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Silicon photonic switches for optical communication applications Lu, Zeqin 2017

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Silicon Photonic Switches for OpticalCommunication ApplicationsbyZeqin LuB. Eng., Shenzhen University, China, 2011M. A. Sc, Huazhong University of Science and Technology, China, 2013A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Electrical and Computer Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)September 2017c© Zeqin Lu 2017AbstractOptical switches are used for network reconfiguration in optical communi-cation systems. Silicon photonics is a low-cost and mature technology todevelop high-performance optical switches. This thesis is a theoretical andexperimental study on silicon photonic switches, featuring broadband, low-power, high-speed, and low-crosstalk performance.Broadband 3-dB couplers are fundamental building blocks for broadbandswitches based on Mach-Zehnder interferometer (MZI) structures. A broad-band 3-dB coupler, which has a 100 nm operation bandwidth with couplingimbalance being much less than its competitors, i.e., adiabatic couplers andmultimode interference couplers, has been theoretically designed and exper-imentally demonstrated.Switches using thermo-optic phase tuning typically have high power con-sumption. In this thesis, two methods to improve the tuning efficiency ofthermo-optic phase shifters have been investigated and employed: 1) us-ing thermal isolation structures and 2) using folded waveguides structures.Accordingly, thermo-optic switches with state-of-the-art, ultra-low powerconsumptions of down to 50µW/pi have been demonstrated.MZI switches using carrier injection phase tuning have high-speed per-formance but with a large switching crosstalk, due to the imbalanced tun-ing loss in the MZI structure. A novel carrier injection switch based on abalanced nested Mach-Zehnder interferometer (BNMZI) structure has beentheoretically proposed. The BNMZI switch has balanced tuning schemes andtherefore can be both high-speed and crosstalk-free. Besides, the switch hasthree switching states: cross, bar, and blocking.Polarization control is necessary for single-mode switches. A high per-formance polarization beamsplitter (PBS), which has a 120 nm operationiiAbstractbandwidth with modal isolations of more than 20 dB, has been designed anddemonstrated, and it can be used for polarization control for single-modeswitches.Characterizing fabrication variability and performing yield predictionfor photonic integrated circuits (PICs) are both challenging for photonicsdesigners. We have developed an accurate and cost-efficient characteriza-tion method for fabrication variations, which extracts waveguide dimensionvariations from the spectral response of a single racetrack resonator. In ad-dition, we have proposed a novel yield prediction method for PICs, which,for the first time in silicon photonics, is able to model the impacts of layout-dependent correlated manufacturing variations and take them into accountin circuit simulations.iiiLay SummaryData switches are critical components in optical communication networks.They are deployed to establish reconfigurable point-to-point optical linksaccording to the dynamic traffic request in networks. This thesis is devotedto develop high-performance optical data switches using a low-cost, well-developed silicon photonics technology.In terms of technical contributions, this research has developed buildingblocks for high-performance integrated optical switches, including a broad-band coupler, low-power phase shifters and a broadband polarization beam-splitter, and has proposed a technical solution for switching crosstalk sup-pression. In terms of design methodology contributions, this research hasdeveloped methods to analyze silicon photonics manufacturing variationsand yield.ivPrefaceThe content of this thesis is mostly based on the publications listed below,which resulted from collaborations with other researchers. Note that onlypublications directly arising from the work presented in this thesis are listedhere. A complete list of publications is given in Appendix A. It should also benoted that many devices demonstrated in this thesis have been re-designedor updated in order to improve their performance. Hence, many of theexperimental results presented in this thesis are original and do not referencethe similar results that were previously published.1. Z. Lu, H. Yun, Y. Wang, Z. Chen, F. Zhang, N. Jaeger, and L.Chrostowski, “Broadband silicon photonic directional coupler usingasymmetric-waveguide based phase control,” Optics Express, vol. 23,3795-3808 (2015).I conceived the idea, conducted the device design, performed the mea-surements and data analysis, and drafted the manuscript. H. Yun andF. Zhang assisted the measurements. L. Chrostowski and N. Jaegersupervised the project. All authors commented on the manuscript.Location: Chapter 2.2. Z. Lu, K. Murray, H. Jayatilleka, L. Chrostowski, “Michelson Inter-ferometer Thermo-Optic Switch on SOI With a 50-µW Power Con-sumption,” IEEE Photonics Technology Letters, vol. 27, 2319-2322(2015).I conceived the idea of combining thermal isolation, folded waveg-uides, and Michelson interferometer structure to improve tuning effi-ciency. K. Murray contributed the idea of using dissimilar waveguidesvPrefacefor crosstalk suppression. I conducted the device design, performedthe measurements and data analysis, and drafted the manuscript. K.Murray assisted the measurements and microscope images. H. Jay-atilleka helped edit the final draft of the manuscript. L. Chrostowskisupervised the project.Location: Chapter 3.3. K. Murray, Z. Lu, H. Jayatilleka, and L. Chrostowski, “Dense dis-similar waveguide routing for highly efficient thermo-optic switches onsilicon,” Opt. Express, vol. 23, 19575-19585 (2015).K. Murray designed the switch, performed measurements on a firstbatch wafer, and drafted the manuscript based on the results. I pro-vided feedback on the switch designs and assisted the measurementson the first batch wafer. I performed measurements on a second batchwafer and obtained the measurement data presented in Fig. 3.9 of thisdissertation. L. Chrostowski supervised the project. H. Jayatillekahelped edit the final draft of the manuscript.Location: Chapter 3.4. Z. Lu, D. Celo, H. Mehrvar, E. Bernier, and L. Chrostowski, “Highperformance silicon photonic tri-state switch based on balanced nestedMach-Zehnder interferometer”, Scientific Reports, to be published (2017).I conceived the idea, modeled the device, performed data analysis, anddrafted the manuscript. H. Mehrvar assisted the modelling of the 8×8switch matrix. L. Chrostowski supervised the project. All authorsprovided feedback on the manuscript.Location: Chapter 4.5. Z. Lu, Y. Wang, F. Zhang, N. A. F. Jaeger, and L. Chrostowski,“Wideband silicon photonic polarization beamsplitter based on point-symmetric cascaded broadband couplers,” Optics Express, vol. 23,29413-29422 (2015).viPrefaceI conceived the idea, designed the devices, performed data analysis,and drafted the manuscript. Y. Wang assisted my layout design andprovided broadband optical I/O solutions. F. Zhang conducted themeasurements. L. Chrostowski supervised the project. All authorshelped edit the paper draft.Location: Chapter 5.6. Z. Lu, J. Jhoja, J. Klein, X. Wang, A. Liu, J. Flueckiger, J. Pond,and L. Chrostowski, “Performance prediction for silicon photonics in-tegrated circuits with layout-dependent correlated manufacturing vari-ability”, Optics Express, vol. 25, 9712-9733 (2017).In the manufacturing characterization project presented in Ch. 6, L.Chrostowski proposed the method of extracting waveguide dimensionvariations (i.e., ∆w and ∆h) of a Micro-ring resonator (MRR) basedon its resonance wavelength variation and group index variation (i.e.,∆λ and ∆ng), and supervised the project. I implemented the extrac-tion model, studied the extraction accuracy, designed the layout forcharacterization, and performed measurements and data analysis. J.Jhoja assisted the measurements.In the yield prediction project presented in Ch. 7, I proposed thesimulation approach, developed the virtual wafer model and someof the component compact models, and performed numerical simu-lations and data analysis. J. Jhoja implemented the GUI interfaceof the Monte Carlo simulation. X. Wang contributed to the direc-tional coupler compact model for the Monte Carlo simulation. L.Chrostowski suggested the virtual wafer approach, programmed theKlayout-INTERCONNECT co-simulation platform, and supervisedthe project.I drafted the manuscript. All authors helped edit the paper draft.Location: Chapter 6 & 7.viiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of Abbreviation . . . . . . . . . . . . . . . . . . . . . . . . . . xxiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Background and Motivations . . . . . . . . . . . . . . . . . . 11.2 Silicon Photonic Switches . . . . . . . . . . . . . . . . . . . . 61.2.1 Switching Elements . . . . . . . . . . . . . . . . . . . 61.2.2 Phase Tuning Schemes . . . . . . . . . . . . . . . . . 81.2.3 Performance Metrics . . . . . . . . . . . . . . . . . . 111.2.4 Remaining Issues . . . . . . . . . . . . . . . . . . . . 141.3 About This Thesis . . . . . . . . . . . . . . . . . . . . . . . . 151.3.1 Objectives and Contributions . . . . . . . . . . . . . . 151.3.2 Thesis Organization . . . . . . . . . . . . . . . . . . . 16viiiTable of Contents2 Broadband 3-dB Couplers for Broadband Switching . . . . 182.1 Broadband 3-dB coupler Designs . . . . . . . . . . . . . . . . 192.1.1 Schematic . . . . . . . . . . . . . . . . . . . . . . . . 192.1.2 Design Principle . . . . . . . . . . . . . . . . . . . . . 212.1.3 Corner Analysis . . . . . . . . . . . . . . . . . . . . . 252.1.4 Characterization Results . . . . . . . . . . . . . . . . 252.2 Broadband Mach-Zehnder Interferometer Switch . . . . . . . 272.2.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . 272.2.2 Characterization Results . . . . . . . . . . . . . . . . 283 Ultra-Low Power Thermo-Optic Switches . . . . . . . . . . 313.1 Design of Ultra-Low Power Thermo-Optic Phase Shifter . . . 323.2 Ultra-Low Power Thermo-Optic On/Off Switches . . . . . . 343.2.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . 343.2.2 Characterization Results . . . . . . . . . . . . . . . . 363.3 Ultra-Low Power Thermo-Optic Cross/Bar Switches . . . . . 403.3.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . 403.3.2 Characterization Results . . . . . . . . . . . . . . . . 403.4 Breakdown Test . . . . . . . . . . . . . . . . . . . . . . . . . 414 Crosstalk-free Carrier Injection Tri-State Switches . . . . 444.1 Switch Design . . . . . . . . . . . . . . . . . . . . . . . . . . 454.1.1 Schematic . . . . . . . . . . . . . . . . . . . . . . . . 454.1.2 Operation Principles . . . . . . . . . . . . . . . . . . 464.1.3 Carrier Injection Phase Shifter Design . . . . . . . . . 504.2 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.3 Crosstalk Suppression Functionality . . . . . . . . . . . . . . 574.3.1 Crosstalk Suppression for Partially-Loaded Switches . 584.3.2 Crosstalk Suppression for Fully-Loaded Switches . . . 595 Polarization Control for Switches . . . . . . . . . . . . . . . . 625.1 Broadband Polarization Beamsplitter . . . . . . . . . . . . . 645.1.1 Principles . . . . . . . . . . . . . . . . . . . . . . . . . 655.1.2 Device Design . . . . . . . . . . . . . . . . . . . . . . 68ixTable of Contents5.1.3 Characterization Results . . . . . . . . . . . . . . . . 725.2 Polarization Control for Switches using Polarization Beam-splitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756 Wafer-Scale Manufacturing Variation Characterization . . 776.1 Characterization Methodology . . . . . . . . . . . . . . . . . 786.1.1 Principle . . . . . . . . . . . . . . . . . . . . . . . . . 786.1.2 Characterization Errors . . . . . . . . . . . . . . . . . 836.2 Characterization Results . . . . . . . . . . . . . . . . . . . . 846.2.1 Within-Die Variations . . . . . . . . . . . . . . . . . . 856.2.2 Within-wafer Variations . . . . . . . . . . . . . . . . . 896.2.3 Literature Results . . . . . . . . . . . . . . . . . . . . 896.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 917 Layout-Dependent Yield Prediction for Photonics IntegratedCircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 937.1.1 Approach . . . . . . . . . . . . . . . . . . . . . . . . . 937.1.2 Simulation Flow Chart . . . . . . . . . . . . . . . . . 947.2 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 977.2.1 Virtual Wafer Model . . . . . . . . . . . . . . . . . . 977.2.2 Parameterized Component Models . . . . . . . . . . . 1007.3 Yield Prediction for Mach-Zehnder Interferometer Switches . 1047.3.1 Switch Layout . . . . . . . . . . . . . . . . . . . . . . 1047.3.2 Input Parameters for Manufacturing Variability . . . 1057.3.3 Yield Prediction Results . . . . . . . . . . . . . . . . 1067.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1108 Conclusion and Future Work . . . . . . . . . . . . . . . . . . 1118.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1118.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118xTable of ContentsAppendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132A Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132A.1 Patents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132A.2 Journal Publications . . . . . . . . . . . . . . . . . . . . . . . 132A.3 Conference Proceedings . . . . . . . . . . . . . . . . . . . . . 134B Derivation of the Transfer Functions of a MZI Switch . . 137C Derivation of Coupling Ratios Extractions for 2×2 Couplers 140xiList of Tables3.1 List for the fabricated on/off switches . . . . . . . . . . . . . 363.2 Performance comparison for the fabricated on/off switches . . 394.1 Phase tuning for the switching states of BNMZI switch. . . . 504.2 Performance of an example BNMZI switch with κ2 = 0.48and Api = 0.8613. . . . . . . . . . . . . . . . . . . . . . . . . . 586.1 Statistical results for the characterized variations for all ofthe wafer dies. . . . . . . . . . . . . . . . . . . . . . . . . . . 886.2 Statistical results for the characterized variations across the200-mm-wafer. . . . . . . . . . . . . . . . . . . . . . . . . . . 896.3 Literature results for wafer-to-wafer fabrication variations . . 906.4 Literature results for within-wafer fabrication variations . . . 907.1 Input parameters for the virtual wafer model . . . . . . . . . 1067.2 Statistical results for the phase errors at 1550 nm for switchdesigns with d=25 µm, d=50 µm, and d=100 µm. . . . . . . 1108.1 Comparisons of high-performance 3-dB couplers demonstratedon the 220 nm SOI platform. . . . . . . . . . . . . . . . . . . 1138.2 Summary of SOI based thermo-optic switches that were ex-perimentally demonstrated in recent years. . . . . . . . . . . . 1148.3 Summary of representative, high-performance PBSs demon-strated on SOI platforms. . . . . . . . . . . . . . . . . . . . . 114xiiList of Figures1.1 (a) Long-haul telecommunication architecture; (b) short-reachdata center communication architecture. . . . . . . . . . . . . 11.2 (a) Diagram for an electrical switch; O/E: optical to electricalconversion; E/O: electrical to optical conversion; (b) diagramfor an optical switch. . . . . . . . . . . . . . . . . . . . . . . . 31.3 Cross section schematic of a typical Silicon-on-Insulator (SOI)wafer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 A 2×2 Mach-Zehnder interferometer switch. (a) Schematic ofthe switch; (b) switching states; (c) and (d) are simulatedspectral responses at the cross and bar state, respectively, fora particular MZI switch design. . . . . . . . . . . . . . . . . . 61.5 An example micro-ring resonator (MRR) switch. (a) Schematicof the switch; (b) spectral responses; (c) switching paths. . . 81.6 Cross section schematics of SOI phase shifters. (a) Carrierdepletion phase shifter; (b) carrier injection phase shifter; (c)thermo-optic phase shifter using a metal heater; (d) thermo-optic phase shifter using a resistive heater integrated in a ribwaveguide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.7 Cross state extinction ratio (ER) of an Mach-Zehnder inter-ferometer (MZI) switch versus the coupling ratios (κ2 and t2)of its 2×2 couplers. Inset illustrates the κ2 and t2 parametersfor the 2× 2 coupler. . . . . . . . . . . . . . . . . . . . . . . 121.8 Diagram that shows the 126 channels within a 100 nm band-width that are used in DWDM applications for a channelspacing of 100 GHz. . . . . . . . . . . . . . . . . . . . . . . . 12xiiiList of Figures2.1 (a) Schematic for a photonic directional coupler; (b) perfor-mance of a directional coupler design. The coupling lengthis 17.5 µm. The coupler waveguides are 500 nm wide by 220nm height, and are separated by a 200 nm gap. . . . . . . . 192.2 (a) Schematic of the proposed broadband 3-dB coupler; (b)cross section schematic of the directional coupler (DC) seg-ment; (c) cross section schematic of the phase shifter segment. 202.3 (a) Supermode profiles in directional couplers; (b) Supermodeprofiles in phase shifter. wg a and wg b refer to waveguide aand waveguide b, respectively. . . . . . . . . . . . . . . . . . . 222.4 Transfer matrix method (TMM) simulation results for anoptimized device with L1 = 33 µm, L2 = 0.55 µm, andL3 = 15 µm. (a) Phase difference of the symmetric andanti-symmetric modes; (b) coupling ratios versus operationwavelength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.5 (a) Broadband 3-dB coupler design with s-bent waveguides asinput and output ports; (b) FDTD simulation configuration;(c) FDTD simulation results. . . . . . . . . . . . . . . . . . . 242.6 Corner analysis for the broadband 3-dB coupler design. (a)Process corners; (b) corner analysis results for the couplingimbalance, |κ2 − t2|. . . . . . . . . . . . . . . . . . . . . . . . 252.7 Block diagram illustrating the indirect measurement. . . . . . 262.8 (a) Measured spectrum for the MZI circuit; (b) extractedcoupling ratios of the fabricated broadband 3-dB couplers. . . 272.9 A 2×2 broadband MZI switch design. (a) Switch schematic;(b) INTERCONNECT simulation; (c) simulated cross stateperformance; (d) simulated bar state performance. . . . . . . 292.10 A fabricated 2×2 broadband MZI switch. (a) Optical im-age for the switch; (b) measured cross state performance; (c)measured bar state performance. Data in (b) and (c) werecalibrated using a pair of GCs connecting by a short waveguide. 30xivList of Figures3.1 Schematics for the proposed ultra-low power phase shifter.(a) Cross section; (b) top view. . . . . . . . . . . . . . . . . . 323.2 Heat transport modelling results for thermo-optic phase shifterswith tuning power of 1mW/m. (a) A proposed design withthermal isolation structure; (b) a regular design without ther-mal isolation structure. . . . . . . . . . . . . . . . . . . . . . . 333.3 Maximum coupling at 1550 nm between two waveguides withdissimilar widths. Waveguide thicknesses are both 220 nm. . 343.4 An ultra-low power Michelson interferometer on/off switch.(a) Schematic of the switch; (b) block diagrams for switchingstates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.5 Optical images for the fabricated ultra-low power thermo-optic on/off switches. (a) A switch without thermal isolationstructure; (b) a switch with thermal isolation structure. . . . 373.6 Block diagram illustrating the measurement setups. (a) Spec-trum characterization; (b) switching speed characterization. . 373.7 Measurement results for Device 6. (a) on/off states trans-mission spectra; (b) transmission at 1550 nm versus tuningpower; (c) time-domain response at 1550 nm. . . . . . . . . . 393.8 Schematic of an ultra-low power MZI cross/bar switch. . . . . 403.9 Measurement results for a fabricated ultra-low power MZIcross/bar switch. (a) Output transmissions at 1550 nm versustuning power; (b) output spectra at the bar state; (c) outputspectra at the cross state. . . . . . . . . . . . . . . . . . . . . 413.10 Breakdown test results for a demonstrated ultra-low powerthermo-optic switch. . . . . . . . . . . . . . . . . . . . . . . . 424.1 (a) Schematic for a Mach-Zehnder interferometer (MZI) switch;(b) Schematic for the proposed balanced nested Mach-Zehnderinterferometer (BNMZI) switch. . . . . . . . . . . . . . . . . . 454.2 Cross state output transmissions as a function of κ2 and Api.(a) Output 1. (b) Output 2. . . . . . . . . . . . . . . . . . . . 48xvList of Figures4.3 Bar state output transmissions as a function of κ2 and Api.(a) Output 1. (b) Output 2. . . . . . . . . . . . . . . . . . . . 494.4 Blocking state output transmissions as a function of κ2. (a)Output 1. (b) Output 2. . . . . . . . . . . . . . . . . . . . . . 504.5 Schematic of a carrier injection phase shifter design on asilicon-on-insulator (SOI) platform. . . . . . . . . . . . . . . . 514.6 Performance of the carrier injection phase shifter with a piphase shift. (a) Change of waveguide absorption, ∆α, versusphase shifter length, L; (b) optical field transmission factor,Api, versus phase shifter length, L. Waveguide propagationloss is not included in the Api calculation. . . . . . . . . . . . 524.7 Electrical responses of the carrier injection phase shifter fora pi phase shift. (a) Injected current, I, versus phase shifterlength, L; (b) power consumption versus phase shifter length,L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.8 Circuit simulation schematics. (a) BNMZI switch; (b) MZIswitch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.9 Performance comparison for the BNMZI switch and the MZIswitch, when the 2× 2 couplers in the switches have identicalκ2. (a) Cross state performance; (b) bar state performance. . 564.10 (a) and (b) are Monte Carlo (MC) simulation results for theBNMZI switch operating at the cross state and the bar state,respectively. (c) and (d) are MC simulation results for theMZI switch operating at the cross state and the bar state,respectively. In the MC simulations, each 2× 2 coupler has arandom κ2 in between 0.48 and 0.52. . . . . . . . . . . . . . . 574.11 Illustration for first-order crosstalk suppression. . . . . . . . . 594.12 (a) Schematic of an example 8×8 dilated Benes switch fabricwith established connections: I1-O5, I4-O4, I6-O1, and I7-O7.(b) Output transmissions of the 8×8 switch without blockingthe idle switches (idle switches are randomly at the cross orbar states). (c) Output transmissions of the 8×8 switch withblocking the idle switches. . . . . . . . . . . . . . . . . . . . . 60xviList of Figures4.13 (a) Schematic of an example 8×8 dilated Banyan switch fab-ric with established connections: I1-O3, I2-O7, I3-O5, I4-O1,I5-O6, I6-O2, I7-O4, and I8-O8. (b) Output transmissionsof the 8×8 switch without blocking the idle switches (idleswitches are randomly at the cross or bar states). (c) Outputtransmissions of the 8×8 switch with blocking the idle switches. 615.1 (a) Edge coupling solution in silicon photonic integrated cir-cuits; (b) fibre Gaussian beam with a waist radius of 2.5 µm;(c) TE0 mode profile in a 180 nm × 220 nm edge couplerwaveguide; (d) TM0 mode profile in a 180 nm × 220 nm edgecoupler waveguide. (e) Power transmission for the coupledTE0 and TM0 modes versus polarization angle, θ, of the fibreGaussian beam. . . . . . . . . . . . . . . . . . . . . . . . . . . 635.2 A proposed polarization control solution for high performancesilicon photonic switches, which uses polarization beam split-ters as input mode filters. . . . . . . . . . . . . . . . . . . . . 645.3 (a) Schematic of a point-symmetric network; (b) responses ofa 3-dB, 2×2 coupler and its point-symmetric network. Theshadow regions mark out the variations of their respectivecross-coupling powers. . . . . . . . . . . . . . . . . . . . . . . 665.4 (a) Schematic of our broadband PBS; (b) schematic of thefirst broadband 3-dB coupler in the PBS. . . . . . . . . . . . 685.5 FDTD simulation results of the broadband 3-dB coupler op-erating at the (a) TE0 mode and (b) TM0 mode. . . . . . . . 695.6 FDTD simulation results for the PBS. (a) Spectral responsesfor the TE0 mode; (b) spectral responses for the TM0 mode;(c) modal isolation at the through port; (d) modal isolationat the cross port. . . . . . . . . . . . . . . . . . . . . . . . . . 705.7 Normalized field intensities of 1550 nm wavelength in the PBSwaveguide cores along propagation length. (a) TE0 mode;(b)TM0 mode. . . . . . . . . . . . . . . . . . . . . . . . . . . 72xviiList of Figures5.8 Scanning electron microscope (SEM) images for one of thefabricated broadband polarization beamsplitters. . . . . . . . 725.9 Sketch of measurement setup. The yellow and pink trianglesare the on-chip grating couplers for the TE0 mode and TM0mode, respectively. . . . . . . . . . . . . . . . . . . . . . . . . 735.10 Measurement results for the fabricated PBS. (a) Spectral re-sponses for the TE0 mode; (b) spectral responses for the TM0mode; (c) modal isolation at the through port; (d) modal iso-lation at the cross port. . . . . . . . . . . . . . . . . . . . . . 745.11 (a) A broadband MZI switch without polarization control; (b)simulated cross state performance of the switch; (c) simulatedbar state performance of the switch. . . . . . . . . . . . . . . 755.12 (a) A broadband switch having polarization control; (b) sim-ulated cross state performance of the switch; (c) simulatedbar state performance of the switch. . . . . . . . . . . . . . . 766.1 (a) Schematic layout of the racetrack resonator test device;(b) transmission spectrum for such a device without fabrica-tion variations. FSR is free-spectral-range. . . . . . . . . . . . 796.2 Simulation results for racetrack resonators with a nominalwaveguide height, h, of 220 nm and various waveguide widths,w. (a) Transmission spectra; (b) group indices at resonances;(c) resonance wavelength versus waveguide width for a se-lected resonance mode; (d) group index versus waveguidewidth for a selected resonance mode. . . . . . . . . . . . . . . 806.3 Simulation results for racetrack resonators with a nominalwaveguide width, w, of 500 nm and various waveguide heights,h. (a) Transmission spectra; (b) group indices at resonances;(c) resonance wavelength versus waveguide height for a se-lected resonance mode; (d) group index versus waveguideheight for a selected resonance mode. . . . . . . . . . . . . . . 82xviiiList of Figures6.4 Error test results in a ∆w deviation range of ±20 nm anda ∆h deviation range of ±10 nm, for the proposed varia-tion characterization method. (a) Width extraction error,Error∆w; (b) height extraction error, Error∆h. . . . . . . . . 846.5 (a) Schematic layout for the racetrack resonator test device;(b) distribution of racetrack resonators on each wafer die; (c)wafer map for the fabricated multi-project-wafer. . . . . . . . 856.6 Characterization results for die #20. (a) Measured spectrafor the 61 identical test devices; (b) extracted ng for the 61devices; (c) distribution map for extracted ∆w; (d) distribu-tion map for extracted ∆h. . . . . . . . . . . . . . . . . . . . 866.7 Characterization results for all of the fabricated wafer dies.(a) Waveguide width variations, ∆w; (b) waveguide heightvariations, ∆h. . . . . . . . . . . . . . . . . . . . . . . . . . . 876.8 Histograms for the characterized variations across the 200-mm-wafer. (a) Width variations, ∆w; (b) height variations,∆h. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 897.1 Proposed simulation approach for photonics yield prediction.Primary simulation steps include: (1) layout-to-schematic trans-formation, (2) virtual wafer simulation and mapping, (3) com-ponents’ performance update, and (4) circuit simulation. . . . 937.2 (a) Detailed simulation flow chart for the proposed approach;(b) and (c) illustrate the simulated virtual wafers for waveg-uide width and height variations, respectively. . . . . . . . . . 947.3 An example circuit consisting of two grating couplers con-nected by a waveguide. (a) Physical layout; (b) simulationschematic in the circuit simulator. . . . . . . . . . . . . . . . 967.4 Illustration for the die selection and variation mapping in thewithin-wafer analysis. . . . . . . . . . . . . . . . . . . . . . . 977.5 Illustration for the manufacturing variation simulations ofwafer-to-wafer analysis. . . . . . . . . . . . . . . . . . . . . . 98xixList of Figures7.6 (a) A 100 mm × 100 mm random distribution map z(x, y)generated with σ=2; (b) a Gaussian filter map g(x, y) gener-ated with l = 4 mm; (c) the correlated variation wafer mapm(x, y). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 997.7 (a) A 100 mm × 100 mm correlated variation wafer mapm(x, y), which is simulated using a coarse simulation mesh;(b) and (c) are the variation maps of a 10 mm × 10 mm dielocated at the top right corner of the wafer, before and afterinterpolation, respectively. . . . . . . . . . . . . . . . . . . . . 997.8 Diagram for ∆w and ∆h averaging in the waveguide compactmodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1027.9 S-parameter component model. (a) Process corners for twoprocess parameters: waveguide width variation, ∆w, and heightvariation, ∆h; (b) and (c) are S31 amplitude and phase of a2×2 directional coupler, respectively. . . . . . . . . . . . . . . 1037.10 Layout decomposition for an Mach-Zehnder interferometerdevice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1047.11 A thermo-optic MZI switch. (a) Physical layout; (b) circuitsimulation schematic in Lumerical INTERCONNECT. . . . . 1057.12 Ideal performance for the 2×2 Mach-Zehnder interferometerswitch. (a) Cross state; (b) bar state. . . . . . . . . . . . . . . 1077.13 Within-wafer yield prediction results for the 2×2 Mach-Zehnderinterferometer switch. (a) Spectral variations at the crossstate; (b) spectral variations at the bar state; (c) histogramsfor the cross state bandwidth; (d) histograms for the bar statebandwidth; (e) histograms for the cross state insertion loss;(e) histograms for the bar state insertion loss. . . . . . . . . . 1087.14 Histograms for phase errors at 1550 nm, for switch designswith d=25 µm, d=50 µm, and d=100 µm. . . . . . . . . . . . 109xxList of Figures8.1 A proposed temperature stabilization solution for MZI switches;(a) Schematic for a MZI switch with feedback control; (b)schematic for series connected temperature sensing diodes(TSD). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117B.1 Schematic for a typical Mach-Zehnder interferometer (MZI)circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137xxiList of AbbreviationBNMZI Balanced Nested Mach-Zehnder InterferometerCMOS Complementary Metal-Oxide-SemiconductorDC Directional CouplerDUV Deep Ultra-VioletDWDM Dense Wavelength-Division MultiplexingER Extinction RatioFSR Free Spectrum RangeFDTD Finite-Difference Time-DomainGC Grating couplerInP Indium PhosphideMC Monte CarloMZI Mach-Zehnder InterferometerMI Michelson InterferometerMPW Multi-Project WaferMRR Micro-Ring ResonatorPBS Polarization Beam-SplitterPM Polarization-MaintainingPIC Photonics Integrated CircuitSEM Scanning Electron MicroscopySi SiliconSiO2 Silicon OxideSOI Silicon-on-InsulatorxxiiList of AbbreviationSWG Sub-Wavelength GratingTMM Transfer Matrix MethodTiN Titanium NitrideWDM Wavelength-Division MultiplexingxxiiiAcknowledgementsI would like to express my heartfelt thanks to my supervisor Prof. LukasChrostowski, for the inspiration, great support and guidance that he hasprovided throughout my PhD, which has been a very wonderful journey inmy life. I appreciate his way of supervision, which encouraged me to startmy research project independently. This challenging experience will trulybenefit my future career.I especially appreciate Prof. Nicolas Jaeger for his generous help on myresearch projects and guidance on my scientific writing, which significantlyboost my PhD research. I give thanks to the rest of my thesis commit-tee members for their invaluable comments and support during my PhDprogram.I thank my group members, Han Yun, Yun Wang, Fan Zhang, MingleiMa, and Hasitha Jayatilleka, for their help and many valuable discussions.Discussions in the lab were very beneficial to my research and have been aninteresting part of my journey.xxivChapter 1Introduction1.1 Background and MotivationsSwitch Switch Switch Switch Switch Switch Metro Backbone Metro Metro Users Users (a)ServerAccessswitchesInterconnectionswitchesOptical linkElectrical link(b)Figure 1.1: (a) Long-haul telecommunication architecture; (b) short-reach data center communication architecture.Optical fibre links, which have high bandwidth and large capacity for datatransmission, are widely deployed in both long-haul telecommunications andshort-reach data center communications, as illustrated in Fig. 1.1. In com-munication networks, data switches are critical network nodes which estab-lish point-to-point communication channels. In long-haul communicationnetworks, optical switching based on wavelength selective switch (WSS) andfree-space micro-electro-mechanical system (MEMS) switch technologies hasbeen deployed for network provisioning and patch panel applications, whereswitching time of milliseconds to seconds is typical. In short-reach datacenter networks, where most of the global data traffic take place, network11.1. Background and Motivationsreconfiguration according to dynamic workloads is frequently requested. Atpresent, the reconfiguration in data center networks are dominated by high-speed electrical switches. Optical switching is currently being promoted forsuch an application, although there is a lack of published examples of realdeployments.Figure 1.2(a) illustrates a reconfigurable optical network through an elec-trical switch, where input optical signals are converted to electrical signalsfor switching and converted back to optical signals after switching. Theoptical/electrical/optical (O/E/O) conversions of an electrical switch makeit convenient for signal reamplification, reshaping, and retiming in electricaldomain, which can be beneficial for some networks in need of such ser-vices. High-speed switching is an advantages for many data center electricalswitches; however, they also have many disadvantages:• The O/E/O conversions require optical transceivers (i.e., receiver forthe optical/electrical conversion and transmitter for the electrical/op-tical conversion), which bring extra power penalty to the switch sys-tem. Commercial electrical switches typically have high power con-sumption, e.g., a 36-port, 100 Gbps per port data center switch, AristaDCS-7500R-36CQ-LC [1], consumes 25W per port, which is 250pJ/bit.• Cost penalty of optical transceivers is another issue. By 2017, theaverage cost for optical transceivers is around $3/Gbps. A simpleestimation can be made that the cost of transceivers in the aforemen-tioned Arista DCS-7500R-36CQ-LC switch is around $36,000, whichis almost 50% of the total price for switch ($73,307/switch released byMay 2017 [2]).• Scalability issues. As electrical switching is incompatible with opti-cal wavelength-division multiplexing (WDM) technology, multiplexers(MUX) and demultiplexers (DMUX) are required for the O/E/O con-versions, as illustrated in Fig. 1.2(a) (In some embodiments, MUXand DMUX are incorporated in the O/E/O transceivers). Such a con-figuration makes it unable to scale up with optical links. For example,21.1. Background and MotivationsO/EDMUX…ElectricalNxNSwitch	chip …O/EO/EO/EO/EO/EO/EO/EO/EE/OE/OE/OE/OE/OE/OE/OE/OE/OOptical signal 1Optical signal 2Optical signal nDMUXDMUXλ1λ2λ3MUXMUXMUXλ1λ2λ3Optical	to	electricalConversionDe-multiplexsignal	Electrical	to	opticalConversion Multiplexsignal	(a)Optical switch matrixSignal 1Signal 2Signal 3Signal 4Signal 2Signal 3Signal 1Signal 4(b)Figure 1.2: (a) Diagram for an electrical switch; O/E: optical toelectrical conversion; E/O: electrical to optical conversion; (b) diagramfor an optical switch.when upgrading each optical link with more WDM channels and/orhigher bit-rate per channel, the O/E/O conversion interfaces and theswitch core need to be rebuilt accordingly.Figure 1.2(b) illustrates the diagram of an optical switch, where signalswitching happens by changing the light paths without processing the signaldata. Optical switching has many advantages as compared with electricalswitching:• Lower cost. Optical switching does not have O/E/O conversions anddoes not require any optical transceiver. Therefore, it can be signifi-31.1. Background and Motivationscantly cheaper.• Optical switching is transparent to data bit-rate (within limitations ofoptical bandwidth, loss budget and other effects), and therefore is be-lieved to be more energy efficient. For example, a 32×32 optical MEMSswitch commercialized by DiCon Fiberoptics [3] has a total power con-sumption of only 2.4W. Conservatively assuming a bit-rate of 100Gbpsper port, the switch has a power consumption of 0.75pJ/bit, being twoorder of magnitude lower than that of the aforementioned electricalswitch. As the bit-rate in the optical link goes higher, the switch canhave even lower energy per bit.• Optical switching is transparent to signal format and protocol (withinlimitations of optical bandwidth, loss budget and other effects) as itdoes not process the signal data, and hence it has simpler systemhardware.Although having many strengths, at present the speeds of optical switches(nanoseconds to milliseconds depending on technologies) are still slower thanthe speeds of electrical switches (sub-nanoseconds). Besides, signal ream-plification, reshaping, and retiming are difficult in optical switches since allsignals are in the optical domain (short distance optical links with smallsignal degradation may not require such services). In practical solutions,it is likely that electrical and optical switches will coexist and cooperate todeliver their own strengths. According to [4], optical switches can be desig-nated to handle slowly changing portion of communication (e.g., data flowsand long packets); electrical switches are suitable for the bursty portion ofcommunication (e.g., short packets).In the past two decades, various optical switches have been developedbased on Indium Phosphide (InP) technologies [5] and MEMS technologies[1, 6]. As compared with InP and MEMS platforms, silicon photonics isa more promising technology to develop integrated optical switches, as itsmanufacturing shares the same fabrication facilities of advanced microelec-tronics, i.e., the complementary metal-oxide-semiconductor (CMOS) tech-nologies, and as a result, silicon photonics can be low-cost and potentially41.1. Background and Motivationsable to integrate with CMOS electronics. With such advantages, siliconphotonics is gaining tremendous momentum in both academia and indus-try. Over the past two decades, various silicon photonic devices have beendemonstrated, and these include passive components (such as waveguides,power splitters, and I/O interfaces) [7–9] and active components (such asmodulators, photodetectors, and tunable filters) [10–12]. One major appli-cation for these photonic devices is high-speed data transceiver. Anotherimportant application for those devices, which is driving more and more at-tention from both academia and industry, is high-performance data switches.Silicon substrateBuried oxide (BOX)SiliconCladding oxide220 nm2~3 μm~725 μm2~3 μmFigure 1.3: Cross section schematic of a typical Silicon-on-Insulator(SOI) wafer.Silicon photonics manufacturing use Silicon-on-Insulator (SOI) wafers.Figure 1.3 shows the cross-section schematic of a typical SOI wafer, the layerstack of which includes an approximately 725 µm thick silicon substrate, a2 to 3 µm thick buried oxide (BOX) layer as the insulator and cladding forwaveguides, a 220 nm thick silicon layer to define planar lightwave circuits(PLCs), and a 2 to 3 µm thick cladding oxide layer for perfection. Suchan SOI layer stack, well-known as 220 nm SOI platform, has been widelyadopted by many photonics foundries, such as IME [13], imec [14], CEA-Leti [15] and IHP [16]. This dissertation develops high-performance photonicswitches based on the 220 nm SOI platform.51.2. Silicon Photonic Switches1.2 Silicon Photonic Switches1.2.1 Switching ElementsSilicon photonic switches operate using interferometers. Most common formsof interferometers are Mach-Zehnder interferometers (MZIs) and micro-ringresonators (MRRs). The actuator for an interferometer based switch is anoptical phase shifter. Light paths of the switch can be changed by changingthe optical phase in the interferometer.1.2.1.1 Mach-Zehnder InterferometerInput 1 Input 2 Output 1 Output 2 Phase	shi(er		2x2 coupler 2x2 coupler Arm 2 Arm 1  φ = [0, π] (a)Input 1Input 2Output 1Output 2Bar state (φ = π)Input1Input2Cross state (φ = 0)Output 1Output 2(b)1520 1540 1560 1580Wavelength (nm)-30-20-100Transmission (dB)Cross stateOutput 1Output 2(c)1520 1540 1560 1580Wavelength (nm)-30-20-100Transmission (dB)Bar stateOutput 1Output 2(d)Figure 1.4: A 2×2 Mach-Zehnder interferometer switch. (a)Schematic of the switch; (b) switching states; (c) and (d) are sim-ulated spectral responses at the cross and bar state, respectively, fora particular MZI switch design.Figure 1.4(a) shows a 2×2 (i.e., 2 inputs and 2 outputs) MZI switch design,61.2. Silicon Photonic Switcheswhich consists of two 2×2 couplers and two balanced waveguide arms. Oneof the waveguide arms has an optical phase shifter for phase tuning. Whenlight enters a switch input, it is equally split by the first 2×2 coupler. Then,the two resulting beams propagate through the waveguide arms, and theyare finally recombined by the second 2×2 coupler. Depending on phasetuning, ϕ, the input light can be switched to either of the switch outputs.The MZI switch can operate at a bar state when ϕ = pi; it can operate at across state when ϕ = 0, as illustrated in Fig. 1.4(b). The derivation of thetransfer functions of a MZI switch is given in Appendix B.As an illustrative example, Figs. 1.4(c) and 1.4(d) respectively showthe simulated performance at the cross state and the bar state of a par-ticular MZI switch, which use 2×2 directional couplers [17] in the switchdesign. In the simulations, the input source was set to the switch input1 shown in Fig. 1.4(a). The phase tuning at the bar state is wavelength-dependent, based on Eq. B.13. Simulation results show that the MZI switchcan operate in the wavelength span from 1538 nm to 1567 nm with switchingcrosstalk (i.e., transmission at the unintended output) of less than -20 dBat both switching states, which can be compatible for wavelength-divisionmultiplexing (WDM) applications.1.2.1.2 Micro-Ring ResonatorsAn add-drop MRR can be designed for signal switching. Such a device,as shown in Fig. 1.5(a), consists of a micro-ring resonator, two waveguidescoupled to the resonator, and an optical phase shifter on the resonator.Figure 1.5(b) shows spectral responses for an example MRR switch, andFig. 1.5(c) illustrates its corresponding switching paths. Fundamentally,an MRR switch has wavelength-dependent performance. Light enters theinput port of an MRR switch can be selectively switched to either the dropport or the through port, depending on its wavelength alignment with theresonance wavelength of the MRR. If the signal wavelength is aligned withthe resonance wavelength, light will be switched to the drop port; otherwise,light will propagate to through port, as shown in Fig. 1.5(c). The resonance71.2. Silicon Photonic SwitchesInput Through Drop Add Phase shifter (a)−20−100  Drop1550 1550.5 1551 1551.5 1552−30−20−100Wavelength (nm)Power transmission (dB)  ThroughInput λ2Input λ1(b)ThroughDropλ1InputAddInputThroughDropλ2Add(c)Figure 1.5: An example micro-ring resonator (MRR) switch. (a)Schematic of the switch; (b) spectral responses; (c) switching paths.wavelength of an MRR is sensitive to the width and thickness variations ofthe waveguide as well as on-chip temperature variations, and as a result, anMRR requires dynamic control and stabilization [12]. The MRR switch isnot the most popular candidate in SOI switch designs due to its wavelength-selective performance and the complexities in control and stabilization.1.2.2 Phase Tuning SchemesIn SOI waveguides, optical phase tuning can be achieved using either theplasma dispersion effect or the thermo-optic effect.1.2.2.1 Plasma Dispersion EffectThe plasma dispersion effect [18] describes the change of refractive indexof a material due to a change of carrier concentration. According to Soerf81.2. Silicon Photonic SwitchesSi substrateBuried oxideP++ I N++Cladding(b)HeaterN++ N N++(a) (c) (d)P N N++P++Figure 1.6: Cross section schematics of SOI phase shifters. (a) Car-rier depletion phase shifter; (b) carrier injection phase shifter; (c)thermo-optic phase shifter using a metal heater; (d) thermo-opticphase shifter using a resistive heater integrated in a rib waveguide.equations [19], the change of refractive index for Si is described by:∆n(at 1550 nm) = −5.4× 10−22∆N1.011 − 1.53× 10−18∆P 0.838 (1.1)where ∆N and ∆P are the changes of carrier concentrations for electronsand holes. The change of carrier concentration also changes the absorptionof Si due to free-carrier absorption, which is given by:∆α(at 1550nm) = 8.88×10−21∆N1.167 +5.84×10−20∆P 1.109 [cm−1] (1.2)In SOI waveguides, the change of carrier concentration can be achievedusing either carrier depletion through a PN junction or carrier injectionthrough a PIN junction, the cross section schematics of which are shown inFigs. 1.6(a) and 1.6(b), respectively. Carrier depletion phase shifters havetuning speeds of greater than tens of GHz, and are typically deployed in high-speed modulator designs [20]; however, they are typically a few millimetreslong due to the carrier depletion being a weak effect. Carrier injection isa comparatively stronger effect than carrier depletion, and carrier injectionphase shifters can be as compact as hundreds of micrometers long [21–23].However, as the change of carrier concentration varies the absorption of sili-con waveguides, MZI switches with phase shifters based on plasma dispersioneffect typically have high insertion loss and large switching crosstalk.91.2. Silicon Photonic Switches1.2.2.2 Thermo-optic EffectThe thermo-optic effect, as the name implies, is the change in the refractiveindex of a material due to a change in temperature. Si has a relatively highthermo-optic coefficient, which is dndT = 1.86×10−4/K at room temperature,making thermo-optic phase tuning very efficient. Optical phase tuning, ∆ϕ,for a thermo-optic phase shifter can be expressed by:∆ϕ ∝ 2piλdndT∆TL (1.3)where λ is wavelength; ∆T is waveguide temperature change introduced bythe phase shifter with a certain amount of tuning power; L is the heatinglength of waveguide. In principle, switches based on this effect have noexcess loss and can be highly compact. These advantages make thermo-optic switches promising in applications that require a large number of phaseshifter elements.On SOI platforms, there are two common methods [17] to implement athermo-optic phase shifter. One method is to heat a waveguide by placing ametal heater above it, which is shown in Fig. 1.6(c). The tuning efficiency ofsuch a phase shifter design is limited by the low thermal conductivity of theSiO2 cladding material and the buffer distance between the heater and thewaveguide. Typically, silicon photonics foundries, such as imec and IME,have standard buffer distances, and as a result, thermo-optic phase shiftersbase on such designs have similar power consumption of more than tens ofmilliwatts [24–26].The other method for thermo-optic phase shifter design is to integrate aheater in a rib waveguide, as depicted in Fig. 1.6(d). This method enables afaster and more efficient heating due to the high thermal conductivity of Si.The integrated heater is formed using an N++/N/N++ structure, wherethe two heavily doped N++ regions are used to make electrical contacts tothe silicon waveguide while the lightly doped N region is a highly resistiveregion for heating. Typically, the clearance distance between the edge ofwaveguide to the edge of N++ region is more than 1 µm in order to reduceoptical absorption loss induced by free-carrier absorption. However, opti-101.2. Silicon Photonic Switchescal absorption loss caused in the lightly doped waveguide core can not beeliminated.1.2.3 Performance MetricsPerformance metrics for silicon photonic switches include crosstalk, extinc-tion ratio, bandwidth, power consumption, switching speed, insertion loss,and footprint.Crosstalk and Extinction RatioCrosstalk in a switch is a measure of the amount of signal leaking into anunintended switch output port. This is often measured using extinctionratio (ER). The ER of a 2×2 switch at a switching state is defined as thedifference, on a logarithmic scale, for the power of the same input signalpresenting at the two switch outputs:ER = 10 log10(PhighPlow) (1.4)where Phigh and Plow are the transmission at the high power output andthe low power output, respectively. For high performance switches, an ERof more than 20 dB is often required. According to theoretical analysisas presented in Appendix B, the cross state ER of a 2×2 MZI switch isdetermined by the cross-coupling ratio, κ2, and through-coupling ratios, t2,of the 2×2 couplers in the switch, as per Eq. B.8; the bar state ER is infinite,as per Eq. B.11. Figure 1.7 shows the calculated ER at the cross state ofan MZI switch as a function of κ2 and t2. In principle, an infinite ER at thecross state can be obtained when κ2 = t2, i.e., the 2×2 couplers have 3-dBcoupling.BandwidthHigh performance photonic switches require a wide bandwidth in order toallow for a large number of ITU channels to be routed. For example, ITU-TRecommendation G.694.1 [27] suggests a channel spacing of 100 GHz for111.2. Silicon Photonic Switchesκ2 (%)t2  (%)  10 20 30 40 50 60 70 80 90102030405060708090Extinction Ratio (dB)051015202530354045502x2 coupler𝜅2t2Figure 1.7: Cross state extinction ratio (ER) of an Mach-Zehnderinterferometer (MZI) switch versus the coupling ratios (κ2 and t2) ofits 2 × 2 couplers. Inset illustrates the κ2 and t2 parameters for the2× 2 coupler.Figure 1.8: Diagram that shows the 126 channels within a 100 nmbandwidth that are used in DWDM applications for a channel spacingof 100 GHz.dense wavelength-division multiplexing (DWDM) applications, and accord-ingly, a switch with a 100 nm bandwidth can route more than 120 channels,as illustrated in Fig. 1.8.The bandwidth of a photonic switch is typically defined as the wavelengthrange over which the ER is above a certain value, typically being 20 dB or121.2. Silicon Photonic Switcheshigher [21, 28]. As we’ve discussed, the ER of an MZI switch is determinedby the coupling ratios of its 2×2 couplers; in other words, the bandwidthof an MZI switch is determined by the 3-dB coupling bandwidth of its 2×2couplers. For the MZI switch shown in Fig. 1.4, the 2×2 couplers of theswitch have wavelength-dependent coupling ratios, which lead to the switchhaving wavelength-dependent ER with a very limited bandwidth at the crossstate that can meet the 20 dB ER requirement (see Fig. 1.4(c).Power ConsumptionFor N×N switch matrices, the power consumption of each individual switchis desired to be as low as possible, in order to reduce the total energy costof systems. The tuning efficiency of an MZI switch is commonly evaluatedusing mW/pi as a figure-of-merit, namely the power required to obtain anoptical phase shift of pi, which is required for switching between the bar andthe cross.Switching SpeedHigh-speed tuning capability is often desired for photonic switches. Typi-cally, the switching speeds of carrier depletion, carrier injection, and thermo-optic phase shifters are on the scales of GHz, MHz, and kHz, respectively.In practice, the required switching speed is determined by the application.Insertion LossThe insertion losses of 2 × 2 couplers and phase shifters contribute to thetotal insertion loss of an MZI switch. Insertion loss is a significant figure-of-merit for large-scale switch matrices.FootprintCost-of-fabrication is one of motivations for compact designs. The typicalcost for a multi-project wafer (MPW) fabrication run in photonics globalfoundries (e.g. imec and IME) is around $500/mm2 to $2000/mm2 [29].131.2. Silicon Photonic SwitchesTaking a demonstrated 32×32 switches [30] as an example, which has afootprint of more than 150 mm2, the fabrication cost of the switch chip atthe prototyping stage is approximately 75,000$ (each prototype can producehundreds to thousands chips). System footprint is limited by photonic de-vice footprints, electrical I/Os, and optical I/Os. Another motivation forcompact designs is to reduce the impacts of fabrication variations [31, 32].Devices that are spatially close to each other tend to have correlated fabrica-tion variations, and therefore have more consistent performance, as discussedin Ch. 7.1.2.4 Remaining IssuesAlthough the research in silicon photonic switches has been making steadyprogress in recent years, commercialization of the technologies still has along way to go. Much work is required to improve the switch performanceat the component level to achieve satisfactory system performance.Most of demonstrated MZI switches have limited operation bandwidths[26, 33–35] due to their 2× 2 couplers having wavelength-dependent perfor-mance. The 3-dB operation bandwidth of 2×2 couplers need to be increasedin order for broadband switching.Many demonstrated thermo-optic MZI switches, although being compactin footprints, have high power consumption of more than tens of milliwatts[24–26, 33, 36–40]. To build N × N switch matrices that consist of hun-dreds switch elements, the power consumption of each element needs to beminimized.MZI switches based on carrier injection phase tuning are superior forhigh-speed applications. However, the inherent loss modulation of carrierinjection phase tuning breaks the power balance in the MZI structure, andtherefore lead to the switch having a larger switching crosstalk. This is along-existing and well-known problem in all the demonstrated carrier injec-tion MZI switches [21–23, 28, 41, 42], which remains to be solved.Silicon photonic “single-mode” waveguides support both fundamentaltransverse electric (TE0) and fundamental transverse magnetic (TM0) modes.141.3. About This ThesisHowever, most silicon photonic switches are designed to operate using ei-ther the TE0 mode or the TM0 mode, and therefore they require polarizationcontrol.Moreover, manufacturing variability is a major issue in photonics inte-grated circuit (PIC) designs. A successful PIC design requires prior knowl-edge of manufacturing variations and efficiently taking into account suchvariations in the design. Unfortunately, fabless designers typically do nothave access to the variability assessment data of photonics MPW fabrica-tions, and also there is currently no circuit simulation tool able to takeinto account layout-dependent correlated variations. These barriers make itdifficult to design large-scale PICs, such as N ×N switch matrices.1.3 About This Thesis1.3.1 Objectives and ContributionsThe objectives of this thesis are to address the aforementioned issues, andfurther propel the development of silicon photonic switching technologies.Contributions of this thesis include:• Design and demonstration of a high-performance broadband 3-dB cou-pler with a 100 nm operation bandwidth, which is a fundamental build-ing block for broadband switches.• Demonstration of thermo-optic switches with state-of-the-art low powerconsumption of down to 50µW/pi, which is approximately 10× lowerthan the power consumption of any thermo-optic switches in literature.• Provided the first solution to the long-existing crosstalk issues of high-speed carrier injection switches.• Proposed the first silicon photonic tri-state switch, which can be usedfor crosstalk suppression in N ×N switch matrices.• Demonstration of a high-performance polarization beamsplitter (PBS),which has a wider bandwidth and higher isolation strengths than other151.3. About This Thesisdemonstrated PBSs. Our device can be used for polarization controlfor photonic switches.• Developed a novel characterization method for fabrication variations.As compared with other demonstrated methods that use two teststructures for characterization, our method only use one test struc-ture and has a sub-nanometer accuracy.• Developed the first yield prediction method with layout-dependentcorrelation parameters for photonic integrated circuits. The proposedmethod has a significant improvement over the conventional MonteCarlo analysis, which has no correlation parameters in the analysismodel. The proposed yield prediction method can be used to studythe performance variations of silicon photonic switches.Together, all of these contributions enable high-performance silicon photonicswitch designs.1.3.2 Thesis OrganizationThis thesis is organized as follows:In Chapter 2, we focus on broadband MZI switch designs. First, wepresent design, modelling, and characterization of a TE0 mode broadband 3-dB coupler. Then, we experimentally demonstrate a broadband MZI switchbased on the demonstrated broadband 3-dB coupler.In Chapter 3, we focus on designs of ultra-low power thermo-optic switches.We start from designs of novel thermo-optic phase shifters, which incorpo-rate thermal isolation structures and folded waveguide structures to improvetuning efficiency. Based on the phase shifter designs, then we demonstrateultra-low power thermo-optic switches.In Chapter 4, we focus on designs of carrier injection switches with bothhigh-speed and crosstalk-free performance. First, we propose a novel car-rier injection tri-state (cross/bar/blocking) switch, and present its operationprinciples. Next, we analyze the cross/bar switching performance of the pro-posed switch, as compared with a regular carrier injection MZI cross/bar161.3. About This Thesisswitch. Finally, we analyze the blocking ability of our proposed tri-stateswitch.Chapter 5 discusses polarization control for silicon photonic switches. Abroadband polarization beamsplitter (PBS) is designed and demonstratedfor polarization control.Chapter 6 demonstrates a novel characterization method for silicon pho-tonics manufacturing. The principles for the characterization method ispresented in details. Based on the proposed method, fabrication variationsof a 200-mm-wafer is characterized.In Chapter 7, we present how to predict performance of PICs with im-pacts of correlated manufacturing variability. We will describe the flow chartof our performance prediction method, and then present numerical modelsfor the method. Finally, we perform performance prediction on several MZIswitch designs.The thesis is concluded in Chapter 8, where we summarize the contribu-tions and significance of this research, and discuss future research directions.17Chapter 2Broadband 3-dB Couplersfor Broadband SwitchingOptical power couplers are essential devices for splitting and combining lightin photonic systems. In silicon photonics, directional couplers (DCs) havebeen widely used as power couplers due to their simple configurations andthe ease with which they can be fabricated on SOI platforms. Figure 2.1shows the schematic of a typical TE0 mode DC, which consists of two par-allel symmetric waveguides separated by a gap. The coupling behavior ofa DC can be explained using supermode analysis [17]. In the two waveg-uide system of a DC, the TE0 mode light entering one of the coupler inputssimultaneously excites the lowest order symmetric and anti-symmetric su-permodes in the two waveguide system, as illustrated in Fig. 2.1, and thepower intensity of the input light is the vector summation of these twosupermodes. The two supermodes propagate at different velocities in thetwo waveguide system, which leads to a change in vector summation, i.e., apower exchange between two waveguides. Unfortunately, the velocity differ-ence for the two supermodes are wavelength-dependent, and as a result, thepower exchange between the two waveguides, i.e., coupling strength, of aDC is wavelength-dependent. As an illustrative example, Fig. 2.1(b) showsthe performance of a typical 3-dB DC design having wavelength-dependentcoupling ratios.As we’ve discussed in section 1.2.3, in MZI switch designs, broadband 3-dB couplers are required for broadband switching performance. In the pasttwo decades, much effort [8, 11, 43–50] has gone into developing broadband3-dB couplers on SOI platforms. Among these works, adiabatic couplers182.1. Broadband 3-dB coupler DesignsSymmetricAnti-symmetricSymmetricAnti-symmetric(a)1500 1550 1600Wavelength (nm)020406080100Coupling Ratio (%)CrossThrough(b)Figure 2.1: (a) Schematic for a photonic directional coupler; (b)performance of a directional coupler design. The coupling length is17.5 µm. The coupler waveguides are 500 nm wide by 220 nm height,and are separated by a 200 nm gap.that use tapered waveguides to split power [8, 43] have promising broad-band properties, but their footprints are usually on the scale of hundreds ofµm2. Recently, broadband couplers based on sub-wavelength grating (SWG)structures have also been demonstrated for their very compact designs; how-ever, the fabrication processes for SWG structures require high-resolutionelectron-beam lithography, which is not available in photonics mass produc-tion foundries, such as IME and imec.In this chapter, we demonstrate a TE0 mode broadband 3-dB couplerthat is compact in size, simple in structure, and is compatible with photonicsmass production processes. Based on this, we demonstrate a TE0 modebroadband MZI switch.2.1 Broadband 3-dB coupler Designs2.1.1 SchematicOur broadband coupler design is based on SOI strip waveguides. Such adevice, as shown in Fig. 2.2(a), is a multi-segment device that consists oftwo DCs and an asymmetric waveguide-based phase shifter. 1-µm-long lin-early tapered waveguides are used to connect the phase shifter to the DCs.The cross-section schematics of the DCs and the phase shifter are shown192.1. Broadband 3-dB coupler DesignsL1 L2Directional coupler Phase shifterL3Directional couplerTaperTaperTaperTaper(a)500 nm 500 nm 400 nm600 nm200 nmSi substrateBuried oxideCladdingDirectional coupler Phase shifter220 nm 220 nm(b) (c)200 nmInput 1Input 2Output 1Output 2a bFigure 2.2: (a) Schematic of the proposed broadband 3-dB coupler;(b) cross section schematic of the directional coupler (DC) segment;(c) cross section schematic of the phase shifter segment.in Figs. 2.2(b) and 2.2(c), respectively. Each DC consists of two 500 nmwide waveguides separated by a 200 nm gap. The phase shifter consists ofone 400 nm wide waveguide and one 600 nm wide waveguide separated bya 200 nm gap. The lengths for the waveguide segments, from left to rightas shown in Fig. 2.2(a), are labeled as L1, L2, and L3, respectively. Thefeature sizes of the broadband coupler design are well-compatible with theprocesses of photonics mass production foundries.Our approach for broadband 3-dB coupling is introducing a wavelength-dependent phase shift between the two DCs, to engineer the wavelength-dependent propagation velocities of the supermodes in the coupler. Byproperly optimizing the coupling lengths of DCs and the delay length of thephase shifter, the wavelength-dependence in the velocity difference of thetwo supermodes can be eliminated, and therefore, broadband (wavelength-independent) 3-dB coupling is possible at the two outputs.202.1. Broadband 3-dB coupler Designs2.1.2 Design PrincipleWe use the transfer matrix method (TMM) to design the broadband 3-dBcoupler. The supermode propagations in the device can be expressed as:[E+,outE−,out]= P3 · T−1 · P2 · T · P1 ·[E+,inE−,in](2.1)where E+,in and E+,out are the electric fields of the lowest order symmet-ric mode at the DC input and output, respectively; E−,in and E−,out arethe electric fields of the lowest order anti-symmetric mode at the DC inputand output, respectively. In this thesis, we use a commercial tool, Lumer-ical MODE Solutions [51], for all the mode calculations. The calculatedmode profiles for the symmetric and the anti-symmetric modes are shown inFig. 2.3(a). Matrices P1, P2, and P3 are the propagation matrices for the su-permodes in the first DC, the phase shifter, and the second DC, respectively,and they are given by:P1 =[e−j2piλn+(λ)L1 00 e−j 2piλ n−(λ)L1](2.2)P2 =[e−j2piλna(λ)L2 00 e−j 2piλ nb(λ)L2](2.3)P3 =[e−j2piλn+(λ)L3 00 e−j 2piλ n−(λ)L3](2.4)where n+(λ) and n−(λ) are wavelength-dependent effective indices of thesymmetric and anti-symmetric modes in the DCs, respectively; na(λ) andnb(λ) are wavelength-dependent effective indices of mode a and mode b inthe phase shifter, respectively. Here, as shown in Fig. 2.3(b), mode a refersto the fundamental mode of the phase shifter that is, in fact, primarilyconfined in waveguide a, and mode b refers to the next higher order modeof the phase shifter that is, in fact, primarily confined in waveguide b.Matrix T and T−1 are transfer matrices for the 1-µm-long tapered waveg-212.1. Broadband 3-dB coupler DesignsDirectional couplersSymmetric modeAnti-symmetric mode(a)Phase shifterMode aMode bwg a wg bwg a wg b(b)Figure 2.3: (a) Supermode profiles in directional couplers; (b) Su-permode profiles in phase shifter. wg a and wg b refer to waveguide aand waveguide b, respectively.uide segments, which describe mode conversions between the supermodes inthe DCs and those in the phase shifter. T is given by:T =[a(λ) b(λ)c(λ) d(λ)](2.5)where coefficients a(λ), b(λ), c(λ), and d(λ) are obtained using a commercialtool, Lumerical FDTD (Finite-Difference Time-Domain) Solutions [51].Assuming that a normalized TE0 mode light is launched into the input 1of the device, as shown in Fig. 2.2(a), it will simultaneously excite the sym-metric and anti-symmetric modes with amplitudes E+,in = E−,in = 1√2 .To achieve broadband 3-dB coupling at the coupler outputs, the electricfields of the two supermodes at the outputs, i.e., E+,out and E−,out, need tohave a wavelength-independent phase difference of 90◦ (the results of vec-tor summation make power intensity equally distributed in the two outputwaveguides). Based on such a goal, we then use the genetic optimizationalgorithm in Matlab [52] to optimize the segment lengths L1, L2, and L3.Figure 2.4(a) shows the calculated phase difference of E+,out and E−,out,i.e., ∆φ(λ) = φE+,out(λ) − φE−,out(λ), for an optimized coupler design with222.1. Broadband 3-dB coupler DesignsL1 = 33 µm, L2 = 0.55 µm, and L3 = 15 µm. The power intensities at thetwo output ports of the device are respectively given by:Poutput1 = | 1√2(E+,out + E−,out)|2 (2.6)Poutput2 = | 1√2(E+,out − E−,out)|2 (2.7)Figure 2.4(b) shows the calculated Poutput1 and Poutput2 for the optimizeddevice. As we can see that broadband 3-dB coupling is possible.1500 1520 1540 1560 1580 1600Wavelength (nm)-1-0.75-0.5-0.250Phase difference (a)1500 1520 1540 1560 1580 1600Wavelength (nm)0102030405060708090100Coupling ratio (%)Output 1Output 2(b)Figure 2.4: Transfer matrix method (TMM) simulation results for anoptimized device with L1 = 33 µm, L2 = 0.55 µm, and L3 = 15 µm.(a) Phase difference of the symmetric and anti-symmetric modes; (b)coupling ratios versus operation wavelength.Next, to physically split the coupler inputs and outputs, s-bent waveg-uides are added at the two ends of the broadband 3-dB coupler design, asshown in Fig. 2.5(a). Then, the broadband 3-dB coupler design is fur-ther confirmed using three-dimensional FDTD simulations, as shown in Fig.2.5(b), and the simulation results are shown in Fig. 2.5(c). We evaluate thecoupler performance based on the imbalance between cross-coupling ratios,κ2, and through-coupling ratios, t2, which is defined as: |κ2 − t2|. Accord-ingly, the FDTD simulation results indicate a maximum imbalance of 3.7%within a 100 nm bandwidth, from 1500 nm to 1600 nm.232.1. Broadband 3-dB coupler DesignsInput 1Input 2Output 1Output 2S-bent waveguides S-bent waveguides(a)Simulation boundaryInput source Through port monitorCross port monitorBroadband 3-dB coupler design(b)1500 1520 1540 1560 1580 1600Wavelength (nm)0102030405060708090100Coupling ratio (%)Cross-coupling (FDTD)Through-coupling (FDTD)(c)Figure 2.5: (a) Broadband 3-dB coupler design with s-bent waveg-uides as input and output ports; (b) FDTD simulation configuration;(c) FDTD simulation results.242.1. Broadband 3-dB coupler Designs2.1.3 Corner AnalysisCorner analysis [17] is a simple method to study impacts of fabrication vari-ations on the performance of SOI devices. For our broadband 3-dB couplerdesign, we consider a ±10 nm variations for the width and the thickness ofcoupler waveguide, i.e., ∆w and ∆h, respectively. Figure 2.6(a) illustratesthe 4 process corners in the analysis. For each process point, FDTD sim-ulation is conducted; all simulation results are collected to understand thedevice’s tolerance to fabrication. Figure 2.6(b) shows corner analysis resultsfor the coupling imbalance of the broadband 3-dB coupler design, whichindicates a worst-case imbalance of 16.7% within a 100 nm bandwidth.ΔwΔh(10 nm, 10 nm)(10 nm, -10 nm)(-10 nm, -10 nm)(-10 nm, 10 nm)Waveguidewh(a)1500 1520 1540 1560 1580 1600Wavelength (nm)01020304050Imbalance, |2  - t2|, (%) w=10nm, h=10nmw=10nm, h=-10nmw=-10nm, h=-10nmw=-10nm, h=10nm(b)Figure 2.6: Corner analysis for the broadband 3-dB coupler design.(a) Process corners; (b) corner analysis results for the coupling imbal-ance, |κ2 − t2|.2.1.4 Characterization ResultsThe broadband 3-dB coupler design was fabricated using an electron-beamlithography process at the University of Washington. We used an indi-rect measurement method to characterize the performance of the fabricateddevices. As shown in Fig. 2.7, the indirect measurement structure is animbalanced MZI circuit, which includes two identical under test couplersfor splitting at the input and combining at the output, and two imbalanced252.1. Broadband 3-dB coupler DesignsBroadband 3-dB couplerBroadband 3-dB couplerInputgrating couplerOutputgrating couplerBroadband LaserAgilent81600BDetectorAgilent81635A1540 1550 1560Wavelength (nm)-60-50-40-30-20-10Transmission (dB)SpectrumMaxima envelopeMinima envelopeIERgrating coupler pair for calibrationFigure 2.7: Block diagram illustrating the indirect measurement.phase arms with a length difference, ∆L, of 259.4 µm. Grating couplers(GCs) [53] were used to couple light into and out of the MZI circuit. Themeasurement structure also includes a pair of GCs connected by a shortwaveguide, which is intended for calibrating the insertion losses of GCs. Inthe measurements, an Agilent 81600B tunable laser was used as the opticalinput source, and an Agilent 81635A optical power sensor was used as theoutput detector for the MZI circuit.The κ2 and t2 of the under test couplers can be extracted from theinterference extinction ratio (IER) of the MZI output spectrum, which isdiscussed in Appendix C. We define IER as the difference on a logarith-mic scale between the minima and maxima transmissions, as illustrated inFig. 2.7. The wavelength-dependent IERs can be obtained by fitting theenvelopes on the minima and maxima of the MZI spectrum. The extractedκ2 and t2 are given by:κ2 = 12(1±1√10IER/10) (2.8)t2 = 1− κ2 (2.9)where we assume that the propagation losses of the two phase arms of theimbalanced MZI circuit are the same and the couplers are lossless. Due tothe fact that IERs of the MZI spectrum are independent to the insertionloss of the MZI circuit (e.g., misalignment loss), the κ2 and t2 of couplers262.2. Broadband Mach-Zehnder Interferometer Switchcan be accurately extracted.Figures 2.8(a) shows the measured spectrum for the MZI circuit, in whichthe insertion loss introduced by the GCs have been calibrated out. Accordingto the results, the insertion loss of the MZI circuit is less than 1 dB, whichindicates the insertion loss of each coupler is less than 0.5 dB. Based on theIERs from the MZI spectrum, we extracted the κ2 and t2 of the fabricatedcouplers using Eqs. 2.8 and 2.9, and the extracted results are shown in Fig.2.8(b). According to the extracted data, the coupler exhibits a maximumimbalance of 4.7% within a 100 nm wavelength bandwidth from 1500 nmto 1600 nm, which is in good agreement with the FDTD simulation resultsgiven in Fig. 2.5(c).1500 1520 1540 1560 1580 1600Wavelength (nm)-40-30-20-100Transmission (dB)SpectrumMaxima envelopeMinima envelope(a)1500 1520 1540 1560 1580 1600Wavelength ( m)0102030405060708090100Coupling ratios (%)Cross-coupling (extracted)Through-coupling (extracted)(b)Figure 2.8: (a) Measured spectrum for the MZI circuit; (b) extractedcoupling ratios of the fabricated broadband 3-dB couplers.2.2 Broadband Mach-Zehnder InterferometerSwitch2.2.1 DesignWe have designed a 2×2, TE0 mode, broadband MZI switch based on thedemonstrated TE0 mode, broadband 3-dB coupler. Figure 2.9(a) shows theschematic for such a switch design, which has a thermo-optic phase shifter oneach phase arm and two broadband 3-dB couplers. We modeled the broad-272.2. Broadband Mach-Zehnder Interferometer Switchband MZI switch using a photonic circuit simulator, Lumerical INTERCON-NECT [51], as shown in Fig. 2.9(b). The performance of the broadband 3-dBcouplers is described using scattering parameters (S-parameters), which areextracted from FDTD simulations. The wavelength-dependent responsesof waveguide phase arms are described using the effective refractive index,group index and group velocity dispersion at the central wavelength of oper-ation bandwidth, as discussed in 7.2.2.1. In the simulations, switch input 1was activated for optical source, as shown in Fig. 2.9(b). Figures 2.9(c) and2.9(d) show the simulation results at the cross and bar states, respectively.According to the results, at both switching states, the switch can operatein a 100 nm bandwidth from 1500 nm to 1600 nm, with ERs of more than25.6 dB.2.2.2 Characterization ResultsThe silicon waveguide structures of our broadband MZI switch were fabri-cated using an electron-beam lithography process, and the electrical layerswere defined using a metal deposition process, both of which were conductedby Applied Nanotools Inc., Canada. Figure 2.9(a) shows an optical imagefor the fabricated switch. On-chip GCs [54] coupled light into and out ofthe switch. A pair of GCs connecting by a short waveguide, being similar tothe GC pair as illustrated in Fig. 2.7, was also fabricated on the same chipto calibrate the insertion losses of GCs. In our measurements, we used anAgilent 81600B tunable laser as the optical input source, both channels ofan Agilent 81635A optical power sensor as the optical output detectors, anda Keithley 2602A dual-channel system source meter as the electrical powersource for phase tuning.Figures 2.10(b) and 2.10(c) show the measured spectral responses of theswitch at the cross state and the bar state, respectively, where the insertionlosses of GCs have been calibrated out. We can see that, at both switchingstates, the ERs are more than 23 dB within the 100 nm bandwidth from1500 nm to 1600 nm, which is in good agreement with the simulation resultsthat are shown in Figs. 2.9(c) and 2.9(d).282.2. Broadband Mach-Zehnder Interferometer SwitchInput 1Input 2Output 1Output 2(a)Output 2Output 1Input(b)1500 1520 1540 1560 1580 1600Wavelength (nm)-50-40-30-20-100Transmission (dB)Cross stateOutput 1 (simulated)Output 2 (simulated)(c)1500 1520 1540 1560 1580 1600Wavelength (nm)-50-40-30-20-100Transmission (dB)Bar stateOutput 1 (simulated)Output 2 (simulated)(d)Figure 2.9: A 2×2 broadband MZI switch design. (a) Switchschematic; (b) INTERCONNECT simulation; (c) simulated crossstate performance; (d) simulated bar state performance.292.2. Broadband Mach-Zehnder Interferometer Switch(a)1500 1520 1540 1560 1580 1600Wavelength (nm)-50-40-30-20-100Transmission (dB)Cross stateERmin = 24.3 dBOutput 2 (measured)Output 1 (measured)(b)1500 1520 1540 1560 1580 1600Wavelength (nm)-50-40-30-20-100Transmission (dB)Bar stateERmin = 23 dBOutput 1 (measured)Output 2 (measured)(c)Figure 2.10: A fabricated 2×2 broadband MZI switch. (a) Opti-cal image for the switch; (b) measured cross state performance; (c)measured bar state performance. Data in (b) and (c) were calibratedusing a pair of GCs connecting by a short waveguide.In this chapter, we have designed and demonstrated a compact, broad-band 3-dB coupler for the TE0 mode, which has coupling ratio imbalancesof less than 4.7%, in a 100 nm bandwidth from 1500 nm to 1600 nm. Theprinciple behind our coupler design is engineering the dispersion of cou-pling strengths in two-waveguide coupler systems by using a multi-segmentwaveguide structure that includes dispersive couplers and dispersive phaseshifters. Based on the broadband 3-dB coupler design, we have experimen-tally demonstrated a broadband MZI switch for the TE0 mode, which hasa 100 nm bandwidth with ERs of more than 23 dB, at both the cross andbar states.30Chapter 3Ultra-Low PowerThermo-Optic Switches 1Photonic switches with low-power consumption and compact size are highlydesired in large-scale switch matrices. As discussed in section 1.2.2, thermo-optic phase shifters can be compact in footprint due to the efficient thermo-optic effect, and are appropriate for compact switch designs. In recent years,various thermo-optic switches [24–26, 33, 36–40] have been demonstratedwith switching power consumption of typically more than tens of milliwatts.For large-scale switch matrix designs, it is always preferable to minimizethe power consumption of individual switch elements, so as to reduce powerbudget of the matrix.According to Eq. 1.3, the tuning strength of a thermo-optic phase shifteris proportional to the heating length, L, and the waveguide temperaturechange, ∆T . Based on this rule, much work has been devoted to reducingthe power consumption of thermo-optic switches [33, 55, 56]. Among theefforts working on increasing heating length, L, a Michelson interferometer(MI) configuration was demonstrated, which can double L as light travelthrough the heated waveguide by twice, and therefore has lower power con-sumption than a regular MZI switch by a factor of two [55]. In [56], ademonstrated MZI switch with spiral waveguide configuration is able to in-crease L, and thus reduce power consumption down to 6.5 mW/pi. Amongthe efforts working on increasing temperature change, ∆T , using thermal1Part of the contents in this chapter have been published in two journal papers listedin the Preface. In terms of academic contributions to the thermo-optic phase shifterdesigns presented in Section 3.1, I conceived the initial idea of combining both thermalisolation structures and folded waveguide structures to improve tuning efficiency. K.Murray contributed the idea of using dissimilar waveguides for crosstalk suppression.313.1. Design of Ultra-Low Power Thermo-Optic Phase Shifterisolation structures is a promising approach [57–60], which remove materi-als surrounding the tuning regions to eliminate thermal leakage pathways.Based on thermal isolation structures, switches with low power consump-tions of down to 400 µW/pi have been reported [60].This chapter presents the design approach to further reduce the powerconsumption of silicon photonic thermo-optic switches. We present a novelthermo-optic phase shifter design featuring ultra-low power consumption.Based on this design, we demonstrate several ultra-low power thermo-opticswitches.3.1 Design of Ultra-Low Power Thermo-OpticPhase ShifterTiN heaterAirSiSiO2ŸŸŸg gw1 w2 w3 wNgwN-18 μm8 μmEtching window12 μm8 μmEtching window(a)ŸŸŸEtching windowEtching windoww1w2w3wNwN-1TiN heater(b)Figure 3.1: Schematics for the proposed ultra-low power phaseshifter. (a) Cross section; (b) top view.Our approach to achieve ultra-low power phase tuning is to increase boththe ∆T and L of thermo-optic phase shifters. Figures 3.1(a) and 3.1(b)illustrate the cross section and top view schematics for our ultra-low powerphase shifter design, respectively. As shown in Fig. 3.1(a), to increase ∆Tin tuning, the phase shifter is isolated by etching away the adjacent SiO2and underlying Si materials of the tuning region, through 8-µm-wide etchingwindows designed on both sides of the phase shifter. The 12-µm-wide regionbetween the etching windows is therefore suspended. Si waveguides and theTiN heater are both located in the suspended region. Mechanical supportfor the suspended region is through the west end and east end of the phaseshifter, as illustrated in 3.1(b). Silicon photonics foundries, such as IME,323.1. Design of Ultra-Low Power Thermo-Optic Phase Shifterhave standard fabrication processes to fabricate such a thermal isolationstructure, and we choose design parameters for our thermal isolation struc-ture based on specific design rules. We use a heat transport modelling solver[51] to simulate the temperature gradient at the cross section of the ultra-low power phase shifter, and the results are shown in Fig. 3.2(a), where thetuning power is 1mW/m in the 2D simulation. For purpose of comparison,we also investigate the temperature gradient of a regular phase shifter with-out thermal isolation structure, and the simulated results are shown in Fig.3.2(b). It can be seen that a much higher ∆T can be achieved in the phaseshifter with thermal isolation than the one without, for the same amount oftuning power.SiO2SiAir(μm)(μm)(a)SiO2Si(μm)(μm)(b)Figure 3.2: Heat transport modelling results for thermo-optic phaseshifters with tuning power of 1mW/m. (a) A proposed design withthermal isolation structure; (b) a regular design without thermal iso-lation structure.In our phase shifter design, waveguides are folded by N times in thesuspended region, as shown in Figs. 3.1(a) and 3.1(b). Such a configurationcan increase the heating length by a factor of N , because the dissipativeheat from heater can heat up more waveguides. However, N is limitedby the width of the suspended region and the optical crosstalk betweenwaveguides. In order to achieve a dense routing while keeping the crosstalkbetween waveguides sufficiently small, dimensions of folded waveguides aredesigned to be dissimilar with widths w1, w2, ... , and wN (the evanescentcoupling between dissimilar waveguides does not achieve the phase match-ing condition [61] so that the maximum power transfer between waveguides333.2. Ultra-Low Power Thermo-Optic On/Off SwitcheswA gap wB 200 400 600 800 1000−90−80−70−60−50−40−30−20−10Gap (nm)Maximum coupling (dB)  wA=400 nm; wB=500 nmwA=500 nm; wB=600 nmwA=400 nm; wB=600 nmFigure 3.3: Maximum coupling at 1550 nm between two waveguideswith dissimilar widths. Waveguide thicknesses are both 220 nm.can be limited). Figure 3.3 shows maximum coupling between dissimilarwaveguides with widths of 400 nm, 500 nm, and 600 nm, at the operationwavelength of 1550 nm, which were simulated based on the approach de-scribed in [17]. According to the results, a maximum coupling of less than-30 dB can be obtained for coupling gaps of greater than 400 nm.3.2 Ultra-Low Power Thermo-Optic On/OffSwitches3.2.1 DesignBased on the ultra-low power phase shifter design, we have demonstratedultra-low power on/off switches with Michelson interferometer (MI) con-figurations. Figure 3.4 shows the schematic for one of the demonstratedswitches. The switch consists of a 2×2, 3-dB adiabatic coupler [43] as boththe input power splitter and output power re-combiner for the switch, twobalanced waveguide phase arms that are folded several times, and two waveg-uide loop mirrors operating as reflectors at the end of the phase arms. Phasearm 1 is designed for phase tuning using our ultra-low power phase shifter.Several etching windows are designed on both sides of the tuning arm toform the thermal isolation structure that is illustrated in Fig. 3.1(a), with343.2. Ultra-Low Power Thermo-Optic On/Off SwitchesTiN heaterAirSi waveguideInputOutput2x2 adiabatic couplerLoop mirrorLoop mirrorTiN Heater6 μm 45 μmPhase arm 1Phase arm 28 μmEtching windows(a)InputOn state (𝛥φ = 0)Output Input OutputOff state (𝛥φ = π)(b)Figure 3.4: An ultra-low power Michelson interferometer on/offswitch. (a) Schematic of the switch; (b) block diagrams for switchingstates.each window being 8-µm-wide and 45-µm-long. The purpose of using severalshort etching windows with supporting bridges in between is to ensure themechanical stability of the suspended region.The MI switch is a 1 × 1 (1 input and 1 output) device. Figure 3.4(b)illustrates the operation principle of the MI switch. Ideally, the switchoperates at the on-state by having a phase tuning, ∆ϕ, of 0, which directsinput signal to the output port; it operates at the off-state by having a phasetuning ∆ϕ of pi, which reflects back the input signal. The phase tuning forsuch a MI switch is given by:∆ϕ ∝ 2piλdndT∆T 2NL (3.1)where λ is the operating wavelength; dndT = 1.86 × 10−4K−1 is the thermo-optic coefficient of Si at room temperature, and ∆T is the temperaturechange for waveguides in the tuning region; N is the folding turns for waveg-uides; L=249 µm is heater length. The MI configuration doubles the phasetuning efficiency because light travels through each phase arm twice, and asa result, 2NL is the total heating length for the phase shifter.353.2. Ultra-Low Power Thermo-Optic On/Off Switches3.2.2 Characterization ResultsThe on/off switch designs were fabricated using a 248 nm deep ultra-violet(DUV) lithography process at the IME. Numerous switches with differentdesign parameters were fabricated on the same wafer to investigate the con-tributions of the thermal isolation and the folded waveguides on the phasetuning efficiency. Table 3.1 lists the fabricated devices. Figures 3.5(a) and3.5(b) respectively show optical images for the fabricated Device 5 and De-vice 6 in a lithography die.To characterize spectral responses, we used an Agilent 81600B tunablelaser as the optical input source, an Agilent 81635A optical power sensoras the optical output detectors, and a Keithley 2602A source meter as theelectrical power source for thermal tuning, as illustrated in Fig. 3.6(a). Tocharacterize switching speeds, we used an electrical square-wave generatoras triggering source to the switches, and used a high-speed photodetectorand an oscilloscope to measure the responses of switches.Table 3.1: List for the fabricated on/off switchesDevice # N Thermal isolation g (nm) wi (nm) 2NL (mm)1 1 No NA w1=500 0.4982 1 Yes NA w1=500 0.4983 7 No 1000 w1,4,7=500,w2,5=600,w3,6=4003.4864 7 Yes 1000 w1,4,7=500,w2,5=600,w3,6=4003.4865 11 No 430 w1,4,7,10=500,w2,5,8,11=600,w3,6,9=4005.4786 11 Yes 430 w1,4,7,10=500,w2,5,8,11=600,w3,6,9=4005.478g is the gap between waveguides, and wi is the width of waveguide i, asdescribed in Fig. 3.1(a). 2NL is the waveguide heating length.363.2. Ultra-Low Power Thermo-Optic On/Off Switches130 μmDevice 5InputOutput2x2 3-dB couplerMetal heater400 μm(a)Etching windows2x2 3-dB couplerMetal heaterInputOutput400 μm130 μmDevice 6(b)Figure 3.5: Optical images for the fabricated ultra-low powerthermo-optic on/off switches. (a) A switch without thermal isolationstructure; (b) a switch with thermal isolation structure.DetectorAgilent81635AInputgrating couplerOutputgrating couplerBroadband LaserAgilent81600BSwitchPower sourceKeithely 2602 A(a)Inputgrating couplerOutputgrating couplerBroadband LaserAgilent81600BSquare-wave generatorSwitchHigh-speed PD(b)Figure 3.6: Block diagram illustrating the measurement setups. (a)Spectrum characterization; (b) switching speed characterization.373.2. Ultra-Low Power Thermo-Optic On/Off SwitchesFirst, we present measurement results for Device 6, which is the bestdesign in terms of tuning efficiency. Figure 3.7(a) presents the spectral re-sponses at both the on-state and off-state for such a switch. The switchhas an insertion loss of less than 5.1 dB in the entire optical C-band, whichincludes the round-trip optical propagation loss in the 4.27 mm long waveg-uide (about 3 dB), the insertion loss for the 32 waveguide bends with radiiof 5 µm (about 0.01 dB per bend [17] and 0.64 dB for the round-trip loss),the insertion loss of the Y-junction [62] waveguide loop mirror (about 0.3 dBper device and 0.6 dB for the round-trip loss), and the optical propagationloss for a 1.3 mm long waveguide connecting the device to the input andoutput GCs in the layout (about 0.3 dB). The insertion loss of the switchwas calibrated by using a pair of GCs connected by a short waveguide,which is similar to the calibration structure shown in Fig. 2.7. As shown inFig. 3.7(b), at the operation wavelength of 1550 nm, the measured powerconsumption to switch from minimum to maximum output transmission is50 µW, and the switching ER is over 25 dB. Figure 3.7(c) shows measuredtime-domain response for the switch triggered by a 100 Hz square-wave sig-nal having a rise time of 300 ns. According to the result, the switch has a10%–90% rise time of 551 µs.For comparisons, measurement results for all switches are summarizedin Table 3.2. According to the results, switching power consumption canbe significantly reduced by increasing folding turns, N , and/or using ther-mal isolation structures, which are supported by Eq. 3.1. However, switcheswith thermal isolation structures have a much longer rise time (i.e., beingslower) than those without. This observation demonstrates a good trade-off between switching power and switching speed in our switch designs. Inpractical deployments, the choice of switch design will be application depen-dent. Thermo-optic switches with thermal isolation structures are suitablefor network reconfiguration within data center, where switching time of mil-liseconds is typical. For packet switching applications, which have typicalswitching time of nanoseconds to microseconds, carrier injection switchesare suitable.383.2. Ultra-Low Power Thermo-Optic On/Off Switches1530 1540 1550 1560 1570Wavelength (nm)-35-30-25-20-15-10-50Transmission (dB)Off stateOn state(a)0 25 50 75 100 125 150 175 200Power Consumption ( W )-35-30-25-20-15-10-50Transmission (dB)50 μWER = 26 dB(b)-1 -0.5 0 0.5 1 1.5 2Time (ms)00.20.40.60.81Normalized TransmissionSwitchTriggerRise time = 551 μs(c)Figure 3.7: Measurement results for Device 6. (a) on/off states trans-mission spectra; (b) transmission at 1550 nm versus tuning power; (c)time-domain response at 1550 nm.Table 3.2: Performance comparison for the fabricated on/off switchesNWithout thermal isolation With thermal isolationRise time Power consumption Rise time Power consumption(ms) (mW) (ms) (mW)1 0.017 17.19 0.520 0.5177 0.018 3.07 0.519 0.09411 0.019 1.75 0.551 0.05393.3. Ultra-Low Power Thermo-Optic Cross/Bar SwitchesPhase arm 1Phase arm 2Input 1Input 2Output 1Output 2Etching windowsTiN Heater2x2 3-dB coupler2x2 3-dB couplerFigure 3.8: Schematic of an ultra-low power MZI cross/bar switch.3.3 Ultra-Low Power Thermo-Optic Cross/BarSwitches3.3.1 DesignBased on the proposed ultra-low power phase shifter design, we have alsodemonstrated ultra-low power, MZI cross/bar switches, which are the essen-tial building blocks for large-scale switch matrices. The schematic of such aswitch, as shown in Fig. 3.8, consists of two 2×2, 3-dB adiabatic couplers[43] and two phase arms based on folded waveguides. The phase arm 1 wasdesigned for phase tuning using the proposed ultra-low power phase shifter.The thermo-optic phase tuning for such an MZI switch is given by:∆ϕ ∝ 2piλdndT∆T NL (3.2)where N is the folding turns for waveguides; L is the heater length, and NLis the total heating length for the phase shifter.3.3.2 Characterization ResultsThe MZI cross/bar switches were fabricated together with the MI on/offswitches. We used the same photonics testing setups shown in Fig. 3.6 tocharacterize the fabricated switches. In our measurements, we used input 1,as labeled in Fig. 3.8, for optical input source and measured the transmis-sions at the two switch outputs. Figure 3.9 presents measurement results forthe best design in terms of power consumption. As shown in Fig. 3.9(a), at403.4. Breakdown Test0 50 100 150 200 250 300Power Consumption ( W )-35-30-25-20-15-10-50Transmission (dB)Output 1Output 284 μWλ=1550 nmCross BarER = 23 dB(a)1530 1540 1550 1560 1570Wavelength (nm)-35-30-25-20-15-10-50Transmission (dB)BAR stateOutput 1Output 2Output 1Output 2(b)1530 1540 1550 1560 1570Wavelength (nm)-35-30-25-20-15-10-50Transmission (dB)CROSS stateOutput 1Output 2Output 1Output 2(c)Figure 3.9: Measurement results for a fabricated ultra-low powerMZI cross/bar switch. (a) Output transmissions at 1550 nm versustuning power; (b) output spectra at the bar state; (c) output spectraat the cross state.1550 nm operation wavelength, the power consumption to switch from oneswitching state to the other is only 84 µW, and the switching ER is over 20dB. Figures 3.9(b) and 3.9(c) show the measured output spectra at the barstate and the cross state, respectively.3.4 Breakdown TestMechanical failures, such as deformation and rupture, in the suspended re-gion of our ultra-low power, thermo-optic phase shifters can cause optical413.4. Breakdown Testinsertion loss, and hence degrade the switching ER. Mechanical strength ofthe demonstrated ultra-low power switches can be tested by measuring theoptical output transmission of a switch versus electrical tuning power. Asour demonstrated switches have similar design parameters for their thermalisolation structures, breakdown test was only performed on Device 2 that islisted in Table 3.1. Figure 3.10 shows breakdown test results for Device 2.We can see that the maximum output transmission of the switch decreaseswhen the tuning power is greater than 37 mW, which indicates that me-chanical failures start to happen at a tuning power of approximately 37 mW(being 71.5× of the cross/bar switching power consumption). Based on thenumber of switching cycles observed from Fig. 3.10, the temperature change∆T that triggers mechanical failures can be inferred, which is approximately670 K. Our breakdown test results are in good agreements with the resultsof a published report [63], which used a similar thermal isolation structureand suggested a reversible over-drive range up to 60× of switching powerconsumption.0 10 20 30 40 50 60 70Power consumption (mW)-20-15-10-50Transmission (dB)Mechanical failure ΔT ≈ 670 K ≈37 mW Figure 3.10: Breakdown test results for a demonstrated ultra-lowpower thermo-optic switch.In summary, in this chapter we have experimentally demonstrated ultra-efficient, thermo-optic on/off switches and cross/bar switches, which haveextremely low power consumptions of down to 50 µW/pi. The ultra-lowpower switching was realized by adopting both thermal isolation structures423.4. Breakdown Testand densely folded waveguides in the phase shifter designs. The powerphases shifters can be further optimized to reduce the optical insertion losswhile maintaining their tuning efficiency.43Chapter 4Crosstalk-free CarrierInjection Tri-State SwitchesAs discussed in section 1.2.2, a common method to achieve high-speed phasetuning on SOI platforms is using P-i-N diodes operating in a carrier injectionmode [21–23, 28, 41, 42]. While providing an efficient optical phase shiftwith a speed of up to hundreds of MHz, carrier injection also producesinherent insertion loss due to free-carrier absorption [18]. This is problematicfor a MZI cross/bar switch that is operating at the bar state, where oneof its phase shifters is tuned by a pi phase shift while the other is not,as illustrated in Fig. 1.4. In such a state, the optical power in the twowaveguide arms of the switch is unbalanced, leading to a large crosstalkat the cross output port [21–23, 28, 42]. Theoretical analysis on the barstate switching crosstalk versus power imbalance in a MZI cross/bar switchhas been reported in [41]. In order to suppress crosstalk, the optical powerinside a MZI cross/bar switch needs to be balanced. Recently, a solution[64] using a nested MZI structure with a variable optical attenuator wasproposed. Although this solution balances the optical power in the switchand therefore achieves low crosstalk performance, the optical bandwidth ofthe switch is strongly limited by its asymmetric interferometer structure. Tothe best of our knowledge, there is no efficient method that can balance theoptical power in a carrier injection based MZI cross/bar switch to achievelow crosstalk performance while maintaining broadband operation.In this chapter, we design a novel carrier injection switch that is bothbroadband and crosstalk-free, and additionally it offers three switching states:cross, bar, and blocking. We will present the design, operation principles,444.1. Switch Designand performance of the proposed switch. We will show the advantages oftri-state switches in the operations of N ×N switch matrices.4.1 Switch Design4.1.1 SchematicFigure 4.1(a) shows the schematic for a regular MZI cross/bar switch. Figure4.1(b) shows the schematic for the proposed tri-state switch, which is a 2×2device based on a balanced nested Mach-Zehnder interferometer (BNMZI)structure. Such a device consists of an input 2×2 coupler, an output 2×2coupler, and two balanced main interference arms with each being a balanced2×2 MZI, i.e., nested MZI A and nested MZI B as shown in Fig. 4.1(b). Eachnested MZI has two identical carrier injection phase shifters. The BNMZIInput 1Input 2Output 1Output 2P+	dopant N+	dopantWaveguidePhase shifter 1Phase shifter 2Legends:(a)Phase shifter 1ab dca’b’ d’c’Input 1Input 2Output 1Output 2Input 2x2 couplerOutput 2x2 couplerNested MZI ANested MZI BPhase shifter 2Phase shifter 3Phase shifter 4(b)Figure 4.1: (a) Schematic for a Mach-Zehnder interferometer (MZI)switch; (b) Schematic for the proposed balanced nested Mach-Zehnderinterferometer (BNMZI) switch.454.1. Switch Designswitch has a balanced architecture, in which the optical path lengths throughthe two main interference arms are equal; as a result, optical broadbandperformance can be achieved.4.1.2 Operation PrinciplesThe transfer matrix method is used to analyze the operation principles of theproposed BNMZI switch. The relationship between the input and outputelectric fields for the two nested MZIs are given by:[EcEd]=[t −jκ−jκ t][A1e−jφ1 00 A2e−jφ2][t −jκ−jκ t] [EaEb](4.1)[Ec′Ed′]=[t −jκ−jκ t][A3e−jφ3 00 A4e−jφ4][t −jκ−jκ t] [Ea′Eb′](4.2)where Ex=a,b,c,d... is the electric field at port x of the nested MZIs, as il-lustrated in Fig. 4.1(b); t and κ are through-coupling coefficient and cross-coupling coefficient for each 2×2 coupler, respectively, and we assume thatall of the 2×2 couplers in the BNMZI switch are identical and lossless, i.e.,t2 + κ2 = 1; φi=1,2,3,4 is the modulated optical phase shift of phase shifteri; Ai=1,2,3,4 is optical field transmission factor of phase shifter i, and it rep-resents the optical field attenuation due to free-carrier absorption in phasetuning. In our switch design, ports a and b’ are both terminated, i.e.,Ea = Eb′ = 0, and accordingly we obtain the electric field transfer functionsfor the light paths from ports b to d and from ports a’ to c’, which are:EdEb= −κ2A1e−jφ1 + t2A2e−jφ2 (4.3)Ec′Ea′= −κ2A4e−jφ4 + t2A3e−jφ3 (4.4)464.1. Switch DesignThe relationship between the input and output electric fields of the BNMZIswitch are given by:[Eout1Eout2]=[t −jκ−jκ t]EdEb 00 Ec′Ea′[ t −jκ−jκ t][Ein1Ein2](4.5)Assuming light is launched into input 1 of the switch, i.e., Ein1 = 1 andEin2 = 0, the two outputs are thus given by:|Eout1|2 = | − t2κ2A1e−jφ1 + t4A2e−jφ2 − t2κ2A3e−jφ3 + κ4A4e−jφ4 |2 (4.6)|Eout2|2 = |−jκt(−κ2A1e−jφ1 +t2A2e−jφ2 +t2A3e−jφ3−κ2A4e−jφ4)|2 (4.7)The nested MZIs A and B of the BNMZI switch can be driven in abalanced manner in order to balance the free-carrier absorption inducedinsertion loss in the switch, and therefore, the switch can be crosstalk-free.The operation principles of the BNMZI switch are described as follows:Cross StateWhen φ1=φ4=0 and φ2=φ3=pi, we have A1=A4=1 and A2=A3=Api, whereApi ≤ 1 is optical field transmission factor for the pi phase tuning and isdependent on the design parameters of the phase shifter, e.g., phase shifterlength and optical confinement of the waveguide, which will be discussedin Section 4.1.3. In such phase tuning, the nested MZI A routes light fromports b to d (see Fig. 4.1(b)) with a digital pi phase shift, and the nestedMZI B routes light from ports a’ to c’ (see Fig. 4.1(b)) also with a digitalpi phase shift. As a result, the BNMZI switch operates in the cross state[17]. In addition, the insertion loss for the light path from ports b to dand that from ports a’ to c’ are balanced in such balanced phase tuning,and hence, the BNMZI switch can be crosstalk-free. Based on Eqs. 4.6 and4.7, we calculate the optical output transmissions of the BNMZI switch as afunction of κ2 and Api, and the results for output 1 and output 2 are shown in474.1. Switch DesignFigs. 4.2(a) and 4.2(b), respectively. According to the results, light launchedat input 1 is cross-switched to output 2. Ideally, when the 2×2 couplers ofthe BNMZI switch are perfect 3-dB couplers, i.e., κ2 = t2 = 0.5, the outputtransmissions are given by:|Eout1|2 = 0; |Eout2|2 = 14(1 +Api)2 (4.8)which shows crosstalk-free performance for any Api.−48−48−48−48−48−48−40−40−40−40−40−40−32−32−32−32−32−32−28−28−28−28−28−28−24−24−24−24−24−24−20−20−20−20−20−20Cross−coupling ratio, κ2Optical field transmission factor, Api Output 1  0.4 0.45 0.5 0.55 0.60.50.60.70.80.9Transmission (dB)−50−40−30−20−100(a)−3−2.5 −2−2 −1.5−1.5−1−1−0.5−0.5Cross−coupling ratio, κ2Optical field transmission factor, Api Output 2  0.4 0.45 0.5 0.55 0.60.50.60.70.80.9Transmission (dB)−50−40−30−20−100(b)Figure 4.2: Cross state output transmissions as a function of κ2 andApi. (a) Output 1. (b) Output 2.Bar StateWhen φ1=φ3=pi and φ2=φ4=0, we have A1=A3=Api and A2=A4=1. Insuch phase tuning, the nested MZI A routes light from ports b to d (seeFig. 4.1(b)) with a digital 0 phase shift, while the nested MZI B routeslight from ports a’ to c’ (see Fig. 4.1(b)) with a digital pi phase shift. As aresult, the BNMZI switch operates in the bar state. And more, the insertionloss for the light path from ports b to d and that from ports a’ to c’ arebalanced in such balanced phase tuning, and hence, the BNMZI switch canbe crosstalk-free. Based on Eqs. 4.6 and 4.7, we calculate the optical outputtransmissions of the switch as a function of κ2 and Api, and the results foroutput 1 and output 2 are shown in Figs. 4.3(a) and 4.3(b), respectively. Ascan be seen from the results, light launched at input 1 is routed to output484.1. Switch Design1. Ideally, when κ2 = t2 = 0.5, the output transmissions are given by:|Eout1|2 = 14(1 +Api)2; |Eout2|2 = 0 (4.9)In this case, the switch is crosstalk-free for any Api.−2−2−1.5−1.5−1−1−0.5−0.5Cross−coupling ratio, κ2Optical field transmission factor, Api Output 1  0.4 0.45 0.5 0.55 0.60.50.60.70.80.9Transmission (dB)−80−60−40−200(a)−64−64−64−64−64−64−56−56−56−56−56−56−56−56−48−48−48−48−48−48−40−40−40−40−40−40 −32−32−32−32Cross−coupling ratio, κ2Optical field transmission factor, Api Output 2  0.4 0.45 0.5 0.55 0.60.50.60.70.80.9Transmission (dB)−80−60−40−200(b)Figure 4.3: Bar state output transmissions as a function of κ2 andApi. (a) Output 1. (b) Output 2.Blocking StateWhen no phase tuning is applied, i.e., φ1 = φ2 = φ3 = φ4 = 0, we haveA1 = A2 = A3 = A4 = 1. In such a state, the nested MZI A routes lightfrom ports b to c (see Fig. 4.1(b)) and the nested MZI B routes light fromports a’ to d’ (see Fig. 4.1(b)), as each nested MZI operates in a cross state.No light is routed to the switch outputs. Both the ports c and d’ can beterminated using waveguide terminators. Figures 4.4(a) and 4.4(b) showthe optical transmissions at output 1 and output 2 as a function of κ2 atsuch a state, which are calculated based on Eqs. 4.6 and 4.7, respectively.According to the results, the optical transmissions at the two outputs areboth low, indicating that the input light is blocked from reaching the twooutputs. Ideally, when κ2 = t2 = 0.5, we obtain:|Eout1|2 = |Eout2|2 = 0 (4.10)494.1. Switch Design0.4 0.45 0.5 0.55 0.6Cross-coupling ratio, 2-50-40-30-20-100Transmission (dB)Output 1(a)0.4 0.45 0.5 0.55 0.6Cross-coupling ratio, 2-50-40-30-20-100Transmission (dB)Output 2(b)Figure 4.4: Blocking state output transmissions as a function of κ2.(a) Output 1. (b) Output 2.which shows that the switch is completely blocked.Table 4.1 summarizes the phase tunings for the three switching states.Note that for all of the three switching states, the deviation of κ2 (κ2 6= 0.5)breaks the balance of power in the switch and consequently causes switchingcrosstalk, which are shown in Figs. 4.2(a), 4.3(b), 4.4(a) and 4.4(b). How-ever, this is an issue due to the imperfect performance of 2×2 3-dB couplersrather than a performance limitation of the proposed BNMZI switch.Table 4.1: Phase tuning for the switching states of BNMZI switch.Switching state φ1 φ2 φ3 φ4Cross 0 pi pi 0Bar pi 0 pi 0Blocking 0 0 0 04.1.3 Carrier Injection Phase Shifter Design4.1.3.1 Free-carrier Absorption LossFigure 4.5 illustrate the schematic for a carrier injection phase shifter thatis designed based on the 220 nm SOI platform. The optical phase tuning504.1. Switch DesignFigure 4.5: Schematic of a carrier injection phase shifter design ona silicon-on-insulator (SOI) platform.∆ϕ for such a phase shifter is given by:∆ϕ = 2piλ∂neff∂n∆nL (4.11)where ∆n is the change of refractive index of Si; ∂neff∂n is susceptibility, i.e., amode-dependent coefficient, and ∂neff∂n ∆n represents the change of effectiveindex of the waveguide; L is the phase shifter length.Based on Eqs. 1.1, 1.2, and 4.11, the change of waveguide absorption,∆α, versus phase shifter length, L, for a pi phase shift can be calculated, andthe results are shown in Fig. 4.6(a). Accordingly, the optical field transmis-sion factor, Api, which describes waveguide loss due to free-carrier absorptionin a pi phase shift, is given by:Api = e−Γ∆α2 L (4.12)where Γ is optical field confinement factor for the light in waveguide. For ex-ample, the TE0 mode light propagating in the phase shifter design shown inFig. 4.5 has an optical field confinement factor of 0.7, which is calculated us-ing an Lumerical MODE Solutions [51]. Figure 4.6(b) shows the calculatedApi versus L for Γ = 0.7. It is found that the free-carrier absorption lossof a carrier injection phase shifter is dependent on its phase shifter length.514.1. Switch Design0 200 400 600 800 1000Phase shifter length L [ m]0102030405060Change of waveguide absorption  [cm-1 ](a)0 200 400 600 800 1000Phase shifter length L [ m]0.80.850.90.951Optical field transmission factor, A(b)Figure 4.6: Performance of the carrier injection phase shifter with api phase shift. (a) Change of waveguide absorption, ∆α, versus phaseshifter length, L; (b) optical field transmission factor, Api, versus phaseshifter length, L. Waveguide propagation loss is not included in theApi calculation.For low loss carrier injection phase shifter designs, L ≥ 200 µm is typicallyrequired, and such a design rule was deployed in many demonstrated de-signs [21–23, 28, 41, 42]. Note that the data presented in Fig. 4.6(b) doesnot include the waveguide propagation loss. However, for very long phaseshifters, the propagation loss (scattering, e.g., 3 dB/cm) will dominate andlead to the switch having a large insertion loss.524.1. Switch Design4.1.3.2 Power ConsumptionWe assume that every electron and hole recombine in the intrinsic Si regionwith a non-radiative recombination time constant τn. For carrier injectioneffect, the change of carrier concentration, ∆N , in the intrinsic Si regionversus the injection current, I, is given by:∆N = IτnqSL(4.13)where q is the electrical charge; S is the area of the intrinsic region. Fora pi phase shift, the injected current, I, versus the phase shifter length, L,can be calculated based on Eqs. 1.1, 4.11, and 4.13, and the results areshown in Fig. 4.7(a). In the calculation, τn = 4 ns is used according to [42].The current-voltage (I-V) relation for the carrier injection phase shifter isdescribed by the Shockley diode equation:I = Is(eqVnkT − 1) (4.14)where k is Boltzmann’s constant; T is absolute temperature; n = 1 is ide-ality factor; Is is reverse bias saturation current for the P-i-N diode shownin Fig. 4.5, which can be calculated based on diode equations. Based onEq. 4.14 and the results shown in Fig. 4.7(a), the pi phase shift power con-sumption versus L can be thus determined, which is shown in Fig. 4.7(b).It is found that the power consumption of a carrier injection phase shifterdecreases with the increase of the phase shifter length.Based on the analysis in above, we can conclude that a long carrierinjection phase shifter design has benefits of both low absorption loss andlow power consumption.4.1.3.3 Tuning SpeedTuning speeds of carrier injection phase shifters are primary limited by thecarrier recombination lifetime in the intrinsic Si region, which is in the scaleof a few nanoseconds [42] and can not be engineered via the layout, except534.2. Performance0 200 400 600 800 1000Phase shifter length L [ m]2.42.62.833.23.4Injected current [mA](a)0 200 400 600 800 1000Phase shifter length L [ m]2.22.42.62.833.2Power consumption [mW](b)Figure 4.7: Electrical responses of the carrier injection phase shifterfor a pi phase shift. (a) Injected current, I, versus phase shifter length,L; (b) power consumption versus phase shifter length, L.by changing the doping concentration of the waveguide.4.2 PerformanceWe compare the BNMZI switch shown in Fig. 4.1(b) with the MZI switchshown in Fig. 4.1(a) by investigating the impacts of κ2 variations on theircross/bar switching performance. Simulations are performed using a pho-tonic circuit simulator, Lumerical INTERCONNECT [51], as shown in Fig.544.2. Performance4.8. In the simulations, each carrier injection phase shifter of the twoswitches is 250 µm long with an optical field confinement factor of 0.7, whichis similar to many demonstrated designs [21–23, 28, 41, 42]. According tothe analysis results shown in Fig. 4.6(b), such a phase shifter design has anApi of 0.8613. The tuning responses of each phase shifter are implementedas a script within the component model in Lumerical INTERCONNECT.BNMZI switch(a)MZI switch(b)Figure 4.8: Circuit simulation schematics. (a) BNMZI switch; (b)MZI switch.We assume that the 2 × 2 couplers in each switch have identical cou-pling strength due to a uniform fabrication variation across the switch.Figure 4.9(a) compares the simulated cross state performance of the twoswitches, and it is found that the BNMZI switch has slightly lower crosstalkthan the MZI switch. Figure 4.9(b) compares the simulated bar state per-formance of the two switches. According to the results, the crosstalk of theMZI switch is greater than -23 dB for the κ2 range from 0.4 to 0.6. Mean-while the crosstalk of the BNMZI switch is well below -37 dB in the sameκ2 range, being much lower than the crosstalk of the MZI switch. For a BN-MZI switch design using high performance 3-dB couplers [65] which haveκ2 in between 0.48 and 0.52, the crosstalk at the bar state can be reducedto below -50 dB. According to the results in above, the proposed BNMZIswitch exhibits better performance than the MZI switch.In practice, the 2 × 2 couplers in switches may have different couplingstrengths due to random fabrication errors. Such an effect can be taken554.2. Performance0.4 0.45 0.5 0.55 0.6Cross-coupling ratio, 2-50-40-30-20-100Transmission (dB)Cross stateThrough (MZI)Cross (MZI)Through (BNMZI)Cross (BNMZI)Crosstalk(a)0.4 0.45 0.5 0.55 0.6Cross-coupling ratio, 2-50-40-30-20-100Transmission (dB)Bar stateThrough (MZI)Cross (MZI)Through (BNMZI)Cross (BNMZI)Crosstalk(b)Figure 4.9: Performance comparison for the BNMZI switch and theMZI switch, when the 2× 2 couplers in the switches have identical κ2.(a) Cross state performance; (b) bar state performance.into account in our performance comparison by using simple Monte Carlo(MC) simulations. In the MC simulations, each 2× 2 coupler has a randomκ2 in between 0.48 and 0.52. Figures 4.10(a) and 4.10(b) show the crossstate and the bar state performance of the BNMZI switch, respectively, in200 MC simulation trials; Figs. 4.10(c) and 4.10(d) present the cross stateand the bar state performance of the MZI switch, respectively, in 200 MCsimulation trials. By comparing the results, we can find that both switcheshave variations in their switching crosstalk due to the random variations ofκ2. At the cross state, both switches have similar switching crosstalk, asshown in Figs. 4.10(a) and 4.10(c); at the bar state, the worst crosstalk ofthe BNMZI switch is almost 10 dB lower than that of the MZI switch, asshown in Figs. 4.10(b) and 4.10(d). Overall, the proposed BNMZI switchexhibits better performance than the MZI switch.It should be noted that the BNMZI switch requires two-fold tuningpower consumption as compared with the MZI switch. However, the powerconsumption can be reduced by increasing the phase shifter length, as perFig. 4.7(b).564.3. Crosstalk Suppression Functionality0 50 100 150 200Simulations-50-40-30-20-100Transmission (dB)BNMZI -- Cross stateWorst crosstalk  -28.7 dB 0 0.2 0.4 .6 0.8 1 1.2 1.4 1.6 1.8 200.20.40.60.811.21.41.61.82ThroughCross(a)0 50 100 150 200Simulations-50-40-30-20-100Transmission (dB)BNMZI -- Bar stateWorst crosstalk -28.8 dB 0 0. 0.4 .6 0.8 1 1.2 1.4 1.6 1.8 200.20.40.60.811.21.41.61.82ThroughCross(b)0 50 100 150 200Simulations-50-40-30-20-100Transmission (dB)MZI -- Cross stateWorst crosstalk -28.5 dB 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 200.20.40.60.811.21.41.61.82ThroughCross(c)0 50 100 150 200Simulations-50-40-30-20-100Transmission (dB)MZI -- Bar stateWorst crosstalk -19 dB 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 200.20.40.60.811.21.41.61.82ThroughCross(d)Figure 4.10: (a) and (b) are Monte Carlo (MC) simulation resultsfor the BNMZI switch operating at the cross state and the bar state,respectively. (c) and (d) are MC simulation results for the MZI switchoperating at the cross state and the bar state, respectively. In the MCsimulations, each 2× 2 coupler has a random κ2 in between 0.48 and0.52.4.3 Crosstalk Suppression FunctionalityAccording to Eqs. 4.8, 4.9, and 4.10, ideally the BNMZI switch can becrosstalk-free if its 2×2 couplers have perfect 3-dB coupling ratios. How-ever, most SOI based 2×2 couplers exhibit unbalanced coupling ratios due toeither imperfect designs or fabrication variations, and as a result, crosstalkwill exist for a BNMZI switch in practice. According to the analytical calcu-574.3. Crosstalk Suppression Functionalitylation results shown in Figs. 4.2, 4.3 and 4.4, Table 4.2 presents performanceof an example BNMZI switch having Api of 0.8613 for a pi phase tuning andκ2 of 0.48 for its imperfect 2×2 couplers (based on the performance of thedemonstrated broadband 3-dB coupler presented in Fig. 2.8(b)).Table 4.2: Performance of an example BNMZI switch with κ2 = 0.48and Api = 0.8613.Cross Bar BlockingThrough-port transmission (dB) -28.61 -0.62 -55.92Cross-port transmission (dB) -0.65 -51.14 -27.97For a N × N photonic switch matrix built on imperfect switching ele-ments, crosstalk can be accumulated along a connection route from an inputto an output, which degrades the performance of the N ×N switch matrix.The unique blocking state of the BNMZI switch is capable of suppressingcrosstalk in N ×N switch matrices, such as dilated Banyan [66, 67], hybriddilated Benes [68], and route-and-select [69] architectures. The strength ofcrosstalk suppression depends on both the architecture and the connectionloading of the switch matrix.4.3.1 Crosstalk Suppression for Partially-Loaded SwitchesFor dilated Benes [66, 67] and hybrid dilated Benes [68] architectures, idleswitches exist in a partially-loaded switch matrix. The first order crosstalk inthese architectures can be eliminated by constraining connection routing toone signal per switching element [68], as illustrated in Fig. 4.11; the secondand higher order crosstalk can be suppressed by assigning blocking stateto the idle switching elements in the matrix. As an illustrative example,we simulate the performance of a half-loaded 8×8 dilated Benes switch,which uses the 2×2 BNMZI switch presented in Table 4.2 as its switchingelements, and we compare the switching crosstalk in the cases with andwithout assigning blocking states to the idle switches. Figure 4.12(a) showsthe schematic of the 8×8 dilated Benes switch with established connections:I1-O5, I4-O4, I6-O1, and I7-O7, where idle switches can be seen in the584.3. Crosstalk Suppression Functionalityλ1First-order crosstalk unsuppressedλ2λ1λ2λ1λ1First-order crosstalk suppressedFigure 4.11: Illustration for first-order crosstalk suppression.connections. In our simulations, waveguide crossings in the 8×8 switch areassume to be lossless and crosstalk-free in order to isolate the impacts of theBNMZI switch on the performance of the 8×8 switch. Figure 4.12(b) showsthe simulated output transmissions of the 8×8 switch when the idle switchesare randomly at the cross or bar state. As a comparison, Fig. 4.12(c) presentsthe simulated output transmissions of the 8×8 switch when the idle switchesare assigned to the blocking state. It can be seen that the worst outputcrosstalk of the 8×8 switch is drastically suppressed by more than 25 dB,from -32.4 dB in the case of without blocking the idle switches, as shown inFig. 4.12(b), down to -59.8 dB in the case of blocking the idle switches, asshown in Fig. 4.12(c).4.3.2 Crosstalk Suppression for Fully-Loaded SwitchesA fully loaded dilated Banyan architecture has a total of 2N(N−1) switchingelements but only uses 2N ∗ log2N switching elements for connections. Idleswitches in the matrix can be blocked for crosstalk suppression. As anillustrative example, we simulate the performance of a fully loaded 8×8dilated Banyan switch, which uses the 2×2 BNMZI switch presented inTable 4.2 as its switching elements, and we compare the switching crosstalkin the cases with and without assigning blocking states to the idle switches.Figure 4.13(a) illustrates the schematic of the 8×8 dilated Banyan switchwith established connections: I1-O3, I2-O7, I3-O5, I4-O1, I5-O6, I6-O2, I7-O4, and I8-O8. In our simulations, waveguide crossings in the 8×8 switch areassumed to be lossless and crosstalk-free in order to isolate the impact of theBNMZI switch on the performance of the 8×8 switch. Figure 4.13(b) show594.3. Crosstalk Suppression FunctionalityO1 O2 O3 O4 O5 O6 O7 O8Output Channel-90-80-70-60-50-40-30-20-100Output transmission (dB)Idle switches in blocking stateI1I4I6I7O1 O2 O3 O4 O5 O6 O7 O8Output Channel-90-80-70-60-50-40-30-20-100Output transmission (dB)Idle switches in random (cross/bar) statesI1I4I6I7I1I2I3I4I5I6I7I8O1O2O3O4O5O6O7O8Worst crosstalk( -32.4 dB)(a)(b)(c)Worst crosstalk( -59.8 dB)Figure 4.12: (a) Schematic of an example 8×8 dilated Benes switchfabric with established connections: I1-O5, I4-O4, I6-O1, and I7-O7.(b) Output transmissions of the 8×8 switch without blocking theidle switches (idle switches are randomly at the cross or bar states).(c) Output transmissions of the 8×8 switch with blocking the idleswitches.the simulated output transmissions of the 8×8 switch where idle switches arerandomly at the cross or bar state. Figure 4.13(c) presents the simulationresults of the 8×8 switch where the idle switches are set to the blockingstate. Obviously, we can see that the worst output crosstalk for the 8×8switch is drastically suppressed by more than 50 dB, from -59.8 dB in thecase of without blocking the idle switches, as shown in Fig. 4.13(b), down to-114.4 dB in the case of blocking the idle switches, as shown in Fig. 4.13(c).In summary, in this chapter we have designed a high-performance tri-state switch based on a novel BNMZI structure. The switch has a balancedarchitecture, in which the optical path lengths are equal in its interferometerarms, so that broadband switching can be achieved. High-speed switching604.3. Crosstalk Suppression FunctionalityO1 O2 O3 O4 O5 O6 O7 O8Output Channel-140-120-100-80-60-40-200Transmission (dB)Idle switches in blocking stateI1I2I3I4I5I6I7I8O1 O2 O3 O4 O5 O6 O7 O8Output Channel-140-120-100-80-60-40-200Transmission (dB)Idle switches in random (cross/bar) statesI1I2I3I4I5I6I7I8I1I2I3I4I5I6I7I8O1O2O3O4O5O6O7O8Worst crosstalk ( -114.4 dB)Worst crosstalk( -59.8 dB)(a)(b)(c)Figure 4.13: (a) Schematic of an example 8×8 dilated Banyan switchfabric with established connections: I1-O3, I2-O7, I3-O5, I4-O1, I5-O6, I6-O2, I7-O4, and I8-O8. (b) Output transmissions of the 8×8switch without blocking the idle switches (idle switches are randomlyat the cross or bar states). (c) Output transmissions of the 8×8 switchwith blocking the idle switches.can be achieved using carrier injection phase tuning. The insertion loss ofcarrier injection phase tuning is balanced in the BNMZI structure due to thebalanced phase tuning to the switch, and hence the switch can be crosstalk-free in operation, which can not be achieved by regular carrier injection MZIswitches [21–23, 28, 41, 42]. As compared with regular carrier injection MZIswitches, the proposed BNMZI switch not only exhibits better performancebut also provides a unique blocking functionality, the later of which can beapplied to crosstalk suppression in N ×N switch matrices.61Chapter 5Polarization Control forSwitchesEdge coupling [17], as illustrated in Fig. 5.1(a), is a common solution tocouple light from optical fibres to silicon waveguides on chips. This approachcouples both TE and TM polarizations, and it has both broadband and lowloss performance. Depending on the polarization of the light in the fibre,the light coupled into a silicon “single-mode” waveguide can be in the TE0mode and/or the TM0 mode. Edge coupling efficiency can be determined byperforming mode overlap calculations for the fibre Gaussian beam with thewaveguide modes. As an example, Fig. 5.1(b) shows the simulated electricfield distribution of a fibre Gaussian beam with a waist radius of 2.5 µm anda polarization angle, θ; Figs. 5.1(c) and 5.1(d) respectively show the electricfield distributions for the TE0 mode and TM0 mode in a 180 nm × 220 nmedge coupler waveguide [17]; Fig. 5.1(e) shows the transmission power forthe coupled TE0 mode and TM0 mode in the waveguide, as a function of θ.According to Fig. 5.1(e), as θ increase, the transmission of the TE0 modedecrease while that of the TM0 mode increase. For optical systems usingpolarization-maintaining (PM) fibres for connections, θ is determined bythe alignment for the slow axis of the PM fibre to the horizontal surface ofthe silicon waveguide. For optical systems using regular single-mode fibres(SMFs) for connections, θ may vary in time due to changes of environmentconditions, such as temperature and stress.Silicon photonic devices are mode-sensitive. Most silicon photonic switchesare designed to operate using only the TE0 mode or the TM0 mode. Insuch switches, if both modes are present, crosstalk will typically increase.62Chapter 5. Polarization Control for SwitchesSilicon Photonics chipTE0 TM0Optical fiber(a)θxyFibre Gaussian beamy(μm)x (μm)(b)Waveguide TE0 modey(μm)x (μm)(c)Waveguide TM0 modey(μm)x (μm)(d)0 10 20 30 40 50 60 70 80 90Polarization angle  (degree)-40-30-20-100Transmission (dB)TE0 modeTM0 mode(e)Figure 5.1: (a) Edge coupling solution in silicon photonic integratedcircuits; (b) fibre Gaussian beam with a waist radius of 2.5 µm; (c)TE0 mode profile in a 180 nm × 220 nm edge coupler waveguide; (d)TM0 mode profile in a 180 nm × 220 nm edge coupler waveguide.(e) Power transmission for the coupled TE0 and TM0 modes versuspolarization angle, θ, of the fibre Gaussian beam.635.1. Broadband Polarization BeamsplitterOutput 1Output 2Phase	shifter	TE0    +   TM0Polarization	beamsplitterPolarization	beamsplitterInput 1Input 2TE0TM0Mach-Zehnder interferometer (MZI) switchFigure 5.2: A proposed polarization control solution for high perfor-mance silicon photonic switches, which uses polarization beam split-ters as input mode filters.As a result, silicon photonic switches require polarization control at switchinputs. One simple solution to polarization control is using polarizationbeamsplitters (PBSs) to filter away the undesired mode the switch inputs,as illustrated in Fig. 5.2. In such a solution, PBSs are required to havelow loss and broadband performance since MZI switches are designed to bebroadband.In this chapter, we present design and characterization results of a high-performance PBS that is broadband (i.e., operate over a wide wavelengthrange), low loss, easy to fabricate, and has a large modal isolation (i.e., effi-ciently separate the two mode types). The demonstrated PBS is integratedwith a broadband MZI switch for polarization control.5.1 Broadband Polarization BeamsplitterIn PICs, the PBS, which splits or combines the orthogonal TE modes andTM modes, is a fundamental component for polarization control. Ideally,a PBS should be broadband, low loss, compact in size, easy to fabricate,and has high isolation. In recent years, various PBS designs [70–83] havebeen reported on SOI platforms. However, most demonstrated devices havedisadvantages such as large excess loss (more than 1 dB), narrow operating645.1. Broadband Polarization Beamsplitterbandwidth (less than 50 nm), and low extinction ratio (less than 15 dB), be-ing incompatible with our proposed solution for polarization control, whichrequires broadband and low loss performance.5.1.1 Principles5.1.1.1 Approach to Split TE0 and TM0 ModesIn properly designed SOI directional couplers, the TM0 mode has muchstronger coupling strength than the TE0 mode due to a dramatic differencein their mode confinements. For a coupler with a crossover length (i.e.,the length to achieve 100% coupling) designed for the TM0 mode, it cancrossover couple the TM0 mode while leaving the TE0 without being signif-icant coupled. As a result, the two modes can be separated at the coupleroutputs.5.1.1.2 Approach for Broadband Crossover CouplingIn order to achieve broadband polarization beamsplitting, broadband crossovercoupling is needed for the TM0 mode. In section 2.1, we have presented a de-sign methodology for broadband 3-dB couplers; however, such methodologyis unable to achieve broadband 100% cross-coupling. To design a broadband100% coupler, we cascade two easy to achieve, broadband 3-dB couplers ina point-symmetric way [84].Figure 5.3(a) shows the schematic of a point-symmetric network consist-ing of two components. The component on the left is an arbitrary 2 × 2coupler and the component on the right is the point-symmetry-transformedversion of the coupler on the left. The unitary transfer matrix for the arbi-trary 2× 2 coupler is given by [84, 85]:T =[t(λ) −κ∗(λ)κ(λ) t∗(λ)](5.1)where t(λ) and κ(λ) are the complex straight-through coupling coefficientand the cross-coupling coefficient, respectively, and t∗(λ) and κ∗(λ) are their655.1. Broadband Polarization BeamsplitterE1 E3 E4 E5 E6 2x2 coupler E2 (a)1480 1500 1520 1540 1560 1580 1600 162000.10.20.30.40.50.60.70.80.91Wavelength (nm)Normalized PowerΔP(λ) ΔP(λ) P4(λ) P6(λ) (b)Figure 5.3: (a) Schematic of a point-symmetric network; (b) re-sponses of a 3-dB, 2×2 coupler and its point-symmetric network.The shadow regions mark out the variations of their respective cross-coupling powers.complex conjugates. λ is the wavelength. The transfer matrix for the point-symmetry-transformed coupler is given by [84]:T180◦ =[t∗(λ) −κ∗(λ)κ(λ) t(λ)](5.2)Therefore, the transfer matrix for the point-symmetric network, which isshown in Fig. 5.3(a), can be expressed as:T · T180◦ =[t(λ)t∗(λ)− κ(λ)κ∗(λ) −2 t(λ)κ∗(λ)2 t∗(λ)κ(λ) t(λ)t∗(λ)− κ(λ)κ∗(λ)](5.3)Given a normalized input electric field at the input 1 shown in Fig. 5.3(a),i.e., E1 = 1 and E2 = 0, we have:[E3E4]= T ·[10],[E5E6]= T · Tpoint−symmetric ·[10](5.4)665.1. Broadband Polarization Beamsplitterand accordingly have:E3(λ) = t∗(λ) (5.5)E4(λ) = κ(λ) (5.6)E5(λ) = t(λ)t∗(λ)− κ(λ)κ∗(λ) (5.7)E6(λ) = 2 t∗(λ)κ(λ) (5.8)where E3 and E4 are the electric fields at the through port and cross portof the 2×2 coupler, respectively. E5 and E6 are the electric fields at thethrough port and cross port of the point-symmetric network, respectively.P3(λ) and P4(λ) are the through-coupling and cross-coupling power of the2×2 coupler, respectively, and for convenience they are taken to be:P3(λ) = |E3(λ)|2 = t(λ)t∗(λ) (5.9)P4(λ) = |E4(λ)|2 = κ(λ)κ∗(λ) (5.10)Assuming that there is no coupling loss (i.e., |t(λ)|2+|κ(λ)|2=1) andaccording to Eqs. 5.7, 5.8, 5.9, and 5.10, we obtain the through-couplingpower, P5(λ), and the cross-coupling power, P6(λ), of the point-symmetricnetwork:P5(λ) = |E5(λ)|2 = |P3(λ)− P4(λ)|2 = |∆P (λ)|2 (5.11)P6(λ) = 1− P5(λ) = 1− |∆P (λ)|2 (5.12)where ∆P (λ) is the coupling imbalance for the 2×2 coupler. According toEqs. 5.11 and 5.12, when ∆P (λ) = 0, we have P5(λ) = 0 and P6(λ) = 1,which achieves crossover-coupling. When the deviation of ∆P (λ) from 0 issmall, then the deviation of P6(λ) from 1 is also small due to their quadraticrelationship; in other words, the cross-coupling power P6(λ) is less sensitiveto unbalanced coupling in the 3-dB 2×2 coupler. As an example, Fig, 5.3(b)shows the cross-coupling power of a 3-dB 2×2 coupler for the TM0 modeand that of its point-symmetric network. Over a large wavelength span, the∆P (λ) varies by ±0.1, as indicated by the red shadow in Fig. 5.3(b), while675.1. Broadband Polarization BeamsplitterP6(λ) remains between 0.96 and 1, as indicated by the blue shadow in Fig.5.3(b).At this point, we have seen that broadband crossover-coupling can beobtained by cascading two 3-dB 2×2 couplers in a point-symmetric con-figuration, which is shown in Fig. 5.3. The principle of using the point-symmetric network for broadband crossover-coupling is similar to that ofthe ∆β reversal couplers [86, 87] well-known in LiNbO3 photonics.5.1.2 Device DesignIn above, we have discussed the approach for polarization beamsplittingbased on directional coupling and the approach to achieve broadband crossover-coupling. By combining the two approaches, we can design a broadbandPBS that crossover-couples the TM0 mode into the cross port over a broadbandwidth while leaving the TE0 mode to propagate to the through portwithout being significantly coupled.500 nm500 nm400 nm600 nm500 nm500 nm500 nm500 nm22.5 μmCoupling section6.2 μmPhase shifter13 μmCoupling sectionTaper1 μm5 μm2 μmTaper1 μm500 nm 500 nmS bend 3 dB coupling region(b)(a)Figure 5.4: (a) Schematic of our broadband PBS; (b) schematic ofthe first broadband 3-dB coupler in the PBS.685.1. Broadband Polarization BeamsplitterOur PBS design is based on the 220 nm SOI platform as depicted inFig. 1.3. As shown in Fig. 5.4(a), the PBS consists of two identical TM0mode broadband 3-dB couplers that are cascaded in a point-symmetric net-work. Figure 5.4(b) shows the schematic for the first broadband 3-dB cou-pler. The second broadband 3-dB coupler is identical to the first couplerbut is flipped around both axis, i.e., it is the point-symmetry-transformedversion of the first coupler.1460 1480 1500 1520 1540 1560 1580 1600 1620Wavelength (nm)-30-27-24-21-18-15-12-9-6-30Transmission (dB)TE0 modeThroughCrossCrossThroughBroadband 3 dB couplerInput(a)1460 1480 1500 1520 1540 1560 1580 1600 1620Wavelength (nm)-30-27-24-21-18-15-12-9-6-30Transmission (dB)TM0 modeThroughCrossCrossThroughBroadband 3 dB couplerInput(b)Figure 5.5: FDTD simulation results of the broadband 3-dB coupleroperating at the (a) TE0 mode and (b) TM0 mode.We design the PBS in a 2 steps process. To begin with, we design broad-band 3-dB couplers for the TM0 mode using the methodology as describedin section 2.1. The geometric parameters of the broadband 3-dB couplersare detailed in Fig. 5.4(b). In the design, we optimize geometric parametersof the coupler to achieve 3-dB coupling for the TM0 mode over a large wave-length span. A large waveguide spacing of 500 nm is used in the broadband3-dB coupler design to achieve a weak coupling strength for the TE0 mode;as a result, the TE0 mode can propagate through the coupler without sig-nificant cross-coupling. Using a FDTD solver [51], we simulate the spectralresponses for the broadband 3-dB coupler design operating at the TE0 andTM0 modes, and simulation results are shown in Figs. 5.5(a) and 5.5(b),respectively. As shown in Fig. 5.5(a), the cross-coupling power for the TE0mode is less than -22 dB across a wavelength range from 1480 nm to 1580695.1. Broadband Polarization Beamsplitternm, whereas, in the same wavelength range the TM0 mode coupling ratiosare close to 3-dB, as shown in Fig. 5.5(b).1460 1480 1500 1520 1540 1560 1580 1600 1620Wavelength (nm)-35-30-25-20-15-10-50Transmission (dB)TE0 modeThroughCross(a)1460 1480 1500 1520 1540 1560 1580 1600 1620Wavelength (nm)-35-30-25-20-15-10-50Transmission (dB)TM0 modeThroughCross(b)1460 1480 1500 1520 1540 1560 1580 1600 1620Wavelength (nm)05101520253035Isolation (dB)Through port1465 nm 1590 nm20 dB bandwidth(c)1460 1480 1500 1520 1540 1560 1580 1600 1620Wavelength (nm)05101520253035Isolation (dB)Cross port1570 nm20 dB bandwidth(d)Figure 5.6: FDTD simulation results for the PBS. (a) Spectral re-sponses for the TE0 mode; (b) spectral responses for the TM0 mode;(c) modal isolation at the through port; (d) modal isolation at thecross port.Then, using the FDTD solver we model the PBS design, which is con-figured by cascading the two identical broadband 3-dB couplers in a point-symmetric manner, as shown in Fig. 5.4(a). Figures 5.6(a) and 5.6(b) showthe simulated output spectral responses for the TE0 mode and TM0 mode,respectively. As we can see, over a wide wavelength range most of the TE0mode light propagates through the device and exits from the through port,while most of the TM0 mode light is coupled to the cross port. Hence,705.1. Broadband Polarization Beamsplitterbroadband polarization beamsplitting is possible.We use modal isolation and bandwidth to evaluate the performance ofour PBS. The isolation at the through port and cross port are defined asfollows:(Isolation at the through port) = P TE0,through − P TM0,through (5.13)(Isolation at the cross port) = P TM0,cross − P TE0,cross (5.14)where P TE0,through and P TE0,cross are the output powers, in logarithmicscale, for the TE0 mode at the through port and cross port, respectively,as shown in Fig. 5.6(a). Similarly, P TM0,through and P TM0,cross are theoutput powers, in logarithmic scale, for the TM0 mode at the through portand cross port, respectively, as shown in Fig. 5.6(b). The bandwidth ofdevice is defined as the wavelength span over which the isolation is abovea certain value, here we use 20 dB. Figures 5.6(c) and 5.6(d) show themodal isolation at the through port and cross port, respectively, which areextracted from the simulated spectral responses. According to the results,our PBS has a 20 dB modal isolation at both the through and cross ports,for a 105 nm bandwidth from 1465 nm to 1570 nm.To illustrate how the behaviours of TE0 and TM0 modes within thePBS, in Figs. 5.7(a) and 5.7(b) respectively, we show the normalized fieldintensities of 1550 nm wavelength in the waveguide cores of the PBS. TheTE0 mode coupling along the propagation length shows reversal behaviourand the total cross-coupled power is suppressed due to its low couplingstrength in the first half of the PBS, as shown in Fig. 5.7(a). The TM0 modecoupling also shows reversal behaviour but the input power is completelycross-coupled due to its strong coupling strength in the first half of thePBS, as shown in Fig. 5.7(b). Such coupling behaviours are similar to theoperation of ∆β reversal couplers [86, 87].715.1. Broadband Polarization Beamsplitter0 10 20 30 40 50 60 70 80Position ( m)-40-30-20-100Normalized field intensity (dB)Waveguide aWaveguide bWaveguide aWaveguide b 0 μm 43.7 μm 87.4 μmTE0 mode(a)0 10 20 30 40 50 60 70 80Position ( m)-40-30-20-100Normalized field inTMnsity (dB)Waveguide aWaveguide bWaveguide aWaveguide b 0 μm 43.7 μm 87.4 μmTM0 mode(b)Figure 5.7: Normalized field intensities of 1550 nm wavelength inthe PBS waveguide cores along propagation length. (a) TE0 mode;(b)TM0 mode.5.1.3 Characterization ResultsOur PBSs were fabricated using an electron-beam lithography process at theUniversity of Washington. Figure 5.8 shows scanning electron microscope(SEM) images for one of our fabricated PBSs.Figure 5.8: Scanning electron microscope (SEM) images for one ofthe fabricated broadband polarization beamsplitters.Figure 5.9 shows a sketch of our measurement setup. Our test devicesinclude two identical PBSs separated by a 20 µm spacing on the SOI wafer.For such a small spacing, fabrication variation for the two identical PBSs isnegligible. As illustrated in Fig. 5.9, one of the PBSs is used for character-725.1. Broadband Polarization BeamsplitterTE0 mode InputTM0 mode InputTE0 mode outputTwo identical PBSs under test20 μm spacing DetectorsAgilent81635ABroadband LaserAgilent81600BPM fibre(slow to slow)PM fibre(slow to fast)TE0 mode outputTM0 mode outputTM0 mode outputFigure 5.9: Sketch of measurement setup. The yellow and pinktriangles are the on-chip grating couplers for the TE0 mode and TM0mode, respectively.izing the TE0 mode responses, while the other is used for the TM0 moderesponses. On-chip grating couplers (GCs), which also work as TE0-pass orTM0-pass polarizers due to their strong polarization dependence, were usedto couple light into and out of our test devices. We also fabricated a pair ofTE0 mode and a pair of TM0 mode GCs, connected by short waveguides forcalibrating the insertion losses. In the characterizations, we used an Agilent81600B broadband laser as the input source and both channels of an Agi-lent 81635A optical power sensor as the output detectors, as illustrated inFig. 5.9. The laser output is TE-polarized. The slow-to-slow PM fibre keepsthe polarization state of the light, and the slow-to-fast PM fibre rotates thepolarization state of the light by 90 degrees at the outputs of fibres thatwere used to inject light into the GCs.Devices were measured over the wavelength range from 1460 nm to 1635nm, with a measurement resolution of 10 pm and an input power at 0 dBm.Figures 5.10(a) and 5.10(b) present the measured output spectra for the TE0mode and TM0 mode, respectively, in which the insertion losses introducedby the GCs have been calibrated out. It is found that the insertion loss ofour PBSs is less than 0.5 dB across the C-band for both the TE0 and TM0modes. In Figs. 5.10(c) and 5.10(d), we plot the extracted modal isolationat the through port and cross port, respectively. For comparison purposes,the modal isolation from simulation results are also plotted in the figures.According to Figs. 5.10(c) and 5.10(d), good agreement is seen betweenthe simulated and the measured results. The measured PBS has a 20 dBmodal isolation at both the cross port and through port, for a bandwidth735.1. Broadband Polarization Beamsplitterof 120 nm, i.e., from 1482 nm to 1602 nm.(a) (b)1460 1480 1500 1520 1540 1560 1580 1600 1620Wavelength (nm)05101520253035Isolation (dB)Through portMeasuredSimulated1482 nm 1602 nm20 dB bandwidth(c)1460 1480 1500 1520 1540 1560 1580 1600 1620Wavelength (nm)05101520253035Isolation (dB)Cross portMeasuredSimulated20 dB bandwidth1602 nm(d)Figure 5.10: Measurement results for the fabricated PBS. (a) Spec-tral responses for the TE0 mode; (b) spectral responses for the TM0mode; (c) modal isolation at the through port; (d) modal isolation atthe cross port.745.2. Polarization Control for Switches using Polarization Beamsplitters5.2 Polarization Control for Switches usingPolarization BeamsplittersAs discussed, most silicon photonic switches are designed to operate usingonly one mode. Taking the TE0 mode, broadband MZI switch that wasdemonstrated in section 2.2 as an example, here we model its performancein a multi-mode operation condition. As shown in Fig. 5.11(a), in our sim-ulations the input source to the switch is a mixture of 80% TE0 mode and20% TM0 mode. Figures 5.11(b) and 5.11(c) show the simulated outputtransmission spectra of the switch at the cross state and bar state, respec-tively. As compared to the switch performance in the single-mode (TE0only) operation condition that is shown in Fig. 2.9, the multi-mode opera-tion causes a huge degradation to the switching ERs at both two switchingstates.InputOutput 1Output 2Phase	shifter	80%TE0 + 20%TM0Broadband MZI switch(a)1500 1520 1540 1560 1580 1600Wavelength (nm)-50-40-30-20-100Transmission (dB)Cross stateOutput 1Output 2ER(b)1500 1520 1540 1560 1580 1600Wavelength (nm)-50-40-30-20-100Transmission (dB)Bar stateOutput 1Output 2ER(c)Figure 5.11: (a) A broadband MZI switch without polarization con-trol; (b) simulated cross state performance of the switch; (c) simulatedbar state performance of the switch.755.2. Polarization Control for Switches using Polarization BeamsplittersThe demonstrated broadband PBS can be used as a front-end mode filterfor the broadband MZI switch, as illustrated in Fig. 5.12(a). Figure 5.12(b)and 5.12(b) show the simulated output transmission spectra of the switchoperating at the cross state and the bar state, respectively. It can be foundthat the switch with polarization control has great improvements in theswitching ERs at both switching states, as compared the switch without.However, the improvements are at the expense of polarization dependentloss (PDL). Polarization control without PDL can be realized by using anautomated polarization receiver [88], and our demonstrated broadband PBSis a critical building block in the receiver design.Phase	shifter	Broadband MZI switch80%TE0 + 20%TM0Broadband PBSOutput 1Output 2InputTM0TE0(a)1500 1520 1540 1560 1580 1600Wavelength (nm)-50-40-30-20-100Transmission (dB)Cross stateOutput 1Output 2ER(b)1500 1520 1540 1560 1580 1600Wavelength (nm)-50-40-30-20-100Transmission (dB)Bar stateOutput 1Output 2ER(c)Figure 5.12: (a) A broadband switch having polarization control;(b) simulated cross state performance of the switch; (c) simulated barstate performance of the switch.76Chapter 6Wafer-Scale ManufacturingVariation CharacterizationThe high refractive index contrast of SOI photonics enables tight confine-ment of light in sub-micrometer waveguides and sharp waveguide bends,making SOI promising for developing PICs with high integration densities.In applications such as WDM, PICs often require precise matching of thecentral wavelength and the waveguide propagation constant between com-ponents on a chip (e.g., ring modulators and optical filters). However, man-ufacturing variability is a challenge [89] in PIC designs. Fabrication errorsin waveguide width and height have significant impacts on the propagationconstant of light in waveguides; therefore, circuits such as interferometersare highly sensitive to manufacturing. For designers, it is critical to be awareof such variations so as to take them into account in PIC designs.Unfortunately, characterizing manufacturing variations in a wafer scaleis challenging in SOI photonics. Although the widths and heights of fabri-cated SOI waveguides can be characterized by using SEM imaging [90] andatomic force microscope (AFM) mapping [91], respectively, they are rathercostly and time-consuming. A more efficient method is to extract waveg-uide widths and heights from the spectral responses of fabricated SOI devices(e.g., micro-disk resonators [31] and Bragg gratings [92, 93]). However, mostdemonstrated methods require either dual-polarization measurement [31] orcomplex spectrum reflection measurement [92]. Therefore, more efforts arerequired to simplify the characterization methods.In this chapter, we propose a simple and accurate method to characterizephotonics manufacturing variations, which is based on the spectral response776.1. Characterization Methodologyvariations of a single racetrack resonator device. We use this method tocharacterize the manufacturing variations of a 200-mm-wafer, which wasfabricated using a 248-nm DUV lithography process.6.1 Characterization Methodology6.1.1 PrincipleAs we know, manufacturing variations in waveguide width, w, and height,h, both affect the waveguide effective index, neff (λ), and consequently re-sult in photonic interferometric devices having variations in their spectralresponses. In turn, it is possible to extract w and h from the spectral re-sponses of fabricated interferometric devices.Based on this, we have designed an all-pass racetrack resonator based onthe 220 nm SOI platform, as the test device to extract waveguide geometryvariations. The schematic layout for such a device is shown in Fig. 6.1(a).Silicon waveguides of the racetrack resonator have a nominal w of 500 nmand a nominal h of 220 nm. The radius, coupling length and coupling gapsof the device are 12 µm, 4.5 µm, and 200 nm, respectively. Figure 6.1(b)shows the calculated through-port transmission spectrum of such a device,which is given by [94]:EthruEin= ei(pi+2piλneff (λ)L)a− te−i2piλneff (λ)L1− taei 2piλ neff (λ)L(6.1)where t=0.9592 is the self-coupling coefficient of the ring coupler at a wave-length of 1550 nm and is obtained from FDTD simulation results; L is theround-trip length of the resonator; a=0.9811 is the round-trip amplitudefactor contributed by waveguide propagation loss in the resonator (assumedto be 10 dB/cm [95]) and coupling loss in the coupler.Manufacturing variations have a direct impact on the resonance wave-lengths, λres, of racetrack resonators. As an example, Fig. 6.2(a) showstransmission spectra for racetrack resonators with various waveguide width,w, where resonance shifts can be directly observed. Manufacturing varia-786.1. Characterization MethodologyR=12 µm4.5 µm500 nm500 nmIn Through(a)1520 1530 1540 1550 1560 1570Wavelength (nm)-10-8-6-4-20Transmission (dB)FSR (b)Figure 6.1: (a) Schematic layout of the racetrack resonator testdevice; (b) transmission spectrum for such a device without fabricationvariations. FSR is free-spectral-range.tions also affect the waveguide group index, ng, at each resonance wavelengthλres. The ng can be extracted from the spectral response and is determinedby [17, 96]:ng =λ2resFSR · L (6.2)where FSR is free-spectral-range and is defined as wavelength spans betweentwo adjacent resonances, as illustrated in Fig. 6.1(b). By quantifying (viasimulations) the variations of λres and ng versus the variations of w andh (i.e., ∂λres∂w ,∂λres∂h ,∂ng∂w and∂ng∂h ), waveguide dimensions of a racetrackresonator can be extracted from its spectral response by:[∆ng∆λres]=[∂ng∂w∂ng∂h∂λres∂w∂λres∂h] [∆w∆h](6.3)[∆w∆h]=[∂ng∂w∂ng∂h∂λres∂w∂λres∂h]−1 [∆ng∆λres](6.4)where ∆w and ∆h are deviations of waveguide width and height relative totheir nominals, respectively; ∆ng and ∆λres are variations of group indexand resonance wavelength relative to their nominals at a resonance mode,respectively.796.1. Characterization Methodology1520 1530 1540 1550 1560 1570Wavelength (nm)-10-8-6-4-20Transmission (dB)w=500 nmw=502 nm(a)1520 1530 1540 1550 1560 1570Resonance wavelength res (nm)4.174.1754.184.1854.194.1954.2Group Index n g w=496 nmw=497 nmw=498 nmw=499 nmw=500 nmw=501 nmw=502 nmw=503 nmw=504 nmA resonance mode  (b)496 498 500 502 504Waveguide width, w (nm)154015421544154615481550Resonance wavelength, res (nm)DataLinear fit(c)496 498 500 502 504Waveguide width, w (nm)4.184.1854.194.1954.2Group index, ngDataLinear fit(d)Figure 6.2: Simulation results for racetrack resonators with a nom-inal waveguide height, h, of 220 nm and various waveguide widths,w. (a) Transmission spectra; (b) group indices at resonances; (c)resonance wavelength versus waveguide width for a selected resonancemode; (d) group index versus waveguide width for a selected resonancemode.806.1. Characterization MethodologyUsing Eq. 6.2, we extract ng from the spectral responses of racetrackresonators with various w and a nominal h of 500 nm. The extracted ngresults are shown in Figure 6.2(b). It is found that ng decreases with anincrease of w whereas its corresponding λres increases. According to [96],the data points forming a downward diagonal line are in the same resonancemode. Based on this relationship, it is possible to identify the data pointsthat belong to one mode and accordingly determine their resonance shiftseven if the shifts are greater than a FSR. Here, we analyze the resonancemode having a nominal λres of 1544.25 nm and ng of 4.1899, as shown in6.2(b). For this mode, we plot the λres versus w and ng versus w in Figs.6.2(c) and 6.2(d), respectively, both of which can be approximated usinglinear fits. From the fitting slopes, we obtain:∂λres∂w= 0.585911 (nm/nm) (6.5)∂ng∂w= −0.001650 (/nm) (6.6)Similarly, we simulate racetrack resonators having a nominal w of 500 nmand various h, and part of the simulated results are shown in Fig. 6.3(a). Weextract the ng at resonances from each simulated spectrum, as shown in Fig.6.3(b). It is found that the data points for each resonance mode change ina upward diagonal direction, with an increase in h. For the resonance modehaving a nominal λres of 1544.25 nm and a nominal ng of 4.1899, the λresversus h and ng versus h are plotted in Figs. 6.3(c) and 6.3(d), respectively.Both the λres versus h and the ng versus h can be approximated using linearfits, and according to the fitting slopes we obtain:∂λres∂h= 1.36330 (nm/nm) (6.7)∂ng∂h= 0.001091 (/nm) (6.8)Given the results of Eqs. 6.5, 6.6, 6.7, and 6.8, the deviations of waveg-uide dimensions can be extracted from the variations of resonance wave-length and group index, base on Eq. 6.4.816.1. Characterization Methodology1520 1530 1540 1550 1560 1570Wavelength (nm)-10-8-6-4-20Transmission (dB)h=220 nmh=221 nm(a)1520 1530 1540 1550 1560 1570Resonance wavelength res (nm)4.174.1754.184.1854.194.1954.2Group Index n gh=217 nmh=218 nmh=219 nmh=220 nmh=221 nmh=222 nmh=223 nmA resonance mode  (b)216 218 220 222 224Waveguide height, h (nm)1538154015421544154615481550Resonance wavelength, res (nm)DataLinear fit(c)216 218 220 222 224Waveguide height, h (nm)4.184.1854.194.1954.2Group index, ngDataLinear fit(d)Figure 6.3: Simulation results for racetrack resonators with a nom-inal waveguide width, w, of 500 nm and various waveguide heights,h. (a) Transmission spectra; (b) group indices at resonances; (c) res-onance wavelength versus waveguide height for a selected resonancemode; (d) group index versus waveguide height for a selected reso-nance mode.826.1. Characterization MethodologyBy measuring the spectral responses for a large number of fabricated,identical test devices spread over a wafer, which is easy to achieve using awafer-scale automated testing setup [17], statistical results for the variationsof waveguide width and height can be obtained. While here the test devicefor the proposed characterization method is based on a racetrack resonator,ring resonators can also be used as test devices. As compared to traditionalcharacterization methods using SEM imaging and AFM mapping, which aretime-consuming and costly (SEM typically cost $20/picture), our proposemethod is efficient and cost-free (including test devices in a layout makes nochange to the fabrication cost).6.1.2 Characterization ErrorsAs the results of Eqs. 6.5, 6.6, 6.7 and 6.8 are based on linear approx-imations, there are numerical errors in our proposed variation extractionmethod, and these errors can be quantified by using the following calibra-tion procedures. First, the transmission spectrum of a racetrack resonatoris simulated with given waveguide width and height deviations, i.e., ∆wgivenand ∆hgiven, respectively. Second, the λres for each resonance mode is ob-tained from the simulated spectrum, and its corresponding ng is extractedby using Eq. 6.2. Third, the ∆λres and ∆ng are calculated for the resonancemode having a nominal λres of 1544.25 nm and a nominal ng of 4.1899. Fi-nally, base on Eq. 6.4, the deviations of waveguide width, ∆wextracted, andwaveguide height, ∆hextracted, are extracted. The width extraction error,Error∆w, and height extraction error, Error∆h, are given by:Error∆w = |∆wgiven −∆wextracted| (6.9)Error∆h = |∆hgiven −∆hextracted| (6.10)For most of 193-nm and 248-nm DUV lithography processes, waveguideetching linewidth is typically controlled to an accuracy of within ±20 nm,and the wafer thickness uniformity is controlled to an accuracy of within ±10nm. In our error tests, extraction errors are investigated in the same ranges.Figures 6.4(a) and 6.4(b) show the calibrated Error∆w and Error∆h, respec-836.2. Characterization ResultsErrorw0.050.050.050.050.050.050.050.050.10.10.1 0.10.10.10.10.10.150.15 0.150.150.150.150.20.20.20.20.20.20.250.250.250.250.250.250.30.30.30.30.30.350.350.350.350.40.40.40.40.450.450.450.450.50.50.50.50.550.550.550.550.60.60.60.60.65 0.650.650.70.70.70.750.80.85-20 -10 0 10 20wgiven  (nm)-10-50510h given (nm)00.10.20.30.40.50.60.70.8(nm)(a)Error h0.050.050.050.050.1 0.10.10.10.10.10.15 0.150.150.150.150.150.2 0.20.20.20.20.20.25 0.250.250.250.250.250.3 0.30.30.30.30.30.35 0.350.350.350.350.350.4 0.40.40.40.40.40.45 0.450.450.5-20 -10 0 10 20wgiven  (nm)-10-50510h given (nm)00.10.20.30.40.5 (nm)(b)Figure 6.4: Error test results in a ∆w deviation range of ±20 nm and a∆h deviation range of ±10 nm, for the proposed variation characterizationmethod. (a) Width extraction error, Error∆w; (b) height extraction error,Error∆h.tively. It is found that the Error∆w is less than 0.85 nm and the Error∆his less than 0.55 nm.6.2 Characterization ResultsUsing the proposed characterization method, we’ve characterized a 200-mm-wafer that was fabricated by a 248-nm DUV lithography process throughIME’s silicon photonics foundry. A total number of 2013 identical racetrackresonators were fabricated in 33 lithography dies in the wafer. The size ofeach die is 7.6 mm × 6 mm (being 1/16 of the size of each 30.4 mm × 24 mmlithography reticle), and each die has 61 identical devices. Figure 6.5(a)shows the schematic layout for a fabricated racetrack resonator, the designparameters of which are the same as those of the design shown in Fig. 6.1(a).Figure 6.5(b) shows the layout distributions for the racetrack resonators oneach die, and Fig. 6.5(c) shows the wafer map for the fabricated 200-mm-wafer. All of the fabricated racetrack resonators were measured using anautomated photonics testing setup, and the temperature of the setup wasstabilized with a control stability of 1 mK.846.2. Characterization Results:Die area(b) (c)(a)1 2 35 6 7 8410 11 12 13 14 15917 18 19 20 21 221624 25 26 27 28 292331 32 33 34 35 363037 38 39 40 4142 43 447.6 mm6 mmFigure 6.5: (a) Schematic layout for the racetrack resonator test device;(b) distribution of racetrack resonators on each wafer die; (c) wafer map forthe fabricated multi-project-wafer.6.2.1 Within-Die VariationsFigure 6.6(a) shows the measured spectra of the devices in die #20, whichis located close to the centre of the wafer. Using Eq. 6.2, we extracted theng of the devices in die #20, and the results are shown in Fig. 6.6(b). Eachcluster of data points in Fig. 6.6(b) represents a resonance mode. The datapoints for the mode being closest to 1544.25 nm is selected for ∆w and ∆hextractions. In the extractions, the ∆λres and ∆ng for each selected datapoint are calculated, relative to a nominal λres of 1544.25 nm and a nominalng of 4.1899 for the selected mode. Then, ∆w and ∆h are extracted usingEq. 6.4. Figures 6.6(c) and 6.6(d) respectively show the extracted ∆w and∆h versus coordinates on the die #20. It is found that ∆w varies from 3.15nm to 9.14 nm, and ∆h varies between -0.44 nm and -3.03 nm.Using the same approach, we’ve characterized the ∆w and ∆h for all ofthe 33 wafer dies, and the results for ∆w and ∆h are shown using scatterplots in Figs. 6.7(a) and 6.7(b), respectively. Each data point in the figurescorresponds to the characterized results of a test device. We used normaldistribution functions to fit the characterized ∆w and ∆h of each die, andsummarized the fitting results in Table 6.1.856.2. Characterization Results1520 1530 1540 1550 1560 1570−50−40−30−20Wavelength (um)Transmission (dB)Die #20(a)1520 1530 1540 1550 1560 15704.154.164.174.184.194.2Wavelength (um)Group index, n gDie #20Selected resonance mode for Δw and Δh extractions (b)x coordinate (µm)y coordinate (µm)Die #20  0 2000 4000 60000200040006000Width deviation, ∆w (nm)456789(c)x coordinate (µm)y coordinate (µm)Die #20  0 2000 4000 60000200040006000Height deviation, ∆h (nm)−3−2.5−2−1.5−1−0.5(d)Figure 6.6: Characterization results for die #20. (a) Measured spec-tra for the 61 identical test devices; (b) extracted ng for the 61 devices;(c) distribution map for extracted ∆w; (d) distribution map for ex-tracted ∆h.866.2. Characterization Results0 4 8 12 16 20 24 28 32 36 40 44Die #-10-505101520Width variation,  w (nm)(a)0 4 8 12 16 20 24 28 32 36 40 44Die #-6-4-2024Height variation,  h (nm)(b)Figure 6.7: Characterization results for all of the fabricated waferdies. (a) Waveguide width variations, ∆w; (b) waveguide height vari-ations, ∆h.876.2. Characterization ResultsTable 6.1: Statistical results for the characterized variations for allof the wafer dies.Die # Width variations, ∆w Height variations, ∆hMean (nm) Standarddeviation(nm)Mean (nm) Standarddeviation(nm)2 9.15 1.30 -3.78 0.625 7.28 2.60 -0.41 1.236 9.43 1.24 -0.26 0.447 8.29 0.94 -1.08 0.408 9.05 1.32 -2.04 0.4810 5.37 1.49 -0.37 0.5111 2.79 2.84 0.07 0.3112 8.36 1.23 -0.56 0.4313 3.50 1.03 -0.40 0.3414 8.36 0.95 -1.00 0.3017 7.55 1.26 -1.04 0.3818 -0.12 2.15 -0.48 0.3819 -1.69 3.06 1.65 0.3820 6.68 1.65 -1.83 0.5221 7.37 1.41 -0.81 0.4622 13.33 1.29 -2.01 0.4024 9.81 1.33 -1.85 0.4925 7.99 1.02 -1.04 0.3326 8.10 1.67 -3.79 0.5227 3.75 1.83 -2.29 0.4328 7.00 1.23 -1.37 0.3529 9.75 1.71 -1.96 0.5731 9.41 1.16 -3.00 0.4332 9.65 1.15 -1.86 0.3533 5.48 1.07 -2.08 0.3534 6.05 2.41 -1.62 0.3335 3.86 4.31 -1.74 0.3238 10.59 1.24 -2.97 0.4839 10.55 1.13 -2.15 0.3740 7.48 1.32 -2.30 0.3941 8.37 1.76 -3.59 0.5143 12.36 1.61 -3.92 0.4444 15.78 1.67 -3.95 0.44886.2. Characterization Results6.2.2 Within-wafer VariationsFigures 6.8(a) and 6.8(b) show the histograms for the characterized ∆w and∆h across the 200-mm-wafer. We fit the histograms using normal distribu-tions to estimate the variations across the 200-mm-wafer, and list the fittingresults in Table 6.2. According to the results, standard deviations for ∆wand ∆h are 3.89 nm and 1.36 nm, respectively.200-mm-wafer-10 -5 0 5 10 15 20Width deviation, w (nm)050100150200250CountDataFit(a)200-mm-wafer-6 -4 -2 0 2 4Thickness deviation, h (nm)050100150200CountDataFit(b)Figure 6.8: Histograms for the characterized variations across the200-mm-wafer. (a) Width variations, ∆w; (b) height variations, ∆h.Table 6.2: Statistical results for the characterized variations acrossthe 200-mm-wafer.∆w ∆hMean (nm) 7.60 -1.69Standard deviation (nm) 3.89 1.366.2.3 Literature ResultsIn recent years, there has been studies investigating manufacturing vari-ations [32, 90–92, 97–100] and correlations [96, 101] of various photonicsfabrication processes. In these reports, many techniques including SEM,ellipsometry, AFM, and indirect measurements were used for characteriza-tions. Here, we summarize the reported wafer-to-wafer and within-wafer896.2. Characterization ResultsTable 6.3: Literature results for wafer-to-wafer fabrication variationsProcess Wafer-to-wafer variationsσ∗∆w σ∗∆himec 193-nm dry lithography [91] 1.26 nmTable 6.4: Literature results for within-wafer fabrication variationsProcess Within-wafer variationsσ∆w σ∆h lcorimec 193-nm dry lithography[90, 91] 2.59 nm 2 nmimec wafer-scale corrective etching[97] 0.83 nmimec wafer-scale corrective etching[98] 3.64 nmimec 193-nm immersionlithography [7] 2.53 nm200-mm-wafer, 193-nm drylithography [99] 0.78 nm300-mm-wafer, 193-nm immersionlithography [99] 2.65 nm248-nm lithography [101] 4.17±0.42 mmIME 248-nm lithography [96] 5 mmimec 193-nm lithography [93] 2.4 nm248-nm lithography [100] 2 nm 4.16 nmvariations in Tables 6.3 and 6.4, respectively. The wafer-to-wafer variationsevaluate the drifts for the mean of waveguide linewidth and height. Asdemonstrated in [91], standard deviation for the mean of waveguide height,σ∗∆h, is 1.26 nm. For within-wafer variations, standard deviations for waveg-uide linewidth, σ∆w, range from 0.78 nm to 2.65 nm; standard deviationsfor waveguide height, σ∆h, range from 0.83 nm to 4.16 nm. According to[96, 101], within-wafer variations are correlated over short distance scales,and the characterized correlation length, lcor, is around 4 mm to 5 mm.From these summarized results, it can be found that fabrication varia-tions vary from foundry to foundry, from process to process, and even fromrun to run. Worse, according to our practical experience, officially released906.3. Summaryresults for manufacturing variability lack of timely updates. For photon-ics designers, the capability to characterized manufacturing variations in acost-efficient and accurate way can be helpful for yield prediction analysis,and our proposed characterization method can satisfy such a need.6.3 SummaryIn this chapter, we have proposed a simple and accurate method for man-ufacturing variation characterization. In our method, each characterizationonly requires a single measurement on the transmission spectrum of a sin-gle racetrack resonator. Waveguide dimension variations are extracted fromthe variation of waveguide group index, ∆ng, and the variation of resonanceshift, ∆λres, both of which are directly obtained from the measured trans-mission spectrum. In practice, the racetrack resonators for characterizationcan be fabricated together with other photonic devices in the same photonicswafer for no extra-cost, and can be measured together with other photonicdevices using an automated photonics test setup [17] for no extra-cost; as aresult, the proposed characterization method is very cost-efficient. Based onthe proposed characterization method, we have experimentally characterizedthe variability of a 200-mm-wafer that was fabricated using a 248-nm DUVlithography process. As compared to other published results on manufactur-ing variability, which are summarized in Tables 6.3 and 6.4, our characterizedresults show a larger standard deviation for waveguide linewidth, which isreasonable since a 248-nm lithography process typically has lower accuracythan a 193-nm lithography process. Our characterized standard deviationfor waveguide height is within the scope of other published results.91Chapter 7Layout-Dependent YieldPrediction for PhotonicsIntegrated CircuitsPhotonics manufacturing variations are spatially-correlated [96, 101]. Ef-ficiently taking such correlated variations into account in PIC designs ischallenging for designers, and unfortunately, there is currently no simula-tion tool that can support such simulations. In fact, correlated manufac-turing variations also exist in electronics, and the well-developed electronicshas sophisticated solutions in their simulation tools, which can be refer-ences to photonics. In electronics simulations, Monte Carlo (MC) analysis[102], which assigns random variations with correlation constraints to circuitcomponents, is typically used for yield prediction. As lengths of electricaldevices are typically small as compared with operation wavelengths, phaseerrors caused by variations are small; therefore, correlation are only appliedto critical components that require matching, typically device pairs. Forexample, the resistor pair of a differential amplifier requires matching asit affects the common-mode-rejection-ratio of the amplifier. However, thelengths of photonic devices are much longer than the operating wavelength;as a result, a small variation in waveguide dimensions can cause a dramaticphase error [7, 32]. Therefore, in photonics manufacturing analysis, corre-lations are required for all of the circuit components. Simply applying theelectronics MC analysis to photonics will face serious scaling issues (e.g., itrequires N2 correlation parameters for N components). Additionally, it isdifficult to determine correlation parameters from photonics physical lay-927.1. Methodologyouts.This chapter presents a statistical yield prediction method for photonics,which can efficiently take into account the layout-dependent correlated man-ufacturing variations. The analysis approach and simulation models will bedetailed. As examples, we will perform yield prediction analysis for a MZIswitch design based on the proposed method.7.1 Methodology7.1.1 ApproachWidth deviations ΔwCircuit	simulationCircuit	simulatorLayoutVariations	characterization	 Virtual	wafer	simulations1Assign coordinate-dependent Δw and Δh to each componentUpdate components’ performance according to obtained Δw and Δh4Component	compact	models3Netlist extraction8.8 9 9.2Channel spacing,  (nm)050100150200CountDataFit1530 1540 1550 1560 1570−40−30−20−100Wavelength (nm)Transmission (dB)  Drop 1Drop 2Δw wafer Δh waferhwWaveguideWaferHeight deviations ΔhData	analysis200-mm-wafer-6 -4 -2 0 2 4Thickness deviation, h (nm)050100150200CountDataFit200-mm-wafer-10 -5 0 5 10 15 20Width deviation, w (nm)050100150200CountDataFitFigure 7.1: Proposed simulation approach for photonics yield pre-diction. Primary simulation steps include: (1) layout-to-schematictransformation, (2) virtual wafer simulation and mapping, (3) compo-nents’ performance update, and (4) circuit simulation.Figure 7.1 sketches our simulation approach for photonics yield predic-tion. Our approach uses an open-source netlisting tool [103] to extractcomponent information as well as connectivity of a photonic circuit fromits physical layout, and transfers the extracted information into a circuit937.1. Methodologysimulator. Correlated manufacturing variations for waveguide widths andthicknesses are modeled as virtual wafers. Then, the generated virtual wafersinformation is transferred to the photonic circuit by assigning each compo-nent’s physical variations based on its layout coordinates. All circuit com-ponents are parameterized to be continuous functions of width and heightso that their performance can be automatically updated according to theobtained physical variations, without having to run any physical-level sim-ulation. Finally, the circuit performance is simulated multiple times (MCanalysis), each time with new virtual wafers, to obtain statistical results forthe performance variations of the circuit.7.1.2 Simulation Flow ChartInterpolate components’ performance according to the obtained variations Create virtual wafers for width variations Δw and height variations Δh Output: Optical spectra Circuit simulation Die #: i ≤ N True Extract component netlist, and import it to circuit simulator Photonic circuit GDSII layout Map Δw andΔh on die #i to photonic circuits Wafer #: j ≤ M Virtual wafer for Δw Virtual wafer for Δh (a) (b) (c) #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 #17 #18 #19 #20 #21 #22 #23 #24 #25 #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 #17 #18 #19 #20 #21 #22 #23 #24 #25 [nm] True Within-wafer analysis Wafer-to-wafer analysis Figure 7.2: (a) Detailed simulation flow chart for the proposed ap-proach; (b) and (c) illustrate the simulated virtual wafers for waveg-uide width and height variations, respectively.The simulation flow chart for the proposed yield prediction approach is947.1. Methodologydetailed in Fig. 7.2(a). Procedures are as follows:• Layout-to-schematic transformation: First, the layout of the sil-icon photonic circuit under test are created (in the example presentedhere, they are designed using KLayout [104], an open-source layouttool). The netlist of the layout, which provides coordinates and de-sign parameters for primitive components, path and dimension infor-mation of waveguides, and connectivity between components, is ex-tracted from the layout using a developed open-source netlisting tool[103], and is then imported into a circuit simulator, Lumerical INTER-CONNECT [51]. As an example, Fig. 7.3(a) shows the physical layoutof a photonic circuit consisting of two grating couplers connected by astrip waveguide, and Fig. 7.3(b) shows the imported circuit simulationschematic for such a layout. The extracted netlist of such a layout is:∗Checking layout f o r e r r o r s :∗Number o f e r r o r s found : 0 .∗Grating coup l e r 1 N$0 N$2 ebeam gc te1550 l i b r a r y =”Design k i t s /ebeam v1 . 2” l ay x=0 lay y=0 sch x=0sch y=0∗Grating coup l e r 2 N$1 N$3 ebeam gc te1550 l i b r a r y =”Design k i t s /ebeam v1 . 2” l ay x =50.0E−6 l ay y=0 sch x=1.2E0 sch y=0 s c h r =180∗waveguide 1 N$2 N$3 ebeam wg integra l 1550 l i b r a r y =”Design k i t s /ebeam v1 . 2” wg length =50.0E−6 wg width=500.0E−9 sch x =600.0E−3 sch y=0 s c h r=0 path= [ [ 0 , 1 2 1 . 2 5 0 ] , [ 5 0 0 0 0 , 1 2 1 . 2 5 0 ] ]• Virtual wafer simulation: Second, in the circuit simulator, we cre-ate a virtual wafer for waveguide width variations, ∆w, and a virtualwafer for waveguide height variations, ∆h, as illustrated in Figs. 7.2(b)and 7.2(c), respectively. Each virtual wafer is characterized by a stan-dard deviation amplitude and a correlated length, both of which arebased on experimental results [32, 90–92, 96–101]. The virtual wafermodel will be described in section 7.2.1.957.1. Methodology(a)(b)Figure 7.3: An example circuit consisting of two grating cou-plers connected by a waveguide. (a) Physical layout; (b) simulationschematic in the circuit simulator.• Variation mapping: The simulated virtual wafers, as illustrated inFigs. 7.2(b) and 7.2(c), can be divided into numerous lithography dieswith identical size. The virtual maps for one of the dies is selected andmapped to the photonic circuit under test. As an example, Fig. 7.4illustrates the die selection and variation mapping for a ring resonatorcircuit. Each circuit component obtains its local ∆w and ∆h accordingto its layout coordinates.• Performance interpolation: The performance of each circuit com-ponent is updated according to the obtained ∆w and ∆h, which isperformed using interpolation in the circuit simulator. The parame-terized component models will be described in section 7.2.2.• Circuit simulation: Finally, the photonic circuit, with updated com-ponents’ performance, is simulated.The proposed method provides two categories of statistically analysis:within-wafer analysis and wafer-to-wafer analysis. The within-wafer analy-sis iterates the steps of ”variation mapping”, ”performance interpolation”,and ”circuit simulation”, to study the circuit performance variations acrossvarious lithography dies, as shown in Fig. 7.2(a). Figure 7.4 illustrates967.2. Modelsthe die selection and variation mapping for the within-wafer analysis. Thewafer-to-wafer analysis includes the within-wafer analysis, and each of itsiteration generates a new ∆w virtual wafer and a new ∆h virtual wafer forthe within-wafer analysis, as illustrated in Fig. 7.5. The iteration numbersfor the within-wafer analysis and wafer-to-wafer analysis, i.e., N and Mrespectively as shown in Fig. 7.2(a), can be defined by users.i = 1 i = 2 i = 3 … … #1 #2 #3 #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 #17 #18 #19 #20 #21 #22 #23 #24 #25 Δw virtual wafer Δh virtual wafer [nm] #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 #17 #18 #19 #20 #21 #22 #23 #24 #25 #1 #2 #3 x y x y x y x y x y x y … Figure 7.4: Illustration for the die selection and variation mappingin the within-wafer analysis.7.2 Models7.2.1 Virtual Wafer ModelWe model the within-wafer manufacturing variations using a correlated sur-face roughness function [105]. Firstly, we generate an uncorrelated randomdistribution map, z(x, y), based on discrete mesh of points in x-y plane, andthe value at each discrete point is a random number following a normal dis-tribution with a mean of 0 and a standard deviation of σ. Then, the randomdistribution map, z(x, y), is convolved with a Gaussian filter, g(x, y), which977.2. Models#1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 #17 #18 #19 #20 #21 #22 #23 #24 #25 #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 #17 #18 #19 #20 #21 #22 #23 #24 #25 #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 #17 #18 #19 #20 #21 #22 #23 #24 #25 #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 #17 #18 #19 #20 #21 #22 #23 #24 #25 #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 #17 #18 #19 #20 #21 #22 #23 #24 #25 #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 #17 #18 #19 #20 #21 #22 #23 #24 #25 Δw  virtual wafer:  Δh  virtual wafer:   j = 1  j = 2  j = 3 … … … [nm] Figure 7.5: Illustration for the manufacturing variation simulationsof wafer-to-wafer analysis.is given by:g(x, y) = 1√pi l2e−( x2l2/2 +y2l2/2 ) (7.1)in which, l is correlation length for variations. The convolved wafer, m(x, y),which has correlated distributions, is given by:m(x, y) = F−[ F [g(x, y)] ·F [z(x, y)] ] (7.2)where F and F− are denotations for the fast Fourier transform and theinverse fast Fourier transform, respectively. As an example, Figs. 7.6(a),7.6(b), and 7.6(c) show a random distribution map, z(x, y), a Gaussian filtermap, g(x, y), and a correlated variation wafer map m(x, y), respectively.Wafer-to-wafer variations are included in our virtual wafer model byadjusting the mean of the correlated variation wafer map, which is given by:m(x, y) = F−[ F [g(x, y)] ·F [z(x, y)] ] + c (7.3)where c is a random number following a normally distribution with a meanof 0 and a standard deviation σ∗. In total, there are three input parameters987.2. Modelsto our virtual wafer model, which are σ, l, and σ∗.To increase computation efficiency, virtual wafers are simulated usinga coarse simulation mesh of 500 µm × 500 µm in the ”virtual wafer sim-ulation” step. In the ”variation mapping” step, the simulated width andheight variations of the selected die are interpolated using a high resolutionmesh of 5 µm × 5 µm. The interpolated high resolution variation maps arethen mapped to photonic circuits. As an example, Fig. 7.7 illustrates thevariations maps before and after the interpolation.(a) (b) (c)Figure 7.6: (a) A 100 mm × 100 mm random distribution mapz(x, y) generated with σ=2; (b) a Gaussian filter map g(x, y) generatedwith l = 4 mm; (c) the correlated variation wafer map m(x, y).(a) (b) (c)Figure 7.7: (a) A 100 mm × 100 mm correlated variation wafer mapm(x, y), which is simulated using a coarse simulation mesh; (b) and(c) are the variation maps of a 10 mm × 10 mm die located at the topright corner of the wafer, before and after interpolation, respectively.997.2. Models7.2.2 Parameterized Component ModelsIn order to consider fabrication variations in circuit simulations, we requireparameterized component models that are continuous with width variations,∆w, and height variations, ∆h. In addition, wavelength-dependency is nec-essary in order to model a circuit over a wavelength range of interest. Thissection describes how waveguides and components are modeled.7.2.2.1 Waveguide Compact ModelWaveguides are fundamental building blocks in PICs. Waveguide propertiescan be described using a waveguide loss and a wavelength-dependent effec-tive refractive index, neff (λ). In our waveguide model, the waveguide lossis based on empirical results (e.g. 2-6 dB/cm for 500 nm ×220 nm waveg-uides), and it can be defined by the user. The neff (λ) is described using athird-order Taylor expansion, which is given by [17]:neff (λ) = neff (λ0) + (λ− λ0) · dneffdλ∣∣∣∣λ=λ0+ (λ− λ0)2 · d2neffdλ2∣∣∣∣λ=λ0(7.4)where λ0=1550 nm is the central wavelength of operation bandwidth; dneffdλand d2neffdλ2 are determined by the group index, ng, and group velocity dis-persion, D, respectively:ng(λ0) = neff (λ0)− λ0dneffdλ∣∣∣∣λ=λ0(7.5)D(λ0) = −λ0cd2neffdλ2∣∣∣∣λ=λ0(7.6)The neff (λ0), ng(λ0) and D(λ0) can be obtained from eigenmode simula-tions.To parameterize the neff (λ) as a continuous function of waveguide width,w, and waveguide height, h, we perform eigenmode simulations for waveg-uides with various geometries (e.g. sweeping w from 300 nm to 1000 nm witha 20 nm step, and sweeping h from 200 nm to 240 nm with a 2 nm step), and1007.2. Modelswe generate a look-up table for the simulated neff (λ0), ng(λ0) and D(λ0) foreach waveguide geometry. According to the look-up table, we use a multi-dimensional spline interpolation method to interpolate the neff (λ0), ng(λ0)and D(λ0) for any waveguide geometry, and accordingly obtain the neff (λ)using Eq. 7.4. The look-up table and the interpolation are implementedwithin our waveguide compact model in Lumerical INTERCONNECT.In our waveguide model, the impacts of the spatially dependent ∆wand ∆h on a waveguide are averaged along its layout path. The waveguidepath information is extracted from the layout, as discussed in section 7.1.2,and is imported into our waveguide model. With the path information, awaveguide is mathematically meshed into pieces by the simulated virtualwafers, and each waveguide piece automatically obtains the ∆w and ∆h atits mesh point, as illustrated in Fig. 7.8. The average waveguide width andheight along the path, i.e., wavg and havg, are given by:wavg = w0 +1NN∑n=1∆wn, havg = h0 +1NN∑n=1hn (7.7)where N is total number of waveguide pieces; ∆wn and ∆hn are width andheight variations for the waveguide section n, respectively. The averagingis implemented as a script within our waveguide model. Based on wavg andhavg, the neff (λ0), ng(λ0) and D(λ0) are determined as described above.7.2.2.2 S-parameter Component ModelsAll of the primitive components, such as y-junction splitter [62], gratingcouplers [53], and directional coupler [65], are described using optical S-parameters [17, 51], which can be obtained by using FDTD solvers, e.g.,Lumerical FDTD Solutions [51]. The optical S-parameters include the am-plitude and phase responses of a primitive component (indicating both trans-mission and reflection parameters). Since these simulations do not providepropagation loss result from waveguide sidewall roughness, we need to addthis separately to the compact model. To parameterize the primitive com-ponent model as a function of ∆w and ∆h, first, we obtain S-parameters1017.2. Models( Δwn+1 , Δhn+1 )( Δwn , Δhn )Mesh sizeFigure 7.8: Diagram for ∆w and ∆h averaging in the waveguidecompact model.for the nominal design and the four process corners of manufacturing vari-ations. We consider a maximum ∆w of ±20 nm and a maximum ∆h of±10 nm for a photonics process. Accordingly, the four corners are (20 nm,10 nm), (-20 nm, 10 nm), (-20 nm, -10 nm) and (20 nm, -10 nm), and thenominal design is (0 nm, 0 nm), as illustrated in Fig. 7.9(a). Then, fora desired (∆w, ∆h) input, we use a multi-dimensional spline interpolationmethod to interpolate the amplitude and phase of the S-parameters. Af-ter interpolation, the S-parameters’ passivity and reciprocity are tested andenforced [17], to avoid violating energy conservation laws. We implementthe S-parameter data and interpolation as a script within the componentmodel in Lumerical INTERCONNECT. As an example, Figs. 7.9(b) and7.9(c) show the S31 amplitudes and phases of a TE0 mode 2×2 directionalcoupler, respectively. The example directional coupler has a coupling lengthof 17.5 µm, a coupling gap of 200 nm, waveguide widths of 500 nm, andwaveguide heights of 220 nm.1027.2. ModelsΔwΔh(20 nm, 10 nm)(20 nm, -10 nm)(-20 nm, -10 nm)(-20 nm, 10 nm)(-10 nm, 5 nm), an interpolated point(a)1500 1520 1540 1560 1580 1600Wavelength (nm)0.40.50.60.70.80.91S 31 amplitude(0 nm, 0 nm)(20 nm, 10 nm)(-20 nm, 10 nm)(-20 nm, -10 nm)(20 nm, -10 nm)(-10 nm, 5 nm) interpolated123417.5 μm(b)1500 1520 1540 1560 1580 1600Wavelength (nm)010203040S 31 phase [radians](0, 0)(20, 10)(-20, 10)(-20, -10)(20, -10)(-10,5) interpolated(c)Figure 7.9: S-parameter component model. (a) Process corners fortwo process parameters: waveguide width variation, ∆w, and heightvariation, ∆h; (b) and (c) are S31 amplitude and phase of a 2×2directional coupler, respectively.7.2.2.3 Sub-Circuit Component ModelsSub-circuit components can be described using both the S-parameter modeland the waveguide model. One example of a sub-circuit component is a 2×2MZI, which can be decomposed into two 2×2 couplers described by the S-parameter model and two waveguides described by the waveguide model, asillustrated in Fig. 7.10. The performance of the MZI, such as extinction ratioand insertion loss, will vary with the width and height variations introducedinto the directional coupler model and the waveguide model.1037.3. Yield Prediction for Mach-Zehnder Interferometer Switches2x2 coupler 2x2 couplerPort 1Port 2Port 3Port 4Port 1 Port 2Port 1 Port 2Port 1Port 2Port 3Port 4Waveguide 1Waveguide 2Figure 7.10: Layout decomposition for an Mach-Zehnder interfer-ometer device.7.3 Yield Prediction for Mach-ZehnderInterferometer Switches7.3.1 Switch LayoutUsing the proposed yield prediction method, this section studies the perfor-mance variations of several MZI switch designs. Figure 7.11(a) shows thelayout of a 2×2 thermo-optic MZI switch, which is generated using Klayout[104]. The MZI switch consists of two broadband 3-dB couplers (i.e., thecoupler design presented in section 2.1) and two balanced waveguide phasearms that are separated by a spacing d of 50 µm. The silicon waveguidesare 220 nm height. The waveguides of the two phase arms are both 500 nmwide. One of the phase arms has a 200 µm long thermo-optic phase shifter.Figure 7.11(b) shows the circuit simulation schematic of the switch,which is loaded from its physical layout using the netlist extraction tool[103] as discussed in section 7.1.2. All of the circuit components have beenparameterized using the methods as described in section 7.2.2. In our sim-ulation settings, input 1 is activated for optical source and both switchoutputs are monitored, as illustrated in Fig. 7.11(b). For simulations at thecross state, the heater applies no phase shift to the waveguide arm; while atbar state, the heater applies a wavelength-dependent phase shift ∆φ(λ) to1047.3. Yield Prediction for Mach-Zehnder Interferometer SwitchesBroadband 3-dB couplerInput Output 1Output 2Broadband 3-dB couplerLheaterdPhase shifterMeal ViaWaveguideMetal wireLayers(a)Output 2Output 1Input(b)Figure 7.11: A thermo-optic MZI switch. (a) Physical layout; (b)circuit simulation schematic in Lumerical INTERCONNECT.the waveguide arm with ∆φ = pi at 1550 nm wavelength.7.3.2 Input Parameters for Manufacturing VariabilityThe input parameters to the virtual wafer model of our yield prediction arelisted in Table 7.1. The wafer size and die size are 100 mm × 100 mm and5 mm × 5 mm, respectively. In total, the wafer includes 400 dies. Standarddeviations for the waveguide width and height, i.e., σ∆w and σ∆h, are setto 3.89 nm and 1.36 nm, respectively, which are based on the characterizedvariations of the 200-mm-wafer as presented in section 6.2.2. The correlationlengths for the width and height variations, i.e., l∆w and l∆h, are both 4mm, based on [96, 101]. Note that simulation results to be shown in this1057.3. Yield Prediction for Mach-Zehnder Interferometer Switchessection depend on the input parameters to the virtual wafer model, andthese parameters can be defined by the user according to the variability ofa specific fabrication process.Table 7.1: Input parameters for the virtual wafer modelWafer size 100 mm × 100 mmDie size 5 mm × 5 mmWithin-wafer variationsσ∆w 3.89 nml∆w 4 mmσ∆h 1.36 nml∆h 4 mmWafer-to-wafer variations σ∗∆w 0σ∗∆h 07.3.3 Yield Prediction ResultsFirst, we perform a circuit simulation without introducing fabrication vari-ations. Figures 7.12(a) and 7.12(b) respectively show the simulated spectralresponses of the switch at the cross state and bar state, without fabricationvariation. We use bandwidth to evaluate the switch performance, and wedefine it as the wavelength span over which the ER is greater than 25 dB.Ideally, the switch has a bandwidth of 132 nm in the wavelength range from1480 nm to 1612 nm at the cross state, and a bandwidth of 112 nm in thewavelength range from 1496 nm to 1608 nm at the bar state. At 1550 nm,the switch has an insertion loss of 0.1 dB for both two switching states.Manufacturing variations affect the switch performance in numerousways. Waveguide dimension variations can vary the coupling ratios of thebroadband 3-dB couplers, and therefore vary the switching ER, as discussedin Section 1.2.3. In addition, the two phase arms may experience differen-tial variations in waveguide geometries, which leads to the switch havingimbalance phase arms with wavelength-dependent phase errors, ∆φerror(λ).As ∆φerror(λ) cannot be completely trimmed in a wide bandwidth by us-ing thermo-optic phase tuning, the switch can only achieve 0 or pi phaseshift in a narrow wavelength range, and therefore its operation bandwidth1067.3. Yield Prediction for Mach-Zehnder Interferometer Switches1480 1500 1520 1540 1560 1580 1600 1620Wavelength (nm)-40-30-20-100Transmission (dB)Cross stateOutput 1Output 21612 nm25 dB bandwidthER=25 dB(a)1480 1500 1520 1540 1560 1580 1600 1620Wavelength (nm)-40-30-20-100Transmission (dB)Bar stateOutput 1Output 21608 nm25 dB bandwidthER=25 dB1496 nm(b)Figure 7.12: Ideal performance for the 2×2 Mach-Zehnder interfer-ometer switch. (a) Cross state; (b) bar state.is impacted. The phase trimming for ∆φerror(λ) also increases the powerconsumption of the switch.Next, we perform a within-wafer analysis to study the performance vari-ations of switch circuit, which simulates the switch performance on each ofthe 400 wafer dies. In each simulation, the phase shifter model is able todetect the ∆φerror(λ) caused by manufacturing variations, and automati-cally apply phase trimming with a target for 1550 nm. Figures 7.13(a) and7.13(b) show the simulated transmission spectra at the cross state and barstate, respectively. It can be found that the cross state performance is quitesensitive to manufacturing variations, while the bar state performance iscomparatively stable. Figures 7.13(c) and 7.13(c) show the histograms forthe the cross state bandwidth and the bar state bandwidth, respectively.According to the results, the cross state bandwidth vary in between 70.8nm and 140 nm, and the bar state bandwidth vary in between 105.7 nmand 137.0 nm. It is surprising that both the cross state and the bar statebandwidths under manufacturing variations can be larger than their resultsin the ideal case, which might be the outcome of multiple impacts. Fig-ure 7.13(e) and 7.13(f) show the statistical results for the insertion loss at1550 nm, at the cross state and bar state, respectively. Based on these re-sults in above, designers can estimate the performance stability of the MZI1077.3. Yield Prediction for Mach-Zehnder Interferometer SwitchesOutput 2Output 1(a)Output 1Output 2(b)60 80 100 120 140Bandwidth for 25 dB ER (nm)020406080CountCross stateIdeal(c)60 80 100 120 140Bandwidth for 25 dB ER (nm)020406080CountBar stateIdeal(d)0.095 0.1 0.105Insertion loss at 1550 nm (dB)020406080CountCross stateIdeal(e)0.095 0.1 0.105Insertion loss at 1550 nm (dB)020406080CountBar stateIdeal(f)Figure 7.13: Within-wafer yield prediction results for the 2×2 Mach-Zehnder interferometer switch. (a) Spectral variations at the crossstate; (b) spectral variations at the bar state; (c) histograms for thecross state bandwidth; (d) histograms for the bar state bandwidth;(e) histograms for the cross state insertion loss; (e) histograms for thebar state insertion loss.1087.3. Yield Prediction for Mach-Zehnder Interferometer Switchesswitch, and accordingly improve the design, e.g., using 3-dB couplers thatis less sensitive to manufacturing variations and using a smaller spacing dfor the two phase arms to reduce the impacts of differential manufacturingvariations.As demonstrated in many reports [96, 101], fabrication variations arecorrelated over short distance scales, leading to adjacent components in alayout having similar performance variations. As a result, compact lay-out is a significant design rule for applications where performance matchingis required. Such a rule also applies to MZI switch designs. For a MZIswitch, the ∆φerror(λ) is dependent on the correlation of the two phasearms. Here, we study the variations of ∆φerror(λ) for switch designs withvarious spacings between its two phase arms, which are d=30 µm, d=50 µm,and d=100 µm. We perform within-wafer yield prediction analysis on eachswitch design. Figure 7.14 shows and compares the phase errors at 1550 nm,∆φerror(1550), for the three different designs. We fit the histograms usingnormal distributions, and the fitting results are listed in Table 7.2. Accord-ing to the results, a larger spacing leads to a larger variation to the phaseerror, since fabrication variations of two phase arms are less correlated whenthey are further apart. Based on the statistical results shown in Fig. 7.14,the power consumption for phase trimming can be estimated.-0.3 -0.2 -0.1 0 0.1 0.2 0.3Phase error at 1550 nm, error(1550)020406080Countd=100 m (data)d=100 m (fit)d=50 m (data)d=50 m (fit)d=25 m (data)d=25 m (fit)Figure 7.14: Histograms for phase errors at 1550 nm, for switchdesigns with d=25 µm, d=50 µm, and d=100 µm.1097.4. SummaryTable 7.2: Statistical results for the phase errors at 1550 nm forswitch designs with d=25 µm, d=50 µm, and d=100 µm.d = 25 µm d = 50 µm d = 100 µmMean for φerror -0.0001 pi -0.0004 pi -0.0007 piStandard deviation for φerror 0.020 pi 0.048 pi 0.093 piTo minimize phase errors ∆φerror(λ), the waveguide spacing, d, needs tobe small; however, reducing d will increase thermal crosstalk from one phasearm to the other, which in turns reduce the efficiency of phase tuning. Heattransport simulations are needed to obtain a small d while having sufficientlysmall thermal crosstalk.7.4 SummaryIn this chapter, we have presented methodologies and mathematical mod-els that enable layout-dependent yield prediction for silicon photonics in-tegrated circuits. Our approach models spatially-correlated manufacturingvariations as virtual wafers and assigns each component’s physical varia-tions based on its layout coordinates so that circuit simulations can capturelayout-dependent, correlated variations. Using the proposed yield predictionmethod, we have analyzed the performance variations of several MZI switchdesigns.110Chapter 8Conclusion and Future Work8.1 ConclusionThis thesis have developed and demonstrated novel SOI components forhigh-performance silicon photonic switches, and have investigated manufac-turing variability issues associated with the switch designs. Each chapterdiscusses one significant aspect towards high-performance switch designs.Major contributions of this research includes:• Design and demonstration of a high-performance, TE0 mode, broad-band 3-dB coupler. Our demonstrated 3-dB coupler has an operationbandwidth of 100 nm, with coupling imbalance of less than 4.7%. Thedemonstrated device is a fundamental building block for broadbandswitching.• Demonstration of state-of-the-art low-power thermo-optic switches,with power consumption of down to 50 µW/pi. Our results is almost10× lower than the power consumption of any thermo-optic switchin literature. The ultra-low power switching is realized by adoptingboth thermal isolation structures and densely folded waveguides in thephase shifter designs.• First realization of a tri-state switch based on a novel BNMZI struc-ture. As compared with regular dual-state (cross/bar) MZI switches,the proposed tri-state switch has great advantages in N × N switchapplications. As a switching element, the tri-state switch can operateat the cross state and the bar state for signal switching, as well as atthe blocking state for crosstalk suppression.1118.1. Conclusion• First efficient solution to the long-existing crosstalk issues of high-speed switches. MZI switches using carrier injection phase tuning canperform in high-speed but have large switching crosstalk due to theimbalanced absorption loss in the carrier injection phase tuning. Ourproposed carrier injection BNMZI switch has a balanced phase tuningscheme, and therefore can have both high-speed and crosstalk-freeperformance.• Design and demonstration of a high-performance PBS, which has a20 dB modal isolations for the TE0 and TM0 modes and a 120 nmoperation bandwidth. As compared to many PBSs demonstrated byother research groups, our device has a wider operation bandwidth.The demonstrated broadband PBS can be used for polarization controlfor silicon photonic switches.• Investigation on silicon photonics manufacturing variations:(a) We have demonstrated a ring resonator based method to char-acterize photonics manufacturing variations. Our method has a sub-nanometer characterization accuracy, and has simpler test structureand testing approach as compared with other demonstrated methods.(b) We have developed a novel yield prediction method for PICs, whichis the first approach in silicon photonics able to take into accountlayout-dependent, correlated manufacturing variations. Before our re-port, Monte Carlo yield analysis for photonics has no correlation con-strains in its parameter models, and therefore can not truly reflect theimpacts of manufacturing variations.The components and design methodologies developed in this thesis haveboth benefits and limitations. Table 8.1 compares the performance of ourdemonstrated broadband 3-dB coupler with several representative 3-dB cou-plers [43, 44, 48, 106] that were demonstrated on the same 220 nm SOI plat-form. According to the comparison, our coupler exhibits best performancein terms of balanced coupling, and is competitive in feature size and opera-tion bandwidth. In terms of fabrication requirements, our coupler and the1128.1. Conclusionadiabatic coupler demonstrated in [43] are both compatible with CMOS fab-rication processes; while other devices [44, 48, 106] require high-resolutionelectron beam lithography process due to the small features in their waveg-uide structures. However, according to the corner analysis results presentedin Fig. 2.6, the performance of our coupler is sensitive to fabrication varia-tions. Our broadband 3-dB coupler design can be optimized to improve itstolerance to fabrication, which is discussed in Section 8.2.Table 8.2 summarizes the performance of SOI thermo-optic switches [24–26, 33, 37–40, 55–60, 107] that were demonstrated in recent years. Accordingto the results, our demonstrated switches have state-of-the-art low powerconsumption, but at the expense of a larger insertion loss. In this research,we focused on investigating the contributions of thermal isolation struc-tures and folded waveguide designs to the reduction of switching power. Forpractical applications, our ultra-low power phase shifter designs can be op-timized to achieve low loss performance, e.g., by reducing the number offolded waveguides.Table 8.3 compares our demonstrated PBS with several representative,high-performance PBSs demonstrated on SOI platforms. According to theresults, our device has superior broadband performance but its device foot-print is at a disadvantage.The yield prediction method presented in Ch. 7 does not take into ac-count the correlated variations within devices. For devices having largefootprints, such an effect should be considered.Table 8.1: Comparisons of high-performance 3-dB couplers demon-strated on the 220 nm SOI platform.Ref. Device length(µm)Bandwidth(nm)Maximum imbalance(%)[48] 14 100 16.2[43] 155 80 14.24[106] ≈14 140 ≈10[44] 50 130 6.93This report 48.55 100 4.71138.1. ConclusionTable 8.2: Summary of SOI based thermo-optic switches that wereexperimentally demonstrated in recent years.Ref. Year Power consumption(mW/pi)Rise time(µs)Insertion loss(dB)[24] 2003 50 3.5 32[25] 2004 210 50 ≈2[107] 2004 6 0.6[38] 2005 120 120 ≈3[39] 2005 90 100[37] 2007 78 19.6[55] 2008 10.6 10.9[55] 2008 13.14 10.6[59] 2008 0.6 3600 ≈4.6[56] 2009 6.5 14 ≈6[57] 2010 0.54 141 ≈2.8[26] 2010 40 30 ≈4[58] 2011 0.49 144 0.3[60] 2012 0.4 1700 1.1[33] 2013 12.7 2.4 ≤2.5[40] 2014 24.77 2.69 0.23This report 2015 0.05 551 ≤5.1Table 8.3: Summary of representative, high-performance PBSsdemonstrated on SOI platforms.Ref. Insertion loss(dB)Modalisolation(dB)Bandwidth(nm)Length(µm)[108] <1 17 35 20[109] 1 20 29 27.5[110] <1 20 57 15[111] 1 20 60 22.5[112] 0.35 20 135 20This report <0.5 20 120 97.41148.2. Future Work8.2 Future WorkWith the accomplished works in this dissertation, suggested future workincludes:• Experimental demonstrations of the proposed BNMZI tri-state switch.• Developing low loss switches. Insertion loss is a challenge for large-scale silicon photonic switch matrices. For example, a demonstrated32 × 32 switch has on-chip insertion loss of 23 dB to 28 dB over theoptical C-band [30], and as a result, in practical applications opti-cal amplifiers will be required to compensate the insertion loss, whichbring both cost and power penalties. The insertion loss of components(such as 2×2 couplers, optical phase shifters, routing waveguides, andwaveguide crossings) need to be reduced in order to avoid the require-ment of amplifiers. In this thesis, our research has only focused onsilicon photonics switches operating at the TE0 mode. Alternatively,it is possible to design switches operating at the TM0 mode, whichhave lower insertion loss due to the mode field having a lower overlapwith waveguide sidewall roughness. Besides, TM0 mode broadband3-dB couplers could be designed shorter than TE0 mode couplers, dueto the fact that the TM0 mode has a stronger coupling strength; as aresult, TM0 mode switches could be more compact in footprints thanTE0 mode switches.• A more thorough study on 2×2 broadband coupler designs. The designapproach for the broadband 3-dB coupler presented in Section 2.1 canbe applied to design broadband couplers having other power splittingratios (such as 10%/90%) or operating at other waveguide modes (suchas TE1 mode). In addition, using multiple coupling segments andphase shifter segments to design broadband couplers can potentiallyimprove the devices’ tolerance to fabrication, which is well worth ofinvestigation.• Improving the component models of the proposed yield prediction1158.2. Future Workmethod, to include the effects of intra-device correlated variations. Forexample, the broadband 3-dB coupler design presented in Ch. 2 canbe decomposed into three sub-components (two DCs and one phaseshifter), with each having layout-dependent physical variations andbeing described by a S-parameter component model.• Thermal stabilization for switches. MZI switches are susceptible tolocal temperature fluctuation, which may cause differential phase er-rors and therefore deteriorate switching ERs. Thermal stabilizationfor MZI switches requires local temperature monitoring and feedbackcontrol. Figure 8.1(a) shows a proposed solution. A temperaturesensing diode (TSD), which is an integrated PN junction doped insilicon waveguide, can be used for on-chip temperature measurement,as the voltage across the diode is temperature-dependent accordingto the diode equation. The measured temperatures can be fed backfor phase tuning so as to compensate the phase errors induced by dif-ferential temperature fluctuations. 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Dai, “High extinction-ratio compact polar-isation beam splitter on silicon,” Electronics Letters, vol. 52, no. 12,pp. 1043–1045, 2016.[112] H. Wu, Y. Tan, and D. Dai, “Ultra-broadband high-performance po-larizing beam splitter on silicon,” Opt. Express, vol. 25, pp. 6069–6075,Mar 2017.131AppendicesAppendix APublicationsA.1 Patents1. Z. Lu and L. Chrostowski, “Photonic Switch with Nested Mach-Zehnder Interferometer”, US Patent, submitted, 85259388US01, (2017).2. R. Chung, Z. Lu, H. Jayatilleka, M. AlTaha, S. Mirabbasi, S. Sharkha,and L. Chrostowski, “Method and apparatus for monitoring and con-trolling a photonic switch using phase sweeping and interference de-tection”, US Patent, submitted, 85063649US02. (2016).3. Z. Lu, K. Murray, and L. Chrostowski, “Optical phase shifter”, USPatent, US20160334648 A1 (2016).A.2 Journal Publications1. Z. Lu, D. Celo, H. Mehrvar, E. Bernier, and L. Chrostowski, “Highperformance silicon photonic tri-state switch (cross/bar/blocking) basedon balanced nested Mach-Zehnder interferometer”, Scientific Reports,to be published (2017).2. Z. Lu, J. Jhoja, J. Klein, X. Wang, A. Liu, J. Flueckiger, J. Pond,and L. Chrostowski, “Performance prediction for silicon photonics in-tegrated circuits with layout-dependent correlated manufacturing vari-ability,” Optics Express, vol. 25, 9712-9733 (2017).132A.2. Journal Publications3. F. Zhang, H. Yun, Y. Wang, Z. Lu, L. Chrostowski, and N. Jaeger,“Compact broadband polarization beam splitter using a symmetricdirectional coupler with sinusoidal bends,” Optics Letter, vol. 42, 235-238 (2017).4. Y. Wang, Z. Lu, H. Yun, F. Zhang, N. Jaeger, and L. Chrostowski,“Compact Broadband Directional Couplers Using Subwavelength Grat-ings,” IEEE Photonics Journal, vol. 8, 1-8 (2016).5. Y. Wang, M. Ma, H. Yun, Z. Lu, X. Wang, N. Jaeger, and L. Chros-towski, “Ultra-Compact Sub-Wavelength Grating Polarization Splitter-Rotator for Silicon-on-Insulator Platform,” IEEE Photonics Journal,vol. 8, 1-9, (2016).6. H. Yun, Y. Wang, F. Zhang, Z. Lu, S. Lin, L. Chrostowski, N. Jaeger,“Broadband 2×2 adiabatic 3 dB coupler using silicon-on-insulator sub-wavelength grating waveguides,” Optics Letter, vol. 41, 3041-3044,(2016).7. A. Khavasi, L. Chrostowski, Z. Lu and R. Bojko, “Significant crosstalkreduction using all-dielectric CMOS-compatible metamaterials,” IEEEPhotonics Technology Letters, vol. 28, 2787-2790 (2016).8. Z. Lu, H. Yun, Y. Wang, Z. Chen, F. Zhang, N. Jaeger, and L.Chrostowski, “Broadband silicon photonic directional coupler usingasymmetric-waveguide based phase control”, Optics Express, vol. 23,3795-3808 (2015).9. Z. Lu, K. Murray, H. Jayatilleka, L. Chrostowski, “Michelson inter-ferometer thermo-optic switch on SOI with a 50-µW power consump-tion”, IEEE Photonics Technology Letters, vol. 27, 2319-2322 (2015).10. Z. Lu, Y. Wang, F. Zhang, N. Jaeger, and L. Chrostowski, “Widebandsilicon photonic polarization beamsplitter based on point-symmetriccascaded broadband couplers,” Optics Express, vol. 23, 29413-29422(2015).133A.3. Conference Proceedings11. K. Murray, Z. Lu, H. Jayatilleka, and Lukas Chrostowski, “Densedissimilar waveguide routing for highly efficient thermo-optic switcheson silicon,” Opt. Express, vol. 23, 19575-19585 (2015).12. Y. Wang, H. Yun, Z. Lu, R. Bojko, W. Shi, X. Wang, J. Flueckiger,F. Zhang, M. Caverley, N. Jaeger, and L. Chrostowski, “Apodizedfocusing fully etched subwavelength grating couplers”, IEEE PhotonicsJournal, vol. 7, 1-10 (2015).13. Y. Wang, W. Shi, X. Wang, Z. Lu, M. Caverley, R. Bojko, L. Chros-towski, and N. Jaeger, “Design of broadband subwavelength gratingcouplers with low back reflection,” Optics Letterer, vol. 40, 4647-4650(2015).14. Z. Chen, J. Flueckiger, X. Wang, F. Zhang, H. Yun, Z. Lu, M. Caver-ley, Y. Wang, N. Jaeger, and L. Chrostowski, “Spiral Bragg gratingwaveguides for TM mode silicon photonics,” Optics Express, vol. 23,25295-25307 (2015).A.3 Conference Proceedings1. Z. Lu (Invited speaker), J. Jhoja, and L. Chrostowski, “Designmethodologies for non-uniformity of on-chip silicon photonics inte-grated circuits”, 2017 Opto-electronics and Communication Confer-ence (OECC), paper 1-4E-5 (2017).2. Z. Lu (Invited speaker), M. Ma, Y. Han, Y. Wang, N. Jaeger,and L. Chrostowski, “Silicon Photonics Polarization Beamsplitter andRotator for On-chip Polarization Control,” IEEE Group IV Photonics(GFP), pp. ThD1, (2016).3. L. Chrostowski (Invited speaker), Z. Lu, J. Flueckiger, X. Wang, J.Klein, A. Liu, J. Jhoja, J. Pond, “Design and simulation of siliconphotonic schematics and layouts,” SPIE Europe, pp. 989114 (2016).134A.3. Conference Proceedings4. L. Chrostowski (Invited speaker), Z. Lu, J. Flückiger, J. Pond, J.Klein, X. Wang, S. Li, W. Tai, E. Hsu, C. Kim, J. Ferguson, C. Cone,“Schematic driven silicon photonics design,” SPIE Photonics West, pp.975103 (2016).5. Y. Wang, H. Yun, Z. Lu, N. Jaeger and L. Chrostowski, “State-of-the-art sub-wavelength grating couplers for silicon-on-insulator platform,”IEEE Canadian Conference on Electrical and Computer Engineering(CCECE), pp. 1-4, (2016).6. M. Ma, K. Murray, M. Ye, S. Lin, Y. Wang, Z. Lu, H. Yun, R. Hu, N.Jaeger, and L. Chrostowski, “Silicon Photonic Polarization Receiverwith Automated Stabilization for Arbitrary Input Polarizations,” Con-ference on Lasers and Electro-Optics (CLEO), pp. STu4G.8, (2016)7. Z. Lu, D. Celo, P. Dumais, E. Bernier, and L. Chrostowski, “Com-parison of photonic 2×2 3-dB couplers for 220 nm silicon-on-insulatorplatforms,” IEEE Group IV Photonics (GFP), pp.57-58, (2015).8. Z. Lu, H. Yun, Y. Wang, Z. Chen, F. Zhang, N. Jaeger, and L.Chrostowski, “Asymmetric-waveguide-assisted 3-dB Broadband Direc-tional Coupler,” Conference on Lasers and Electro-Optics (CLEO), pp.SM1I.8, (2015).9. H. Yun, Z. Lu, Yun Wang, W. Shi, L. Chrostowski and N. Jaeger,“2×2 Broadband Adiabatic 3-dB Couplers on SOI Strip Waveguidesfor TE and TM modes,” Conference on Lasers and Electro-Optics(CLEO), pp. STh1F.8, (2015).10. Y. Wang, H. Yun, Z. Lu, R. Bojko, F. Zhang, M. Caverley, N. Jaeger,and L. Chrostowski, “Apodized Focusing Fully Etched Sub-wavelengthGrating Couplers With Ultra-low Reflections,” Conference on Lasersand Electro-Optics (CLEO), pp. SM1I.6, (2015).11. Z. Chen, J. Flueckiger, X. Wang, H. Yun, Y. Wang, Z. Lu, F. Zhang,N. Jaeger, L. Chrostowski, “Bragg Grating Spiral Strip Waveguide Fil-135A.3. Conference Proceedingsters for TM Modes,” Conference on Lasers and Electro-Optics (CLEO),pp. SM3I.7, (2015).12. F. Zhang, H. Yun, V. Donzella, Z. Lu, Y. Wang, Z. Chen, L. Chros-towski, N. Jaeger, “Sinusoidal Anti-coupling SOI Strip Waveguides,”Conference on Lasers and Electro-Optics (CLEO), pp. SM1I.7, (2015).136Appendix BDerivation of the TransferFunctions of a MZI Switch2x2 coupler2x2 coupler𝜅2t2Input 1Input 2Output 1Output 2ϕ1ϕ2 𝜅2t2Figure B.1: Schematic for a typical Mach-Zehnder interferometer(MZI) circuit.Here, we derive the output transfer functions of a MZI switch using thetransfer matrix method. Considering a typical MZI circuit as shown inFig. B.1, the relationship between the input and output electric fields of theMZI circuit can be expressed by:[Eout1Eout2]=[t −jκ−jκ t][e−jφ1 00 e−jφ2][t −jκ−jκ t] [Ein1Ein2](B.1)where Ein1 and Ein2 are the electric fields at the two inputs, and Eout1 andEout2 represent the electric fields at the two outputs; t and κ are the through-coupling coefficient and cross-coupling coefficient, respectively, for each 2×2coupler, and the 2×2 couplers in the MZI are assumed to be identical; φ1and φ2 are the optical phase shifts of the two phase arms.Assuming light is launched into the input 1 only, i.e., Ein1 = 1 and137Appendix B. Derivation of the Transfer Functions of a MZI SwitchEin2 = 0, the output electric fields of the circuit are given by:Eout1 = t2e−jφ1 − κ2e−jφ2 (B.2)Eout2 = −jκte−jφ1 − jκte−jφ2 (B.3)And accordingly, output transmissions are given by:Pout1 = |Eout1|2 = (κ4 + t4 − 2κ2t2 cos(∆φ)) (B.4)Pout2 = |Eout2|2 = 2κ2t2(1 + cos(∆φ)) (B.5)where ∆φ = |φ1 − φ2| is the phase difference between the two waveguidearms. The input light to the MZI circuit can be selectively switched toeither of the outputs depending on the phase difference, ∆φ.For a ∆φ of 0, Eqs. B.4 and B.5 can be simplified as:Pout1 = (κ2 − t2)2 (B.6)Pout2 = 4κ2t2 (B.7)Due to the fact that the 2×2 couplers are designed for balanced coupling,i.e., κ2 and t2 are equal or close to 0.5, we have Pout2 > Pout1, i.e., the switchoperates in the cross switching state and routes the input light to the output2. In such a state, we define the switching ER as:ERcross = 10 log10(Pout2Pout1) = 10 log10(4κ2t2(κ2 − t2)2 ) (B.8)As it is shown that the cross state ER is dependent to the coupling ratios,κ2 and t2, of the 2×2 couplers in the MZI circuit.For a ∆φ of pi, Eqs. B.4 and B.5 can be simplified as:Pout1 = (κ2 + t2)2 (B.9)Pout2 = 0 (B.10)In this case, the switch operates in the bar state, which routes the input138Appendix B. Derivation of the Transfer Functions of a MZI Switchlight to the output 1. We define the switching ER at the bar state as:ERbar = 10 log10(Pout1Pout2) = 10 log10((κ2 + t2)20 ) =∞ (B.11)As we can see that the bar state ER is infinite and is independent to thecoupling ratios, κ2 and t2, of the 2×2 couplers in the MZI circuit. Notethat the bar state results given in Eqs. B.9, B.10, and B.11 are based onthe assumption that ∆φ has no wavelength-dependence. For a wavelength-dependent phase shift, ∆φ(λ), which has a pi phase shift for the centralwavelength, λ0, we have:∆φ(λ0) = pi =2piλ0∆nL (B.12)where ∆n is the change of waveguide refractive index required for the piphase shift for λ0; L is waveguide length. Accordingly, ∆φ(λ) can be givenby:∆φ(λ) = 2piλ∆nL = λ0λpi (B.13)where λ is operation wavelength. By substituting Eq. B.13 into Eqs. B.4 andB.5, wavelength-dependent performance at the bar state can be calculated.As λ0λ is close to 1 (considering a 100 nm wavelength span centred at 1550nm), we obtain:Pout1(λ) ≈ (κ2 + t2)2 (B.14)Pout2(λ) ≈ 0 (B.15)ERbar(λ) = 10 log10(Pout1(λ)Pout2(λ)) ≈ ∞ (B.16)which indicates that the wavelength-dependent bar state ER is insensitiveto κ2 and t2.139Appendix CDerivation of CouplingRatios Extractions for 2×2CouplersAs per Appendix B, the responses of a MZI circuit are sensitive to thecoupling ratios, κ2 and t2, of its 2×2 couplers. Conversely, the responses ofa MZI circuit can be used to characterize the κ2 and t2 of 2×2 couplers.For a MZI circuit with imbalanced phase arms, as illustrated in Fig. B.1,each output transmission will go through minima and maxima when sweep-ing the operation wavelength, due to the wavelength-dependent phase de-lay, ∆φ(λ). Based on the output transmission functions given by Eqs. B.4and B.5, we define interference extinction ratio (IER) for each output port,which is the difference on a logarithmic scale between minima and maximatransmissions, as given by:IERout1 = 10 log10(Pout1,maxPout1,min) = 10 log10((κ2 + t2)2(κ2 − t2)2 ) (C.1)IERout2 = 10 log10(Pout2,maxPout2,min) = 10 log10(4κ2t20 ) =∞ (C.2)where Pout1,max and Pout1,min are maxima and minima transmissions at theoutput 1, respectively; Pout2,max and Pout2,min maxima and minima trans-missions at the output 2, respectively. According to the results, IERout1is dependent to κ2 and t2, and therefore the spectral responses at output1 can be used to characterize κ2 and t2; however, IERout2 is independentto κ2 and t2, and hence the spectral responses at output 2 is invalid for140Appendix C. Derivation of Coupling Ratios Extractions for 2×2 Couplerscharacterization.Assuming the 2×2 couplers are lossless, i.e., κ2 + t2 = 1, based on Eq.C.1, the extracted coupling ratios are given by:κ2 = 12(1±1√10IERout110) (C.3)t2 = 1− κ2 (C.4)141

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