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Silicon photonic waveguide Bragg gratings Wang, Xu 2013

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Silicon Photonic Waveguide Bragg GratingsbyXu WangB.Sc., Huazhong University of Science and Technology, 2007M.A.Sc., Huazhong University of Science and Technology, 2009A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Electrical and Computer Engineering)The University Of British Columbia(Vancouver)December 2013? Xu Wang, 2013AbstractSilicon is the most ubiquitous material in the electronics industry, and is now ex-pected to revolutionize photonics. In just over ten years, silicon photonics hasbecome a key technology for photonic integrated circuits. By taking advantageof silicon-on-insulator (SOI) wafers and the existing complementary metal-oxidesemiconductor (CMOS) fabrication infrastructure, silicon photonic chips are nowbeing delivered with low cost and rapidly increasing functionality.This thesis presents the integration of a fundamental optical device - Bragggrating - into SOI waveguides. Various types of waveguides and grating structureshave been investigated. All designs are fabricated using CMOS foundry services.We have also explored various applications using the fabricated devices.From the beginning, we focused on strip waveguide uniform gratings, as theseare the most simple to design and fabricate. We have studied many design varia-tions, supported by experimental results. In parallel, we have provided insight intopractical issues and challenges involved with the design, fabrication, and measure-ment, such as the lithography effects, thermal sensitivity, and wafer-scale nonuni-formity. We then introduce phase-shifted gratings that can achieve very high qual-ity factors and be employed in various applications. We have also demonstratedsampled gratings and the Vernier effect in strip waveguides.To obtain narrow-band gratings, we propose the use of a rib waveguide. Wealso propose a multi-period grating concept by taking advantage of the multiplesidewalls of the rib waveguide, to increases the design flexibility for custom op-tical filters. The wafer-scale data shows that rib waveguide gratings have betterperformance uniformity than strip waveguide gratings, and that the wafer thick-ness variation is critical. Additionally, we have demonstrated very compact Braggiigratings using a spiral rib waveguide.Finally, we demonstrate slot waveguide Bragg gratings and resonators, whichhas great potential for sensing, modulation, and nonlinear optics. We have alsodeveloped a novel biosensor using a slot waveguide phase-shifted grating that hasa high sensitivity, a high quality factor, a low limit of detection, and can interrogatespecific biomolecular interactions.iiiPrefaceThis thesis is mostly based on the publications listed below, which resulted fromcollaborations with other researchers. Note that only publications directly arisingfrom the work presented in this thesis are listed here. A complete list of publi-cations is given in Appendix A. It should also be noted that many experimentalresults have been redone on a single fabrication run in order to yield more mean-ingful comparisons. Hence, many of the figures are original figures and do notreference the original similar figures that were previously published.Book Chapter1. X. Wang, W. Shi, and L. Chrostowski, ?Silicon photonic Bragg gratings,?in High-Speed Photonics Interconnects, L. Chrostowski and K. Iniewski, Ed.CRC Press, 2013, pp. 51-85.I wrote Page 51?66 of the book chapter, which is closely related to Chap-ter 2 and Chapter 3 in this thesis. W. Shi wrote the other parts of the bookchapter. L. Chrostowski supervised the project and assembled and edited themanuscript.Journal Publications1. X. Wang, S. Grist, J. Flueckiger, N. A. F. Jaeger, and L. Chrostowski, ?Sili-con photonic slot waveguide Bragg gratings and resonators,? Opt. Express,vol. 21, no. 16, pp. 19029-19039, 2013.I conceived the idea, conducted the device design, performed the measure-ments and data analysis, and wrote the manuscript. S. Grist contributed toivthe conception of the idea and took the SEM images. J. Flueckiger assistedwith the measurements. L. Chrostowski and N. A. F. Jaeger supervised theproject. All authors commented on the manuscript.Location: Chapter 4.2. X. Wang, J. Flueckiger, S. Schmidt, S. Grist, S. T. Fard, J. Kirk, M. Doer-fler, K. C. Cheung, D. M. Ratner, and L. Chrostowski, ?A silicon photonicbiosensor using phase-shifted Bragg gratings in slot waveguide,? J. Biopho-tonics, vol. 6, no. 10, pp. 821-828, 2013.I conceived the idea, conducted the device design, and wrote the manuscript.J. Flueckiger and S. Schmidt coordinated the project. S. Grist contributed tothe conception of the idea and took the SEM images. S. T. Fard helped withthe data analysis. S. Schmidt, J. Flueckiger, S. Grist, J. Kirk, and M. Doerflerperformed the measurements and contributed to the data analysis. K. C. Che-ung, D. M. Ratner, and L. Chrostowski supervised the project. All authorscommented on the manuscript.Location: Section 4.4.3. X. Wang, W. Shi, H. Yun, S. Grist, N. A. F. Jaeger, and L. Chrostowski,?Narrow-band waveguide Bragg gratings on SOI wafers with CMOS com-patible fabrication process,? Optics Express, vol. 20, no. 14, pp. 15547-15558, 2012.I conceived the idea, conducted the device design, performed the measure-ments and data analysis, and wrote the manuscript. W. Shi contributed to theconception of the idea. H. Yun assisted with the measurements. S. Grist tookthe SEM images. L. Chrostowski and N. A. F. Jaeger supervised the project.All authors commented on the manuscript.Location: Chapter 2 and Chapter 3.4. X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, ?Uniformand sampled Bragg gratings in SOI strip waveguides with sidewall corru-gations,? IEEE Photonics Technology Letters, vol. 23, no. 5, pp. 290-292,2011.vI conceived the idea, conducted the device design, performed the measure-ments, and wrote the manuscript. W. Shi and L. Chrostowski contributed tothe device design. R. Vafaei assisted with the measurements. L. Chrostowskiand N. A. F. Jaeger gave many advices during the course of the project andassisted in editing the manuscript. This work was done as the course projectfor EECE 571U.Location: Chapter 2.Conference Proceedings1. X. Wang, H. Yun, N. A. F. Jaeger, and L. Chrowtowski, ?Multi-period Bragggratings in silicon waveguides,? in IEEE Photonics Conference 2013, Belle-vue, WA, September 2013, paper WD2.5.N. A. F. Jaeger and I conceived the idea. I conducted the device design,performed the measurements, and wrote the manuscript. H. Yun assistedwith the measurements. N. A. F. Jaeger and L. Chrostowski supervised theproject. All authors commented on the manuscript.Location: Section 3.3.1.2. X. Wang, H. Yun, and L. Chrowtowski, ?Integrated Bragg gratings in spiralwaveguides,? in CLEO 2013, San Jose, CA, June 2013, paper CTh4F.8.I conceived the idea, conducted the device design, and wrote the manuscript.H. Yun performed the measurements. L. Chrostowski supervised the project.All authors commented on the manuscript.Location: Section 3.6.3. S. T. Fard, S. M. Grist, V. Donzella, S. A. Schmidt, J. Flueckiger, X. Wang,W. Shi, A. Millspaugh, M. Webb, D. M. Ratner, K. C. Cheung, and L. Chros-towski, ?Label-free silicon photonic biosensors for use in clinical diagnos-tics,? in SPIE Photonics West, San Francisco, CA, February 2013, paper862909.I conducted the design of the grating device and wrote the correspondingsection in the manuscript. S. T. Fard led the writing of the whole manuscript.viS. M. Grist, V. Donzella, S. A. Schmidt, J. Flueckiger, W. Shi, A. Millspaugh,and M. Webb contributed to the design, measurements, and data analysisduring the course of the project. D. M. Ratner, K. C. Cheung, and L. Chros-towski supervised the project. All authors commented on the manuscript.Location: Section 2.6.3.4. X. Wang, W. Shi, M. Hochberg, K. Adams, E. Schelew, J. Young, N. Jaeger,and L. Chrowtowski, ?Lithography simulation for the fabrication of siliconphotonic devices with deep-ultraviolet lithography,? in Group IV Photonics,San Diego, CA, August 2012, pp. 288-290.I conceived the idea, conducted the design, measurements and numericalsimulations, and wrote the manuscript. W. Shi, M. Hochberg, and K. Adamscontributed to the project through discussions. E. Schelew assisted with thenumerical simulations. J. Young, N. Jaeger, and L. Chrowtowski supervisedthe project. All authors commented on the manuscript.Location: Section 2.3.5. X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski,?Narrow-band transmission filter using phase-shifted Bragg gratings in SOIwaveguide,? in IEEE Photonics Conference, Arlington, VA, October 2011,pp. 869-870.I conceived the idea, conducted the device design, performed the measure-ments, and wrote the manuscript. W. Shi contributed to the project throughdiscussions. S. Grist took the SEM images. H. Yun assisted with the mea-surements. N. A. F. Jaeger, and L. Chrowtowski supervised the project. Allauthors commented on the manuscript.Location: Section 2.6.2.viiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Silicon Photonics . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Motivation and Application . . . . . . . . . . . . . . . . 11.1.2 State of the Art and Challenges . . . . . . . . . . . . . . 41.2 Bragg Gratings . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3 Silicon Photonic Bragg Gratings . . . . . . . . . . . . . . . . . . 121.3.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 131.3.2 Thesis Organization . . . . . . . . . . . . . . . . . . . . 152 Strip Waveguide Bragg Gratings . . . . . . . . . . . . . . . . . . . . 162.1 Strip Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2 Uniform Gratings . . . . . . . . . . . . . . . . . . . . . . . . . . 20viii2.2.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.2 Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.2.3 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . 242.2.4 Measurement . . . . . . . . . . . . . . . . . . . . . . . . 252.2.5 Design Variations . . . . . . . . . . . . . . . . . . . . . . 352.3 Lithography Effects . . . . . . . . . . . . . . . . . . . . . . . . . 462.4 Thermal Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . 512.5 Wafer-Scale Performance . . . . . . . . . . . . . . . . . . . . . . 522.6 Phase-shifted Gratings . . . . . . . . . . . . . . . . . . . . . . . 582.6.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582.6.2 Design Variations . . . . . . . . . . . . . . . . . . . . . . 622.6.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . 702.7 Sampled Gratings . . . . . . . . . . . . . . . . . . . . . . . . . . 732.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773 Rib Waveguide Bragg Gratings . . . . . . . . . . . . . . . . . . . . . 783.1 Rib Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . 793.2 Uniform Gratings . . . . . . . . . . . . . . . . . . . . . . . . . . 803.2.1 Design and Fabrication . . . . . . . . . . . . . . . . . . . 803.2.2 Measurement Results . . . . . . . . . . . . . . . . . . . . 823.3 Multi-period Gratings . . . . . . . . . . . . . . . . . . . . . . . . 863.3.1 Dual-Period Grating . . . . . . . . . . . . . . . . . . . . 863.3.2 Four-Period Grating . . . . . . . . . . . . . . . . . . . . 873.4 Thermal Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . 903.5 Wafer-Scale Performance . . . . . . . . . . . . . . . . . . . . . . 923.6 Spiral Gratings . . . . . . . . . . . . . . . . . . . . . . . . . . . 993.6.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 1003.6.2 Results and Discussion . . . . . . . . . . . . . . . . . . . 1033.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1054 Slot Waveguide Bragg Gratings . . . . . . . . . . . . . . . . . . . . . 1064.1 Slot Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . 1074.2 Uniform Gratings . . . . . . . . . . . . . . . . . . . . . . . . . . 109ix4.2.1 Design and Fabrication . . . . . . . . . . . . . . . . . . . 1094.2.2 Measurement Results . . . . . . . . . . . . . . . . . . . . 1124.3 Phase-Shifted Gratings . . . . . . . . . . . . . . . . . . . . . . . 1144.3.1 Design and Fabrication . . . . . . . . . . . . . . . . . . . 1144.3.2 Measurement Results . . . . . . . . . . . . . . . . . . . . 1164.4 Biosensing Applications . . . . . . . . . . . . . . . . . . . . . . 1184.4.1 Silicon Photonic Biosensors . . . . . . . . . . . . . . . . 1194.4.2 Design and Fabrication . . . . . . . . . . . . . . . . . . . 1214.4.3 Experiments and Discussion . . . . . . . . . . . . . . . . 1224.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1285 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . 1295.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1295.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135A Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150A.1 Book Chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . 150A.2 Journal Publications . . . . . . . . . . . . . . . . . . . . . . . . . 150A.3 Conference Proceedings . . . . . . . . . . . . . . . . . . . . . . 152xList of TablesTable 2.1 Maximum output power (continuous power during sweep) ofAgilent 81600B Option 201 [1]. . . . . . . . . . . . . . . . . . 34Table 3.1 Statistics of strip and rib waveguide Bragg gratings (WBG). . . 99Table 3.2 Mode mismatch loss between two bent waveguides (WG). . . . 103Table 4.1 Design variations for uniform slot waveguide Bragg gratings. . 109xiList of FiguresFigure 1.1 Common waveguide geometries in silicon-on-insulator. . . . . 4Figure 1.2 Longitudinal effective index profile of a uniform grating (z isthe propagation direction, ? is the grating period, ne f f 1 is thelow effective refractive index and ne f f 2 is the high effectiverefractive index). . . . . . . . . . . . . . . . . . . . . . . . . 8Figure 1.3 Typical spectral responses of a uniform Bragg grating. . . . . 9Figure 1.4 A typical silicon photonic chip and a Canadian dime. . . . . . 14Figure 2.1 Schematic of a strip waveguide cross section (not to scale). . . 17Figure 2.2 Simulated electric field of the fundamental modes in 500 nmstrip waveguides: (a) TE mode with air cladding, (b) TM modewith air cladding, (c) TE mode with oxide cladding, and (d)TM mode with oxide cladding. . . . . . . . . . . . . . . . . . 18Figure 2.3 SEM image of a 500 nm strip waveguide. The waveguide wasmilled using a focused ion beam (FIB) to expose the cross sec-tion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Figure 2.4 Schematic of a uniform strip waveguide grating. . . . . . . . 20xiiFigure 2.5 Typical design flow for a uniform Bragg grating: 1) choose acertain waveguide cross section, 2) calculate the mode profileand effective refractive index, then calculate the grating pe-riod based on the Bragg condition, 3) calculate the couplingcoefficient for a particular bandwidth (assuming the grating issufficiently long and a high reflectivity is needed), 4) calculatethe corrugation width with the assistance of mode simulationand lithography simulation, 5) calculate the grating length. . . 21Figure 2.6 Simulated electric field of the second TE mode in a 500 nmstrip waveguide with oxide cladding. The majority of the elec-tric field is on the sidewalls, resulting in a much lower effectiveindex and a much higher propagation loss than the fundamen-tal TE mode. . . . . . . . . . . . . . . . . . . . . . . . . . . 21Figure 2.7 Schematic diagram of the device layout (not to scale): (a) in-dividual fiber configuration, (b) fiber array configuration. . . . 24Figure 2.8 An approach to increase the device packing efficiency usingthe fiber array configuration. The grating devices are locatedin the bundle on the right side, and the routing waveguides runbetween the grating couplers. . . . . . . . . . . . . . . . . . . 25Figure 2.9 Top view SEM image of a fabricated strip waveguide gratingwith design parameters: W = 500 nm, ?W = 80 nm. Notethat the rectangular corrugations we used in the design wererounded due to the lithography. . . . . . . . . . . . . . . . . . 26Figure 2.10 Tilted view SEM image of a fabricated Y-branch as illustratedin Figure 2.7(a). . . . . . . . . . . . . . . . . . . . . . . . . . 26Figure 2.11 Top view SEM image of a fabricated grating coupler (GC). Thelayout of the GC was illustrated in Figure 2.8, and the squaretiles were added around the GC to meet the density rule. . . . 27Figure 2.12 Part of a fabricated chip showing the compact routing approachillustrated in Figure 2.8. . . . . . . . . . . . . . . . . . . . . 27Figure 2.13 A measurement setup using two individual fibers. . . . . . . . 28xiiiFigure 2.14 Block diagram of the advanced experimental setup. PD: pho-todetector, EDFA: erbium-doped fiber amplifier, TEC: thermo-electric cooler. . . . . . . . . . . . . . . . . . . . . . . . . . 29Figure 2.15 An advanced measurement setup using a fiber array. . . . . . 30Figure 2.16 Full view of the advanced measurement setup. . . . . . . . . . 31Figure 2.17 Captured image during experiment. The chip uses a layoutsimilar to Figure 2.8, and the grating couplers are aligned withthe fibers in the array. . . . . . . . . . . . . . . . . . . . . . . 32Figure 2.18 Measured transmission spectra of a straight waveguide (WG)and a Bragg grating using: (a) the low SSE option, and (b) thehigh power option. Comparison between the low SSE optionand the high power option for: (c) the spectra of the straightwaveguide, and (d) the normalized response of the grating bysubtracting the spectra of the straight waveguide . Note thatthe laser output power was set to be 0 dBm (i.e., 1 mW). . . . 33Figure 2.19 Measured transmission spectra of a Bragg grating using thehigh power option under various sweeping conditions. Insetshows the zoom-in view around the Bragg wavelength. Thesmall ripples out of the stop band are due to the FP effects inthe measurement system. . . . . . . . . . . . . . . . . . . . . 35Figure 2.20 Measured transmission spectra for gratings with different grat-ing periods, showing the red shift with increasing grating pe-riod. Fixed parameters: air cladding, W = 500 nm, ?W =20 nm, N =1000. . . . . . . . . . . . . . . . . . . . . . . . . 36Figure 2.21 Bragg wavelength extracted from Figure 2.20 versus gratingperiod. The slope of the linear curve fit is 2.53, which is ingood agreement with the calculation using Eq. 2.1. . . . . . . 37Figure 2.22 Measured transmission spectra for various corrugation widths,showing the bandwidth increases with increasing corrugationwidth. Fixed parameters: air cladding, W = 500 nm, ? =325 nm, and N =3000. . . . . . . . . . . . . . . . . . . . . . 38xivFigure 2.23 Measured bandwidth versus corrugation widths on 500 nm stripwaveguide with air cladding. The data points for 10 nm, 40nm, 80 nm, and 160 nm corrugations correspond to the spectrain Figure 2.22. The linear fit shows that the coupling coef-ficient (i.e., grating index contrast) is approximately propor-tional to the corrugation width. . . . . . . . . . . . . . . . . . 38Figure 2.24 Measured transmission spectra for gratings with 20 nm corru-gation on a 500 nm waveguide and on a 450 nm waveguide.Fixed parameters: air cladding, ?W = 20 nm and N =1000.The period for the 500 nm waveguide and the 450 nm waveg-uide is 325 nm and 340 nm, respectively. . . . . . . . . . . . 39Figure 2.25 Simulated electric field of the fundamental TE mode in a 500 nm(top) and a 450 nm (bottom) strip waveguide, both with aircladding. The field intensity around the sidewall of the 450 nmwaveguide is stronger than that of the 500 nm waveguide. . . . 40Figure 2.26 Measured bandwidth as a function of corrugation width on500 nm (blue) and 450 nm (red) strip waveguides with aircladding. The gratings on narrower waveguide show largerbandwidths and a larger slope in the linear fit, due to increasedmodal overlap with the sidewalls. . . . . . . . . . . . . . . . 40Figure 2.27 Measured transmission spectra for gratings with air cladding(blue) and with oxide cladding (green). For the oxide-clad de-vice, the wavelength is longer due to the larger average ef-fective index and the bandwidth is smaller due to the reducedindex contrast. Fixed parameters: W=500 nm, ?W=160 nm,?=325 nm, N =3000. . . . . . . . . . . . . . . . . . . . . . 41Figure 2.28 Measured bandwidth as a function of corrugation width on500 nm strip waveguide with air cladding (blue) and with ox-ide cladding (green). The gratings with oxide cladding showsmaller bandwidths and a smaller slope in the linear fit, due tothe reduced index contrast. . . . . . . . . . . . . . . . . . . . 41xvFigure 2.29 Measured out-of-band transmission spectra for gratings withvarious corrugation widths and lengths. Fixed parameters: aircladding, W = 500 nm, ? = 325 nm. The propagation loss iswithin the range of 2.5?4.5 dB/cm and is independent of thecorrugation width. . . . . . . . . . . . . . . . . . . . . . . . 42Figure 2.30 Measured transmission spectra of gratings with 20 nm corru-gation width for various lengths, showing bandwidth broaden-ing effect with increasing N and wavelength variations due tofabrication variations. Fixed parameters: air cladding, W =500 nm, ?= 325 nm. . . . . . . . . . . . . . . . . . . . . . . 43Figure 2.31 Measured transmission spectra of gratings with (a) 10 nm and(b) 80 nm corrugation width for various lengths, showing sim-ilar trends as Figure 2.30. Fixed parameters: air cladding,W = 500 nm, ?= 325 nm. . . . . . . . . . . . . . . . . . . . 44Figure 2.32 Schematic illustration of corrugation shapes (not to scale). . . 45Figure 2.33 Measured bandwidth as a function of corrugation width for dif-ferent shapes. Fixed parameters: oxide cladding, W = 500 nm,? =320 nm, N =2000. The bandwidth and the slope of thelinear fit become smaller as the shape goes from rectangular totrapezoidal to triangular, due to the reduced Fourier componentand coupling coefficient. . . . . . . . . . . . . . . . . . . . . 46Figure 2.34 Lithography simulation for device A: (a) original design, (b)simulation result. . . . . . . . . . . . . . . . . . . . . . . . . 48Figure 2.35 Spectral comparison (transmission) for device A. Original de-sign: FDTD simulation using the structure in Figure 2.34(a),post-litho simulation: FDTD simulation using the structure inFigure 2.34(b). . . . . . . . . . . . . . . . . . . . . . . . . . 48Figure 2.36 Bandwidth versus corrugation width on 500 nm strip waveg-uides with air cladding. The post-litho simulation agrees wellwith the measurement result, while the original designs showbandwidths of about three times larger. . . . . . . . . . . . . 49xviFigure 2.37 Lithography simulation for a photonic crystal cavity with threemissing holes in the centre. XOR: Boolean operation of XOR(exclusive or) between the original and simulated layouts. Thetwo cavity side holes (H1 and H2) are displaced in order toachieve a high Q-factor. . . . . . . . . . . . . . . . . . . . . 50Figure 2.38 Measured transmission spectra of a strip waveguide grating atdifferent temperatures, showing the red shift with increasingtemperature. The design parameters are: air cladding, W =500 nm, ?W = 20 nm, ?= 330 nm, and N =1000. . . . . . . 51Figure 2.39 Bragg wavelength versus temperature corresponding to the mea-sured spectra in Figure 2.38, showing a thermal sensitivity ofabout 84 pm/oC. . . . . . . . . . . . . . . . . . . . . . . . . 52Figure 2.40 Wafer map (available chips are listed in the legend). . . . . . . 54Figure 2.41 Performance nonuniformity of the strip waveguide grating onWafer A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Figure 2.42 Performance nonuniformity of the strip waveguide grating onWafer B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Figure 2.43 Performance nonuniformity of the strip waveguide grating asa function of the column number. Each error bar is symmet-ric and the length is two standard deviations (within each col-umn). The general trend of the decrease in wavelength andthe increase in bandwidth is due to the intentional increase inexposure dose from left to right columns. . . . . . . . . . . . 57Figure 2.44 Schematic of a phase-shifted strip waveguide grating. . . . . . 58Figure 2.45 Spectral responses of a uniform and a phase-shifted grating.Note that the only difference between the two devices is theinclusion of the phase shift. . . . . . . . . . . . . . . . . . . . 59Figure 2.46 Top view SEM image of a fabricated strip waveguide phase-shifted grating. Design parameters: W = 500 nm, ?W = 80 nm,? = 320 nm. Note that the phase shift in the central regioncan be identified by measuring the spacing between the grat-ing grooves. Here, the spacing with the phase shift is 480 nm,corresponding to 1.5 times the grating period (320 nm). . . . . 60xviiFigure 2.47 Transmission spectra for phase-shifted gratings with differentphase-shift length. Multiple resonance peaks occur for longcavity length due to the reduced free spectral range. . . . . . . 61Figure 2.48 Transmission spectra for phase-shifted gratings with differentN. Fixed parameters: oxide cladding, W = 500 nm, ?W =60 nm, ?= 320 nm. As N is increased, the stop band becomesdeeper due to the increasing reflectivity, and the resonant peakbecomes sharper due to the reduced coupling loss and higherQ factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Figure 2.49 Transmission spectra for phase-shifted gratings with different?W . Fixed parameters: oxide cladding, W = 500 nm, N = 200,?= 320 nm. As ?W is increased, the stop band becomes widerand deeper due to the increasing coupling coefficient, and theresonant peak becomes sharper due to the reduced couplingloss and higher Q factor. . . . . . . . . . . . . . . . . . . . . 63Figure 2.50 Contour plot of the Q factor as a function of ?W and N. Fixedparameters: oxide cladding, W = 500 nm, ? = 320 nm. TheQ factor increases towards the top-right corner of the contour,i.e., large N and/or ?W (essentially a high mirror reflectivity). 64Figure 2.51 Measured Q factor as a function of (a) ?W (corresponding tothe top boundary of the contour plot in Figure 2.50) and (b)N (corresponding to the right boundary of the contour plot inFigure 2.50). . . . . . . . . . . . . . . . . . . . . . . . . . . 65Figure 2.52 Transmission spectra (unnormalized) for phase-shifted grat-ings with different N. Fixed parameters: air cladding, W =500 nm, ?W = 60 nm, and ? = 330 nm. The peak amplitudedrops significantly after N=200, as it goes beyond the criticalcoupling condition. . . . . . . . . . . . . . . . . . . . . . . . 66Figure 2.53 Maximum transmission and Q factor of an FP cavity as a func-tion of R. Simulation parameters: ? = 3 dB/cm, L = 100 ?m,G = 0.9931. The maximum transmission decreases dramati-cally after the critical coupling condition, when the couplingloss equals the waveguide loss: R=?G=0.9965. . . . . . . . . 67xviiiFigure 2.54 Maximum Q factor experimentally observed. Design param-eters: air cladding, W = 500 nm, ?W = 40 nm, N =300, and?= 330 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . 67Figure 2.55 Measured transmission spectra (raw) of a high-Q phase-shiftedgrating at various input power levels. At 0 dBm input power,the resonance becomes asymmetric and the peak wavelengthis skewed to the right. . . . . . . . . . . . . . . . . . . . . . . 68Figure 2.56 Measurement setup for biosening. Reagents were introducedto the sensor using a reversibly bonded PDMS flow cell andChemyx Nexus 3000 Syringe Pump at 10 ?L/min. Note thatthe input/output grating couplers are placed far away from thesensor on the chip. . . . . . . . . . . . . . . . . . . . . . . . 71Figure 2.57 Top: transmission spectra for various concentrations of NaCl(note: 1 M=1 mol/L=1000 mol/m3). Bottom: peak wave-length shift versus bulk refractive index, showing a sensitivityof 58.52 nm/RIU. . . . . . . . . . . . . . . . . . . . . . . . . 72Figure 2.58 Schematic of a sampled grating. . . . . . . . . . . . . . . . . 73Figure 2.59 Measured transmission and reflection spectra of two sampledgratings. Design parameters: air cladding, W = 500 nm, ?W =20 nm, Z1 = 6.4 ?m. Each device includes 20 sampling peri-ods (i.e., total length is 20 Z0). The peak spacing for Z0/Z1 = 4is 1.5 times larger than that for Z0/Z1 = 6, in agreement withEq. 2.17. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Figure 2.60 Layout for the Vernier effect using two sampled gratings withslightly mismatched sampling periods. . . . . . . . . . . . . . 75Figure 2.61 Measured reflection spectra of two individual sampled gratings(top) and the Vernier effect (bottom). The only major peak forthe Vernier effect occurs where the peaks of individual sam-pled gratings are well aligned (at 1530 nm). . . . . . . . . . . 76Figure 3.1 Schematic of the rib waveguide cross section (not to scale):Wrib =500 nm, and Wslab =1 ?m. . . . . . . . . . . . . . . . 79xixFigure 3.2 Simulated electric field of the fundamental TE mode in the ribwaveguide with air cladding. The field intensity is low aroundthe sidewalls, allowing for weak perturbations to the mode us-ing relatively large sidewall corrugations. . . . . . . . . . . . 80Figure 3.3 Cross-sectional SEM image of a rib waveguide with gratingson the slab. . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Figure 3.4 Top view SEM images of fabricated rib waveguide gratingsdesigned with 60 nm corrugations on the rib (left) and 80 nmcorrugations on the slab (right). . . . . . . . . . . . . . . . . 82Figure 3.5 Top view SEM image of the transition from the strip waveg-uide to the rib waveguide grating using a linear taper. . . . . . 82Figure 3.6 Measured transmission responses of two rib waveguide grat-ings with corrugations on the slab, each showing only one dipin a wide wavelength range without higher-order leaky modes. 83Figure 3.7 Zoomed-in view of Figure 3.6 around the Bragg wavelength.The dots are the measured values, and the solid curves are thefits using the analytical expression in Eq. 1.9. As expected, thegrating with larger corrugations shows a slightly larger band-width and a higher reflectivity. . . . . . . . . . . . . . . . . . 84Figure 3.8 Extracted coupling coefficient versus designed corrugation widthfor various grating structures on a chip with oxide cladding.The strip waveguide is 500 nm wide and has the largest cou-pling coefficient, while the grating-on-slab configuration hasthe smallest coupling coefficient. . . . . . . . . . . . . . . . . 85Figure 3.9 Schematic diagram of a dual-period rib waveguide grating (notto scale). Design parameters: ?1 = 290 nm, ?2 = 295 nm,?Wrib = 80 nm, ?Wslab = 100 nm, and the grating length is580 ?m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87Figure 3.10 (a) Measured (unnormalized) transmission spectrum of the dual-period grating: ?1 and ?2 correspond to ?1 and ?2, respec-tively. (b) Normalized response around the two Bragg wave-lengths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88xxFigure 3.11 Dual-period grating: simulation vs. measurement. In the topgraph, the solid blue curve shows the simulated effective indexof the fundamental TE mode; the green and red dashed curvescorresponds to the effective indices that are needed using ?1and ?2, respectively; thus, the intersection points correspondto the two Bragg wavelengths. . . . . . . . . . . . . . . . . . 89Figure 3.12 Schematic diagram of the 4-period rib waveguide grating (notto scale). Design parameters: ?1 = 285 nm, ?2 = 290 nm,?3 = 295 nm, ?4 = 300 nm, ?Wrib = 80 nm, ?Wslab = 100 nm,and the grating length is 580 ?m. . . . . . . . . . . . . . . . 89Figure 3.13 Measured spectral responses of a 4-period grating. ?1, ?2, ?3,and ?4 correspond to ?1, ?2, ?3, and ?4, respectively. . . . . 90Figure 3.14 Bragg wavelength shift of a dual-period rib waveguide gratingat different temperatures: (a) plot around ?2, (b) plot around ?1. 91Figure 3.15 Bragg wavelengths versus temperature corresponding to thespectra in Figure 3.14, showing thermal sensitivities of about85 pm/oC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Figure 3.16 Wavelength nonuniformity of the dual-period grating on WaferA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94Figure 3.17 Bandwidth nonuniformity of the dual-period grating on WaferA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Figure 3.18 Wavelength nonuniformity of the dual-period grating on WaferB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96Figure 3.19 Bandwidth nonuniformity of the dual-period grating on WaferB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Figure 3.20 Performance nonuniformity of the dual-period grating as a func-tion the column number. Each error bar is symmetric and thelength is two standard deviations (within each column). Allvariations are random except the bandwidth variations for ??2,which show that the bandwidth increases from left to rightcolumns due to the intentional exposure dose variation. . . . . 98Figure 3.21 Top view of the spiral grating design. . . . . . . . . . . . . . 100xxiFigure 3.22 Optical microscope images of the fabricated device with N=10.(a) Whole layout. (b) Enlarged image of center region of thespiral. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Figure 3.23 Effective index change of the rib waveguide versus bending ra-dius for device with NR=10. The index change from R =10 ?mto R =22.5 ?m is remarkable, while for R larger than 22.5 ?m,the index change is very small. . . . . . . . . . . . . . . . . . 102Figure 3.24 SEM image of the fabricated spiral gratings. . . . . . . . . . . 103Figure 3.25 (a) Measured transmission spectra of the two spiral gratings.(b) Enlarged plot around the Bragg wavelength. . . . . . . . . 104Figure 4.1 Schematic of a slot waveguide cross section (not to scale). . . 107Figure 4.2 Simulated electric field of the fundamental TE mode in a slotwaveguide with the following design parameters: oxide cladding,Warm = 270 nm, and Wslot = 150 nm. The field intensity isstrongly confined inside the slot region. . . . . . . . . . . . . 108Figure 4.3 SEM image of the focused ion beam (FIB) milled cross sec-tion of a fabricated device (the small hole in the centre wasdue to the incomplete coating of platinum deposited to protectthe waveguides during the FIB milling). Design parameters:Warm = 270 nm, and Wslot = 150 nm. . . . . . . . . . . . . . 108Figure 4.4 Schematic diagrams (not to scale) of the slot waveguide Bragggratings with corrugations (a) inside and (b) outside. . . . . . 109Figure 4.5 Top view SEM images of the fabricated slot waveguide Bragggratings: (a) corrugation inside for Wslot = 150 nm, Warm =270 nm, and ?Win = 20 nm. (b) corrugations outside for Wslot =150 nm, Warm = 270 nm, and ?Wout = 40 nm. . . . . . . . . . 110Figure 4.6 Schematic of the strip-to-slot mode converter (not to scale). . 111Figure 4.7 SEM image of a strip-to-slot mode converter as illustrated inFigure 4.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Figure 4.8 Measured raw spectra of a uniform grating designed on WG1with ?Wout = 10 nm, showing a deep notch with an extinctionratio greater than 40 dB at about 1550 nm. . . . . . . . . . . . 112xxiiFigure 4.9 Measured transmission spectra of the uniform gratings designedon WG1. (a) corrugations inside, (b) corrugations outside. Forboth configurations, the stop-band becomes broader with in-creasing corrugation width. . . . . . . . . . . . . . . . . . . . 113Figure 4.10 Measured bandwidth versus designed corrugation width on WG1and WG2. WG1 with inside corrugations shows the largestbandwidth due to the strongest perturbation. . . . . . . . . . . 113Figure 4.11 Phase-shifted Bragg gratings with corrugations on the outsideof the slot waveguide: (a) schematic diagram (not to scale),(b) SEM image showing the phase shift region of a fabricateddevice, (c) transmission spectrum simulated by FDTD with thefollowing geometric parameters: WG1, ?Wout = 40 nm, andN = 50. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Figure 4.12 Electric field distributions for light incident from the left at(a) 1543 nm and (b) 1550 nm. The simulation parameters arethe same as in Figure 4.11(c). The field was recorded at themiddle of the silicon waveguide in the vertical direction (i.e.,corresponding to the plane of y=110 nm in Figure 4.2). . . . . 116Figure 4.13 Measured raw spectra of a phase-shifted grating designed onWG1 with ?Wout = 40 nm and N = 300. . . . . . . . . . . . . 117Figure 4.14 (a) Measured transmission spectra for phase-shifted gratingsdesigned on WG1 with ?Wout = 40 nm and various lengths,(b) Q factor as a function of N. . . . . . . . . . . . . . . . . . 117Figure 4.15 Schematic diagram of the sensor integrated with the microflu-idic channel. . . . . . . . . . . . . . . . . . . . . . . . . . . 121Figure 4.16 SEM image of the fabricated device. Note that the phase shiftin the central region can be identified by measuring the spacingbetween the grating grooves. Here, the spacing with the phaseshift is 660 nm, corresponding to 1.5 times the grating period. 122Figure 4.17 Measured transmission spectrum of the sensor immersed indeionized water. . . . . . . . . . . . . . . . . . . . . . . . . . 123xxiiiFigure 4.18 Measurement results for various NaCl concentrations: (a) trans-mission spectra for all the measurements, (b) peak wavelengthshift during the salt steps. Each color represents a NaCl con-centration. Steps 1 and 6 correspond to 0 mM, and Steps 2to 5 correspond to 62.5 mM, 125 mM, 250 mM, and 500 mMsolutions, respectively. . . . . . . . . . . . . . . . . . . . . . 124Figure 4.19 Measured and simulated peak wavelength shift as a function ofthe refractive index of the salt solution. For the experimentaldata, the symmetric error bars are two standard deviation unitsin length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Figure 4.20 Biosensing experimental results: (a) depicts the resonance wave-length shifts as the experiment progressed while (b) illustratesreagent sequencing corresponding to regions [A-E] in (a). Re-gion A = Protein-A (1 mg/mL), B = anti-streptavidin (SA)(125 ?g/mL), C = Bovine Serum Albumen (BSA) (2 mg/mL),D = streptavidin (SA) (1.8 ?M), E = Biotin-BSA (2.5 mg/mL).Introduction of reagent in each region was followed by a PBS-wash, as shown by the short, black-dashed line mid-way througheach region. . . . . . . . . . . . . . . . . . . . . . . . . . . . 126Figure 5.1 A proposed active grating device ? high-speed modulator basedon a p-n junction: (a) mask layout and (b) schematic of thecross section of the p-n junction. . . . . . . . . . . . . . . . . 134xxivList of AbbreviationsCMOS Complementary Metal-Oxide-SemiconductorDBR Distributed Bragg ReflectorDFB Distributed Feedback LaserDRC Design Rule CheckerDUV Deep UltravioletEDA Electronic Design AutomationEDFA Erbium-Doped Fiber AmplifierFBG Fiber Bragg GratingFCA Free-Carrier AbsorptionFCD Free-Carrier DispersionFDTD Finite?Difference Time?DomainFIB Focused Ion BeamFP Fabry-PerotFSR Free Spectral RangeFWHM Full Width at Half MaximumGaAs Gallium ArsenideGC Grating CouplerGe GermaniumICP Inductively Coupled PlasmaInP Indium PhosphideLiNbO3 Lithium NiobateLOD Limit of DetectionMPW Multi?Project WaferMZI Mach?Zehnder InterferometerxxvNA Numerical ApertureOSA Optical Spectrum AnalyzerPD PhotodetectorPDMS PolydimethylsiloxanePDK Process Design KitRIE Reactive-Ion EtchingRIU Refractive Index UnitSDL Schematic Driven LayoutSEM Scanning Electron BeamSi SiliconSiO2 Silicon OxideSOI Silicon-on-InsulatorSSE Source Spontaneous EmissionTE Transverse ElectricTM Transverse MagneticTPA Two-Photon AbsorptionUV UltravioletWDM Wavelength Division MultiplexingxxviAcknowledgmentsTo begin with, I am deeply grateful to my supervisor Prof. Lukas Chrostowski,who has been a tremendous source of support and guidance over the past fewyears. I have truly enjoyed working with Lukas and appreciated the opportunitiesthat were made possible by him. His passion and diligence have been an impor-tant influence on me. This thesis would also not have been possible without Prof.Nicolas A. F. Jaeger, who has been an unofficial co-supervisor and in whose labmost of my experiments were performed. I also thank Prof. Shahriar Mirabbasi forserving on my supervisory committee and for his helpful comments on my work.I would like to thank many students (including former students) in our researchgroup: Wei Shi, Behnam Faraji, Raha Vafaei, Jonas Flueckiger, Samantha Grist,Han Yun, Charlie Lin, Yun Wang, Michael Caverley, Miguel A. Guillen-Torres,Robert Boeck, and Sahba T. Fard. They contributed to this work in various waysover the years and also made my time in the lab a lot of fun. I enjoyed the count-less hours of brainstorming and discussion, and fixing every little problem just gotmuch easier with their help. Our visiting students, Gwen Yu and Mengyu Weng,who collected lots of data for this thesis, certainly deserve my thanks. I also wantto thank Yiheng Lin for helping me take good pictures using the microscope inProf. Guangrui Xia?s lab.I gratefully acknowledge the NSERC Si-EPIC program for the financial sup-port and training in the past two years. I also acknowledge CMC Microsystems forenabling the fabrication of most of our chips and for organizing the Canada-widesilicon photonics workshops. In particular, I want to thank Dr. Dan Deptuck andDr. Jessica Zhang for their assistance. I would like to thank Lumerical Solutionsand Mentor Graphics for their software and excellence technical support, as well asxxviiour collaborations. My special thanks would go to the foundries where our deviceswere actually fabricated: IMEC (Belgium), IME (Singapore), and BAE (UnitedStates), and to the two major MPW service providers: ePIXfab and OpSIS.One of the wonderful things about my PhD has been collaborating with manyresearchers in other fields. These include bioengineers at the University of Wash-ington (particularly Shon Schmidt and Prof. Daniel M. Ratner); and microwavephotonic experts at INRS (particularly Dr. Maurizio Burla and Prof. Jose Azana)and Chinese Academy of Sciences (Prof. Ming Li). Our collaborations have beenvery exciting and productive, and I greatly appreciate their efforts and help. I alsoenjoyed the fruitful discussions with the nanophotonics group at the University ofDelaware led by Prof. Michael Hochberg.It is a pleasure to recall my internship at TeraXion, which not only gave mevaluable industrial experience but also allowed me to know Quebec City. In partic-ular, I would like to thank Dr. Yves Painchaud and Dr. Michel Poulin for their helpthroughout the course of the internship.Finally, to acknowledge debts that have accumulated over years, I thank myfamily, for their love, understanding, and endless support.xxviiiChapter 1IntroductionSilicon photonics has great potential to bringing together two technological areasthat have transformed the last century ? electronics and photonics, and is gainingtremendous momentum in both academia and industry. The Bragg grating is afundamental component in various optical devices and has applications in areas asdiverse as communications, lasers, and sensors. In this thesis, we will present theintegration of Bragg gratings in silicon photonic waveguides, using a wide varietyof waveguide geometries and grating profiles, and explore their applications.1.1 Silicon PhotonicsSilicon photonics is currently one of the most active disciplines within the field ofoptics and photonics [2?4]. Over the past decade, the silicon photonics communityhas made spectacular progress in developing a wide variety of photonic devices onsilicon. Recently, the move to commercial products, as well as large-scale systemintegration, has just begun. In this section, we will briefly discuss the motivationsand applications for silicon photonics, and then give a short overview of the stateof the art and some challenges in this area.1.1.1 Motivation and ApplicationIntegration is a major driving force behind today?s rapid development of siliconphotonics. It allows photonic devices to be made cheaply and in large quantities1using standard semiconductor fabrication techniques, and offers the possibility ofintegration with electronic circuits to provide increased functionality. It is wellknown that silicon wafers have the lowest cost (per unit area) and the highest crys-tal quality of any semiconductor materials [3]. In the mature microelectronics in-dustry, it is able to fabricate millions of transistors in a single integrated circuit(IC), and offer them at such a low price that they have become ubiquitous in ourdaily lives. There is no doubt that, the integration of a large number of photonicfunctions onto a single chip can bring similar advantages to photonics as what sil-icon integration has done for electronics: compactness, dramatic cost reductions,enhanced performance, large-scale system with increased functionality, etc. Butthen the question is: which material or platform is appropriate for such integra-tion? Silicon is definitely the most successful material for electronics, but is it agood choice for photonics?Currently, the photonics market is shared by several material systems, includ-ing compound semiconductors such as indium phosphide (InP) and gallium ar-senide (GaAs), elementary semiconductors such as silicon (Si) and germanium(Ge), silica and rare-earth-doped glasses, lithium niobate (LiNbO3), and polymers[5]. Each material is selected for particular applications and devices. On the sys-tem level, it is common to find more than one of these materials used in differentcomponents. A typical example is the optical fiber communication system, wherealmost all of the above materials are used (e.g., InP for lasers, silica for fibres,LiNbO3 for modulators, erbium-doped glass for optical amplifiers, Si for controlcircuits made with CMOS, InGaAs/Ge for detectors, etc). This makes the devicemanufacturing industry fragmented, and more importantly, the discrete photoniccomponents are packaged separately, which eventually results in very high pack-aging cost, low yield, and large size of the final product.Silicon is optically transparent at key wavelengths (1310 nm and 1550 nm)used for telecommunications, so it could be used to create waveguides and otherpassive devices. An ideal platform for creating waveguides is silicon-on-insulator(SOI), which consists of a top (active) silicon layer supported by a buried oxidelayer with a bottom silicon substrate. The strong optical confinement offered bythe high refractive index contrast between Si (n = 3.48) and air (n = 1) or SiO2(n = 1.44) makes it possible to shrink the waveguide cross section to submicron2levels. For example, 500 nm in width and 220 nm in height are typical dimensionsfor an SOI strip waveguide that can support single-mode operation. In contrast,a single-mode optical fibre for telecommunication wavelengths (1.55 ?m) usuallyhas a core diameter of about 8 ?m. The strong optical confinement also allows forvery tight bends (bend radius can be on the order of a few microns) and functionalwaveguide elements of ten to a few hundred microns. Therefore, large-scale inte-gration of many functional elements on a single chip is within reach. Currently, thenumber of components integrated on silicon photonic chips is still very small (Sunet al. reported 4096 in [6]), but there is no doubt that this number, as well as thecircuit complexity, will be increasing rapidly in the next few years.Another key value of using silicon for photonics is to make most, and ideallyall, of the devices using the existing fabrication facilities used to build advancedelectronic chips. In the microelectronics industry, integrated circuit production fa-cilities are expensive to build and maintain, but the foundry model separates theoperation of the fabrication plant (also known as ?fab?) from the design: fablesscompanies avoid costs by not owning such facilities and concentrate on the de-sign, while pure-play foundries focus on fabricating ICs for other companies andkeeping their fabs at full utilization. This CMOS fabrication infrastructure opensthe door for commercialization and large-scale production of silicon photonic ICs[7]. The recent development of multi-project-wafer (MPW) services [8, 9] has al-ready made advanced CMOS-compatible processes [10, 11] widely available tothe community at modest cost, and will help promote the growth of fabless pho-tonic companies. Note that ?CMOS-compatibility? means photonic devices can befabricated using CMOS process tools (e.g., lithography and etching) and materials(e.g., silicon), however, it does not mean using the tools and materials in exactly thesame way as for traditional CMOS. There is wide agreement in the silicon photon-ics community that a device fabricated in a commercial CMOS fab (e.g., 200 mmor 300 mm pilot line) is supposed to be ?CMOS-compatible?.In terms of applications, a lot of research effort has been focused on short-reach optical interconnects, such as data centres and high-performance computing.In this digital age, data explosion is happening at every level from scalable cloudcomputing centres to new powerful consumer devices. In order to meet the de-mand for rapidly increasing data transfer rate, the widespread adoption of optical3interconnects is inevitable, owing to their inherent advantages over their electri-cal counterparts in terms of bandwidth, distance, and power consumption [12].Silicon photonics is one of the leading candidate technologies for optical intercon-nects [13], due to its unique combination of low fabrication costs, performance en-hancements resulting from electronic ? photonic integration, and CMOS compat-ibility. Apart from data communications, there are many other applications beingexplored, including biosensors [14, 15], gas sensors [16], optomechanics [17, 18],quantum optics [19?22] nonlinear optics [23], mid-infared optics [24], integratedmicrowave photonics [25?27], coherent communications [28], and so on.1.1.2 State of the Art and ChallengesTo date, all of the essential components to build an optical interconnect on silicon[29] ? including lasers [5], modulators [13], detectors [30], waveguides [31], andvarious passive components [32] ? have already been demonstrated.Silicon waveguides, the earliest to attract the attention of researchers [33], havebeen studied extensively over the past two decades. There are a number of waveg-uide geometries that have been developed in silicon. The most common are stripwaveguides, rib waveguides, and slot waveguides, as illustrated in Figure 1.1. StripStrip Waveguide! Rib Waveguide! Slot Waveguide!BOX!Substrate!Figure 1.1: Common waveguide geometries in silicon-on-insulator.waveguides often have small cross sections for single-mode operation and are oftenused to build compact and efficient devices. However, the strong optical confine-ment comes with some drawbacks: relatively low fabrication tolerance and high4scattering loss due to sidewall roughness. Typical reported propagation losses forstrip waveguides are currently in the 2?3 dB/cm range using commercial processes[8, 9]. Rib waveguides have larger cross sections and the propagation loss can beeffectively reduced (e.g. 0.27 dB/cm [34, 35]) because of the reduced overlap be-tween the optical mode and the waveguide sidewalls. However, sharp bends areno longer possible due to the much weaker optical confinement. Therefore, a goodsolution is to use rib waveguides for long-distance straight connections and to usestrip waveguides for where bends are needed. While the optical mode is alreadytightly confined in strip waveguides, the mode size can be further reduced by us-ing a slot waveguide. A typical slot waveguide consists of two arms of siliconseparated by a narrow trench filled with a lower index material [36]. The elec-tric field is highly concentrated in the slot due to the dielectric discontinuity. Thisproperty allows for much stronger interactions between the optical mode and thesurrounding materials. Therefore, slot waveguides are very promising for sensingapplications [16], as well as electro-optical modulators [37], and nonlinear optics[38]. The connection between these different types of waveguides can be realizedusing tapers [35, 39].A silicon laser ? arguably the most important active photonic device among all? is actually the most challenging to realize [40]. Currently, due to the lack of anefficient on-chip light source, most silicon photonic chips couple light from an ex-ternal laser using edge [41] or grating couplers [42?44]. Although the coupling ef-ficiency has been significantly improved, the potential of an on-chip laser source isinvaluable. Traditional semiconductor lasers use direct bandgap compound semi-conductors, such as GaAs or InP. As an indirect bandgap material, silicon is notnaturally capable of efficient photon emission. However, due to the intense interestin silicon photonics, a number of breakthroughs have been accomplished in the pastdecade [5]. Successful examples of realizing lasers on silicon include: silicon Ra-man lasers [45], germanium-on-silicon lasers [46] with bandgap engineering tech-niques, and hybrid silicon lasers [47] in which the silicon is bonded to compoundsemiconductors (such as InP). The last approach is of great interest, because it cancombine the superior gain characteristics of compound semiconductors with thesuperior passive waveguide characteristics of silicon. As a result, many structuresfor hybrid silicon lasers have been demonstrated: Fabry-Perot (FP) lasers [48], dis-5tributed feedback (DFB) lasers [49], distributed Bragg reflector (DBR) lasers [50],sampled gratings DBR (SGDBR) lasers [51], microring [52] and microdisk lasers[53]. In many of these hybrid lasers, specifically DBR, DFB, and SGDBR lasers,Bragg gratings are used as the basic elements to select only one cavity mode tolase. However, the incompatibility of III-V materials with standard CMOS processis still an open issue.Another crucial device is the silicon optical modulator, which has also beenimproved dramatically in recent years [13]. When applying an electric field to amaterial, electro-optic effects occur: a change in the refractive index is known aselectro-refraction (e.g., the Pockels effect and the Kerr effect), whereas a change inthe absorption coefficient is known as electro-absorption (e.g., the Franz?Keldysheffect and the quantum-confined Stark effect). However, these traditional effectsare very weak in pure silicon at wavelengths of 1.3 ? 1.55 ?m [54]. The most com-mon method to achieve modulation in silicon so far has been to exploit the plasmadispersion effect, where a change in free carrier density results in a change in therefractive index. The control of free carrier density can be achieved through mech-anisms such as carrier injection, accumulation or depletion [13]. The refractiveindex change can be converted to intensity modulation by using a Mach?Zehnderinterferometer (MZI) in which the refractive index change is used to shift the rel-ative phase of two propagating waves such that they interfere either constructivelyor destructively [55], or using a resonant structure in which the resonant conditionis controlled by the refractive index [56]. Several figures of merit are usually usedto characterize a modulator, including modulation speed (bandwidth) and depth(extinction ratio), optical bandwidth, insertion loss, area efficiency (footprint) andpower consumption. Ideally, silicon optical modulators will need to have highmodulation speed and extinction ratio, large optical bandwidth, small footprints,low insertion loss and ultra-low power consumption. They must also be CMOS-compatible. However, these requirements often contradict each other, and thereforean innovative engineering solution is necessary to achieve an optimal trade-off [13].In general, MZI-based modulators have a large working spectrum (>20 nm) [57],whereas typical resonator-based modulators can only work within ?0.1 nm [58].However, the use of resonant structures has demonstrated more advantages overMZI, including much smaller footprint, much lower modulation voltage and power6consumption, lower insertion loss, higher extinction ratio with comparable mod-ulation speed [59, 60], etc. In addition to conventional resonant structures suchas micro-rings and micro-disks, Bragg gratings can also be used to form micro-cavities, and therefore, can join in the development of silicon modulators.Again, due to its inherently large bandgap, silicon itself is not efficient forphoton detection at wavelengths of 1.3 ? 1.55 ?m. Currently, most research onintegrated photodetectors (PD) is focused on using Ge as the absorption mate-rial, due to its much higher absorption coefficient and its CMOS-compatibility.Waveguide-coupled Ge photodetectors are of particularly interest as they enabledirect integration with silicon waveguides, and they also have better performancethan normal-incidence photodetectors. As the state of the art, a responsivity of0.95 A/W at 1550 nm with 36 GHz 3-dB bandwidth has been demonstrated [61].Another exciting trend in silicon photonics is the transition from device devel-opment to system-level integration. Although device improvement will continueto be important, it is expected that over the next few years, the number of sys-tem designers will grow much faster than that of device engineers [62]. A typicalsystem example is an on-chip wavelength division multiplexing (WDM) architec-ture [63]. Intel, the world?s largest semiconductor chip maker, has demonstrateda 50G silicon photonics link in 2011, which has hybrid silicon lasers, modulators,multiplexers, demulitplexers, and photodetectors all integrated on chip [64].Silicon photonics is also beginning to be a significant industry in its own right[62]. Electronics giants such as Intel, IBM, Samsung, Oracle, Cisco, and manyothers have been very active in the development of this technology. Luxtera, afabless startup founded in 2001, is one of the earliest on the commercializationpath. They have shipped a million 10G active optical cables enabled by siliconphotonics [65], and are now moving towards 100G. Teraxion, a Canadian opticalcomponent company, has been developing silicon photonic coherent receivers inthe past few years and reported the smallest integrated receiver in the industryfor coherent detection [28]. There are a number of other startups, not only in thecommunication sector, but also in other sectors, such as Genalyte that makes siliconphotonic biosensor chips [66].There are many challenges still remaining to be addressed. To name a few, sil-icon photonic devices are very sensitive to temperature variations on the chip, due7to the large thermo-optic coefficient of silicon. Owing to the electronic-photonicintegration, it is possible to integrate thermal feedback mechanisms, but the sys-tem complexity and power consumption will definitely be higher. The polarizationindependence is also an important issue for many applications. In terms of fabrica-tion, although the fabrication facilities are the same as for CMOS electronics, thisdoes not mean that the processes are exactly the same; on the contrary, the pro-cess flows for fabricating electronic-photonic integrated circuits are very differentfrom those of electronics alone. Such processes are complicated and expensive todevelop, and significant effort will be required to keep them stable [7]. Moreover,yield management will be critical in the near future.1.2 Bragg GratingsIn the simplest configuration, a Bragg grating is a structure with periodic modu-lation of the effective refractive index (ne f f ) in the propagation direction of theoptical mode, as shown in Figure 1.2. This modulation is commonly achieved byneff1neff2?neffzFigure 1.2: Longitudinal effective index profile of a uniform grating (z isthe propagation direction, ? is the grating period, ne f f 1 is the low effectiverefractive index and ne f f 2 is the high effective refractive index).varying the refractive index (e.g., alternating material) or the physical dimensionsof the waveguide. At each boundary, a reflection of the travelling light occurs, andthe relative phase of the reflected signal is determined by the grating period andthe wavelength. The repeated modulation of the effective index results in multipleand distributed reflections. The reflected signals only interfere constructively ina narrow band around one particular wavelength, namely the Bragg wavelength.Within this range, light is strongly reflected. At other wavelengths, the multiple8reflections interfere destructively and cancel each other out, and as a result, light istransmitted through the grating. Figure 1.3 shows the typical spectral response of1540 1545 1550 1555 156000.20.40.60.81Wavelength (nm)Response  ReflectionTransmissionRpeak??B?Figure 1.3: Typical spectral responses of a uniform Bragg grating.a uniform Bragg grating. The Bragg wavelength is given as:?B = 2?ne f f (1.1)where ? is the grating period, and ne f f is the effective index of the structure withoutthe grating. Based on coupled-mode theory [67], the effect of the periodic structureis to couple forward-going and backward-going waves in the grating. We can writethe electric field as a sum of forward (S) and backward (R) propagating waves:E(z) = R(z)exp(? j?0z)+S(z)exp(? j?0z) (1.2)where ?0 is the Bragg propagation constant:?0 =2pi?Bne f f (1.3)9Following the derivation in [67], we obtain the coupled-mode equations:dRdz+ j??R =? j?S (1.4)dSdz? j??S = j?R (1.5)Here, ? is often defined as the coupling coefficient of the grating and can be inter-preted as the amount of reflection per unit length. For a stepwise effective indexvariation as shown in Figure 1.2 (?n = ne f f 2?ne f f 1), the reflection at each inter-face can be written as ?n/2ne f f according to the Fresnel equations. Each gratingperiod contributes two reflections, therefore the coupling coefficient is:? = 2?n2ne f f1?=2?n?B(1.6)For a sinusoidal effective index variation n(z) = ne f f +?n/2 ? cos(2?0z), the cou-pling coefficient is reduced by a factor of pi/4 [67]:? =pi?n2?B(1.7)Similarly, for other effective index variations, we can take the Fourier expansions:n(z) = ne f f +?i?ni/2 ? cos(i ? 2?0z), and the coupling coefficient can be derivedfrom the first-order Fourier component: ? = pi?n1/(2?B). For example, the cou-pling coefficient of a triangular grating is reduced by a factor of 2/pi compared tothe square case (Eq. 1.6):? =4?npi?B(1.8)The solutions of the coupled-mode equations are given in [67] with details.The reflection coefficient for a uniform grating with a length of L can be describedby:r =? i? sinh(?L)? cosh(?L)+ i?? sinh(?L) (1.9)10with?2 = ?2??? 2 (1.10)Here, ?? is the propagation constant deviation from the Bragg wavelength:?? = ? ??0 =2pine f f (? )? ?2pine f f (?B)?B??2ping? 2B?? (1.11)with ?? << ?0. In this expression, the wavelength dependence of the effectiveindex is considered, hence the group index ng appears:ng = ne f f ??dne f fd? (1.12)For the case where ?? = 0, Eq. 1.9 is written as r =?i tanh(?L), therefore, thepeak power reflectivity at the Bragg wavelength is:Rpeak = tanh2(?L) (1.13)and the reflection has a pi/2 phase at the Bragg wavelength.The bandwidth is another critical figure of merit for Bragg gratings. There areseveral definitions of bandwidth, however, the most easily identifiable one is thebandwidth between the first nulls around the main reflection peak. Using Eq. 1.9and Eq. 1.10, we can easily obtain the condition for zero reflectivity:? ?2 = ?? 2??2 =(MpiL)2, M = 1,2,3... (1.14)Next, we will explain this in a relatively intuitive manner. Using the coupled-modeequations (Eq. 1.4 and Eq. 1.5), we can also write the forward propagation waveas:d2Sdz2+(?? 2??2)S = 0 (1.15)When ?? is smaller than ? , i.e., the wavelength is very close to the Bragg wave-length, we can see that S resembles a wave with exponentially decaying amplitude.This is easy to understand because the light is strongly reflected. As the wavelength11gets closer to the Bragg wavelength (i.e., ?? becomes smaller), the decay will befaster because the reflection becomes stronger (i.e., the interference is more con-structive). This also means that the penetration depth becomes shorter for smaller?? . When ?? is larger than ? , i.e., the wavelength is outside of the main reflectionband, S resembles a wave with a propagation constant of??? 2??2. In this case,the boundaries of the grating will act like abrupt interfaces, thus forming a FP-likecavity. The nulls in the reflection spectrum are analogous to the FP resonances(L??? 2??2 = Mpi). At these wavelengths, light is transmitted through the cav-ity, thus resulting in zero reflectivity. Using M = 1, the bandwidth between the firstnulls around the main reflection peak can be determined by [67]:?? =? 2Bping??2 +(pi/L)2 (1.16)From Eq. 1.16, we can see that the bandwidth is determined by both ? and L. How-ever, for sufficient long gratings (piL ?), the bandwidth is primarily determinedby ? (i.e., the grating index contrast). Note that this bandwidth is larger than the 3-dB bandwidth, which is also often used for the characterization of Bragg gratings.It should also be noted that, for the sake of simplicity, the analysis above assumesthat the grating is lossless. However, losses can be accounted for by replacing ??by ?? ? j?0 in Eq. 1.10, where ?0 is the loss coefficient for the field (the losscoefficient for the intensity is 2?0).1.3 Silicon Photonic Bragg GratingsRecent advances in silicon photonics have led to the integration of Bragg gratingson the SOI platform, with the first demonstration in 2001 by Murphy et al. [68].Generally, an integrated Bragg grating is formed in a waveguide with physicalcorrugations that lead to the modulation of the effective refractive index in thewaveguide. This is in contrast to the manufacture of fiber Bragg gratings (FBG),where the fiber is photosensitive and exposed to intense ultraviolet (UV) light sothat the material refractive index is modulated in the fiber core. Other than usingphysical corrugations, there are a few other approaches to make gratings in silicon,such as amorphous silicon gratings [69], ion implanted Bragg gratings [70, 71],12carrier-induced gratings with a p-i-n junction [72]; however, these approaches aremuch less common and are beyond the scope of this discussion.1.3.1 ObjectivesIntegrated Bragg gratings will be an essential building block for silicon photonics.Although the research in this area has been making steady progress in recent years,much more effort is still needed to improve the grating performance, especiallywhen using CMOS fabrication techniques. Furthermore, there are many potentialdevices and applications to be explored.First, the demonstration of integrated Bragg gratings has been mostly based onSOI rib waveguides with large cross sections [68, 73?75]. However, the currenttrend in silicon photonic circuits requires smaller devices for improved cost effi-ciency. Therefore, we will focus on the integration of Bragg gratings in siliconwaveguides with small cross sections, particularly at the submicron level.As mentioned earlier, strip waveguides are usually submicron. A small pertur-bation on the sidewalls can cause a considerable grating coupling coefficient, thusresulting in a large bandwidth. The bandwidths reported by others are generallyon the orders of a few tens of nanometers [76, 77]. Tan et al. have demonstratedsmaller bandwidths on the orders of a few nanometers, but the grating structuresare more complicated, such as using weakly coupled pillars outside of the waveg-uide [78], or using two coupled waveguides [79, 80]. For many applications suchas WDM, even narrower bandwidths (e.g., <100 GHz or 0.8 nm) are required.Simard et al. have demonstrated strip waveguide gratings with 3-dB bandwidthssmaller than 50 GHz, however, it was achieved at the expense of using a multi-mode waveguide (1200 nm wide) and a third-order grating [81]. Therefore, oneof our objectives is to design narrow-band first-order gratings without sacrificingsingle-mode operation.Often, uniform gratings exhibit large side-lobes in their reflection spectra, asshown in Fig. 1.3. It is well known that apodization can help with side-lobe sup-pression ( ?apodization? refers to gradually increasing and then decreasing the grat-ing coupling coefficient along the waveguide), which makes the gratings nonuni-form. Actually, most gratings in practical applications are nonuniform [82]. There-13fore, we will investigate various nonuniform grating structures and study their ap-plications.1 cm!Figure 1.4: A typical silicon photonic chip and a Canadian dime.In terms of fabrication, electron beam (e-beam) lithography was typically usedfor the fabrication of SOI Bragg gratings. Although e-beam lithography can makevery small features, it is unsuitable for commercial applications [31]. In this thesis,we will explore the possibilities of using CMOS-compatible processes, particularlyusing MPW services. Unless stated otherwise, all devices in this thesis were fabri-cated at IMEC, Belgium, using their relatively mature silicon photonic technologywith 193 nm deep UV lithography [8]. Figure 1.4 shows one of our silicon photonicchips fabricated at IMEC, compared with a Canadian dime (the smallest Canadiancoin in size). This chip has thousands of devices designed by more than 20 studentsfrom across Canada. The dimension of the chip is 12.73 mm?12.95 mm, whereasthe diameter of the dime is 18.03 mm [83].14Another major objective of this thesis is to provide insight into practical issuesand challenges involved with the design, fabrication, and characterization.1.3.2 Thesis OrganizationThis reminder of this thesis is organized into three main chapters, each focusing ona specific waveguide geometry, and a concluding chapter.In Chapter 2, we focus on strip waveguide Bragg gratings. We will start withthe fundamentals: mode profile and simple uniform gratings. Technical detailsabout the design, layout, and measurement are also given in this chapter. We alsopresent a number of design variations. The lithographic effects and a predictionmodel are then discussed. The thermal sensitivity and the wafer-scale nonunifor-mity are also investigated. Finally, we will discuss phase-shifted gratings in stripwaveguides and their various applications.In Chapter 3, we focus on rib waveguide Bragg gratings. Again, we will startwith the fundamentals: mode profile and simple uniform gratings. We will thenpresent apodized gratings to reduce the side-lobes. We also demonstrate two ad-vanced grating structures: multi-period gratings and spiral gratings. Finally, wewill present the thermal sensitivity and the wafer-scale nonuniformity.In Chapter 4, we focus on slot waveguide Bragg gratings. We demonstrate thedesign, fabrication, and characterization of both uniform and phase-shifted grat-ings. We investigate a number of design variations for both types of device. Wealso show a novel silicon photonic biosensor using a slot waveguide phase-shiftedgrating.Finally, the main conclusions and the future work are described in Chapter 5.15Chapter 2Strip Waveguide Bragg GratingsIn this chapter, we will discuss the simplest type of integrated Bragg grating: astrip waveguide Bragg grating. It is simple because the grating and the waveguidecan be defined in a single lithography step. We will briefly discuss the funda-mentals of strip waveguides, and then describe how a uniform grating is designed,fabricated, and characterized. We will explore many design variations, such as thecorrugation width and the grating period. An important issue with the CMOS fab-rication process is that the fabricated corrugations are always rounded due to thelithographic effects; therefore, we propose a prediction model to take into accountthe lithographic distortions in the design-fabrication-test flow. We also present thethermal sensitivity and the wafer-scale nonuniformity of strip waveguide gratings,which are very important for practical applications. We will also discuss phase-shifted gratings and give a few examples of applications. Finally, we experimen-tally demonstrate sampled gratings and the Vernier effect.2.1 Strip WaveguideThe strip waveguide is one of the most common types of silicon photonic waveg-uides, as illustrated in Figure 2.1. It is basically a thin strip of silicon on top of theburied oxide layer. The buried oxide layer needs to be thick enough to isolate thewaveguide from the bottom silicon substrate. Specifically, in Figure 2.1, the thick-ness of the top silicon layer is only 220 nm, while the buried oxide layer is 2 ?m16W!220 nm!Si!SiO2! 2 ?m!Si substrate! 750 ?m!Figure 2.1: Schematic of a strip waveguide cross section (not to scale).thick. Note that this is a popular SOI wafer currently used for silicon photonics,particularly in CMOS foundries, and we will use it throughout the thesis. In gen-eral, there are two options for the top cladding material: air and SiO2. However,it can be other low index materials. For example, in biosensing applications, thewaveguide is usually immersed in water, which has a refractive index between airand SiO2 (n? 1.33).The strip width (W ) is the only dimension to be designed. In general, a single-mode waveguide is preferred for Bragg grating designs. In this thesis, we use acommercial tool, Lumerical MODE Solutions, for all the mode calculations [84].Figure 2.2 shows the simulated mode profiles for 500 nm strip waveguides: (a)and (b) are with air cladding, (c) and (d) are with oxide cladding. In a rectangularwaveguide, there are two families of modes, the transverse electric (TE) modesand the transverse magnetic (TM) modes. TE means the electric field is parallel tothe substrate, while TM means the electric field is perpendicular to the substrate.In a more precise manner, the modes in Figure 2.2 are TE-like (or quasi-TE ) andTM-like (or quasi-TM) modes, depending on whether they are mostly polarizedin the x or y direction. The main field components of the TE-like modes are Exand Hy, while those of the TM-like modes are Ey and Hx. For simplicity, however,we will use ?TE? and ?TM? hereafter. Due to the high index contrast between thesilicon and the cladding material, the fundamental TE modes are strongly confined17x (?m)y (?m)W=500 nm, Air Cladding, TE  ?0.5 0 0.5?0.200.20.400.20.40.60.81x (?m)y (?m)W=500 nm, Air Cladding, TM  ?0.5 0 0.5?0.200.20.400.20.40.60.81x (?m)y (?m)W=500 nm, Oxide Cladding, TM  ?0.5 0 0.5?0.200.20.400.20.40.60.81x (?m)y (?m)W=500 nm, Oxide Cladding, TE  ?0.5 0 0.5?0.200.20.400.20.40.60.81(a)! (b)!(c)! (d)!Figure 2.2: Simulated electric field of the fundamental modes in 500 nm stripwaveguides: (a) TE mode with air cladding, (b) TM mode with air cladding,(c) TE mode with oxide cladding, and (d) TM mode with oxide cladding.in the silicon core, as shown in Figure 2.2(a) and (c). The TM modes, however,have relatively low intensities inside the silicon but much higher intensities outsideof the top and bottom interfaces. We also see that, in Figure 2.2(b), the intensitydistribution above and below silicon is asymmetric, due to the fact that the buriedoxide has a higher refractive index than the top air cladding. When the cladding isoxide, the mode profile becomes symmetric, as shown in Figure 2.2(d).For air cladding, to obtain a single TE mode operation at 1550 nm, the waveg-uide width is usually larger than 300 nm to support a fundamental mode but smallerthan 600 nm to avoid higher-order modes [85]. Again, note that in this regime, thewaveguide supports one TE-like mode, as well as one TM-like mode. In this thesis,however, we only focus on TE mode operation. For oxide cladding, the maximumwaveguide width to suppress the second TE mode is about 450 nm, smaller thanthat for air cladding.The propagation loss of a silicon waveguide is mainly the scattering loss dueto the waveguide roughness. The roughness of the sidewalls arises from the lithog-18raphy and etching process, and generally, is higher than the roughness of the topand bottom interfaces. From Figure 2.2(a) and (c), we also see that the TE modeshave considerable evanescent field around the sidewalls. Therefore, the propaga-tion loss of TE modes is dominated by the sidewall roughness. At 1550 nm, typicalpropagation losses of strip waveguides are in the 2?3 dB/cm range [8, 9]. Thermaloxidation is a technique to smooth the sidewalls and thus reduce the waveguideloss, but it could be detrimental to sidewall gratings.Figure 2.3 shows the scanning electron beam (SEM) image of a fabricated stripwaveguide. It can be seen that the cross section is not perfectly rectangular andFigure 2.3: SEM image of a 500 nm strip waveguide. The waveguide wasmilled using a focused ion beam (FIB) to expose the cross section.that the sidewalls have a small angle (typically 10o). Such geometric imperfectionswill slightly affect the mode profile and the effective index of the waveguide, andconsequently, affect the Bragg gratings on the waveguide.19A main advantage of strip waveguide is that it enables very tight and low-lossbends. There are several loss mechanisms in bends, but the major one is the mode-mismatch loss in strip waveguides [86]. The bending loss depends on the bendingradius, increasing sharply for smaller bends. For a 450?220 nm strip waveguidefabricated at IMEC, the bending loss is 0.071 dB, 0.02 dB, and 0.009 dB per 90obend for a bending radius of 1 ?m, 3 ?m, and 5 ?m respectively [32]. In this thesis,we will use bends larger than 3 ?m so that the bending losses are negligible.2.2 Uniform GratingsIn this section, we will present the design of uniform Bragg gratings in strip waveg-uides. We will discuss several design variations. Many details about the layout andmeasurement are also given.2.2.1 DesignFigure 2.4 shows the schematic of a uniform grating in a strip waveguide usingrectangular sidewall corrugations. The corrugation on each sidewall has a widthof ?W and comprises recessed and protruding portions (??W /2). We chose thisconfiguration rather than the recessed-only or protruding-only configuration, be-cause for varying corrugation widths, the average effective index is approximatelyconstant so that the Bragg wavelength will not shift dramatically.?W!W!?!N x ?!Figure 2.4: Schematic of a uniform strip waveguide grating.Figure 2.5 shows a typical design flow for a uniform Bragg grating. Usually, westart the design by first choosing a waveguide width. As discussed in Section 2.1,we prefer a single-TE mode waveguide, and this requires a submicron waveguidewidth (i.e., <600 nm with air cladding, and <450 nm with oxide cladding). How-20W!neff!?W ? = 2neff??!? ?? = ?2?ng ? 2 + ?L"#$ %&'2?? R = tanh2(?L)L Lithography Figure 2.5: Typical design flow for a uniform Bragg grating: 1) choose acertain waveguide cross section, 2) calculate the mode profile and effectiverefractive index, then calculate the grating period based on the Bragg condi-tion, 3) calculate the coupling coefficient for a particular bandwidth (assumingthe grating is sufficiently long and a high reflectivity is needed), 4) calculatethe corrugation width with the assistance of mode simulation and lithographysimulation, 5) calculate the grating length.x (?m)y (?m)W=500 nm, Oxide Cladding, 2nd TE  ?0.5 0 0.5?0.200.20.400.20.40.60.81Figure 2.6: Simulated electric field of the second TE mode in a 500 nm stripwaveguide with oxide cladding. The majority of the electric field is on thesidewalls, resulting in a much lower effective index and a much higher prop-agation loss than the fundamental TE mode.21ever, this criterion can be relaxed a bit. For example, in the case of a 500 nmwaveguide with oxide cladding, the confinement of the second TE mode is veryweak, as shown Figure 2.6. The majority of the electric field is on the sidewalls,thus resulting in a much lower effective index (1.49) than the fundamental TEmode (2.45), as well as a much higher propagation loss. Therefore, in practice, thissecond TE mode can be neglected in a Bragg grating design.Once the waveguide width is determined, the effective index of the fundamen-tal TE mode is known from the mode calculation, then the grating period can becalculated using the Bragg condition (i.e., Eq. 1.1). The next parameter to be con-sidered is the corrugation width, which determines the coupling coefficient and thestop bandwidth. Note that the lithography effect should also be taken into account,as will be discussed later. The last parameter to be considered is the grating length,or the number of grating periods (N), which determines the peak reflectivity.2.2.2 LayoutWhen the design parameters are ready, the next step is to create the mask layout,generally in a file format called GDSII, which is the de facto industry standard forIC fabrication. To generate a GDSII file, there are many commercial electronicdesign automation (EDA) software and free GDSII utilities. Here we list a fewtools that are used in the work of this thesis:? KLayout: an excellent and free GDS viewer that also provides basic editingcapabilities [87].? dw-2000: an integrated environment that includes a full-featured layout ed-itor and a comprehensive design rule checker (DRC). It also allows for theuse of a technology package (e.g., CMC-IMEC SOI Technology Package)[88].? Mentor Graphics Pyxis Layout: a full-custom IC design platform that sup-ports an extensive set of functions, especially the AMPLE scripting lan-guage, process design kit (PDK), automatic routing (IRoute), schematic drivenlayout (SDL), and integration with other Mentor Graphics tools such as Cal-ibre nmDRC and Calibre nmLVS [89].22In a GDSII layout, a careful design hierarchy is very important. Typically, thefull chip consists of many building block cells replicated and placed in higher levelcells. The proper use of cells can greatly minimize the data volume and reducethe time of generating, reading, and editing. This is particularly true for the designof Bragg gratings. For example, to generate a uniform grating, the most efficientapproach is to make one grating period as a cell, and then make an array of thiscell as a higher-level cell. All the three tools mentioned above support hierarchicaloperations, but Pyxis Layout is most powerful.In practice, there are many design constraints, depending on the fabricationprocess. The first requirement is that the vertices of all objects must also conformto a discrete grid (e.g., 1 nm or 5 nm). For a Bragg grating design, this requiresthat the grating period is an integer number of grid points. Ideally, the final layoutshould not violate any design rules before submitted to the foundry, such as theminimum feature sizes (e.g., width, spacing, enclosure) and density rules. This issometimes a huge obstacle to the design of Bragg gratings. For example, all thesidewall corrugations could be detected as violations to the minimum feature sizerule. Yet, it is often possible to waive such DRC errors, as they have little impacton the process yield. However, the density rules are always mandatory becausethey may affect the yield of other customers on the chip. In order to meet the targetdensity rules, most modern processes need addition of dummy tiles to the layout toensure the density is consistent (for various reasons such as planarization).Figure 2.7 shows the schematic of two layout configurations. Each configura-tion consists of one input port and two output ports (transmission and reflection).Each port is an integrated waveguide-to-fiber grating coupler (GC) designed for TEpolarization [42, 43, 90]. We use a Y-branch splitter to collect the reflected light.The first configuration uses two individual fibers, one for input, and the other fortransmission or reflection, while the second configuration uses a fiber array (PLCConnections PM fiber array with 127 ?m pitch, 4 or 8 channels). Although the firstconfiguration may provide more flexibility to the layout, the second configurationhas more advantages. First, it allows for the simultaneous measurement of bothtransmission and reflection. Second, it is easier and faster to perform automaticalignment. Third, the coupling efficiency is more stable.23Input!Transmission!Reflection!Y-Branch! Grating!Input! Transmission!Reflection!Y-Branch!(a)!(b)! Grating!Figure 2.7: Schematic diagram of the device layout (not to scale): (a) indi-vidual fiber configuration, (b) fiber array configuration.Figure 2.8 shows an approach to design a space-efficient layout using the fiberarray configuration. On the right side are Bragg grating devices with many designvariations. The routing waveguides run between the GCs, with a 4 ?m center-to-center waveguide spacing, which is sufficient to avoid cross-talk between adjacentwaveguides. Note that this routing block is generated using scripts in Pyxis Layoutand can be re-used for similar designs.2.2.3 FabricationFigure 2.9 shows the top view SEM image of a fabricated strip waveguide grating.Again, the device was fabricated at IMEC using 193 nm DUV lithography (ASMLPAS5500/1100 ArF scanner) and inductively coupled plasma (ICP) reactive-ionetching (RIE) dry etching. Clearly, we can see that the gratings actually fabricatedare severely rounded, resembling sinusoidal shapes. This is due to the smoothingeffect of the lithography and will reduce the grating coupling coefficient. We willfurther discuss this effect in Section 2.3.24127 ?m"254 ?m"Figure 2.8: An approach to increase the device packing efficiency using thefiber array configuration. The grating devices are located in the bundle on theright side, and the routing waveguides run between the grating couplers.Figure 2.10 and Figure 2.11 show the SEM images of a Y-branch and a GC,respectively. The small square boxes in Figure 2.11 were the result of tiling, whichare necessary to meet the density rules as mentioned above. Figure 2.12 shows amicroscope image of a compact layout example using the approach in Figure 2.8.2.2.4 MeasurementThe measurement setup typically consists of a tunable laser source, optical powersensors, fibers, and stages. Depending on the layout configuration, the fibers canbe either two individual fibers, or a multi-channel fiber array. Figure 2.13 shows asetup using individual fibers, each of which is motor-controlled; and the softwarerecords the received power in real time [91, 92].We also have an advanced setup using a multi-channel fiber array. Figure 2.14shows the block diagram of the overall setup. The chip is placed on an automatedmicro-positioning stage while the fiber array is fixed during the measurement. The25Figure 2.9: Top view SEM image of a fabricated strip waveguide grating withdesign parameters: W = 500 nm, ?W = 80 nm. Note that the rectangularcorrugations we used in the design were rounded due to the lithography.Figure 2.10: Tilted view SEM image of a fabricated Y-branch as illustratedin Figure 2.7(a).26Figure 2.11: Top view SEM image of a fabricated grating coupler (GC). Thelayout of the GC was illustrated in Figure 2.8, and the square tiles were addedaround the GC to meet the density rule.Figure 2.12: Part of a fabricated chip showing the compact routing approachillustrated in Figure 2.8.27Figure 2.13: A measurement setup using two individual fibers.measurement is fully automated, i.e., the software loads a file that contains thecoordinates of all the GCs, automatically moves the stage to align a particular setof GCs with the fiber array, performs the wavelength sweep, records the data, andproceeds with the next device. The alignment usually takes less than a minute.The time to complete the wavelength sweeping depends on the wavelength range,resolution, sweeping speed of the tunable laser, number of scans, etc. In this thesis,we used a high-end tunable laser (Agilent 81600B opt. 201) that has a wide tuningrange (1460 nm ? 1640 nm), high wavelength accuracy, and high sweep speeds.For the simultaneous measurement of transmission and reflection, we used a dual-channel optical power sensor (Agilent 81635A). For a full-range sweep using a0.01 nm resolution, the average measurement time (including the alignment) wasabout 2.5 minutes per device. With recent software and hardware updates, thissetup can now work at about 0.6 minute per device [93]. The minimum resolutionof the spectral measurements is 0.1 pm. As shown in Figure 2.15, the setup alsohas an RF probe that is used for the electrical testing of active devices such asmodulators and detectors. A full view of the actual setup is shown in Figure 2.16.The RF probe is connected to the network analyzer (Agilent PNA E8361A)to perform high-speed measurement of S-parameters. As shown in Figure 2.15,28Stage!TEC!SOI Chip!laser sources!detectors!Agilent Lightwave!Measurement System!?!EDFA!Optical Filter!Vector Network Analyzer! Source Measure Unit!TEC Controller!Motion Controller!Microscope!Camera!Fiber Array!GCs!Pads!Bragg grating!PD!+"RF! DC!Bias Tee!Probe!GND!R!T!Figure 2.14: Block diagram of the advanced experimental setup. PD: pho-todetector, EDFA: erbium-doped fiber amplifier, TEC: thermoelectric cooler.the copper plate under the chip can be thermally controlled; the red and black ca-bles are connected to the temperature controller (SRS LDC501, see part 3 in Fig-ure 2.16). Most of the measurement, however, was performed at room temperature,unless stated otherwise. A camera is affixed to the microscope, and Figure 2.17shows a captured image during measurement. The multiple channels are clearlyseen in the fiber array and are well aligned with the GCs on the chip.We should point out that the tunable laser (Agilent 81600B) has two outputs:one with a high output power and the other with a low source spontaneous emission293!1!6!4!1.? Fiber array!2.? RF probe!3.? SOI chip!4.? TEC!5.? Rotation stage!6.? RF connectors !5!2!Figure 2.15: An advanced measurement setup using a fiber array.301!2! 3!9!7!4!6!5!10!12!13!8!11!1.? Fiber array !2.? Micro probe holder !3.? TEC controller!4.? Photodiode!5.? Microscope!6.? Bias Tee!7.? Vector network analyzer!8.? Source measure unit!9.? Camera!10.?Agilent lightwave measurement system!11.? Stage motion controller!12.?EDFA!13.?Optical filter!Figure 2.16: Full view of the advanced measurement setup.31Fibers!GCs!Figure 2.17: Captured image during experiment. The chip uses a layout sim-ilar to Figure 2.8, and the grating couplers are aligned with the fibers in thearray.(SSE). Bragg grating devices generally exhibit high extinction ratios. Therefore, itis necessary to choose the low SSE output of the tunable laser, which offers a highsignal-to-SSE ratio and the large dynamic range needed to completely characterizethe devices [94]. Figure 2.18(a) shows the measured transmission, using the lowSSE option, of a straight waveguide without gratings, and a grating device withthe following design parameters: W = 500 nm, ?W = 80 nm, ? = 325 nm, andN = 3000. Note that overall envelope arises from the intrinsic response of thegrating couplers [90]. When using the high power option, the stop band of thegrating is cut off at around -51 dB, as shown in Figure 2.18(b). It is also surprisingthat the power slightly decreases versus the wavelength within the stop band, whichis contrary to the response of the straight waveguide. Figure 2.18(c) also shows thatfor the same straight waveguide, the spectra using the two options are substantiallydifferent at the short wavelength range. This is because the laser power was set at0 dBm but the maximum power of the low SSE output is actually less than 0 dBm321460 1480 1500 1520 1540 1560 1580?90?80?70?60?50?40?30?20Wavelength (nm)Power (dBm)Low SSE  Straight WGGratings1460 1480 1500 1520 1540 1560 1580?90?80?70?60?50?40?30?20Wavelength (nm)Power (dBm)High Power  Straight WGGratings1460 1480 1500 1520 1540 1560 1580?60?50?40?30?20Wavelength (nm)Power (dBm)Straight WG  Low SSEHigh Power1460 1480 1500 1520 1540 1560 1580?60?40?20020Wavelength (nm)Normalized Response (dB)Gratings  High PowerLow SSE(d)!(b)!(c)!(a)!Figure 2.18: Measured transmission spectra of a straight waveguide (WG)and a Bragg grating using: (a) the low SSE option, and (b) the high poweroption. Comparison between the low SSE option and the high power optionfor: (c) the spectra of the straight waveguide, and (d) the normalized responseof the grating by subtracting the spectra of the straight waveguide . Note thatthe laser output power was set to be 0 dBm (i.e., 1 mW).at the short wavelength range, as shown in Table 2.1. The intrinsic response of thegrating device is obtained by subtracting the response of the straight waveguidefrom the measured raw response of the grating, as shown in Figure 2.18(d). Wecan see that the extinction ratio is limited to only 20 dB by the high power option,whereas the low SSE option shows an extinction ratio of about 40 dB and manysmall details become uncovered.Tunable lasers equipped with low SSE outputs are usually expensive. In casethey are not available, changing the sweeping settings can help optimize the dy-33Output%1%(low%SSE)% Output%2%(high%power)%?%+3%dBm%peak%(typical)% ?%+9%dBm%peak%(typical)%?%+2%dBm%peak%(1520%nm%to%1610%nm)% ?%+8%dBm%peak%(1520%nm%to%1610%nm)%?%?2%dBm%peak%(1475%nm%to%1625%nm)% ?%+4%dBm%peak%(1475%nm%to%1625%nm)%?%?7%dBm%peak%(1455%nm%to%1640%nm)% ?%?1%dBm%peak%(1455%nm%to%1640%nm)%Table 2.1: Maximum output power (continuous power during sweep) of Ag-ilent 81600B Option 201 [1].namic range of the measurement. Figure 2.19 shows the measured spectra usingthe high power option of the tunable laser under 4 different sweeping conditions.First, the laser output power was set at 0 dBm. We performed the wavelength sweepusing two methods: (1) a full-range continuous sweep and (2) a segmented sweepthat consists of 10 segments. We can see that there is little difference between thesetwo measurements. Then we set the laser output power at 10 dBm and re-run thewavelength sweep using the two methods. We observe that the measured power isindeed higher but not as much as 10 dB. This is due to the fact that the maximumoutput power of the laser is actually 9 dBm and is wavelength dependent, as shownin Table 2.1. For the segmented sweep, we can see that the power is increased by9 dB around 1550 nm but less than 4 dB at 1470 nm, which agrees with the laserspecifications in Table 2.1. For the continuous sweep, the spectrum discontinuitydisappears but at the expense of reduced power, because the laser power is almostkept constant at the starting point of the sweep. Finally, the stop band is alwayscut off at around -51 dB, confirming that the dynamic range is limited by the lasernoise. In short, if the integrity of the broad band response is important (e.g., theoverall response of the grating coupler), users should choose an output power thatcan be reached all over the sweep range (in the above case, the setting is 0 dBm).However, if the narrow band dynamic range is more critical (e.g., to reveal thefeatures at the bottom of the stop band of the gratings), one could use the highestoutput power (in the above case, the setting is 10 dBm).341470 1480 1490 1500 1510 1520 1530 1540 1550 1560 1570 1580?55?50?45?40?35?30?25?20?15?10Wavelength (nm)Power (dBm)Tunable Laser: High Power Option1523 1524 1525 1526 1527 1528?50?40?30?209 dBLaser Setting: 0 dBmLaser Setting: 10 dBm(no segmentation)Laser Setting: 10 dBm(10 segments)Figure 2.19: Measured transmission spectra of a Bragg grating using the highpower option under various sweeping conditions. Inset shows the zoom-inview around the Bragg wavelength. The small ripples out of the stop band aredue to the FP effects in the measurement system.2.2.5 Design VariationsIn this section, we discuss a number of variations that are fundamental to a uniformgrating design.2.2.5.1 Grating PeriodBased on the Bragg condition (i.e., Eq. 1.1), we expect that the Bragg wavelengthwould increase with increasing grating period. This was observed experimentally.Figure 2.20 shows the measured transmission spectra for three gratings with differ-ent periods: 320 nm, 325 nm, and 330 nm. The increment in the Bragg wavelengthis about 12.6 nm. Note that there is a common, but inaccurate, formula to calculatethe wavelength shift: ?? = (??/?)? , which gives a ?? of larger than 23 nm in351460 1480 1500 1520 1540 1560 1580?35?30?25?20?15?10?505Wavelength (nm)Response (dB)  ? = 325 nm? = 330 nm? = 320 nmFigure 2.20: Measured transmission spectra for gratings with different grat-ing periods, showing the red shift with increasing grating period. Fixed pa-rameters: air cladding, W = 500 nm, ?W = 20 nm, N =1000.this case. However, this formula misses the fact that ne f f is wavelength dependent,and therefore, the group index should be taken into account somehow. Here is amore accurate approximation:d?d?=???ne f fng=? 22?2ng(2.1)which essentially adds another factor of ne f f /ng so that the dispersion effect istaken into account. For a regular strip waveguide, ne f f is usually smaller than ng(for this particular waveguide: ng = 4.36). Based on Eq. 1.12, this indicates thatne f f decreases as wavelength increases. Figure 2.21 shows the measured Braggwavelength as a function of the grating period. The linear curve fitting shows thatd?/d? is 2.53, which closely matches with the calculated value of 2.515 usingEq. 2.1.36320 322 324 326 328 3301510151515201525153015351540Period (nm)Bragg Wavelength (nm)y = 2.53x + 700.45Figure 2.21: Bragg wavelength extracted from Figure 2.20 versus gratingperiod. The slope of the linear curve fit is 2.53, which is in good agreementwith the calculation using Eq. 2.1.2.2.5.2 Corrugation WidthThe corrugation width determines the coupling coefficient (?) and thus the band-width of a grating. Figure 2.22 shows the measured transmission spectra for var-ious corrugation sizes from 10 nm to 160 nm on a 500 nm waveguide with aircladding. The bandwidth is plotted versus the corrugation width in Figure 2.23,showing an approximately linear relationship with a slope of about 0.18.2.2.5.3 Waveguide WidthThe coupling coefficient (?) depends not only on the corrugation width but alsoon the waveguide width. Figure 2.24 shows the measured transmission spectra oftwo devices that have the same corrugation width but different waveguide width,one is 500 nm and the other is 450 nm. We can see that the bandwidth is larger onthe narrower waveguide, because the interaction between the sidewall corrugationand the optical mode becomes stronger. As can be seen in Figure 2.25, the fieldintensity around the sidewall of the 450 nm waveguide is stronger than that of the371480 1500 1520 1540 1560?60?50?40?30?20?10010Wavelength (nm)Response (dB)  ?W=10 nm ?W=40 nm?W=80 nm?W=160 nmFigure 2.22: Measured transmission spectra for various corrugation widths,showing the bandwidth increases with increasing corrugation width. Fixedparameters: air cladding, W = 500 nm, ?= 325 nm, and N =3000.0 50 100 150 200051015202530Corrugation Width (nm)Bandwidth (nm)y = 0.18418x + 0.20254Figure 2.23: Measured bandwidth versus corrugation widths on 500 nm stripwaveguide with air cladding. The data points for 10 nm, 40 nm, 80 nm, and160 nm corrugations correspond to the spectra in Figure 2.22. The linear fitshows that the coupling coefficient (i.e., grating index contrast) is approxi-mately proportional to the corrugation width.381510 1515 1520 1525 1530?35?30?25?20?15?10?505Wavelength (nm)Response (dB)  W=500 nmW=450 nmFigure 2.24: Measured transmission spectra for gratings with 20 nm corruga-tion on a 500 nm waveguide and on a 450 nm waveguide. Fixed parameters:air cladding, ?W = 20 nm and N =1000. The period for the 500 nm waveg-uide and the 450 nm waveguide is 325 nm and 340 nm, respectively.500 nm waveguide.Figure 2.26 plots the bandwidth versus the corrugation width for gratings onthe two waveguides. Again, we see that the bandwidths are larger on the 450 nmwaveguide. Also, the linear relationship remains for the 450 nm waveguide, with alarger slope of about 0.25.2.2.5.4 CladdingAll results in the previous three sections are for devices with air cladding. In thissection, we will present more results of devices with oxide cladding. Figure 2.27shows the spectra for two devices that have exactly the same parameters except forthe cladding. We see that the device with oxide cladding has a longer Bragg wave-length due to the increased effective index; meanwhile, its bandwidth is smallerbecause the index contrast is reduced.Figure 2.28 shows the measured bandwidth as a function of the corrugationwidth for oxide-cladding devices, compared with air-cladding devices. The slopefor oxide cladding is about 0.12, which is 1.5 times smaller than that for air cladding.39x (?m)y (?m)W=500 nm, Air Cladding, TE  ?0.5 0 0.5?0.200.20.400.20.40.60.81x (?m)y (?m)W=450 nm, Air Cladding, TE  ?0.5 0 0.5?0.200.20.400.20.40.60.81Figure 2.25: Simulated electric field of the fundamental TE mode in a 500 nm(top) and a 450 nm (bottom) strip waveguide, both with air cladding. The fieldintensity around the sidewall of the 450 nm waveguide is stronger than that ofthe 500 nm waveguide.10 15 20 25 30 35 40024681012Corrugation Width (nm)Bandwidth (nm)  y1 = 0.18132x + 0.13634y2 = 0.24722x + 0.30776W=500 nmW=450 nmFigure 2.26: Measured bandwidth as a function of corrugation width on500 nm (blue) and 450 nm (red) strip waveguides with air cladding. Thegratings on narrower waveguide show larger bandwidths and a larger slope inthe linear fit, due to increased modal overlap with the sidewalls.401480 1500 1520 1540 1560 1580?50?40?30?20?10010Wavelength (nm)Response (dB)  oxide claddingair claddingFigure 2.27: Measured transmission spectra for gratings with air cladding(blue) and with oxide cladding (green). For the oxide-clad device, the wave-length is longer due to the larger average effective index and the bandwidthis smaller due to the reduced index contrast. Fixed parameters: W=500 nm,?W=160 nm, ?=325 nm, N =3000.20 40 60 80 100 120 140 160051015202530Corrugation Width (nm)Bandwidth (nm) air cladding:slope = 0.18 oxide cladding:slope = 0.12   Figure 2.28: Measured bandwidth as a function of corrugation width on500 nm strip waveguide with air cladding (blue) and with oxide cladding(green). The gratings with oxide cladding show smaller bandwidths and asmaller slope in the linear fit, due to the reduced index contrast.412.2.5.5 LengthThe propagation loss is an important figure-of-merit for a grating waveguide. Itnot only leads to the insertion loss in the transmission but also limits the maximumreflectivity. As will be discussed in Section 2.6, the propagation loss is also criticalfor grating cavities. To extract the propagation loss using the cutback method, wedesigned gratings with various lengths. As shown in Figure 2.29, we do observe aslight decrease of power in the out-of-band transmission when the grating numberis increased from 3000 to 15000. However, the decrease is very small (comparableto the alignment error of the measurement) and the noise becomes more signifi-cant. Therefore, it is difficult to obtain an accurate propagation loss value fromthese data. At a rough estimate, the propagation loss is within the range of 2.5?4.5 dB/cm, comparable to that of a straight waveguide without gratings. We alsoobserve that the propagation loss is independent of the corrugation width (at leastfor the range that we used: 10 nm to 80 nm).1470 1475 1480 1485 1490 1495 1500?4?202 ?W=10 nm  N=3000N=9000N=150001470 1475 1480 1485 1490 1495 1500?4?202 ?W=20 nm  N=1000N=3000N=9000N=150001470 1475 1480 1485 1490 1495 1500?4?202 ?W=80 nm  N=3000N=9000N=15000Figure 2.29: Measured out-of-band transmission spectra for gratings withvarious corrugation widths and lengths. Fixed parameters: air cladding,W = 500 nm, ? = 325 nm. The propagation loss is within the range of 2.5?4.5 dB/cm and is independent of the corrugation width.42Theoretically, as the length is increased, the bandwidth should not increase, andactually, the bandwidth may decrease if the coupling is very weak, see Eq. 1.16.On the contrary, we experimentally observe that the stop band gets broader whenthe grating gets longer, as shown in Figure 2.30 and Figure 2.31 .1510 1512 1514 1516 1518 1520 1522 1524 1526 1528 1530?40?200Response (dB) ?W=20 nm  N=10001510 1512 1514 1516 1518 1520 1522 1524 1526 1528 1530?40?200Response (dB)  N=30001510 1512 1514 1516 1518 1520 1522 1524 1526 1528 1530?40?200Response (dB)  N=90001510 1512 1514 1516 1518 1520 1522 1524 1526 1528 1530?40?200Wavelength (nm)Response (dB)  N=15000Figure 2.30: Measured transmission spectra of gratings with 20 nm corru-gation width for various lengths, showing bandwidth broadening effect withincreasing N and wavelength variations due to fabrication variations. Fixedparameters: air cladding, W = 500 nm, ?= 325 nm.For example, as shown in Figure 2.30, when N is 1000, the transmission spec-trum is very clean and resembles an ideal grating response. When N is 3000, thestop band begins to have some irregular ripples while the bandwidth is approxi-mately the same. When N is 9000 and above, the noises become significant and thebandwidth becomes larger. This is primarily due to the top Si thickness variations(i.e., the strip thickness varies along the waveguide so that the effective index fluc-tuate). For simplicity, we consider Si only as the top Si layer later on. Also worthmentioning is that the Bragg wavelength is shifting, again due to the Si thicknessvariations. Note that for each N, the devices are packed together, whereas for dif-ferent N, the devices are placed far apart. Presumably, the Si thickness variation431510 1512 1514 1516 1518 1520 1522 1524 1526 1528 1530?40?200Response (dB)?W=10 nm  N=30001510 1512 1514 1516 1518 1520 1522 1524 1526 1528 1530?40?200Response (dB)  N=90001510 1512 1514 1516 1518 1520 1522 1524 1526 1528 1530?40?200Wavelength (nm)Response (dB)  N=15000(a)1500 1505 1510 1515 1520 1525 1530 1535 1540?40?200Response (dB)?W=80 nm  N=30001500 1505 1510 1515 1520 1525 1530 1535 1540?40?200Response (dB)  N=90001500 1505 1510 1515 1520 1525 1530 1535 1540?40?200Wavelength (nm)Response (dB)  N=15000(b)Figure 2.31: Measured transmission spectra of gratings with (a) 10 nm and(b) 80 nm corrugation width for various lengths, showing similar trends asFigure 2.30. Fixed parameters: air cladding, W = 500 nm, ?= 325 nm.44is small within a small area, therefore, the Bragg wavelength shifts in a similarmanner from N=3000 to N=15000 in Figure 2.30 and Figure 2.31. Keep in mindthat the Si thickness variation is random though, as will be further discussed inSection 3.5. The blue shift in Figure 2.30 and Figure 2.31 is just a special case.2.2.5.6 ShapeSo far, we have only discussed gratings that use rectangular corrugations. In addi-tion, we have also designed gratings with trapezoidal and triangular corrugations,as illustrated in Figure 2.32 [95]. As discussed in Section 1.2, the coupling coeffi-Trapezoidal!Rectangular!Triangular!W!?!?W!Figure 2.32: Schematic illustration of corrugation shapes (not to scale).cient can be obtained from the first-order Fourier component of the grating profile.Therefore, for the same corrugation width, we can obtain the following relation-ships:?Tra = ?Rec ?2?2pi (2.2)?Tri = ?Rec ?2pi (2.3)Figure 2.33 shows the measured bandwidth for the three shapes. The ratio be-tween the slopes of the three curves is 1:0.88:0.66, which agrees very well with theabove analysis. However, for the sake of simplicity, we will keep using rectangularcorrugations in the reminder of this thesis.4510 15 20 25 30 35 40 45 500123456Corrugation Width (nm)Bandwidth (nm)  y1 = 0.072x + 0.13y2 = 0.096x + 0.14y3 = 0.11x + 0.29RectangularTrapezoidalTriangularFigure 2.33: Measured bandwidth as a function of corrugation width for dif-ferent shapes. Fixed parameters: oxide cladding, W = 500 nm, ? =320 nm,N =2000. The bandwidth and the slope of the linear fit become smaller as theshape goes from rectangular to trapezoidal to triangular, due to the reducedFourier component and coupling coefficient.2.3 Lithography Effects 1Due to the high refractive index contrast, most silicon photonic devices are highlysensitive to dimensional variations and require high-resolution fabrication pro-cesses. As previously mentioned, electron-beam lithography has been used ex-tensively for fabrication in research, but it is unsuitable for commercial applica-tions. Alternatively, DUV lithography, especially at 193 nm [96], has been provento be capable of making high-quality photonic devices in silicon, and, more im-portantly, it is CMOS-compatible and can be used for high-volume production.However, with DUV lithography, it is difficult to optimize the illumination settings1A version of Section 2.3 has been published: X. Wang, W. Shi, M. Hochberg, K. Adams,E. Schelew, J. Young, N. Jaeger, and L. Chrowtowski, ?Lithography simulation for the fabrication ofsilicon photonic devices with deep-ultraviolet lithography,? in Group IV Photonics, San Diego, CA,August 2012, pp. 288-290.46for various types of patterns simultaneously, e.g., the settings that are optimized forisolated structures such as photonic wires are usually not ideal for dense structuressuch as photonic crystals [96]. Moreover, researchers are developing devices withfeature sizes that are even smaller than the resolution limit. In particular, integratedwaveguide Bragg gratings suffer from serious lithographic distortions. Therefore,it is important to include the effects of the fabrication process in the design flowso that they are properly accounted for [97]. Image distortions that happen duringfabrication of electronic circuits in CMOS advanced processes are routinely cor-rected, but such corrections may not be compatible with the significantly differentand more diverse structures that are encountered in silicon photonics circuits.In this section, we propose a model to predict the fabrication imperfections ofsilicon photonic devices during the lithography process. After lithography simula-tion, we simulate the spectral responses of the virtually fabricated grating devices,and we obtain good matching between the simulation and experimental results.First, we chose a device to calibrate the lithography model so that the post-lithography simulation fit the experimental data. Then, the model is fixed for allother devices. Here, the device used for calibration is a 500 nm strip waveguidegrating designed with 40 nm rectangular corrugations (named as device A). To im-plement the lithography simulation, we use a commercial tool that has been widelyused in the microelectronics industry ? Mentor Graphics Calibre [89]. For theoptical system, we use a conventional circular illumination source. The numericalaperture (NA) and the partial coherence factor (? ) are the key parameters that deter-mine the corrugation distortions; we use NA = 0.6 and ? = 0.6 in our simulations.Note that these parameters were not provided by the foundry, but were estimatedso that the post-lithography simulation fit the experimental data for device A andwere then fixed for all other devices. Also, these parameters are within the rangedefined by the stepper?s technical specifications. Figure 2.34 shows the simulationresults for device A. We can see that the corrugations are greatly smoothed, andtheir effective amplitudes are also reduced.After lithography simulation, we simulate the spectral responses of the vir-tually fabricated grating devices using a three-dimensional (3D) finite-differencetime-domain (FDTD) method [84], and then compare them with the original designas well as the measurement results of the devices actually fabricated. Figure 2.3547(a)!(b)!Figure 2.34: Lithography simulation for device A: (a) original design, (b)simulation result.shows the transmission spectra for device A. It can be seen that the original de-1500 1510 1520 1530 1540 1550?40?35?30?25?20?15?10?505Wavelength (nm)Transmission (dB)  OriginalDesignPost?Litho SimulationMeasurementFigure 2.35: Spectral comparison (transmission) for device A. Original de-sign: FDTD simulation using the structure in Figure 2.34(a), post-litho simu-lation: FDTD simulation using the structure in Figure 2.34(b).sign has a bandwidth of about 23 nm, in contrast, the post-litho simulation shows amuch narrower bandwidth of about 8 nm. Note that the thickness of the waveguide48was slightly reduced by a few nanometers in the simulation in order to match theBragg wavelength, which has little effect on the bandwidth. The amplitude mis-match between the measurement and post-litho simulation is partially due to thecalibration errors (e.g., the ripples in Figure 2.19).Figure 2.36 plots the simulated and measured bandwidths versus the designedcorrugation widths. Again, the post-litho simulation agrees very well with the mea-surement, whereas the mismatch between the original design and the measurementis very large. As a rule of thumb, the actual bandwidth is about 3x smaller than theoriginal design value.0 20 40 60 80 100 120 140 16005101520253035404550Corrugation Width (nm)Bandwidth (nm)Device A  Original DesignPost?Litho SimulationMeasurementFigure 2.36: Bandwidth versus corrugation width on 500 nm strip waveg-uides with air cladding. The post-litho simulation agrees well with the mea-surement result, while the original designs show bandwidths of about threetimes larger.This technique can be applied to many other silicon photonic devices, espe-cially ones that are sensitive to lithographic distortions. For example, Figure 2.37shows the simulation result for a photonic crystal cavity. We can see that the sim-ulated bulk holes are smaller than the designed ones, therefore, a bias should beapplied to the bulk holes in the mask to obtain the desired hole sizes. Due to the49optical proximity effect, the edge holes are smaller than the bulk holes [96], and thedisplacement of the two cavity side holes introduces extra distortions. Therefore,differential bias needs to be applied to the holes next to the cavity, and this cannotbe easily done without lithography simulations.original simulated + XOR 425 nm 155 nm 270 nm 258 nm 265 nm 105 nm 85 nm 165 nm 270 nm 425 nm H1? H2?Figure 2.37: Lithography simulation for a photonic crystal cavity with threemissing holes in the centre. XOR: Boolean operation of XOR (exclusive or)between the original and simulated layouts. The two cavity side holes (H1and H2) are displaced in order to achieve a high Q-factor.We believe that this work is an important step in the direction of design-for-manufacturing in the field of silicon photonics. Note that this work only considersthe optical model (the light incident on the photoresist) [98]. There are, of course,many other physical effects that need to be accounted for, e.g., the photoresistmodel, the etching process, and the Si thickness variations. Fortunately, the devel-opment of silicon photonic fabrication can benefit greatly from the vast library ofknowledge that already exists in the microelectronics industry, as well as the con-tinued advancements. Specifically, we believe that this model could be improvedby using test patterns in EDA tools such as Mentor Graphics Calibre [89].502.4 Thermal SensitivityMost silicon photonic devices are highly sensitive to temperature variations onthe chip, due to the large thermo-optic coefficient of silicon. In this section, westudy the thermal sensitivity of strip waveguide gratings. As previously shown inFigure 2.15 and Figure 2.16, the silicon chip can be thermally controlled using thetemperature controller.1526 1528 1530 1532 1534 1536?30?25?20?15?10?505Wavelength (nm)Transmission (dB)  20oC25oC30oC35oC40oC45oCTFigure 2.38: Measured transmission spectra of a strip waveguide grating atdifferent temperatures, showing the red shift with increasing temperature. Thedesign parameters are: air cladding, W = 500 nm, ?W = 20 nm, ?= 330 nm,and N =1000.Figure 2.38 shows the transmission spectra of a strip waveguide grating at dif-ferent temperatures. Clearly, the Bragg wavelength shifts to longer wavelengths asthe temperature is increased. Figure 2.39 plots the Bragg wavelength versus thetemperature, showing a linear slope of about 84 pm/oC.By taking the derivative of Eq. 1.1 with respect to temperature, we obtain:d?dT=?ngdne f fdT=?ngdne f fdndndT(2.4)5120 25 30 35 40 451530.515311531.515321532.51533Temperature (oC)Bragg Wavelength (nm) y=0.084364x +1528.9978Figure 2.39: Bragg wavelength versus temperature corresponding to the mea-sured spectra in Figure 2.38, showing a thermal sensitivity of about 84 pm/oC.where the thermo-optic coefficient in silicon is [99]:dndT= (1.86?0.08)?10?4/K (2.5)Using Eq. 2.4, the simulated thermo-optic dependence of the Bragg wavelength isabout 80 pm/oC, in good agreement with the measurement result.2.5 Wafer-Scale PerformanceOne of the major issues with silicon photonics is that most devices are sensitiveto dimensional variations, including waveguide width variations caused during thelithography process as well as thickness variations of the top silicon layer causedduring the manufacturing of the SOI wafer. These variations can be present eitherat the device scale (1?100 ?m), chip scale (1?20 mm) or wafer scale (150 mm?300 mm). Typically, local variations at the device or chip scale (1 nm) are muchsmaller than the global variations found across a full wafer (10 nm) [100]. To make52waveguides more robust to dimensional variations, one can increase the waveguidedimensions or use the less confined TM-polarization, however, both approachesrequire much larger bending radius. Post-fabrication trimming is a technique tocompensate the fabrication variations [101], but at the expense of increased fabri-cation complexity and costs. Alternatively, active components (e.g., thermal tun-ing) can be used for accurate compensation, however, this approach leads to higherpower consumption and increased circuit complexity. Therefore, it is still neces-sary to improve the uniformity of passive devices to a practical level. Selvarajaet al. demonstrated the nonuniformity of ring resonators, Mach?Zehnder interfer-ometers, and arrayed waveguide gratings, showing a nonuniformity in the spectralresponse of <0.6 nm within a chip and <2 nm between chips [100]. Zortman et al.used microdisk resonators to extract thickness and width variations from the reso-nant wavelength deviations, which were within 0.85 nm on a single die and 8 nmacross the wafer [102].In this section, we present the wafer-scale nonuniformity of our strip waveguidegrating devices. As a part of a multi-project run, the grating devices are replicatedon two 200 mm wafers, one with air cladding (Wafer A) and the other with oxidecladding (Wafer B). Each wafer contains many chips (or dies) arranged in columnsand rows, as shown in Figure 2.40. The size of a chip is 12.73?12.95 mm2.There are two etch processes in the fabrication. The first etch is a 70 nm par-tial (shallow) etch for fiber grating couplers and rib waveguides. The second etchis a 220 nm full etch for strip waveguides, photonic crystals, etc. For the deepetch process, the exposure dose across the wafer is increased from left to right forresearch purposes [96]. This results in a reduction in width for strip waveguides(and an increase in hole size for photonic crystals) from column -4 to column 2;therefore, this is an intentional fabrication variation. As will be discussed in thenext Chapter about rib waveguide gratings, the exposure dose for the partial etchis fixed, so the shallow-etched structures are supposed to be on target everywhereacross the wafer.To evaluate the device nonuniformity across the wafer, we chose a grating sam-ple with the following design parameters: W = 500 nm, ?W = 20 nm, ?=330 nm,and N =1000. Figure 2.41, Figure 2.42, and Figure 2.43 show the performancenonuniformity on Wafer A and Wafer B, respectively.53!4 !3 !2 !1 0 1 2 33 1 2 3 4 32 5 6 7 8 9 10 21 11 12 13 14 15 16 17 18 10 19 20 21 22 23 24 25 26 0 Available!1 27 28 29 30 31 32 !1 2!8!2 33 34 35 36 37 38 !2 9!15!3 !3 23!29!4 !3 !2 !1 0 1 2 3 30!35Figure 2.40: Wafer map (available chips are listed in the legend).We can observe the following:? Wavelength: The wavelength variation is remarkably large, i.e., >30 nm onboth wafers. The average wavelength on Wafer B is about 11 nm larger thanthat on Wafer A, due to the higher index of the cladding. Moreover, the twowafers show a similar trend that the wavelength decreases from left to rightcolumns. This agrees with the intentional exposure dose variation, i.e., thewaveguide width decreases and thus the effective index becomes smaller.? Bandwidth: The bandwidth variation is also noteworthy. On Wafer A, theaverage bandwidth is about 4.24 nm and the variation is about 1.17 nm. OnWafer B, the average bandwidth gets smaller to 2.92 nm, due to the weakerindex contrast as discussed in Section 2.2.5.4; and the variation also getssmaller to 0.33 nm. Moreover, the two wafers show a similar trend that thebandwidth increases from left to right columns. This also agrees with theintentional exposure dose variation, i.e., the waveguide width decreases andthus the coupling becomes stronger as discussed in Section 2.2.5.3.54Figure 2.41: Performance nonuniformity of the strip waveguide grating onWafer A.55Figure 2.42: Performance nonuniformity of the strip waveguide grating onWafer B.56?5 ?4 ?3 ?2 ?1 0 1 2 3150015101520153015401550ColumnWavelength (nm)  Wafer AWafer B?5 ?4 ?3 ?2 ?1 0 1 2 32.533.544.555.5ColumnBandwidth (nm)  Wafer AWafer BFigure 2.43: Performance nonuniformity of the strip waveguide grating as afunction of the column number. Each error bar is symmetric and the lengthis two standard deviations (within each column). The general trend of thedecrease in wavelength and the increase in bandwidth is due to the intentionalincrease in exposure dose from left to right columns.57In addition to the intentional waveguide width variations, the Si thickness varia-tions also play a key role in the overall uniformity. For example, the devices in thesame column also show random wavelength variations that cannot be predicted.We will discuss Si thickness variations in more detail in Chapter 3.2.6 Phase-shifted Gratings 22.6.1 BasicsWe know that a uniform grating has a stop band around the Bragg wavelengthin the transmission spectrum. If a phase shift is introduced in the middle of thegratings, as illustrated in Figure 2.44, a narrow resonant transmission window willW!?W! ?!N x ?! N x ?!Figure 2.44: Schematic of a phase-shifted strip waveguide grating.appear within the stop band, as shown in Figure 2.45. This structure can also beviewed as an FP cavity ? the etalon is as thin as the phase shift, and the frontgrating section and the rear grating section act as mirrors of the FP etalon [103].Figure 2.46 shows a fabricated strip waveguide phase-shifted grating. This gratingcan be used as a simple band-pass transmission filter, or in semiconductor lasersto enable single frequency operation [67]. The transmission window has a verynarrow Lorentzian line shape. The position and the size of the phase shift determinethe center wavelength and the sharpness of transmission window. In general, thephase shift is placed in the exact center so that the resonance peak is the sharpest,and the length of the phase shift is equal to a grating period so that there is always2Parts of Section 2.6 have been published: X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger,and L. Chrostowski, ?Narrow-band transmission filter using phase-shifted Bragg gratings in SOIwaveguide,? in IEEE Photonics Conference, Arlington, VA, October 2011, pp. 869-870.581530 1535 1540 1545 1550 1555 1560 1565 157000.20.40.60.81Wavelength (nm)Transmission  UniformPhase?Shifted1530 1535 1540 1545 1550 1555 1560 1565 157000.20.40.60.81Wavelength (nm)Reflection  UniformPhase?ShiftedFigure 2.45: Spectral responses of a uniform and a phase-shifted grating.Note that the only difference between the two devices is the inclusion of thephase shift.one resonance peak around the center of the stop band.If the length of the phase shift is very long (e.g., 500?), it is possible to generatemultiple resonance peaks within the stop band, as shown in Figure 2.47. Again,this can be interpreted as a Fabry-Perot (FP) cavity, where the two grating sectionsact as wavelength-selective mirrors separated by the phase shift. There are manylongitudinal modes in the FP cavity, but only those within the reflection band aresupported. As the cavity length is increased, the mode spacing becomes narrower,so the number of supported modes increases [104].To evaluate the sharpness of the resonance peak, we introduce an importantparameter: quality (Q) factor. In the context of resonators, Q factor is defined as59480 nm!320 nm!Figure 2.46: Top view SEM image of a fabricated strip waveguide phase-shifted grating. Design parameters: W = 500 nm, ?W = 80 nm, ?= 320 nm.Note that the phase shift in the central region can be identified by measuringthe spacing between the grating grooves. Here, the spacing with the phaseshift is 480 nm, corresponding to 1.5 times the grating period (320 nm).2pi times the ratio of the stored energy to the energy dissipated per oscillation cycle:Q = 2pi f0?EdE /dt = ?0?p (2.6)where f0 is the resonant frequency, E is the stored energy, ?0 is the angular fre-quency, and ?p is the photon lifetime. For high values of Q, the following definition601530 1540 1550 1560 1570?25?20?15?10?50Wavelength (nm)Transmission (dB)  1?500?Figure 2.47: Transmission spectra for phase-shifted gratings with differentphase-shift length. Multiple resonance peaks occur for long cavity length dueto the reduced free spectral range.is also mathematically accurate and commonly used:Q =f0? f=?0?? (2.7)where ? f and ?? are the full width at half maximum (FWHM) frequency andbandwidth of the resonance, respectively.For a phase-shifted Bragg grating (and in fact for all optical resonators in gen-eral), the Q factor is determined by two loss mechanisms: coupling loss and waveg-uide loss [105]. The coupling loss depends on the grating length and the gratingcoupling coefficient, both of which can be adjusted through design. The waveg-uide loss, by contrast, is inherent in the fabrication and it arises primarily from thewaveguide roughness. Again, we can interpret a phase-shifted grating as an FPcavity, and the photon lifetime is given by:?p =ngc(?+?m)(2.8)61where ? is the waveguide propagation loss, and ?m is the distributed mirror loss:?m =ln?R1R2L(2.9)where R1 and R2 are the mirror reflectivities, and L is the cavity length. Note thatboth ? and ?m here are in units of m?1. When R1 and R2 approach unity (corre-sponding to large ?L of the two grating sections), the photon lifetime is limited bythe waveguide propagation loss, and we can rewrite Eq. 2.6 to obtain the intrinsicQ factor [14]:QI = ?0?p =?0 ?ngc ??[m?1]=2pi ?ng ?4.34? ?100 ?? [dB/cm](2.10)As discussed in Section 2.2.5.5, the loss values for strip waveguide gratings arein the range of 2.5?4.5 dB/cm. Assuming that the loss is 4 dB/cm and ng = 4.36(simulated value for a 500 nm waveguide with air cladding), the calculated QI isabout 1.9? 105 at 1550 nm. As will be shown in the next section, this value iscomparable to the maximum Q value that we have observed experimentally.2.6.2 Design VariationsThis section describes how the transmission spectra varies with respect to variousgrating parameters.The effects of variations in grating length and corrugation width are shown inFigure 2.48 and Figure 2.49, respectively. In Figure 2.48, as N is increased from125 to 250, the stop band becomes deeper. This is because more light is reflectedback as the grating becomes longer, i.e., higher reflectivity or larger R1 and R2 (seeEq. 1.13). More importantly, the resonant peak becomes sharper and the Q factorincreases from 1900 to 3?104. This is also due to the increasing R1 and R2. FromEq. 2.9 and Eq. 2.8, we can see that the distributed mirror loss decreases, thusresulting in a longer photon lifetime and a higher Q factor. When N is fixed at 200and the corrugation width is increased from 40 nm to 80 nm, the stop band becomesbroader and deeper, as shown in Figure 2.49. This is easy to understand if we recallour discussion in Section 1.2. Specifically, larger corrugation results in larger ? ,thus leading to higher reflectivity and broader bandwidth. We also see that the621500 1510 1520 1530?40?35?30?25?20?15?10?505Wavelength (nm)Transmission (dB)  1512 1514 1516 1518?40?35?30?25?20?15?10?50Wavelength (nm)Transmission (dB)  N=150N=175N=200N=225N=250N=125N=125N=250Figure 2.48: Transmission spectra for phase-shifted gratings with different N.Fixed parameters: oxide cladding, W = 500 nm, ?W = 60 nm, ? = 320 nm.As N is increased, the stop band becomes deeper due to the increasing reflec-tivity, and the resonant peak becomes sharper due to the reduced coupling lossand higher Q factor.1500 1505 1510 1515 1520 1525 1530?50?40?30?20?100Wavelength (nm)Transmission (dB)  ?W=60 nm?W=80 nm?W=40 nmFigure 2.49: Transmission spectra for phase-shifted gratings with different?W . Fixed parameters: oxide cladding, W = 500 nm, N = 200, ?= 320 nm.As ?W is increased, the stop band becomes wider and deeper due to the in-creasing coupling coefficient, and the resonant peak becomes sharper due tothe reduced coupling loss and higher Q factor.63resonant peak becomes sharper and the Q factor increases from 3000 to 3.3?104.Again, this is due to the higher reflectivity, similar to the case in Figure 2.48.Figure 2.50 shows the contour plot of the Q factor as a function of N and ?W .The top and right boundaries of the contour plot are also plotted in Figure 2.51.?W (nm)Nlog10(Q)  40 60 8015017520022525033.23.43.63.844.24.44.64.85Figure 2.50: Contour plot of the Q factor as a function of ?W and N. Fixedparameters: oxide cladding, W = 500 nm, ?= 320 nm. The Q factor increasestowards the top-right corner of the contour, i.e., large N and/or ?W (essentiallya high mirror reflectivity).Obviously, to obtain a high Q factor, one would use a large N and/or ?W (essen-tially a higher mirror reflectivity). However, it is important to note again that theQ factor will be ultimately limited by the waveguide loss. Here, we give anotherset of data to show this limitation in Figure 2.52. When N is 150, the transmittivityof resonance peak is very high. As N is increased beyond 150, the peak amplitudedramatically decreases. When N is 300, the resonance is buried into the noisesand is hardly seen. This can be interpreted as increasing the mirror reflectivity(R, intensity reflectivity) of an FP cavity. For a loss-less FP cavity (? = 0), themaximum transmission is unity [103]. However, if we include loss or gain, the6440 50 60 70 80012345678 x 104?W (nm)Q factor  N=250100 150 200 250012345678 x 104NQ factor  ?W=80nm(a) (b)Figure 2.51: Measured Q factor as a function of (a) ?W (corresponding tothe top boundary of the contour plot in Figure 2.50) and (b) N (correspondingto the right boundary of the contour plot in Figure 2.50).peak transmission is no longer unity. Let the intensity loss (or gain) per pass be G,defined as G = Iout put/Iinput , the maximum transmission can be written [103]:Tmax =(1?R)2G(1?GR)2 (2.11)assuming that the FP cavity is symmetric, i.e., identical mirrors (analogous to astandard phase-shifted grating). In the case of loss, G is less than 1, so Tmax is lessthan unity. When R approaches unity, Tmax dramatically decreases, though Q stillincreases, as shown in Figure 2.53. Note that this is also analogous to the caseof reducing the coupling coefficient in a ring resonator, where the peak amplitudein the drop port becomes smaller and the extinction ratio in the through port alsobecomes smaller.By measuring many devices with different parameters, we have observed aminimum FWHM linewidth of about 8 pm (i.e., 1 GHz), as shown in Figure 2.54.This results in a maximum Q factor of 1.9?105, which matches with the previouscalculation in Section 2.6.1 using Eq. 2.10.It is also important to note that when the Q factor is very high, the measured res-651520 1525 1530 1535 1540?90?80?70?60?50?40?30?20Wavelength (nm)Transmission (dB)N=1501520 1525 1530 1535 1540?90?80?70?60?50?40?30?20Wavelength (nm)Transmission (dB)N=2001520 1525 1530 1535 1540?90?80?70?60?50?40?30?20Wavelength (nm)Transmission (dB)N=2501520 1525 1530 1535 1540?90?80?70?60?50?40?30?20Wavelength (nm)Transmission (dB)N=300Figure 2.52: Transmission spectra (unnormalized) for phase-shifted gratingswith different N. Fixed parameters: air cladding, W = 500 nm, ?W = 60 nm,and ? = 330 nm. The peak amplitude drops significantly after N=200, as itgoes beyond the critical coupling condition.onance peak is power-dependant, as shown in Figure 2.55. When the input poweris -10 dBm, the resonance has an almost ideal symmetric Lorentzian shape with a3-dB linewidth of 20 pm (corresponding to a Q factor of about 7.6?104). However,when the input power is 0 dBm, the shape of the resonance is skewed to the right.This is because the high Q factor and the small modal volume result in high en-ergy intensities and thus strong light-matter interaction. In this particular case, thepower that actually enters into the device is about -6 dBm (0.25 mW), which canbe regarded as a threshold for nonlinearities. The nonlinear optical effects includethe Kerr effect that changes the refractive index and two-photon absorption (TPA)that generates free carriers and causes subsequent free-carrier dispersion (FCD)and free-carrier absorption (FCA). The heat generated from two-photon absorption660.9 0.92 0.94 0.96 0.98 1?25?20?15?10?50RT max (dB)3.544.555.56log10(Q)Figure 2.53: Maximum transmission and Q factor of an FP cavity as a func-tion of R. Simulation parameters: ? = 3 dB/cm, L = 100 ?m, G = 0.9931.The maximum transmission decreases dramatically after the critical couplingcondition, when the coupling loss equals the waveguide loss: R=?G=0.9965.1510 1520 1530 1540 1550?80?70?60?50?40?30?20?10010Wavelength (nm)Transmission (dB)1529.25 1529.3 1529.35 1529.4?40?35?30?25?20?15?10?5Wavelength (nm)Transmission (dB)8 pmQ 5 1.9 ? 105Figure 2.54: Maximum Q factor experimentally observed. Design parame-ters: air cladding, W = 500 nm, ?W = 40 nm, N =300, and ?= 330 nm.671510 1520 1530 1540 1550 1560?80?70?60?50?40?30?20?10Wavelength (nm)Power (dBm)  1528.8 1528.85 1528.9 1528.95?50?45?40?35?30?25?20?15Wavelength (nm)Power (dBm)  Pin = ?10 dBmPin = 0 dBmPin = ?10 dBmPin = ?5 dBmPin = 0 dBmPin = ?5 dBm20 pm(a) (b)Figure 2.55: Measured transmission spectra (raw) of a high-Q phase-shiftedgrating at various input power levels. At 0 dBm input power, the resonancebecomes asymmetric and the peak wavelength is skewed to the right.and free-carrier absorption also raises the temperature and causes additional refrac-tive index change by the thermo-optic effect. All these nonlinear effects combineand can lead to bi-stability or self-pulsation phenomena in high-Q silicon photoniccavities [106, 107]. Taking all these effects into account, the steady-state charac-teristic equation for a two-port system (including phase-shifted gratings) can befound [107]:?0?2QC|s1|2 = |a|2(???0?)2 +|a|24[?0?QI+?0?QC+?T PAc2n2VT PA|a|2+e3n2?2?0(?T PAc2n2VT PA|a|42h???reconVFC)(1m?2e ?e+1m?2h ?h)]2(2.12)where a is the normalized cavity field amplitude (|a|2 equals the cavity energy),s1 is the input waveguide field amplitude (|s1|2 equals the input power), QI is theintrinsic quality factor as defined by Eq. 2.10, QC is the coupling quality factor(i.e., replacing the waveguide loss by the distributed mirror loss in Eq. 2.10), ?T PAis the TPA coefficient, VT PA is the cavity volume for TPA, VFC is the cavity volumefor free carriers, and ?recon is the carrier recombination time. m?e and m?h are the68effective masses of electrons and holes, respectively. ?e and ?h are the carriermobilities of electrons and holes, respectively. The constants c, e, ?0, and h? are thespeed of light in vacuum, the elementary charge, the vacuum permittivity, and thereduced Planck constant, respectively. The cavity resonance wavelength includingnonlinear effects can be given as [107]:? ? =2pic?0?= ?0??0e22n0n?2?0(?T PAc2n2VT PA|a|42h???reconVFC)(1m?e+1m?h)+?0n0?n?T |a|2RT[?T PAc2n2VT PA|a|2 +e3n2?2?0(?T PAc2n2VT PA|a|42h???reconVFC)(1m?2e ?e+1m?2h ?h)]+?0n0n2cnVKerr|a|2 (2.13)where ?0 is the resonant wavelength in the linear regime, ?n/?T is the thermal-optic coefficient, RT is the thermal resistance, n2 is the Kerr coefficient, and VKerris the cavity volume for Kerr effect, which is equal to that for TPA.In Eq. 2.12, we can observe that the second term on the right-hand side causesthe asymmetry of the resonance spectrum at high input powers. On the right-handof Eq. 2.13, the second term corresponds to the FCD-induced blue shift, the thirdterm corresponds to the thermal-optic red shift, and the last term corresponds to theKerr effect. At room temperature, the thermal-optic effect dominates the bistabilityin high-Q silicon photonic cavities [107], therefore, we observed the red shift ofthe resonant wavelength in Figure 2.55(b).In summary, high-Q phase-shifted gratings are potential for use in nonlinearoptics. On the other hand, to avoid such nonlinearities and to remain in the linearregime, it is important to perform the measurement with low enough power.692.6.3 Applications 3Phase-shifted Bragg gratings have various applications, such as biosensing [15,105], microwave photonics [27, 108], and ultrafast optical signal processing [109].In this section, we present an example of using a strip waveguide phase-shiftedgrating for biosensing.Integrated waveguide Bragg gratings are promising candidates for sensing ap-plications, including biosensors and gas sensors. In this section, we demonstrateits capability as a biosensor but the theory applies to gas sensors as well. For abulk refractive index (RI) change, ?n f luid , the Bragg wavelength shift ??B can bedescribed by:??B?B=?n f luidng?ne f f?n f luid(2.14)The sensitivity is the slope of wavelength shift versus bulk refractive index change:S =??B?n f luid=?Bng?ne f f?n f luid(2.15)and its unit is nm/RIU (refractive index unit). The limit of detection (LOD) isthe minimum detectable refractive index change and there are usually two defini-tions: 1) change in index corresponding to one resonator linewidth, and 2) a systemdetection limit corresponding to the index change for a standard deviation in themeasurement noise. The first definition describes the intrinsic device performanceand thus is also known as intrinsic LOD:?nmin =?BQS(2.16)Note that there are many other definitions in the literature, especially from thebiological perspectives; however, we only focus on the optical properties in thiswork.Figure 2.56 shows the measurement setup for biosensing. Aqueous solutions3Parts of Section 2.6.3 have been published: S. T. Fard, S. M. Grist, V. Donzella, S. A. Schmidt,J. Flueckiger, X. Wang, W. Shi, A. Millspaugh, M. Webb, D. M. Ratner, K. C. Cheung, and L. Chros-towski, ?Label-free silicon photonic biosensors for use in clinical diagnostics,? in SPIE PhotonicsWest, San Francisco, CA, February 2013, paper 862909.70Microfluidic !PDMS !Fiber array!SOI Chip!Figure 2.56: Measurement setup for biosening. Reagents were introducedto the sensor using a reversibly bonded PDMS flow cell and Chemyx Nexus3000 Syringe Pump at 10 ?L/min. Note that the input/output grating couplersare placed far away from the sensor on the chip.of NaCl were prepared in concentrations of 62.5 mM, 125 mM, 250 mM, 1 M, and2 M. The refractive indices were measured using a refractometer. The Bragg grat-ing sensors were exposed to the solutions at a flow rate of 10 ?L/min. Figure 2.57shows the experimental results of the sensitivity analysis of a strip waveguidephase-shifted grating with the following design parameters: W = 500 nm, ?W =40 nm, ? = 320 nm, and N =300. A sensitivity of 58.52 nm/RIU is measured,which is close to the simulated value of about 55 nm/RIU. The quality factor (Q)of this device is measured to be 27600, which leads to an intrinsic LOD of about9.3?10?4 RIU. As will be discussed in Chapter 4, we have also designed a biosen-sor using phase-shifted gratings in slot waveguides, which shows an improved in-711516 1516.5 1517 1517.5?50?45?40?35?30?25Wavelength (nm)Power (dBm)  2 M1 M125 mM0 mM62.5 mM250 mM500 mM1.335 1.34 1.345 1.35?0.200.20.40.60.811.21.4Refractive Index (RIU)Peak Wavelength Shift (nm)S=58.52nm/RIU  ExperimentSimulationFigure 2.57: Top: transmission spectra for various concentrations of NaCl(note: 1 M=1 mol/L=1000 mol/m3). Bottom: peak wavelength shift versusbulk refractive index, showing a sensitivity of 58.52 nm/RIU.72trinsic LOD of about 3?10?4 RIU.2.7 Sampled Gratings 4In this section, we present another important grating structure called sampled grat-ings. A sampled grating is formed by applying a sampling function to a conven-Z0!Z1! ?!?W! W!Figure 2.58: Schematic of a sampled grating.tional uniform grating so that the grating elements are removed in a periodic fash-ion, as illustrated in Figure 2.58. The grating burst length is Z1, and the samplingperiod is Z0. The reflectivity of this structure can be obtained from the coupled-mode theory, which predicts that every spatial Fourier component of the dielectricperturbation contributes a peak to the reflection spectrum [110]. The multiplicationof the sampling function and the uniform grating function in the spatial domain willbe translated into the convolution of the single Fourier component of the uniformgrating at the Bragg wavelength with the comb of Fourier components in the sam-pling function. Therefore, it leads to a reflection spectrum with periodic maxima[111]. Figure 2.59 shows the measured spectral responses of two sampled gratingson strip waveguides, where periodic maxima were clearly observed. The spacingbetween reflection peaks can be approximated by [111]:?spacing ?? 2B2ngZ0(2.17)4Parts of Section 2.7 have been published: X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L.Chrostowski, ?Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corruga-tions,? IEEE Photonics Technology Letters, vol. 23, no. 5, pp. 290-292, 2011.731460 1470 1480 1490 1500 1510 1520 1530?20?15?10?505Transmission (dB)Z0/Z1=41460 1470 1480 1490 1500 1510 1520 1530?20?100Reflection (dB)1460 1470 1480 1490 1500 1510 1520 1530?20?15?10?505Transmission (dB)Z0/Z1=61460 1470 1480 1490 1500 1510 1520 1530?20?100Wavelength (nm)Reflection (dB)Figure 2.59: Measured transmission and reflection spectra of two sampledgratings. Design parameters: air cladding, W = 500 nm, ?W = 20 nm, Z1 =6.4 ?m. Each device includes 20 sampling periods (i.e., total length is 20 Z0).The peak spacing for Z0/Z1 = 4 is 1.5 times larger than that for Z0/Z1 = 6, inagreement with Eq. 2.17.74This can be confirmed by comparing the spectra of the two devices in Figure 2.59,i.e., the peak spacing for Z0/Z1 = 4 is 1.5 times larger than that for Z0/Z1 = 6.These comb-like spectra can be deployed in tunable lasers to achieve a widetuning range through the Vernier effect [111]. They can also be used for multi-channel add/drop multiplexers and dispersion compensations. Figure 2.60 showsa layout example for achieving Vernier effect using two slightly mismatched sam-pled gratings. The measurement results are shown in Figure 2.61, where only theInput!Y-Branch!Sampled Grating 1!Reflection!Sampled Grating 2!Figure 2.60: Layout for the Vernier effect using two sampled gratings withslightly mismatched sampling periods.reflection peaks at 1530 nm are well aligned.The suppression ratio of the side peaks is about 10 dB; however, this can befurther improved by active tuning and/or optimizing the grating design such asusing apodization to reduce the sidelobes. By adding active tuning components(e.g., thermal heaters) to each of the sampled gratings, the peak alignment canbe adjusted. Specifically, a small index change in one sampled grating relativeto the other can cause adjacent reflection maxima to come into alignment, thusshifting the final selected wavelength by a large amount [111]. This is similar tothe principle of Vernier scale, i.e., a small shift in one arm can cause a substantialchange in the alignment of the marks. For tunable lasers based on Vernier effect,lasing occurs at the pair of maxima that are aligned.751480 1500 1520 1540 1560 1580?20?15?10?505Reflection (dB)Individual Sampled Grating  Z0/Z1=4Z0/Z1=51480 1500 1520 1540 1560 1580?40?30?20?100Wavelength (nm)Reflection (dB)Vernier EffectFigure 2.61: Measured reflection spectra of two individual sampled gratings(top) and the Vernier effect (bottom). The only major peak for the Verniereffect occurs where the peaks of individual sampled gratings are well aligned(at 1530 nm).762.8 SummaryIn this chapter, we have studied Bragg gratings in standard single-mode strip waveg-uides working at TE polarization. We predict that this family of devices will findmany applications because it only requires a single etch (and is clearly more robustthan slot waveguides, which will be discussed in Chapter 4). The bandwidth hasbeen demonstrated as large as 30 nm (e.g., using 160 nm corrugations on a 500 nmstrip waveguide with air cladding) and could be even larger by using larger corru-gations or narrower waveguides. The strong coupling strength is particularly usefulfor designing high-Q phase-shifted gratings, as we have discussed in Section 2.6.However, it is more challenging to design narrow-band gratings in strip waveg-uides. We have demonstrated bandwidths of about 1 nm using 10 nm corrugations(see Figure 2.33), but this is much smaller than the typical minimum feature size(also called critical dimension) of the current fabrication processes and is even ap-proaching the limit of the grid size (e.g., 5 nm for the processes used in this thesis).Simard et al. have demonstrated strip waveguide gratings with bandwidths smallerthan 1 nm, however, it was achieved at the expense of using a multi-mode waveg-uide (1200 nm wide) and a third-order grating (860 nm period).Another critical issue is the fabrication nonuniformity ? the effective index ofa strip waveguide is sensitive to both width and thickness of the waveguide. There-fore, very good fabrication quality is needed. Specifically, the Si thickness unifor-mity of the wafer, as well as the linewidth uniformity of the fabrication process,has to be precisely controlled.77Chapter 3Rib Waveguide Bragg GratingsIn the last chapter, we have discussed many grating structures using strip waveg-uides. It is clear that strip waveguide Bragg gratings have relatively large band-widths (e.g., >1 nm even for a 10 nm corrugation width). However, numerousapplications require narrow bandwidths, such as in wavelength-division multiplex-ing (WDM) systems. Also, our wafer-scale test has shown that strip waveguidegratings are very sensitive to fabrication variations. An alternative is to use ribwaveguides, which typically have larger cross-sections and can reduce the fabrica-tion challenges. In this chapter, we will demonstrate several types of narrow-bandBragg gratings using rib waveguides. We first discuss the basics of rib waveguides,and then demonstrate simple uniform gratings using rib waveguides.1 We also pro-pose a multi-period Bragg grating concept using rib waveguides. The sidewallsof the rib and the slab are corrugated using different periods, resulting in multipleBragg wavelengths that are controlled separately. We then present the thermal sen-sitivity and the wafer-scale nonuniformity of rib waveguide gratings. Finally, wedemonstrate rib waveguide Bragg gratings using a spiral geometry, which is to ourknowledge the most compact Bragg grating filter to date.1Parts of Section 3.1 and Section 3.2 have been published: X. Wang, W. Shi, H. Yun, S. Grist,N. A. F. Jaeger, and L. Chrostowski, ?Narrow-band waveguide Bragg gratings on SOI wafers withCMOS compatible fabrication process,? Optics Express, vol. 20, no. 14, pp. 15547-15558, 2012.783.1 Rib WaveguideThe rib waveguide (also known as ridge waveguide) is another important waveg-uide geometry used in silicon photonics. In fact, the first demonstration of siliconphotonic Bragg gratings uses a rib waveguide [68]. In general, it refers to a waveg-uide that consists of an infinite slab with a strip superimposed onto it. The waveg-uide geometry is often designed to be single mode [33]. However, a nominallysingle-mode rib waveguide can have higher-order leaky modes, which can causeunwanted dips in the transmission spectrum on the shorter wavelength side of thefundamental Bragg wavelength. To separate these leaky modes away from the fun-damental mode, it is necessary to shrink the waveguide dimensions [68]. This isa general trend in silicon photonics as well, because small waveguide dimensionsare desired for small bending radius and high integration density. However, mostintegrated Bragg gratings were demonstrated in bulky rib waveguides (e.g., up to afew microns [68, 73, 74, 112]) until our recent work in [113].Figure 3.1 shows the cross section of the rib waveguide that we used for thegrating design. It differs from the commonly used rib geometry, which usually hasWrib!220 nm!70 nm!Si!SiO2!Wslab!2 ?m!Si substrate!Figure 3.1: Schematic of the rib waveguide cross section (not to scale):Wrib =500 nm, and Wslab =1 ?m.an infinite slab. In contrast, the finite slab strengthens the mode confinement andthus allows for relatively tighter bends. Again, the silicon thickness is 220 nm,and the shallow etch depth is 70 nm. The rib width (Wrib) is 500 nm, and the slab79width (Wslab) is 1 ?m. As shown in Figure 3.2, most light is confined under the rib.x (?m)y (?m)  ?0.5 0 0.5?0.200.20.400.20.40.60.81Figure 3.2: Simulated electric field of the fundamental TE mode in the ribwaveguide with air cladding. The field intensity is low around the sidewalls,allowing for weak perturbations to the mode using relatively large sidewallcorrugations.The overlap between the electrical field with the sidewalls is very low around boththe rib and slab sidewalls. This overlap reduction makes it possible to introduceweaker effective index perturbations compared to the strip waveguide gratings, thusallowing for smaller coupling coefficients and narrower bandwidths. Additionally,the waveguide propagation loss is also reduced. Figure 3.3 shows the cross-sectionof a fabricated rib waveguide.3.2 Uniform Gratings3.2.1 Design and FabricationThere are several configurations to make gratings on rib waveguides. The gratingcorrugations can be on the top surface [68, 74], or on the sidewalls, where the side-walls can be corrugated either on the rib [73] or on the slab [114]. The top-surface-corrugated configuration usually has a fixed etch depth, therefore, it is difficult toadjust the grating coupling coefficient. In contrast, the sidewall-corrugated con-figuration is much more flexible. The grating coupling coefficient can be easilycontrolled by varying the corrugation width, which is essential for complex gratingstructures, such as apodized gratings that can suppress reflection side lobes [114].80Figure 3.3: Cross-sectional SEM image of a rib waveguide with gratings onthe slab.Therefore, we use the latter configuration in our work. The gratings are realizedby introducing periodic sidewall corrugations either on the rib or slab. Figure 3.4shows the SEM images of two fabricated devices. The grating period ? is designedto be 290 nm, with a duty cycle of 50%, and the number of grating period N is 2000.Note that we used square corrugations in the layout, but again, the gratings actuallyfabricated are rounded due to the lithography effects, as we already discussed inChapter 2.As mentioned in Chapter 1 and Chapter 2, strip waveguides typically exhibitmuch less bending loss than rib waveguides, therefore we use strip waveguidesfor routing. A double-layer linear taper was designed for the transition betweenthe strip and rib waveguides, as shown in Figure 3.5. The taper is 30 ?m long toensure that the transition loss is negligible [34].81Figure 3.4: Top view SEM images of fabricated rib waveguide gratings de-signed with 60 nm corrugations on the rib (left) and 80 nm corrugations onthe slab (right).Rib Waveguide Grating!Linear Taper!Strip Waveguide!10 ?m!Figure 3.5: Top view SEM image of the transition from the strip waveguideto the rib waveguide grating using a linear taper.3.2.2 Measurement ResultsFigure 3.6 and Figure 3.7 show the measured spectral responses of two rib waveg-uide gratings with oxide cladding. The corrugations are designed on the slab, andthe corrugation width is 80 nm and 100 nm, respectively. For both devices, onlyone dip exists in the transmission spectrum in a wide wavelength range, as can beseen in Figure 3.6. This indicates that the higher-order leaky modes are far awayfrom the fundamental mode and thus can be ignored.821480 1500 1520 1540 1560 1580?12?10?8?6?4?202Transmission (dB)  ?Wslab=80 nm?Wslab=100 nm1480 1500 1520 1540 1560 1580?25?20?15?10?505Wavelength (nm)Reflection (dB)  ?Wslab=80 nm?Wslab=100 nmFigure 3.6: Measured transmission responses of two rib waveguide gratingswith corrugations on the slab, each showing only one dip in a wide wavelengthrange without higher-order leaky modes.More importantly, Figure 3.7 shows that the first-null bandwidth is only about1.12 nm for ?Wslab = 80 nm and 1.19 nm for ?Wslab = 100 nm. The 3-dB band-widths are 0.74 nm and 0.86 nm, respectively. Based on the curve fitting in Fig-ure 3.7, we obtain that the coupling coefficient ? is 2.52?103 m?1 for ?Wslab =80 nm, and is 3.25?103 m?1 for ?Wslab = 100 nm. The ratio between these two? is 1:1.29, comparable to the corrugation size ratio (1:1.25). This confirms that ?is approximately proportional to the corrugation size. However, we should recallthat the bandwidth is determined not only by ? but also the grating length L (see831516 1517 1518 1519 1520 1521?12?10?8?6?4?20Transmission (dB)  1516 1517 1518 1519 1520 1521?25?20?15?10?505Wavelength (nm)Reflection (dB)  ?Wslab=80 nm?Wslab=80 nm?Wslab=100 nm?Wslab=100 nmFigure 3.7: Zoomed-in view of Figure 3.6 around the Bragg wavelength. Thedots are the measured values, and the solid curves are the fits using the analyt-ical expression in Eq. 1.9. As expected, the grating with larger corrugationsshows a slightly larger bandwidth and a higher reflectivity.84Eq. 1.16), especially for a small ? . In this case, the term pi/L in the square rootof Eq. 1.16 equals 5.42?103 m?1, which is actually larger than the two ? valuesabove. This explains that the first-null bandwidth does not increase proportionallyto the corrugation size, i.e., the bandwidth ratio is only 1:1.06. Also, as expected,the larger ? for ?Wslab = 100 nm causes a higher extinction ratio in the transmis-sion and a larger peak amplitude in the reflection.If we apply the same corrugation widths on a 500 nm strip waveguide, the first-null bandwidths are definitely much larger (?10 nm, see Figure 2.28). To obtain asimilar bandwidth around 1 nm using strip waveguides, the corrugation width hasto be 10 nm or even smaller, which can pose severe fabrication challenges.Figure 3.8 shows the comparison of the coupling coefficients using differentgrating structures. The coupling coefficient was extracted by curve-fitting the mea-sured spectral response using Eq. 1.9, as shown in Figure 3.7. We can see that101 102103104105Corrugation Width (nm)Coupling Coefficient (m?1 ) Strip waveguide gratingsRib waveguide: gratings on ribRib waveguide: gratings on slabFigure 3.8: Extracted coupling coefficient versus designed corrugation widthfor various grating structures on a chip with oxide cladding. The strip waveg-uide is 500 nm wide and has the largest coupling coefficient, while the grating-on-slab configuration has the smallest coupling coefficient.85the green curve is well above the other two curves, i.e., strip waveguide gratingsusually have very large ? and bandwidths. For the same corrugation width, thecorrugation-on-slab configuration results in a smaller ? than the corrugation-on-rib configuration. This can be attributed to the fact that the optical field distributionat the slab sidewalls is weaker than at the rib sidewalls, as shown in Figure 3.2.The smallest ? we obtained in Figure 3.8 is about 1?103 m?1, corresponding to?Wslab = 30 nm. If we take this value into Eq. 1.16 and assume the grating is longenough, the first-null bandwidth is expected to be about 0.2 nm.3.3 Multi-period Gratings 2Simple uniform grating structures only have one Bragg reflection band. However,optical filters with flexible spectral responses are of great interest for many appli-cations. For example, in the last chapter we have demonstrated sampled gratingswith a comb-like reflection spectrum, and phase-shifted gratings with a high-Qresonance within the stop-band of the transmission spectrum. For applications thatrequire custom spectral responses, it might be necessary to cascade a number ofgrating sections with different periods. However, the performance of cascadedBragg gratings is sensitive to the Si thickness variation and the nonuniformity ofthe fabrication process.In this section, we demonstrate a multi-period Bragg grating concept, by takingadvantage of the multiple sidewalls of the rib waveguide. The sidewalls of the riband the slab are corrugated using different periods, resulting in two or more Braggwavelengths that are controlled separately. This approach not only increases thedesign flexibility for custom optical filters but also reduces the device size andfabrication errors.3.3.1 Dual-Period GratingFigure 3.9 illustrates the design of a dual-period Bragg grating using the rib waveg-uide. The grating periods on the rib and on the slab are ?1 = 290 nm and ?2 =2Parts of Section 3.3 have been published: X. Wang, H. Yun, N. A. F. Jaeger, and L. Chrowtowski,?Multi-period Bragg gratings in silicon waveguides,? in IEEE Photonics Conference 2013, Bellevue,WA, September 2013, paper WD2.5.86?Wslab!Wrib!?2!Wslab!?Wrib!?1!Figure 3.9: Schematic diagram of a dual-period rib waveguide grating (notto scale). Design parameters: ?1 = 290 nm, ?2 = 295 nm, ?Wrib = 80 nm,?Wslab = 100 nm, and the grating length is 580 ?m.295 nm, respectively. In order to obtain similar coupling coefficients for the twogratings, the corrugation widths on the rib and on the slab are designed to be?Wrib = 80 nm and ?Wslab = 100 nm, respectively. The grating length is 580 ?m,including 2000 periods on the rib and 1966 periods on the slab.Figure 3.10(a) shows the measured raw transmission spectrum of a fabricateddevice within a wide wavelength range. We can clearly observe two sharp dips at?1 and ?2, corresponding to ?1 and ?2, respectively. The normalized response isshown in Figure 3.10(b). It can be seen that both dips show an extinction ratio ofmore than 14 dB, as well as a 3-dB bandwidth of about 1 nm. The spacing betweenthe two dips is 17.63 nm. We also show that the experimental result matches verywell with the simulations results, as shown in Figure 3.11. We expect that the twodips can be manipulated separately by adjusting the grating period. The bandwidthcan also be tailored by choosing an appropriate corrugation size.3.3.2 Four-Period GratingThis multi-period concept can be further extended. Figure 3.12 illustrates the de-sign of a 4-period Bragg grating using the rib waveguide. Instead of using symmet-ric corrugations on the rib or slab layer, we use asymmetric corrugations to increasethe number of gratings. The grating periods are ?1 = 285 nm and ?2 = 290 nm,?3 = 295 nm and ?4 = 300 nm, respectively. The corrugation widths on the riband on the slab are still ?Wrib = 80 nm (for ?2 and ?3) and ?Wslab = 100 nm (for?1 and ?4), respectively. The grating length is still 580 ?m, including 2035?2,2000?2, 1966?3, and 1933?4.871480 1500 1520 1540 1560 1580?40?35?30?25?20?15?10Wavelength (nm)Transmission (dB)1510 1515 1520 1525 1530 1535 1540 1545?18?16?14?12?10?8?6?4?202Wavelength (nm)Transmission (dB) 1.06 nm! 1.04 nm!17.63 nm!(a)!(b)!?1!?2!Figure 3.10: (a) Measured (unnormalized) transmission spectrum of the dual-period grating: ?1 and ?2 correspond to ?1 and ?2, respectively. (b) Normal-ized response around the two Bragg wavelengths.881500 1510 1520 1530 1540 15502.52.552.62.652.7Effective Index1500 1510 1520 1530 1540 1550?15?10?50Wavelength (nm)Transmission (dB)TE0!?!2?1!__!?!2?2!__!?1! ?2!Figure 3.11: Dual-period grating: simulation vs. measurement. In the topgraph, the solid blue curve shows the simulated effective index of the funda-mental TE mode; the green and red dashed curves corresponds to the effectiveindices that are needed using ?1 and ?2, respectively; thus, the intersectionpoints correspond to the two Bragg wavelengths.?Wslab!Wrib!?1!Wslab!?Wrib!?3!?2!?4!Figure 3.12: Schematic diagram of the 4-period rib waveguide grating (notto scale). Design parameters: ?1 = 285 nm, ?2 = 290 nm, ?3 = 295 nm,?4 = 300 nm, ?Wrib = 80 nm, ?Wslab = 100 nm, and the grating length is580 ?m.891480 1500 1520 1540 1560 1580?30?25?20?15?10?505Wavelength (nm)Response (dB)  RT?1" ?2" ?3" ?4"Figure 3.13: Measured spectral responses of a 4-period grating. ?1, ?2, ?3,and ?4 correspond to ?1, ?2, ?3, and ?4, respectively.Figure 3.13 shows the measured spectral responses of a fabricated device. Wecan clearly observe four Bragg wavelengths, each corresponding to one gratingperiod. Note that the extinction ratios of the four notches are lower than those inFigure 3.10, because the coupling coefficients are reduced by half. In summary,this multi-period grating concept increases the design flexibility and allows formore custom optical functions.3.4 Thermal SensitivityIn this section, we use the dual-period grating discussed in the Section 3.3.1 tostudy the thermal sensitivity of rib waveguide gratings. Figure 3.14 shows howthe Bragg wavelengths shift with temperatures. Clearly, both Bragg wavelengthsare red-shifted as the temperature is increased. As shown in Figure 3.15, the ther-mal sensitivities of the two Bragg wavelengths are approximately the same: about85 pm/oC. These values are also very close to the measured thermal sensitivity ofstrip waveguide gratings in Section 2.4, i.e., 84.4 pm/oC.901516 1517 1518 1519 1520?10?8?6?4?202Wavelength (nm)Transmission (dB)  30oC25oC20oC 35oC 40oC1533 1534 1535 1536 1537?25?20?15?10?505Wavelength (nm)Transmission (dB)  30oC25oC 40oC20oC 35oC(a)!(b)!?1!?2!T!T!Figure 3.14: Bragg wavelength shift of a dual-period rib waveguide gratingat different temperatures: (a) plot around ?2, (b) plot around ?1.9120 25 30 35 40151515201525153015351540Temperature (oC)Bragg Wavelength (nm) ?2: y=0.085859x +1532.2256?1: y=0.084952x +1514.9176Figure 3.15: Bragg wavelengths versus temperature corresponding to thespectra in Figure 3.14, showing thermal sensitivities of about 85 pm/oC.3.5 Wafer-Scale PerformanceNext, we will study the wafer-scale performance of rib waveguide gratings, againusing the dual-period grating device discussed in the Section 3.3.1. We use thesame wafers that we used for strip waveguide gratings in the last chapter (recallin Section 2.5 that Wafer A has air cladding and Wafer B has oxide cladding).We may also recall that the exposure dose for the deep etch is increased from leftto right across the wafer, so the slab width should decrease from column -4 tocolumn 2. On the other hand, the exposure dose for the partial etch is fixed, so theshallow-etched rib is supposed to be on target everywhere across the wafer. FromFigures 3.16 to Figure 3.20 , we have the following important observations:Wavelength? The wavelength variations are much smaller than that for the strip waveguidegrating, i.e., 6?8 nm vs. >30 nm.? The wavelength variations are random, whereas for the strip waveguide grat-92ing, the two wafers show a clear trend that the wavelength decreases from leftto right columns (see Figures 2.41 to 2.43). This is because the rib waveg-uide is much less sensitive to the slab width than the strip waveguide to thewaveguide width. Therefore, the Si thickness variation, which is random,is the dominant source of variation for rib waveguide gratings, despite ofthe large and intentional slab width variations induced by the exposure dosesweep.? ?1 and ?2 show almost the same variations. This is expected because thetwo wavelengths come from the same waveguide and thus are subject to thesame waveguide variations. This is also reflected by the spacing between ?1and ?2, namely, the spacing variation is only about 0.2 nm on both wafers.? The average values of ?1 and ?2 on Wafer B is about 4 nm larger than thoseon Wafer A, due to the higher index of the cladding.Bandwidth? For ??2, both wafers show a similar trend that the bandwidth increases fromleft to right columns. This agrees with the intentional exposure dose varia-tion, i.e., the slab width decreases and thus the coupling becomes stronger.? For ??1, the variations are smaller and more random than that for ??2.Table 3.1 lists the wafer-scale statistics of the measurement data. The generalconclusion is that rib waveguide gratings have better uniformity than strip waveg-uide gratings. Another finding is that the Bragg wavelength variation of rib waveg-uide gratings is mainly caused by the Si thickness variations. Hence improving theSOI thickness uniformity is very important. It is fortunate that wafer manufacturersare always improving the uniformity over time, driven by the CMOS industry thatis now developing 14 nm technologies. In the silicon photonics area, the state-of-the-art foundry process can achieve tight within-wafer silicon thickness variationof 3? < 2.5 nm [8]. Hopefully, within the next few years, the wafer specificationscan be further improved to meet the strict requirement of silicon photonic devicesin a cost-effective way.93Figure 3.16: Wavelength nonuniformity of the dual-period grating on WaferA.94Figure 3.17: Bandwidth nonuniformity of the dual-period grating on WaferA.95Figure 3.18: Wavelength nonuniformity of the dual-period grating on WaferB.96Figure 3.19: Bandwidth nonuniformity of the dual-period grating on WaferB.97?6 ?5 ?4 ?3 ?2 ?1 0 1 2 3 415101515152015251530153515401545?2?2?1?1ColumnWavelength (nm)?6 ?5 ?4 ?3 ?2 ?1 0 1 2 3 411.11.21.31.41.51.61.7??2??2??1??1ColumnBandwidth (nm)Wafer B!Wafer A!Wafer B!Wafer A!Figure 3.20: Performance nonuniformity of the dual-period grating as a func-tion the column number. Each error bar is symmetric and the length is twostandard deviations (within each column). All variations are random exceptthe bandwidth variations for ??2, which show that the bandwidth increasesfrom left to right columns due to the intentional exposure dose variation.98Device& Parameter&Wafer&A&(air&cladding)! Wafer&B&(oxide&cladding)!Mean& Range& Standard&Devia;on& Mean& Range& Standard&Devia;on&Strip&WBG& ?& 1523.52&nm& 31.90&nm& 8.80&nm& 1534.76&nm& 33.56&nm& 8.99&nm&??& 4.24&nm& 1.17&nm& 0.31&nm& 2.92&nm& 0.33&nm& 0.09&nm&Rib&WBG&?1& 1515.91&nm& 6.73&nm& 2.12&nm& 1519.75&nm& 7.63&nm& 1.66&nm&?2& 1533.18&nm& 6.91&nm& 2.17&nm& 1537.34&nm& 7.85&nm& 1.70&nm&?2L?1& 17.26&nm& 0.18&nm& 0.06&nm& 17.59&nm& 0.21&nm& 0.05&nm&??1& 1.12&nm& 0.06&nm& 0.02&nm& 1.34&nm& 0.07&nm& 0.02&nm&??2& 1.48&nm& 0.25&nm& 0.06&nm& 1.26&nm& 0.15&nm& 0.04&nm&Table 3.1: Statistics of strip and rib waveguide Bragg gratings (WBG).3.6 Spiral Gratings 3We have shown that rib waveguide gratings can achieve narrow bandwidths. Sincethe perturbations are very weak, a very long length is required to obtain a highreflectivity. However, this is often not desired from the layout perspective becausethe high aspect ratio makes it difficult to integrate them efficiently in photonicintegrated circuits. More importantly, the performance of long Bragg gratings ismore likely to be affected by the Si thickness variations, as we already discussedin Section 2.2.5.5. If the fabrication is done using electron beam lithography, longBragg gratings may also suffer from stitching errors due to the limited writing field.Therefore, it is important to pack long Bragg gratings in a small area.Recently, Zamek et al. [115] demonstrated Bragg gratings based on a curvedstrip waveguide with weakly coupled pillars, showing a length of 920 ?m within anarea of 190 ?m?114 ?m and a stop bandwidth of 1.7 nm. The packing efficiency,defined as L/?A where L is the length and A is the area, is about 6.2 [115]. Tofurther improve the packing efficiency, spiral geometries can be used [116, 117].3Parts of Section 3.6 have been published: X. Wang, H. Yun, and L. Chrowtowski, ?IntegratedBragg gratings in spiral waveguides,? in CLEO 2013, San Jose, CA, June 2013, paper CTh4F.8.99Simard et al. demonstrated third-order Bragg gratings in multimode strip waveg-uides, showing a length of 2 mm within an area of 200 ?m?190 ?m, attainingpacking efficiency of about 10.2 [116].In this section, we demonstrate first-order Bragg gratings in a single-moderib waveguide using a spiral geometry. Our results show not only a significantlyimproved packing efficiency of about 21.8, but also a very narrow bandwidth of0.26 nm.3.6.1 DesignThe rib waveguide is the same as in the last few sections, and we chose to usethe rib sidewalls for the construction of gratings. As illustrated in Figure 3.21, theFigure 3.21: Top view of the spiral grating design.gratings are designed on the rib using sidewall corrugations. On each side of therib, the corrugation width is designed to be 50 nm. The period of the first-ordergrating is kept constant at 290.9 nm in the whole spiral.Figure 3.22 shows the optical microscope images of a fabricated device. Thespiral consists of a series of half circles with different diameters (D), while theradius of curvature is kept constant within each half circle. As shown in Fig-ure 3.22(b), the diameters of the two smallest half circles (Dmin) in the centre,i.e., the S-shape, are 20 ?m. The spacing between two adjacent half circles, orthe spiral pitch (P), is 5 ?m to ensure low crosstalk. Note that this value is quiteconservative and could be reduced (e.g. to 3 ?m) to further improve the space100efficiency. Therefore, the diameters of the half circles except for the S-shape startGC (Input)!GC (Output)! 150 ?m!20 ?m!5 ?m!(a)! (b)!Figure 3.22: Optical microscope images of the fabricated device with N=10.(a) Whole layout. (b) Enlarged image of center region of the spiral.from 45 ?m and increment with a step of 5 ?m. The length and area of the spiralis determined by the largest half circle, and, as shown in Figure 3.22(a), the largesthalf circle is the outmost one on the right, with clockwise light propagation. Ex-cluding this largest half circle and the S-shape, the spiral can be divided equallyinto left and right, each with N half circles. The diameter of the largest half circlecan then be described as:Dmax = 2Dmin +(2NR +1)P (3.1)and the total length of the spiral grating is:L =pi2[4(NR +1)Dmin +(2N2R +2NR +1)P](3.2)In this work, we present two proof-of-concept designs, one with NR = 5, Dmax =95 ?m, L= 1.233 mm, and the other with NR = 10, Dmax = 145 ?m, L= 3.118 mm.In the spiral, the variation of the bending radius potentially causes two issues:the variation in the effective index and the mode mismatch loss. First, we simulatethe effective index of the waveguide as a function of bending radius (R), as shownin Figure 3.23. We can see that for R larger than 22.5 ?m, the effective indexvariation is very small (<1.2?10?4) and thus is negligible. However, from R =22.5 ?m to R = 10 ?m, the effective index is increased by about 1.8?10?3, which10110 15 20 30 40 50 60 7005101520x 10?4Radius (?m)Effective Index ChangeFigure 3.23: Effective index change of the rib waveguide versus bending ra-dius for device with NR=10. The index change from R=10 ?m to R=22.5 ?mis remarkable, while for R larger than 22.5 ?m, the index change is very small.is obviously undesirable for a perfectly uniform grating. To improve upon thisin future, one can consider slightly decreasing the grating period in the S-shapeto compensate for the higher effective index. Alternatively, one may increase thebending radius of the S-shape while keeping the grating period constant, and reducethe spiral pitch to maintain the packing efficiency. The second approach also has anadvantage of reducing the mode mismatch loss at the centre point of the S-shape,as will be discussed below. Table 3.2 lists the mode mismatch losses at differentplaces in the spiral. At the centre point of the S-shape, the change in bendingorientation causes a remarkable mode mismatch loss, which is about 0.13 dB forR=10 ?m. This is clearly the dominant source of mode mismatch loss in the spiral,as the second largest one is only about 0.01 dB (at the ending points of the S-shape), and the third largest one is already negligible (at the connection pointsbetween R = 22.5 ?m and R = 25 ?m). If the R of the S-shape is increased to15 ?m, the mode mismatch loss is reduced to about 0.06 dB, and effective indexvariation is also reduced to 5.8?10?4, as shown in Figure 3.23.102WG#A# WG#B# Loss#(dB)#R#=#10#?m# R#=#10#?m# 0.1336#R#=#10#?m# R#=#22.5#?m# 0.0102#R#=#22.5#?m# R#=#25#?m# 6.6157?1095##indicates#bending#in#the#opposite#direcEon.#Table 3.2: Mode mismatch loss between two bent waveguides (WG).3.6.2 Results and DiscussionFigure 3.24 shows the SEM image of the fabricated gratings. Figure 3.25 shows500 nm!Figure 3.24: SEM image of the fabricated spiral gratings.the measured transmission spectra of the two fabricated devices. We can see thatthere is only one sharp dip in each curve within a wide wavelength range (120 nm),indicating single-mode operation. Additionally, the envelopes of the two curvesoverlap very well, which means that the longer device does not introduce muchexcess loss, thus indicating that the propagation loss of the spiral waveguide gratingis low. As shown in Figure 3.25(b), the shorter device shows an extinction ratioof about 6.5 dB and a 3-dB bandwidth of 0.28 nm. For the longer device, theextinction ratio increases to about 23 dB since more light is reflected, while the1031511 1512 1513 1514 1515 1516 1517?45?40?35?30?25?20?15Wavelength (nm)Transmission (dB)  N=5N=101460 1480 1500 1520 1540 1560 1580?45?40?35?30?25?20?15?10Wavelength (nm)Transmission (dB)  N=5N=10(a)!(b)!Figure 3.25: (a) Measured transmission spectra of the two spiral gratings. (b)Enlarged plot around the Bragg wavelength.3-dB bandwidth is slightly reduced to 0.26 nm. The reduction in the first-nullbandwidth is more distinguishable, i.e., from 0.6 nm for N = 5 to 0.32 nm for N =10, which agrees with the theories for Bragg gratings with weak index modulations(see Eq. 1.16). We also observe a slight Bragg wavelength shift of about 0.35 nmbetween the two devices, which is most likely due to the Si thickness variations. Interms of footprint, the longer device occupies an area of 141 ?m?146 ?m, whichis smaller than previously reported Bragg gratings in curved waveguides [115] andspiral waveguides [116]. The length, in contrast, is much longer, and shows a104greatly improved packing efficiency of 21.8. Again, we expect that the packingefficiency can be further improved by reducing the spiral pitch (e.g. to 3 ?m).In summary, we have experimentally demonstrated integrated first-order Bragggratings in silicon spiral waveguides using a CMOS-compatible fabrication pro-cess. The devices exhibit high packing efficiencies as well as very narrow band-widths. Compared with long straight waveguide gratings, the spiral shape is moredesirable for large-scale integrated photonic circuits; meanwhile, it can reduce theeffects of Si thickness variations on the grating performance. Further work willinclude the optimization of the S-shape to reduce the mode mismatch loss and ef-fective index perturbations.3.7 SummaryIn this chapter, we have studied Bragg gratings in rib waveguides. This familyof devices is especially useful for narrow-band applications, such as WDM filters.Although this particular rib geometry has a finite slab and requires two etches, itis also possible to design gratings with similar performance based on the morecommonly used rib geometry and using only one etch (i.e., with infinite slab andcorrugations on the rib). The coupling coefficient has been demonstrated as low asabout 1?103 m?1, which corresponds to a bandwidth of only 0.2 nm.The multi-period grating structure is very useful for making custom opticalfunctions, with the additional benefits of reducing the device size and the effectsof fabrication nonuniformity. We find that our rib waveguide gratings have muchbetter uniformity than strip waveguide gratings, and that the Si thickness variationis the only major cause of the wavelength variation. We also show that the spiralgrating is not only favourable for the real estate on chip but also has the potentialto minimize the effects of the Si thickness variation.105Chapter 4Slot Waveguide Bragg GratingsOptical sensing is one of the promising applications for silicon photonic Bragggratings [15, 77]. The sensitivity is determined by the overlap between the electricfield and the surrounding medium [14, 15]. In Section 2.6.3, we have demonstrateda biosensor using a strip waveguide phase-shifted grating. Since the electric fieldis concentrated in the silicon, only weak evanescent field tails are available for thesensing, resulting in a low sensitivity of only about 58 nm/RIU. To improve the sen-sitivity, we propose to use slot waveguides for Bragg gratings. Unlike strip or ribwaveguides, slot waveguides are very sensitive to the RI change of the cladding be-cause the electric field is concentrated in the low-index slot region. In this Chapter,we will present a comprehensive study on slot waveguide Bragg gratings, includingboth uniform and phase-shifted gratings.1 We will investigate a number of designvariations for both types of device. We also demonstrate a biosensor using a slotwaveguide phase-shifted grating. Experimental results show a high bulk sensitivityof 340 nm/RIU and a high Q factor of about 1.5?104, which togethers results inan intrinsic LOD of only 3?10?4 RIU. Finally, we demonstrate its capability ofinterrogating specific biomolecular interactions.1A version of Sections 4.1?4.3 has been published: X. Wang, S. Grist, J. Flueckiger,N. A. F. Jaeger, and L. Chrostowski, ?Silicon photonic slot waveguide Bragg gratings and res-onators,? Opt. Express, vol. 21, no. 16, pp. 19029-19039, 2013.1064.1 Slot WaveguideSlot waveguide was first proposed by Almeida et al. in 2004 [36]. The large di-electric discontinuity at the high-index-contrast interfaces lead to a very strong op-tical confinement in the slot, which is promising for sensing and nonlinear optics.Figure 4.1 illustrates the cross section of a slot waveguide. It consists of two sili-Warm!220 nm!Si!SiO2! 2 ?m!Si substrate!Warm!Si!Wslot!Figure 4.1: Schematic of a slot waveguide cross section (not to scale).con arms separated by a low-index slot region. The geometric parameters includethe arm width (Warm) and the slot width (Wslot), both of which are defined by thelithography, and the waveguide height (H), which is fixed at 220 nm. The claddingmaterial can be air, water, glass, or other low-index materials. In Section 4.2 andSection 4.3, we will use silicon oxide as the cladding material. In Section 4.4, thecladding material is the analyte to be measured. Figure 4.2 shows the simulated TEmode profile of a slot waveguide with oxide cladding. It can be clearly seen thatthe electric field is strongly confined inside the slot region. There are also weakevanescent fields decaying on the outer sides of the waveguide, which slightly addto the light-matter interaction, and, as will be discussed below, can also be usedfor the construction of Bragg gratings. The SEM image of the cross section of afabricated slot waveguide is shown in Figure 4.3.107x (?m)y (?m)  ?0.6 ?0.4 ?0.2 0 0.2 0.4 0.6?0.200.20.400.20.40.60.81Figure 4.2: Simulated electric field of the fundamental TE mode in a slotwaveguide with the following design parameters: oxide cladding, Warm =270 nm, and Wslot = 150 nm. The field intensity is strongly confined insidethe slot region.Figure 4.3: SEM image of the focused ion beam (FIB) milled cross sectionof a fabricated device (the small hole in the centre was due to the incom-plete coating of platinum deposited to protect the waveguides during the FIBmilling). Design parameters: Warm = 270 nm, and Wslot = 150 nm.1084.2 Uniform GratingsIn this section, we present the design of uniform Bragg gratings in slot waveguides.A number of design variations will be discussed. Experimental results show highextinction ratios of 40 dB and bandwidths ranging from 2 nm to more than 20 nm.4.2.1 Design and FabricationThe gratings are formed with periodic sidewall corrugations either on the insideor the outside of the slot waveguide, as shown in Figure 4.4. Both configurationscan modulate the effective index of the optical mode. Here, we present our designsof uniform gratings in two different waveguides (WG1 and WG2) with variouscorrugation widths (?Win or ?Wout). Table 4.1 lists all of our design variations. All(a)!(b)!?Win!?Wout!Warm!Wslot!Warm!?!Figure 4.4: Schematic diagrams (not to scale) of the slot waveguide Bragggratings with corrugations (a) inside and (b) outside.WG### Wslot# Warm# neff# ?# ?Win# ?Wout#1# 150#nm# 270#nm# 1.85# 420#nm#10,#20#nm# 0#0# 10,#20,#30,#40#nm#2# 200#nm# 270#nm# 1.80# 430#nm#10,#20,#30,#40#nm# 0#0# 10,#20,#30,#40#nm#Table 4.1: Design variations for uniform slot waveguide Bragg gratings.109devices have 1000 grating periods. The effective index (ne f f ) of each waveguidewas calculated at 1550 nm. The grating period (?) was chosen to obtain a Braggwavelength close to 1550 nm while being compatible with the foundry design rules.Figure 4.5 shows the top view SEM images of two fabricated devices. Again,we used square sidewall corrugations in the mask layout, as illustrated in Fig-ure 4.4. However, as is clearly seen in Figure 4.5, the fabricated corrugations wererounded and resemble sinusoidal shapes due to lithographic effects.500 nm!500 nm!(a)! (b)!Figure 4.5: Top view SEM images of the fabricated slot waveguide Bragggratings: (a) corrugation inside for Wslot = 150 nm, Warm = 270 nm, and?Win = 20 nm. (b) corrugations outside for Wslot = 150 nm, Warm = 270 nm,and ?Wout = 40 nm.In order to minimize the total footprint and bending losses, we use 500 nm widestrip waveguides for the routing, as well as for the Y-branch design. The couplingbetween the strip and slot waveguides is realized through mode converters [118].As shown in Figure 4.6, one arm of the slot waveguide expands linearly in thecoupling region and eventually becomes the strip waveguide. The other arm isslightly tilted in the coupling region, with its width and distance from the first armunchanged; then after the coupling region, it bends away and tails off. The couplinglength is 5 ?m to ensure that the coupling loss is negligible [118?120]. Figure 4.7shows the SEM image of a fabricated strip-to-slot mode converter.110500 nm!5 ?m!x (?m)y (?m)  ?0.6 ?0.4 ?0.2 0 0.2 0.4 0.6?0.200.20.400.20.40.60.81x (?m)y (?m)W=500 nm, Air Cladding, TE  ?0.5 0 0.5?0.200.20.400.20.40.60.81Figure 4.6: Schematic of the strip-to-slot mode converter (not to scale).Figure 4.7: SEM image of a strip-to-slot mode converter as illustrated inFigure 4.6.1114.2.2 Measurement ResultsFigure 4.8 shows the measured raw spectral responses of a uniform grating. Thetransmission spectrum shows a deep notch with an extinction ratio greater than40 dB. The centre wavelength is about 1550 nm, in good agreement with the designvalue. Accordingly, a peak is seen in the reflection spectrum. The peak power isabout 3 dB below the transmission level, corresponding to the extra loss of theY-branch. The Y-branch also has weak parasitic back-reflection due to the abruptwaveguide discontinuity, which limits the noise floor of the reflection spectrum.1500 1520 1540 1560 1580 1600?70?65?60?55?50?45?40?35?30?25?20Wavelength (nm)Response (dB)  ReflectionTransmissionFigure 4.8: Measured raw spectra of a uniform grating designed on WG1with ?Wout = 10 nm, showing a deep notch with an extinction ratio greaterthan 40 dB at about 1550 nm.Figure 4.9 shows the measured transmission spectra for the devices based onWG1. The spectra were normalized by using a straight waveguide as a referenceto subtract the insertion loss, i.e., the envelope of the transmission spectrum inFigure 4.8. We can see that all the devices exhibit high extinction ratios of about40 dB. As the corrugation width is increased, the stop-band becomes broader dueto the increased grating coupling coefficient.The bandwidths for all design variations are also plotted versus corrugationwidth in Figure 4.10. We can see that the bandwidth ranges from 2 nm to more than20 nm. The green curve is well above the other three curves, and the device using1121540 1550 1560 1570 1580?50?40?30?20?100Wavelength (nm)Transmission (dB)?Win=10 nm?Win=20 nm1540 1545 1550 1555 1560?50?40?30?20?100Wavelength (nm)Transmission (dB)?Wout=10 nm?Wout=20 nm?Wout=30 nm?Wout=40 nm(a)! (b)!Figure 4.9: Measured transmission spectra of the uniform gratings designedon WG1. (a) corrugations inside, (b) corrugations outside. For both configu-rations, the stop-band becomes broader with increasing corrugation width.10 15 20 25 30 35 4024681020?W (nm)Bandwidth (nm)  WG1?InWG1?OutWG2?InWG2?OutFigure 4.10: Measured bandwidth versus designed corrugation width onWG1 and WG2. WG1 with inside corrugations shows the largest bandwidthdue to the strongest perturbation.113WG1 with 20 nm inside corrugations have the largest grating coupling coefficient.An intuitive explanation is that the optical field is strongly confined in the slot,as shown in Figure 4.2, and a small corrugation can have a large impact on thefield. Increasing the slot width reduces the optical confinement in the slot, and,therefore, the effect of a particular corrugation inside the slot of WG2 is smallerthan it is in WG1, which is why the red curve is below the green curve. Whenthe corrugations are placed on the outside of the slot waveguide, in both WG1 andWG2, the bandwidths are narrower and very similar to each other, due to the factthat the evanescent field tails are relatively weak.4.3 Phase-Shifted GratingsIn this section, we will discuss phase-shifted gratings in slot waveguides. Experi-mental results show Q factors up to 3?104. This is higher than all reported valuesfor slot waveguide ring resonators, which usually suffer from large bending lossesand mode mismatch losses.4.3.1 Design and FabricationFigure 4.11(a) shows the schematic of a phase-shifted Bragg grating using corru-gations on the outside of the slot waveguide. The length of the phase shift is equalto one grating period. On each side of the phase shift, there are N grating periodsthat function as a distributed Bragg reflector (DBR). The principle of operation isthe same as in strip waveguide, as discussed in Section 2.6, i.e., a cavity is createdby the phase shift and a resonant peak will appear at the centre of the stop-bandof the transmission spectrum. The only difference is that the optical mode is con-centrated in the slot region. Figure 4.11(b) shows a top view SEM image of afabricated device, with the phase shift highlighted in the dashed box.In order to better understand this structure, we also performed 3D-FDTD sim-ulations. Figure 4.11(c) shows a simulated transmission spectrum featuring a sharpresonant peak at the centre of the stop-band. Figure 4.12 shows the electric fielddistributions for the on-resonance state and an off-resonance state. Again, we cansee that the electric field is strongly confined in the slot region, whether the wave-length is on- or off-resonance. In Figure 4.12(a), the wavelength is 1543 nm, lo-114Phase Shift!(a)!500 nm!(b)!1500 1520 1540 1560 1580 160000.20.40.60.81Wavelength (nm)Transmission(c)!?"N x ?" N x ?"Figure 4.11: Phase-shifted Bragg gratings with corrugations on the outsideof the slot waveguide: (a) schematic diagram (not to scale), (b) SEM imageshowing the phase shift region of a fabricated device, (c) transmission spec-trum simulated by FDTD with the following geometric parameters: WG1,?Wout = 40 nm, and N = 50.cated in the left valley of the stop-band in Figure 4.11(c). The incoming light ismostly reflected back by the first DBR mirror on the left. As the wavelength shiftsto the resonant peak at 1550 nm, the cavity starts to resonate and light is concen-trated around the phase shift, as shown in Figure 4.12(b).As discussed in Section 2.6, we have known that the intrinsic Q factor of aphase-shifted grating is limited by the waveguide loss (see Eq. 2.10). Comparedwith conventional low-loss waveguides on silicon (i.e., strip and rib waveguides),slot waveguides exhibit relatively high losses. Typical reported loss values for slotwaveguides are on the order of 10 dB/cm [119, 121, 122]. Assuming that the lossis 10 dB/cm and ng = 3.35 (simulated value for WG1 in Table 4.1), the calculatedQI is about 5.89?104 at 1550 nm. If this resonator is critically coupled [14], thetotal Q is reduced by a factor of two and becomes about 2.95? 104. As will befurther discussed in next section, these approximations give values comparable to115z (?m)"x (?m)" "0.6"0.4"0.2"0.0"-0.2"-0.4"-0.6"-2                    4                    10                   16                   22                   28                   34                   40                   46"x (?m)" "0.6"0.4"0.2"0.0"-0.2"-0.4"-0.6"-2                    4                    10                   16                   22                   28                   34                   40                   46"(a)"(b)"z (?m)"phase shift"start" end"Figure 4.12: Electric field distributions for light incident from the left at (a)1543 nm and (b) 1550 nm. The simulation parameters are the same as inFigure 4.11(c). The field was recorded at the middle of the silicon waveg-uide in the vertical direction (i.e., corresponding to the plane of y=110 nm inFigure 4.2).the maximum Q values that we have observed experimentally.4.3.2 Measurement ResultsWe designed a number of phase-shifted gratings based on WG1 and WG2 (seeTable 4.1), using both inside-corrugation and outside-corrugation configurations.For each configuration, we used the largest corrugation width listed in Table 4.1in order to obtain the largest grating coupling coefficient. Figure 4.13 shows themeasured raw spectral responses of a phase-shifted grating. A sharp resonant peakis clearly seen at the centre of the stop-band in the transmission spectrum and,accordingly, a deep notch appears in the reflection spectrum.We varied the length of the gratings to study its impact on the Q factor. Fig-ure 4.14(a) shows a set of transmission spectra for devices based on WG1 with1161520 1530 1540 1550 1560 1570 1580?65?60?55?50?45?40?35?30Wavelength (nm)Response (dB)  TransmissionReflectionFigure 4.13: Measured raw spectra of a phase-shifted grating designed onWG1 with ?Wout = 40 nm and N = 300.(a)!100 200 300 400 500102103104105NQ factor  WG1,?Wout=40 nmWG1,?Win=20 nmWG2,?Wout=40 nmWG2,?Win=40 nm1530 1540 1550 1560 1570?35?30?25?20?15?10?50Wavelength (nm)Transmission (dB) N=200N=300N=400N=500(b)!Figure 4.14: (a) Measured transmission spectra for phase-shifted gratingsdesigned on WG1 with ?Wout = 40 nm and various lengths, (b) Q factor as afunction of N.117?Wout = 40 nm and for various lengths. As N is increased from 200 to 500, thestop-band becomes deeper because more light is reflected back. Also, the resonantpeak becomes sharper and the Q factor increases from 800 to 1.55?104, althoughthe peak amplitude slightly decreases. The Q factor is also plotted as a functionof N for all design variations in Figure 4.14(b). We can see that the green curve iswell above the other three curves, which verifies that WG1 with ?Win = 20 nm hasthe largest grating coupling coefficient. However, when N exceeds 200, the cavitybecomes over coupled and the amplitude of the resonant peak drops dramaticallyso that it cannot be observed. The blue and black curves are on the bottom andoverlap with each other, which verifies that WG1 and WG2 with ?Wout = 40 nmhave small, and similar, grating coupling coefficients. Finally, the red curve is inbetween the other three, again in agreement with the result in Figure 4.10, andshows the maximum Q factor of about 3?104 at N = 500. This is the highest Qfactor reported for slot waveguide resonators. This is also very close to the cal-culated Q factor under critical coupling condition, assuming that the wavelengthpropagation loss is 10 dB/cm. Recently, a few approaches have been reported toreduce the loss figures for slot waveguides [119, 123, 124]. For example, Spott etal. reported the lowest loss of 2 dB/cm by using asymmetric slot structures, but atthe expense of reduced optical confinement and a relatively complicated fabricationprocess [124]. However, we expect that further improvements in the lithographyand etching processes will reduce the loss of slot waveguides and lead to betterperformance for slot waveguide Bragg gratings.4.4 Biosensing Applications 2In this section, we present a novel silicon photonic biosensor using a phase-shiftedBragg grating in a slot waveguide. We experimentally demonstrate a high sensitiv-ity of 340 nm/RIU measured in salt solutions and a high quality factor of 1.5?104(in an aqueous medium), enabling a low LOD of 3?10?4 RIU. We also demon-strate the device?s ability to interrogate specific biomolecular interactions, resulting2A version of Section 4.4 has been published: X. Wang, J. Flueckiger, S. Schmidt, S. Grist,S. T. Fard, J. Kirk, M. Doerfler, K. C. Cheung, D. M. Ratner, and L. Chrostowski, ?A silicon photonicbiosensor using phase-shifted Bragg gratings in slot waveguide,? J. Biophotonics, vol. 6, no. 10,pp. 821-828, 2013.118in the first of its kind label-free biosensor.4.4.1 Silicon Photonic BiosensorsSilicon photonic biosensors have demonstrated great potential for label-free on-chip detection of biomolecules [14, 125]. Various optical structures [126, 127],such as microring [128?132] and microdisk resonators [14, 133], Bragg gratings[77, 134], and photonic crystals [135], have been developed on the SOI platform forbiological sensing applications. Nearly all of these sensors are based on measuringthe RI change of the surrounding environment, which allows for real-time anddirect detection of molecular interactions near the sensor surface. We know that thesensitivity is determined by the overlap between the electric field and the analyte.In many silicon photonic sensors (e.g., strip-waveguide-based ring resonators andBragg gratings, disk resonators, conventional photonic crystals), the majority of theelectric field is confined in the high-index material (i.e., silicon), thus it is difficultto interact with the analyte efficiently and the sensitivity is low. For example, inSection 2.6.3, we have demonstrated a strip waveguide grating sensor with a high Qfactor of 27600, but the sensitivity is only 58 nm/RIU, which leads to an intrinsicLOD of 9.3?10?4 RIU, similar to that of a strip waveguide ring resonator (e.g.,1.1?10?3 RIU in [128]).To enhance the sensitivity, an effective solution is to use slot waveguide struc-tures [36]. In slot waveguides, the electric field is concentrated inside the low-indexslot, leading to an increased field overlap with the analyte and hence a higher sensi-tivity. A slot waveguide ring resonator was first developed for biosensing applica-tions by Barrios et al. [136] on a Si3N4?SiO2 platform, showing a bulk sensitivityof 212 nm/RIU. This structure has also been demonstrated on the SOI platform byClaes et al. [137], showing a higher sensitivity of 298 nm/RIU, as well as a muchsmaller footprint due to the high index contrast of the material system.We also know that the LOD is another important parameter to evaluate the sen-sor performance. For single-resonator silicon photonic sensors, the LOD dependsnot only on the sensitivity but also on the Q factor and the system noise [14]. Forthe purpose of comparing different single-resonator sensors (neglecting the mea-surement system noise), the intrinsic LOD is defined as the RI change correspond-119ing to one resonance linewidth, which is inversely proportional to the sensitivityand the Q factor (see Eq. 2.16). Therefore, it is necessary to have both high sensi-tivity and high Q factor to minimize the intrinsic LOD. The afore-mentioned slotwaveguide ring resonators have shown high sensitivities, however, their Q factorsare typically very low, which is primarily limited by the high bending loss, modemismatch loss, and scattering loss due to waveguide roughness [137]. AlthoughBaehr-Jones et al. [121] demonstrated slot ring resonators with exceptionally highQ values (>20000 in air) in 2005, they pointed out that there are significant chal-lenges in the design and fabrication. Thus, their record Q values have not been re-produced since then, and in fact, other reported Q values since then are much lower(e.g., Barrios et al. reported Q=330 [136] and Claes et al. reported Q=1800 [137],both in water). Moreover, in general, ring resonators have limited free spectralranges (FSR) and demanding tolerance on the structural geometry (e.g., in orderto achieve a high extinction ratio, the critical coupling condition must be satisfied,which requires a strict control of the coupling region). Recently, another structurecalled a slotted photonic crystal [138, 139] has gained attention in this field due toits small modal volume and greatly enhanced light-matter interaction. However, itpresents additional design and fabrication challenges.As already demonstrated in the previous sections, slot waveguide Bragg grat-ings and resonators do not suffer from the high bending losses and mode mismatchlosses of slot waveguide ring resonators. Therefore, a much higher Q factor can beachieved with slot waveguide phase-shifted gratings. By combining the high sensi-tivity of the slot with the high Q factor of the phase-shifted grating, we experimen-tally obtained an intrinsic LOD of 3?10?4 RIU at 1550 nm. To our knowledge,this is the best experimental result for slot-based biosensors. Additional advan-tages of this sensor include simple optical design, a high extinction ratio, a smallfootprint, a large range for RI change (owing to single-mode operation), rapid in-tegration with microfluidic channels, and compatibility with commercial CMOSfabrication technology. Commercial CMOS compatibility is particularly impor-tant for producing high-volume, low-cost, and possibly disposable sensor chips byleveraging the economies of scale of the CMOS foundry process. To evaluate theperformance of this sensor, the silicon chip is integrated with a reversibly bondedpolydimethylsiloxane (PDMS) microfluidic chip. We observe that the experimen-120tal performance of the sensor is in excellent agreement with numerical simulations.The performance of the biosensor in a modified biological sandwich assay is alsopresented.4.4.2 Design and FabricationFigure 4.15 shows the schematic diagram of the sensor. The design parameters areas follows: Warm = 270 nm, Wslot = 150 nm, ?Wout = 40 nm, ? = 440 nm, andN = 150. The simulated Bragg wavelength is around 1530 nm when the claddingis water (n =1.33). The total length of this sensor is about 132 ?m. The footprint,however, is very small because the sensor is just a waveguide that is less than 1 ?mwide, with a total area smaller than 132 ?m2. An SEM image of the fabricatedSiO2!Si!Light!Phase shift!Fluidic channel!Figure 4.15: Schematic diagram of the sensor integrated with the microfluidicchannel.device is shown in Figure 4.16.The microfluidic channels were fabricated using PDMS soft lithography [140].Briefly, SU-8 photoresist (MicroChem) was spin cast onto standard silicon wafersto a thickness of approximately 80 ?m, then patterned using UV exposure througha transparency mask containing the microfluidic channel designs. After resist de-121500 nm!Phase !shift!Uniform !grating!660 nm!440 nm!Figure 4.16: SEM image of the fabricated device. Note that the phase shift inthe central region can be identified by measuring the spacing between the grat-ing grooves. Here, the spacing with the phase shift is 660 nm, correspondingto 1.5 times the grating period.velopment PDMS prepolymer and curing agent (Sylgard), mixed at a ratio of 10:1,were cast onto the mold and cured. The PDMS was then demolded and the indi-vidual microfluidic chips were diced and their inlet and outlet holes bored. Fluidicconnections were made using friction fit fluid dispensing tips (EFD) interfaced withstandard silastic tubing and connected to a syringe pump (Chemyx Nexus 3000).NaCl solutions of varying concentrations (in deionized water) were used for therefractive index sensitivity calibration of the sensor. For these experiments, the sy-ringe pump was used to deliver deionized water, 62.5 mM, 125 mM, 250 mM, and500 mM solutions through the microfluidic channels atop the sensors, interrupt-ing flow briefly between reagent changes. The refractive indices of these solutionswere measured using a digital refractometer (Reichert AR200).4.4.3 Experiments and DiscussionFigure 4.17 shows the measured transmission spectrum of the sensor immersed indeionized water. As expected, a sharp resonance peak appears at the centre of the1221520 1525 1530 1535 1540?55?50?45?40?35?30?25?20Wavelength (nm)Power (dBm)Q ? 1.5 x 104"Figure 4.17: Measured transmission spectrum of the sensor immersed indeionized water.stop band. The FWHM linewidth of this resonance is about 0.1 nm, correspondingto a Q factor of about 1.5?104. This ?in-water? Q factor is much higher thanthose of the reported slot waveguide ring resonators [136, 137] and the slottedphotonic crystal cavities [138]. Also of interest is that the resonance peak exhibitsa large extinction ratio of larger than 20 dB, which is rarely seen in other slot-basedbiosensors such as ring resonators.Bulk SensitivityFigure 4.18(a) shows the measured transmission spectra of the sensor covered withdifferent NaCl concentrations. For each concentration, we measured the opticalspectra multiple times (every?1.5 minutes) to verify the reliability and repeatabil-ity. The peak wavelength shift during the six steps is also shown in Figure 4.18(b).Since the refractive indices of the salt solutions are already known, we plot thepeak wavelength shift as a function of the refractive index in Figure 4.19. Weclearly observe that the experimental result agrees well with the simulation result.The sensitivity (S) is about 340 nm/RIU, which is higher than those of the reportedslot waveguide ring resonators [136, 137, 141?143].1231528 1528.5 1529 1529.5 1530 1530.5 1531 1531.5 1532?55?50?45?40?35?30?25?20Wavelength (nm)Power (dBm)1&6    2  3     4           5 !0 10 20 30 40 5015291529.21529.41529.61529.815301530.21530.41530.61530.81531Measurement NumberPeak Wavelength (nm)1        2          3        4          5         6 !(a)!(b)!Sa pl !Figure 4.18: Measurement results for various NaCl concentrations: (a) trans-mission spectra for all the measurements, (b) peak wavelength shift during thesalt steps. Each color represents a NaCl concentration. Steps 1 and 6 corre-spond to 0 mM, and Steps 2 to 5 correspond to 62.5 mM, 125 mM, 250 mM,and 500 mM solutions, respectively.1241.332 1.333 1.334 1.335 1.336 1.337 1.338 1.339?0.500.511.522.5Refractive Index (RIU)Peak Wavelength Shift (nm)S=340nm/RIU  ExperimentSimulationFigure 4.19: Measured and simulated peak wavelength shift as a functionof the refractive index of the salt solution. For the experimental data, thesymmetric error bars are two standard deviation units in length.Based on the Q factor (1.5?104) and the sensitivity (340 nm/RIU), the intrinsicLOD is about 3?10?4. This intrinsic LOD is, to date, the best experimental resultfor slot-based biosensors.BiosensingTo demonstrate the biosensing capability, we conducted a modified sandwich assayinvolving well-characterized biomolecules with high binding affinities. The results,together with the accompanying reagent sequencing, are shown in Figure 4.20(a)and (b) respectively. Reagents were delivered to the sensor at 10 ?L/min viareversibly-bonding PDMS microfluidics, briefly pausing flow to switch reagents.To limit the effects of thermal drift, the optical stage was thermally controlled to30C, thereby negating minor perturbations in the ambient temperature of the room.Optical scans of the resonant peaks were taken every 45 seconds and a signal base-line was established using phosphate buffered saline (PBS) for 20 minutes priorto sequencing other reagents. Lorentzian fitting of the optical spectra was used todetermine the resonance wavelength.To orient the capture antibody on the sensor surface, Protein-A (1 mg/mL)1250 50 100 15015301531153215331534Peak Wavelength (nm)Time (min)012345Relative Wavelength Shift (nm)A B C D EBSABiotinProtein-ABSAAnti-SASAA BDPBSSensorEC(a)!(b)!Figure 4.20: Biosensing experimental results: (a) depicts the resonancewavelength shifts as the experiment progressed while (b) illustrates reagentsequencing corresponding to regions [A-E] in (a). Region A = Protein-A(1 mg/mL), B = anti-streptavidin (SA) (125 ?g/mL), C = Bovine Serum Al-bumen (BSA) (2 mg/mL), D = streptavidin (SA) (1.8 ?M), E = Biotin-BSA(2.5 mg/mL). Introduction of reagent in each region was followed by a PBS-wash, as shown by the short, black-dashed line mid-way through each region.126was passively adsorbed to its surface [144] followed by a PBS wash to removeun-bound or loosely bound protein as shown in region [A] of Figure 4.20(a) and(b). Next, the capture antibody, anti-Streptavidin (antiSA, 125 ?g/mL), was intro-duced to functionalize the sensor?s surface. Upon adsorption, the 160 kDa proteinresults in a 2 nm resonant wavelength shift, as can be clearly seen in region [B].To ensure our biological interactions were specific, the functionalized sensor waschallenged with bovine serum albumin (BSA, 2 mg/mL), as shown in Region [C].After a PBS wash, the signal drops towards the pre-BSA baseline, as expected.We hypothesize that the slight residual BSA is the result of incomplete rinsing byPBS or by permanent adsorption of BSA to the sensor surface resulting from in-complete coverage of the first Protein-A monolayer [145]. Next, we introducedthe target analyte, Streptavidin (SA, 1.8 ?M), resulting in irreversible binding toantiSA even after the PBS rinse, as shown in region [D]. Finally, to illustrate asecondary amplification step, capture of biotinylated BSA (b-BSA, 2.5 mg/mL) tothe immobilized SA is shown in region [E]. To validate that the wavelength shiftsare as expected, we performed a quantitative analysis on the first protein mono-layer based on observations by Coen et al. [145]. They determined coverage ofthe first monolayer on the waveguide surface to be 10-50% and that the successfulimmobilization of an IgG?s Fc domain to a Protein-A receptor occurred on the sec-ond or third add layer. This presents a challenge in quantifying an exact numberof bound molecules, especially for subsequent steps where molecules have multi-ple binding domains that may or may not be occupied. In addition, Claes et. al.discovered that biomolecules do not completely adhere and bind within the slot[137], creating additional uncertainty for an accurate analysis. Using LumericalMODE solver, we modelled a 1 nm thick monolayer of Protein-A (42 kDa with aRI = 1.48 [146]) assuming: (1) moderate packing density on the waveguide surfacedue to steric hindrances, (2) limited diffusion into the slot, and (3) a sparse 3 nmfilm representing the second add layer. The simulated wavelength shift is twicethe experimentally observed value, indicating 50% surface coverage with a 1 nmfilm. Based on the relative size and molecular weights of the subsequent molecules[147, 148], the resulting proportional wavelength shifts are also as expected. Thissimple assay demonstrates the specific and selective biosensing capability of ournovel sensor and its potential for use in clinically relevant diagnostic settings.127Future work will include the integration of this sensor in architectures that al-low for multiplexing and reference sensors, ultimately enabling more sophisticatedlabel-free assays. In addition, surface functionalization strategies and chemistrieswe recently published in [149] will be explored to demonstrate its capability as amedical diagnostic sensor for use in complex media like saliva, serum, and wholeblood.4.5 SummaryThe integration of Bragg gratings in slot waveguides offers many new possibilities.It combines the superior sensing ability of slot waveguides with the flexibility inthe design of the spectral response of Bragg gratings. The uniform gratings showhigh extinction ratios of 40 dB and bandwidths ranging from 2 nm to more than20 nm. The phase-shifted gratings show Q factors up to 3?104, much higher thanmost reported values for slot waveguide ring resonators. This family of devicesalso has great potential for optical modulation, nonlinear optics and optical signalprocessing.128Chapter 5Conclusion and Future Work5.1 ConclusionIn this thesis, we have studied silicon photonic waveguide Bragg gratings. Threetypes of waveguides ? strip, rib, and slot waveguides ? have been investigated,each as a dedicated chapter. In each chapter, we presented the design and exper-imental results of various grating devices. We have also demonstrated a numberof applications using our grating devices. The major contributions of this researchinclude:1. Towards CMOS-compatible silicon photonics. Most of the early work onintegrated waveguide Bragg gratings relies on e-beam lithography fabrica-tion. Though attractive for prototyping, e-beam lithography has one fataldrawback ? low throughput, e.g., it could literally take hours to write onlyone wafer, preventing it from real productions. In this thesis, all of the sil-icon chips were fabricated using commercial CMOS fabrication facilities,paving the way for the future development and commercialization of siliconphotonic Bragg gratings.2. A comprehensive study of uniform Bragg gratings in strip waveguides. Wehave investigated almost all possible design variations, including grating pe-riod, corrugation width, waveguide width, cladding material, grating length,and corrugation shape. The experimental results for most design variations129agree with theoretical analysis and/or simulation results. However, we shouldemphasize the results for grating length variations. We have observed thatthe propagation losses of 500 nm strip waveguide gratings are within therange of 2.5?4.5 dB/cm, independent of the corrugation width. To our knowl-edge, this is the first report on the propagation loss of silicon photonic Bragggratings. More interestingly, we have observed that as the grating length isincreased beyond a certain value, the bandwidth becomes broader, which isprimarily due to Si thickness variations.3. Lithography effects. We have demonstrated a model to predict the fabrica-tion imperfections of silicon photonic devices during the lithography pro-cess. This model has been validated for silicon photonic Bragg gratings bycomparing the simulation results of the virtually fabricated gratings and theexperimental results.4. Technical achievements:(a) Layout. We have discussed a number of practical techniques from thelayout point of view, such as using design hierarchy in the GDSII file,generating cells using scripts in Pyxis Layout, using Y-branch to char-acterize the reflection port, two common layout configurations ? indi-vidual fibers vs. fiber array, and a compact layout approach to increasethe space-efficiency on the chip.(b) Characterization. We have shown the importance of using a tunablelaser with low SSE to characterize grating devices with high extinc-tion ratios. In the absence of such a tunable laser source, we shouldoptimize the sweeping settings to obtain the largest dynamic range.5. Phase-shifted gratings in strip waveguides.(a) A comprehensive study of phase-shifted gratings in strip waveguides.We have discussed the basics of phase-shifted gratings, such as thestructure, physical interpretation from the cavity point of view, the Qfactor and the waveguide loss limitations. We have also investigated130several important design variations, including grating length and cor-rugation width. A maximum Q factor of 1.9?105 has been experimen-tally demonstrated. Optical nonlinearity has also been observed forhigh-Q phase-shifted gratings.(b) Application in biosensing. We have demonstrated a biosensor using astrip waveguide phase-shifted grating, showing a sensitivity of about58 nm/RIU and a Q factor of 27600, which leads to an intrinsic LODof about 9.3?10?4 RIU.(c) Application in microwave photonics and ultrafast optical signal pro-cessing [27, 108, 109].6. Sampled grating and the Vernier effect. We have demonstrated sampled grat-ings, as well as the Vernier effect using two slightly-mismatched sampledgratings, for the first time on the silicon photonics platform. They can beused in tunable lasers to achieve a wide tuning range.7. Narrow-band uniform Bragg gratings in rib waveguides. We have studiedsidewall corrugations either on the rib or on the slab. Experimental resultsshow that for the same corrugation width, the corrugation-on-slab configu-ration results in a smaller ? than the corrugation-on-rib configuration. Thesmallest ? we have obtained is about 1?103 m?1, corresponding to a band-width of about 0.2 nm.8. Multi-period gratings. We have demonstrated a multi-period grating con-cept, by taking advantage of the multiple sidewalls of the rib waveguide.The sidewalls of the rib and the slab are corrugated using different periods,resulting in two or more Bragg wavelengths that are controlled separately.This approach not only increases the design flexibility for custom opticalfilters but also reduces the device size and fabrication errors.9. Thermal sensitivity. We have studied the thermal sensitivities of strip andrib waveguide Bragg gratings, both showing that the Bragg wavelength in-creases with temperature by about 84 pm/oC.13110. Wafer-scale performance. We have studied the wafer-scale nonuniformity ofstrip and rib waveguide gratings. The general conclusion is that rib waveg-uide gratings have better uniformity than strip waveguide gratings. Anotherfinding is that the Bragg wavelength variation of rib waveguide gratings isprimarily caused by the Si thickness variations. Hence improving the SOIthickness uniformity is very important.11. Spiral gratings. We have demonstrated compact first-order Bragg gratingsusing a spiral rib waveguide. Our results show not only a significantly im-proved packing efficiency of about 21.8, but also a very narrow 3-dB band-width of 0.26 nm.12. Slot waveguide Bragg gratings.(a) We have demonstrated both uniform and phase-shifted gratings in slotwaveguides. The gratings are formed with periodic sidewall corruga-tions either on the inside or the outside of the slot waveguide. Experi-mental results show bandwidths ranging from 2 nm to more than 20 nmfor uniform gratings, and Q factors up to 3?104 for phase-shifted grat-ings.(b) Application in biosensing. We have demonstrated a novel biosensor us-ing a slot waveguide phase-shifted grating. Experimental results showa sensitivity of about 340 nm/RIU and a Q factor of 1.5?104, enablingan intrinsic LOD of about 3?10?4 RIU (lowest intrinsic LOD for slot-based biosensors). We have also demonstrated the device?s ability tointerrogate specific biomolecular interactions.5.2 Future Work? Apodized grating. As we have seen, uniform gratings often have large side-lobes in their reflection spectra. To reduce the level of the side-lobes, apodiza-tion should be used, i.e., varying the amplitude of the index modulation alongthe length of the grating. Fortunately, apodization is a mature technique thathas been widely used for fiber Bragg gratings and there are various apodiza-tion profiles [82, 150]. However, we should point out that to characterize132the reflection of apodized gratings, the Y?branch we used in this thesis is notappropriate because it has weak parasitic back-reflection due to the abruptwaveguide discontinuity, which limits the noise floor of the reflection spec-trum. To solve this problem, directional couplers or adiabatic couplers couldpossibly be used [151].? TM gratings. In this thesis, we have only focused on Bragg gratings operat-ing at TE polarization. Alternatively, we could design Bragg gratings at TMpolarization, which has a few advantages. First, the TM mode has very lowintensities around the waveguide sidewalls, therefore, the propagation loss islower than that of the TE mode. This also allows for smaller coupling coeffi-cients and is useful for narrow-band gratings. Moreover, the effective indexof the TM mode is much smaller than that of the TE mode, which meansthat the grating period has to be increased (by a factor of about 1.5) and thusreducing the fabrication challenge.? Active grating devices. Since the grating devices are sensitive to dimensionalvariations, it is necessary to develop tunable grating devices with accuratecontrol, e.g., using thermal heating or p-i-n structures. It is also interestingto design high-speed modulators using p-n junctions, as illustrated in Fig-ure 5.1.? More applications. In this thesis, we have demonstrated a number of ap-plications, however, we think that they represent just the tip of the iceberg.We expect that silicon photonic Bragg gratings will find more applicationsin silicon lasers [50], WDM systems, biosensors, microwave photonics, andoptical signal processing.? Last but not the least, real products! There are still many challenges thatmust be overcome before large-scale production can occur. Nonetheless,we expect that the silicon photonics community will keep making progresstowards the commercialization of silicon photonic chips. Specifically forsilicon photonic Bragg gratings, considerable effort will need to be given toimproving the fabrication process, e.g., using immersion lithography, betterwafer uniformity, and yield control.133(a)!(b)!p! n! n++!p++!SiO2! SiO2!Si! Si!metal! contact! metal! contact!90 nm!Figure 5.1: A proposed active grating device ? high-speed modulator basedon a p-n junction: (a) mask layout and (b) schematic of the cross section ofthe p-n junction.134Bibliography[1] Agilent Technologies, Agilent 81600B Tunable Laser Source Family (2013).? pages xi, 34[2] M. Lipson, ?Guiding, modulating, and emitting light on silicon ? challengesand opportunities,? J. Lightwave Technol. 23, 4222?4238 (2005). ? pages1[3] B. Jalali and S. Fathpour, ?Silicon photonics,? J. Lightwave Technol. 24,4600?4615 (2006). ? pages 2[4] R. Soref, ?The past, present, and future of silicon photonics,? IEEE J. Sel.Top. Quantum Electron. 12, 1678?1687 (2006). ? pages 1[5] D. Liang and J. E. Bowers, ?Recent progress in lasers on silicon,? NaturePhoton. 4, 511?517 (2010). ? pages 2, 4, 5[6] J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, ?Large-scale nanophotonic phased array,? Nature 493, 195?199 (2013). ? pages3[7] M. Hochberg and T. Baehr-Jones, ?Towards fabless silicon photonics,? Na-ture Photon. 4, 492?494 (2010). ? pages 3, 8[8] http://www.epixfab.eu, (Retrieved on Nov. 22, 2013). ? pages 3, 5, 14, 19,93[9] http://www.opsisfoundry.org, (Retrieved on Nov. 22, 2013). ? pages 3, 5,19[10] T.-Y. Liow, K.-W. Ang, Q. Fang, J.-F. Song, Y.-Z. Xiong, M.-B. Yu, G.-Q.Lo, and D.-L. Kwong, ?Silicon modulators and germanium photodetectorson SOI: Monolithic integration, compatibility, and performance optimiza-tion,? IEEE J. Sel. Top. Quantum Electron. 16, 307?315 (2010). ? pages3135[11] T.-Y. Liow, J. Song, X. Tu, A.-J. Lim, Q. Fang, N. Duan, M. Yu, and G.-Q. Lo, ?Silicon optical interconnect device technologies for 40 Gb/s andbeyond,? IEEE J. Sel. Top. Quantum Electron. 19, 8200312 (2013).? pages3[12] D. A. B. Miller, ?Device requirements for optical interconnects to siliconchips,? Proc. IEEE 97, 1166?1185 (2009). ? pages 4[13] G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, ?Siliconoptical modulators,? Nature Photon. 4, 518?526 (2010). ? pages 4, 6[14] L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun,M. Webb, B. Nie, Z. Liang, K. C. Cheung, S. A. Schmidt, D. M. Ratner, andN. A. F. Jaeger, ?Silicon photonic resonator sensors and devices,? Proc. SPIE8236, 823620 (2012). ? pages 4, 62, 106, 115, 119[15] S. Talebi Fard, S. M. Grist, V. Donzella, S. A. Schmidt, J. Flueckiger,X. Wang, W. Shi, A. Millspaugh, M. Webb, D. M. Ratner, K. C. Cheung, andL. Chrostowski, ?Label-free silicon photonic biosensors for use in clinicaldiagnostics,? Proc. SPIE 8629, 862909 (2013). ? pages 4, 70, 106[16] J. T. Robinson, L. Chen, and M. Lipson, ?On-chip gas detection in siliconoptical microcavities,? Opt. Lett. 16, 4296?4301 (2008). ? pages 4, 5[17] J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, andR. Baets, ?Tunable optical forces between nanophotonic waveguides,? Na-ture Nano. 4, 510?513 (2009). ? pages 4[18] D. Van Thourhout and J. Roels, ?Optomechanical device actuation throughthe optical gradient force,? Nature Photon. 4, 211?217 (2010). ? pages 4[19] J. Mower and D. Englund, ?Efficient generation of single and entangledphotons on a silicon photonic integrated chip,? Phys. Rev. A 84, 052326(2011). ? pages 4[20] D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki,C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller,J. L. O?Brien, and M. G. Thompson, ?Quantum interference and manipu-lation of entanglement in silicon wire waveguide quantum circuits,? New J.Phys. 14, 045003 (2012). ? pages[21] N. Matsuda, H. Le Jeannic, H. Fukuda, T. Tsuchizawa, W. J. Munro,K. Shimizu, K. Yamada, Y. Tokura, and H. Takesue, ?A monolithically in-136tegrated polarization entangled photon pair source on a silicon chip,? Sci.Rep. 2 (2012). ? pages[22] J. O?Brien, B. Patton, M. Sasaki, and J. Vuc?kovic?, ?Focus on integratedquantum optics,? New J. Phys. 15, 035016 (2013). ? pages 4[23] J. Leuthold, C. Koos, and W. Freude, ?Nonlinear silicon photonics,? NaturePhoton. 4, 535?544 (2010). ? pages 4[24] R. Soref, ?Mid-infrared photonics in silicon and germanium,? Nature Pho-ton. 4, 495?497 (2010). ? pages 4[25] D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Cap-many, ?Integrated microwave photonics,? Laser & Photonics Reviews 7,506?538 (2013). ? pages 4[26] M. Ko, J.-S. Youn, M.-J. Lee, K.-C. Choi, H. Rucker, and W.-Y. Choi, ?Sil-icon photonics-wireless interface IC for 60-GHz wireless link,? IEEE Pho-ton. Technol. Lett. 24, 1112?1114 (2012). ? pages[27] M. Burla, L. R. Corte?s, M. Li, X. Wang, L. Chrostowski, and J. A. na,?Integrated waveguide Bragg gratings for microwave photonics signal pro-cessing,? Opt. Express 21, 25120?25147 (2013). ? pages 4, 70, 131[28] http://teraxion.com/en/crx-sff, (Retrieved on Nov. 22, 2013). ? pages 4, 7[29] C. Xia, L. Chao, and T. H. K., ?Device engineering for silicon photonics,?NPG Asia Mater. 3, 34?40 (2011). ? pages 4[30] J. Michel, J. Liu, and L. C. Kimerling, ?High-performance Ge-on-Si pho-todetectors,? Nature Photon. 4, 527?534 (2010). ? pages 4[31] W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luys-saert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, ?Nanophotonicwaveguides in silicon-on-insulator fabricated with CMOS technology,? J.Lightwave Technol. 23, 401?412 (2005). ? pages 4, 14[32] W. Bogaerts, S. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos,D. Van Thourhout, and R. Baets, ?Silicon-on-insulator spectral filters fab-ricated with CMOS technology,? IEEE J. Sel. Top. Quantum Electron. 16,33?44 (2010). ? pages 4, 20[33] R. A. Soref, J. Schmidtchen, and K. Petermann, ?Large single-mode ribwaveguides in GeSi-Si and Si-on-SiO2,? IEEE J. Quantum Electron. 27,1971?1974 (1991). ? pages 4, 79137[34] P. Dong, W. Qian, S. Liao, H. Liang, C.-C. Kung, N.-N. Feng, R. Shafi-iha, J. Fong, D. Feng, A. V. Krishnamoorthy, and M. Asghari, ?Low lossshallow-ridge silicon waveguides,? Opt. Express 18, 14474?14479 (2010).? pages 5, 81[35] W. Bogaerts and S. K. Selvaraja, ?Compact single-mode silicon hybridrib/strip waveguide with adiabatic bends,? IEEE Photon. J. 3, 422?432(2011). ? pages 5[36] V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, ?Guiding and confininglight in void nanostructure,? Opt. Lett. 29, 1209?1211 (2004). ? pages 5,107, 119[37] R. Ding, T. Baehr-Jones, W.-J. Kim, A. Spott, M. Fournier, J.-M. Fedeli,S. Huang, J. Luo, A. K.-Y. Jen, L. Dalton, and M. Hochberg, ?Sub-voltsilicon-organic electro-optic modulator with 500 MHz bandwidth,? J. Light-wave Technol. 29, 1112?1117 (2011). ? pages 5[38] C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esem-beson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold,?All-optical high-speed signal processing with silicon-organic hybrid slotwaveguides,? Nature Photon. 3, 216?219 (2009). ? pages 5[39] Y. Liu, T. Baehr-Jones, J. Li, A. Pomerene, and M. Hochberg, ?Efficient stripto strip-loaded slot mode converter in silicon-on-insulator,? IEEE Photon.Technol. Lett. 23, 1496?1498 (2011). ? pages 5[40] R. Won, ?Integrating silicon photonics,? Nature Photon. 4, 498?499 (2010).? pages 5[41] C. Kopp, S. Bernabe?, B. Bakir, J.-M. Fedeli, R. Orobtchouk, F. Schrank,H. Porte, L. Zimmermann, and T. Tekin, ?Silicon photonic circuits: On-CMOS integration, fiber optical coupling, and packaging,? IEEE J. Sel. Top.Quantum Electron. 17, 498?509 (2011). ? pages 5[42] G. Roelkens, D. Vermeulen, S. Selvaraja, R. Halir, W. Bogaerts, andD. Van Thourhout, ?Grating-based optical fiber interfaces for silicon-on-insulator photonic integrated circuits,? IEEE J. Sel. Top. Quantum Electron.17, 571?580 (2011). ? pages 5, 23[43] A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, andP. De Dobbelaere, ?A grating-coupler-enabled CMOS photonics platform,?IEEE J. Sel. Top. Quantum Electron. 17, 597?608 (2011). ? pages 23138[44] L. He, Y. Liu, C. Galland, A.-J. Lim, G.-Q. Lo, T. Baehr-Jones, andM. Hochberg, ?A high-efficiency nonuniform grating coupler realized with248-nm optical lithography,? IEEE Photon. Technol. Lett. 25, 1358?1361(2013). ? pages 5[45] H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia,?A continuous-wave Raman silicon laser,? Nature 433, 725?728 (2005). ?pages 5[46] J. Liu, X. Sun, R. Camacho-Aguilera, L. C. Kimerling, and J. Michel, ?Ge-on-Si laser operating at room temperature,? Opt. Lett. 35, 679?681 (2010).? pages 5[47] M. J. R. Heck, H.-W. Chen, A. W. Fang, B. R. Koch, D. Liang, H. Park,M. N. Sysak, and J. E. Bowers, ?Hybrid silicon photonics for optical inter-connects,? IEEE J. Sel. Top. Quantum Electron. 17, 333?346 (2011). ?pages 5[48] A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bow-ers, ?Electrically pumped hybrid AlGaInAs-silicon evanescent laser,? Opt.Express 14, 9203?9210 (2006). ? pages 5[49] A. W. Fang, E. Lively, Y.-H. Kuo, D. Liang, and J. E. Bowers, ?A distributedfeedback silicon evanescent laser,? Opt. Express 16, 4413?4419 (2008). ?pages 6[50] A. W. Fang, B. R. Koch, R. Jones, E. Lively, D. Liang, Y.-H. Kuo, andJ. E. Bowers, ?A distributed Bragg reflector silicon evanescent laser,? IEEEPhoton. Technol. Lett. 20, 1667?1669 (2008). ? pages 6, 133[51] M. N. Sysak, J. O. Anthes, D. Liang, J. E. Bowers, O. Raday, and R. Jones,?A hybrid silicon sampled grating DBR tunable laser,? in IEEE Conferenceon Group IV Photonics (GFP), Cardiff, UK pp. 55?57 (2008). ? pages 6[52] D. Liang, M. Fiorentino, T. Okumura, H.-H. Chang, D. T. Spencer, Y.-H.Kuo, A. W. Fang, D. Dai, R. G. Beausoleil, and J. E. Bowers, ?Electrically-pumped compact hybrid silicon microring lasers for optical interconnects,?Opt. Express 17, 20355?20364 (2009). ? pages 6[53] J. V. Campenhout, L. Liu, P. R. Romeo, D. V. Thourhout, C. Seassal, P. Re-greny, L. D. Cioccio, J.-M. Fedeli, and R. Baets, ?A compact SOI-integratedmultiwavelength laser source based on cascaded InP microdisks,? IEEEPhoton. Technol. Lett. 20, 1345?1347 (2008). ? pages 6139[54] R. A. Soref and B. R. Bennett, ?Electrooptical effects in silicon,? IEEE J.Quantum Electron. 23, 123?129 (1987). ? pages 6[55] L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. D.Keil, and T. Franck, ?High speed silicon Mach-Zehnder modulator,? Opt.Express 13, 3129?3135 (2005). ? pages 6[56] Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, ?Micrometre-scale siliconelectro-optic modulator,? Nature 435, 325?327 (2005). ? pages 6[57] L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen,N. Izhaky, and M. Paniccia, ?40 Gbit/s silicon optical modulator for high-speed applications,? Electron. Lett. 43, 1196?1197 (2007). ? pages 6[58] M. Lipson, ?Compact electro-optic modulators on a silicon chip,? IEEE J.Sel. Top. Quantum Electron. 12, 1520?1526 (2006). ? pages 6[59] F. Gardes, A. Brimont, P. Sanchis, G. Rasigade, D. Marris-Morini,L. O?Faolain, F. Dong, J. Fedeli, P. Dumon, L. Vivien, T. Krauss, G. Reed,and J. Marti, ?High-speed modulation of a compact silicon ring resonatorbased on a reverse-biased pn diode,? Opt. Express 17, 21986?21991 (2009).? pages 7[60] P. Dong, S. Liao, D. Feng, H. Liang, D. Zheng, R. Shafiiha, C.-C. Kung,W. Qian, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, ?LowVpp, ultralow-energy, compact, high-speed silicon electro-optic modulator,?Opt. Express 17, 22484?22490 (2009). ? pages 7[61] S. Liao, N.-N. Feng, D. Feng, P. Dong, R. Shafiiha, C.-C. Kung, H. Liang,W. Qian, Y. Liu, J. Fong, J. E. Cunningham, Y. Luo, and M. Asghari,?36 GHz submicron silicon waveguide germanium photodetector,? Opt. Ex-press 19, 10967?10972 (2011). ? pages 7[62] M. Hochberg, N. Harris, R. Ding, Y. Zhang, A. Novack, Z. Xuan, andT. Baehr-Jones, ?Silicon photonics: the next fabless semiconductor indus-try,? IEEE Solid-State Circuits Magazine 5, 48?58 (2013). ? pages 7[63] A. Liu, L. Liao, Y. Chetrit, J. Basak, H. Nguyen, D. Rubin, and M. Pan-iccia, ?Wavelength division multiplexing based photonic integrated circuitson silicon-on-insulator platform,? IEEE J. Sel. Top. Quantum Electron. 16,23?32 (2010). ? pages 7140[64] S. Koehl, A. Liu, and M. Paniccia, ?Integrated silicon photonics: Harnessingthe data explosion,? Optics & Photonics News 22, 24?29 (2011). ? pages7[65] http://www.luxtera.com/, (Retrieved on Nov. 22, 2013). ? pages 7[66] http://genalyte.com/technology-overview/, (Retrieved on Nov. 22, 2013).?pages 7[67] J. Buus, M.-C. Amann, and D. J. Blumenthal, Tunable Laser Diodes andRelated Optical Sources, 2nd Ed. (John Wiley & Sons, Inc., 2005).? pages9, 10, 12, 58[68] T. E. Murphy, J. T. Hastings, and H. I. Smith, ?Fabrication and character-ization of narrow-band Bragg-reflection filters in silicon-on-insulator ridgewaveguides,? J. Lightwave Technol. 19, 1938?1942 (2001). ? pages 12,13, 79, 80[69] L. Liao, A. Liu, S. Pang, and M. J. Paniccia, ?Tunable Bragg grating filtersin SOI waveguides,? in Optical Amplifiers and Their Applications/IntegratedPhotonics Research, paper IThE2 (2004). ? pages 12[70] S. Homampour, M. P. Bulk, P. E. Jessop, and A. P. Knights, ?Thermal tuningof planar Bragg gratings in silicon-on-insulator rib waveguides,? PhysicaStatus Solidi (C) 6, S240?S243 (2009). ? pages 12[71] R. Loiacono, G. T. Reed, G. Z. Mashanovich, R. Gwilliam, S. J. Henley,Y. Hu, R. Feldesh, and R. Jones, ?Laser erasable implanted gratings forintegrated silicon photonics,? Opt. Express 19, 10728?10734 (2011). ?pages 12[72] Q. Fang, J. F. Song, X. Tu, L. Jia, X. Luo, M. Yu, and G. Q. Lo, ?Carrier-induced silicon Bragg grating filters with a p-i-n junction,? IEEE Photon.Technol. Lett. 25, 810?812 (2013). ? pages 13[73] J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, ?Optical waveg-uides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,? J. Vac. Sci. Technol. B 20, 2753?2757 (2002). ? pages13, 79, 80[74] I. Giuntoni, A. Gajda, M. Krause, R. Steingru?ber, J. Bruns, and K. Peter-mann, ?Tunable Bragg reflectors on silicon-on-insulator rib waveguides,?Opt. Express 17, 18518?18524 (2009). ? pages 79, 80141[75] I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda,J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, ?Deep-UV tech-nology for the fabrication of Bragg gratings on SOI rib waveguides,? IEEEPhoton. Technol. Lett. 21, 1894?1896 (2009). ? pages 13[76] D. T. H. Tan, K. Ikeda, R. E. Saperstein, B. Slutsky, and Y. Fainman, ?Chip-scale dispersion engineering using chirped vertical gratings,? Opt. Lett. 33,3013?3015 (2008). ? pages 13[77] A. S. Jugessur, J. Dou, J. S. Aitchison, R. M. De La Rue, and M. Gnan, ?Aphotonic nano-Bragg grating device integrated with microfluidic channelsfor bio-sensing applications,? Microelectron. Eng. 86, 1488?1490 (2009).? pages 13, 106, 119[78] D. T. H. Tan, K. Ikeda, and Y. Fainman, ?Cladding-modulated Bragg grat-ings in silicon waveguides,? Opt. Lett. 34, 1357?1359 (2009). ? pages 13[79] D. T. H. Tan, K. Ikeda, and Y. Fainman, ?Coupled chirped vertical gratingsfor on-chip group velocity dispersion engineering,? Appl. Phys. Lett. 95,141109 (2009). ? pages 13[80] D. T. H. Tan, K. Ikeda, S. Zamek, A. Mizrahi, M. P. Nezhad, A. V. Krish-namoorthy, K. Raj, J. E. Cunningham, X. Zheng, I. Shubin, Y. Luo, andY. Fainman, ?Wide bandwidth, low loss 1 by 4 wavelength division mul-tiplexer on silicon for optical interconnects,? Opt. Express 19, 2401?2409(2011). ? pages 13[81] A. Simard, N. Belhadj, Y. Painchaud, and S. LaRochelle, ?Apodized silicon-on-insulator Bragg gratings,? IEEE Photon. Technol. Lett. 24, 1033?1035(2012). ? pages 13[82] T. Erdogan, ?Fiber grating spectra,? J. Lightwave Technol. 15, 1277?1294(1997). ? pages 13, 132[83] http://www.mint.ca/, (Retrieved on Nov. 22, 2013). ? pages 14[84] http://www.lumerical.com, (Retrieved on Nov. 22, 2013). ? pages 17, 47[85] P. Dumon, ?Ultra-compact integrated optical filters in silicon-on-insulatorby means of wafer-scale technology,? Ph.D. thesis, Ghent University (2007).? pages 18[86] L. Chrostowski, Silicon Photonics Design (Lukas Chrostowski, 2013). ?pages 20142[87] http://www.klayout.de, (Retrieved on Nov. 22, 2013). ? pages 22[88] http://www.designw.com/, (Retrieved on Nov. 22, 2013). ? pages 22[89] http://www.mentor.com/, (Retrieved on Nov. 22, 2013). ? pages 22, 47, 50[90] Y. Wang, ?Grating coupler design based on silicon-on-insulator,? Master?sthesis, University of British Columbia (2013). ? pages 23, 32[91] C. Lin, ?Photonic device design flow: from mask layout to device measure-ment,? Master?s thesis, University of British Columbia (2012). ? pages25[92] H. Yun, ?Design and characterization of a dumbbell micro-ring resonatorreflector,? Master?s thesis, University of British Columbia (2013). ? pages25[93] http://siepic.ubc.ca/probestation, (Retrieved on Nov. 22, 2013).? pages 28[94] E. Leckel, J. Sang, E. U. Wagemann, and E. Mueller, ?Impact of sourcespontaneous emission (SSE) on the measurement of DWDM components,?in Optical Fiber Communication Conference, paper WB4 (2000). ? pages32[95] X. Wang, W. Shi, M. Hochberg, K. Adam, E. Schelew, J. F. Young, N. A. F.Jaeger, and L. Chrostowski, ?Lithography simulation for the fabrication ofsilicon photonic devices with deep-ultraviolet lithography,? in IEEE Confer-ence on Group IV Photonics (GFP), San Diego, CA, 2012, paper ThP 17(2012). ? pages 45[96] S. K. Selvaraja, P. Jaenen, W. Bogaerts, D. VanThourhout, P. Dumon,and R. Baets, ?Fabrication of photonic wire and crystal circuits in silicon-on-insulator using 193-nm optical lithography,? J. Lightwave Technol. 27,4076?4083 (2009). ? pages 46, 47, 50, 53[97] W. Bogaerts, P. Bradt, L. Vanholme, P. Bienstman, and R. Baets, ?Closed-loop modeling of silicon nanophotonics from design to fabrication and backagain,? Optical and Quantum Electronics 40, 801?811 (2008). ? pages 47[98] K. Adam, Y. Granik, A. Torres, and N. B. Cobb, ?Improved modeling perfor-mance with an adapted vectorial formulation of the Hopkins imaging equa-tion,? in Optical Microlithography XVI pp. 78?91 (2003). ? pages 50[99] G. Cocorullo and I. Rendina, ?Thermo-optical modulation at 1.5 ?m in sili-con etalon,? Electron. Lett. 28, 83?85 (1992). ? pages 52143[100] S. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, ?Sub-nanometer linewidth uniformity in silicon nanophotonic waveguide devicesusing CMOS fabrication technology,? IEEE J. Sel. Top. Quantum Electron.16, 316 ?324 (2010). ? pages 52, 53[101] A. H. Atabaki, A. A. Eftekhar, M. Askari, and A. Adibi, ?Accurate post-fabrication trimming of ultra-compact resonators on silicon,? Opt. Express21, 14139?14145 (2013). ? pages 53[102] W. A. Zortman, D. C. Trotter, and M. R. Watts, ?Silicon photonics manu-facturing,? Opt. Express 18, 23598?23607 (2010). ? pages 53[103] A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communi-cations, Sixth Edition (Oxford University Press, 2007). ? pages 58, 64,65[104] S. Srinivasan, A. W. Fang, D. Liang, J. Peters, B. Kaye, and J. E. Bowers,?Design of phase-shifted hybrid silicon distributed feedback lasers,? Opt.Express 19, 9255?9261 (2011). ? pages 59[105] P. Prabhathan, V. M. Murukeshan, Z. Jing, and P. V. Ramana, ?CompactSOI nanowire refractive index sensor using phase shifted Bragg grating,?Opt. Express 17, 15330?15341 (2009). ? pages 61, 70[106] P. Barclay, K. Srinivasan, and O. Painter, ?Nonlinear response of siliconphotonic crystal microresonators excited via an integrated waveguide andfiber taper,? Opt. Express 13, 801?820 (2005). ? pages 68[107] X. Sun, X. Zhang, C. Schuck, and H. X. Tang, ?Nonlinear optical effects ofultrahigh-Q silicon photonic nanocavities immersed in superfluid helium,?Sci. Rep. 3 (2013). ? pages 68, 69[108] M. Burla, L. Romero Cortes, M. Li, X. Wang, L. Chrostowski, and J. Azana,?On-chip ultra-wideband microwave photonic phase shifter and true timedelay line based on a single phase-shifted waveguide Bragg grating,? inIEEE Microwave Photon. Conf. pp. W2?3 (2013). ? pages 70, 131[109] M. Burla, M. Li, L. Romero Cortes, X. Wang, L. Chrostowski, and J. Azana,?2.5 THz bandwidth on-chip photonic fractional Hilbert transformer basedon a phase-shifted waveguide Bragg grating,? in IEEE Photon. Conf. pp.436?437 (2013). ? pages 70, 131[110] A. Yariv and P. Yeh, Optical Waves in Crystal (New York: Wiley, 1984). ?pages 73144[111] V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, ?Theory, design, and per-formance of extended tuning range semiconductor lasers with sampled grat-ings,? IEEE J. Quantum Electron. 29, 1824?1834 (1993). ? pages 73, 75[112] S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, andY. Wada, ?Largely-tunable wideband Bragg gratings fabricated on SOI ribwaveguides employed by deep-RIE,? Electron. Lett. 43, 630?631 (2007).?pages 79[113] X. Wang, W. Shi, H. Yun, S. Grist, N. A. F. Jaeger, and L. Chrostowski,?Narrow-band waveguide Bragg gratings on SOI wafers with CMOS-compatible fabrication process,? Opt. Express 20, 15547?15558 (2012). ?pages 79[114] G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, ?Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveg-uides,? IEEE Photon. Technol. Lett. 23, 6?9 (2011). ? pages 80[115] S. Zamek, D. T. H. Tan, M. Khajavikhan, M. Ayache, M. P. Nezhad, andY. Fainman, ?Compact chip-scale filter based on curved waveguide Bragggratings,? Opt. Lett. 35, 3477?3479 (2010). ? pages 99, 104[116] A. D. Simard, Y. Painchaud, and S. LaRochelle, ?Integrated Bragg gratingsin spiral waveguides,? Opt. Express 21, 8953?8963 (2013). ? pages 99,100, 104[117] X. Wang, H. Yun, and L. Chrostowski, ?Integrated Bragg gratings in spiralwaveguides,? in Conference on Lasers and Electro-Optics, San Jose, CA,paper CTh4F.8 (2013). ? pages 99[118] J. Blasco and C. Barrios, ?Compact slot-waveguide/channel-waveguidemode-converter,? in Conference on Lasers and Electro-Optics Europe(CLEO/Europe) p. 607 (2005). ? pages 110[119] A. Saynatjoki, L. Karvonen, T. Alasaarela, X. Tu, T. Y. Liow, M. Hiltunen,A. Tervonen, G. Q. Lo, and S. Honkanen, ?Low-loss silicon slot waveguidesand couplers fabricated with optical lithography and atomic layer deposi-tion,? Opt. Express 19, 26275?26282 (2011). ? pages 115, 118[120] R. Palmer, L. Alloatti, D. Korn, W. Heni, P. Schindler, J. Bolten, M. Karl,M. Waldow, T. Wahlbrink, W. Freude, C. Koos, and J. Leuthold, ?Low-losssilicon strip-to-slot mode converters,? IEEE Photon. J. 5, 2200409 (2013).? pages 110145[121] T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, ?High-Q opticalresonators in silicon-on-insulator-based slot waveguides,? Appl. Phys. Lett.86, 081101 (2005). ? pages 115, 120[122] H. Zhang, J. Zhang, S. Chen, J. Song, J. Kee, M. Yu, and G.-Q. Lo, ?CMOS-compatible fabrication of silicon-based sub-100-nm slot waveguide with ef-ficient channel-slot coupler,? IEEE Photon. Technol. Lett. 24, 10?12 (2012).? pages 115[123] R. Ding, T. Baehr-Jones, W.-J. Kim, X. Xiong, R. Bojko, J.-M. Fedeli,M. Fournier, and M. Hochberg, ?Low-loss strip-loaded slot waveguides insilicon-on-insulator,? Opt. Express 18, 25061?25067 (2010). ? pages 118[124] A. Spott, T. Baehr-Jones, R. Ding, Y. Liu, R. Bojko, T. O?Malley,A. Pomerene, C. Hill, W. Reinhardt, and M. Hochberg, ?Photolithographi-cally fabricated low-loss asymmetric silicon slot waveguides,? Opt. Express19, 10950?10958 (2011). ? pages 118[125] H. K. Hunt and A. M. Armani, ?Label-free biological and chemical sensors,?Nanoscale 2, 1544?1559 (2010). ? pages 119[126] X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, ?Sen-sitive optical biosensors for unlabeled targets: A review,? Anal. Chim. Acta620, 8?26 (2008). ? pages 119[127] M. S. Luchansky and R. C. Bailey, ?High-Q optical sensors for chemicaland biological analysis,? Anal. Chem. 84, 793?821 (2012). ? pages 119[128] K. D. Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, ?Silicon-on-insulator microring resonator for sensitive and label-free biosensing,?Opt. Express 15, 7610?7615 (2007). ? pages 119[129] A. L. Washburn, L. C. Gunn, and R. C. Bailey, ?Label-free quantitation ofa cancer biomarker in complex media using silicon photonic microring res-onators,? Anal. Chem. 81, 9499?9506 (2009). PMID: 19848413. ? pages[130] M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg,T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, ?Label-free biosensor arraysbased on silicon ring resonators and high-speed optical scanning instrumen-tation,? IEEE J. Quantum Electron. 16, 654?661 (2010). ? pages[131] M. S. Luchansky and R. C. Bailey, ?Silicon photonic microring resonatorsfor quantitative cytokine detection and T-cell secretion analysis,? Anal.Chem. 82, 1975?1981 (2010). PMID: 20143780. ? pages146[132] J. Flueckiger, S. M. Grist, G. Bisra, L. Chrostowski, and K. C. Cheung,?Cascaded silicon-on-insulator microring resonators for the detection ofbiomolecules in PDMS microfluidic channels,? Proc. SPIE 7929, 79290I(2011). ? pages 119[133] S. M. Grist, S. A. Schmidt, J. Flueckiger, V. Donzella, W. Shi, S. T. Fard,J. T. Kirk, D. M. Ratner, K. C. Cheung, and L. Chrostowski, ?Siliconphotonic micro-disk resonators for label-free biosensing,? Opt. Express 21,7994?8006 (2013). ? pages 119[134] A. S. Jugessur, M. Yagnyukova, J. Dou, and J. S. Aitchison, ?Bragg-gratingair-slot optical waveguide for label-free sensing,? Proc. SPIE 8231, 82310N(2012). ? pages 119[135] S. Mandal and D. Erickson, ?Nanoscale optofluidic sensor arrays,? Opt. Ex-press 16, 1623?1631 (2008). ? pages 119[136] C. A. Barrios, K. B. Gylfason, B. Sa?nchez, A. Griol, H. Sohlstro?m, M. Hol-gado, and R. Casquel, ?Slot-waveguide biochemical sensor,? Opt. Lett. 32,3080?3082 (2007). ? pages 119, 120, 123[137] T. Claes, J. Molera, K. De Vos, E. Schacht, R. Baets, and P. Bienstman,?Label-free biosensing with a slot-waveguide-based ring resonator in siliconon insulator,? IEEE Photon. J. 1, 197?204 (2009). ? pages 119, 120, 123,127[138] B. Wang, M. A. Dundar, R. Notzel, F. Karouta, S. He, and R. W. van derHeijden, ?Photonic crystal slot nanobeam slow light waveguides for refrac-tive index sensing,? Appl. Phys. Lett. 97, 151105 (2010). ? pages 120,123[139] M. Scullion, A. D. Falco, and T. Krauss, ?Slotted photonic crystal cavitieswith integrated microfluidics for biosensing applications,? Biosens. Bioelec-tron. 27, 101?105 (2011). ? pages 120[140] Y. Xia and G. M. Whitesides, ?Soft lithography,? Annu. Rev. Mater. Sci. 28,153?184 (1998). ? pages 121[141] C. A. Barrios, M. J. B. nuls, V. Gonza?lez-Pedro, K. B. Gylfason, B. Sa?nchez,A. Griol, A. Maquieira, H. Sohlstro?m, M. Holgado, and R. Casquel,?Label-free optical biosensing with slot-waveguides,? Opt. Lett. 33, 708?710 (2008). ? pages 123147[142] K. B. Gylfason, C. F. Carlborg, A. Kazmierczak, F. Dortu, H. Sohlstro?m,L. Vivien, C. A. Barrios, W. van der Wijngaart, and G. Stemme, ?On-chiptemperature compensation in an integrated slot-waveguide ring resonatorrefractive index sensor array,? Opt. Express 18, 3226?3237 (2010).? pages[143] C. F. Carlborg, K. B. Gylfason, A. Kazmierczak, F. Dortu, M. J. Banuls Polo,A. Maquieira Catala, G. M. Kresbach, H. Sohlstrom, T. Moh, L. Vivien,J. Popplewell, G. Ronan, C. A. Barrios, G. Stemme, and W. van der Wi-jngaart, ?A packaged optical slot-waveguide ring resonator sensor array formultiplex label-free assays in labs-on-chips,? Lab Chip 10, 281?290 (2010).? pages 123[144] W. L. DeLano, M. H. Ultsch, A. M. de, Vos, and J. A. Wells, ?Convergentsolutions to binding at a protein-protein interface,? Science 287, 1279?1283(2000). ? pages 127[145] M. C. Coen, R. Lehmann, P. Gro?ning, M. Bielmann, C. Galli, and L. Schlap-bach, ?Adsorption and bioactivity of protein a on silicon surfaces studied byAFM and XPS,? J. Colloid Interface Sci. 233, 180?189 (2001). ? pages127[146] J. Vo?ro?s, ?The density and refractive index of adsorbing protein layers,?Biophys. J. 87, 553?561 (2004). ? pages 127[147] S. Darst, M. Ahlers, P. Meller, E. Kubalek, R. Blankenburg, H. Ribi,H. Ringsdorf, and R. Kornberg, ?Two-dimensional crystals of streptavidinon biotinylated lipid layers and their interactions with biotinylated macro-molecules,? Biophys. J. 59, 387?396 (1991). ? pages 127[148] A. Weisenhorn, F.-J. Schmitt, W. Knoll, and P. Hansma, ?Streptavidin bind-ing observed with an atomic force microscope,? Ultramicroscopy 42?44,1125?1132 (1992). ? pages 127[149] J. T. Kirk, N. D. Brault, T. Baehr-Jones, M. Hochberg, S. Jiang, and D. M.Ratner, ?Zwitterionic polymer-modified silicon microring resonators forlabel-free biosensing in undiluted humanplasma,? Biosens. Bioelectron. 42,100?105 (2013). ? pages 128[150] K. Ennser, M. Zervas, and R. Laming, ?Optimization of apodized linearlychirped fiber gratings for optical communications,? IEEE J. Quantum Elec-tron. 34, 770?778 (1998). ? pages 132148[151] J. Xing, K. Xiong, H. Xu, Z. Li, X. Xiao, J. Yu, and Y. Yu, ?Silicon-on-insulator-based adiabatic splitter with simultaneous tapering of velocity andcoupling,? Opt. Lett. 38, 2221?2223 (2013). ? pages 133149Appendix APublicationsA.1 Book Chapters1. X. Wang, W. Shi, and L. Chrostowski, ?Silicon photonic Bragg gratings,?in High-Speed Photonics Interconnects, L. Chrostowski and K. Iniewski, Ed.CRC Press, 2013, pp. 51-85.2. X. Wang and L. Chrostowski, ?High-speed directly-modulated injection-locked VCSELs,? in Integrated Microsystems: Electronics, Photonics, andBiotechnology, K. Iniewski, Ed. CRC Press, 2011, pp. 471-507.A.2 Journal Publications1. M. Burla, L. R. Cortes, M. Li, X. Wang, L. Chrostowski, and J. Azana, ?Inte-grated waveguide Bragg gratings for microwave photonics signal processing(Invited Paper),? Opt. Express, vo. 21, no. 21, pp. 25120-25147, 2013.2. X. Wang, S. Grist, J. Flueckiger, N. A. F. Jaeger, and L. Chrostowski, ?Sili-con photonic slot waveguide Bragg gratings and resonators,? Opt. Express,vol. 21, no. 16, pp. 19029-19039, 2013.3. X. Wang, J. Flueckiger, S. Schmidt, S. Grist, S. T. Fard, J. Kirk, M. Doer-fler, K. C. Cheung, D. M. Ratner, and L. Chrostowski, ?A silicon photonic150biosensor using phase-shifted Bragg gratings in slot waveguide,? J. Biopho-tonics, vol. 6, no. 10, pp. 821-828, 2013.4. W. Shi, H. Yun, C. Lin, M. Greenburg, X. Wang, Y. Wang, S. T. Fard,J. Fluckekiger, N. A. F. Jaeger, and L. Chrostowski, ?Ultra-compact, flat-topdemultiplexer using anti-reflection contra-directional couplers for CWDMnetworks on silicon,? Opt. Express, vol. 21, no. 6, pp. 6733-6738, 2013.5. W. Shi, X. Wang, C. Lin, H. Yun, Y. Liu, T. Baehr-Jones, M. Hochberg,N. A. F. Jaeger, and L. Chrostowski, ?Silicon photonic grating-assisted, contra-directional couplers,? Opt. Express, vol. 21, no. 3, pp. 3633-3650, 2013.6. X. Wang, W. Shi, H. Yun, S. Grist, N. A. F. Jaeger, and L. Chrostowski,?Narrow-band waveguide Bragg gratings on SOI wafers with CMOS-compatiblefabrication process,? Optics Express, vol. 20, no. 14, pp. 15547-15558,2012.7. W. Shi, X. Wang, W. Zhang, H. Yun, C. Lin, L. Chrostowski, and N. A. F. Jaeger,?Grating-coupled silicon microring resonators,? Applied Physics Letters,vol. 100, no. 12, pp. 121118, 2012.8. X. Wang and L. Chrostowski, ?High-speed Q-modulation of injection-lockedsemiconductor lasers,? IEEE Photonics Journal, vol. 3, no. 5, pp. 936-945,2011.9. W. Shi, X. Wang, W. Zhang, L. Chrostowski, and N. A. F. Jaeger, ?Contradi-rectional couplers in silicon-on-insulator rib waveguides,? Optics Letters,vol. 36, no. 5, pp. 3999-4001, 2011.10. X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, ?Uniformand sampled Bragg gratings in SOI strip waveguides with sidewall corru-gations,? IEEE Photonics Technology Letters, vol. 23, no. 5, pp. 290-292,2011.151A.3 Conference Proceedings1. L. Chrostowski, X. Wang, J. Flueckiger, Y. Wu, Y. Wang, and S. TalebiFard, ?Impact of fabrication non-uniformity on chip-scale silicon photonicintegrated circuits,? in Optical Fiber Communication Conference, San Fran-cisco, CA, March 2014, paper Th2A.37.2. M. Burla, L. R. Cortes, M. Li, X. Wang, L. Chrostowski, and J. Azana,?On-chip ultra-wideband microwave photonic phase shifter and true time de-lay line based on phase-shifted waveguide Bragg gratings,? in InternationalTopical Meeting on Microwave Photonics (MWP), Alexandria, VA, October2013, paper W2-3.3. X. Wang, H. Yun, N. A. F. Jaeger, and L. Chrostowski, ?Multi-period Bragggratings in silicon waveguides,? in IEEE Photonics Conference 2013, Belle-vue, WA, September 2013, paper WD2.5.4. M. Burla, M. Li, L. R. Cortes, X. Wang, L. Chrostowski, and J. Azana,?2.5 THz bandwidth on-chip photonic fractional Hilbert transformer basedon a phase-shifted waveguide Bragg grating,? in IEEE Photonics Conference2013, Bellevue, WA, September 2013, paper WD2.2.5. X. Wang, H. Yun, and L. Chrostowski, ?Integrated Bragg gratings in spiralwaveguides,? in CLEO 2013, San Jose, CA, June 2013, paper CTh4F.8.6. W. Shi, H. Yun, C. Lin, X. Wang, J. Flueckiger, N. Jaeger, and L. Chros-towski, ?Silicon CWDM demultiplexers using contra-directional couplers,?in CLEO 2013, San Jose, CA, June 2013, paper CTu3F.5.7. Y. Wang, W. Shi, X. Wang, J. Flueckiger, H. Yun, N. A. F. Jaeger, andL. Chrostowski, ?Fully etched grating coupler with low back reflection,? inSPIE Photonics North, Ottawa, ON, June 2013, paper 89150U.8. S. T. Fard, S. M. Grist, V. Donzella, S. A. Schmidt, J. Flueckiger, X. Wang,W. Shi, A. Millspaugh, M. Webb, D. M. Ratner, K. C. Cheung, and L. Chros-towski, ?Label-free silicon photonic biosensors for use in clinical diagnos-152tics,? in SPIE Photonics West, San Francisco, CA, February 2013, paper862909.9. X. Wang, W. Shi, M. Hochberg, K. Adams, E. Schelew, J. Young, N. A. F. Jaeger,and L. Chrostowski, ?Lithography simulation for the fabrication of siliconphotonic devices with deep-ultraviolet lithography,? in Group IV Photonics,San Diego, CA, August 2012, pp. 288-290.10. W. Shi, X. Wang, C. Lin, H. Yun, Y. Liu, T. Baehr-Jones, M. Hochberg,N. A. F. Jaeger, and L. Chrostowski, ?Electrically tunable resonant filtersin phase-shifted contra-directional couplers,? in Group IV Photonics, SanDiego, CA, August 2012, pp. 78-80.11. W. Shi, M. Greenberg, X. Wang, Y. Wang, C. Lin, N. A. F. Jaeger, andL. Chrostowski, ?Single-band add-drop filters using anti-reflection, contra-directional couplers,? in Group IV Photonics, San Diego, CA, August 2012,pp. 21-23.12. H. Yun, W. Shi, X. Wang, L. Chrostowski, and N. A. F. Jaeger, ?Dumbbellmicroring reflector,? in SPIE Photonics North, Montreal, QC, June 2012,paper 8424-82.13. W. Shi, X. Wang, W. Zhang, H. Yun, N. A. F. Jaeger, and L. Chrostowski,?Integrated microring add-drop filters with contradirectional couplers,? inConference on Lasers and Electro-Optics, San Jose, CA, May 2012, pa-per JW4A.91.14. W. Shi, X. Wang, H. Yun, W. Zhang, L. Chrostowski, and N. A. F. Jaeger,?Integrated silicon contradirectional couplers: modeling and experiment,? inSPIE Photonics Europe, Brussels, Belgium, April 2012, paper 8424-82.15. W. Shi, X. Wang, H. Yun, W. Zhang, L. Chrostowski, and N. A. F. Jaeger,?Add-drop filters in silicon grating-assisted asymmetric couplers,? in Opti-cal Fiber Communication Conference, Los Angeles, CA, March 2012, pa-per OTh3D.315316. L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun,M. Webb, B. Nie, Z. Liang, K. C. Cheung, S. A. Schmidt, D. M. Ratner, andN. A. F. Jaeger, ?Silicon photonic resonator sensors and devices,? in SPIEPhotonics West, San Francisco, CA, Janurary 2012, paper 823620.17. X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski,?Narrow-band transmission filter using phase-shifted Bragg gratings in SOIwaveguide,? in IEEE Photonics Conference, Arlington, VA, October 2011,pp. 869-870.18. X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, ?Silicon-on-insulator Bragg gratings fabricated by deep UV lithography,? in AsiaCommunications and Photonics Conference, Shanghai, China, December2010, pp. 501-502.19. X. Wang, B. Faraji, W. Hofmann, M.-C. Amann, and L. Chrostowski, ?Inter-ference effects on the frequency response of injection-locked VCSELs,? inIEEE International Semiconductor Laser Conference, Kyoto, Japan, 2010,pp. 85-86.154

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