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Silicon photonic modulators and filters for optical interconnects Caverley, Michael 2015

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Silicon Photonic Modulators and Filters for OpticalInterconnectsbyMichael CaverleyB.A.Sc., The University of British Columbia, 2013A 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)August 2015c©Michael Caverley, 2015AbstractThe goal of this work is to enhance the performance of and demonstrate new ap-plications for silicon photonic modulators and filters. We demonstrate a varietyof novel designs and applications of silicon photonic devices for integrated opticalinterconnects. First, we demonstrate a biasing scheme for travelling-wave Mach-Zehnder modulators in which the bias voltage is applied separately from the datasignal. Using this biasing scheme, there is no low frequency cutoff and there isno power consumption in the termination resistor from the bias voltage, which re-sults in an improved modulator having a lower overall power consumption. Weexperimentally show, as a proof-of-concept, successful high-speed modulation, ata data rate of 28 Gb/s, of a modulator which uses this biasing scheme. Next, wepresent a novel modulator design in which a microring modulator is placed intoeach arm of a Mach-Zehnder interferometer. This design uses the sharp phase re-sponse of a microring resonator near its resonance so that the light experiencesa large phase change when a voltage is applied to the p-n junction phase shifterswithin the microring. We use temporal coupled mode theory to simulate the time-domain response of this modulator. We then demonstrate a novel modulator designwhich uses a quarter-wave phase-shifted Bragg grating. The modulator, whichwas fabricated using 193 nm optical lithography, has open eye diagrams at a datarate of 32 Gb/s. We also show that using a 231-1 pseudorandom binary sequencepattern, the modulator has a bit error rate (BER) less than 10-12 at a data rate of20 Gb/s and has a BER less than 10-10 at a data rate of 25 Gb/s. Finally, we demon-strate a contra-directional grating coupler-based filter on silicon in an optical add-drop multiplexer configuration and show that it can successfully add and drop a12.5 Gb/s signal at the same wavelength without substantial signal degradation.iiPrefaceThis thesis is based on four publications on which I am the principal author. Mostof Chapter 2 is based on the following publication (which has been accepted) [1]:1. M. Caverley, H. Yun, L. Chrostowski, and N. A. F. Jaeger, “A low-powerbiasing scheme for silicon-on-insulator traveling-wave modulators,” to bepresented at 12th International Conference on Group IV Photonics, 2015.c©2015 IEEE. Material including text and figures used with permission.H. Yun, N. A. F. Jaeger, and I conceived the idea. H. Yun designed the deviceand also did the mask layout. L. Chrostowski obtained access to the fabricationtechnology used in this project. H. Yun and I measured the device and I performedthe data analysis. I wrote the manuscript and N. A. F. Jaeger provided feedbackand edited the manuscript.Chapter 3 is based on the following publication [2]:2. M. Caverley, H. Jayatilleka, Y. Wang, L. Chrostowski, and N. A. F. Jaeger,“Microring modulator using drop-port phase interference,” in IEEE Photon-ics Conference, 2014. c©2014 IEEE. Material including text and figures usedwith permission.N. A. F. Jaeger and I conceived the idea for the design. I performed the parameterextraction from the previously fabricated devices and I implemented and per-formed the time-domain simulations. H. Jayatilleka assisted with developing theparameter extraction methods. Y. Wang assisted in the device’s design in the earlystages of the project. L. Chrostowski obtained access to the fabrication technologyiiiused in this project. I wrote the manuscript and all of the co-authors providedfeedback. N. A. F. Jaeger edited the manuscript.Chapter 4 is based on the following publication (which is in press) [3]:3. M. Caverley, X. Wang, K. Murray, N. A. F. Jaeger, and L. Chrostowski,“Silicon-on-insulator modulators using a quarter-wave phase-shifted Bragggrating,” IEEE Photonics Technology Letters, 2015, in press. c©2015 IEEE.Material including text and figures used with permission.X. Wang and L. Chrostowski conceived the idea. L. Chrostowski obtained accessto the fabrication technology used in this project. I designed the devices andperformed most of the mask layout. X. Wang assisted with choosing designvariations. K. Murray created the mask layout script for generating the gratings. Icreated a measurement setup and used it to measure the devices. I performed thedata analysis and I wrote the manuscript. K. Murray and L. Chrostowski providedfeedback on the manuscript. N. A. F. Jaeger provided feedback and edited themanuscript.Chapter 5 is based on the following publication [4]:4. M. Caverley, R. Boeck, L. Chrostowski, and N. A. F. Jaeger, “High-speeddata transmission through silicon contra-directional grating coupler opticaladd-drop multiplexers,” in CLEO: Science and Innovations, p. JTh2A.41,2015. c©2015 Optical Society of America. Material including text and fig-ures used with permission.R. Boeck, N. A. F. Jaeger, and I conceived the idea. R. Boeck designed the de-vice and performed the mask layout. I performed the experiment, performed dataanalysis, and wrote the manuscript. L. Chrostowski provided feedback about themanuscript and obtained access to the fabrication technology used in this project.R. Boeck and N. A. F. Jaeger provided feedback and edited the manuscript.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Silicon Photonics . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Basics of Optical Communication Systems . . . . . . . . . . . . . 21.3 Thesis Objective . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3.1 Modulators on SOI . . . . . . . . . . . . . . . . . . . . . 31.3.2 WDM Filters on SOI . . . . . . . . . . . . . . . . . . . . 61.4 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 72 A Low-Power Biasing Scheme for Silicon-On-Insulator Travelling-Wave Modulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1 Mach-Zehnder Modulators . . . . . . . . . . . . . . . . . . . . . 102.2 Device Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11v2.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 132.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Microring Modulator Using Drop-Port Phase Interference . . . . . 153.1 Device Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2 Transient Response . . . . . . . . . . . . . . . . . . . . . . . . . 213.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 Silicon-On-Insulator Modulators Using a Quarter-Wave Phase-Shifted Bragg Grating . . . . . . . . . . . . . . . . . . . . . . . . . . 294.1 Uniform Bragg Gratings on SOI . . . . . . . . . . . . . . . . . . 294.2 Phase-Shifted Bragg Gratings . . . . . . . . . . . . . . . . . . . . 364.3 Phase-Shifted Bragg Grating Modulators . . . . . . . . . . . . . . 414.4 Device Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.5 Layout and Test . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.6 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . 494.6.1 Passive Measurement Results . . . . . . . . . . . . . . . 494.6.2 Active Measurement Results . . . . . . . . . . . . . . . . 524.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595 High-Speed Data Transmission Through Silicon Contra-DirectionalGrating Coupler Optical Add-Drop Multiplexers . . . . . . . . . . . 605.1 Contra-Directional Couplers . . . . . . . . . . . . . . . . . . . . 605.2 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . 625.2.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . 645.2.2 Data Transmission Measurements . . . . . . . . . . . . . 665.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686 Summary, Conclusions, and Suggestions for Future Work . . . . . . 696.1 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . 696.2 Suggestions for Future Work . . . . . . . . . . . . . . . . . . . . 70Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72viList of TablesTable 4.1 Phase-shifted Bragg grating parameter variations. . . . . . . . 42Table 4.2 List of components used in the measurement setup. . . . . . . 49Table 4.3 Circuit model fitting results. . . . . . . . . . . . . . . . . . . . 55Table 5.1 Contra-DC design parameters. . . . . . . . . . . . . . . . . . . 63viiList of FiguresFigure 1.1 Diagram of an optical communication system which uses WDM. 3Figure 2.1 Schematic of a MZM. Here, symmetric Y-branches are used asthe power splitters/combiners. . . . . . . . . . . . . . . . . . 11Figure 2.2 (a) Device layout of the travelling-wave MZM used to demon-strate the biasing scheme and (b) a cross-sectional schematicof the travelling-wave structure and the waveguide with the p-njunction [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Figure 2.3 Spectral response of the modulator at various reverse bias volt-ages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Figure 2.4 Measured eye diagrams of the modulator at (a) 12.5 Gb/s, (b)20 Gb/s, and (c) 28 Gb/s. . . . . . . . . . . . . . . . . . . . . 14Figure 3.1 Schematic of the proposed modulator [2]. . . . . . . . . . . . 17Figure 3.2 Diagram of the waveguide used in the MRM. . . . . . . . . . 17Figure 3.3 Simulated and measured group indices as functions of wave-length for the rib waveguide used in the MRM design. . . . . 18Figure 3.4 Through-port spectral responses of a previously fabricatedMRM with various reverse bias voltages applied to the MRM’sp-n junction. . . . . . . . . . . . . . . . . . . . . . . . . . . 18Figure 3.5 Diagram of a microring showing the various coupling coeffi-cients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19viiiFigure 3.6 Change in effective index and loss as a function of the p-njunction’s reverse bias voltage determined using measurementresults from a previously fabricated MRM. . . . . . . . . . . 21Figure 3.7 Simulated drop-port (a) power spectral response and (b) phaseresponse for MRM 1 and MRM 2 with both 0 V and 5 V beingapplied each of their p-n junctions. . . . . . . . . . . . . . . . 22Figure 3.8 Simulated optical eye diagrams for different static phase shifts:(a) ϕ = 0, (b) ϕ = 0.6, (c) ϕ = 1.2, (d) ϕ = 1.6. . . . . . . . . 25Figure 3.9 Simulated modulation ER and modulation IL as a function ofthe static phase offset, ϕ . . . . . . . . . . . . . . . . . . . . . 26Figure 3.10 Photonic circuit representation using INTERCONNECT of (a)the proposed modulator and (b) the MRM component. . . . . 27Figure 3.11 Comparison the time-domain simulation results of the pro-posed modulator using both the TCM model and INTERCON-NECT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Figure 4.1 Diagram of a waveguide Bragg grating. The red lines indicatethe geometry of the unperturbed waveguide. . . . . . . . . . . 30Figure 4.2 Simulated through- and reflect-port spectral responses of a uni-form Bragg grating shown, for demonstration purposes, to il-lustrate the features of a Bragg grating’s spectral response.The simulated Bragg grating had the following parameters:κ = 8000m−1, Λ= 310nm, N = 1000, λb = 1530nm. . . . . 35Figure 4.3 Diagram of a quarter-wave phase-shifted Bragg grating withthe phase shift indicated by the cross-hatched region. . . . . . 36Figure 4.4 Diagram showing how a Fabry-Pe´rot cavity using Bragg grat-ing reflectors can be broken down into individual sectionswhich can be represented using a transfer matrix. . . . . . . . 37ixFigure 4.5 Simulated through- and reflect-port spectral responses of aphase-shifted Bragg grating shown to illustrate the featuresof its through- and reflect-port spectral responses. The sim-ulated phase-shifted Bragg grating had the same parametersas the Bragg grating shown in Figure 4.2 (i.e., κ = 8000m−1,Λ = 310nm, N = 1000, λb = 1530nm) except that a quarter-wave phase shift was added in the centre of the grating. . . . . 39Figure 4.6 (a) Schematic of the quarter-wave phase-shifted Bragg gratingmodulator, including a zoomed-in view of the region near thephase-shift. (b) Schematic showing the design of the waveg-uide and the lateral p-n junction [3]. . . . . . . . . . . . . . . 43Figure 4.7 (a) Optical microscope image of the fabricated modulator [3].(b) Layout of the modulator in the same region as the imagein (a). (c) Layout of the input taper that converts from the450 nm wide strip waveguide used for routing to the rib waveg-uide used inside the modulator. . . . . . . . . . . . . . . . . . 44Figure 4.8 (a) Image of the mask layout for a group of 12 modulators inwhich an efficient device layout scheme was used to minimizethe group’s footprint. (b) Zoomed in view of the mask lay-out in (a) showing the efficient waveguide routing scheme. (c)Schematic showing the layout of the device [3]. . . . . . . . . 47Figure 4.9 Picture of the entire measurement setup. Descriptions for thelabeled components are in Table 4.2. . . . . . . . . . . . . . . 48Figure 4.10 Close-up picture of the optical probe station. Descriptions forthe labeled components are in Table 4.2. . . . . . . . . . . . . 48Figure 4.11 Measured through- and reflect-port spectral responses of themodulator. The spectral response of a reference straightwaveguide is also shown. . . . . . . . . . . . . . . . . . . . . 50Figure 4.12 Measured normalized through- and reflect-port spectral re-sponses of the modulator. Also shown are the curve fittedthrough-port and calculated reflect-port spectral responses. . . 51Figure 4.13 Measured spectral response of the reflect-port notch with vari-ous reverse bias voltages applied to the device. . . . . . . . . 52xFigure 4.14 Diagram showing the experimental setup used to measure (a)the modulator’s |S21| and (b) the eye diagrams and BERs ofthe modulator [3]. . . . . . . . . . . . . . . . . . . . . . . . . 54Figure 4.15 Electro-optic |S21| of the modulator measured with various re-verse bias voltages ranging from 0 V to −3 V being applied.The dashed grey line indicates the −3 dB level. . . . . . . . . 55Figure 4.16 Measured S11 magnitude and phase at 0 V bias as well as thefitted S11 magnitude and phase. . . . . . . . . . . . . . . . . 56Figure 4.17 Circuit model of the modulator used for fitting the S11. . . . . 56Figure 4.18 Measured eye diagrams of the modulator at: (a) 12.5 Gb/s, (b)20 Gb/s, (c) 25 Gb/s, (d) 32 Gb/s [3]. . . . . . . . . . . . . . . 58Figure 4.19 Measured BERs versus received optical power at the PD atdata rates of 12.5 Gb/s, 20 Gb/s, and 25 Gb/s using both 27-1and 231-1 PRBS patterns. . . . . . . . . . . . . . . . . . . . . 58Figure 5.1 Diagram of the contra-DC OADM showing a zoom-in of thecoupling region (similar to the design used in [137]). . . . . . 62Figure 5.2 Plot showing the phase-matching condition for the contra-DC. λa and λb are the intra-waveguide Bragg wavelengths forwaveguides A and B, respectively and λd is the wavelength atwhich inter-waveguide coupling occurs. . . . . . . . . . . . . 63Figure 5.3 (a) Measured spectral response of the filter and (b) spectralresponse of the filter near the stopband. . . . . . . . . . . . . 65Figure 5.4 Schematic of the experiment used to characterize the contra-DC OADM’s performance. . . . . . . . . . . . . . . . . . . . 66xiFigure 5.5 Measured eye diagram of: (a) data from the MZI modulatorprior to entering the filter’s input port; (b) data passing fromthe input port to the drop port when the device is only drop-ping the signal; (c) data passing from the input port to the dropport while another signal is being added; (d) data from the MZImodulator prior to entering the filter’s add port; (e) data pass-ing from the add port to the through port when the device isonly adding a signal; (f) data passing from the add port to thethrough port while another signal is being dropped [4]. . . . . 67Figure 5.6 Measured eye diagrams of the dropped signal (with no othersignal being input to the add port) from the contra-DC OADM(a) before and (b) after going through 25.26 km of single-modefibre. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67xiiList of AcronymsOOK on-off-keyingWDM wavelength-division multiplexingMUX multiplexerCMOS complementary metal-oxide-semiconductorQSFP quad small form-factor pluggableDEMUX demultiplexerGC grating couplerVNA vector network analyzerBERT bit error rate testerTLS tunable laser sourcecontra-DC contra-directional couplerMZI Mach-Zehnder interferometerMZM Mach-Zehnder modulatorSOI silicon-on-insulatorMRM microring modulatorMDM microdisk modulatorPRBS pseudorandom binary sequencexiiiBER bit error rateOADM optical add-drop multiplexerFSR free spectral rangeGS ground-signalMMI multi-mode interferometerER extinction ratioPPG pulse pattern generatorEDFA erbium doped fibre amplifierOTF optical tunable filterVOA variable optical attenuatorPD photodetectorDCA digital communications analyzerED error detectorIL insertion lossTCM temporal coupled modePM polarization-maintainingNRZ non-return-to-zeroBW bandwidthSS sidelobe suppressionFDTD finite-difference time-domainxivAcknowledgmentsI first would like to thank my supervisors, Dr. Lukas Chrostowski and Dr. NicolasJaeger, for all of the support they have given me. I thank Dr. Lukas Chrostowskifor all of the opportunities he has provided which have allowed me to completethis work and I thank Dr. Nicolas Jaeger for the countless hours of support he hasgiven me and for his mentorship.I also want to thank all of my colleagues that I have worked with. I espe-cially want to thank Robert Boeck, Hasitha Jayatilleka, Kyle Murray, Miguel A´ngelGuille´n Torres, Han Yun, Yun Wang, and Xu Wang for all of their support.I also acknowledge the Natural Sciences and Engineering Research Councilof Canada as well as the SiEPIC program for financial support. Additionally, Iacknowledge CMC Microsystems, Lumerical Solutions, Inc., Mentor Graphics, aswell as Anritsu Corporation for the use of their MP1800A Signal Quality Analyzer.Part of this work was conducted at the University of Washington NanofabricationFacility, a member of the NSF National Nanotechnology Infrastructure Network.xvChapter 1Introduction1.1 Silicon PhotonicsOver the past decade, there has been an enormous amount of research in the fieldof silicon photonics. The interest has been fuelled by the possibility of fabricat-ing photonic circuits using complementary metal-oxide-semiconductor (CMOS)compatible processes that are used to make electronic circuits. Integration of bothphotonic and electronic circuits on the same chip can enable a new generation ofhigh-speed, low power, and low cost optical devices for communications appli-cations in data centres and high-performance computers [5–8]. Photonic circuitsare formed by connecting a variety of individual optical devices together, such asmodulators, detectors, filters, and switches, using waveguides. These individualdevices are the building blocks of more complex systems, such as optical intercon-nects, which are one of the primary applications of silicon photonics at present.Optical interconnects using silicon photonics are considered to be an emergingtechnology for high performance computing and data centre applications [8, 9].There are numerous companies that are currently developing silicon photon-ics devices for optical interconnect applications. IBM has recently announced thatit has developed a 100 Gb/s fully integrated wavelength multiplexed silicon chip[10]. Luxtera also recently announced that it has developed a 100 Gb/s quad smallform-factor pluggable (QSFP) optical module using silicon photonics [11]. Fin-isar has recently demonstrated a 56 Gb/s silicon photonic transceiver which was1hybridly integrated with electronic circuits [12]. Furthermore, Aurrion has devel-oped a platform on which InP is heterogeneously integrated with silicon substrates,and using this platform, they have demonstrated O-band lasers as well as photode-tectors and electroabsorption modulators having bandwidths greater than 35 GHz[13, 14]. Mellanox has demonstrated, on silicon-on-insulator (SOI), a wavelength-division multiplexing (WDM) transmitter and receiver that can operate at speeds inexcess of 100 Gb/s [15]. In addition to the above, there are numerous other compa-nies and research groups around the world that are making efforts towards makingsilicon photonics a viable technology for use in optical interconnects.1.2 Basics of Optical Communication SystemsThe goal of an optical communication system is to send data from a transmitter toa receiver through a communications medium [16]. A diagram of a simple opticalcommunication system is shown in Figure 1.1. The communications medium can,for example, be an optical fibre (used for long haul communications applications)or be a waveguide (used in integrated photonics applications). In a communica-tion system, the transmitter converts an electrical signal containing the data beingtransmitted into the optical domain by modulating an optical carrier. External mod-ulation is typically used in which there is a laser, which generates the optical carrierat the desired wavelength, followed by a modulator, which encodes the data ontothe carrier. For transmitting digital information, the most basic encoding is on-off-keying (OOK), where the optical signal is switched between a high level and a lowlevel to represent a binary 1 and 0, respectively. An advantage of using light totransmit information is that WDM can be used to send optical signals at differentwavelengths in parallel through the communications medium, which increases thetotal data transmission capacity of the communications medium. In a system us-ing WDM, there are multiple transmitters operating at different wavelengths andthe signal from each transmitter is combined using a multiplexer (MUX) prior toentering the communications medium. On the receive side, the optical signal isfirst demultiplexed using a demultiplexer (DEMUX) in order to separate the sig-nals that are on each optical carrier. Then, each of the optical signals is convertedto an electrical signal using a photodetector. The electrical signal containing thedata can then be processed further.2λ1 λ2 λn λn λ2 λ1 … λ1 λ2 λn Communications medium MUX DEMUX Laser λ1 Modulator Tx. 1 Data  signal Laser λ2 Modulator Tx. 2 Data  signal Laser λn Modulator Tx. n Data  signal Detector Rx. 1 Data  signal Detector Rx. 2 Data  signal Detector Rx. n Data  signal Figure 1.1: Diagram of an optical communication system which uses WDM.1.3 Thesis ObjectiveThis thesis focuses on modulators and MUXs/DEMUXs for use in integrated op-tical interconnects. In this section, we will first discuss modulators on SOI andintroduce the modulators, and the improvements made to them, that are presentedin this thesis. Then, we will discuss MUXs/DEMUXs on SOI and introduce ourwork about filters for use in MUXs/DEMUXs.1.3.1 Modulators on SOIModulators are critical components in WDM systems since they have an effect onmany performance metrics of a link, such as its data rate and total power consump-tion. Modulators on silicon most often use the free-carrier plasma dispersion effectto change the refractive index of silicon [17]. Modulators using the free-carrierplasma dispersion effect are typically constructed by forming a p-n or a p-i-n junc-tion in a waveguide. The change in free carriers that are present when a voltage isapplied across the junction causes the effective index of the waveguide to change.There are two principal operating regimes: forward biasing the junction and re-verse biasing the junction. Typically, p-i-n junctions are used with forward biasingand p-n junctions are used with reverse biasing. When the junction is forward bi-3ased, carriers are injected into the junction, and when the junction is reverse biased,carriers are removed from the junction. The change in refractive index is generallylarger under forward bias than reverse bias, however, under forward bias, the mod-ulation speed can be limited (e.g., < 1GHz) by the carrier recombination time [18],whereas reverse bias operation is much faster (e.g., > 40GHz).There are two categories of modulators on silicon that are most prominent,Mach-Zehnder modulators (MZMs) [19–43] and microring modulators (MRMs) /microdisk modulators (MDMs) [18, 44–69]. MZMs operate by changing the phasein one or both arms of an Mach-Zehnder interferometer (MZI) by way of changingthe refractive indices of the waveguides in the arms, thus controlling the amount oflight that leaves the MZI at its output. Since the refractive index changes offeredby the free-carrier plasma dispersion effect are very small, MZMs using reversebiased p-n junctions have typically employed phase shifters that are several mil-limetres long and require the use of travelling-wave electrodes in order to veloc-ity match the optical and microwave signals [34]. Travelling-wave MZMs havingspeeds greater than 40 Gb/s have been demonstrated [20, 24, 25, 27, 32, 34, 35],and travelling-wave MZMs having low drive voltages have also been demonstratedwhich required peak-to-peak voltages less than 1 V [42, 43].On the other hand, MRMs or MDMs can be very compact and have high-speeds, low losses, and low power consumptions due to the fact that they are reso-nant devices. Since the first demonstration of an MRM on SOI in 2005 [18], therehave been tremendous improvements in the performance of resonant modulatorsbased on MRMs or MDMs. MRMs having speeds greater than 25 Gb/s have beendemonstrated [46, 47, 49–51, 54]. Also modulators involving multiple rings, bothcoupled [62] or uncoupled [53], have been demonstrated. MRMs using vertical p-njunctions [52] and MDMs with vertical p-n junctions [68, 69] have been recentlydemonstrated. These devices with vertical p-n junctions have had excellent per-formance in terms of their electro-optic responses and power consumptions, withthe device in [68] having a power consumption of less than 1 fJ/bit. However, bothMRMs and MDMs are narrowband devices and are sensitive to temperature vari-ations and fabrication imperfections and, therefore, require the use of resonancewavelength tuning and/or stabilization schemes [70–78].Modulators can also be created using Fabry-Pe´rot resonators. On SOI, there4have been numerous demonstrations of modulators that have used Fabry-Pe´rotresonators. In early work on SOI Fabry-Pe´rot modulators, Barrios et. al. pro-posed and demonstrated a tunable Fabry-Pe´rot resonator which used Bragg grat-ings, defined by periodically deep-etching a rib waveguide, to form the reflectorsand used a p-i-n junction for tuning [79, 80]. Schmidt et. al. demonstrated a 6 µmlong Fabry-Pe´rot modulator which had a speed of 250 Mb/s [81]. More recently,Meister et. al. demonstrated an 8.8 µm long Fabry-Pe´rot modulator which useda node-matched p-i-n junction to reduce losses [82]. They also demonstrated a3 µm long node-matched Fabry-Pe´rot modulator with speeds of 10 Gb/s [83]. Ourgroup recently demonstrated a quarter-wave phase-shifted Bragg grating modu-lator which was fabricated using 248 nm optical lithography [84], however, highspeed, large-signal modulation was not demonstrated. Recently, an SOI electri-cally tunable Bragg grating Fabry-Pe´rot filter, which used a 24.025 µm long cavity,was demonstrated and modulation was shown up to 3.5 Gb/s [85]. Furthermore,tunable Bragg grating filters using p-n and p-i-n junctions have been demonstratedon SOI [86, 87].In this thesis we present three novel designs for modulators. We first presentthe design of a travelling-wave MZM which uses a low-power biasing scheme.Travelling-wave MZMs use transmission lines and, therefore, need to be termi-nated to the characteristic impedance of the transmission line in order to preventmicrowave reflections caused by an impedance mismatch. Most prior demonstra-tions of travelling-wave MZMs used voltage driving signals in which a DC biasvoltage was added directly to the RF signal. This DC bias voltage causes an ad-ditional power to be consumed in the termination resistor. In the design presentedhere, the DC bias is applied separately from the RF signal so that the there is no DCpower consumption in the termination resistor, while at the same time, the RF sig-nal is terminated to the transmission line’s characteristic impedance. Also, usingthis scheme, a bias-tee circuit or an integrated level-shifter circuit is not required atthe RF input in order to apply the bias. As a proof-of-concept, we show measure-ment results of a fabricated device using this biasing scheme and demonstrate thatthe device has open eye diagrams at data rates up to 28 Gb/s.We then present the theoretical study of a modulator design which incorporatesMRMs into each arm of an MZI. Unlike in the travelling-wave MZM, which re-5quires electrodes that are millimetres in length to achieve large phase shifts, MRMscan be used to achieve similar phase shifts and are much more compact. The drop-port spectral response of an MRM changes sharply with wavelength so that when avoltage is applied to the p-n junction within the MRM, the light at the drop port ofthe MRM experiences a large phase shift. We show that using this design, the mod-ulator’s extinction ratio (ER) can be tuned while operating at a fixed wavelengthby changing the static phase shift between both arms of the MZI. We developed amodel of the device based on realistic parameters extracted from devices that havebeen previously fabricated on an SOI platform. The model uses temporal coupledmode (TCM) theory and was used to simulate the time-domain response of thedevice.Next, we present the design and measurement of a novel phase-shifted Bragggrating modulator. The Bragg grating is formed by periodically varying the widthof a waveguide (i.e., by adding corrugations). By adding a phase-shift in the corru-gation pattern at the centre of the grating, a Fabry-Pe´rot resonator is formed, wherethe uniform grating segments on each side of the phase-shift act as the “mirrors”of the resonator. We had the modulator fabricated using an SOI platform whichused 193 nm optical lithography. We present measurement results which showthat the modulator has open eye diagrams at data rates of up to 32 Gb/s. Bit errorrates (BERs) less than 10−12 were obtained at data rates of up to 25 Gb/s usinga 27-1 pseudorandom binary sequence (PRBS) pattern and at data dates of up to20 Gb/s using a 231-1 PRBS pattern. A BER of less than 10−10 was achieved at25 Gb/s using a 231-1 PRBS pattern.1.3.2 WDM Filters on SOIFilters are used in WDM systems to multiplex and/or demultiplex signals. Thereare several types of filters that have been demonstrated on SOI. For example, therehave been many demonstrations of ring-resonator-based filters, such as the onesin [88–92]. Ring resonator-based filters can achieve very good performance, e.g.,have high input-to-through-port suppressions, narrow bandwidths, and large adja-cent and non-adjacent channel isolations. However, a challenge with using ring-resonator-based filters is that they have free spectral ranges (FSRs) which can limit6the number of channels that can be used. To overcome this limitation, the FSRsof ring resonator-based filters can be expanded by, for example, using the Verniereffect [93–95] or by having wavelength-selective coupling to the rings [96]. How-ever, like MRMs and MDMs, a challenge when using these types of filters is thatthey require the use of wavelength tuning techniques to correct for impairmentsdue to fabrication variations. There are other types of filters, that are not resonantdevices, which have been demonstrated on SOI, such as arrayed waveguide grat-ings [97–99] and echelle gratings [100–103]. However, these types of filters canhave large device footprints.In this work, we investigate a filter based on a contra-directional coupler(contra-DC). A contra-DC filter uses corrugated waveguides, like those used inthe phase-shifted Bragg grating modulator, however, in this case the corrugationsare added to two closely-spaced parallel waveguides. Contra-DC filters, unlike ringresonator-based filters, do not have periodic spectral responses, which is desirablefor maximizing the number of channels in a WDM system. However, they typicallyhave wider bandwidths making then more suitable for coarse WDM applicationswith fewer channels [104, 105]. There have been numerous prior demonstrationsof contra-DCs filters on SOI [104–109]. However, until this work was completed,there had not been any demonstrations of successful data transmission through acontra-DC filter. In our work, we show that a contra-DC can operate as a multi-plexer, demultiplexer, and an optical add-drop multiplexer (OADM), at data ratesof 12.5 Gb/s, by performing an experiment in which data is simultaneously addedand dropped from the contra-DC OADM at the same wavelength.1.4 Thesis OverviewThis thesis is divided into six chapters. The first chapter presents a brief introduc-tion to the current state of silicon photonics and gives a brief introduction to WDMcommunication systems. It also gives an overview of modulators and WDM fil-ters on SOI and introduces the topics covered. The next four chapters are eachdedicated to a device being investigated and the content in each chapter is basedon work that we have published. Chapter 2 presents a low-power biasing schemefor travelling-wave MZMs on SOI. Chapter 3 describes our proposed modulator7design that incorporates MRMs into an MZI and presents simulation results usingTCM theory. In Chapter 4, the design, measurement, and analysis of a novel phase-shifted Bragg grating modulator is given. Chapter 5 presents measurement resultsshowing successful data transmission at 12.5 Gb/s through a contra-DC OADM.Finally, in Chapter 6, the summary, conclusions, and suggestions for future workare provided.8Chapter 2A Low-Power Biasing Scheme forSilicon-On-InsulatorTravelling-Wave ModulatorsSilicon photonics optical modulators are expected to play a key role in future op-tical interconnect applications due to their high speeds, low power consumptions,and compact sizes. Among the various types of modulator that have been proposed,travelling-wave MZMs have become a preferred choice because of their veryhigh speeds and their reduced sensitivity to fabrication and temperature variations[24, 26, 34]. There have been many recent demonstrations of silicon travelling-wave MZMs which have used a variety of electrode designs and biasing schemes[20, 22, 24–26, 34, 37, 40, 110, 111]. In this section, we propose, and demonstrate,a biasing scheme for travelling-wave MZMs in which the DC bias on the p-n junc-tion is applied separately from the RF signal, instead of being applied by addingthe DC bias to the RF signal. This scheme allows the RF signal, without a DC off-set, to be applied to the modulator, which is beneficial because then there is no DCpower being consumed in the termination resistor. Using this scheme, the energyefficiency of travelling-wave MZMs can be increased. Also, this scheme removesthe need for a bias-tee circuit or an integrated level-shifter circuit at the RF inputin order to apply the bias and it does not cut off the low frequency components ofthe RF signal.92.1 Mach-Zehnder ModulatorsAn MZM uses an MZI to convert phase modulation of light into intensity modula-tion. A schematic of an MZM is shown in Figure 2.1. The electric field of the lightentering the MZM is monochromatic and can be represented by Ein(t) = E ′ine− jω0t ,where E ′in is the complex amplitude of the electric field and ω0 is the angular fre-quency of the light. The light is then split between the two arms of the MZM,using a 50% power splitter, where the complex amplitude of the electric field en-tering arm 1 and arm 2 is E ′1 = E ′ine− jφ1,in/√2 and E ′2 = E ′ine− jφ2,in/√2, respec-tively. φ1,in and φ2,in are the propagation phases through the power splitter forthe light entering arm 1 and arm 2, respectively. There is a p-n junction in eacharm of length L which, via the free-carrier plasma dispersion effect, changes theeffective index of the waveguide when a voltage is applied across the junction,thereby applying a voltage-dependent phase shift to the light passing through thewaveguide. The complex amplitudes of the electric fields after passing throughthe waveguide in arm 1 and arm 2 are given by E ′1,out = E ′1e− jβ1(V1)L−α(V1)L/2 andE ′2,out = E ′2e− jβ2(V2)L−α(V2)L/2, respectively. The propagation constants in each arm,β1 and β2, depend on the voltage applied to the p-n junction in each arm and aregiven byβ1(V1) = 2pi (neff(λ0)+∆neff(V1))λ0 , (2.1)andβ2(V2) = 2pi (neff(λ0)+∆neff(V2))λ0 , (2.2)where neff is the wavelength-dependent effective index of the waveguide, ∆neff isthe voltage-dependent change in the effective index, λ0 is the wavelength in free-space, and V1 and V2 are the voltages applied to the p-n junctions in arm 1 and arm2, respectively. Also, α is the per-length power loss coefficient for the waveguide,which is also voltage-dependent since applying a voltage across the p-n junctionalso changes the waveguide’s loss. The fields in the two arms are combined usinga 50% power combiner and the field at the output of the device, E ′out , is given byE ′out = 1√2(E′1,oute− jφ1,out +E ′2,oute− jφ2,out ), (2.3)10where φ1,out and φ2,out are the propagation phases through the power combiner forthe light leaving arm 1 and arm 2, respectively. In order to modulate the light at theoutput of the MZI, voltages V1 and V2 are switched between an “on” state voltage,Von, and an “off” state voltage, Voff. Therefore, assuming that the bit sequence willbe in the “on” state and “off” state with equal probabilities, the signal would havea DC component of (Von +Voff)/2. In order to keep the p-n junction in the reverse-biased or zero-biased regime, both Voff and Von must be less than or equal to 0 V.For example, Voff could be 0 V and Von could be −5 V. Therefore, there would be a−2.5 V DC component in the signal. It is this DC component which causes a staticpower draw in the termination resistor and, using the biasing scheme presentedhere, is applied separately from the RF signal.!Ein !Eout = 12 ( !E1,oute− jφ1,out + !E2,oute− jφ2,out )Lp-n junctions !E1,out = !E1e− jβ1(V1 )L−α (V1 )L/2!E2,out = !E2e− jβ2 (V2 )L−α (V2 )L/2!E2 = !Ein2 e− jφ2,in!E1 = !Ein2 e− jφ1,inFigure 2.1: Schematic of a MZM. Here, symmetric Y-branches are used asthe power splitters/combiners.2.2 Device DesignTo demonstrate this biasing scheme, we designed a travelling-wave MZM as shownin Figure 2.2(a). The modulator was fabricated at IME, Singapore. In this design,the input light is split into two arms of the modulator using an adiabatic coupler[112]. A length imbalance of 127 µm is added between the two arms. The shorterarm, which has a length of 5 mm, is modulated using a travelling wave electrode.The cross-section of this structure is shown in Figure 2.2(b). The RF signal elec-trode is connected directly to the p-doped side of the p-n junction and the DC bias isconnected to an electrode on the metal 1 layer that is connected to the n-doped side11of the junction. The RF ground electrode, which is on the metal 2 layer, is placedover the DC bias electrode and is capacitively coupled to it. The capacitance-per-unit-length between the DC bias and RF ground electrodes was designed to beabout 10 times larger than the capacitance per unit length of the p-n junction sothat the combined series capacitance per unit length at high frequencies is nearlythe same as the p-n junction’s capacitance per unit length. The RF signal electrodeis terminated in 50Ω to the RF ground at the end of the transmission line. Us-ing this biasing scheme, the DC bias does not need to be combined with the RFsignal as has often been the case in previous demonstrations [20, 22, 25, 34, 37],thus eliminating the DC power consumption due to biasing. This scheme also dis-penses with the use of a bias-tee circuit or an integrated level-shifter circuit at theRF input. Furthermore, using this scheme, there is no low frequency cutoff of theRF signal. As shown in Figure 2.2(b), the DC bias needs to be applied through aninductive element to isolate the DC and RF signals [113].RF Ground RF Signal 50 Ω Termination …5 mm DC Bias RF Ground RF Signal n p n++ p++ Metal 1 Metal 2 +	  -­‐	  DC Bias (a) (b) 90 nm 130 nm 500 nm Figure 2.2: (a) Device layout of the travelling-wave MZM used to demon-strate the biasing scheme and (b) a cross-sectional schematic of thetravelling-wave structure and the waveguide with the p-n junction [1].122.3 Experimental ResultsIn this section, we present data for a modulator that uses our biasing scheme. First,the spectral response of the modulator was measured at various reverse bias volt-ages, applied through the DC bias input. The results in Figure 2.3 show that themodulator has a Vpi of about 6 V. To measure the high-speed performance of thedevice, signal-ground-ground-signal probes were contacted on both the right andleft sides of the device. The RF signals were applied through the lower ground-signal (GS) pair on the left side probe and a 50Ω termination resistor was con-nected to the lower GS pair on the right side probe. The DC bias was appliedthrough the upper GS pair on the right side probe. The cables connecting theDC power supply to the probe supplied the required inductance. Non-return-to-zero (NRZ) 231-1 PRBS RF signals, generated using an Anritsu MP1800A’s pat-tern generator module, were applied to the modulator. The voltage swing was 3 Vppand the bias, applied through the DC bias input, was 3 V. Figures 2.4(a), 2.4(b),and 2.4(c) show the eye diagrams measured at data rates of 12.5 Gb/s, 20 Gb/s,and 28 Gb/s, respectively. At each data rate, the eye diagrams are clearly open,demonstrating that travelling-wave MZMs using this biasing scheme can achievesuccessful high-speed operation.2.4 SummaryA new biasing scheme for travelling-wave MZMs has been proposed which elimi-nates the DC power consumption in the termination resistor and it dispenses withthe use of a bias-tee circuit or an integrated level-shifter circuit to apply the DCbias. Single-arm modulation using this biasing scheme has been demonstrated atdata rates up to 28 Gb/s with open eye diagrams being achieved. The power reduc-tion gained by using this biasing scheme can substantially reduce the overall powerconsumption of an optical interconnect that uses MZMs. Also, this biasing schemeis not limited to being used with single-arm modulation and can be used in a dif-ferential drive configuration to apply DC biases to both arms of a travelling-waveMZM.131546 1548 1550 1552 1554 1556 1558Wavelength (nm)−50−45−40−35−30−25−20Power(dBm)0 V1.5 V4.5 V6 VFigure 2.3: Spectral response of the modulator at various reverse bias volt-ages.(a) (b) (c) Figure 2.4: Measured eye diagrams of the modulator at (a) 12.5 Gb/s, (b)20 Gb/s, and (c) 28 Gb/s.14Chapter 3Microring Modulator UsingDrop-Port Phase InterferenceMicroring-based modulators have emerged as promising candidates for use in opti-cal interconnects owing to their small device footprints, low power consumptions,and fast speeds [114]. MRMs are often used, however, it remains challenging tomeet post-fabrication design targets such as modulation insertion losses (ILs) andmodulation ERs for MRMs due to their sensitivities to undesired fabrication vari-ations in their coupling coefficients and in their waveguide losses [115]. It is wellknown that the ER of an MRM is wavelength dependent [114]. This can make itchallenging to design an array of MRMs, each operating at a different wavelength,where all of the MRMs have the same performance characteristics. In this section,we propose a modulator which has a tunable modulation IL and modulation ERwhile operating at a fixed wavelength. Our modulator would also allow for dy-namic control of the modulator’s performance, which could be used to counteractthese performance variations.3.1 Device DesignThe modulator design is shown in Figure 3.1, in which an add/drop MRM phaseshifter is inserted into each arm of an MZI. The drop-port spectral response ofan MRM has a sharp frequency dependent phase change at resonance, which this15modulator design uses to achieve a large phase shift for a small change in theMRM’s resonance frequency. The MRM used in this modulator design is basedon MRMs that were previously fabricated at IME, Singapore. The MRM uses arib waveguide with a slab height of 90 nm and rib height of 130 nm, as shown inFigure 3.2. The MRM has a radius of 10 µm and is symmetrically coupled to thebus waveguides (i.e., the power coupling coefficients at the through and drop portsare the same). A lightly doped lateral p-n junction is formed over about 70% ofthe ring’s circumference. The remaining waveguide, without a p-n junction, has anin-silicon doped heater placed across it in order to tune the resonance wavelengthsof the MRMs.In order to accurately simulate our proposed modulator, we extracted severalparameters from previously fabricated MRMs which will be used to simulate thedevice. First, the group index, ng, of the waveguide in each of the MRMs wasmeasured. In order to measure ng, the spectral responses of 8 previously fabricatedMRMs were measured and, using their FSRs, ng for each was calculated using[116]ng = λ2rLrt∆λFSR , (3.1)where λr is the resonance wavelength, Lrt is the round-trip length of the ring, and∆λFSR is the measured FSR. A linear interpolation between the measured valueswas used in order to approximate the wavelength-dependent variation of ng, andthen the average group index for all 8 MRMs was calculated. The group index wasalso simulated using MODE Solutions eigenmode solver by Lumerical Solutions,Inc. Both the measured and simulated group indices are shown in Figure 3.3 andthere is close agreement between the average measured ng and the simulated ng.The spectral response of one of the MRMs was then measured with variousreverse bias voltages applied to its p-n junction. The measured spectral responsesare shown in Figure 3.4. From the measured spectral responses, ∆neff as a functionof the p-n junction’s reverse bias voltage was extracted by measuring the resonancewavelength shift, ∆λr, as the reverse bias voltage was increased, and by using theequation [116]∆neff = ng∆λrFrλr , (3.2)1610 µm Heater n p ar = !are− jωtEin = !Eine− jωt − jκc− jκc − jκc− jκc EoutEd1Ed2 +ϕEi2Ei1 MRM 2 MRM 1 Figure 3.1: Schematic of the proposed modulator [2].90 nm 1 µm n++ n p p++ 130 nm 500 nm Figure 3.2: Diagram of the waveguide used in the MRM.where Fr is the ratio of the p-n junction’s length to the ring’s round-trip length.∆αdB, which is the change in optical loss in units of dB/cm due to changes inthe carrier concentration within the waveguide, was extracted as a function of thebias voltage using a method similar to the one used in [117]. The method andthe equations we present here are modified from those presented in [117], the dif-ference being that here we extract the parameters from a symmetrically coupledring whereas in [117] the parameters are extracted from an all-pass ring. In thismethod, the through field coupling coefficients, t1 and t2, for the ring, as well as itsround-trip field loss coefficient, a, are extracted from the ring’s spectral response.As shown in Figure 3.5, t1 is the through field coupling coefficient for the coupler171525 1530 1535 1540 1545 1550 1555 1560Wavelength (nm)3.873.883.893.903.913.92GroupindexMeasured (average)Measured (points)SimulatedFigure 3.3: Simulated and measured group indices as functions of wave-length for the rib waveguide used in the MRM design.1548.70 1548.75 1548.80 1548.85 1548.90 1548.95Wavelength (nm)−20−15−10−50Normalizedpower(dB)0 V1 V2 V3 V4 V5 VFigure 3.4: Through-port spectral responses of a previously fabricated MRMwith various reverse bias voltages applied to the MRM’s p-n junction.18at the through port of the ring and t2 is the through field coupling coefficient for thecoupler at the drop port of the ring.Input Through Drop − jκc1− jκc2t1t2Figure 3.5: Diagram of a microring showing the various coupling coeffi-cients.First, the ring’s finesse, F , and the ER of its through-port spectral response ateach of the resonances, ER, were measured. F is defined asF =∆λFSR∆λFWHM, (3.3)where ∆λFWHM is the full-width-at-half-maximum of the spectral response at res-onance. ER, can be related to a, t1, and t2 asER =[(at2 + t1)(1−at1t2)(at2− t1)(1+at1t2)]2. (3.4)Similarly, F can be related to a, t1, and t2 ascos(pi/F ) = 2at1t21+a2t21 t22. (3.5)If we define the quantities A and B asA = cos(pi/F )1+ sin(pi/F ) , (3.6)andB = 1− 1ER[1− cos(pi/F )1+ cos(pi/F )], (3.7)19then, at2 and t1 can be determined using(at2, t1) =√AB ±√AB −A, (3.8)where at2 and t1 are the two solutions of the system of equations formed by Eqs.3.4-3.7. Eq. 3.8, however, doesn’t indicate which solution corresponds to at2 ort1. Since, in this case, the ring is symmetrically coupled (i.e., t1 = t2), at2 < t1 andthe two solutions can be distinguished, with the smaller solution being at2, and wecan then obtain a by dividing the solution at2 by t1. We determined a from thespectral response measured for each reverse bias voltage applied. a is related to theper-length power loss (in units of m−1), α , byα = −2lnaLrt . (3.9)The voltage-dependent per-length loss of the p-n junction, ∆α , is given by∆α = α−α0Fr , (3.10)where α0 is the measured α with 0 V applied to the p-n junction. Finally, thevoltage-dependent loss from the p-n junction in units of dB/cm, ∆αdB, is givenby ∆αdB = ∆α/(10ln10). The results of the parameter extraction are shown inFigure 3.6. ∆neff and ∆αdB as functions of voltage were both curve-fitted to apower law. The resulting curve fit equations are ∆neff(V ) = 3.475× 10−5V 0.8101and ∆αdB(V ) = −0.782V 0.6824 dB/cm. These results were used as inputs to sim-ulate the proposed modulator and to predict its performance. Using these results,Figure 3.7(a) shows the simulated power spectral response and Figure 3.7(b) showsthe simulated phase response of the MRM with 0 V and 5 V being applied to the p-n junction. The resonance wavelength of MRM 1 was adjusted (which, in practicecould be accomplished by heating the ring) to have the same resonance wavelengthas MRM 2 when 5 V is applied to its p-n junction. The device operates in a push-pull fashion, i.e., when 0 V is applied to MRM 1 and 5 V is applied to MRM 2,there is no phase shift between the two MRMs, corresponding to the modulator be-ing in the “on” state. When 5 V is applied to MRM 1 and 0 V is applied to MRM 2,20there is a large phase shift between the two MRMs corresponding to the modulatorbeing in the “off” state. It should be noted that the intensity of the light coupledout of the drop port is also modulated, which can be seen in Figure 3.7(a). Heatersare placed in the MZI arms after the drop-port outputs of the MRMs which can beused to adjust the static phase shift between the two arms and enable control of themodulator’s IL and ER.0 1 2 3 4 5Reverse bias voltage (V)0.00.20.40.60.81.01.21.41.61.8ne↵⇥1043.02.52.01.51.00.50.0↵dB(dB/cm)Figure 3.6: Change in effective index and loss as a function of the p-n junc-tion’s reverse bias voltage determined using measurement results froma previously fabricated MRM.3.2 Transient ResponseThe transient response of the proposed modulator was simulated using TCM theoryusing the equations given in [118–120]. The equation describing a single MRM (inthis case MRM 1) is given byda′rdt = j(ω−ω′0(t))a′r−( 12τ`(t) +12τe +12τd)a′r− j√ 1τeE ′i1, (3.11)210.20 0.15 0.10 0.05 0.00 0.05 0.10 0.15 0.20Relative wavelength (nm)5.04.54.03.53.02.52.01.5Phase(rad)0 V - Ring 15 V - Ring 15 V - Ring 20 V - Ring 20.20 0.15 0.10 0.05 0.00 0.05 0.10 0.15 0.20Relative wavelength (nm)0.00.20.40.60.81.0Normalizedpower(a.u.)0 V - Ring 15 V - Ring 15 V - Ring 20 V - Ring 2(a) (b) Figure 3.7: Simulated drop-port (a) power spectral response and (b) phaseresponse for MRM 1 and MRM 2 with both 0 V and 5 V being appliedeach of their p-n junctions.22where a′r and E ′i1 are the complex amplitudes of the electric field inside the res-onator and of the input electric field to the MRM, respectively. E ′i1 is related to E ′inby E ′i1 = E ′ine− jφ1,in/√2, where φ1,in is the propagation phase through the Y-branchsplitter of the light entering arm 1. Similarly, for arm 2, E ′i2 is related to E ′in byE ′i2 = E ′ine− jφ2,in/√2, where φ2,in is the propagation phase through the Y-branchsplitter of the light entering arm 2. Since Y-branches are being used here, thephases φ1,in and φ2,in would be the same. τ` is the photon lifetime associated withthe intrinsic losses, which is a function of time because the p-n junction voltagechanges during modulation. It is given byτ`(t) = 1vg [α0 +Fr∆α(v(t))] , (3.12)where vg is the group velocity, α0 is the optical power loss (in units of m−1) whenno voltage is applied to the junction, and v(t) is the time-varying input voltage. τeand τd are the photon lifetimes associated with the resonator coupling losses for thethrough port and drop port, respectively, and are equal because symmetric couplingis used. Provided κ2c is small, τe and τd are approximately given byτe = τd ≈Lrtvgκ2c, (3.13)where κc is the field coupling coefficient. ω ′0 is the resonance angular frequency ofthe MRM, and is also a function of time because the p-n junction voltage changeswith time. ω ′0 is given byω ′0(t) = ω0(1− Fr∆neff (v(t))ng), (3.14)where ω0 is the resonance angular frequency when no voltage is applied. Thecomplex amplitude of the electric field at the drop port of the MRM is given byE ′d =− j√ 1τda′r. (3.15)23Finally, the complex amplitude of the electric field at the output of the modulatoris given byE ′out = 1√2(E ′d1e− jφ1,out +E ′d2e− j(φ2,out+ϕ)), (3.16)where φ1,out and φ2,out are the propagation phases of the light that is passing throughthe Y-branch combiner and leaving arm 1 and arm 2, respectively, and ϕ is the staticphase shift added to arm 2.Using α0 = 173m−1(7.51dB/cm), which was measured from the fabricatedMRM, and ng = 3.89, κ2c was chosen to be 0.0207 in order to give the MRMa full-width-at-half-maximum bandwidth of about 10 GHz. In the time-domainsimulations, the simulated ng (including wavelength dependency) was used. Usingthe simulated ng instead of the measured ng does not significantly affect the resultsbecause there is very close agreement between the simulated ng and the measuredng, as seen in Figure 3.3. The modulator was simulated with a 5 Vpp, 10 Gb/spseudorandom input bitstream of 1000 bits which was filtered by a 40 GHz low-pass RC filter. Optical eye patterns were also simulated for various values of ϕas shown in Figure 3.8. Figure 3.9 shows the modulation ERs and modulationILs as ϕ is increased. Near ϕ = 0, the modulator is biased near the maximum ofthe MZI’s transfer function where its phase sensitivity (i.e., the amount the outputintensity changes for a given phase change in the MZI arms from the MRMs) islow, resulting in a low modulation ER. As ϕ increases, the MZI’s phase sensitivityincreases and, eventually, the phase shift between both branches will reach pi duringthe signal swing, resulting in a large modulation ER. However, as ϕ increases, themodulation ER trades off with modulation IL. This behaviour is advantageousbecause the modulation ER and modulation IL can be chosen by changing ϕ .In order to confirm that the TCM model accurately represents the transientbehaviour of the modulator, the modulator was also simulated using INTERCON-NECT by Lumerical Solutions, Inc., which is an optical circuit simulation softwarepackage. A photonic circuit representation of the modulator was created within IN-TERCONNECT as shown in Figure 3.10(a). In the model, a laser source outputslight at a wavelength of 1550.3456 nm into a Y-branch which splits the light intotwo branches. Within each branch, there is a component representing the MRM.At the output of MRM 2, a static phase shift of 1.2 rad is added. The outputs of240.00 0.05 0.10 0.15Time (ns)0.00.20.40.60.81.0Intensity(a.u.)(a)Mod. ERMod. IL0.00 0.05 0.10 0.15Time (ns)0.00.20.40.60.81.0Intensity(a.u.)(b)0.00 0.05 0.10 0.15Time (ns)0.00.20.40.60.81.0Intensity(a.u.)(c)0.00 0.05 0.10 0.15Time (ns)0.00.20.40.60.81.0Intensity(a.u.)(d)Figure 3.8: Simulated optical eye diagrams for different static phase shifts:(a) ϕ = 0, (b) ϕ = 0.6, (c) ϕ = 1.2, (d) ϕ = 1.6.the two branches are combined using a Y-branch prior to being recorded by anoptical oscilloscope monitor in the simulation. Figure 3.10(b) shows the photoniccircuit representation of the MRM component. The MRM consists of couplersfor both the through and drop ports. The power coupling coefficient for each wasset to 0.0207 to match the value used in the TCM model. The waveguide com-ponent simulates the round-trip propagation through the ring. The waveguide’swavelength-dependent neff and ng were simulated using MODE Solutions, usingthe same values that were used in the TCM simulation. The p-n junction com-ponent applies the voltage-dependent ∆neff and ∆αdB. The same ∆neff and ∆αdBvoltage relationships were used for both the TCM and INTERCONNECT mod-250.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Phase o↵set (rad)1.52.02.53.03.54.04.55.05.5ModulationIL(dB)51015202530ModulationER(dB)Figure 3.9: Simulated modulation ER and modulation IL as a function of thestatic phase offset, ϕ .els. Using the same voltage signals at 10 Gb/s and the same parameters, the outputsignals for both models were simulated and are shown in Figure 3.11. There isvery close agreement between the two models, confirming that the TCM modelaccurately represents the transient behaviour of the modulator.3.3 SummaryIn this section, a novel modulator design was presented which has a tunable ILand ER, allowing the modulator’s performance to be adjusted without switchingthe operating wavelength. Also, transient simulation results of the modulator wereshown, which used realistic input parameters that were extracted from a previ-ously fabricated modulator. Lastly, the results from the TCM model presentedhere were compared to the results obtained by using INTERCONNECT. The twomodels, which used the same input parameters and the same component param-eters, agreed closely with each other indicating that the TCM model accuratelyrepresents the transient behaviour of the modulator and suggests that a fabricatedmodulator should have performance that is similar to the simulated results.26(a) (b) Figure 3.10: Photonic circuit representation using INTERCONNECT of (a)the proposed modulator and (b) the MRM component.270 1 2 3 4 5Time (ns)0.00.10.20.30.40.50.6Intensity(a.u.)TCMInterconnectFigure 3.11: Comparison the time-domain simulation results of the proposedmodulator using both the TCM model and INTERCONNECT.28Chapter 4Silicon-On-Insulator ModulatorsUsing a Quarter-WavePhase-Shifted Bragg GratingA Bragg grating is a device which, at certain wavelengths, strongly reflects lightentering it. By placing a quarter-wavelength phase shift in the grating at its centre,a resonant cavity is formed, which creates a strong, wavelength dependent, confine-ment of light in and around the phase-shifted region. By changing the resonancewavelength of the cavity by, for example, using a p-n junction and the free-carrierplasma dispersion effect, the cavity can be brought in and out of resonance, re-sulting in a change in the light intensities leaving the device. In this section, thetheory, measurements, and an analysis of a novel quarter-wave phase-shifted Bragggrating modulator on SOI are presented.4.1 Uniform Bragg Gratings on SOIA Bragg grating is a structure which has a periodic variation in refractive indexalong the direction of light propagation. To create Bragg gratings in silicon waveg-uides, a periodic variation in the effective index of the waveguide is created byperiodically varying the waveguide geometry. An often used method of varyingthe geometry is to create periodic sidewall corrugations by varying the waveguide29width. A diagram of a waveguide Bragg grating having sidewall corrugations isshown in Figure 4.1.Λ	Input Reflect Through W	ΔW	Figure 4.1: Diagram of a waveguide Bragg grating. The red lines indicate thegeometry of the unperturbed waveguide.The geometry of a waveguide Bragg grating having sidewall corrugations isdetermined by several parameters. A uniform Bragg grating is typically composedof N identical segments, where each segment has a narrow waveguide section witha width of W−∆W and has a wide waveguide section with a width of W +∆W , witha duty cycle of 50%. The lengths of the narrow waveguide section and the widewaveguide section are both Λ/2 so that each of the N segments has a length Λ.Hence, the Bragg grating has an average waveguide width W and has a corrugationamplitude of ∆W .The operation of a waveguide Bragg grating can be understood by using cou-pled mode theory. In the coupled mode analysis of such a grating, the gratingcan be considered as a uniform waveguide having a width W that has its widthbeing perturbed by the corrugations. The corrugations have the effect of period-ically varying the dielectric constant profile of the waveguide along the length ofthe grating. The periodically varying dielectric constant profile causes the forwardpropagating mode in the waveguide, having a propagation constant β+, to be cou-pled into the backward propagating mode in the waveguide, having a propagationconstant β−. This coupling is appreciable only when the phase matching conditionis met, which is given by [121] β+−β− = m 2piΛ , for an integer m. In this work, weare only considering gratings for which m = 1. In a waveguide, β− =−β+, sincethe modes are propagating in opposite directions. Therefore, if we denote β+ as β ,30then the phase matching condition can be written as 2β = 2piΛ , where β is given byβ =2pineff,avg(λ0)λ0, (4.1)where neff,avg is the wavelength-dependent effective index of the unperturbedwaveguide. Using the phase matching condition, the Bragg wavelength, λb, whichis the wavelength at which phase matching occurs, is given by the solution ofλ02Λ = neff,avg(λ0). (4.2)At wavelengths near λb, light is reflected from the Bragg grating and atother wavelengths, light is transmitted through the Bragg grating. The reflectionand transmission spectral responses of Bragg gratings can be determined usingcoupled-mode theory. The derivations of the spectral responses given here arebased on, and closely follow the derivations given in Section 12.7 in [121]. Thecoupled mode equations for a Bragg grating aredA(z)dz =− jκej∆β zB(z)dB(z)dz = jκ∗e− j∆β zA(z)(4.3)where A(z) and B(z) are the amplitudes of the forward and backward propagatingmodes in the Bragg grating, respectively and κ is the coupling coefficient whichdetermines the strength of the coupling from the forward propagating mode to thebackward propagating mode. κ can be simulated by using finite-difference time-domain (FDTD) simulation techniques by simulating one grating period while us-ing Bloch boundary conditions [122], however, lithography smoothing effects mayneed to be taken into account [123]. κ can also be determined experimentally fromthe measured spectral response of fabricated devices [123]. ∆β is the propagationconstant mismatch, and is given by ∆β = 2β − 2piΛ . The system of equations givenin Eq. 4.3 can be written in matrix form asddzX =[0 − jκe j∆β zjκ∗e− j∆β z 0]X , (4.4)31whereX =[A(z)B(z)]. (4.5)Eq. 4.4 is a system of two first order homogeneous differential equations withvariable coefficients and can be converted to a system with constant coefficientsby using a suitable transformation. If we define A′(z) = e− j ∆β z2 A(z) and B′(z) =e j ∆β z2 B(z), thenddzX′ =WX ′, (4.6)whereW =[− j ∆β2 − jκjκ∗ j ∆β2](4.7)andX ′ =[A′(z)B′(z)]. (4.8)Now that the equations have constant coefficients, the solution can be easily foundand is given by X(z) = eWzC, whereC =[c1c2](4.9)is a vector of the two constants which are found using the boundary conditions ofthe problem. The matrix exponential, eWz, can be computed by diagonalizing Wusing the fact that eWz = UeDzU−1, where U is a matrix having the eigenvectorsof W as its columns and D is a matrix having each of the eigenvalues of W on itsdiagonal. The eigenvalues of W are ξ1 = s and ξ2 =−s, where s =√|κ|2−∆β 2/4and the corresponding eigenvectors areψ1 =[− ∆β2κ∗ − j sκ∗1], ψ2 =[− ∆β2κ∗ + j sκ∗1]. (4.10)32Using these values, the diagonal matrix, D, isD =[s 00 −s](4.11)and the matrix of eigenvectors, U , isU =[− ∆β2κ∗ − j sκ∗ − ∆β2κ∗ + j sκ∗1 1]. (4.12)The inverse of U , used for diagonalization, isU−1 =[j κ∗2s 12 + j ∆β4s− j κ∗2s 12 − j ∆β4s]. (4.13)Using X =UeDzU−1C, the solutions of Eq. 4.6 areA′(z) =− j c2κs sinh(sz)+ c1[cosh(sz)− j∆β2s sinh(sz)]B′(z) = j c1κ∗s sinh(sz)+ c2[cosh(sz)+ j∆β2s sinh(sz)] (4.14)Transforming back to A(z) and B(z) we getA(z) =(− j c2κs sinh(sz)+ c1[cosh(sz)− j∆β2s sinh(sz)])e j ∆β z2B(z) =(j c1κ∗s sinh(sz)+ c2[cosh(sz)+ j∆β2s sinh(sz)])e− j ∆β z2(4.15)By setting z = 0, we find that the constants c1 and c2 correspond to A(0) and B(0),respectively. The complex amplitudes of the electric fields for the forward andbackward propagating modes in the Bragg grating can be obtained by includingthe propagation phase, and are given bya(z) = A(z)e− jβ zb(z) = B(z)e jβ z(4.16)33Therefore we have[a(z)e j pizΛb(z)e− j pizΛ]=[cosh(sz)− j ∆β2s sinh(sz) − j κs sinh(sz)j κ∗s sinh(sz) cosh(sz)+ j ∆β2s sinh(sz)][a(0)b(0)](4.17)Eq. 4.17 can be rearranged so that the field at z = 0 is expressed as a function thefields at a distance z along the grating. By doing this, we arrive at[a(0)b(0)]=[cosh(sz)+ j ∆β2s sinh(sz) j κs sinh(sz)− j κ∗s sinh(sz) cosh(sz)− j ∆β2s sinh(sz)][a(z)e j pizΛb(z)e− j pizΛ](4.18)In Eq. 4.18, the e± j pizΛ terms represent the propagation phase through the Bragggrating and will switch between +1 and−1 depending on the length of the grating,assuming that the length of the grating segments are be an integer multiple of theperiod. Using Eq. 4.18, the field reflection factor for a grating of length L = NΛ isgiven byb(0)a(0)∣∣∣∣b(L)=0=− jκ∗ sinh(sL)scosh(sL)+ j(∆β/2)sinh(sL) . (4.19)Also, the field transmission factor is given bya(L)a(0)∣∣∣∣b(L)=0=se− j piLΛscosh(sL)+ j(∆β/2)sinh(sL) . (4.20)The reflect-port power transmission factor, R, is given byR = |b(0)|2|a(0)|2∣∣∣∣b(L)=0=|κ|2 sinh2(sL)s2 cosh2(sL)+(∆β/2)2 sinh2(sL) , (4.21)and the through-port power transmission factor, T , is given byT = |a(L)|2|a(0)|2∣∣∣∣b(L)=0=s2s2 cosh2(sL)+(∆β/2)2 sinh2(sL) , (4.22)In order to illustrate the spectral response of a Bragg grating, the simulatedthrough- and reflect-port spectral responses of a uniform Bragg grating are shown34in Figure 4.2. The simulated grating had a κ of 8000 m−1, a Λ of 310 nm, an Nof 1000 (giving a length, L, of 310 µm), and λb was chosen to be 1530 nm. Thethrough-port spectral response consists of a wide stopband at wavelengths near λb.The reflect-port spectral response consists of a main lobe centred at λb and is sur-rounded on each side by many sidelobes. Between each of the sidelobes, there arenulls in the response where R becomes close to zero. The peak reflectivity of themain lobe, Rpeak, occurs at λb, (i.e., ∆β = 0) and is given byRpeak = tanh2(|κ|L). (4.23)1524 1526 1528 1530 1532 1534 1536Wavelength (nm)0.00.20.40.60.81.0Normalizedpower(a.u.) ReflectThroughλb Rpeak Figure 4.2: Simulated through- and reflect-port spectral responses of a uni-form Bragg grating shown, for demonstration purposes, to illustrate thefeatures of a Bragg grating’s spectral response. The simulated Bragggrating had the following parameters: κ = 8000m−1, Λ = 310nm,N = 1000, λb = 1530nm.354.2 Phase-Shifted Bragg GratingsA phase-shifted Bragg grating is formed by shifting the corrugation pattern by aquarter of the resonance wavelength in the waveguide (or equivalently by half ofa grating period) at the centre of the grating. A diagram of a phase-shifted Bragggrating is shown in Figure 4.3. The presence of a phase shift creates a Fabry-Pe´rotresonator in the phase-shift shifted region, where the “mirrors” of the Fabry-Pe´rotresonator are formed by the Bragg grating sections on each side of the phase-shiftshifted region. The phase shift creates a narrow transmission window at the centreof the stopband of the through-port spectral response, and creates a correspondingnotch in the centre of the main lobe of the reflect-port spectral response. The centrewavelength of the peak/notch corresponds to the wavelength at which the Fabry-Pe´rot cavity is on resonance and at this wavelength, light is confined in the regionnear the phase shift.Λ	ΔW	Λ / 2	W	Phase shift Input Reflect Through Figure 4.3: Diagram of a quarter-wave phase-shifted Bragg grating with thephase shift indicated by the cross-hatched region.The spectral response of a phase-shift shifted Bragg grating was calculatedusing a matrix-based method [121]. In this method, the Bragg gratings on theleft and right sides of the phase shift are represented by transfer matrices G1 andG2, respectively, and the phase shift is represented by a transfer matrix P. Thespectral response of the device can be obtained by multiplying the transfer matricesrepresenting each section of the device. This concept is illustrated in Figure 4.4.The equation used to determine the spectral response was[a0b0]= G1PG2[a3b3]=[M11 M12M21 M22][a3b3], (4.24)where a0 and b0 are the field amplitudes of the forward and backward propagating36modes in the device, respectively, at the input to the device. Also, a3 and b3 arethe field amplitudes of the forward and backward propagating modes in the device,respectively, at the output of the device. Furthermore, we haveGn =[cosh(s′`n)+ j ∆β ′2s′ sinh(s′`n) j κs′ sinh(s′`n)− j κs′ sinh(s′`n) cosh(s′`n)− j ∆β′2s′ sinh(s′`n)](4.25)for n = 1,2 andP =[e jβ ′`FP 00 e− jβ ′`FP]. (4.26)`1 and `2 are the lengths of the Bragg grating segments represented by G1 and G2,respectively and `FP is the length of the Fabry-Pe´rot cavity, which has a length ofΛ/2. It should be noted that, for simplicity, the propagation phase terms in Eq.4.18 have not been included in matrix Gn since the inclusion of the phase will notaffect the power spectral response of the device, which is what we are interested incalculating. The through-port spectral response of the phase-shifted Bragg gratinga0b0!"## $%&& a1b1!"## $%&&G1	ℓ1Bragg grating 1 a2b2!"## $%&& a3b3!"## $%&&G2	ℓ2P	ℓFP Bragg grating 2 Phase shift Figure 4.4: Diagram showing how a Fabry-Pe´rot cavity using Bragg gratingreflectors can be broken down into individual sections which can berepresented using a transfer matrix.37is given byT = |a3|2|a0|2∣∣∣∣b3=0=1|M11|2 (4.27)and the reflect-port spectral response is given byR = |b0|2|a0|2∣∣∣∣b3=0=|M21|2|M11|2 . (4.28)Compared to the derivation given above for the Bragg grating’s spectral response,in this derivation for a phase-shifted grating, propagation loss has been included byadding a loss term to the propagation constant. We have s′ = (|κ|2− (∆β ′/2)2) 12and ∆β ′ = 2β ′− 2pi/Λ. β ′ is the complex propagation constant that includes thewaveguide losses and is given by β ′ = β − jα/2, where β is the propagation con-stant of the fundamental mode of the unperturbed waveguide and α is the per-length power loss coefficient. β here is also given byβ =2pineff,avg(λ0)λ0. (4.29)Figure 4.5 illustrates the through- and reflect-port spectral responses of a phase-shifted Bragg grating. The simulated grating used the same parameters as theBragg grating demonstrated in Figure 4.2, i.e., it had a κ of 8000 m−1, a Λ of310 nm, an N of 1000, and λb was chosen to be 1530 nm. Also, the simulateddevice was assumed to be lossless, i.e., α = 0. A quarter-wave phase shift wasadded to the centre of the grating, as shown in Figure 4.3. The important feature ofthe through-port spectral response is the presence of a narrow transmission peak,which has a Lorentzian lineshape, in the centre of the stopband. The reflect-portspectral response has a corresponding notch at the centre of the main lobe. Thesharpness of the transmission peak (and also the reflection notch) depends on thequality factor (Q) of the resonator, which is a measure of the energy storage capac-ity of the resonator.The most general definition of Q is [121]Q = ω0 Energy stored in resonatorPower dissipated in resonator = ω0E−dEdt, (4.30)381524 1526 1528 1530 1532 1534 1536Wavelength (nm)0.00.20.40.60.81.0Normalizedpower(a.u.)ReflectThroughFigure 4.5: Simulated through- and reflect-port spectral responses of a phase-shifted Bragg grating shown to illustrate the features of its through- andreflect-port spectral responses. The simulated phase-shifted Bragg grat-ing had the same parameters as the Bragg grating shown in Figure 4.2(i.e., κ = 8000m−1, Λ= 310nm, N = 1000, λb = 1530nm) except thata quarter-wave phase shift was added in the centre of the grating.where E is the energy stored in the resonator. We can rearrange the equation to getdEdt =−ω0Q E . (4.31)This equation describes an exponential decay process where ω0/Q is the decay rateof the energy. Thus, Q/ω0 is the time constant associated with the energy decayand is called the photon lifetime (τp) of the resonator. We can now writedEdt =−1τpE . (4.32)The solution of Eq. 4.32, assuming the initial condition that E = E0 at t = 0, is39given byE = E0e−tτp , (4.33)which indicates that the energy loss is an exponential decay process. In reality,there are multiple decay processes within the resonator arising from the differentloss mechanisms. For a phase-shifted Bragg grating, there is the intrinsic loss ofthe resonator, which we will take as the loss from roughness, loss from scattering,and the loss from the presence of dopants. The intrinsic loss of the resonator hasa single time constant associated with it, denoted as τi. There are also couplinglosses associated with the loss of energy from light escaping the cavity because thegrating’s reflectivity, R, is always < 1. Therefore, for each Bragg grating reflector,there is a time constant associated with the coupling losses, denoted as τcn, wheren = 1,2. The total energy decay rate for all loss contributions is the summation ofthe individual decay rates for each process, therefore, we can writedEdt =−( 1τi+1τc1+1τc2)E . (4.34)The total photon lifetime of the resonator can therefore be written asτp =( 1τi+1τc1+1τc2)−1. (4.35)Also, the intrinsic Q factor is given by Qi =ω0τi and the coupling Q factor for eachBragg grating reflector is given by Qcn = ω0τcn. Therefore, we can write the totalQ factor of the resonator as1Q =1Qi +1Qc1 +1Qc2 . (4.36)For a high Q resonator, Q can be determined from the full-width-at-half-maximumbandwidth, ∆λBW, of the transmission peak by using [116]Q = λr∆λBW, (4.37)where λr is the resonance wavelength.404.3 Phase-Shifted Bragg Grating ModulatorsQuarter-wave phase-shifted Bragg gratings on the SOI platform have been investi-gated for use in numerous applications that utilize resonant cavities. Such applica-tions include sensing [124–126], wavelength filtering [127], and lasers [128, 129].In this section, we demonstrate an SOI quarter-wave phase-shifted Bragg grating ina modulator application. The modulator presented here has improved performancecompared to our previous design in [84] because here we used 193 nm opticallithography instead of 248 nm optical lithography, which was used in [84]. Weattribute the improved performance to the use of 193 nm lithography because asshown in [123], a sidewall corrugated, strip waveguide Bragg grating fabricatedusing 193 nm lithography has a higher coupling coefficient (i.e., κ) than the samegrating fabricated using 248 nm lithography, due to reduced lithography smooth-ing. The modulator we present is, to the best of our knowledge, the first quarter-wave phase-shifted Bragg grating modulator on SOI for which high-speed datatransmission has been demonstrated.A quarter-wave phase-shifted Bragg grating modulator is, in principle, similarto an MRM with three main differences: 1) the resonant cavity is formed in astraight line instead of a ring, which is potentially more compact; 2) the cavityoperates using only the fundamental mode, meaning that there is only one resonantpeak [i.e., no FSR], whereas a ring typically has an FSR of several nanometres;3) the device has two ports (input/reflect, through) and modulated light is presentat both ports, whereas an add-drop MRM has four ports with two of them (drop,through) having the modulated light.4.4 Device DesignThe design of the modulator is shown in Figure 4.6(a). There are six parametersdefining a particular design: the grating period, Λ, the average waveguide width,W , the corrugation amplitude, ∆W , the number of periods, N, the duty cycle, D, andthe fill factor, Fpn. Most of these parameters are labeled in Figure 4.6(a). The fillfactor, which is the percentage of the device that has a p-n junction in the waveg-uide, is given by Fpn = Lpn/L. In the modulator, the gratings are formed by addingsidewall corrugations with a period ofΛ and an amplitude of ∆W , and a D of 50% to41a rib waveguide having an average width of W . A quarter-wave phase shift is addedto the corrugation pattern in the centre of the modulator. A lateral p-n junction isformed in the waveguide, over the entire length of the device. As shown in Fig-ure 4.6(b), the waveguide, for all of the design variations, has a 160 nm rib heightand a 60 nm slab height. Also, for all of the variations, the waveguide is dopedso that the p-n junction is formed in the centre of the waveguide. As explainedpreviously, modulation is achieved by using the free-carrier plasma dispersion ef-fect [17] by applying a reverse bias voltage across the p-n junction. By applying areverse bias to the junction, the effective index of the waveguide is changed, whichalso changes the resonance wavelength of the Fabry-Pe´rot cavity. Modulation isachieved by bringing the Fabry-Pe´rot cavity in and out of resonance, switching thelight at the outputs between an “on” state and an “off” state. The silicon slab oneither side of the waveguide is also doped so that there is an electrical connection toa highly-doped region. The highly-doped silicon region facilitates a low resistanceconnection between the tungsten vias, which are used to connect the copper metallayer to the doped silicon, and the p-n junction. Also, there are tapers at the inputand at the output of the modulator which converts the 450 nm wide strip waveg-uides used for routing to the rib waveguide used in the modulator. The modulatorswere fabricated at imec, Belgium, using the ISIPP25G platform [130].Table 4.1: Phase-shifted Bragg grating parameter variations.Parameter VariationsPeriod (Λ) 310 nm, 320 nm, 330 nm# Segments (N) 301, 401, 501Average width (W ) 450 nmCorrugation amplitude (∆W ) 40 nm, 60 nm, 80 nm, 100 nmDuty cycle (D) 50%Fill factor (Fpn) 100%, 50%42Input Reflect Through (a) (b) 60 nm 525 nm 1 µm n++ n p p++ 160 nm Silicide Cu electrode W vias Corrugations p n n+ p+ ΔWW ΛLLpnFigure 4.6: (a) Schematic of the quarter-wave phase-shifted Bragg gratingmodulator, including a zoomed-in view of the region near the phase-shift. (b) Schematic showing the design of the waveguide and the lateralp-n junction [3].In the remaining sections, measurement results for the modulator with Λ =310nm, ∆W = 100nm, W = 450nm, N = 501, D = 50%, and Fpn = 100% willbe presented. The modulator has a total length L = 155.465µm. Figure 4.7(a) isa microscope image of this modulator, which shows the Cu electrodes and probecontact pads and Figure 4.7(b) shows the mask layout of the modulator in the sameregion as the image in Figure 4.7(a). Figure 4.7(c) shows the layout of a taperthat converts the strip waveguide used for routing to the rib waveguide used in themodulator.43Probe contact pads Reflect Input Through Reflect Input Through (a) (b) (c) Figure 4.7: (a) Optical microscope image of the fabricated modulator [3]. (b)Layout of the modulator in the same region as the image in (a). (c) Lay-out of the input taper that converts from the 450 nm wide strip waveg-uide used for routing to the rib waveguide used inside the modulator.444.5 Layout and TestIn order to efficiently make use of the available chip space, a space-efficient devicelayout scheme [126] was used to place all 72 modulator variations on the mask.The devices were placed on the mask in 6 groups of 12 devices. The layout ofone group of 12 devices is shown in Figure 4.8(a). Within each group, the gratingcouplers (GCs) are placed on the left side and the devices are placed on the rightside. The routing waveguides for the devices are routed between the GCs for thedevices. As a result, the number of devices in a group is limited by the number ofrouting waveguides that can fit between two GCs. Also, the layout was designedso that there is sufficient space between the GCs and the probe contact pads sothat the fibre array, used to couple light into and out of the chip, and the electricalprobes do not interfere with each other while measuring the devices. The GCs,which have a pitch of 127 µm, are used along with the fibre array to couple lightinto and out of the chip. Within each group, there are also straight waveguide teststructures at the beginning and the end of the array of modulators. A zoomed-inview of the layout for one group is shown in Figure 4.8(b). For each device, a 2×1multi-mode interferometer (MMI) was placed before the input to the modulatorso that the modulator’s reflect-port spectral response could be measured. This isshown schematically in Figure 4.8(c). In order to conduct both passive optical andRF measurements of these devices, I built a measurement setup that uses an opticalprobe station based on the one described in [123]. An image of the entire setup isshown in Figure 4.9. The optical probe station, which is shown in Figure 4.10, isused to perform optical measurements. There is also other measurement equipmentin the setup which are used to characterize the electro-optical performance of thedevices.Within the optical probe station, the chip that is being measured is placed on topof a temperature-controlled pedestal. The temperature of the pedestal is controlledby a thermoelectric cooler and by using a thermistor placed inside the pedestal inorder to measure the temperature. A temperature controller uses feedback from thethermistor to set and stabilize the temperature by applying an appropriate currentto the thermoelectric cooler. The temperature-controlled pedestal is placed on a tiltstage, used to adjust the pitch and roll of the chip, and on a rotation stage, used to45adjust the yaw of the chip. The pedestal, tilt stage, and rotation stage are placed ona computer-controlled motorized 2-axis translation stage. The fibre array consistsof an array of polarization-maintaining fibres having a pitch of 127 µm, matchingthe pitch of the GCs on the chip. The fibre array is positioned very close to thesurface of the chip, typically about 10 µm above the surface of the chip in orderto obtain efficient coupling of light into and out of the chip. A vertically-mountedmanual translation stage is used to raise and lower the fibre array. There are alsoadjustments for each of the three degrees of rotational freedom of the fibre arrayi.e., pitch, roll, and yaw. These adjustments are controlled by two goniometers anda rotation stage that are mounted on the vertical translation stage. In order to makean optical measurement of a device on the chip, the chip is moved, using the 2-axistranslation stage, so that the fibre array is positioned over the GCs for the device.In order to measure the optical spectra of a device, an Agilent 81682A sweepablelaser and an Agilent optical power meter (such as an Agilent 81635A) in an Agilent8164A mainframe are used to perform a wavelength sweep and record the opticalpower at equally-spaced wavelength steps. There is also a Keysight N7714A tun-able laser for measurements requiring a high laser output power. To perform RFmeasurements, there is an HP 8510C 50 GHz vector network analyzer (VNA) toperform small signal measurements, and there is an Antirsu MP1800A bit error ratetester (BERT) used for doing large signal measurements. An Agilent 86100A digi-tal communications analyzer (DCA) mainframe with an Agilent 83484A samplingoscilloscope plugin is used for measuring eye diagrams. There is a probe posi-tioner, which is mounted on a platform next to the pedestal, onto which a 40 GHzGS probe is placed. The GS probe is used to apply electrical signals to the devicein order to characterize both its DC and RF performance. A list of all of thesecomponents can be found in Table 4.2.Additionally, I developed an open sourced software package written in Python,called pyOptomip [131], which is used to control the setup and perform measure-ments. The software allows for performing spectral response measurements usingAgilent tunable lasers and power meters. It also controls the translation stage andcan perform automatic optical measurements of devices on a chip. There is also agraphical user interface so that the measurements can be easily controlled.46Input Reflect Through 2×1 MMI Bragg modulator (a) (b) (c) 127 µm 127 µm Figure 4.8: (a) Image of the mask layout for a group of 12 modulators inwhich an efficient device layout scheme was used to minimize thegroup’s footprint. (b) Zoomed in view of the mask layout in (a) show-ing the efficient waveguide routing scheme. (c) Schematic showing thelayout of the device [3].471 6 4 5 2 3 Figure 4.9: Picture of the entire measurement setup. Descriptions for the la-beled components are in Table 4.2.17 12 9 16 8 7 15 11 10 13 14 Figure 4.10: Close-up picture of the optical probe station. Descriptions forthe labeled components are in Table 4.2.48Table 4.2: List of components used in the measurement setup.Number Description1 Optical probe station2 Agilent 8164A mainframe3 Keysight N7714A4 Anritsu MP1800A BERT5 Agilent 86100A DCA6 HP 8510C VNA7 40 GHz GS probe8 Fibre array and holder9 Temperature controlled pedestal10 Pedestal tilt adjustment stage11 Pedestal rotation adjustment stage12 2-axis translation stage13 Two goniometers to adjust fibre array rotation14 Rotation stage to adjust fibre array rotation15 Linear translation stage for vertical fibre array movement16 Microscope and camera17 Probe positioner4.6 Measurement ResultsIn this section, the measurement results from both a passive and active characteri-zation of the modulator are presented.4.6.1 Passive Measurement ResultsFigure 4.11 shows both the through- and reflect-port spectral responses of the mod-ulator as well as the spectral response of a straight waveguide test structure, which49had routing waveguides of similar length to those used for the modulator. We be-lieve that the ripples present in the modulator’s spectral responses are due to anunintended Fabry-Pe´rot resonance formed between the MMI and the input to themodulator. These ripples can be mitigated in future designs by designing the tapersat the input and output of the device [shown in Figure 4.7(c)] to ensure that thereare low back reflections at the transition between the tapers to the rib waveguideused in the modulator. We believe that the ripples can also be mitigated by usinga power splitter (e.g., a Y-branch or an MMI) that has lower back reflections ascompared to the MMI used in the device presented here.By curve fitting the grating’s through-port spectral response, the grating’s cou-pling strength, κ , and its cavity loss, α can be estimated. In order to estimate κand α , a non-linear least squares curve fitting algorithm was used to fit Eq. 4.27to the measured normalized through-port spectral response, where κ and α werethe fit parameters. For curve-fitting purposes, neff,avg (as a function of wavelength)1520 1525 1530 1535 1540Wavelength (nm)−35−30−25−20−15−10Power(dBm)ThroughReflectReference waveguideFigure 4.11: Measured through- and reflect-port spectral responses of themodulator. The spectral response of a reference straight waveguideis also shown.501520 1525 1530 1535 1540Wavelength (nm)−25−20−15−10−50Normalizedpower(dB)Through - MeasuredReflect - MeasuredThrough - Curve fitReflect - CalculatedFigure 4.12: Measured normalized through- and reflect-port spectral re-sponses of the modulator. Also shown are the curve fitted through-portand calculated reflect-port spectral responses.was simulated using MODE Solutions eigenmode solver by Lumerical Solutions,Inc. From fitting, κ was determined to be 25600 m−1 and α was determined to be1044 m−1 (45.3 dB/cm). Figure 4.12 shows both the measured normalized through-and reflect-port spectral responses of the modulator as well as the curve-fit through-port spectral response. Also shown is the calculated reflect-port spectral response(using the fitted κ and α values), which was shifted vertically by adding 1.87 dB ofloss relative to the through-port spectral response (to account for loss due to split-ting at the MMI, routing waveguide losses, and losses in the GCs) in order to alignit to the measured spectral response. The measured reflect-port spectral responseideally would have about 3 dB additional loss as compared to the through-portspectral response, however, due to variations in the reflect-port and through-portGC losses, the additional loss was only 1.87 dB.511529.0 1529.2 1529.4 1529.6 1529.8 1530.0 1530.2Wavelength (nm)−24−22−20−18−16−14−12Power(dBm)5.84 dB0 V-1 V-2 V-3 VFigure 4.13: Measured spectral response of the reflect-port notch with vari-ous reverse bias voltages applied to the device.4.6.2 Active Measurement ResultsThe DC modulation performance of the device was characterized by measuringthe spectral response of the modulator while varying the reverse bias voltage. Thereflect-port spectral response has a sharp notch, which is favourable for modula-tion, therefore, for all the results presented, the modulated output signal was takenfrom the reflect port. Figure 4.13 shows the spectral response near the reflect-portnotch at bias voltages ranging from 0 V to −3 V. The results show that the spec-trum shifts by 102 pm with −3 V being applied, giving a static modulation ER of5.84 dB at a wavelength of 1529.62 nm. The quality factor of the resonator was de-termined, using Eq. 4.37, to be about 5960. The through port can also be used formodulation, however, the static modulation ER at the same wavelength, with thesame voltage being applied, was only 2.33 dB. The static modulation ER, whenusing the reflect port, could be increased by designing the Fabry-Pe´rot cavity sothat it is closer to being critically coupled. This can be accomplished, for example,by reducing the peak reflectivity of the Bragg gratings, which can be implemented52by reducing the length of the gratings or by reducing the coupling strength of thegratings (i.e., κ), since reducing either would reduce the reflectivity of the gratings(see Eq. 4.23). Doing this could also result in a decrease in the modulator’s Q fac-tor, since Qc1 and Qc2 would decrease. However, this could also give the modulatora higher optical loss in the “on” state at the operating wavelength. Another way toincrease the static modulation ER would be to reduce the cavity losses. This couldbe accomplished, for example, by using a lower carrier concentration in the p-njunction. However, reducing the carrier concentration would decrease the changein refractive index from the free-carrier plasma dispersion effect, and, therefore,would reduce the resonance wavelength shift, counteracting the increased staticmodulation ER gained by being closer to critical coupling. It would also increasethe modulator’s Q factor, especially if Q was bring limited by the cavity losses,since a reduction in the losses would cause Qi to increase. An increase in Q couldlimit the modulator’s speed if the speed was photon-lifetime-limited.The high-speed performance of the modulator was characterized by first mea-suring its small-signal electro-optic |S21|. A diagram of the setup used for thismeasurement is shown in Figure 4.14(a). Light from a tunable laser source (TLS)was input into the device. The signal from a VNA was passed through a 40 GHzbias tee, which was used to apply a bias voltage. A 40 GHz ground-signal probewas used to apply the signal to the device. A 50 GHz photodetector (PD) was usedto convert the optical signal to an electrical signal prior to entering port 2 of theVNA. Figure 4.15 shows the measured |S21| results for bias voltages ranging from0 V to −3 V. At each bias voltage, the wavelength was chosen so that the devicewas operating in the linear regime. At a 0 V bias, the 3-dB bandwidth was 21 GHzand when the bias voltage was −3 V, the 3-dB bandwidth increased to 26.5 GHz.The electrical S11 was also measured, using a 0 V bias, and was fitted to a lumped-element circuit model of the modulator [47]. The measured and fitted S11 resultsare shown in Figure 4.16 and the circuit model is shown in Figure 4.17. In thecircuit model, Cp is the probe contact pad capacitance, Rs is the series resistancefrom the electrode to the p-n junction, Cj is the p-n junction’s capacitance, Cox isthe capacitance to the Si substrate, and Rsi is the resistance of the Si substrate. Theresults from the circuit model fitting are shown in Table 4.3.The large-signal performance of the modulator was also investigated. A dia-53Bragg modulator TLS PD VNA Port 1 Port 2 +	  -­‐	  Bias Tee DC Source EDFA VOA Bragg modulator DCA ED TLS λ=1529.62 nm  PD PPG OTF (a) (b) Figure 4.14: Diagram showing the experimental setup used to measure (a) themodulator’s |S21| and (b) the eye diagrams and BERs of the modulator[3].540 5 10 15 20 25 30 35 40Frequency (GHz)−14−12−10−8−6−4−20Normalized|S 21|(dB)0 V-1 V-2 V-3 VFigure 4.15: Electro-optic |S21| of the modulator measured with various re-verse bias voltages ranging from 0 V to −3 V being applied. Thedashed grey line indicates the −3 dB level.Table 4.3: Circuit model fitting results.Parameter ValueCp 4.25 fFCox 69.4 fFRsi 1.70 kΩCj 99.9 fFRs 51.6Ω550 5 10 15 20 25 30 35 40Frequency (GHz)9876543210S 11Magnitude(dB)9080706050403020100S 11Phase(deg)Magnitude - MeasuredMagnitude - FitPhase - MeasuredPhase - FitFigure 4.16: Measured S11 magnitude and phase at 0 V bias as well as thefitted S11 magnitude and phase.CpCoxRsi RsCjFigure 4.17: Circuit model of the modulator used for fitting the S11.gram of the setup used for these measurements is shown in Figure 4.14(b). First,the modulator’s eye diagrams were measured at data rates of 12.5 Gb/s, 20 Gb/s,25 Gb/s, and 32 Gb/s. The TLS was set to output at a wavelength of 1529.62 nm.The NRZ 231-1 PRBS electrical signals used for this measurement were gener-ated using a pulse pattern generator (PPG) which applied a 3 Vpp signal with a-1.5 V bias (the PPG was set to apply a 1.5 Vpp signal to a 50Ω load, but sincethe modulator has a high impedance, the Vpp applied to the modulator was about563 V). The modulated optical signal was sent through an erbium doped fibre am-plifier (EDFA) followed by a bandpass optical tunable filter (OTF), to reduce thenoise caused by amplified spontaneous emission from the EDFA. A variable op-tical attenuator (VOA) was used to control the amount of optical power receivedby a 22 GHz photodetector (PD). For measuring eye diagrams, the PD was con-nected to a 50 GHz DCA. The measured eye diagrams are shown in Figure 4.18.At 12.5 Gb/s and 20 Gb/s, the eyes are open with ERs of 3.96 dB and 4.11 dB, re-spectively. At 25 Gb/s, the eye begins to close, and has an ER of 3.78 dB, and at32 Gb/s the eye is more closed and has an ER of 3.26 dB. The average energy perbit for the modulator, which is given by Ebit = (CjV 2pp)/4 [61], can be calculatedusing the fitted value of Cj from the S11 measurement. Using Vpp = 3V, Ebit is225 fJ/bit. The Ebit of our modulator is higher than that of the MDM in [68], whichhas the lowest Ebit to date of ∼1 fJ/bit. The MDM in [68] used an advanced fab-rication process which allowed the creation of vertical p-n junctions, which gavethe modulator a resonance wavelength shift-per-volt of 250 pm/V. This is muchhigher than the resonance wavelength shift-per-volt of 34 pm/V that our modulatorhas. The Ebit of our modulator would therefore be improved by using a verticalp-n junction, since the voltage required to get the same resonance wavelength shiftwould be reduced.To further characterize the modulator, its BER was measured using the setupshown in Figure 4.14 with the PD instead connected to an error detector (ED).The BERs were measured using both 27-1 and 231-1 PRBS patterns at 12.5 Gb/s,20 Gb/s, and 25 Gb/s while varying the received power at the PD using the VOA. Inall cases, the output voltage of the PPG was set to 1.5 Vpp. The results of the BERmeasurements are shown in Figure 4.19. A BER less than 10-12 was obtained atdata rates up to 25 Gb/s, using a 27-1 PRBS pattern, and at data rates up to 20 Gb/s,using a 231-1 PRBS pattern. At 25 Gb/s, using a 231-1 PRBS pattern, a BER lessthan 10-10 was achieved.57(a) (b) (c) 12.5 Gb/s 20 Gb/s 25 Gb/s (d) 32 Gb/s ER: 3.96 dB  ER: 4.11 dB  ER: 3.78 dB  ER: 3.26 dB  Figure 4.18: Measured eye diagrams of the modulator at: (a) 12.5 Gb/s, (b)20 Gb/s, (c) 25 Gb/s, (d) 32 Gb/s [3].0 2 4 6 8 10 12Received optical power (dBm)No errors−12−10−8−6−4−2log10(BER)12.5 Gb/s (27−1)20 Gb/s (27−1)25 Gb/s (27−1)12.5 Gb/s (231−1)20 Gb/s (231−1)25 Gb/s (231−1)Figure 4.19: Measured BERs versus received optical power at the PD at datarates of 12.5 Gb/s, 20 Gb/s, and 25 Gb/s using both 27-1 and 231-1PRBS patterns.584.7 SummaryIn this chapter, a quarter-wave phase-shifted Bragg grating modulator, which wasfabricated on SOI using 193 nm optical lithography, was demonstrated. First wedescribed the theory of operation for uniform and phase-shifted Bragg gratings.Then, we described the modulator design and presented measured spectral re-sponses of the modulator. We then showed that open eye diagrams were achievedat data rates of up to 32 Gb/s. Also, BERs of less than 10-12 were achieved up to25 Gb/s using a 27-1 PRBS pattern and a BER of less than 10-10 was achieved usinga 231-1 PRBS pattern at 25 Gb/s.59Chapter 5High-Speed Data TransmissionThrough SiliconContra-Directional GratingCoupler Optical Add-DropMultiplexersSilicon photonics optical interconnects using WDM are potential solutions tothe increasing demand for high data rates. Silicon contra-DCs, using gratings,have been investigated for use as add-drop filters in on-chip WDM systems[104, 107, 133–136]. Compared to ring resonator based filters, contra-DC-basedfilters do not have periodic spectral responses [136], however, they typically havelarger bandwidths making them suitable for coarse WDM applications [104]. Inthis section, we demonstrate data transmission at 12.5 Gbit/s through an SOIcontra-DC OADM.5.1 Contra-Directional CouplersA contra-DC is similar to a Bragg grating in the sense that a periodic perturbationis used to couple light from one propagating mode to another. However, unlike in60a Bragg grating, where the mode coupling is from the forward propagating modein a waveguide to the backward propagating mode in the same waveguide, in acontra-DC, the mode coupling can be from the forward propagating mode in awaveguide to the backward propagating mode in a second, adjacent waveguide. Adiagram of the contra-DC design being investigated in this section is shown in Fig-ure 5.1. In this design, the contra-DC was formed by adding side-wall corrugationsto the strip waveguides in the coupling region. The waveguides had a height of 220nm and there was an oxide cladding. There were also anti-reflection gratings, thatwere out of phase with the corrugations in the coupling region, which are there tosuppress intra-waveguide Bragg reflections [104], which will be discussed furtherbelow. In a contra-DC, the light propagating in waveguide A will strongly coupleto the backward propagating mode in waveguide B (i.e., inter-waveguide coupling)when the phase matching condition given by βa +βb = m 2piΛ is met [121]. Here,βa and βb are the propagation constants of the supermodes in waveguides A and Bwithout gratings, respectively, Λ is the grating period, and m = 1 since first-ordergratings are being used. The propagation constants are given byβa =2pineff,a(λ0)λ0(5.1)andβb =2pineff,b(λ0)λ0, (5.2)where neff,a and neff,b are the wavelength-dependent effective indices of the super-modes in waveguides A and B, respectively, and λ0 is the wavelength. Withinwaveguides A and B, there can also be intra-waveguide coupling, where the peri-odic perturbations can cause wavelength-selective reflections, like in a Bragg grat-ing. This will occur when the phase matching condition for a Bragg grating is met,given by 2βa = 2piΛ in waveguide A and given by 2βb = 2piΛ in waveguide B.The device being investigated in this section has the parameters shown in Ta-ble 5.1. The inter-waveguide and intra-waveguide phase matching conditions forthis device were simulated by plotting the effective indices for waveguides A andB, the average of the effective indices for waveguides A and B, and λ0/(2Λ) asfunctions of wavelength, as shown in Figure 5.2. The wavelengths at which the ef-61Input Drop Through Add Waveguide A Waveguide B LcdWaWb ΔWa ΔWaΔWbΔWb ΛGFigure 5.1: Diagram of the contra-DC OADM showing a zoom-in of the cou-pling region (similar to the design used in [137]).fective index curves and the λ0/(2Λ) curve intersect are the wavelengths at whichphase matching occurs. The MODE Solutions eigenmode solver, from LumericalSolutions, Inc., was used to simulate neff,a and neff,b as functions of wavelength.The wavelength at which inter-waveguide coupling occurs, λd , is 1532.14 nm,the wavelength at which intra-waveguide coupling in waveguide A occurs, λa, is1504.38 nm, and the wavelength at which intra-waveguide coupling in waveguideB occurs, λb, is 1562.24 nm5.2 Measurement ResultsThe contra-DC OADM, with the design parameters listed in Table 5.1, was fab-ricated using electron beam lithography at the University of Washington [138].Figure 5.3(a) shows the measured spectral response of the contra-DC OADM andFigure 5.3(b) shows a zoomed-in view of the spectral response near the through-port stopband. The stopband is centred at a wavelength of 1536.4 nm (i.e., λd forthe fabricated device) and has a through-port suppression (i.e., the through-port621500 1520 1540 1560 1580 1600Wavelength (nm)2.252.302.352.402.452.502.552.60E↵ectiveindexλb λd λa neff,aneff,bneff,a + neff,b2λ02ΛFigure 5.2: Plot showing the phase-matching condition for the contra-DC. λaand λb are the intra-waveguide Bragg wavelengths for waveguides Aand B, respectively and λd is the wavelength at which inter-waveguidecoupling occurs.Table 5.1: Contra-DC design parameters.Parameter ValueWa 450 nmWb 550 nm∆Wa 30 nm∆Wb 40 nmG 140 nmΛ 312 nmLcd 156 µm63ER) of about 20 dB. The drop-port spectral response has a 3 dB bandwidth (BW)of about 4.5 nm and has a sidelobe suppression (SS) of about 4.4 dB, which wasmeasured as the difference between the power at 1536.4 nm and the maximumsidelobe power. The sidelobe suppression can be increased by using apodization[107]. The filter also has some co-directional coupling from the input port to theadd port. The amount of co-directional power coupling is about 3% in the regionnear the stopband. In Figure 5.3, the approximate wavelengths at which intra-waveguide coupling occurs in waveguides A and B (i.e., λa and λb, respectivelyfor the fabricated device) are labeled. However, due to the use of anti-reflectionsgratings, the reflections have almost been eliminated because the reflections fromthe gratings in the coupling region are pi out of phase with the reflections from theanti-reflection gratings, causing the reflected light to interfere destructively [122].5.2.1 Experimental SetupTo characterize the contra-DC OADM’s performance, we used the setup shown inFigure 4.9. A schematic of the experiment is shown in Figure 5.4. The experimenthad two separate optical paths; the input-to-drop path and the add-to-through path.The input-to-drop path used an Agilent 81960A laser and the add-to-through pathused an Agilent N7711A laser. The other optical components used in the two paths(modulators, optical fibres, EDFAs, OTFs, and optical receivers) were the same.In each path, the tunable lasers were set to output light at a wavelength of 1536.4nm and an output power of 8 dBm. The light was coupled into a 10 GHz com-mercial lithium niobate MZM, which had a polarization-maintaining (PM) fibre atits output. A 12.5 Gb/s NRZ 231− 1 PRBS signal was generated for each opticalpath using a PPG. To bias the modulators, the NRZ signal was passed through a15 GHz bias-tee for the add path and a 26 GHz bias-tee for the drop path beforegoing to the modulators. Several metres of extra PM fibre were added after themodulator in the input-to-drop path (as compared to the add-to-through path) sothat the PRBS signals in the two optical paths would be uncorrelated. The modu-lated light was coupled in to and out of the chip through vertical grating couplers[139] using an array of PM fibres. The output signal was amplified using an EDFAand then passed through a tunable filter to suppress the noise from the EDFA. Theeye diagrams were measured using an optical receiver in a DCA.641500 1510 1520 1530 1540 1550 1560 1570 1580Wavelength (nm)50403020100Power(dBm)DropThroughCo-directionalλd λb λa 1525 1530 1535 1540 1545 1550Wavelength (nm)35302520151050Normalizedpower(dB)DropThroughBW SS ER (a) (b) Figure 5.3: (a) Measured spectral response of the filter and (b) spectral re-sponse of the filter near the stopband.65EDFA TLS 1 λ0=1536.4 nm MZI Modulator 1 Input Drop Through Add TLS 2 λ0=1536.4 nm MZI Modulator 2 Contra-DC OADM EDFA PPG DCA OTF +	   -­‐	  +	   -­‐	  Bias Tees 12.5 Gb/s PRBS 231-1 Figure 5.4: Schematic of the experiment used to characterize the contra-DCOADM’s performance.5.2.2 Data Transmission MeasurementsFigure 5.5 shows the measured eye diagrams for data transmitted at 12.5 Gb/sthrough the contra-DC OADM when the data is being dropped only, added only,and simultaneously added and dropped. Figures 5.5(a) and 5.5(d) show eye dia-grams of the data from the MZI modulators going to the input port and add portof the OADM, respectively, so that the signal quality at the output of the sys-tem can be compared to the signal quality of the data which is being input to theOADM. Figure 5.5(b) shows that when the OADM is dropping a signal only, thenthere is minimal distortion in the signal. However, when a signal is being addedand dropped at the same time, as shown in Figure 5.5(c), then the signal qual-ity of the dropped signal is reduced and the eye is less open. Figures 5.5(e) and5.5(f) show similar behaviours for the signal being added. Our results show thatdespite reduced signal qualities, the eyes remained open for both the added anddropped signals, demonstrating successful data transmission at 12.5 Gbit/s throughthis contra-DC OADM.Figure 5.6 shows the measured eye diagrams for data which has been dropped(with no other signal being input to the add port) from the contra-DC OADM before[Figure 5.6(a)] and after [Figure 5.6(b)] going through 25.26 km of Corning SMF-28TM single-mode fibre (see [140]). The two eyes have similar openings, which66(a) Input Drop Through Add Input Drop Through Add Input Drop Through Add Input Drop Through Add (b) (c) (d) (e) (f) MZI Modulator 1 MZI Modulator 2 Figure 5.5: Measured eye diagram of: (a) data from the MZI modulator priorto entering the filter’s input port; (b) data passing from the input portto the drop port when the device is only dropping the signal; (c) datapassing from the input port to the drop port while another signal is beingadded; (d) data from the MZI modulator prior to entering the filter’s addport; (e) data passing from the add port to the through port when thedevice is only adding a signal; (f) data passing from the add port to thethrough port while another signal is being dropped [4].shows that contra-DC OADMs have potential for use in applications which requiredata transmission through long lengths of fibre.(a) (b) Input Drop Through Add Input Through Add 25.26 km SMF Figure 5.6: Measured eye diagrams of the dropped signal (with no other sig-nal being input to the add port) from the contra-DC OADM (a) beforeand (b) after going through 25.26 km of single-mode fibre.675.3 SummaryWe have demonstrated successful data transmission at 12.5 Gb/s through acontra-DC OADM when it is only dropping a signal, only adding a signal, andsimultaneously adding and dropping signals at the same wavelength. Our resultsshow that OADMs based on contra-DCs can be a viable choice for use in siliconphotonic optical interconnects.68Chapter 6Summary, Conclusions, andSuggestions for Future Work6.1 Summary and ConclusionsIn this work, we have demonstrated a variety of novel designs and/or applicationsof silicon photonic devices. We demonstrated a biasing scheme for travelling-waveMZMs in which the DC bias voltage is applied separately from the RF signal. Us-ing this biasing scheme, there is no DC power consumption from the bias voltagein the termination resistor, which results in a lower overall power consumptionfor the modulator. Also, this scheme removes the need for a bias-tee circuit oran integrated level-shifter circuit at the RF input in order to apply the bias. As aproof-of-concept, we had fabricated a modulator which uses this biasing schemeand showed successful high-speed modulation up to 28 Gb/s. Using this design,the overall energy efficiency of optical interconnects using travelling-wave MZMscan be increased. We then proposed a novel modulator design in which an MRMis placed into each arm of an MZI. This design uses the sharp phase response ofa microring resonator near its resonance so that the light experiences a large phaseshift when a voltage is applied to the p-n junction phase shifters within the ring.By using ring resonators, large phase shifts can be achieved while the device hasa small footprint as compared to travelling-wave MZMs, where millimetre longphase shifters are required. We then used TCM theory to simulate the time-domain69response of the modulator. Device parameters extracted from devices that werepreviously fabricated on the IME silicon photonics platform were used as inputs tothe model in order to obtain a realistic simulation of the modulator’s performance.The parameter extraction and simulation methodology used here can also be usedwith other types of devices in order to realistically simulate their performances.Next, we demonstrated a novel modulator design which uses a quarter-wave phase-shifted Bragg grating. We had the modulator fabricated using the ISIPP25G fab-rication platform, which used 193 nm optical lithography, and we showed that thedevice has open eye diagrams up to 32 Gb/s. We also showed that using a 231-1PRBS pattern, the device has BERs of less than 10-12 at data rates of up to 20 Gb/sand has a BER of less than 10-10 at a data rate of 25 Gb/s. Lastly, we showeda contra-DC filter on SOI being used as an OADM. We experimentally showedthat the contra-DC OADM was able to successfully add and drop a signal at thesame wavelength using a data rate of 12.5 Gb/s with minimal signal degradation.Our results show that contra-DC OADMs have the potential to be used in opticalinterconnects that utilize coarse WDM.6.2 Suggestions for Future WorkIn the proof-of-concept travelling-wave MZM we measured to demonstrate thelow-power biasing scheme, only one signal electrode was modulated. In futureiterations of this design, both arms of the MZI can be modulated using this biasingscheme.In the simulations of our proposed modulator that uses MRM phase shifters,realistic process-dependent parameters were used to accurately simulate the mod-ulator’s performance, however, we have not compared our simulation results tomeasurement results from a fabricated modulator. Such a comparison would beuseful to confirm that the simulations that use realistic parameters accurately pre-dict the performance of fabricated devices. Also, in the device presented here, weused the drop-port output from the MRMs, which has a pi phase shift near reso-nance. The through port, which has a 2pi phase shift near resonance, can instead beused to obtain a larger phase shift for a given applied voltage. A detailed compari-son should be performed which looks at the trade-offs between modulation IL andmodulation ER for the two designs in order to determine which design is optimal.70For the phase-shifted Bragg modulator, the tapers at the input and output ofthe device (shown in Figure 4.7) that transition between the 450 nm strip waveg-uides (for routing) to the rib waveguide (in the modulator) should be re-designedso that the amount of back reflections are significantly reduced. Reducing the backreflections should reduce, or eliminate, the Fabry-Pe´rot ripples that are currentlypresent in the device’s spectral response. Also, the device should be further op-timized so that the ER of the notch in the reflect-port spectral response is higher,which would give the device a higher modulation ER. Another idea that can beexplored is to investigate the effect of reducing the p-n junction’s fill factor (i.e.,Fpn) on the device’s performance. When the device is on resonance, the light isconfined within the resonant cavity in and around the phase-shifted region and,as a result, a large portion of the electro-optical interaction between the light andthe p-n junction occurs within this region. Therefore, we expect that reducing Fpnwould not significantly impact the achievable wavelength shift for a given appliedvoltage. Reducing Fpn would also reduce the device’s capacitance which could re-sult in reduced power consumption. However, we expect that if Fpn is too small,then there would be a substantially reduced overlap between the p-n junction andthe light in the resonator, which at some point would have a detrimental effect onthe achievable wavelength shift. Therefore, we expect that for some Fpn, the powerconsumption would be minimized, however, the required drive voltage would behigher.The contra-DC OADM that we investigated used uniform gratings which hadthe same grating corrugation amplitude along the entire length of the device. Asa result, the spectral response had very large sidelobes which are not desirablein a WDM system because the sidelobes could cause crosstalk with neighbouringchannels. Apodization of the gratings, where the corrugation amplitude is reducednear the ends of the device, can be used to substantially reduce the sidelobes. Amulti-channel contra-DC OADM should be created which uses apodization on eachof the contra-DC filters. 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