed at the operating wave-length, while minimal group delay is observed across the C-band. The group delayresponse for the filter includes the response of the input and output GCs. Here,we believe the measurement resolution was limited by the high losses and noiseintroduced by the input and output GCs (the group delay of a GC test structure isalso shown in Figure 2.17).1530 1535 1540 1545 1550 1555 1560Wavelength (nm)0100200300400Group Delay (ps)GC ResponseFilter Through ResponseFigure 2.17: Group delay at the through-port of the filter (when operated inthe overcoupled region) and of a grating coupler test structure (zeroset arbitrarily). A single spike in the filter’s group delay is observed atthe resonant wavelength. Reprinted with permission from [1] c© TheOptical Society of America.2.6 SummaryIn this chapter, we have demonstrated a BW-tunable, MRR-based filter with FSR-free through- and drop-port responses for WDM applications. The device is trulyFSR-free at the through-port as resonance-induced amplitude and phase responsesare virtually non-existent at the suppressed resonant modes of the MRR. The fil-37ter is capable of achieving drop-port BWs as high as 60 GHz and as low as 25GHz. Our filter is capable of achieving an nAi greater than 26.7 dB for a 400-GHzWDM grid, while also maintaining the true FSR-free response with minimum SM-SRs greater than 15.25 dB. The device can be used to compensate for fabricationvariations, allowing one to control the filter to achieve the as-designed device per-formance.While the devices presented in this chapter where fabricated using an e-beamlithography process, DUV lithography could also be used. However, the perfor-mance of grating-based devices fabricated using DUV lithography typically suf-fers more drastically from lithographic distortions. In the following chapter, wedemonstrate how lithography smoothing and proximity effects from the DUV pro-cess affect the performance of SOI devices that include grating-based components,like contra-DCs, and present a method to compensate for such lithography effectsduring device design flow.38Chapter 3Effect of Lithography on SOI,Grating-Based Devices for Sensorand TelecommunicationsApplicationsGrating-based devices on the SOI platform, such as Bragg gratings [114, 129], sub-wavelength structures [130, 131], and contra-DCs [72], have attracted considerableinterest for use in sensors [132–134] and in telecommunications systems [73, 135].Due to their small feature sizes, grating-based devices such as Bragg gratingsand contra-DCs have typically been fabricated using e-beam lithography processeswhich can consistently resolve such feature sizes. However, the low throughputof the e-beam process makes it unsuitable for large-scale production of photonicdevices. For high volume production, CMOS-compatible processes, such as DUVlithography, have been proven suitable [136]. However, the performance of deviceswith feature sizes that are smaller than the resolution limit is affected by lithogra-phy effects such as smoothing [137] and proximity effects [74]. For example, forBragg gratings designed with rectangular-shaped, side-wall gratings, the smooth-ing of the gratings mainly affects the central wavelength and coupling strength,κ0, of fabricated devices [137, 138]. Therefore, to truly enable the high-volume39production of photonic systems that integrate such grating-based devices, it is im-portant to account for the effect of DUV lithography during the device and systemdesign flow.In this chapter, using a computational lithography smoothing prediction model[77], we demonstrate how smoothing and proximity effects affect the performanceof devices that include gratings. In particular, we use the example of an MRR withintegrated contra-DC couplers. The MRR with integrated contra-DCs was cho-sen to investigate the effects of lithography, as it contains both a ring-based cavityand grating-assisted couplers. These components have been demonstrated in bothsensor and telecommunication applications, and, stand-alone, would exhibit dis-crepancies between as-designed and as-fabricated performance due to lithographic-effects. Using analytical models, we demonstrate the effect of lithography on im-portant MRR characteristics such as BW, IL, and adjacent SMSR and discuss amethod to account for lithography effects in future device designs. We also presentthe lithography prediction model for contra-DCs fabricated using 193 nm DUVlithography. We show that the prediction model achieves good agreement withfabricated test structures. We also validate that, like Bragg gratings, the centralwavelengths and coupling strengths of the fabricated contra-DCs are affected bythe lithography.3.1 Device Behaviour and ModellingFSR-free, MRR filters with integrated contra-DCs have been experimentally demon-strated using e-beam lithography [1, 88]. By integrating contra-DCs into the cou-pling regions of a ring resonator, FSR-free drop-port responses, large SMSRs, andlarge adjacent channel isolations have been achieved. Other wide-FSR, microringring devices have been demonstrated in the literature [69, 84, 85], however, thesedevices are not compact, as they consist of multiple rings, each of which requirestuning to align their resonant wavelengths.Figure 3.1 shows a schematic of the MRR under investigation. The device con-sists of an add-drop MRR with a bent contra-DC integrated into the through-portcoupling region, and a conventional directional coupler in the drop-port couplingregion. The design parameters of the device presented in this paper are similar40Input ThroughDropRWBWRΛΔWBΔWR gFigure 3.1: Schematic of an MRR with an integrated contra-directional cou-pler. c©2019 IEEE.to those described in [1] and [88]. To achieve an FSR-free response, the contra-DC should suppress all MRR modes except for the one at, or near, the contra-DCcentral wavelength. This requires that the spacing between the first nulls of thecontra-DC drop-port response, ∆λnull , where no light is coupled to the resonator,is equal to twice the FSR of the MRR (2FSRring = ∆λnull). Full suppression ofthe amplitude responses at all other undesired resonant wavelengths occurs if thiscondition is met.In our bent contra-DC design and modelling, we make an approximation andassume straight waveguides since the radius of curvature of the waveguides in ourMRR is relatively large. Assuming 220 nm thick strip waveguides (surroundedby silicon dioxide), based on the phase match condition given by Equation 2.1,to set λ0 of the contra-DC close to 1550 nm, the bus grating waveguide, WB, andring grating waveguide,WR, were 450 nm and 550 nm, respectively, and the gratingperiod, Λ, was 318 nm. A graphical solution to the phase match condition is shownin Figure 3.2. Based on Equation 2.12, by setting R to 34 µm, and choosing aκ0 value of 6900 m-1, 2FSRring = ∆λnull is achieved for N = 335. As will bediscussed in the following sections of this paper, the desired coupling strength ofthe contra-DC is achieved by controlling the corrugation depths of the bus and ring41waveguides (∆WB and ∆WR, respectively) and the gap width (g) between the twograting waveguides. The total device response is modeled analytically based on thetransfer functions presented in Section 2.3 (where, here, the drop-port MZI-coupleris replaced with a simple directional coupler). The power coupling coefficientsand waveguide effective indices were simulated in FDTD Solutions and MODESolutions, both by Lumerical Inc. In our simulations, we assumed a waveguidepropagation loss of 3 dB/cm and that the power coupling coefficient of the drop-port coupler was 29%. The simulated drop-port response of the MRR is shown inFigure 3.3.𝒏𝒆𝒇𝒇,𝟒𝟓𝟎 + 𝒏𝒆𝒇𝒇,𝟓𝟓𝟎𝟐𝜆2Λ𝒏𝒆𝒇𝒇,𝟒𝟐𝟗 + 𝒏𝒆𝒇𝒇,𝟓𝟐𝟖𝟐Figure 3.2: Graphical solutions for the phase match condition of a contra-DCwith Λ = 318 nm and 1) WB = 450 nm and WR = 550 nm (blue line) and2) WB = 429 nm and WR = 528 nm (red line).As can be seen in Figure 3.3, the MRR side modes directly adjacent to theoperating wavelength are completely suppressed. The first contra-DC nulls alignwith the adjacent MRR side modes and no light is coupled to the resonator cavityat the corresponding wavelengths (“null-coupling”), demonstrating an effectivelyinfinite, adjacent SMSR. Here, we define the adjacent SMSR as the minimum dif-421530 1535 1540 1545 1550 1555 1560 1565Wavelength (nm)-50-45-40-35-30-25-20-15-10-50Transmission (dB)Figure 3.3: Simulated spectral response of our MRR drop-port (blue). Dottedgrey lines show the locations of the suppressed MRR sides modes (ad-jacent to the operating wavelength), due to null-coupling to the cavityvia the contra-DC (red). c©2019 IEEE.ference (in dB) between the transmission of the MRR at the operating wavelengthand its transmission at the locations of either of the directly adjacent MRR modes.The device has a predicted insertion loss of 0.4 dB and an operating 3-dB BWof 46 GHz. Due to dispersion, at wavelengths further from λ0, at non-adjacentside modes, the contra-DC nulls and MRR side modes are not perfectly aligned,resulting in minor peaks in the drop-port response. Nevertheless, the sinc-function-like response of the contra-DC ensures that there is still significant suppression ofthese non-adjacent side modes, as the amount of light coupled to the cavity at thenon-adjacent side mode wavelengths is small as compared to that at the centralwavelength.433.2 Effect of Lithography on Filter PerformanceAs previously discussed, the suppression of the MRR side modes is heavily depen-dent on the κ0 of the contra-DC. By varying the corrugation depths and the gapbetween the waveguides, κ0 can be controlled. Figure 3.4a shows a GDS image ofour contra-DC. The device has rectangular corrugations with ∆WB equal to 30 nm,∆WR equal to 40 nm, and an average gap equal to 280 nm, which yields a κ0 valueclose to our design target of 6,900 m-1. The full length of the contra-DC was sim-ulated in FDTD Solutions, and the κ0 was determined using equation 2.10. Dueto the small feature sizes and proximity of the grating waveguides, the contra-DCis particularly prone to fabrication variations, including lithographic-effects [77],[122]. Lithography affects the κ0 and central wavelength of the contra-DC, leadingto discrepancies between as-designed and as-fabricated MRR performance, mainlyregarding the operating wavelength, adjacent SMSRs and the 3-dB bandwidth.We applied a computational lithography smoothing prediction model, devel-oped for 193 nm DUV lithography [77], to demonstrate the influence on MRRperformance when lithography effects are not considered during the device de-sign flow and layout. While fabricated devices are often sensitive to other fabrica-tion imperfections such as wafer thickness and waveguide width variability [122],[139], here, we focus solely on lithographic-effects. Figure 3.4b shows the resultof the lithography prediction model on the contra-DC in our MRR. Figure 3.4c, wepresent a scanning electron microscope (SEM) image of a fabricated, bent contra-DC test structure. Comparing the prediction-model and SEM, we can see thatthe model accurately predicts the change in corrugation profile from a rectangu-lar to a sinusoidal-like shape and that the inner corrugations are smoothed to agreater extent than the outer corrugations. The change in corrugation shape is dueto smoothing, while the discrepancies between the smoothing of the inner and outercorrugations is due to proximity effects [77]. As a result, the average widths of thebus and ring waveguides are also reduced from 450 nm to 429 nm and from 550 nmto 528 nm, respectively, as per Figure 3.4b.In Figure 3.5, we present the measured drop-port spectrum of a contra-DC teststructure fabricated using 193-nm DUV lithography. This test structure shares thesame device parameters as our design, as mentioned above, however, the corruga-44ΔW = 26 nmΔW = 18 nmGap = 325 nmΔW = 40 nmΔW = 30 nmGap = 280 nm200 nm(c)(b)(a)W1 = 550 nmW1 = 528 nmW2 = 450 nmW2 = 429 nmFigure 3.4: (a) Mask layout of a section of our as-designed contra-DC. (b)The predicted outcome of our lithography model. Smoothing andproximity effects can be clearly seen on the corrugations. (c) Ascanning electron microscope image of our as-fabricated contra-DC.c©2019 IEEE.45tion widths were slightly larger (∆WB equaled 40 nm and ∆WR equaled 50 nm). Thelithography has two main effects on fabricated contra-DC performance. Firstly, thesmoothing reduces the average waveguide widths of the contra-DC waveguides.This results in a change in the phase-match condition and, hence, a shift in thecontra-DC central wavelength from the as-designed value. As seen in Figure 3.5,the central wavelength of the as-fabricated contra-DC is 1534 nm, as comparedto our as-designed value of 1548 nm. Assuming that the fabricated waveguideswere 220 nm thick, this result is consistent with the phase-match conditions fora contra-DC with WB = 429 nm and WR = 528 nm, as plotted in Figure 3.2. Itshould also be noted that the central wavelength deviation is typically also affectedby wafer thickness variations [114], [140]. Here, based on the phase-match con-dition for the prediction-model device, we present a test structure from a die thatwe believe is closest to having a 220 nm silicon thickness. Secondly, lithographic-effects reduce the coupling strength, κ0, of as-fabricated contra-DCs (as comparedto the as-designed values). The smoothing and proximity effects reduce the corru-gation depths and alters the profiles of the gratings and increases the average gapbetween the two waveguides, resulting in a decrease in coupling between the for-ward and backward propagating modes of the two-waveguide system [72, 115]. Todemonstrate this effect on the as-fabricated κ0, we simulate the as-designed andprediction-model contra-DC test structures in FDTD and compare their drop portresponses to the response of the measured device. The drop-port spectrum resultsare shown Figure 3.5, with the simulated responses detuned to the central wave-length of the fabricated test structure. After detuning, the simulated response ofthe prediction-model device shows good agreement with the measured test struc-ture (1534 nm). We determine κ0 from the simulated responses, and observe thatthe expected κ0 value, based on the ideal structure of 9,350 m-1, is reduced to ap-proximately 1,900 m-1 after applying the prediction-model. If lithographic-effectswere not taken into account during design flow, the reduced κ0 of the contra-DCwould have detrimental effects on the overall performance of the fabricated MRRwith integrated contra-DCs.For our MRR design, after applying the lithography model, the κ0 of the contra-DC is reduced to approximately 1,600 m-1 as compared to the design value of6,900 m-1. The average widths of the bus and ring waveguides are also reduced461531 1532 1533 1534 1535 1536 1537Wavelength (nm)-55-50-45-40-35-30-25-20-15-10-50Transmission (dB)  Test structure (measured)  Litho-model (FDTD)  "As-designed" (FDTD)Figure 3.5: Drop-port response of an as-fabricated contra-DC test structure(red), simulated prediction-model (black) and simulated as-designed(blue) contra-DC test structures (detuned to the central wavelengthof the drop-port response of the as-fabricated test structure, 1534nm). Lithographic-effects reduce the coupling strength, κ0, from thesimulated/expected value of 9,350 m-1 to approximately 1,900 m-1.c©2019 IEEE.from 450 nm to 429 nm and from 550 nm to 528 nm, respectively. In Figure 3.6a,we plot the simulated MRR drop-port response with the adjusted κ0 value andeffective and group indices of the waveguides. The operating wavelength of theMRR is now 1534 nm due to the new phase-match condition for the contra-DC,and the maximum suppression condition is no longer met due to the change in κ0and group index of the ring waveguide. In our simulation, we suppress the adjacentMRR side mode to the left of the operating wavelength by aligning to the firstcontra-DC null to the left of the central wavelength. This results in the adjacent sidemode to the right of the operating wavelength not being fully suppressed as ∆λnullis less than 2FSRring. With a change in the group index of the ring waveguide,the wavelengths of the MRR resonant modes are also different. However, we stilldefine the adjacent SMSR for a channel spacing to be equal to the FSR of our target47design. As seen in Figure 3.6b, as compared to our target design, the adjacentSMSR is now 26 dB due to the reduced κ0 and the change in the cavity resonancecondition.Figure 3.6: a) Simulated spectral drop-port response after applying thelithography model to the contra-DC test structure (solid). Simulatedas-designed response detuned to the central wavelength of the post-lithography response (dashed), shown for reference. The MRR sidemode adjacent to the right of the operating wavelength is not fully sup-pressed due to a reduced κ0 and the change in the cavity resonance con-dition. The insertion loss of the MRR increases and the 3-dB band-width of the MRR decreases. b) Zoom-in of the un-suppressed adjacentMRR mode. The adjacent channel SMSR is reduced to 26 dB since∆λnull < 2FSRring. c©2019 IEEE.The operating bandwidth also decreases, from 41 GHz to 21 GHz. This isbecause the reduction in κ0 reduces the effective power coupling coefficient of thecoupler and the amount of light coupled into and out of the ring. The insertion lossof the device also increased by 5.5 dB. Clearly, the effects of lithography resultin large discrepancies between as-fabricated and as-designed performance MRRperformance. While the operating wavelength of the MRR can be adjusted usingseparate thermal tuners placed over the contra-DC and the ring waveguide, the κ0and ∆λnull of the contra-DC cannot be adjusted post-fabrication. In the followingsection, we demonstrate how our lithography model can be used to compensate forlithographic-effects during device design flow.483.3 Compensating for Lithographic-EffectsAs part of the design flow, we compensate for the effects of DUV lithography byutilizing a lithography model [77] that predicts the shapes of specific, as-fabricateddevice features. The lithography model is built using a set of known parameters forthe intended foundry process and using calibration measurements obtained from atest pattern [77]. The test pattern was fabricated using the intended DUV process.Figure 3.4a shows the model’s predicted, as-fabricated outcome of our as-designeddevice (Figure 3.4b), as compared to the actual fabricated outcome, as seen in theSEM image (Figure 3.4c). We see good agreement between the predicted deviceshapes generated by our model and the fabricated device.ΔW = 60 nmΔW = 50 nmGap = 228 nmW1 = 550 nmW2 = 450 nmW2 = 429 nmW1 = 528 nmΔW = 40 nmΔW = 30 nmGap = 245 nm(a)(b)Figure 3.7: a) Mask layout of a section of our re-designed contra-DC. (b) Thepredicted outcome of our lithography model. The κ0 of the prediction-model of the re-designed device matches that of the as-designed contra-DC (see Figure 3.4a). c©2019 IEEE.49Figure 3.8: Simulated drop-port spectra of the as-design contra-DC (red)and lithography prediction-model of the re-designed device (blue).c©2019 IEEE.To compensate for the lithographic-effects that reduce the κ0 of our contra-DCs, we propose a design approach using the prediction model, similar to thatpresented in [77]. In our approach we aim to produce a re-designed contra-DCin which the κ0 of the prediction-model device matches that of our as-designedcontra-DC. This is done by re-designing the contra-DC with a narrower gap andlarger corrugations depths than intended (to compensate for smoothing and proxim-ity effects), then by applying the lithography model, and, finally, by running FDTDsimulations of the entire contra-DC to confirm that the prediction-model perfor-mance of the re-designed contra-DC matches the target contra-DC performance.This approach was applied to our as-designed contra-DC (see Figure 3.4a). There-designed contra-DC with adjusted design parameters is shown in Figure 3.7a,with the lithography prediction-model of this re-designed device shown in Fig-ure 3.7b. This set of new design parameters was obtained by iteratively simu-lating variations of post-lithography devices until we converged on a design thatyielded our target κ0 value. The κ0 of the prediction-model of the re-designedcontra-DC (7,250 m-1) is close to our intended design value (6,900 m-1). The sim-50ulated drop-port spectra of the as-designed contra-DC and the prediction modelof the re-designed contra-DC show good agreement, as shown in Figure 3.8. Thesimulated drop-port spectrum of the as-designed device is detuned to the centralwavelength of the prediction-model device (1534 nm). Our re-design methodologycurrently does not compensate for the central wavelength variations between theas-designed and as-fabricated device, which can be compensated for using thermaltuners. Here, we only compensate for the reduction in κ0 by varying the contra-DCgap and corrugation depths. Future iterations of the re-design approach will needto compensate for the variations in average waveguide widths after lithography sothat the as-fabricated, re-designed contra-DC shares the same central wavelengthand κ0 of the as-designed device.3.4 SummaryIn this chapter, we demonstrated how DUV lithography affects the performance ofgrating-based SOI devices. Smoothing and proximity effects, due to lithography,result in differences between the shapes of features on the mask layout and on thefabricated structures. As a result, if these effects are not taken into account duringdesign flow and layout, discrepancies arise between the “as-designed” and “as-fabricated” device performance. Here, we focused on an MRR with an integratedcontra-DC. Using a computational lithography model, we predicted and simulatedthe device performance and showed how lithographic-effects adversely affect theperformance of the MRR as regards the device BW, IL, and adjacent SMSR. Wealso verified the computational lithography model used in our simulations by usingSEM images and fabricated test structures and we have concluded that it is possi-ble to effectively account for lithographic-effects in the device design flow usingthe lithography model. By doing so, one can significantly improve the agreementbetween the performance of as-designed and as-fabricated devices during futuredevice and system design flow.In the following chapter, we experimentally demonstrate how lithography smooth-ing and proximity effects affected the performance of a fabricated MRR-basedmodulator with an integrated contra-DC, where lithography effects were not com-pensated for during device design flow and layout.51Chapter 4Free-Spectral-Range-Free,Microring-Based CouplingModulator with IntegratedContra-Directional CouplersMRR-based modulators have been demonstrated as integral components for next-generation optical interconnects and WDM applications. However, an inherentdrawback of using MRR modulators in WDM systems is their FSR. The FSRlimits the aggregate data rate of the system, as it restrains the number of chan-nels that can be selectively modulated within a particular band. In this chapter,we experimentally demonstrate an FSR-free, MRR-based, coupling modulator thatintegrates a bent, grating-based contra-DC into a microring cavity to achieve anFSR-free response at its through-port. Our modulator suppresses the amplitude re-sponse at all but one resonant, operating mode (hence, has an FSR-free response).In our modulator, coupling modulation is used and is achieved by modulating arelatively short, 210 µm long, p-n junction phase-shifter in a two-point coupler(which forms the drop-port coupler of the MRR). We demonstrate open eyes at 2.5Gbps and discuss how the effects of DUV lithography on the contra-DC limited theelectro-optic bandwidth of the fabricated modulator to 2.6 GHz. In this chapter,52we also cover details of the device design and theory and the small and large signalcharacterization of the device, including an analysis of the effects of lithographyon the “as-fabricated” device performance. We also discuss how to significantlyimprove the electro-optic bandwidth in future implementations by accounting forthese lithographic effects in the device design flow and layout.4.1 Device DesignThe modulator consists of an MZI-assisted MRR, with a bent contra-DC integratedin the through-port coupling region of the cavity, in order to achieve the FSR-freethrough-port response, and a two-point, or MZI-coupler, integrated into the drop-port coupling region to enable optical amplitude modulation via coupling modula-tion. A schematic of the modulator is shown in Figure 4.1. To achieve the FSR-freethrough-port response, the spacing between the nulls of the contra-DC drop-portresponse, ∆λnull (see Equation 4.1) should be equal to twice the FSR of the mi-croring cavity (i.e., 2FSRring = ∆λnull). When the “null coupling” wavelengths ofthe contra-DC drop-port response are aligned with the resonant wavelengths of thecavity, no light is coupled to the cavity. Hence, the resonance modes of the cavityat such wavelengths will be suppressed and the device will have a single operat-ing mode at, or near, the contra-DC central wavelength, where sufficient light iscoupled to the cavity.The bent contra-DC was designed for strip waveguides with a silicon thicknessof 220 nm and an oxide cladding. The cavity and contra-DC parameters used herewere the same as those used in [88]. The average widths of the bus grating waveg-uide, WB, and ring grating waveguide, WR, were 450 nm and 550 nm, respectively.We set the radius of curvature of the ring grating waveguide, R, to 34 µm and thegrating period of the contra-DC, Λ, to 318 nm to place the operating wavelengthof the modulator close to 1550 nm. In order to satisfy 2FSRring = ∆λnull , the over-all length of the contra-DC and κ0, the distributed field coupling coefficient perunit length of the contra-DC, were then determined. With the total length of themicroring cavity equal to 213.62 µm (2piR), a contra-DC with κ0 = 6,900 m-1 andN = 335 corrugations satisfied 2FSRring = ∆λnull . κ0 of the contra-DC is controlledby varying the corrugation depths of the bus and ring waveguides (∆WB and ∆WR,53Heaterpn-junctionFigure 4.1: Schematic of the modulator. Inset shows the design parametersof the bent contra-DC.respectively) and the average gap width, g, between the two waveguides. In ourdesign, ∆WB and ∆WR, were 30 nm and 40 nm, respectively, and g was 280 nm. ATiN thermal heater was placed above the contra-DC (not shown in the schematic)to align the contra-DC and ring responses, and another heater was placed across thesection of the ring not covered by the contra-DC to tune the operating wavelengthof the device.The optical signal modulation in our modulator was achieved via couplingmodulation. In our design, we use an MZI-coupler in the drop-port coupling re-gion of the MRR (see Figure 4.1), where, by applying a phase shift to the lowerMZI-coupler arm, or “modulation-arm,” results in both a shift in the resonancewavelength of the MRR and a change in the through-port transmission amplitude[127, 141]. It should be noted that using a single-end electrical drive signal in themodulation-arm results in both a shift in the resonant wavelength of the MRR anda change in the through-port transmission amplitude [127, 141]. This is in contrastto ring-based coupling modulators demonstrated in the literature that use push-pull54drive signals. When using a push-pull drive configuration, there is no shift in theresonant wavelength of the MRR. As a result, MRR modulators have been demon-strated with optical modulation rates that exceed the conventional cavity linewidthlimitation as the bandwidth of the modulator is not limited by the cavity photonlifetime [108, 109].The modulation-arm shown has two p-n junction segments embedded in 500 nmwide rib waveguides, for optical modulation, each with lengths equal to 210 µm.Four 5 µm long linear tapers are used to transition to and from 550 nm strip waveg-uides segments to the 500 nm rib waveguide segments (see Figure 4.1a). The totallength of the modulation-arm is 460 µm. To form the junctions in the rib waveg-uides, lightly doped p and n levels with implant densities of 5 x 1017 cm-3 and3 x 1017 cm-3, respectively, are used. To reduce the series resistance of the junc-tion, intermediate p+ and n+ doped levels, with densities of 2 x 1018 cm-3 and3 x 1018 cm-3, respectively, are used and to create ohmic contacts, highly dopedp++ and n++ levels, with densities of 1 x 1020 cm-3, are used. A cross section of apn diode segment, with dimensions for each doping layer, is shown in Figure 4.2.For the directional couplers in the MZI-coupler, the coupling length and the gapfor each are 10 µm and 200 nm, respectively. A 400 µm long, 2 µm wide TiNheater is also placed over the modulation-arm in order to induce the static phaseshift required to optimize the extinction ratio and to set the operating point of themodulator.PP+P++ N++N+N0.80 μm0.5 μm0.40 μm 0.40 μm 0.80 μmFigure 4.2: Cross-section of the p-n junction segment integrated in themodulation-arm (not shown to scale).554.2 DUV LithographyThe modulator was designed to be fabricated using a 193-nm DUV lithographyprocess. However, photonic structures, like gratings, fabricated using DUV lithog-raphy processes are particularly sensitive to lithographic-effects such as smooth-ing and proximity effects [77, 114, 122, 138]. As a result, the κ0s and centralwavelengths of fabricated devices deviate from the “as-designed” values. Thesedeviations would negatively impact the performances of the fabricated modula-tors, affecting the fabricated ∆λnulls and changing the amount of power coupled tothe cavity via the contra-DC (|kc|2). These effects are realized by considering theequations for ∆λnull and |kc|2, given by [88, 116],∆λnull =2λ 20pi[ng,R(λ0)+ng,B(λ0)]√κ20 +(piLc)2 (4.1)and|kc|2 = | − jκ0 sinh(sLc)scosh(sLc)+ j∆β2 sinh(sLc)|2, (4.2)respectively, where λ0 is the contra-DC central wavelength, s =√κ20 − ∆β24 , and∆β = βR+βB− 2piΛ . Here, βB and ng,B and βR and ng,R are the propagation constantsand group indices of the bus and ring waveguides, respectively. From Equation 4.1and 2FSRring = ∆λnull , changing κ0 from its optimal value reduces the suppres-sion of the adjacent and non-adjacent MRR side modes, while from Equation 4.2,changing κ0 alters the amount of coupling to the cavity at the through-port, whichchanges the cavity linewidth of the modulator. Ideally, lithography models, cal-ibrated to their specific process, would be provided by the foundry to enable thedesigner to account for lithography effects during device design flow and layout,but access to such models were not available at the time of our design. However,from SEM images of other grating-based devices demonstrated in the literature, themost evident effect of DUV lithography tends to be smoothing, where the rectan-gular corrugation profiles of the devices turn into sinusoidal-like profiles, reducingthe effective amplitudes of the corrugations. Based on this observation, and in theabsence of such lithography models, at the time of our design we made the assump-56tion that the dominant effect of the lithography on the fabricated device would besmoothing of the corrugation profile, and, hence, could estimate the reduction in κ0due to smoothing based on coupled-mode theory [115]. From coupled-mode the-ory, for a sinusoidal effective index variation, the coupling coefficient is reduced bya factor of pi/4 (as compared to a rectangular variation with the same corrugationdepths) [142]. To compensate for the lithography smoothing, in our design, weadjusted the corrugation depths of our contra-DC to increase the κ0 value by closeto a factor of 4/pi. By increasing the corrugation depths of the rectangular grat-ing profile to ∆WB equals 40 nm and ∆WR equals 50 nm, the simulated κ0 of thecontra-DC was 9,350 m-1. Based on our coupled-mode theory approximation toaccount for smoothing, we determined that, with these new ∆WB and ∆WR values,the “as-fabricated”, lithography-smoothed κ0 should be close to the design valueof 6,900 m-1 (9,350 m-1 x pi/4 = 7,340 m-1).4.3 Device SimulationThe device was modelled based on the through-port transfer function of the MRRgiven by Equation 2.19 in Section 2.3, where, here, φarm = φpn+φheater to accountfor the phase shifts induced by the modulation-arm p-n junction phase shifter (φpn)and thermal heater (φheater). The waveguide effective indices were simulated inMODE Solutions by Lumerical, Inc. The power coupling coefficient of the direc-tional couplers of the modulator was 10%, based on FDTD simulations. In ourmodelling, we also assume a waveguide propagation loss of 3 dB/cm for un-dopedwaveguides and 7 dB/cm for doped waveguides. In these simulations, we assumeda κ0 value of 5,420 m-1 (which is the original design value reduced by a factorof 4/pi). Figure 4.3a shows the through-port response of the modulator with theinitial static phase shift in the modulation-arm set to 0. An FSR-free response canbe seen across the C-band with a single resonance near 1550 nm. Based on thesimulated values, the calculated ∆λnull and FSRring of the device were approxi-mately 5.44 nm and 2.72 nm, which come close to satisfying 2FSRring = ∆λnull .Even though the κ0 used in the simulation was less than the design value, signifi-cant suppression of the adjacent MRR side modes is still observed. The alignmentof the ring response with the contra-DC response is shown in Figure 4.3a for ref-57erence. We then set the static phase shift to 4.25 radians, to operate the modulatorclose to its linear operating regime. To demonstrate the static modulation depth ofthe design, for Figure 4.3b, we simulate the through-port spectral responses at thisoperating point with a range of reverse-bias voltages applied to the two p-n junc-tion segments of the modulation-arm. In this simulation, we assumed a linearizedp-n junction model with a VpiLpi of 2.0 V-cm. As seen in Figure 4.3b, both theresonant wavelength and extinction ratio increases with (reverse-bias) voltage. Astatic modulation depth of 5 dB close to 1547.9 nm is achieved for a peak-to-peakvoltage swing (Vpp) of 5 V. The cavity linewidth at the operating static phase shiftis approximately 20 GHz, sufficient for data rates of at least 20 Gbps.a) b)Figure 4.3: a) Theoretical through-port response of the modulator with thestatic phase of the modulation-arm set to 0. An FSR-free response isobserved across the C-band with a single resonance mode located near1550 nm. The contra-DC drop-port response (dotted-red) and locationsof the suppressed resonant wavelengths are shown for reference (dotted-black). b) Through-port response of the modulator for various reversebias voltages applied to the modulation-arm p-n junction with the staticphase shift set to 4.25 radians.4.4 Experimental ResultsIn this section, we present experimental results for the fabricated device. The de-vice was fabricated via a Multi-Project Wafer (MPW) shuttle run using 193-nm58DUV lithography. Figure 4.4 shows a micrograph of the fabricated modulator. Thepads on the left were used for DC tuning the modulator and the pads on the rightwere used for applying the RF signal to the modulation-arm. Not shown in thefigure are the fiber grating couplers (GCs) used for the optical input and output.We first present the DC characterization of the device, followed by the small andlarge signal characterization of the modulator. As will be demonstrated, the effectof lithography smoothing and proximity effects were underestimated during de-vice design flow, resulting in the fabricated modulator having a small EOBW andnon-fully-suppressed resonance modes in through-port response.GSGNDTunercontraTunerringTunerMZIContra-DC test structureModulator150 μmFigure 4.4: Micrograph of the fabricated modulator showing DC (left-side)and RF (right-side) signal pads. The contra-DC test structure is alsoshown, located close to the modulator.4.4.1 DC Device CharacterizationTo perform the DC characterization of the modulator, first the contra-DC thermalheater was used to align the contra-DC response to that of the ring. The ring heaterwas then used to set the operating wavelength of the modulator, while an additionalvoltage was applied to the contra-DC heater to track the resulting wavelength shift.Once the operating wavelength was set, the modulation-arm heater was used totune the drop-port coupling coefficient and to set the operating point of the modula-59tor. Lastly, the cavity heaters were adjusted again to compensate for the additionalwavelength shift that accompanied the tuning of the modulation-arm. Figure 4.5ashows the through-port response of the modulator with the modulation-arm tunedclose to critical coupling (here, VMZI = 9.10V). An FSR-free through-port responseis observed across the 60 nm wavelength range, with a single major resonancemode visible near 1530 nm. The spectral responses shown were calibrated to re-move the effects of the input and output GCs. While small in magnitude, the minornotches seen in the spectrum are non-fully-suppressed resonance modes and area consequence of lithography effects on the fabricated device, as will be furtherdiscussed in Section 4.4.3. Here, the contra-DC and ring responses were alignedso that the right adjacent resonance mode was completely suppressed.The measured cavity linewidth of the modulator near critical coupling was3.11 GHz, which was significantly less than the simulated value. The reducedcavity linewidth was also a consequence of the effects of DUV lithography on thefabricated contra-DC’s κ0 value. To determine the fabricated κ0 value, we fit themeasured through-port response to the analytic equation for the modulator. Fromthe fit, the κ0 obtained was 1,700 m-1, which was considerably less than the de-sign value of 6,900 m-1. The κ0 obtained from the fit agreed well with the valueextracted from the on-chip bent contra-DC test structure that was measured. Thetest structure was located close to the modulator (see Figure 4.4) and the κ0 valuewas extracted using the method presented in [123]. From the fit, we also obtainedthe waveguide loss (2 dB/cm) and power coupling coefficient of the directionalcouplers, |k1|2, (5.8 %), and used these parameters to simulate the through-portresponse of the fabricated device. The simulated response, shown in Figure 4.5a,shows good agreement with the measured response. A zoom-in of the measuredthrough-port response, and simulated fit, near the operating wavelength is shownin Figure 4.5b. The reduced cavity linewidth (and, in turn, the increased loadedQ-factor of the device), as compared to the theoretical design, can be explainedby the reduction in the power that was coupled the to the cavity via the fabricatedcontra-DC. With κ0 equal to 1,700 m-1, the maximum power coupling coefficientof the contra-DC (at the resonant wavelength) was reduced as compared to the de-sign/expected value. Here, we calculate the cavity linewidth and loaded Q-factorof a critically-coupled, add-drop, ring resonator (using the equations presented in60a) b)c)3.11 GHzFigure 4.5: a) Measured through-port spectral response, with the modulation-arm tuned close to critical coupling, overlayed with the theoretical re-sponse generated using device parameters obtained by curve-fitting themeasured response to analytical equations. b) Zoom-in on the operatingresonance mode. c) Analytical cavity linewidth and Q-factor of an add-drop ring resonator at critical coupling, as a function of κ0, assuming acontra-DC through-port coupler. The calculated loaded Q-factor factor(63,000) and cavity linewidth (3.11 GHz) closely match the measuredvalues.[124]) as functions of κ0, using the parameters obtained from the fit and by as-suming the through-port power coupling coefficient was given by the maximumof |kc|2. As shown in Figure 4.5c, the calculated values for a contra-DC with κ0equal to 1,700 m-1, closely match the measured cavity linewidth (3.11 GHz) and61Q-factor (63,000). The increase in Q-factor limited the maximum achievable datarate of the fabricated modulator, due to the cavity photon lifetime limit [143]. Thisis demonstrated in the high-speed characterization of the device.a) b)c)Figure 4.6: a) ER of the modulator as functions of voltage applied to themodulation-arm heater. b) Measured through-port spectra for vari-ous reverse-bias voltages applied to a p-n junction segment in themodulation-arm. c) Static modulation depth as functions of wavelengthfor a bias voltage of -2 V and Vpp swings of 2 V and 4 V. Dotted lineshows the operating wavelength (1529.56 nm) where the static modula-tion depths are 3.75 dB and 6 dB for 2 Vpp and 4 Vpp, respectively.Figure 4.6a shows the extinction ratio (ER) of the modulator as a function ofvoltage applied to the modulation-arm heater, with critical coupling being achievedat around 9.40 V. Figure 4.6b shows the through-port response of the modulator at62the operating wavelength for various reverse bias voltages applied to one of the p-njunction segments of the modulation-arm. The static ER of the modulator was setto 25 dB, using the modulation-arm thermal tuner, before applying a voltage to thep-n junction. The VpiLpi of the junction was measured to be 2.64 V-cm using theon-chip test structures. In Figure 4.6c, we plot the static modulation depth of themodulator as functions of wavelength for a bias voltage of -2 V and Vpp swingsof 2 V and 4 V. We show that large extinction ratios are still achievable for smallphase shifts induced by the p-n junction. This is because in high-Q resonators,like ours, the intracavity power is large compared to the input signal. Thus, verysmall changes in the coupling coefficient allows for a large change in the mod-ulated optical signal coupled out of the cavity [144], while the rest of the poweris recirculated. Larger modulation depths are achievable, closer to resonance dueto the large change in slope of the through-port transmission, however, at the ex-pense of higher insertion losses and slower data rates due to reduced modulationbandwidths.4.4.2 High-Speed Characterization and TestingTo characterize the high-speed performance, we performed small-signal measure-ments of the modulators EOBW. A block diagram of the experimental setup upused for the characterization is shown in Figure 4.7a. The EOBW was measuredusing an Agilent E8361A 67 GHz vector network analyzer (VNA) and a 40 GHzGS probe. The signal from port 1 of the VNA was passed through to the devicevia a 40 GHz bias tee, which set the DC bias of the modulation-arm. Light froma tunable laser source (TLS) was input to the device. The modulated optical sig-nal from the output of the modulator was passed through an erbium doped fiberamplifier (EDFA) to compensate for losses due to the on-chip input and outputGCs. A bandpass optical tunable filter (BPF) was then used to filter out most ofthe noise caused by amplified spontaneous emission in the EDFA. An HP 11982A15 GHz lightwave converter was used to convert the optical signal at the outputof the BPF to an electrical signal before entering port 2 of the VNA. Figure 4.8ashows the measured S21 of the modulator for a bias voltage of -2 V at two oper-ating wavelengths detuned from resonance (the measured S21 was normalized to63the value at 10 MHz). The modulation response for a 1.0 GHz detuning from res-onance (blue) has an EOBW bandwidth of 2.6 GHz, which is similar to the cavitylinewidth and confirms that the modulator was indeed limited by the reduced cavitylinewidth due to lithography effects. We also show the response of the modulatorfurther detuned from resonance, where a peak occurs in the modulation bandwidthresponse, extending the EOBW bandwidth to 3.9 GHz. This peak occurs due to in-tracavity dynamics [108, 143]. While operating at such wavelengths can improvethe bandwidth of the modulator, modulation depths at those wavelengths, i.e., fur-ther detuned from resonance, are insufficient for error-free data transmission (seeFigure 4.6c).VNADUT EDFA BPFTLSReceiverPPGDUT EDFA BPFTLSDCA + Receiver Plug-inb)a)Figure 4.7: Block diagrams of the experimental setups used a) to measure themodulator EOBW and b) to generate eye-diagrams.Figure 4.7b shows the block diagram of the experimental setup used to performthe large signal characterization of the modulator. A pulse pattern generator (PPG)64b)a)Figure 4.8: a) Measured EOBW of the modulator. The EOBW for a 1.0 GHzdetuning from resonance was 2.6 GHz. b) Optical eye diagram at themodulator through-port for a 2.488 Gbps, 2 Vpp drive signal.was used to generate a 2.488 Gbps, 231-1 pseudo-random binary sequence (PRBS)with a Vpp of 2 V. The pattern was passed through the bias tee (used to bias themodulator at -2 V and to combine the AC electrical signal) before being passed tothe modulator via an unterminated GS probe. The modulated optical signal, fromthe output of the modulator, was then passed through the EDFA and BPF. Thefiltered RF data was then passed into an Agilent 86100A digital communicationsanalyzer (DCA) mainframe with a 20 GHz HP 83485A optical/electrical plug-in.The TLS output was detuned from resonance by 0.65 GHz, after setting the reso-nance wavelength and static operating point using the cavity and modulation-armthermal heaters. Figure 4.8b shows the measured eye diagram. Here, we demon-strate open eyes at a baud rate of 2.488 Gbps with an ER of 3.5 dB. The ER of themodulator could have been improved by also applying the electrical signal acrossa second p-n junction segment in the modulation-arm, however, here we show thata significant eye is achievable due to the high loaded-Q factor of the fabricateddevice. Eye-diagrams with larger ERs were possible at shorter wavelengths (seeFigure 4.6a) using a single 210 µm segment (albeit, at a lower baud rate), however,the EDFA limited the “zero” level of the optical signal, thus limiting the measur-able ER of the DCA. As will be discussed, in order to improve the bandwidth ofthe modulator, future iterations of the design will need to compensate for lithog-65raphy effects during device design flow and layout by utilizing properly calibratedlithography models. For higher baud rates, these designs will also require the useof longer p-n junction segments to achieve the same ER, for the same p-n junctiondesign, due to the decrease in loaded Q-factor (i.e., the increase in bandwidth). Thedrive voltage will depend on the VpiLpi of the modulator, which could be improvedby using different junction designs with higher modulation efficiencies such as in-terleaved [98, 145] or U-junction [146] designs.4.4.3 Adjacent and Non-Adjacent Resonance SuppressionWhile we have shown that our modulator has only a single major resonance mode,and is FSR-free in principle, minor notches are visible in the through-port responseand are a consequence of lithography effects. These notches are the non-fully-suppressed resonance modes, where the contra-DC nulls and ring resonances werenot perfectly aligned. This was due to κ0 deviating from the design value and ∆λnull(a function of κ0) not being exactly 2FSRring. The reduction in κ0, from the designvalue, was due to both lithography smoothing and proximity effects introducedduring device fabrication, which not only altered the shape of the grating-profile,but also the corrugation depths, the average waveguide widths, and the averagegap between the two grating waveguides [77]. Lithography effects also explain theshift in the operating wavelength of the tuned, fabricated device to 1530 nm fromthe design value of 1550 nm. Accounting for lithography effects to achieve thedesired operating wavelength would also help minimize the power consumption ofthe modulator heaters used to set the operating wavelength of the device.In Figure 4.9, we plot the contra-DC response for our κ0 design value of6,900 m-1 and the ring response of the cavity. The intersection of the two curves(indicated by the blue circles in the figure) is the amount of coupling to the cavitywhen the contra-DC nulls are optimally aligned to the resonance modes. Whilethe adjacent modes align directly with the contra-DC nulls (-55 dB coupling tothe ring), due to dispersion, at non-adjacent modes, the contra-DC nulls do notalign perfectly. However, the amount of coupling to the ring saturates at the non-adjacent modes because of the contra-DC’s sinc-like coupling response and thecoupling is reduced from -5 dB at the operating mode to, in the worst-case, -38 dB66at a non-adjacent resonance mode. With lithography effects compensated for, andthe optimal alignment achieved, the non-adjacent resonance modes will, clearly, behighly suppressed.1510 1520 1530 1540 1550 1560 1570 1580 1590Wavelength (nm)-45-40-35-30-25-20-15-10-50Coupling to the cavity (dB)Figure 4.9: Contra-DC response for our κ0 design value of 6,900 m-1 (solid-red) and ring response of the cavity (dotted-black). The intersectionof the two curves (blue circles) is the amount of coupling to the cavitywhen the contra-DC nulls are optimally aligned to the resonance modes.The coupling to the cavity saturates at wavelengths far from the operat-ing mode (less than -38 dB, shown by the shaded blue area).When the contra-DC and ring responses cannot be perfectly aligned, like in ourfabricated modulator with κ0 equal to 1,700 m-1, we show that the two suppressedmodes adjacent to the operating mode are likely to have the largest magnitudes dueto the sinc-like response of the contra-DC. In Figure 4.5a, we aligned the contra-DC and ring responses to completely suppress the right adjacent resonance modeand to show the worst-case adjacent suppressed mode depth (which in our case,was located outside of the C-band). Because the left adjacent contra-DC null wasnot exactly aligned to a resonance mode, and the contra-DC side lobe is large, here,67close to critical coupling, the left adjacent suppressed mode depth is the deepest(but is still less than 1.75 dB). At non-adjacent resonance modes, due to the sinc-like roll-off of the power coupled to the cavity, the suppressed mode depths arevery small as the resonator becomes severely under-coupled regardless of the drop-port coupler coupling coefficient. As a result, even when the contra-DC nulls donot align to non-adjacent resonance modes, the non-adjacent, non-fully-suppressedresonance mode depths will be very shallow relative to the adjacent depths. Thedepths of all non-adjacent, non-fully-suppressed modes were less than 0.80 dB.While the suppressed mode depths are shallow, the effect of intermodulationcrosstalk [147] needs to be considered. In Figure 4.10a, we plot the measured modedepth of the left adjacent, non-fully-suppressed mode as a function of p-n junctionbias around the operating point of the modulator. As can be seen in the figure, themode depth is less than 1.75 dB, with a worst-case static modulation depth of lessthan 0.25 dB for the same 2 Vpp drive voltage used to generate our eye diagrams.While, here, the worst case modulation depth was 0.25 dB for the left adjacentmode (see Figure 4.10b), which we aligned outside the C-band, if the operatingresonance mode was aligned symmetrically between the two adjacent contra-DCnulls, the modulation depth would have been less. Assuming that future modulatordesigns can correctly compensate for lithography effects, virtually complete sup-pression of these adjacent resonance modes should be obtainable. However, thenon-adjacent resonance modes far from the operating wavelength may contributeto the intermodulation crosstalk due to dispersion, as discussed above. Still, us-ing the modulator parameters obtained from our curve fitting and test structures,we demonstrate that the crosstalk here is small by simulating the static modulationdepth at the largest (and first observable within the C-band) non-adjacent, non-fully-suppressed mode at around 1554 nm (see Figure 4.5a). Here, with κ0 equalto 1,700 m-1, the static modulation depth at 1554 nm was less than 0.01 dB for a2 Vpp swing, which was expected because of the severe undercoupling of the cavityat this wavelength (see the discussion above). From this analysis, for our fabricatedmodulator, as biased, we expect the crosstalk contribution to be less than 0.01 dBfrom the adjacent or any non-adjacent resonance mode in the C-band.Clearly, based on our analysis, in order to mitigate the channel crosstalk, lithog-raphy effects need be taken into account and compensated for during the device68a) b)~ 0.25 dBFigure 4.10: a) Measured through-port spectra at the left adjacent resonancemode for various reverse-bias voltages (with the right adjacent modesuppressed). b) Static modulation depth as functions of wavelength fora bias voltage of -2 V and a Vpp swing of 2 V.design flow to ensure that the adjacent and non-adjacent resonances modes of as-fabricated devices are effectively suppressed. Recently, after our modulator de-sign was submitted for fabrication, a lithography model (for the DUV process thatwe used) that predicts the shapes of specific, as-fabricated device features, wasdemonstrated in the literature [77]. The lithography model was built using a setof known parameters and calibration measurements obtained from test patternsthat were fabricated using the DUV process. We were able to apply the lithogra-phy model post priori and we compared the simulated response of our as-designedcontra-DC (with the lithography model applied) to the measured response of theas-fabricated, on-chip test structure. Figure 4.11 shows good agreement betweenthe predicted device performance and the measured device performance. In futureiterations of the modulator design and layout, the lithography model can be appliedduring the design flow to help ensure that the as-fabricated device performance willmatch the as-design device performance. Examples of this design methodology aredemonstrated in both [2] and [77].69-3 -2 -1 0 1 2 3Wavelength detuning (nm)-50-40-30-20-100Contra-DC Response (dB)  Measured  PredictedFigure 4.11: Measured response of an as-fabricated contra-DC test structureand predicted response of the as-designed contra-DC after applyinglithography models. The responses are detuned to the central wave-length of the as-fabricated test structure response (1530 nm).4.5 SummaryIn this chapter, we have experimentally demonstrated an FSR-free, MRR-basedmodulator with open eyes at a data rate of 2.5 Gbps. The FSR-free response atthe through-port of the modulator was achieved by integrating a grating-assisted,contra-DC into the microring cavity. The modulator was fabricated using 193-nmDUV lithography, which affected the contra-DC performance due to lithographysmoothing and proximity effects. This resulted in a large discrepancy between theas-designed and as-fabricated electro-optic bandwidth of the modulator, limitingthe data rate. Moreover, the lithographic effects introduced non-fully-suppressedresonance modes in the through-port response. However, we showed that the ef-fect of these non-fully-suppressed modes on channel crosstalk is not substantialand could be mitigated if lithography models could be used to compensate for thelithographic effects. Accounting for these lithographic effects will minimize dis-crepancies between as-designed and as-fabricated modulator performance and willenable modulators that facilitate higher aggregate data rates in ring-based, single-bus, WDM transmitter architectures that are currently limited by the MRR’s FSRs.70Chapter 5Summary, Conclusions, andSuggestions for Future Work5.1 Summary and ConclusionsIn this thesis, we have demonstrated SOI, FSR-free, MRR-based filters and modu-lators that use contra-DCs integrated into the MRR cavity to achieve the FSR-freeresponses. We have also analyzed the effects of DUV lithography on the perfor-mance of these devices. In Chapter 2, we demonstrated an FSR-free, microring-based filter, with a minimum SMSR (20.8 dB) which is greater the values presentedin previous demonstrations of FSR-free, MRR filters in the literature. Moreover,we have shown that by integrating an MZI-coupler into to the drop-port region ofthe microring cavity, independent control of the fabricated filter’s drop-port cou-pling coefficient could be achieved. As a result, we have demonstrated a recon-figurable filter bandwidth that can be tuned over a 35 GHz range from 25 GHz to60 GHz. We have also shown that the device is truly FSR-free at the through-port,as resonance-induced amplitude and phase responses are virtually non-existent atthe suppressed resonant modes of the MRR. While we have concluded that ourdesign has advantages over other wide-FSR filters presented in the literature, suchas quadruple Vernier resonators, further work needs to be done to reduce the filterAi, nAi, and SMSR values to meet commercials specifications for 100-GHz and200-GHz spacing DWDM applications. Potential methods to improve the perfor-71mance of MRR-based filters with integrated contra-DCs will be discussed in thefollowing section. In Chapter 3, we have demonstrated how DUV lithography canaffect the performance of grating-based devices such as contra-DCs. Using lithog-raphy models developed for DUV processes, we have simulated and analyzed theeffects of lithography on the performance of an MRR with an integrated contra-DC.We have shown that if lithography effects are not compensated for during devicedesign flow, large discrepancies result between the predicted “as-fabricated” and“as-designed” device performance as regards the device bandwidth, insertion loss,and adjacent SMSR. We have concluded that if lithography models can be usedto compensate for lithographic effects during device design flow and layout in or-der to design a contra-DCs in which the as-fabricated device spectral responsesmatch the expected as-designed spectral responses. Lastly, in Chapter 4, we havedemonstrated a novel, proof-of-concept, MRR-based modulator with an FSR-freeresponse at its through-port. Here, a contra-DC was integrated into a microringcavity to achieve the FSR-free response and coupling modulation was used for theoptical signal modulation. We have obtained open eye diagrams at a data rate of2.5 Gbps. The data rate of the modulator was limited by the small EOBW of themodulator, which we have demonstrated was a consequence of the effects of DUVlithography on the contra-DC. While we have demonstrated an FSR-free responsewith shallow suppressed mode depths, the effects of the lithography induced, non-fully-suppressed resonances modes on potential channel modulation crosstalk havealso been discussed. We have concluded that if the effects of lithography wereproperly compensated for during device design, higher EOBWs could be achievedand the effect of modulation crosstalk can be minimized, enabling dense channelspacing in MRR-based WDM transmitters. Future design considerations for themodulator are discussed in the following section.5.2 Suggestions for Future WorkIn this thesis, while we have demonstrated MRR-based filters for WDM with noFSR limitations, further work is required to reduce the SMSR of the filter in orderto meet specifications for commercial 100-GHz and 200-GHz spacing DWDM ap-plications. By reducing the SMSR, commercial specifications for the Ai (< 25 dB)72Input ThroughThroughInputDropTwo-stage cascaded contra-DC…………Figure 5.1: Schematic of the proposed filter; an FSR-free MRR filter cas-caded with a two-stage, series-cascaded contra-DC.and nAi (< 35 dB) of the filter can be met [148]. Here, we propose that by cas-cading an FSR-free MRR filter with an N-stage series-cascaded, apodized contra-DC-based (SC-contra-DC) [64, 76], devices with larger SMSRs can be achieved.A block diagram of the proposed device using a two-stage SC-contra-DC is shownin Figure 5.1. In the proposed filter, by aligning the drop-port passband of theSC-contra-DC with the operating mode of the MRR, the MRR response outsideof the SC-contra-DC passband will be attenuated by at least the SMSR of the SC-contra-DC. With the SC-contra-DC effectively “cleaning-up” the drop-port signalof the MRR filter, devices with large Ais and nAis can be achieved. In our work, wedemonstrated an SMSR of approximately 21 dB and the work in [76] demonstratedone- and two-stage filters with SMSRs greater than 20 dB and 40 dB, respectively.As a result, if the SC-contra-DC passband is designed and aligned correctly, chan-73nel isolations greater than 40 dB should be achievable, which would meet commer-cial specifications. While in Figure 5.1 we show an MRR with a simple directionalcoupler in the drop-port coupling region, a tunable MZI-coupler could be usedinstead to enable bandwidth reconfigurability.When designing SOI devices with grating-based components, like contra-DCs,we have demonstrated that lithography models, calibrated to the specific fabrica-tion process, need to be used during device design flow. As a result, our FSR-freemodulator should be redesigned in order to compensate for the lithography effects.By accounting for these effects, the fabricated modulator should; 1) have mini-mal adjacent and non-adjacent non-fully-suppressed mode depths, minimizing thecontributions to the intermodulation crosstalk, 2) a higher data rate due to a cavitylinewidth and EOBWs that matches the desired designed performance metrics. Aspreviously mentioned, by increasing the cavity linewidth, a larger phase shift inthe MZI-coupler will be required to generate the same extinction ratios that weredemonstrated in this thesis. This will require a redesign of the p-n junction phaseshifters to achieve higher phase shift efficiencies in order to maintain low drive volt-ages with the higher bandwidth conditions. Moreover, further design optimizationcan be done to reduce the insertion loss of the modulator. A full characterizationof the updated modulator should also performed, including measurements such asbit error rate (BER) testing and further testing to determine the power penalty dueto crosstalk from any non-fully-suppressed resonance modes. Lastly, if large ex-tinction ratios are achievable for OOK, the drive signals can be reconfigured todemonstrate higher data rates via PAM-4 modulation.74Bibliography[1] A. Mistry, M. Hammood, H. Shoman, L. Chrostowski, and N. A. F. 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