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Silicon photonic filters for wavelength-division multiplexing and sensing applications Wei, Shi 2012

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Silicon Photonic Filters for Wavelength-Division Multiplexing and Sensing Applications by Wei Shi B.Sc., Huazhong University of Science and Technology, Wuhan, China, 2004 M.A.Sc., Shenzhen University, Shenzhen, China, 2007 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in The Faculty of Graduate Studies (Electrical and Computer Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) August 2012 c© Wei Shi 2012 Abstract This thesis is a theoretical and experimental study of novel silicon pho- tonic filters, such as traveling-wave resonators (TWRs) and grating-assisted, contra-directional couplers (contra-DCs), for on-chip wavelength-division- multiplexing (WDM) systems and sensing applications. To measure optical losses of photonic components such as Y-branch split- ters and waveguide crossings, we have developed a ring-resonator based tech- nique which is accurate, simple, and space-efficient. A number of novel devices have been demonstrated using commercial CMOS-photonics fabri- cation foundries, with the aim of developing large-scale photonic integrated circuits using the standard process development tools. Two types of wavelength-selective, TWR-based reflective filters have been demonstrated for applications such as remote sensing and tunable lasers. Ultra-compact, high-Qmicrodisk resonators have been demonstrated, with radii of down to 1.5 µm, free spectral ranges (FSRs) of up to 71 nm, loaded Q’s of up to 88,000, and unloaded Q’s of over 100, 000. Contra-DCs have been studied using coupled-mode theory. An add-drop filter designed using contra-DCs in slab-modulated rib waveguides has been proposed and demonstrated, which shows a flat-top response and a narrow bandwidth of 50–100 GHz, promising for dense-WDM applications. Also, we proposed an out-of-phase grating design to suppress the intra-waveguide reflection in contra-DCs. Using this novel anti-reflection (AR) design, we have demonstrated an add-drop filter with a single-band, flat-top response and a wide channel bandwidth of 6.5 nm, which enables athermal operation in a large temperature span of > 70 K. This AR contra-DC can be used to build an on-chip coarse-WDM system for power-efficient, ultra-high-speed optical interconnects. Furthermore, we have proposed and demonstrated an ii Abstract electrically tunable phase-shifted contra-DC. In order to overcome the challenges facing microring resonators, such as limited FSRs and difficulty in controlling the bus-resonator coupling, we have proposed to integrate contra-DCs with microring resonators for selective bus-resonator coupling. Using this method, we have demonstrated a single dominant resonant mode in a microring resonator that originally has a small FSR of 1.3 nm. This grating-coupled microring resonator is promising for applications that need a huge free spectral range, such as cascaded resonator sensor arrays and ultra-high-bandwidth WDM systems. iii Preface Parts of this thesis are based on the author’s manuscripts, which have been or will be published, resulting from collaborations between multiple researchers. A version of Chapter 2 will be published: • Wei Shi, Ting K. Chang, Han Yun, Wen Zhang, Yun Wang, Char- lie Lin, Nicolas A. F. Jaeger, Lukas Chrostowski, “Differential mea- surement of transmission losses of integrated optical components using waveguide ring resonators”, SPIE Proceedings, Photonics North, Mon- treal, Canada, 2012 (Accepted). The author contributed the idea, conducted the devices’ design, and wrote the manuscript. The author and Ting K. Chang conducted the data processing and analysis. Han Yun drew the mask layout. Wen Zhang measured the devices. Yun Wang did the numerical modelling of the Y-branch splitters. Charlie Lin assisted in drawing the mask lay- out. Prof. Chrostowski and Prof. Jaeger helped with many suggestions in the course of the project and assisted in editing the manuscript. A version of Section 3.1 has been published: • Wei Shi, Raha Vafaei, Miguel A. G. Torres, Nicolas A. F. Jaeger, and Lukas Chrostowski, “Design and characterization of microring reflec- tors with a waveguide crossing” Optics Letters, vol. 35: pp. 2901-2903, 2010. The author contributed the idea, conducted the devices’ design, mod- eling, measurement, and analysis, and wrote the manuscript. Raha iv Preface Vafaei and Miguel Torres assisted in the measurement. Prof. Chros- towski and Prof. Jaeger helped with numerous suggestions in the course of the project and assisted in editing the manuscript. A version of Section 3.2 has been accepted for publication: • Wei Shi, Han Yun, Wen Zhang, Charlie Lin, Yun Wang, Nicolas A. F. Jaeger, and Lukas Chrostowski, ”Ultra-Compact, High-Q Silicon Microdisk Reflectors”, Optics Express, 2012. The author contributed the idea, conducted the device design and analysis, and wrote the manuscript. Han Yun drew the mask layout. Wen Zhang measured the devices. Charlie Lin assisted in drawing the mask layout. Yun Wang conducted the numerical modeling of the Y-branch splitter. Prof. Chrostowski and Prof. Jaeger helped with nu- merous suggestions in the course of the project and assisted in editing the manuscript. Parts of Section 4.3 have been published: • Wei Shi, Xu Wang, Han Yun, Wen Zhang, Lukas Chrostowski, Nico- las A. F. Jaeger, “Add-drop filters in silicon grating-assisted asymmet- ric couplers”, OFC/NFOEC, Los Angeles, US: p. OTh3D.3, 03/2012. The author contributed the idea, conducted the device design and analysis, and wrote the manuscript. Xu Wang and Wei Shi drew the mask layout. Han Yun and Wen Zhang measured the devices. Prof. Chrostowski and Prof. Jaeger helped with numerous suggestions in the course of the project and assisted in editing the manuscript. A version of Section 4.4 has been published: • W. Shi, X. Wang, W. Zhang, L. Chrostowski, and N. A. F. Jaeger “Contradirectional couplers in silicon-on-insulator rib waveguides”, Optics Letters, vol. 36: pp. 3999-4001, 2011. The author contributed the idea, conducted the devices’ design and analysis, drew the mask layout, and wrote the manuscript. Xu Wang v Preface contributed to the publication through discussions. Han Yun and Wen Zhang measured the devices. Prof. Chrostowski and Prof. Jaeger helped with numerous suggestions in the course of the project and assisted in editing the manuscript. A version of Section 4.5 will be published: • Wei Shi, Xu Wang, Charlie Lin, Han Yun, Yang Liu, Tom Baehr- Jones, Michael Hochberg, Nicolas A. F. Jaeger, and Lukas Chros- towski, “Electrically Tunable Resonant Filters in Phase-Shifted Contra- Directional Couplers”, San Diego, CA, 29/08/2012 (Accepted, Paper # WP 2). The author contributed the idea, conducted the devices’ design and analysis, and wrote the manuscript. Wei Shi and Lukas Chrostowski measured the devices. Charlie Lin, Wei Shi, and Lukas Chrostowski drew the mask layout. Xu Wang contributed to the publication through discussionss. Xu Wang and Han Yun assisted in drawing the mask. Yang Liu and Tom Baehr-Jones assisted in the measurement. Tom Baehr-Jones and Prof. Michael Hochberg developed the measurement system. Yang Liu, Michael Hochberg and Tom Baehr-Jones con- tributed to the fabrication process qualification and the development of grating couplers used in the experiments. Michael Hochberg provided many suggestions and assisted in editing the manuscript. Prof. Chros- towski and Prof. Jaeger helped with numerous suggestions in the course of the project and assisted in editing the manuscript. A version of Section 4.6 will be published: • Wei Shi, Mark Greenberg, Xu Wang, Yun Wang, Charlie Lin, Nico- las A. F. Jaeger, and Lukas Chrostowski, “Single-Band Add-Drop Fil- ters Using Anti-Reflection, Contra-Directional Couplers”, San Diego, CA, 29/08/2012 (Accepted, Paper # WA 7). The author contributed the idea, conducted the device design and analysis, drew the mask layout, measured the devices, and wrote the vi Preface manuscript. Mark Greenberg fabricated the devices. Xu Wang con- tributed to the publication through discussions. Yun Wang designed the grating couplers. Charlie Lin assisted in drawing the mask layout. Prof. Chrostowski and Prof. Jaeger helped with numerous suggestions in the course of the project and assisted in editing the manuscript. A version of Chapter 5 has been published: • Wei Shi, Xu Wang, Wen Zhang, Han Yun, Charlie Lin, Lukas Chros- towski, and Nicolas A. F. Jaeger “Grating-coupled silicon microring resonator”, Appl. Phys. Lett., vol. 100: pp. 12118-12118-4, 2012. The author contributed the idea, conducted the device design and analysis, and wrote the manuscript. Xu Wang drew the mask layout. Wen Zhang measured the devices. Han Yun and Charlie Lin assisted in the mask drawing and the measurement. Prof. Chrostowski and Prof. Jaeger helped with numerous suggestions in the course of the project and assisted in editing the manuscript. vii Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . xviii List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Silicon Photonics . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Wavelength-Division Multiplexing . . . . . . . . . . . 1 1.1.2 Silicon Resonator Sensors . . . . . . . . . . . . . . . . 5 1.2 About This Thesis . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.2 Methodology: A Fabless Research . . . . . . . . . . . 8 1.2.3 Thesis Organization . . . . . . . . . . . . . . . . . . . 9 2 Differential Measurement of Optical Component Losses . 12 2.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 viii Table of Contents 2.2 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Measurement System . . . . . . . . . . . . . . . . . . . . . . 17 2.4 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . 18 2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3 Wavelength-Selective Reflectors Using Traveling-Wave Res- onators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.1 Microring Reflectors Integrated With Waveguide Crossings . 24 3.1.1 Design and Simulation . . . . . . . . . . . . . . . . . 24 3.1.2 Characterization . . . . . . . . . . . . . . . . . . . . . 29 3.2 Ultracompact Microdisk Reflectors . . . . . . . . . . . . . . . 31 3.2.1 Device Structure . . . . . . . . . . . . . . . . . . . . . 32 3.2.2 Numerical Simulation of the Bus-Microdisk Coupling 33 3.2.3 Experiment and Results . . . . . . . . . . . . . . . . 36 3.2.4 Multichannel Reflective Sensing System . . . . . . . . 39 3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4 Grating-Assisted, Contra-Directional Couplers . . . . . . . 41 4.1 Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.2 Contra-Directional Couplers in Strip Waveguides . . . . . . . 46 4.3 Contra-Directional Couplers in Rib Waveguides . . . . . . . 48 4.3.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.3.2 Results and Analysis . . . . . . . . . . . . . . . . . . 50 4.3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.4 Anti-Reflection Contra-Directional Couplers . . . . . . . . . 55 4.4.1 Principle and Design . . . . . . . . . . . . . . . . . . 57 4.4.2 Experimental Results and Discussion . . . . . . . . . 59 4.5 Phase-Shifted Contra-Directional Couplers . . . . . . . . . . 61 4.5.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.5.2 Optical Spectra . . . . . . . . . . . . . . . . . . . . . 64 4.5.3 Electrical Tuning . . . . . . . . . . . . . . . . . . . . 66 4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 ix Table of Contents 5 Grating-Coupled Microring Resonators . . . . . . . . . . . . 69 5.1 Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 6 Conclusion and Future Work . . . . . . . . . . . . . . . . . . 81 6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 6.2.1 On the Traveling-Wave Resonators . . . . . . . . . . 87 6.2.2 On the Contra-Directional Couplers . . . . . . . . . . 88 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 x List of Tables 6.1 Performances of the demonstrated silicon photonic filters. . . 85 6.2 Performances of the silicon photonic filters demonstrated in this thesis (*) and the state-of-art devices demonstrated by other groups for specific applications. . . . . . . . . . . . . . . 86 xi List of Figures 1.1 Performances of the top 500 supercomputers in the world [4]. 2 1.2 Schematic of a DWDM multiplexer/demultiplexer using series- coupled ring resonators and on-chip Ge PIN detectors. Figure from Ref. [13] with permission. . . . . . . . . . . . . . . . . . 6 1.3 Microfluidic measurement setup at UBC [30]: the optical in- put fibre is connected to a tunable laser source with wave- length at around 1550 nm and the output optical fiber is connected to an optical power sensor. The measurements are performed on a temperature controlled stage. Fluidic tubing are connected to a syringe pump. . . . . . . . . . . . . . . . . 7 1.4 Research cycle. . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1 (a) Schematic of a racetrack-shape microring resonator; (b) Schematic of a racetrack-shape microring resonator with a number of Y- branch splitters inserted in its optical cavity. . . . . . . . . . 13 2.2 (a) Optical image of the microring resonators with and with- out inserted Y-branch splitters; (b) SEM image of an S-shape Y-branch splitter. . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 Calculated magnitude of the straight-through coupling coef- ficient as a function of wavelength. The insets are (a) calcu- lated mode distribution of the even mode and (b) SEM image of the coupler used in a fabricated microring resonator. . . . . 17 2.4 Measurement setup. . . . . . . . . . . . . . . . . . . . . . . . 18 2.5 Measured and fit transmission spectra of the microring res- onators with (a) none, (b) 2 pairs, and (c) 4 pairs of Y-branch splitters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 xii List of Figures 2.6 Measured roundtrip losses of the microring resonators with various pairs of Y-branch splitters: (a) Optical losses at reso- nant wavelengths; (b) optical loss as a function of the number of Y-branch splitters. . . . . . . . . . . . . . . . . . . . . . . . 20 2.7 Measured through-port response of a microring resonator with 1 mW input power. . . . . . . . . . . . . . . . . . . . . . . . . 22 3.1 SEM image of the device with the transfer-matrix elements labeled. The insets show details of the waveguide crossing and the coupler. . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 Simulated reflection spectra for several coupling conditions: (a) high reflectivity, high extinction ratio; (b) low reflectivity, high extinction ratio; (c) high reflectivity, low extinction ratio. 27 3.3 (a) Difference between the maximum reflectivity and the minimum reflectivity and (b) extinction ratio calculated as functions of the coupling coefficients. . . . . . . . . . . . . . . 28 3.4 Measurement schematic with an inset showing an image of the Y-branch power splitter. . . . . . . . . . . . . . . . . . . . 29 3.5 Measured and simulated reflection spectra at 25 oC (an es- timated insertion loss of 38 dB is included in the simulation; the optical paths are tuned to fit the free spectral range and the resonance peaks). . . . . . . . . . . . . . . . . . . . . . . . 30 3.6 Reflection spectra vs. temperature around 25 oC. . . . . . . 30 3.7 Reflected power as a function of temperature at λ0 = 1533.4 nm. 31 3.8 (a) Perspective view of a microdisk reflector. (b) Simulated spectra (1st-order TE-like transverse mode) of a microdisk reflector with R = 2.5 µm and G = 200 nm, assuming ideal 3-dB Y-branch splitters and a propagation loss of α = 1 dB/cm. 33 3.9 Perspective view of the FDTD model in calculating the cou- pling coefficient of the 1st TE-like mode of a microdisk res- onator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 xiii List of Figures 3.10 Numerical simulation of a microdisk resonator with R = 2.5 µm: (a) mode distributions of the first two TE-like modes with the silica-clad; (b) calculated effective indices of the first two TE modes of a bent waveguide as functions of waveguide width. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.11 Calculated Qc as functions of wavelength with various coupler gaps for a microdisk resonator with R = 2.5 µm. . . . . . . . 36 3.12 Measurement schematic with the insets showing the SEM im- ages of the Y-branch splitters. The insets show the SEM im- ages of an Y-branch splitter, for the reflection measurement, and an S-bend Y-branch splitter, with a 5-µm-opening, in the reflector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.13 Measured spectra of a microdisk reflector with [R, G]' [2.5 µm, 200 nm]: (a) transmission; (b) reflection and transmission (zoomed in near the resonant wavelegnth). The inset shows an SEM image of the microdisk resonator. . . . . . . . . . . . 38 3.14 Measured spectra of a silica-clad microdisk reflector with [R, G] ' [1.5 µm, 160 nm]: (a) transmission; (b) reflection and transmission (zoomed in near the resonant wavelength). The insets show SEM images of an air-clad device with the same radius. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.15 Measured and fit transmission spectra of: (a) a ring resonator; (b) a ring resonator with 2 pairs of Y-branch splitters.The insets show the device geometries. . . . . . . . . . . . . . . . 39 3.16 Sensing system using cascaded microdisk reflectors and an optical circulator. . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.1 Schematic of the contradirectional couplers with the fibre grating couplers (FGC) for optical testing. . . . . . . . . . . . 44 4.2 Calculated effective indices and the phase-match conditions of a contra-DC. . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.3 Calculated coupling efficiency and phase of the drop-port re- sponse of a contra-DC. . . . . . . . . . . . . . . . . . . . . . . 46 xiv List of Figures 4.4 SEM image of a contra-DC in sidewall-modulated strip waveg- uides. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.5 Measured through-port and drop-port spectra of a contra-DC in sidewall-modulated strip waveguides. The inset shows the zoomed-in spectra near λD. . . . . . . . . . . . . . . . . . . . 48 4.6 Two perturbation schemes. . . . . . . . . . . . . . . . . . . . 49 4.7 contra-directional couplers in SOI rib waveguides: (a) cross- sectional geometry with the calculated intensity distributions of the fundamental TE-like modes of the rib waveguides; (b) top view of the device geometry; (c) SEM image showing the parabolically broadening transition from the strip waveguides to the rib waveguides; (d) SEM image showing the corruga- tions of a device with the propagation constants labeled and the directions of propagation indicated. . . . . . . . . . . . . 51 4.8 Calculated effective indices of the fundamental TE-like modes of the rib waveguides. n′b and λ ′ D are the effective index and the Bragg wavelength, respectively, for Wb = 1 µm. . . . . . . 52 4.9 Measured spectra of a device with [D, G] = [220 nm, 1 µm]. The input power is 1 mW with an insertion loss of ∼17 dB due to the fiber-coupling to the FGCs.. . . . . . . . . . . . . . 53 4.10 Measured and simulated drop-port spectrum of a device with [D, G] = [220 nm, 1 µm]. . . . . . . . . . . . . . . . . . . . . 54 4.11 Dielectric perturbation distribution along the longitudinal di- rection. The inset is the SEM image of the tilted cross-section of a device. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.12 Measured drop-port spectra with different corrugation pa- rameters: (a) [D, G] = [220 nm, 800 nm]; (b) [220 nm, 1 µm]; and (c) [120 nm, 1 µm]. . . . . . . . . . . . . . . . . . . . . . 55 4.13 Measured and simulated drop-port bandwidth vs. coupler gap for various sizes of corrugation, showing the inverse expo- nential relationship (numerical modeling was only performed for the D=220 nm devices since FIB-SEM cross-sectional im- ages were only available for these devices). . . . . . . . . . . . 56 xv List of Figures 4.14 (a) Schematic top view of a contra-DC without the AR design; (b) Calculated effective indices of the first two TE-like modes in the device illustrated in (a). . . . . . . . . . . . . . . . . . 58 4.15 (a) Schematic top view of an Ar contra-DC; (b) SEM images of the AR contra-DC. . . . . . . . . . . . . . . . . . . . . . . 59 4.16 Measured through-port optical spectrum normalized using the response of a pair of fibre grating couplers: (a) without the anti-reflection design; (b) with the anti-reflection design. Insets: SEM images of the devices. . . . . . . . . . . . . . . . 60 4.17 a) Schematic top-view of a contra-directional coupler; b) Phase- shifted contra-directional coupler; c) Cross-sectional views of the contra-directional couplers at the positions (C1 and C2) indicated in (a) and (b). . . . . . . . . . . . . . . . . . . . . . 63 4.18 (a) Measured optical spectra (Inset: Extended view of the optical spectrum (1500-1560 nm) of the through port, show- ing single-mode operation, superimposed on the fibre grating coupler’s spectral response); (b) Simulated optical spectra. . . 65 4.19 Drop-port spectra with various currents . . . . . . . . . . . . 67 4.20 Resonant-wavelength shift as a function of current . . . . . . 68 4.21 Frequency response. . . . . . . . . . . . . . . . . . . . . . . . 68 5.1 (a) Schematic of the proposed grating-coupled microring res- onator. The red solid lines and the blue dashed lines in- dicate the optical paths associated with the grating-assisted contradirectional coupling, kg, and the broadband codirec- tional coupling, kb, respectively. (b) SEM image (top view) of the sidewall-modulated contradiretional coupler used in the grating-coupled microring resonator. . . . . . . . . . . . . . . 71 5.2 Illustration of the operation principle: (a) spectral responses of the microring resonator with and the contradirectional cou- pler; (b) spectral response of the grating-coupled microring resonator, with the side-mode suppression ratio (SMSR) la- beled. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 xvi List of Figures 5.3 Measured spectra of the grating-coupled add-drop microring resonator: (a) through-port; (b) drop-port. The insets show the zoomed-in spectra near the selected longitudinal mode. . 75 5.4 Calculated effective indices of the first two TE-like modes of the contradirectional coupler and the mode conditions. The inset shows the calculated electrical-intensity distribution of the coupled modes in the contradirectional coupler. . . . . . . 77 5.5 Measured spectral responses of the contradirectional coupler with 2000 periods of gratings. The inset shows the zoomed-in spectra near that drop-port peak wavelength. . . . . . . . . . 78 5.6 Calculated spectra: (a) through-port response of the conven- tional microring resonator; (b) coupling coefficient (kg) of the grating-assisted contradirectional coupler; (c) the through- port response of the grating-coupled microring resonator. A propagation loss of 4 dB/cm is used in the calculation. . . . . 79 5.7 Coupling schemes of a circular microring geometry: (a) broad- band point-coupling; (b) grating-assisted wavelength-selective coupling. The blue dashed lines and the red solid lines indi- cate the optical paths associated with the broad-band codirec- tional coupling, kb, and the grating-assisted contradirectional coupling, kg, respectively . . . . . . . . . . . . . . . . . . . . . 80 6.1 Schematic of the proposed dual-channel design of AR contra- DCs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 6.2 Proposed multiplexer/demultiplexer using AR contra-DCs. . 89 6.3 Schematic of the spectral responses of the proposed multi- plexer/demultiplexer. . . . . . . . . . . . . . . . . . . . . . . . 89 xvii List of Abbreviations AR Anti-Reflection Contra-DC Contra-Directional Coupler CMOS Complementary Metal-Oxide-Semiconductor CWDM Coarse WDM DWDM Dense WDM EDFA Erbium Doped Fiber Amplifier FDTD Finite-Difference Time-Domain FLOP Floating-Point Operations Per Second FGC Fiber Grating Coupler FSR Free Spectral Range LOD Limit Of Detection MZI Mach-Zehnder Interferometer PDK Process Design Kit PS Phase-Shifted SEM Scanning Electron Microscope SOI Silicon On Insulator TE Transverse Electric TWR Traveling-Wave Resonator WDM Wavelength-Division Multiplexing WGM Whispering Gallery Mode xviii List of Symbols a Roundtrip optical loss C Transfer matrix of a directional coupler D Corrugation width Ea Normalized electric field in Waveguide a Eb Normalized electric field in Waveguide b Ein Input electrical field Ei Electric field components at the ith port Et Through-port output electrical field G Coupler gap kb Broadband co-directional coupling kg Grating-assisted, contra-directional coupling L Waveguide or coupler length l Roundtrip length of a traveling-wave resonator LOD Limit of detection LODabs LOD determined by the water absorption LODabs LOD determined by the resonator N Number of grating periods na Effective index in Waveguide a nav Average effective index nb Effective index in Waveguide b neff Effective index ng Group index P Transfer matrix of optical paths Q Loaded quality factor Qabs Quality factor due to the water absorption xix List of Symbols Qc Coupling quality factor Qi Intrinsic quality factor R Radius Rp Maximum reflectivity Rv Minimum reflectivity S Longitudinal distribution of the dielectric perturbation S′ Normalized sensitivity of a resonator sensor S1 First-order Fourier component of S T Through-port power transmission t Field straight-through coupling coefficient Tc Total power transfer coefficient of a directional coupler Wa Width of Waveguide a Wb Width of Waveguide b α Waveguide propagation loss coefficient β Propagation constant βa Propagation constant in Waveguide a βb Propagation constant in Waveguide b δ Roundtrip phase η Coupling efficiency κ Field cross-coupling coefficient, for directional couplers, or Distributed coupling coefficient, for contra-directional couplers Λ Grating pitch λD Drop-port peak wavelength λa Bragg wavelength in Waveguide a λb Bragg wavelength in Waveguide b λ Wavelength ω Optical frequency 4β Propagation constant mismatch 4ε Dielectric perturbation 4ε1 First-order Fourier component of the dielectric perturbation 4εp Dielectric perturbation peak xx Acknowledgements Thanks to all the people who have helped me during my PhD journey. xxi To my parents. xxii Chapter 1 Introduction 1.1 Silicon Photonics The field of silicon photonics has gained significant momentum over the past decade. Silicon waveguides have very low optical losses and high op- tical confinement, which enable a variety of applications, including optical interconnects and sensing applications. 1.1.1 Wavelength-Division Multiplexing Optical Interconnects Future progress in computer technology is becoming increasingly dependent on ultra-fast data transfer between and within microchips [37]. As shown in Fig. 1.1, the speeds of the top 500 supercomputers increased exponentially during the last two decades and will soon reach the Exascale (1018 FLOPs) in 2020. There will be huge bandwidth demands to support this increase. Leading companies such as Intel and IBM, who see silicon photonics as a means for keeping on track with Moore’s Law, have invested heavily in the development of silicon photonic circuits to provide much faster data rates. The main driving force behind these efforts comes from the great potential 1 1.1. Silicon Photonics for integrating optical devices with microelectronic chips using established complementary metal-oxide-semiconductor (CMOS) facilities. In fact, most of the devices demonstrated in this thesis were fabricated using CMOS- photonics foundries. Figure 1.1: Performances of the top 500 supercomputers in the world [4]. Wavelength-Division Multiplexing Systems In optical communications, wavelength-division multiplexing (WDM) is a technology which multiplexes a number of optical carrier signals onto a sin- gle optical fiber by using different wavelengths. Today, there exist at least two industrial WDM standards, with differences in the spacing of the wave- lengths and the number of channels [2]: • Dense WDM – DWDM (ITU-T G.694.1, 2002): wavelengths are po- sitioned in a grid having exactly 100 GHz (0.8 nm) spacing in optical frequency, with a reference frequency fixed at 193.10 THz (1552.52 nm); other similar standards use 50 GHz and even 25 GHz channel spacing. 2 1.1. Silicon Photonics • Coarse WDM – CWDM (ITU-T G.694.2, 2003): wavelengths are from 1271 to 1611 nm with a channel spacing of 20 nm. DWDM is designed to leverage the capabilities (and cost) of erbium doped fiber amplifiers (EDFAs) for long-distance communications, which are effective for wavelengths between approximately 1525–1565 nm (C band), or 1570–1610 nm (L band). Due to the closer spacing between the wavelength channels, DWDM systems have to maintain more stable wavelengths or fre- quencies than those needed for CWDM. CWDM is used for short-distance communications (e.g., fiber to the home) and is not limited by EDFAs, allow- ing implementation of passive WDM systems that do not use temperature controllers or electrical power. WDM on Silicon On-chip WDM networks are a promising solution for high-speed silicon opti- cal interconnects, as they reduce the number of optical input-output connec- tions, are more space efficient, and are likely more energy-efficient than their single-channel counterparts. Intel has recently demonstrated a 4-channel, 50 Gbps (12.5 Gbps x 4) inter-chip silicon optical link [10]. There have been many WDM filters developed for the silicon platform. Add-drop filters based on microring/microdisk resonators are among the most studied silicon WDM filters. A proposed WDM architecture, using cascaded microring resonators, is shown in Fig. 1.2. Although significant progress has been achieved, many challenges remain for realizing on-chip WDM systems. These challenges include: 3 1.1. Silicon Photonics • Microring resonators have multiple resonant modes and, thus, lim- ited free-spectral ranges (FSRs), which limits the number of usable wavelength channels. The FSRs of state-of-the-art WDM filters using microring resonators are ∼20 nm [62]. The FSR can be extended by shrinking the size of the resonator, however, the bending loss increases significantly when the bend radius is smaller than 5 µm. Microdisks are less lossy and can be more compact than microrings [39, 52]. Sec- tion 3.3 will demonstrate an ultra-compact microdisk resonator with a radius of 1.5 µm and an ultra-wide FSR of 71 nm. • Difficulty in achieving flat-top filtering responses. Microring/microdisks have Lorentzian-shape responses and very narrow bandwidth, giving rise to challenges in stabilizing the wavelength. A flat-top response can only be obtained with increased complexity, e.g. using series-coupled racetrack resonators with the vernier effect [14]. Also, the optical losses increase dramatically as the number of cascaded rings increases [63]. To achieve ideal filtering responses, we have investigated grating- based, contra-directional couplers (contra-DCs) which will be seen in Chapter 4. • Silicon is very sensitive to temperature. As we will see in Section 3, microring resonators have a thermal sensitivity of near 0.1 nm/K in their resonant wavelengths. Considering that microring resonators have limited FSRs and very narrow bandwidths, DWDM is required for microring-based WDM networks. As previously mentioned, this requires wavelength stabilization; in one implementation, it was esti- 4 1.1. Silicon Photonics mated that over 80% of the total power consumed by each resonator device was on thermal control [69], not to mention the complexity of the temperature monitoring and feedback control. • The effective indices of silicon waveguides are very sensitive to man- ufacturing non-uniformity [69]. Therefore, it is difficult to accurately predict resonant wavelengths of fabricated microring resonators. This issue can be solved by, e.g., thermal trimming, with a cost of increased power budget [69]. It was estimated that in order to overcome man- ufacturing non-uniformity, thermal trimming would add 17% on the total power consumed by each resonant device. Considering these challenges intro consideration, the requirements on silicon photonic filters for low-cost, on-chip WDM systems include flat-top responses for low signal distortion, wide channel bandwidths (> 4.5nm) for high tolerance to temperature fluctuations (+/− 25 oC), and an ultra-wide FSR or usable band (> 300 nm in CWDM, ITU-T G.694.2) for a wide wavelength grid (20-nm spacing between the adjacent channels in CWDM) and low channel crosstalk. In Chapter 4, we will demonstrate our effort in exploring a wide-bandwidth, FSR-free add-drop filter for athermal CWDM systems on silicon. 1.1.2 Silicon Resonator Sensors Recent advances in the silicon photonic sensor literature have demonstrated clinically relevant sensitivities, and an expanded repertoire of biocompat- ible chemistries capable of interrogating a variety of biological molecules 5 1.1. Silicon Photonics ! Ge ORX Ge ORX Ge ORX Ge ORX Ge ORX Ge ORX !"#! $!$!$#!%&! ! ! !"! !'! !""! !"%!!"(!!%&! Figure 4.1: Schematic of a C-band demultiplexer using series-coupled ring resonators and on-chip Ge PIN detectors. 80 Figure 1.2: Schematic f a DWDM multiplexer/demultiplexer using series- coupled ring resonators and on-chip Ge PIN detectors. Figure from Ref. [13] with permission. [21, 30]. Additionally, by leveraging existing CMOS fabrication processes, silicon photonic sensors offer significant advantages in economies of scale over traditional biosensing platforms, allowing for the integration of thou- sands of sensors on a single millimetre-scale chip [21]. Optical sensors based on microring resonators have been proposed and developed using a variety of materials and for a variety of applications [21, 30]. At UBC, multiple resonator arrays have been cascaded and integrated with PDMS micro-fluidics, as shown in Fig. 1.3, for real-time detection of biomolecules in experiments such as antigen-antibody binding reaction ex- periments using Human Factor IX proteins [21, 30]. There are multiple im- portant performance criteria for comparing various sensor geometries, such 6 1.1. Silicon Photonics same straight waveguide fabricated out of Su-823. One resonator was covered by a cladding and the second resonator was exposed to the analytes. The covered resonator was used to compensate for temperature drifts. Dai et al. amongst others investigated the use of cascaded resonators theoretically24-26. Gylfason et al. used a multi-mode interference splitter integrated on the same chip as the resonators to address 8 rings using only one input grating coupler22. The waveguide’s output is focused onto a single pixel photodiode array. The resonators are etched into a silicon nitride film on top of silicon oxide layer. The concept of a lab-on-a-chip combines sample handling and analysis in one single chip, thereby offering the possibility of a portable analysis platform. Picoliter sample volumes can be handled inside micrometer scale fluidic channels using valves and pumps integrated into silicon or polymer chips 27. It is of great interest to include sensor technology into these lab-on-chip devices to automate parallel processing and therefore lower cost and increase throughput. Ksendzov et al. clamped a flow cell down onto the sensor chip28. They achieved sealing by using an o-ring and pressure. However they are not able to expose individual resonators with different analytes. Washburn et al. and Luchansky et al. used a laser cut Mylar gasket aligned over top of the microring arrays to define microfluidic channels1, 11. They closed the channels off with a Teflon lid and sandwiched the different layers between an aluminum chip holders. These microwells are only useful for steady state measurements. Because mass transport is diffusion limited, they are not suitable to determine dynamics of fast reactions, e.g. binding events of proteins. Moreover, in order to be able to run several experiments with different analytes or different concentrations in parallel individual resonators need to be addressed and exposed. Carlborg et al. used a microfluidic channel network in poly(dimethylsiloxane) (PDMS), with a separate fluid channel to each sensor for sample delivery10. We propose the use of cascaded ring resonators together with a PDMS microfluidic network fabricated by soft lithography to expose each ring individually with different solutions. The SOI substrate with the planar waveguides and the PDMS with the microchannels are reversibly bonded to each other. The use of cascaded ring resonators offers the possibility to measure transmission spectra of multiple rings in different channels simultaneously. The volume refractive index sensitivity of the racetrack resonator is determined by injecting a water – glycerin mixture with different mixing ratios and known refractive indices. 2. MATERIALS AND METHODS Figure 1.  The measurement setup: the optical input fiber is connected to a tunable laser source with wavelength at around 1550 nm and the output optical fiber is connected to an optical power sensor. The measurements are performed on a temperature controlled stage. Fluidic tubing are connected to a syringe pump.  2.1 Fabrication of SOI ring resonators The SOI nanophotonic single-mode waveguides were fabricated with deep UV lithography (193 nm) and standard CMOS etching processes as part of IMEC’s passive photonic ePIXfab cSOI process. It is possible to get features down Proc. of SPIE Vol. 7929  79290I-2 Downloaded from SPIE Digital Library on 02 Apr 2011 to 128.189.123.53. Terms of Use:  http://spiedl.org/terms PDMS with micro-channels Optical fibre input Optical fibre output Micro-fluidic network SOI substrate with ring resonators PDMS with micro-channels Fluidic input Figure 1.3: Microfluidic measurement setup at UBC [30]: the optical in- put fibre is conne ted t a tunabl l ser sourc with wavelength at around 1550 nm and the output optical fiber is connected to an optical power sen- sor. The measurements are performed on a temperature controlled stage. Fluidic tubing are connected to a syringe pump. as normalized sensitivity, S′, the quality factor, Q, and the Limit of Detec- tion (LOD) [21]. The sensitivity of a resonator is dependent on the overlap of the evanescent field and the sample. The Q factor of a resonator can be expressed by 1 Q = 1 Qabs + 1 Qi + 1 Qc (1.1) where Qabs, Qi, and Qc are the Q components determined by the water absorption, the intrinsic loss of the resonator (including material absorption, surface absorption and scattering, and mode radiation losses), and the bus- resonator coupling, respectively. The LOD is determined by the sensitivity and the Q factor: LOD = 1 S′Q = 1 S′Qabs + 1 S′ ( 1 Qi + 1 Qc ) = LODabs + LODr (1.2) 7 1.2. About This Thesis The “absorption” LOD (LODabs) is determined by the the water ab- sorption at a particular wavelength and is the same for all the types of resonator filters [21]. It determines the best LOD achievable, no matter which resonator geometry is used. Therefore, in order to push the LOD to- wards LODabs, we need to improve the resonator-determined LOD, LODr by enhancing the intrinsic quality factor of the resonator, Qi, and engineer- ing the bus-resonator coupling, Qc. Meanwhile, for a cascaded-resonator sensing system, one would like to extend the FSR as much as possible so that we can fit more sensing channels, similar to WDM systems. These considerations have motivated the work that will be described in Section 3. 1.2 About This Thesis 1.2.1 Objectives The objective of this thesis is to investigate novel photonic filters on the silicon platform and to explore their capabilities for on-chip WDM systems and sensing applications. The long-term objective of this work is to use these photonic filters and develop large-scale integrated photonic circuits for various applications, such as high-speed optical interconnects and sensors. 1.2.2 Methodology: A Fabless Research This work uses the practice of fabless silicon photonics [22, 33]. Most of the devices demonstrated in this thesis were fabricated using commercial CMOS-photonics fabrication facilities, or ‘fabs’. Our research methodol- ogy is illustrated in Fig. 1.4. Each design cycle starts with an idea emerg- 8 1.2. About This Thesis ing through literature review, workshops, conferences, and/or brain storm- ing. The device model is based on standard SOI materials and the process design kit (PDK) provided by the fab. Afterwards, the device is simu- lated and optimized using analytical models and numerical tools such as eigen-mode solvers (Lumerical MODE Solutions) and finite-difference time- domain (Lumerical FDTD Solutions). Then, the mask layout is designed, again, strictly following the PDK. We have used two fabs in this work: Imec, Belgium, accessed via ePIXfab and CMC Microsystems, and BAE Systems, accessed via OpSIS. After receiving fabricated chips from the fabs, testings and measurement are performed, followed by data processing and analysis. The models are then verified and improved upon by comparing the simu- lated results with the experiments. The fabrication effects and errors are calibrated; these fabrication effects are taken into consideration in the sub- sequent design cycles. Eventually, the research is described for publication and/or conference presentation. This fabless methodology ensures that the device performance can be well predicted and, therefore, the developed de- vices can potentially go to component libraries and be repeatedly used in future photonic circuits. 1.2.3 Thesis Organization This thesis is organized as follows: In Chapter 2, we describe our setup for spectral measurement and demon- strate how to use microring resonators to measure the transmission losses of integrated optical components, such as Y-branch splitters and waveguide crossings, and discuss the advantages, limitations, and potential improve- 9 1.2. About This Thesis Figure 1.4: Research cycle. ments to this ring-resonator-based technique. This purpose of this chapter is to explore an accurate, simple, and space-efficient/cost-efficient optical loss measurement method for device design and optimization and evaluation of silicon photonic fabrication. An S-shaped Y-branch splitter’s insertion loss is measured to illustrate this technique. This splitter is used in the compact, high-Q, microdisk reflector demonstrated in Chapter 3. In Chapter 3, we demonstrate design, modeling, and characterization of 10 1.2. About This Thesis two reflective filters using traveling-wave resonators. The first device uses a microring resonator integrated with a waveguide crossing and functions as a reflective notch filter. The second device uses a microdisk resonator and functions as a reflective band-pass filter. Important characteristics of TWRs, such as longitudinal and transverse modes, quality factors, bus-resonator coupling, and temperature sensitivity are investigated in experiment and numerical simulation. In Chapter 4, we investigate a class of grating-based add-drop filters, contra-DCs, using coupled mode theory, and demonstrate several novel contra-DC based devices, including an add-drop filter in slab-modulated rib waveguides and a resonant filter using phase-shifted contra-DCs. These de- vices have particular spectral features targeting different applications which will be discussed there. In particular, we demonstrate a wide-bandwidth, single-band contra-DC with a novel anti-reflection deisgn; our aim is to de- velop photonic filters that are suitable for on-chip, CWDM applications. Chapter 5 presents an idea of integrating the two classes of filters, i.e., TWRs and contra-DCs, investigated in Chapter 3 and Chapter 4, respec- tively. In this chapter, a grating-coupled microring resonator is demon- strated, where two contra-DCs are integrated with a micoring resonator for selective excitation/suppression of the longitudinal modes in the resonator. A grating-based bend coupling scheme is also proposed. This effort is to- wards single mode operation of microring resonators, as well as more precise control of the bus-resonator coupling. The thesis is concluded in Chapter 6 with a brief summary and a dis- cussion about future research directions. 11 Chapter 2 Differential Measurement of Optical Component Losses 1 Compact optical components, such as Y-branch power splitters and waveg- uide crossings [16], have been developed for the silicon platform and have been used to achieve novel devices, such as Mach-Zehnder interferometer (MZI) modulators [36] and waveguide ring reflectors [48]. Y-branch split- ters were also used to measure reflective signals of Bragg gratings [61]. Precise measurement of losses of these optical components is critical for design and optimization of photonic devices and integrated circuits. We anticipate that these optical components will be intensively used as the in- tegration scale keeps increasing and a wide range of high-volume silicon photonic products will begin to emerge in the next few years [12]. There- fore, an accurate, simple, and space-efficient method of characterizing their optical losses is required for evaluation and calibration of silicon photonics manufacturing. The conventional method of measuring optical losses, i.e., direct transmission measurement through fiber-to-waveguide coupling, usu- 1A version of Chapter 2 will be published: Wei Shi, Ting K. Chang, Han Yun, Wen Zhang, Yun Wang, Charlie Lin, Nicolas A. F. Jaeger, Lukas Chrostowski, “Differential measurement of transmission losses of integrated optical components using waveguide ring resonators”, SPIE Proceedings, Photonics North, Montreal, Canada, 2012 (Accepted). 12 2.1. Methodology ally requires multiple measurements to compensate for the uncertainty in the fibre-to-waveguide coupling and reflections that may cause significant errors when the measured losses are comparable with, or smaller than, the fibre-to-waveguide coupling losses. In addition, this conventional method may require a lot of space when measured losses are small and a series of optical components have to be cascaded to increase the total loss for reliable measurement. In this section, we demonstrate a ring-resonator-based technique for transmission-loss measurement of integrated optical components (Y-branch splitters in this case), which is independent of fiber-to-waveguide coupling losses and suitable for measuring small optical losses. 2.1 Methodology 4 5 90 Ei Et 55 Ei Et  . . . n n (a) (b) Figure 2.1: (a) Schematic of a racetrack-shape microring resonator; (b) Schematic of a racetrack-shape microring resonator with a number of Y-branch splitters inserted in its optical cavity. The power transmission of a microring all-pass filter, illustrated in Fig. 2.1a, is given by 13 2.1. Methodology 2 )A34;G)BC13'%D)30%4.)+E)$3&4)$.,+&%1+$,)F31()&+&.=)>)C%3$,=)G)C%3$,=)H)C%3$,)%&8)I)C%3$,)+E)L-MN)!"J$%&'(.,)3&,.$1.8)3&;)) )))))) )A34;<)BC13'%D)30%4.)+E)%)$3&4)$.,+&%1+$)E+$) ) A34;H)BC13'%D)30%4.)+E)%)$3&4)$.,+&%1+$)F31()>))'%D3J$%13+&)+E)L-MN)!"J$%&'(,;)) ) ) C%3$,)+E)L-MN)!"J$%&'(.,)3&,.$1.8)3&;)) )))))))))) )A34;O)BC13'%D)30%4.)+E)$3&4)$.,+&%1+$,)F31() ) A34;I)BC13'%D)30%4.)+E)$3&4)$.,+&%1+$,)F31()&+&.=)>)C%3$,=)G)C%3$,=)H)C%3$,)%&8)I)C%3$,=)) ) >)C%3$,=)G)C%3$,=)H)C%3$,)%&8)I)C%3$,)+E),0%DD)9"))J34)9",(%C.)!"J$%&'(.,)3&,.$1.8)3&;))))))))))))))))))))) ) ,(%C.)!"J$%&'(.,)3&,.$1.8)3&;))))))))))))))))) )))))))))))))))A34;P)BC13'%D)30%4.)+E)%)$3&4)$.,+&%1+$)E+$)'%D3J$%13+&)+E),0%DD)9",(%C.)!"J$%&'(.,;)))))))))))))))) 3 2 µm (a) (b) Figure 2.2: (a) Optical image of the microring resonators with and without inserted Y-branch splitters; (b) SEM image of an S-shape Y-branch splitter. T = |Et|2 |Ein|2 = |t|2 + a2 − 2a · |t| · cos(δ) 1 + a2 · |t|2 − 2a · |t| · cos(δ) (2.1) where t, a, and δ are the lumped straight-through coupling coefficient, the roundtrip loss, and roundtrip phase, respectively. The roundtrip phase is wavelength dependent and given by δ = 2pi · l · neff λ (2.2) where l, neff , and λ are the roundtrip length, the effective index, and the wavelength, respectively. The transmission power at the resonant frequency with δ = m · 2pi (m is an integer) approaches zero when the critical cou- pling condition [65], i.e., t = a, is satisfied. The extinction ratio and the linewidth are determined by the roundtrip loss and the coupling condition 14 2.2. Design [50, 65]. With a chosen coupling coefficient, the spectral response is very sensitive to the roundtrip loss. Therefore, we can measure optical losses of optical components by inserting them into a microring resonator, as shown in Fig. 2.1b, and characterizing the resonator’s transmission spectrum. Here we use Y-branch splitters to illustrate the proposed approach. Specifically, we use the following steps to characterize optical loss of a Y- branch splitter: 1. Measure transmission spectra, T (λ), of a ring resonator with a number of Y-branch splitters inserted in the ring cavity, as well as a reference ring without any Y-branch splitter; 2. Calculate the coupling coefficient (the ring resonators have the same coupler design); 3. Extract the waveguide loss of the reference ring resonator by varying neff and a and fitting experimental results using Eq. 1; 4. Extract the total round-trip loss of the ring resonator with a number of Y-branch splitters by fitting experimental results using Eq. 1; 5. Calculate the insertion loss of the Y-branch splitters by subtracting the waveguide loss calculated in Step 3 from the calculated loss in Step 4. 2.2 Design Shown in Fig. 2.2, the Y-branch splitter consists of a stem waveguide and two S-shape branch waveguides (bend radius of 5 µm, width of 500 nm), 15 2.2. Design tangentially contacting each other. This design is very compact and allows a flexible opening width that can be tuned easily by controlling the radiance of the arc waveguides. An ideal symmetric Y-branch splitter would have a 3 dB optical loss when light travels from its stem waveguide to either of its two branch waveguides. The insertion loss we are measuring is caused by optical radiation and scattering during the mode transition through the splitting section. In order to avoid the impact of this intrinsic 3 dB loss on the transmission spectrum, we combine two Y-branch splitters back-to- back to form an MZI and inserted various numbers of such MZIs, or splitter pairs, into the ring cavity, as shown in Fig. 2.1b. Our MZIs have a symmetric design with short arms (10 µm), hence, any loss due to interference in the MZIs should be negligible. The microring resonator without any Y-branch splitter was designed following Rouger et. al [44], with a round-trip length of 510 µm, using 220- nm-high, 500-nm-wide silicon strip waveguides on a 2-µm-thick buried oxide. A T-shape geometry was chosen for easy insertion of various numbers of Y- branch splitters. The directional coupler was designed to have a coupling length of 15 µm and a coupler gap of 200 nm, targeting at a slightly under- coupled condition, i.e., t & a. The straight-through coupling coefficient, shown in Fig. 2.3, was calculated using an eigen-mode solver (Lumerical MODE Solutions [3]). The fabrication was performed by Imec, Belgium, accessed via ePIXfab, using a CMOS-compatible SOI technology with 193-nm lithography. A mi- croscopic photo of the devices and an SEM image of the Y-branch splitter are shown in Fig. 2.2. TE-preferred fiber grating couplers (FGCs) [15] were 16 2.3. Measurement System 3 1500 1520 1540 1560 1580 1600 0.91 0.92 0.93 0.94 0.95 0.96 0.97 Wavelength, nm St ra igh t− Th ro ug h Co up lin g Co ef fic ien t 2 4 2 4 S E M  P ic tu re s  o f S o m e S E M  P ic tu re s  o f S o m e B u ild in g -B lo c k s /C o m p o n e n ts B u ild in g -B lo c k s /C o m p o n e n ts fro m  th e  2 0 0 9 -2 0 1 0  C o u rs e /W o rk s h o p fro m  th e  2 0 0 9 -2 0 1 0  C o u rs e /W o rk s h o p (a) (b) Figure 2.3: Calculated magnitude of the straight-through coupling coeffi- cient as a function of wavelength. The insets are (a) calculated mode dis- tribution of the even mode and (b) SEM image of the coupler used in a fabricated microring resonator. used for the measurements. 2.3 Measurement System The measurement setup is shown in Fig. 2.4. A single mode polarizing fiber was used for the input. A multimode fiber was used for the output. The spectra were measured using a Lightwave Measurement System (Agilent 8164A) [7] with an external-cavity, diode laser source (Agilent 81600B, tun- ing range: 1440 nm to 1640 nm) [8] and a low-polarization dependence, op- tical power sensor (Agilent 81634A) [6]. Triggered synchronization between the tunable laser and the optical power sensor enabled a fast wavelength 17 2.4. Results and Analysis SOI Manual Setup Input Fiber (to Laser) Output Fiber (to Sensor) Heat Sink TEC Microscope Figure 2.4: Measurement setup. sweep of up to 80 nm/s [6, 7, 9]. The photonic chip (not shown in Fig. 2.4) was mounted on a copper heat sink connected to a TEC controller (Stanford Research Systems, Model LDC501) [54]. The temperature, unless specified, was stabilized at 25 oC. 2.4 Results and Analysis Fig. 2.5 shows the measured and fit spectra at wavelengths near 1550 nm. We can clearly see the effect of optical losses induced by the Y-branch splitters on the transmission spectra as the number of pairs increases – the notch peak becomes less sharp and, eventually, hard to recognize. The microring resonator without any Y-branch splitter has a deep notch at the resonant wavelength in the transmission spectrum, showing an extinction ratio of 12 dB and a 3 dB bandwidth of 50 pm corresponding to a quality factor 18 2.5. Discussion 1547.71547.81547.9 1548 1548.11548.2 −12 −10 −8 −6 −4 −2 0 Tr an sm iss io n,  d B Wavelength, nm   Experimental Fit 1546.5 1546.6 1546.7 1546.8 1546.9 −12 −10 −8 −6 −4 −2 0 Tr an sm iss io n,  d B Wavelength, nm   Experimental Fit 1544.9 1545 1545.11545.21545.31545.4 −12 −10 −8 −6 −4 −2 0 Tr an sm iss io n,  d B Wavelength, nm   Experimental Fit (a) (b) (c) Figure 2.5: Measured and fit transmission spectra of the microring res- onators with (a) none, (b) 2 pairs, and (c) 4 pairs of Y-branch splitters. (Q) of over 30,000. The extinction ratio is significantly reduced to less than 8 dB and 2 dB when 2 pairs and 4 pairs of Y-branch splitters are inserted into the ring cavity, respectively. Fig. 2.6a shows round-trip losses of the microring resonators with none, 2 pairs, and 4 pairs of Y-branch splitters, at their resonant wavelengths, extracted using Eq. 2.1 and the steps described in Section 2. The boxplot, following the standard in descriptive statistics [1], for the optical losses at all the resonant wavelengths is shown in Fig. 2.6b, where the mean shows a good linear relationship between the optical loss and the number of Y-branch splitters inserted in the microring resonator. The optical loss of each pair of Y-branch splitters is determined to be 2.6 dB, i.e., 1.3 dB per Y-branch splitter. 2.5 Discussion Based on the results demonstrated above, we can see many advantages to using this ring-resonator-based technique for optical loss measurements. 19 2.5. Discussion 4 Two pairs Four pairs Ring 1490 1500 1510 1520 1530 1540 1550 1560 15700 5 10 15 Wavelength (nm) Lo ss  (d B) 5 0 2 4 6 8 10 12 14 0 2 40 2 4 Number of Splitter Pairs Lo ss  (d B ) 25%-75% 1.5 IQR range Median Outlier Saturday, 25 August, 12(a) (b) Figure 2.6: Measured roundtrip losses of the microring resonators with var- ious pairs of Y-branch splitters: (a) Optical losses at resonant wavelengths; (b) optical loss as a function of the number of Y-branch splitters. Firstly, it enables accurate measurement of small optical losses. The small- est measurable optical loss is intrinsically limited by the roundtrip loss (less than 1 dB in this case) of the ring waveguide. Secondly, this technique relies on characterizing transmission spectra rather than power floors and, therefore, avoids the impact of alignment errors, i.e., we can measure op- tical losses of optical components without concern for fiber-to-waveguide coupling. Last but not least, this method is very space efficient because the microring resonators are very compact and only a small number of devices are needed. This is important for saving on-chip real estate, considering the cost of CMOS-photonic manufacturing. However, this method also have limitations. Firstly, it is unsuitable for measuring very large losses. If the measured loss is so large that it makes the resonator significantly deviated from the critical coupling condition, the 20 2.5. Discussion extinction ratio will become very small and the transmission response will be insensitive to variations in the roundtrip loss [65]. Secondly, optical reflec- tion and backwards scattering, caused by the FGCs and optical components, could lead to undesired fluctuations in the spectrum, making it difficult to achieve good curve fits; Figure 2.7 shows the measured through-port re- sponse of a microring resonator (without Y-branch splitters) across a wide spectral range; we can clearly see the ripples in the insertion loss and the fluctuation in the extinction ratio. These fluctuations result in the data scat- tering seen in Fig. 2.6; this can be improved by optimizing the FGC design to suppress the reflection. In addition, the fitting accuracy is sensitive to the calculation accuracy of the coupling coefficient. The errors of the coupling calculation are mainly due to the non-uniformity of wafer thickness and and fabrication errors. A potential approach to improve the measurement ac- curacy is to add another bus waveguide coupled to the microring resonator to form an add-drop filter and use the drop-port response to calculate the optical losses. The reason why we have to calculate the coupling coefficient using the all-pass filters is because the total loss cannot be directly obtained from the through-port response, as seen in Fig. 2.5. Using an add-drop fil- ter, we can easily calculate the total loss of a microring resonator using its 3 dB bandwidth without calculating the coupling coefficient, making the loss measurement simpler and more accurate. 21 2.6. Summary 1480 1500 1520 1540 1560 −40 −35 −30 −25 −20 Wavelength (nm) Po w er , d Bm Figure 2.7: Measured through-port response of a microring resonator with 1 mW input power. 2.6 Summary In summary, we have demonstrated a ring-resonator-based technique for op- tical loss measurement of optical components in the context of silicon pho- tonic integrated circuits. This technique is space efficient and independent of fiber-to-waveguide coupling errors. The experimental results show that transmission spectra of microring resonators are very sensitive to optical losses and, therefore, can be used for high-accuracy, high-efficiency mea- surement of optical losses. The accuracy of this technique is intrinsically limited by losses of ring waveguides. The present work is based on all-pass filters, where the measurement accuracy is also dependent on the calculation of bus-resonator coupling. The measurement accuracy, as well as efficiency, can be improved by using drop-port reponses of add-drop filters which will be investigated in future work. 22 Chapter 3 Wavelength-Selective Reflectors Using Traveling-Wave Resonators Travelling-wave resonators (TWRs) including microring and microdisk res- onators, have been used for implementing a variety of wavelength-selective reflectors, including reflective band-pass filters [24, 40, 41] and reflective notch filters [46, 55]. These TWR reflectors are promising for applications such as tunable lasers [23], remote sensing [48, 55], wavelength-division mul- tiplexing (WDM) drop filters [59], and reflective optical modulators. In par- ticular, reflective sensors are very useful for harsh or special circumstances where a single input/output fiber is preferred [55]. A main advantage of TWRs over Bragg gratings lies in the device miniaturization, for which many efforts have been made for the silicon platform because of the great potential for large-scale electronic-photonic integration [17]. In this section, we design and characterize two novel TWR reflectors – one reflective notch filter and one reflective band-pass filter. 23 3.1. Microring Reflectors Integrated With Waveguide Crossings 3.1 Microring Reflectors Integrated With Waveguide Crossings2 Enabling more flexible routing, waveguide crossings are considered as im- portant components in large-scale photonic integration. Here we present a novel microring reflector employing a well designed waveguide crossing [16], which shows that low-loss, low-crosstalk waveguide crossings, originally de- signed for complex integrated photonic circuits, can be incorporated into micro-cavity resonators to implement new functions. Having a high extinc- tion ratio and a high sensitivity, the proposed device can, potentially, be used as a reflective notch filter in optical-communication applications or as a thermal, chemical, or other sensor. 3.1.1 Design and Simulation As shown in Fig. 3.1, the reflector consists of a dual-coupler microring resonator that is “twisted” using a waveguide crossing to achieve reflection. We use the transfer-matrix method [24] to analyze this device. The field components of the couplers are expressed as Ei = [ai bi ci di] T , i = 1, 2, 3, or 4 (3.1) The function of a directional coupler can be described by a transfer matrix [24]: 2A version of Section 3.1 has been published: Wei Shi, Raha Vafaei, Miguel A. G. Torres, Nicolas A. F. Jaeger, and Lukas Chrostowski, “Design and characterization of microring reflectors with a waveguide crossing” Optics Letters, vol. 35: pp. 2901-2903, 2010. 24 3.1. Microring Reflectors Integrated With Waveguide Crossings Figure 3.1: SEM image of the device with the transfer-matrix elements labeled. The insets show details of the waveguide crossing and the coupler. C = 1 iκ  −t 1 0 0 −Tc t 0 0 0 0 −t 1 0 0 −Tc t  (3.2) where κ = |κ|e−(iβ+α)Lc and t = |t|e−(iβ+α)Lc are the coupling coefficients, β is the propagation constant, α is the loss coefficient, Lc is the coupling length, and Tc = |κ|2 + |t|2 is the total power transfer coefficient. The relation between the left port and the right port of the bus waveguide is given by E1 = C12P23C34E4 (3.3) C12 and C34 are the coupler transfer matrices. P23 is the transfer matrix for propagation through the waveguide sections of lengths, L1 and L2, and is 25 3.1. Microring Reflectors Integrated With Waveguide Crossings given by P23 =  0 0 0 PL1 0 0 P−1L2 0 0 PL2 0 0 P−1L1 0 0 0  (3.4) where PL1(2) = te −(iβ+α)L1(2) and t is the transmission coefficient of the waveguide crossing. Assuming that the optical signal is input from the left port, i.e., the incoming signal Ein = a1 and c4 = 0, we can calculate the reflected signal Er = d1 and the through signal Et = b4 using Eq. 3.3 with the following relationships: a4 = b1e −(iβ+α)L3 , d4 = c1e(iβ+α)L3 (3.5) The device is designed based on 500-nm-wide, 220-nm-high silicon-on- insulator strip waveguides, with a gap of 200 nm in the coupling regions and a waveguide bend radius of 30 µm. Losses are an important factor for reli- able design of microring-resonator reflectors [20]. A waveguide propagation loss α = 5 dB/cm and a power transfer coefficient of the couplers Tc = 0.9, extracted in previous work [22], are used in our simulation. The waveg- uide crossing, using parabolically broadened waveguides and a double-etch scheme, is described in detail in Ref. [16]. An SEM image of the crossing is shown in Fig. 3.1 (inset). It has a transmission coefficient of 0.96 and a crosstalk lower than -40 dB [16], confirmed by FDTD, that is ignored in our simulation. The waveguide effective indices are calculated by a 2D finite-difference mode solver [28]. The coupling coefficients of the directional 26 3.1. Microring Reflectors Integrated With Waveguide Crossings 1532 1532.5 1533 1533.5 1534 1534.5 1535 −40 −35 −30 −25 −20 −15 −10 −5 0 Wevelength, nm R ef le ct ivi ty , d B   (a) |κ12|=0.84, |κ34|=0.77 (b) |κ12|=0.58, |κ34|=0.25 (c) |κ12|=0.84, |κ34|=0.86 Figure 3.2: Simulated reflection spectra for several coupling conditions: (a) high reflectivity, high extinction ratio; (b) low reflectivity, high extinction ratio; (c) high reflectivity, low extinction ratio. couplers are calculated using coupled-mode theory [44]. Coupling coefficients are critical to the performance of microring res- onators [24] and, as shown in Fig. 3.2, significantly affect the shape, mag- nitude, Q factor, and extinction ratio of the spectrum. Therefore, we use a racetrack shape to carefully control the coupling coefficients. To find the optimal coupling condition, we scan the reflection spectrum as a function of κ12 and κ34 and calculate Rp−Rv and 10log(Rp/Rv), where Rp and Rv are the maximum reflectivity and the minimum reflectivity, respectively. Based on the results shown in Fig. 3.3, we choose κ12 to be 0.84 and κ34 to be 0.77 in order to have both high reflectivity and high extinction ratio. 27 3.1. Microring Reflectors Integrated With Waveguide Crossings Figure 3.3: (a) Difference between the maximum reflectivity and the min- imum reflectivity and (b) extinction ratio calculated as functions of the coupling coefficients. 28 3.1. Microring Reflectors Integrated With Waveguide Crossings Reflection port Through port Fiber outputFiber input Temperature controller Heat sink Input port Figure 3.4: Measurement schematic with an inset showing an image of the Y-branch power splitter. 3.1.2 Characterization The device was fabricated by ePIXfab at IMEC using 193-nm lithography. The measurement schematic is shown in Fig. 3.4. Periodic grating couplers [15] are used to couple light into and out of the waveguides. A Y-branch power splitter is used to split the reflected light. The chip is mounted, with thermal paste, on a copper heat sink connected to a temperature monitor and controller. A Q factor of ∼ 12,500 and an extinction ratio greater than 25 dB were measured, as shown in Fig. 3.5. The reflection spectra vs. temperature are shown in Fig. 3.6 where we can see that the resonance wavelength has a temperature dependence of 0.09 nm/K. Fig. 3.7 presents the reflected power as a function of temperature at a fixed wavelength. By actively tuning the operating wavelength we can achieve a high sensitivity in a wide range [44]. 29 3.1. Microring Reflectors Integrated With Waveguide Crossings Figure 3.5: Measured and simulated reflection spectra at 25 oC (an esti- mated insertion loss of 38 dB is included in the simulation; the optical paths are tuned to fit the free spectral range and the resonance peaks). Figure 3.6: Reflection spectra vs. temperature around 25 oC. 30 3.2. Ultracompact Microdisk Reflectors 0 = 1553.4 nm Figure 3.7: Reflected power as a function of temperature at λ0 = 1533.4 nm. 3.2 Ultra-Compact Microdisk Reflectors3 Most of the TWR reflectors demonstrated so far are based on microring res- onators [24, 41, 48, 55]. In comparison with microrings, microdisks can have smaller footprints, wider free-spectral ranges (FSRs), and higher intrinsic quality factors (Q) [18, 39, 52]. These advantages are desirable for on-chip WDM and sensing applications. For example, wider FSR means more us- able channels in a cascaded TWR sensing system. For thermally tunable WDM filters and lasers using silicon TWRs [68], the power needed to shift the whole spectrum of a TWR by one FSR is independent of the size [25]. Therefore, smaller radius or wider FSR means higher tunability (in nm/W). In this Section, we present narrow-bandwidth reflectors using silicon mi- crodisk resonators, fabricated using a CMOS-photonic technology. We have 3A version of Section 3.2 has been accepted for publication: Wei Shi, Han Yun, Wen Zhang, Charlie Lin, Yun Wang, Nicolas A. F. Jaeger, and Lukas Chrostowski, ”Ultra- compact, high-Q silicon microdisk reflectors”, Optics Express, 2012. 31 3.2. Ultracompact Microdisk Reflectors adopted the scheme of integrating a TWR and two Y-branch splitters to ob- tain wavelength-selective reflection, which was first demonstrated by Paloczi et al. using a polymer microring with a large radius of ∼ 100 µm and a small FSR of ∼ 2 nm [40]. The use of microdisks in our design gives rise to numer- ous advantages, as mentioned above, including µm-scale miniaturization and ultra-wide FSRs covering the entire span of the C-band in optical communi- cations. The implementation of our devices on the silicon platform indicates great potential for integration with other electronic and photonic devices. We also present numerical modeling of the coupling between a waveguide and a microdisk using the 3D finite-difference time-domain (FDTD) method. 3.2.1 Device Structure Figure 3.8 shows the proposed reflector that consists of a silicon microdisk resonator and two Y-branch splitters. As shown in Fig. 3.8, the input light is split by the first Y-branch splitter into two beams that travel through the microdisk add-drop filter in the clockwise and counter-clockwise directions, respectively. Assuming ideally symmetric splitters, the reflector’s transmis- sion and reflection should be the same as the through and drop responses, respectively, of a microdisk add-drop filter. For example, Fig. 3.8(b) shows the simulated spectra of a microdisk reflector using the coupling coefficients calculated using the method discussed below. The resonant wavelengths are dropped by the opposite-side waveguides and then recombined by the first Y-branch splitter as the reflected signals. The other wavelengths are recom- bined by the second Y-branch splitter at the transmission port. The devices demonstrated are made of silicon with a height of 220 nm. The Y-branch 32 3.2. Ultracompact Microdisk Reflectors splitter, as described in Chapter 2, is very compact and has an adjustable opening width; the branches are tapered to 400-nm-wide bus waveguides of the microdisk for more efficient coupling between the bus waveguides and the resonator. Input Reflection Transmission R 220 nm G 400 nm SiO2 Cladding 1490 1500 1510 1520 1530 1540 0 0.2 0.4 0.6 0.8 1 Wavelength (nm) N or m al iz ed  T ra ns m iss io n / R ef le ct io n   Transmission Reflection −0.1 0 0.1 0 0.5 1 Wavelength detuning (nm) (a) (b) Figure 3.8: (a) Perspective view of a microdisk reflector. (b) Simulated spectra (1st-order TE-like transverse mode) of a microdisk reflector with R = 2.5 µm and G = 200 nm, assuming ideal 3-dB Y-branch splitters and a propagation loss of α = 1 dB/cm. 3.2.2 Numerical Simulation of the Bus-Microdisk Coupling Transverse and longitudinal modes of a microdisk can be found using a mode solver or the finite-difference time-domain (FDTD) method [21]. The bus-resonator coupling condition is critical to a TWR’s transmission prop- erties, such as extinction ratio and Q [65]. The coupling coefficient can be calculated using coupled-mode analysis [53], however, it does not consider the effect of phase perturbations of the bus waveguide and the resonator. Such perturbations can be important as they make the coupling more dis- persive [53]. Numerical simulation using the 3D-FDTD method does not have the approximation of no phase-perturbation. Therefore, its accuracy 33 3.2. Ultracompact Microdisk Reflectors is only limited by numerical errors. The microdisk, even with a very small radius, down to a couple of µm, still has multiple whispering gallery modes (WGMs). In order to distinguish a specific mode (fundamental mode in this case) from other WGMs, we use a wide bent waveguide to approximate the microdisk in the 3D-FDTD simulation of the bus-microdisk coupling, as illustrated in Fig. 3.9, with the selected mode imported from a mode solver as the input optical source. The 1st and 2nd TE-like modes of a microdisk (R = 2.5 µm), calculated using the mode solver, are shown in Fig. 3.10(a). We can see that the electric field of the fundamental mode approaches zero ∼ 1 µm away from the disk edge, which indicates that the mode profile is hardly affected if the microdisk is replaced by a bent waveguide wider than 1 µm. This method is verified numerically in Fig. 3.10(b) where we can see that the effective index of the fundamental mode becomes constant when the bent waveguide is wider than 1 µm. A width of 1.2 µm is chosen in the 3D-FDTD calculation of the coupling coefficient. The calculated quality factor due to the bus-microdisk coupling (Qc) is shown in Fig. 3.11 using Qc = −pilng λlog|t| (3.6) where l, ng, λ, and t are the roundtrip length, the group index, the wave- length, and the straight-through coupling coefficient, respectively. It is worth pointing out that, even though the microdisk can be treated as a multimode waveguide in simulation, the disk geometry enables many applications; for example, the disk center can be used as a support in an undercut structure or be metalized for thermal or electrical tuning. 34 3.2. Ultracompact Microdisk Reflectors 1.2 µm 400 nm Figure 3.9: Perspective view of the FDTD model in calculating the coupling coefficient of the 1st TE-like mode of a microdisk resonator. 0 0.5 1 1.5 2 2.5 3 3.5 0 0.2 0.4 0.6 0.8 1 Radial distance from disk center (µm) N or m al iz ed  |E |2 , a. u .   1st TE mode 2nd TE mode 0.5 1 1.5 2 2.5 1.7 1.8 1.9 2 2.1 2.2 2.3 Waveguide width (µm) Ef fe ct iv e in de x   1st TE mode, Air−clad 1st TE mode, Silica−clad 2nd TE mode, Air−clad 2nd TE mode, Silica−clad (a) (b) Figure 3.10: Numerical simulation of a microdisk resonator with R = 2.5 µm: (a) mode distributions of the first two TE-like modes with the silica-clad; (b) calculated effective indices of the first two TE modes of a bent waveguide as functions of waveguide width. 35 3.2. Ultracompact Microdisk Reflectors 1480 1500 1520 1540 1560 1580 104 105 106 Wavelength (nm) Q c   Silica−clad, G=160 nm Silica−clad, G=200 nm Silica−clad, G=240 nm Air−clad, G=160 nm Air−clad, G=200 nm Air−clad, G=240 nm Figure 3.11: Calculated Qc as functions of wavelength with various coupler gaps for a microdisk resonator with R = 2.5 µm. 3.2.3 Experiment and Results The devices demonstrated here were fabricated using a CMOS-compatible technology with 193-nm optical projection lithography by Imec, Belgium accessed via ePIXfab. The measurement schematic is shown in Fig. 3.12. Fiber grating couplers [15], designed for TE polarization, were used for mea- surement. Figure 3.13 shows the measured transmission and reflection spectra of an air-clad device with a radius, R, of 2.5 µm and a gap between the microdisk resonator and the bus waveguide, G, of 200 nm. Although the microdisk resonator intrinsically has multiple transverse modes, only the fundamental mode is effectively excited due to the very weak coupling between the bus waveguides and the higher-order modes in the microdisk resonator. The FSR between the resonant peaks at 1492.37 nm and 1533.1 nm is about 41.6 nm. 36 3.2. Ultracompact Microdisk Reflectors Through port Reflection port Fibre input Fibre output 10 µm 2 µm 1µm 1 µm W Figure 3.12: Measurement schematic with the insets showing the SEM im- ages of the Y-branch splitters. The insets show the SEM images of an Y-branch splitter, for the reflection measurement, and an S-bend Y-branch splitter, with a 5-µm-opening, in the reflector. As shown in Fig. 3.13(a), the 3-dB bandwidth of the reflection spectrum at 1492.37 nm is about 17 pm, corresponding to a high Q of ∼ 88, 000. Using the calculated coupling coefficient or Qc, the intrinsic quality factor, Qi, is estimated to be over 10 5. Figure 3.14 shows the measured spectra of another device with a smaller radius of 1.5-µm and an ultra-wide FSR of over 71 nm. The device has a very small effective area, including one microdisk resonator (∼ 4×3 µm2) and two Y-branch splitters (∼ 4×6 µm2 each), of approximately 4 × 15 µm2. The 3-dB bandwidth of the reflection spectrum, shown in Fig. 3.14(b), is about 0.37 nm, corresponding to a Q of ∼ 4,000, much lower than the 2.5-µm-radius device; this indicates higher losses due to the smaller radius. The insertion losses of the reflectors mainly come from the Y-branch splitters. Their losses are measured using the microring-resonator-based technique described in Section 2. The measured and fit spectra of the ring resonators with and without Y-branch splitters are shown in Fig. 3.15. The 37 3.2. Ultracompact Microdisk Reflectors 1490 1500 1510 1520 1530 1540 0 0.2 0.4 0.6 0.8 1 Wavelength (nm) N or m al iz ed  T ra ns m iss io n / R ef le ct io n   Transmission Reflection FSR=41.6 nm 1492.3 1492.35 1492.4 1492.45 0 0.2 0.4 0.6 0.8 1 Wavelength (nm) N or m al iz ed  T ra ns m iss io n / R ef le ct io n   Transmission Reflection 17 pm (a) (b) Figure 3.13: Measured spectra of a microdisk reflector with [R, G]' [2.5 µm, 200 nm]: (a) transmission; (b) reflection and transmission (zoomed in near the resonant wavelegnth). The inset shows an SEM image of the microdisk resonator. 1480 1490 1500 1510 1520 1530 1540 1550 0 0.2 0.4 0.6 0.8 1 Wavelength (nm) N or m al iz ed  T ra ns m iss io n / R ef le ct io n   Transmission Reflection FSR=71 nm 1543.5 1544 1544.5 1545 1545.5 1546 0 0.2 0.4 0.6 0.8 1 Wavelength (nm) N or m al iz ed  T ra ns m iss io n / R ef le ct io n   Transmission Reflection 0.38 nm (a) (b) Figure 3.14: Measured spectra of a silica-clad microdisk reflector with [R, G] ' [1.5 µm, 160 nm]: (a) transmission; (b) reflection and transmission (zoomed in near the resonant wavelength). The insets show SEM images of an air-clad device with the same radius. 38 3.2. Ultracompact Microdisk Reflectors 1544 1545 1546 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 Wavelength (nm) P o w e r (d B m ) Fit Measurement In Out 1541 1542 1543 1544 -24 -23 -22 Wavelength (nm) P o w e r (d B m ) Fit Measurement In Out (a) (b) Figure 3.15: Measured and fit transmission spectra of: (a) a ring resonator; (b) a ring resonator with 2 pairs of Y-branch splitters.The insets show the device geometries. optical loss of each Y-branch splitter is determined to be 1.4 dB, which causes a significant loss of over 2.8 dB in each reflector, as well as undesired reflections in the optical circuit. The insertion loss can be significantly reduced by optimizing the Y-branch splitters [45]. 3.2.4 Multichannel Reflective Sensing System Reflective band-pass filters, combined with a single optical fiber delivering both input and output signals, are particularly useful for remote sensing applications [48, 55]. Here we propose a multichannel reflective sensing sys- tem, shown in Fig. 3.16, using cascaded microdisk resonators with slightly different radii. Due to their ultra-wide FSRs, the demonstrated microdisk reflectors will enable more channels than microring resonators do in a cas- caded sensing system [30]. Furthermore, since all the microdisk resonators share one Y-branch splitter, the average footprint of each channel will be mainly determined by the microdisk resonators. 39 3.3. Summary 1µm W . . . Broadband input λ1 λ1 λ2 λ2 λn-1 λn λnλn-1 Transmission λ1, λ2 ....  λn Port1 Port3 Port 2 Reflection Figure 3.16: Sensing system using cascaded microdisk reflectors and an optical circulator. 3.3 Summary In summary, we have demonstrated two wavelength-selective TWR reflec- tors. The first one uses a mirroring resonator integrated with a waveguide crossing and functions as a reflective notch filter. An extinction ratio of greater than 25 dB has been obtained. The second one uses a microdisk resonator integrated with Y-branch splitters. A high Q of 88,000 (Qi over 105) has been measured for a 2.5-µm-radius microdisk device. With small footprints, high Q, and wide FSRs, these devices are promising for next- generation, on-chip applications. In particular, they can be used as high- sensitivity, wide-range sensors for harsh or special circumstances where a single input/output fibre is preferred [48, 55]. Using the demonstrated high- Q, wide-FSR microdisk reflectors, we have proposed a cascaded-resonator system that is promising for multi-channel sensing applications. 40 Chapter 4 Grating-Assisted, Contra-Directional Couplers As essential components for wavelength-division multiplexing (WDM) sys- tems, add-drop filters have been extensively developed for the SOI platform [17]. Among these devices, ring-resonator add-drop filters have received much attention [17, 48]. Nevertheless, microring resonators have Lorentzian drop-port responses and limited free spectral ranges (FSRs), for which an ideal drop-port response can only be obtained with increased complexity, e.g., using series-coupled racetrack resonators with the Vernier effect [14]. Bragg gratings are widely used in optical communications and sensing ap- plications, such as wavelength filters, dispersion engineering, tunable lasers, and reflective sensors. They do not suffer from having an FSR and have a flat-peak spectrum that can be easily tailored by choosing an appropriate dielectric-perturbation structure, e.g., sidewall modulated [61], top-surface modulated [31], slab modulated [34], or cladding modulated [56], and the geometry parameters, e.g., grating period and size, waveguide width, and apodization profile. However, most demonstrated Bragg devices operate in reflection mode (2-port device). This brings about the challenging require- 41 4.1. Principle ment to integrate an optical circulator. Grating-assisted, contra-directional couplers (contra-DCs) have no, or very weak, reflection at the operating wavelength and, thus, intrinsically function as wavelength-selective add- drop filters (4-port device), circumventing the need for optical isolators or circulators [67]. Wide-bandwidth add-drop filters based on grating-assisted contra-directional coupling have recently been demonstrated in GaInAsP photonic-crystal waveguides [42] and in SOI sidewall-modulated strip waveg- uide [57, 58]. In this chapter, we investigate grating-assisted, contra-directional cou- plers (contra-DCs) in silicon optical waveguides. We first review the operat- ing principle of contra-DCs. Then we demonstrated two types of contra-DCs with different waveguide geometries – side-wall modulated strip waveguides and slab-modulated rib waveguides. Next, we demonstrate a novel anti- reflection design for ultra-wide spectral operation. At the end, we demon- strate a resonator using phase-shifted contra-DCs whose resonant wave- length is electrically tunable. 4.1 Principle As illustrated in Fig. 4.1, the contra-DC is a four-port device. It consists of two waveguides with dielectric perturbations formed in the gap region. The two waveguides are designed to have significantly different propagation constants and, thus, no or very weak broadband, co-directional coupling. This coupler asymmetry can be easily obtained by varying the waveguide widths due to the high dispersion of SOI waveguides. Therefore, band- 42 4.1. Principle limited, contra-directional coupling can be obtained near the phase-match condition determined by the perturbation/grating pitch [67]. This phase- match condition determines the drop-port central wavelength, λD, and is given by 4 β = |βa|+ |βb| −m2pi Λ = 0 (4.1) where βa, βb, and Λ are the propagation constants in waveguide a and waveguide b and the grating pitch, respectively, and m is chosen to be 1 for the first-order grating design. Also, strong intra-waveguide reflections can happen at the Bragg conditions of the individual Bragg waveguides. As an example, Fig. 4.2 shows the calculated effective indices obtained using a mode solver (waveguide geometries will be described in the 4.5), illustrating how to determine the wavelengths of interest based on the phase-match conditions [66]: λa = 2naΛ and λb = 2nbΛ are the wavelengths for the intra- waveguide Bragg reflections of waveguide a and b, respectively, where na and nb are the effective indices and Λ is the grating pitch; λD = 2navΛ is the drop-port central wavelength and corresponds to the contra-directional coupling, where nav = (na + nb)/2. In a typical design of first-order gratings (i.e., 1/2-λ pitch), the contra- DC, as opposed to add-drop filters using microrings or microdisks, has single- band transmission at λD, i.e., no FSR, in its drop-port response. However, the usable spectral range is still limited by the spacing between λD and λa or λb due to the intra-waveguide Bragg reflections. Therefore, two notches, at λa and λD, are typically observed in the through-port spectrum [47, 50, 58]. 43 4.1. Principle Shi, Wei ©2011 Design principles of contradirectional couplers  Principle: efficient coupling requires phase match   Suppression of codirectional coupling  Two waveguides with different widths  Contradirecional coupling  Periodic dielectric perturbation between two waveguides 8 indices are calculated using the FDTD mode solutions with 5 nm meshes. The transmission The 1510 1515 1520 1525 1530 !45 !40 !35 !30 !25 !20 !15 Wavelength [nm] P o w e r [d B m ]   Drop Through ! a +  + ! a ! ! a +  + ! b ! Fig. 2. One-column figure set with the figure environ- ment. !"#! !"## !"#$ !"#% & &'! &'# &'$ &'% &'" &'( &') &'* &'+ ! ,-./0/1234 5167 ! " #$ % &'( ) * + ) ,& ) - .' " / 0% 12 13 !"#! !"## !"#$ !"#% & &'! &'# &'$ &'% &'" &'( &') &'* &'+ ! ,-./0/1234 5167 8 9 :6 - 0;< / = > / ?0 / @ 3; 9 1 5- 'A '7 !"#! !"## !"#$ !"#% & &'! &'# &'$ &'% &'" &'( &') &'* &'+ ! ,-./0/1234 5167 8 9 :6 - 0;< / = > / ?0 / @ 3; 9 1 5- 'A '7 &'$" 16&'(# 16 !')( 16 4%5 465 4-5 Fig. 3. One-column figure set with the figure environ- ment. Sample code for the preamble is as follows: \documentclass[10pt,twocolumn]{article} \usepackage{ol} %% Figures should be placed in body %% of manuscript and %% sized appropriately. The command \twocolumn[...] must be placed around the titlepage elements in the two-column option. Note that proper figure, table, and caption environments should be used (see samples below). Displayed equations may be the most problematic for two-column display.Optics Letters equations are usu- ally set in one column; breaks and alignment should bring out the structure of the math: κ = ω 4 ∫∫ ψ∗a(x, y) · ε1(x, y) ψb(x, y) dx dy (1) Photonic bandgap !λ = 2λ 2 0 pi(ng,a + ng,b) | κ | (2) !β = β1 − β2 −mλ Λ = 0 (3) Ėx,y = 1 2 (1 + jα) (Gx,y − γ)Ex,y + κEx,y (t− τ) exp (−jΩx,yτ) + (βspN) 1/2ξx,y. (4) Ėx,y = 1 2 (1 + jα) (Gx,y − γ)Ex,y + κEx,y (t− τ) exp (−jΩx,yτ) + (βspN) 1/2ξx,y. (5) Use standard LaTeX or AMSTeX environ- ments. For equations that must span two columns, it is possible to use a float environment, e.g., \begin{figure*}...\end{figure*}. Such an en- vironment will not interfere with figure or table numbering (which is controlled by the caption), but it will cause equations to float, often with unwanted consequences. Figures should be set to one-column size (∼8.3 cm) whenever possible; tables should also be set to one col- umn whenever possible, but tables with more than five columns will probably need to be set to two columns. For two-column layout, figures and tables can be set across both columns with the alternate figure and table environ- ment commands \begin{figure*}...\end{figure*} instead of \begin{figure}...\end{figure}. Note that tables are typeset and cannot be reduced in size like art, which may require more space than in the submitted paper. Sample figure environment: \begin{figure}[htb] \centerline{ \includegraphics[width=8.3cm]{richardson-f1.eps}} \caption{Sample figure.} \end{figure} References callouts are now formatted with the cite package, which produces bracketed reference style (e.g., [1]). For online callouts, e.g., see [1], the words “Ref.” and “Refs.” are not required. Before submitting, authors who use BibTeX should first run BibTeX, then paste the contents of the output file *.bbl into the *.tex manuscript file. Our electronic submissions system cannot process BibTeX directly. The following files are included in this distribu- tion: • OLpagelength.tex Template and instructions • ol2.sty Style file • ol.bst BibTeX style file for short-form citations (as published) 2 Figure 4.1: Schematic of the contradirectional couplers with the fibre grating couplers (FGC) for optical testing. 1480 1500 1520 1540 1560 2.45 2.5 2.55 2.6 2.65 2.7 Wavelength (nm) Ef fe ct iv e in de x n a nb n av λ / 2Λ λ a λb λD Figure 4.2: Calculated effective indices and the phase-match conditions of a contra-DC. This spacing can be extended by increasing the coupler asymmetry (i.e., na − nb), e.g., increasing the difference of the waveguide widths [47], as will be shown in 4.4. We will also demonstrate a novel design to completely eliminate the intra-waveguide Bragg reflections in 4.5. The coupling coefficient of a contra-DC is given by η = |κ|2sinh2(sL) s2cosh2(sL) + (4β/2)2sinh2(sL) (4.2) 44 4.1. Principle where L is the total coupling length and the parameter s is determined by s2 = |κ|2 − (4β/2)2 [66]. The parameter κ is the distributed coupling coefficient, representing the coupling strength between the two waveguides, and is given by [66] κ = ω 4 ∫∫ Ea ∗(x, y) · 4ε1(x, y) Eb(x, y) dx dy (4.3) where ω is the optical frequency; Ea and Eb are the normalized electric- field distributions of the coupled modes in the contra-DC; 4ε1 is the first- order Fourier component of the dielectric perturbation. From Eq. 4.3 we can see that the coupling strength is determined by the overlap between the mode distributions and the dielectric perturbation. This equation is based on coupled mode theory [66] which not only allows us to calculate the coupling efficiency but also helps us to understand the difference between the two types of contra-DCs demonstrated in the following two subsections. Figure 4.3 shows the typical drop-port response of a contra-DC (waveg- uide geometries will be described in the 4.5, but without the phase shift) calculated using the effective indices shown in Fig. 4.2, with κ = 16, 300, Λ=300 nm, and a period number of 1,000. In our simulation of the spectral response, only the inter-waveguide coupling is considered; the effect of the intra-waveguide Bragg reflections on the drop-port response is not included, since the spacing between λD and λa or λb is much larger than the band- width of the drop-port in our design. We can see in the following sections that this approximation is reasonable (good agreement between simulation and experiment has been obtained), particularly for the anti-reflection de- 45 4.2. Contra-Directional Couplers in Strip Waveguides 1520 1525 1530 0 0.5 1 1.5 2 2.5 Wavelength (nm) η,  φ /  pi   η φ / pi Figure 4.3: Calculated coupling efficiency and phase of the drop-port re- sponse of a contra-DC. sign (discussed in Section 4.4) where the intra-waveguide Bragg reflections are significantly suppressed. 4.2 Contra-Directional Couplers in Strip Waveguides4 The contra-DC demonstrated in this section consists of two strip waveguides (SW) with different widths, Wa = 400 nm andWb = 500 nm. An SEM image of the fabricated device is shown in Fig. 4.4. The dielectric perturbations are formed by corrugating the sidewalls of the strip waveguides in the gap region. The grating pitch is chosen to be 330 nm. The SW couplers have a 4Parts of Section 4.3 has been published: Wei Shi, Xu Wang, Han Yun, Wen Zhang, Lukas Chrostowski, Nicolas A. F. Jaeger, “Add-drop filters in silicon grating-assisted asymmetric couplers”, OFC/NFOEC, Los Angeles, US: p. OTh3D.3, 03/2012. 46 4.2. Contra-Directional Couplers in Strip Waveguides waveguide height of 220 nm, a coupler gap of 150 nm, and a period number of 2000. The devices were fabricated by Imec, Belgium accessed via ePIXfab, using 193-nm lithography. 1470 1480 1490 1500 1510 1520 1530−35 −30 −25 −20 −15 −10 −5 0 Wavelength, nm No rm ali ze d Re sp on se , d B 1510 1512 1514 1516 1518−35 −30 −25 −20 −15 −10 −5 0 Wavelength, nm No rm ali ze d Re sp on se , d B 1470 1480 1490 1500 1510 1520 1530−35 −30 −25 −20 −15 −10 −5 0 Wavelength, nm No rm al ize d Re sp on se , d B 1510 1512 1514 1516 1518−35 −30 −25 −20 −15 −10 −5 0 Wavelength, nm No rm al ize d Re sp on se , d B λD λa Through Drop 500 nm 330 nm 20 nm 150 nm 400 nm 500 nm (a) (b) Figure 4.4: SEM image of a contra-DC in sidewall-modulated strip waveg- uides. The through-port and drop-port spectra of the contra-DC are shown in Fig. 4.5(b). The spacing between λa and λD is 38 nm, able to cover the entire span of the C-band for DWDM applications. The drop-prop spectrum has a 3 dB bandwidth of 0.59 nm. The intra-waveguide Bragg reflection at λa shows a much wider bandwidth of ∼ 3 nm, which means that the coupling between the forward propagating wave and the backward propagating wave in the input waveguide sees a stronger perturbation than the coupling across the two waveguides. This is because the inter-waveguide coupling strength is dependent on the overlap of the mode profiles and the perturbation, as shown in Eq. 4.3 and illustrated in Fig. 4.6a. A more efficient perturbation scheme would be to locate the dielectric perturbation in the middle of the coupler, as shown in Fig. 4.6b, where the strongest mode overlap can be obtained. We will use this more efficient perturbation scheme in the next subsection where slab-modulated rib waveguides are used 47 4.3. Contra-Directional Couplers in Rib Waveguides 1470 1480 1490 1500 1510 1520 1530−35 −30 −25 −20 −15 −10 −5 0 Wavelength, nm No rm ali ze d Re sp on se , d B 1510 1512 1514 1516 1518−35 −30 −25 −20 −15 −10 −5 0 Wavelength, nm No rm ali ze d Re sp on se , d B 1470 1480 1490 1500 1510 1520 1530−35 −30 −25 −20 −15 −10 −5 0 Wavelength, nm No rm al ize d Re sp on se , d B 1510 1512 1514 1516 1518−35 −30 −25 −20 −15 −10 −5 0 Wavelength, nm No rm al ize d Re sp on se , d B λD λa Through Drop 500 nm 330 nm 20 nm 150 nm 400 nm 500 nm (a) (b) Figure 4.5: Measured through-port and drop-port spectra of a contra-DC in sidewall-modulated strip waveguides. The inset shows the zoomed-in spectra near λD. in achieving narrow-bandwidth add-drop filters. 4.3 Contra-Directional Couplers in Rib Waveguides5 In this section, we present add-drop filters using contra-directional cou- plers in SOI rib waveguides. Compared with sidewall-modulated strip- waveguides [19, 57, 61], rib waveguides can have larger corrugations (hun- dreds of nanometers vs. tens of nanometers) due to the lower effective-index contrast. Therefore, they have higher fabrication tolerances and more pre- 5A version of Section 4.4 has been published: W. Shi, X. Wang, W. Zhang, L. Chros- towski, and N. A. F. Jaeger “Contradirectional couplers in silicon-on-insulator rib waveg- uides”, Optics Letters, vol. 36: pp. 3999-4001, 2011. 48 4.3. Contra-Directional Couplers in Rib Waveguides −6 −4 −2 0 2 4 6 −0.2 0 0.2 0.4 0.6 0.8 1 −6 −4 −2 0 2 4 6 −0.2 0 0.2 0.4 0.6 0.8 1 Perturbation Perturbation na nb na nb |Ea|2 |Eb|2 |Ea|2 |Eb|2 (a) (b) Figure 4.6: Two perturbation schemes. cise control of weak coupling coefficients needed to obtain narrow-bandwith filters. 4.3.1 Design As shown in Fig. 4.7, the proposed contra-directional coupler consists of two SOI rib waveguides with a grating formed by first-order periodic cor- rugations in the middle of the silicon slab between the two ribs. The rib height and the slab thickness are 70 nm and 150 nm, respectively. The rib widths can be varied to tailor the mode profiles and effective indices. Strip waveguides with a width of 500 nm and a height of 220 nm are used for the input/output ports. Fiber grating couplers (FGCs) [15] are used to couple light into and out of the strip waveguides. Parabolically broadened silicon slabs, as shown in Fig. 4.7 (c), are used to obtain a smooth transition from the strip waveguides to the rib waveguides. This scheme has been shown to be effective in reducing transmission losses and suppressing undesired reflections [17, 48]. Fabrication is performed by ePIXfab at IMEC using 193-nm optical projection lithography that has shown the capacity to reli- 49 4.3. Contra-Directional Couplers in Rib Waveguides ably pattern features on the scale of a few hundred nanometers [15, 17]. The fabricated devices have the following parameters: a width of waveguide a, Wa, of 400 nm, a width of waveguide b, Wb, of 500 nm, a corrugation period length, Λ, of 290 nm, and a period number, N , of 4000. The corrugation width, D, and the coupler gap, G, are varied to tailor the filter bandwidth. The fundamental TE-like modes of the rib waveguides, without pertur- bation, are solved using a mode solver with a 5 nm mesh. The intensity dis- tribution is shown in Fig. 4.7(a). The calculated effective indices are shown in Fig. 4.8, from which we can find the Bragg wavelengths, λa = 2naΛ and λb = 2nbΛ, due to the intra-waveguide reflections, as well as the drop-port peak wavelength, λD = (na + nb)Λ, due to the inter-waveguide coupling. Fig. 4.9 shows the measured spectra of a rib-waveguide contra-directional coupler. The Bragg wavelengths predicted by the simulation agree well with the experimental results. The device shows a low excess loss of less than 1 dB for the whole drop-port passband. The spacing between λa and λD is about 10 nm and can be controlled by varying Wa and Wb. As shown in Fig. 4.8, when Wb is increased to 1 µm, the spacing between λa and the new peak, λ′D, is extended to over 30 nm, applicable to state-of-the-art DWDM (dense WDM) systems. 4.3.2 Results and Analysis The coupling coefficient, κ, is a function of the mode distributions and the dielectric perturbation. It is noticed that the actual corrugation profile is not rectangular, as in the original design, due to the pattern-size effect in the plasma etching, as is clearly seen in the SEM image in Fig. 4.11. This 50 4.3. Contra-Directional Couplers in Rib Waveguides 150 nm 70 nm WbWa D G SiO2 Si Air Corrugation (a) Figure 4.7: contra-directional couplers in SOI rib waveguides: (a) cross- sectional geometry with the calculated intensity distributions of the fun- damental TE-like modes of the rib waveguides; (b) top view of the device geometry; (c) SEM image showing the parabolically broadening transition from the strip waveguides to the rib waveguides; (d) SEM image showing the corrugations of a device with the propagation constants labeled and the directions of propagation indicated. 51 4.3. Contra-Directional Couplers in Rib Waveguides 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 2.55 2.6 2.65 2.7 2.75 λ ' bλD λ ' Dλbλa na (na+nb)/2 nb (na+nb)/2 nb Wavelength [nm] E ff ec ti v e In d ex ' ' Figure 4.8: Calculated effective indices of the fundamental TE-like modes of the rib waveguides. n′b and λ ′ D are the effective index and the Bragg wavelength, respectively, for Wb = 1 µm. effect causes weaker coupling strength and thus a narrower bandwidth [61] and has been considered in our comparison between the simulation and the experimental results. In this work we use a triangular shape to approximate the transverse distribution of the dielectric perturbation (as marked on the SEM image in Fig. 4.11) with a linear transition between the perturbation peak, 4εp, and the unperturbed section in the longitudinal direction. Then the dielectric perturbation can be expressed as 4 ε(x, y, z) = S(z)4 εp(x, y) (4.4) As shown in Fig. 4.11, the periodic function S(z) describes the longitudinal distribution of the perturbation. Now κ can be calculated by κ = picS1 2λD ∫∫ Ea ∗(x, y) · 4εp(x, y) Eb(x, y) dx dy (4.5) 52 4.3. Contra-Directional Couplers in Rib Waveguides Figure 4.9: Measured spectra of a device with [D, G] = [220 nm, 1 µm]. The input power is 1 mW with an insertion loss of ∼17 dB due to the fiber-coupling to the FGCs.. where Ea and Eb are the normalized electric-field distributions of the fun- damental TE-like modes of the rib waveguides, and S1 is the first-order Fourier-expansion coefficient of S(z). As shown in Fig. 4.10, the calcu- lated spectrum is in good agreement with the measurement. The calculated band sidelobes are about -5 dB, which can be suppressed by apodization techniques [66, 67]. For fixed rib widths, we can tailor the bandwidth by varying the cor- rugation width or the coupler gap. Fig. 4.12 shows the drop-port spectra of three devices with bandwidths in a range of 0.35 nm to 1.38 nm. The bandwidth for D = 220 nm as a function of G is calculated by using Eqs. (4.2-4.5) with the mode distributions extracted from the mode solver. As seen in Fig. 4.13, the simulation shows good agreement with experiment. Fig. 4.13 also shows the measured drop-port bandwidths of the devices with smaller corrugations, demonstrating an inverse exponential dependence of 53 4.3. Contra-Directional Couplers in Rib Waveguides Shi, Wei ©2012 Simulation vs. Experiment 17 Measured and simulated drop-port bandwidth vs. coupler gap κ ¼ picε1 2λD Z Z E"aðx; yÞ ·Δεpðx; yÞEbðx; yÞdxdy; ð3Þ where Ea and Eb are the normalized electric-field distri- butions of the fundamental TE-like modes of the rib waveguides and ε1 is the first-order Fourier-expansion coefficient of SðzÞ. As shown in Fig. 3, the calculated spectrum is in good agreement with the measurement. The calculated band sidelobes are about −5 dB, which can be suppressed by apodization techniques [4,11]. For fixed rib widths, we can tailor the bandwidth by varying the corrugation width or the coupler gap. Figure 5 shows the drop-port spectra of three devices with band- widths in a range of 0:35 nm to 1:38 nm. The bandwidth for D ¼ 220 nm as a function of G is calculated by using Eqs. (1)–(3) with the mode distributions extracted from the mode solver. As seen in Fig. 6, the simulation shows good agreement with experiment. Figure 6 also shows the measured drop-port bandwidths of the devices with smaller corrugations, demonstrating an inverse exponen- tial dependence of the bandwidth on the coupler gap. To summarize, we have designed and characterized the add-drop filters using contradirectional couplers in SOI rib waveguides that can be easily integrated with photonic wires by using parabolic slab tapers. Our mea- sured bandwidths ranged from 0:35 nm to 1:38 nm, de- pending on the corrugation size and the coupler gap. The pattern-size effect of the plasma-etch has been con- sidered in the calculations using coupled-mode theory and the mode solutions. The simulated results show good agreement with experiment. In conclusion, the demon- strated SOI rib-waveguide contradirectional couplers offer an FSR-free, accurately controlled solution for nar- row-bandwidth add-drop filters and should find wide applications in optical communications. We acknowledge S. Grist for the SEM images, CMC Mi- crosystems for making this project possible, Lumerical Solutions Inc. for the MODE Solutions, Design Workshop Technologies Inc. for the mask layout software, and the Natural Sciences and Engineering Research Council of Canada for their financial support. References 1. W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. V. Thourhout, and R. Baets, IEEE J. Sel. Top. Quantum Electron. 16, 33 (2010). 2. W. Shi, R. Vafaei, M. Á. G. Torres, N. A. F. Jaeger, and L. Chrostowski, Opt. Lett. 35, 2901 (2010). 3. P. Cheben, P. J. Bock, J. H. Schmid, J. Lapointe, S. Janz, D.-X. Xu, A. Densmore, A. Delâge, B. Lamontagne, and T. J. Hall, Opt. Lett. 35, 2526 (2010). 4. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, 2007). 5. X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, IEEE Photon. Technol. Lett. 23, 290 (2011). 6. I. Giuntoni, D. Stolarek, A. Gajda, G. Winzer, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2010), paper OThJ5. 7. M. Qiu, M. Mulot, M. Swillo, S. Anand, B. Jaskorzynska, and A. Karlsson, Appl. Phys. Lett. 83, 5121 (2003). 8. D. T. H. Tan, K. Ikeda, and Y. Fainman, Appl. Phys. Lett. 95, 141109 (2009). 9. D. T. H. Tan, K. Ikeda, S. Zamek, A. Mizrahi, M. P. Nezhad, A. V. Krishnamoorthy, K. Raj, J. E. Cunningham, X. Zheng, I. Shubin, Y. Luo, and Y. Fainman, Opt. Express 19, 2401 (2011). 10. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, J. Lightwave Technol. 23, 401 (2005). 11. P. Yeh and H. F. Taylor, Appl. Opt. 19, 2848 (1980). Fig. 5. (Color online) Measured drop-port spectra with dif- ferent corrugation parameters: (a) ½D;G& ¼ ½220nm; 800nm&; (b) ½220nm; 1 μm&; and (c) ½120nm; 1 μm&. Fig. 6. (Color online) Measured and simulated drop-port bandwidth versus coupler gap for various sizes of corrugation, showing the inverse exponential rel tionship (numerical mod- eling was only performed for the D ¼ 220 nm devices since FIB-SEM cross-sectional images were only available for these devices). October 15, 2011 / Vol. 36, No. 20 / OPTICS LETTERS 4001 peak, λ0D, is extended to over 30 nm, pplicable to state- of-the-art DWDM (dense WDM) systems. The drop-port spectrum is calculat d sing coupled- mode theory [4], with the reflectivity (i.e., the contradir- ectional coupling efficiency) given by η ¼ jκj 2 sinh2ðsLÞ s2 cosh2ðsLÞ þ ðΔβ=2Þ2 sinh2ðsLÞ ; ð1Þ where Δβ ¼ βþa − β−b − 2pi=Λ and s2 ¼ jκj2 − ðΔβ=2Þ2 [4]. The coupling coefficient, κ, is a function of the mode dis- tributions and the dielectric perturbation. It is noticed that the actual corrugation profile is not rectangular, as in the original design, due to the pattern-size effect in the plasma etching, as is clearly seen in the SEM image in Fig. 4. This effect causes weaker coupling strength and thus a narrower bandwidth [5] and has been considered in our comparison between the simulation and the ex- perimental results. In this Letter, we use a triangular shape to approximate the transverse distribution of the dielectric perturbation (as marked on the SEM image in Fig. 4) with a linear transition between the perturba- tion peak, Δεp, and the unperturbed section in the long- itudinal direction. Then the dielectric perturbation can be expressed as Δεðx; y; zÞ ¼ SðzÞΔεpðx; yÞ: ð2Þ As shown in Fig. 4, the periodic function SðzÞ describes the longitudinal distribution of the perturbation. Now κ can be calculated by Fig. 2. (Color online) Calculated effective indices of the fundamental TE-like modes of the rib waveguides. n0b and λ0b are the effective-index and the Bragg wavelength, respectively, for Wb ¼ 1 μm. 1510 1512 1514 1516 1518 1520 1522 1524 1526 1528 1530 -40 -35 -30 -25 -20 -15 Wavelength [n ] Po w er  [d Bm ] Drop Through 1522 1522.5 15230 0.2 0.4 0.6 0.8 1 Wavelength [nm] N or m al iz ed  R ef le ct io n [a .u .] Experiment Simulation λa λD Fig. 3. (Color online) Measured spectra of a device with ½D;G& ¼ ½220nm; 1 μm&. The input power is 1mW with an inser- tion loss of ∼17dB due to the fiber-coupling to th FGCs. The inset shows the zoomed-in drop-port spect um and the simu- lated results. Fig. 4. (Color online) Dielectric perturbation distribution along the longitudinal direction. The inset is the SEM image of the tilted cross-section of a device. Fig. 1. (Color online) Contradirectional couplers in SOI rib waveguides: (a) cross-sectional geometry with the calculated intensity distributions of the fundamental TE-like modes of the rib waveguides; (b) top view of the device geometry; (c) SEM image showing the parabolically broadening transition from the photonic wires to the rib waveguides; (d) SEM image showing the corrugations of a device with the propagation constants labeled and the directions of propagation indicated. 4000 OPTICS LETTERS / Vol. 36, No. 20 / October 15, 2011 Measured and simulated drop-port  spectrum Wei Shi, Opt . Let t ., 36, p. 3999 Figure 4.10: Measured and simulated drop-port spectrum of a device with [D, G] = [220 nm, 1 µm]. Figure 4.11: Dielectric perturbation distribution along the longitudinal di- rection. The inset is the SEM image of the tilted cross-section of a device. the bandwidth on the coupler gap. 4.3.3 Summary To summarize, we have designed and characterized the add-drop filters using contra-directional couplers in SOI rib waveguides that can be easily inte- grated with strip waveguides by using parabolic slab tapers. Our measured bandwidths ranged from 0.35 nm to 1.38 nm, depending on the corrugation size and the coupler gap. The pattern-size effect of the plasma-etch has been considered in the calculations using coupled-mode theory and the mode so- lutions. The simulated results show good agreement with experiment. In 54 4.4. Anti-Reflection Contra-Directional Couplers Figure 4.12: Measured drop-port spectra with different corrugation param- eters: (a) [D, G] = [220 nm, 800 nm]; (b) [220 nm, 1 µm]; and (c) [120 nm, 1 µm]. conclusion, the demonstrated SOI rib-waveguide contra-directional couplers offer an FSR-free, accurately controlled solution for narrow-bandwdith add- drop filters and should find wide applications in optical communications. 4.4 Anti-Reflection Contra-Directional Couplers6 Two main issues related to WDM applications in silicon photonics lie in the high thermal sensitivities of the effective indices of silicon optical waveguides [48] and the fabrication-induced non-uniformity [69]. It has been anticipated that thermal tuning will have a significant impact on the overall power budget of silicon photonics technology [69]. Therefore, considering cost and power consumption, technologies with wide channel grids within a broad band, e.g., coarse WDM (CWDM), may be more promising than finer-grid 6A version of Section 4.5 will be published: Wei Shi, Xu Wang, Charlie Lin, Han Yun, Yang Liu, Tom Baehr-Jones, Michael Hochberg, Nicolas A. F. Jaeger, and Lukas Chros- towski, “Electrically Tunable Resonant Filters in Phase-Shifted Contra-Directional Cou- plers”, San Diego, CA, 29/08/2012 (Accepted, Paper # WP 2). 55 4.4. Anti-Reflection Contra-Directional Couplers 700 800 900 1000 1100 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Coupler Gap, G [nm] B a n d w id th [n m ] D=220 nm, Experimental D=220 nm, Numerical D=180 nm, Experimental D=180 nm, Exponential Fit D=120 nm, Experimental D=120 nm, Exponential Fit Figure 4.13: Measured and simulated drop-port bandwidth vs. coupler gap for various sizes of corrugation, showing the inverse exponential relationship (numerical modeling was only performed for the D=220 nm devices since FIB-SEM cross-sectional images were only available for these devices). technologies, e.g., dense WDM (DWDM), on the silicon-on-insulator (SOI) platform in the near future for a wide variety of applications, e.g., optical interconnects. Although various WDM devices have been demonstrated on the SOI platform, few of them are suitable for CDWM applications. For example, optical add-drop filters using microring or microdisk resonators are a common approach for on-chip WDM systems [52]. However, they have Lorentzian responses and limited free-spectral ranges (FSRs) [52]. The smallest microdisk demonstrated is ∼ 1.5 µm in radius with an FSR of ∼ 70 nm [51, 52], allowing only three CWDM channels (ITU-T G.694.2). It is also challenging to have wide-bandwidth, flat-top responses using high- order microring/microdisk resonators since losses increase dramatically with the number of cascaded resonators. The contra-DCs demonstrated in the previous sections provide a promis- 56 4.4. Anti-Reflection Contra-Directional Couplers ing solution for flat-top, no-FSR add-drop filters. However, these devices still suffer from intra-waveguide Bragg reflections, which weakens their applica- bility. The widest detuning, demonstrated so far, of the intra-waveguide Bragg wavelength from the coupling wavelength is 38 nm [49] that covers the entire span of the C-band but is insufficient for CWDM applications. Here, we demonstrate a novel add-drop filter using an anti-reflection (AR) contra-DC allowing for single-band operation in an ultra-broad spectrum (e.g., in CWDM). 4.4.1 Principle and Design As we have discussed in the previous sections, both band-limited, contra- directional coupling and intra-waveguide reflections can happen at the corre- sponding wavelengths. As an example, Fig. 4.14 shows a sidewall-modulated contra-DC and the calculated effective indices using a mode solver (waveg- uide geometries will be described below) and the Bragg wavelengths. In a typical design of first-order gratings (i.e., 1/2-λ pitch), the contra-DC, as opposed to add-drop filters using microrings or microdisks, has single-band transmission at λD, i.e., no FSR, in its drop-port response. However, the usable spectral range is still limited by the spacing between λD and λa or λb due to the intra-waveguide Bragg reflections. As we have seen in Sec- tion 4.3, this spacing can be extended by increasing the coupler asymmetry (i.e., |na − nb|), e.g., increasing the difference of the waveguide widths [47], nevertheless, this approach is still limited by reasonable insertion losses and single-mode operation. To overcome the issue of intra-waveguide Bragg reflections, we have de- 57 4.4. Anti-Reflection Contra-Directional Couplers (a) Through Input Drop .. . Add ⇤ .. . Wb Wa λa λD Through Input .. . Add .. . Wa λD ⇤ Drop ∆Wb ∆Wa ∆Wb Wb ∆Wb ∆Wa ∆Wa /2 (b) 1500 1520 1540 1560 1580 1600 2.3 2.35 2.4 2.45 2.5 2.55 Wavelength, nm Ef fe ct iv e in de x nb n av n a λ/(2Λ) W a Wb h λ a λD λb Figure 4.14: (a) Schematic top view of a contra-DC without the AR design; (b) Calculated effective indices of the first two TE-like modes in the device illustrated in (a). veloped an AR design in the Bragg waveguides. The structure is illustrated in Fig. 4.15(a), in which periodic perturbations are formed on both sides of each waveguide. As opposed to conventional Bragg waveguides (where the gratings on both sides are in-phase [58]), in this AR design the grat- ings on the inside and the outside of each waveguide are out of phase by a quarter-wavelength. Therefore, the light reflected by the gratings on each side of a waveguide will see a destructive interference and, thus, the intra- waveguide Bragg reflection can be significantly suppressed (as shown in the experimental results below). It is important to be aware that the greatest contribution to the inter-waveguide coupling is due to the gratings in the gap region, which are still in-phase. To demonstrate the concept of out-of-phase gratings, we fabricated the contra-DCs, with and without the AR design, using e-beam lithography and plasma etching. The devices are based on side-wall-modulated SOI strip 58 4.4. Anti-Reflection Contra-Directional Couplers (a) Through Input Drop .. . Add ⇤ .. . Wb Wa λa λD Through Input .. . Add .. . Wa λD ⇤ Drop ∆Wb ∆Wa ∆Wb Wb ∆Wb ∆Wa ∆Wa /2 (b) Λ/2 DropInput Figure 4.15: (a) Schematic top view of an Ar contra-DC; (b) SEM images of the AR contra-DC. waveguides with heights of 220 nm, an input/through waveguide width, Wa, of 500 nm, an add/drop waveguide width, Wb, of 450 nm, and an average coupler gap of about 60 nm. The corrugation amplitude on the sidewalls, 4Wa and 4Wb, are 50 nm and 30 nm, respectively. The gratings have a pitch, Λ, of 320 nm, a duty cycle of 50%, and a period number, N , of 800 (corresponding to an effective length of 256 µm). 4.4.2 Experimental Results and Discussion The measured results for the through ports of the devices, with and without the AR design, are shown in Fig. 4.16. We can see that there are two notches in the through-port spectrum of the non-AR device (i.e., only in- phase corrugations are formed on the sidewalls between two waveguides). The first notch, at 1528 nm, is due to the internal Bragg reflection of the input/through waveguide, while the second notch, at 1550 nm, corresponds to the contra-directional coupling between the waveguides. The spacing between the two notches is about 22 nm, which allows only one CWDM 59 4.4. Anti-Reflection Contra-Directional Couplers 1460 1490 1520 1550 1580 1610 1640 −25 −20 −15 −10 −5 0 Wavelength, nm N or m al iz ed  T ra ns m iss io n,  d B λ a λ D Shi, Wei ©2012 Measured Spectra 23 Single-side design Double-side corrugations with quarter-wavelength phase mismatch λD λa λD 1460 480 1500 1520 15 1560 1580 1600 1620 1640−25 −20 −15 −10 −5 0 Wavelength, nm No rm ali ze d Re sp on se , d B  1460 1480 1500 1520 1540 1560 1580 1600 1620 1640−25 −20 −15 −10 −5 0 Wavelength, nm No rm ali ze d Re sp on se , d B  (a) 1460 1490 1520 1550 1580 1610 1640 −25 −20 −15 −10 −5 0 Wavelength, nm N or m al iz ed  T ra n sm iss io n,  d B λ D 6.5 nm Shi, Wei ©2012 Measured Spectra 23 Single-side design Double-side corrugations with quarter-wavelength phase mismatch λD λa λD 1460 1480 1500 1520 1540 1560 1580 1600 1620 1640−25 −20 −15 −10 −5 0 Wavelength, nm No rm ali ze d Re sp on se , d B  1460 1480 1500 1520 1540 1560 1580 1600 1620 1640−25 −20 −15 −10 −5 0 Wavelength, nm No rm ali ze d Re sp on se , d B  (b) Figure 4.16: Measured through-port optical spectrum normalized using the response of a pair of fibre grating couplers: (a) without the anti-reflection design; (b) with the anti-reflection design. Insets: SEM images of the de- vices. 60 4.5. Phase-Shifted Contra-Directional Couplers channel (20 nm in ITU-T G.694.2). These results show good agreement with the values predicted using Fig. 4.14(b). The through-port spectrum of the AR device is shown in Fig. 4.16(b). In contrast to the former case, this novel design shows only a single, deep notch within a wide spectral range (180 nm), the entire span of the tunable laser. By controlling the coupler gap and the corrugation amplitude, the notch bandwidth can be engineered ranging from sub-nanometers to nanometers [48, 58] and, in this case, is ∼ 6.5 nm. The chosen bandwidth implies that the add-drop filter should be able to operate in a temperature span of > 70 oC without thermal control (the thermal sensitivity of the device was characterized as 0.09 nm/K). These results suggest that this novel athermal device is promising for on- chip, broad-spectrum WDM applications. 4.5 Phase-Shifted Contra-Directional Couplers7 Silicon photonic resonators are promising for large-scale photonic integrated circuits in a wide range of applications in optical communications and sens- ing systems [21, 43]. High-Q optical resonators can by obtained using 1D photonic crystals (PCs) [32] or Bragg gratings [60]. We have recently demon- strated a transmission filter, or Bragg-grating based resonator, using phase- shifted Bragg gratings with a highQ of 100,000 [60]. Like normal Bragg grat- ings, these Bragg-grating based resonators also operate in reflection mode (2-port device) and have the challenging requirement to integrate an optical 7A version of Section 4.5 will be published: Wei Shi, Mark Greenberg, Xu Wang, Yun Wang, Charlie Lin, Nicolas A. F. Jaeger, and Lukas Chrostowski, “Single-Band Add-Drop Filters Using Anti-Reflection, Contra-Directional Couplers”, San Diego, CA, 29/08/2012 (Accepted, Paper # WA 7). 61 4.5. Phase-Shifted Contra-Directional Couplers circulator. The contra-DCs, as demonstrated in previous sections, have no, or very weak, reflection at the operating wavelength, so they intrinsically function as wavelength-selective 4-port device [67]. In this section, we demonstrate a novel resonantor by introducing a 1/4-λ phase-shift into the grating-assisted contra-directional coupler. We further extend this concept into an electri- cally tunable, 4-port optical switch. It is promising for systems operating in ultra-wide spectral ranges, e.g., 1211 to 1611 nm in CWDM. 4.5.1 Design As shown in Fig. 4.17(a), the contra-directional coupler consists of two waveguides with different widths and with periodic dielectric perturbations formed in the coupling region. The device is based on an SOI rib-waveguide structure with a rib height of 210 nm and a slab thickness of 110 nm. The coupler has an input/through waveguide width, Wa, of 600 nm, an add/drop waveguide width, Wb, of 400 nm, and a coupler gap, G, of 200 nm. The dielectric perturbations are formed on both the sidewalls of the waveguide ribs and the slab between them, to achieve a strong coupling. The corruga- tion amplitude on the rib-sidewalls, 4Wa and 4Wb, are 50 nm and 30 nm, respectively. The grating pitch, Λ, is 300 nm with a duty cycle of 50%. The period number, N , is chosen to be 700, corresponding to a device length of 210 µm. A 1/4-λ phase-shift, as shown in Fig. 4.17(b), is introduced in the centre of the coupler (i.e., 350 grating periods on each side of the phase-shift). A p-i-n configuration is used for frequency tuning. The n+ (5.5× 1018 cm−3) and p+ (5.7× 1018 cm−3) regions are 200 nm away from 62 4.5. Phase-Shifted Contra-Directional Couplers Through Input Drop ⇤ .. . .. . Add Grating C2 C1 Through Input Drop ⇤ ⇤Phase Shift .. . .. . Add Grating C2 C1 (a) (b) Wa WbG p+ p++n+n++ n Contact p Contact p+ p++n+n++ n Contact p Contact∆Wb ∆Wa Grating C1 C2 (c) Figure 4.17: a) Schematic top-view of a contra-directional coupler; b) Phase- shifted contra-directional coupler; c) Cross-sectional views of the contra- directional couplers at the positions (C1 and C2) indicated in (a) and (b). 63 4.5. Phase-Shifted Contra-Directional Couplers the edges of the waveguide ribs. Thus, the intrinsic region includes 600 nm of slab and 1 µm of rib waveguide, for a total distance of 1.6 µm. The devices were fabricated by BAE Systems via the OpSIS foundry service [26]. Fibre grating couplers [38] were used for the optical measurement. 4.5.2 Optical Spectra The measured and simulated spectra of the phase-shifted device are shown in Fig. 4.18. A resonant peak and, correspondingly, a deep notch are clearly shown in the middle (at 1519.6 nm) of the through-port spectrum and the drop-port spectrum, respectively, within a stop-band of about 7 nm. The central wavelength of the device can be varied by controlling the grating pitch [47]. Therefore, we can use multiple such devices, with a spectral spacing, e.g., of 20 nm (ITU-T G.694.2), in a CWDM system. The through- port transmission peak has an out-of-band rejection ratio of more than 17 dB and a 3-dB bandwidth of 0.2 nm corresponding to a Q of about 7,000. The notch in the drop-port response has an extinction ratio of over 24 dB. These performance metrics can further be improved by optimizing the coupling strength and the coupler length. The device was simulated using coupled- mode theory [66], with the modes calculated by a mode solver, and the transfer-matrix method, as in Ref. [47, 48]. As seen in the Fig. 4.18(b), the simulation results show good agreement with experiment. It is worth point- ing out that the filter is resonant at the central wavelength of the drop-port response, i.e., at the phase-match condition of the contra-directional cou- pling that significantly detuned (by over 20 nm in this case) from the Bragg condition of the intra-waveguide reflection. This means that, as opposed 64 4.5. Phase-Shifted Contra-Directional Couplers 1515 1520 1525 −30 −25 −20 −15 −10 −5 0 Wavelength, nm N or m al iz ed  R es po ns e,  d B   Through port Drop port 1500 1510 1520 1530 1540 1550 1560 −22 −20 −18 −16 −14 −12 −10 −8 −6 −4 −2 0 (a) −4 −3 −2 −1 0 1 2 3 4 −25 −20 −15 −10 −5 0 Wavelength Detuning, nm R es po ns e,  d B   Through port Drop port (b) Figure 4.18: (a) Measured optical spectra (Inset: Extended view of the optical spectrum (1500-1560 nm) of the through port, showing single-mode operation, superimposed on the fibre grating coupler’s spectral response); (b) Simulated optical spectra. 65 4.6. Summary to conventional transmission filters using Bragg cavities (e.g., VCSELs or Bragg waveguides [60]), no or very weak Bragg reflection happens at the operating wavelength or within the stop-band. 4.5.3 Electrical Tuning The device is electrically probed and the spectra for various tuning currents are shown in Fig. 4.19. The device yields a wavelength shift of 0.8 nm for a current of 1.5 mA and operates under 1.0 V. This tuning response is plotted in Fig. 4.20 and has a tuning coefficient of -0.73 nm/mA. Noticing that the current is uniformly injected into the whole device along the longitudinal direction, the tuning efficiency may be significantly enhanced by optimizing the overlap of the current density with the longitudinal optical intensity dis- tribution. In this uniform injection case, the electrical tuning shifts both the Bragg stop-band as well as the resonant mode simultaneously (not shown in figure). For large tuning currents, free-carrier absorption introduces excess loss, thus, reducing the Q and the extinction ratio. For example, at 3 mA, the Q is reduced to 2,000. The small-signal modulation frequency response of the device is shown in Fig. 4.21 and has a 3-dB bandwidth of 90 MHz limited by the lifetime of the injected carriers. 4.6 Summary We have conducted theoretical and experimental investigation on silicon contra-DCs using either side-wall-modulated strip waveguides or slab-modulated rib waveguides. 66 4.6. Summary 1518.4 1518.6 1518.8 1519 1519.2 1519.4 1519.6 1519.8 1520 −25 −20 −15 −10 −5 0 Wavelength, nm N or m al iz ed  R es po ns e,  d B   0.0mA, 0.0V 0.08mA, 0.827V 0.15mA, 0.852V 0.3mA, 0.883V 0.4mA, 0.898V 0.6mA, 0.920V 0.8mA, 0.938V 1.0mA, 0.957V 1.5mA, 0.990V Figure 4.19: Drop-port spectra with various currents We also demonstrated three novel photonic filters in contra-DCs. The first device is an add-drop filter in the slab-modulated rib waveguides that can be easily integrated with strip waveguides by using parabolic slab ta- pers. Our measured bandwidths ranged from 0.35 nm to 1.38 nm, depend- ing on the corrugation size and the coupler gap. The pattern-size effect of the plasma-etch has been considered in the calculations using coupled-mode theory and the mode solutions. The simulated results show good agree- ment with experiment. This rib-waveguide contra-DC offer an FSR-free, accurately controlled solution for narrow-bandwdith add-drop filters for op- tical communications. The second device is a wide-bandwidth add-drop filter using SOI contradirectional couplers with a novel anti-reflection de- sign. Single-band operation, with a bandwidth of 6.5nm and an extinction ratio of over 20 dB, has been experimentally obtained. This novel anti- reflection design enables athermal operation in a wide temperature range and is attractive for on-chip CWDM applications. Furthermore, we have 67 4.6. Summary 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 Current (mA) ∆ λ (nm )   Experimental data Fit Figure 4.20: Resonant-wavelength shift as a function of current . 108 109 −100 −90 −80 −70 −60 Frequency, Hz R es po ns e,  d B   RF: −19 dBm, DC: 0.3 mA, 1519.65 nm RF: −19 dBm, DC: 1.0 mA, 1519.25 nm −20 dB/decade Noise floor Figure 4.21: Frequency response. proposed and experimentally demonstrated an electrically tunable resonant filter using phase-shifted contradirectional couplers in silicon waveguides. This novel resonant filter is promising for applications such as high-speed optical switching and modulation in photonic integrated circuits. 68 Chapter 5 Grating-Coupled Microring Resonators8 In the last two chapters, we have investigated multiple devices based on two classes of wavelength filtering components: TWRs and grating-based couplers. They both have advantages and disadvantages. TWRs, such as microrings and microdisks, are very compact, typically in a scale of µm. However, TWRs suffer from having limited FSRs, which limits the number of usable channels in WDM systems and detectable range in sensing appli- cations. In contrast, grating-based devices, such as contra-DCs, do not have the issue of FSRs, but they are relatively long (hundreds of µm to mm). In this chapter, we demonstrate a novel photonic resonator based on the in- tegration of TWRs with contra-DCs, in an effort towards compact, high-Q resonators without the limitation of FSRs. Microring resonators are expected to be essential components in next- generation, integrated photonic circuits. A variety of microring-based de- vices have been developed for the complementary metal-oxide-semiconductor 8A version of Chapter 5 has been published: Wei Shi, Xu Wang, Wen Zhang, Han Yun, Charlie Lin, Lukas Chrostowski, and Nicolas A. F. Jaeger “Grating-coupled silicon microring resonator”, Appl. Phys. Lett., vol. 100: pp. 12118-12118-4, 2012. 69 Chapter 5. Grating-Coupled Microring Resonators (CMOS) compatible silicon-on-insulator (SOI) platform, with applications in optical communications, computing platforms, optical-signal processing, and sensing [35, 48, 64]. To selectively excite or suppress longitudinal modes of microring resonators for broader-band operation, major effort has gone into engineering optical ring cavities, e.g., using series-coupled or cascaded multiple rings with the Vernier effect [14] or inserting Bragg gratings inside the ring cavity [11]. Control of the couplings between the microrings and the bus waveguides is also critical for shaping the spectral responses [65], which is challenging when the bend radius is scaled down to a few micrometers. Here, we propose to use grating-assisted asymmetric couplers[67] for selec- tive resonance excitation and experimentally demonstrate a grating-coupled microring resonator. In contrast to broadband directional couplers used by conventional mi- croring resonators, grating-assisted couplers have limited bandwidths which provide the proposed microring resonators with an extra degree of freedom for longitudinal-mode selectivity. Highly-efficient silicon grating-assisted couplers have recently been demonstrated using sidewall-modulated strip waveguides [57] and slab-modulated rib waveguides [47]. Their coupling ef- ficiencies and bandwidths can be easily tailored by controlling the waveguide geometries and dielectric perturbations [47, 57]. Integrating these grating- assisted couplers into a microring resonator enables accurate control of the couplings between the microring and its bus waveguides, as well as provides an extended usable band that, otherwise, is limited by the free-spectral range (FSR) determined by the optical round-trip length of the ring cavity. The principle of the mode selectivity will be discussed below in the context of a 70 5.1. Principle Input Drop Through (a) kg kb (b) kg kb Wb Wr R kg 1 µm Figure 5.1: (a) Schematic of the proposed grating-coupled microring res- onator. The red solid lines and the blue dashed lines indicate the optical paths associated with the grating-assisted contradirectional coupling, kg, and the broadband codirectional coupling, kb, respectively. (b) SEM image (top view) of the sidewall-modulated contradiretional coupler used in the grating-coupled microring resonator. proof-of-concept device presented here. 5.1 Principle The schematic of the device is illustrated in Fig. 3.8(a). It functions as an add-drop filter consisting of a racetrack resonator and a pair of grating- assisted contradirectional couplers. Each contradirectional coupler is com- posed of two optical waveguides (with different widths and, therefore, dif- ferent effective indices) and periodic dielectric perturbations in the coupling region. With one input, optical resonances within the ring cavity could be excited in two directions: clockwise and conter-clockwise, associated with the broadband codirectional coupling, kb, and the grating-assisted contradi- rectional coupling, kg, respectively. Due to the different propagation con- stants, the broadband codirectional coupling is very weak, hence the ring 71 5.2. Experiment Microring λ Grating-coupled microring λ SMSR (b) Contradirectional coupler (a) Figure 5.2: Illustration of the operation principle: (a) spectral responses of the microring resonator with and the contradirectional coupler; (b) spectral response of the grating-coupled microring resonator, with the side-mode suppression ratio (SMSR) labeled. oscillates primarily in the direction opposite to a regular ring resonator, i.e., counter-clockwise for a signal at the input port. For the counter-clockwise resonance associated with kg, efficient coupling between the two waveguides only occurs near the wavelength that satisfies the phase-match condition [67]. Therefore, the longitudinal modes outside of the drop-port passband would not be effectively excited. The operating principle is illustrated in Fig. 5.2, showing the drop-port spectrum of the grating-coupled micror- ing resonator as a result of filtering the spectral response of the microring resonator by the wavelength-selective coupling of the grating-assisted con- tradirectional couplers. 5.2 Experiment The device was fabricated using a CMOS-compatible SOI technology. The ring cavity and the bus waveguides are made of 210-nm-high silicon pho- tonic strip waveguide on a 2-µm-thick buried oxide with a 2-µm-thick oxide 72 5.2. Experiment cladding. The ring waveguide width, Wr, is about 470 nm. The bus waveg- uide width, Wb, is about 370 nm. The dielectric perturbations, as shown in Fig. 3.8(b), are formed by corrugating the sidewalls between the cou- pler waveguides, with a corrugation depth of about 15 nm, a perturbation period, Λ, of 330 nm, and a period number of 400. The coupler gap is about 210 nm. The circular waveguides of the resonator have a bend radius, R, of 20 µm. The fabrication was performed by Imec, Belgium, accessed via ePIXfab, using 193-nm lithography. TE-preferred fiber grating couplers (FGCs) [15] were used for measurement. The measured spectra of a grating-coupled microring add-drop filter with the design described above are shown in Fig. 5.3. A dominant longitudinal mode, at 1504.6 nm, of the ring cavity is selected within our laser’s tuning span of over 130 nm. The drop-port spectrum shows a side-mode suppression ratio of more than 8 dB, which is limited by the modes immediately adjacent to the selected mode. Considering the small FSR (1.3 nm) of the ring cavity, this indicates a strong mode selectivity of the contradirectional couplers. Be- sides the adjacent modes, the other small resonant peaks are caused by the residual broadband codirectonal coupling, which can be further suppressed by increasing the coupler’s asymmetry, i.e., the effective-index difference be- tween the coupled modes. The through-port spectrum has the envelope of the FGCs’ response, with a coupling loss of -18.5 dB at the transmission peak near 1518 nm. As seen in the inset of Fig. 5.3(a), the extinction ratio is more than 10 dB at the selected mode. The inset of Fig. 5.3(b) shows the drop-port spectral shape at the selected mode with an out-of-band-rejection ratio of 19 dB and a 3-dB bandwidth of 60 pm that corresponds to a quality 73 5.2. Experiment factor (Q) of about 25,000, comparable with conventional microring res- onators using broadband directional couplers. This means that the gratings do not introduce significant additional losses. In addition to the longitudi- nal modes of the ring cavity, the through-port spectrum also shows a deep notch at 1465 nm, which is caused by the intra-waveguide reflection, i.e., the Bragg reflection inside the input bus waveguide, consistent with the fol- lowing modelling and experimental results for the isolated contradirectional coupler. To verify the wavelength selectivity, we calculate the TE-like modes in the contradirectional coupler using an eigenmode solver. Shown in Fig. 5.4, nr and nb are the wavelength-dependent effective indices of the ring waveg- uide and the bus waveguide, respectively. The calculated results are shown in Fig. 5.4, from which we can find the Bragg wavelengths, λr = 2Λnr and λb = 2Λnb, due to the intra-waveguide Bragg reflections and the drop- port peak wavelength, λD = 2Λnavr, navr = (nr + nb)/2, due to the inter- waveguide coupling [47, 67]. The longitudinal modes of the ring cavity satisfy the resonant condition: mλm = nrLr, m = 1, 2, 3..., where λm and Lr are the mth resonant wavelength and the round-trip length, respectively. In Fig. 5.4, we can see that the 623rd mode, at 1504.6 nm, is nearest to λD, and, therefore, is selected by the contradirectional coupler. The spacing between λD and λb or λr is about 40 nm, easily covering the span (35 nm) of the entire optical-communication C-band. Notably, Bragg refection at λb happens inside the input waveguide and, therefore, has a significant effect on the through-port spectrum, as shown in Fig. 5.3. However, the effect of Bragg reflection at λr is negligible because very little light at this wavelength 74 5.2. Experiment 1460 1485 1510 1535 1560 −40 −35 −30 −25 −20 Wavelength, nm (a) P o w er , d B m 1504.5 1504.6 1504.7 −30 −25 −20 Wavelength, nm P o w er , d B m 1460 1485 1510 1535 1560 −50 −45 −40 −35 −30 −25 Wavelength, nm (b) P o w er , d B m 1504.4 1504.6 1504.8 −40 −30 −20 Wavelength, nm P o w er , d B m 60 pm Figure 5.3: Measured spectra of the grating-coupled add-drop microring resonator: (a) through-port; (b) drop-port. The insets show the zoomed-in spectra near the selected longitudinal mode. 75 5.2. Experiment is coupled into the ring waveguide. A separate contradirectional coupler, using the same cross-sectional de- sign as in the grating-coupled microring resonator, but with longer gratings (2000 periods), was also fabricated on the same chip. Its measured spectra are shown in Fig. 5.5. The drop-port spectrum has a peak at 1504.7 nm. The through-port also shows a deep notch around 1465 nm that corresponds to the intra-waveguide Bragg reflection. These results are in good agreement with the simulation and the experimental results of the grating-coupled mi- croring resonator, confirming the mode selectivity of the contradirecitonal coupler used in it. As shown in the inset of Fig. 5.5, the bandwidth between the first nulls near λD is about 0.9 nm. Following the procedure described in our previous work [47], the distributed coupling coefficient of the contradi- rectional coupler is determined to be 2000 m−1. Using the transfer-matrix method[47], the lumped distributed propagation loss of the ring cavity is determined to be 4 dB/cm. Thermal tuning was also performed using a thermoelectric temperature controller [48]. The gratings and the micror- ing have the same temperature sensitivity of 0.09 nm/K, which indicates that the mode selectivity is insensitive to environmental temperature or refractive-index variations. Using the coupled-mode analysis for the coupling efficiency of the contra- DCs (Chapter 4) and the transfer-matrix method for the microring resonator (Chapter 3), the transmission spectra of the microring resonators, with and without using the grating-assisted contradirectional couplers, are calculated and shown in Fig. 5.6. Due to the shorter length, the contradirectional cou- plers integrated in the microring resonator have a wider first-null bandwidth 76 5.3. Discussion of 4 nm, covering two FSRs of the ring cavity, which results in the limited suppression of the modes adjacent to the selected mode. 1460 1480 1500 1520 1540 1560 1580 2 2.1 2.2 2.3 2.4 2.5 2.6 Wavelength, nm Ef fe ct iv e in de x n r n avr nb λ/(2Λ) mλ/L r m=621:625 Wb Wr h λb λD λr Figure 5.4: Calculated effective indices of the first two TE-like modes of the contradirectional coupler and the mode conditions. The inset shows the calculated electrical-intensity distribution of the coupled modes in the contradirectional coupler. 5.3 Discussion Although our initial design for the purpose of demonstrating the concept works, we see significant room for improvement. Firstly, the side-mode sup- pression ratio can be enhanced by using a smaller radius to increase the FSR of the ring cavity and improving the alignment between λD and the se- lected longitudinal mode. Considering wafer non-uniformity and fabrication errors, the tuning of operating frequencies is important for integrated silicon resonant devices. In CMOS-photonics fabrication, non-uniformity across a die or wafer contributes the most to frequency shift or spectral misalign- 77 5.3. Discussion 1460 1470 1480 1490 1500 1510 1520 −65 −60 −55 −50 −45 −40 −35 −30 −25 Wavelength, nm Po w er , − dB m   Through Drop 1504 1505 −50 −40 −30 λ, nm Po w er , − dB m Figure 5.5: Measured spectral responses of the contradirectional coupler with 2000 periods of gratings. The inset shows the zoomed-in spectra near that drop-port peak wavelength. ment between various resonant components[69]. In the device presented here, this issue is much relaxed due to the close proximity of the grating and the ring cavity. Reasonably good, though not perfect, alignment has been achieved. Nevertheless, in general, symmetric-corrugation design can minimize the sensitivity of the grating central wavelength to variations in corrugation depths[61], and better alignment can be obtained with inde- pendent control of the refractive indices of the grating-assisted coupler and the ring cavity, either by active tuning, such as local heating or carrier injection (e.g., in the configuration shown in Fig. 5.1(a), we can heat the bend-waveguide sections or inject carriers into them via a pin junction), or by doing permanent trimming, such as ion implantation[5]. In addition, the usable band, i.e., the spacing between λD and λb or λr, can be further extended by increasing the coupler asymmetry. Since the phase-matching 78 5.3. Discussion 1500 1502 1504 1506 1508 1510 −12 −10 −8 −6 −4 −2 0 Th ro ug h− po rt tra ns m iss io n,  d B Wavelength, nm   0 0.012 0.024 0.036 0.048 0.06 0.072 |k g | (a) (b) (c) Figure 5.6: Calculated spectra: (a) through-port response of the conven- tional microring resonator; (b) coupling coefficient (kg) of the grating- assisted contradirectional coupler; (c) the through-port response of the grating-coupled microring resonator. A propagation loss of 4 dB/cm is used in the calculation. condition for the contradirectional coupler can always be achieved by choos- ing an appropriate grating pitch, greater asymmetry would be desired for further suppressing the broadband codirectional coupling, which is benefi- cial for greater mode selectivity. Furthermore, a circular geometry can be used for a more compact cavity. In order to obtain an appropriate cou- pling efficiency, the racetrack configuration is used in many conventional microring resonators [14, 47] due to the difficulty in controlling the point coupling. However, for the grating-coupled microring resonator, as illus- trated in Fig. 5.7, the dielectric perturbations can be easily formed on bent waveguides without concern about bend-induced phase-mismatch, enabling control of coupling efficiency at the selected mode by choosing an appro- priate period number. To optimize the design with the above mentioned points taken into consideration, thorough modelling and analysis should be 79 5.4. Summary conducted in future work. Input Through Input Through (a) (b) kb kb kgkg Figure 5.7: Coupling schemes of a circular microring geometry: (a) broad- band point-coupling; (b) grating-assisted wavelength-selective coupling. The blue dashed lines and the red solid lines indicate the optical paths associ- ated with the broad-band codirectional coupling, kb, and the grating-assisted contradirectional coupling, kg, respectively 5.4 Summary In summary, we have proposed and demonstrated a grating-coupled silicon microring resonator. For a microring resonator with a small FSR of 1.3 nm, a dominant longitudinal mode, with a side-mode suppression ratio of 8 dB, has been selectively excited within a broad spectrum of over 130 nm. Its perfor- mance can be further enhanced by optimizing the designs of the gratings and the ring cavity. Due to the high-quality of the CMOS-photonics fabrication, the gratings do not introduce significant additional losses. Therefore, the high-Q performance of the microring resonator is maintained. This high-Q, single-mode operation is desired by many applications such as multichannel sensing systems[30]. The concept of the grating-coupled microring resonator can be applied to other microring-based devices to achieve various functions for a wide variety of applications. 80 Chapter 6 Conclusion and Future Work 6.1 Conclusion In summary, we have studied, in theory and experiment, traveling-wave res- onators devices and contra-directional couplers. Multiple novel photonic fil- ters have been designed, simulated, and characterized. Contributions made in this fabless research using CMOS-photonics manufacturing include: • Demonstration of grating-assisted, contra-directional couplers (contra- DCs) in silicon rib waveguides, with narrow bandwidths of 50–100 GHz for DWDM applications; • Demonstration of single-band, flat-top add-drop filters in silicon using contra-DCs, with wide bandwidths of up to 6.5 nm (athermal opera- tion in a temperature span of >70 K), for on-chip CWDM systems; • Demonstration of a single dominant resonant mode in a microring resonator within a spectral range of 180 nm (limited by the tunable laser used in the experiment), using contra-DCs; • Demonstration of phase-shifted contra-DCs which are grating-based four-port resonant filters with single-band operation; 81 6.1. Conclusion • Demonstration of silicon microdisk reflectors for tunable lasers and remote sensing applications; • Demonstration of ultra-compact, high-Q microdisk resonators, using CMOS-photonics manufacturing, with radii of down to 1.5 µm, FSRs of up to 71 nm, loaded Q’s of up to 88,000 (λ ∼ 1.5 µm), and unloaded Q’s of over 100, 000; • Development of a ring-resonator-based method for measuring optical losses of integrated optical components, a step toward to an accurate, efficient technique for calibration of silicon-photonics manufacturing; • Development of an optical characterization system, including fiber to waveguide coupling alignment, temperature control, computer control, and optical transmission measurement. The important performance parameters of the devices demonstrated in this work are summarized in Table 6.1. For on-chip applications such as TWR reflectors for tunable lasers or remote sensing, CWDM, and high-Q resonator sensors, we have compared our developed devices with the state- of-the art devices developed by other groups and listed the important per- formance parameters in Table 6.2. We conclude this thesis by identifying the potential of our developed photonic filters for various applications: • DWDM requires a channel bandwidth of 50 to 100 GHz. Poten- tially, microdisks, contra-DCs, and GC-microrings can all be used for DWDM networks. However, we need to consider the power efficiency of thermal trimming necessary due to the manufacturing non-uniformity. 82 6.1. Conclusion In this sense, mirodisks are most promising for their very compact size, although they have Lorentzian-shape responses and multiple- transverse modes. A flat-top response can be achieved by series cou- pling 2 or 3 microdisks. A novel method of using doping to have a single transverse mode will be discussed in the next section as part of future work. Microrings are less suitable since their FSRs are less than the span of the communication C-band. • CWDM has wider channel spacings and bandwidths. It allows for a relaxed tolerance to temperature and manufacturing non-uniformity; this gives rise to a more attractive power budget than DWDM since no thermal trimming or tuning is required. The best candidate among the investigated devices is the AR conta-DC. Wide-bandwidth Si or Si3N4 demultiplexers (8 to 12 channels) have recently been demonstrated using echelle gratings [29] or arrayed waveguide gratings (AWG) [27], showing excellent performance (summarized in Table 6.2), however, they are very bulky. Using the AR contra-DCs, the size of the demul- tiplexer can be shrunk by 1,000 times. The TWRs are not suitable due to their limited FSRs. For example, the state-of-the-art high- order microring resonator filters have a 1-dB pass band of about 2.5 nm and a FSR of 18 nm, allowing only 6 channels [62]. Even though the microdisk with a 1.5 µm radius has an ultra-wide FSR of 71 nm, it can only cover 3 CWDM channels. GC-microring resonators can potentially have a single longitudinal mode and, therefore, are not limited by FSRs. Multiple GC-microrings can be coupled in series to 83 6.1. Conclusion obtain wide-bandwidth, flat-top responses, which should be considered as future work. • Optical Routing or Switch: microdisks are the best candidate for opti- cal routing or switching in DWDM systems due to their very compact size and, thus, high tuning efficiency (in nm/mW). In a special sit- uation, if one wants to use an ultra-wide band, e.g., 1200 to 1700 nm, with a fine grid, e.g., 100 GHz, then the GC-microrings and the narrow-bandwidth CDC could be the options. • Tunable Lasers: again, tuning efficiency is the most important fac- tor. The demonstrated microdisk reflector is one of the most compact wavelength-selective reflectors and, therefore, allows a highly compet- itive tuning efficiency. • Optical Loss Measurement: Microring resonators have been shown to be an efficient method to measure the transmission losses of optical components. Standard process control cells based on this approach should be included in future fabrication runs, to determine losses of important components including y-branches, waveguide crossings, 90◦ bends, doped waveguides, rib to strip waveguide converters, etc. • Sensing: In principle, all the resonators, including microdisks, micror- ings, and PS conta-DCs, can be used. The microdisk demonstrated the best performance in terms of Q and size. GC-microrings are very attractive for cascaded sensing systems since they allow high-Q oper- ation within an almost unlimited detection range. 84 6.1. C on clu sion Devices Response Bandwidth Q Size FSR Applications Microring Lorentzian 40 pm – 0.15 nm 10k–30k 5 –100 µm < 20 nm Loss measurement (Radius) Sensing Tunable Laser Microdisk Lorentzian 17 pm – 0.4 nm 4k–88k 1.5–2.5 µm 40–71 nm Sensing (Radius) DWDM Routing/Switch Modulator Tunable Laser Contra-DCs Flat-top 0.35 – 6.5 nm – 240 µm–1.2 mm no CWDM (Length) DWDM Routing/Switch PS Contra-DCs Lorentzian 0.2 nm 7k L=210 µm no Modulator (Length) Routing/Switch GC-Microring Lorentzian 60 pm 25k 20 µm no Sensing (Radius) DWDM Routing/Switch Tunable Laser Table 6.1: Performances of the demonstrated silicon photonic filters. 85 6.1. C on clu sion Applications Devices Response Bandwidth/Q Size FSR or Usable Band TWR reflector Microring∗ Lorentzian 0.12 nm/12.5k R = 30 µm ∼1 nm (notch) Microring [55] Lorentzian 0.2 nm/8k R = 200 µm 1.15 nm TWR reflector Microdisk∗ Lorentzian 0.4 nm R = 1.5 µm 71 nm (band-pass) Microring [40] Lorentzian N/A R = 100 µm 2 nm Microring [11] Gaussian-like 0.4 nm R = 30 µm no CWDM or AR contra-DC∗ Flat-top 6.5 nm 210× 2 µm2 no Wide-BW filter Contra-DC [58] Flat-top 3 nm 2000 µm2/4 25 nm Microring [62] Flat-top 2.5 nm 700 µm2 18 nm Echelle grating [29] Flat-top 5.5 nm 13× 6 mm2/12 N/A AWG [27] Flat-top ∼12 nm ∼ 3× 4 mm2/8 N/A TWR resonator Microdisk∗ Lorentzian 17 pm/88k (Qi > 100k) R = 2.5 µm 42 nm (High-Q) GC-microring∗ Lorentzian 60 pm/25k R = 20 µm no Microdisk [52] Lorentzian 28.6 pm/35k (Qi ∼ 88k) R ∼ 2 µm 57 nm Table 6.2: Performances of the silicon photonic filters demonstrated in this thesis (*) and the state-of-art devices demonstrated by other groups for specific applications. 86 6.2. Future Work 6.2 Future Work 6.2.1 On the Traveling-Wave Resonators With the demonstrated compact size, high Q’s, and ultra-wide FSRs, mi- crodisks have great potential for reconfigurable add-drop filters, in DWDM systems, and multichannel sensors. Suggested future work includes: • Single transverse-mode operation may be achieved by doping the cen- tral region of a microdisk. This is because the high-order transverse modes have better profile overlap with the doping and, therefore, see higher losses than the fundamental mode. A careful mode calculation is needed. • Microdisk based active devices such as optical modulators and switches, using the above mentioned single-transverse-mode design should be developed. Temperature monitoring and a thermal tuning mechanism can be included inside the disk itself to enable dynamic feedback con- trol. • A number of microdisk add-drop filters can be cascaded to construct a DWDM multiplexer/demultiplexer, using the architecture shown in Fig. 1.2. • The microring resonator integrated with a bent-waveguide contra-DC, shown in Fig. 5.7, should be developed for achieving a compact, single- longitudinal-mode TWR. A large number of these TWRs can be cas- caded for a multichannel sensing system. 87 6.2. Future Work 6.2.2 On the Contra-Directional Couplers The long term goal is to develop power-efficient on-chip WDM systems. Future work on the demonstrated AR contra-DCs includes: • Grating apodization. The demonstrated contra-DCs have strong side lobes which may give rise to crosstalk between adjacent channels. These side lobes can be suppressed by using apodization techniques as commonly done in fiber and waveguide Bragg gratings[66]. • Dual-channel add-drop filters in AR contra-DCs, where two drop-port waveguides share a single input-through waveguide for a more compact design. The schematic of the proposed dual-channel add-drop filter using AR contra-DCs is shown in Fig. 6.1. ... ... Through Drop 1 Input Add 1 Λ Perturbation ...... ...... ... ... Drop 2 Add 2 Input ... Through...... ...... ... ... Drop 1 ... ... Drop 2 ... ... ...... ... ... Drop 3 ... ... Drop 4 ... ... ...... ... ... Drop n-3 ... ... Drop n-2 ... ... ...... ... ... Drop n-1 ... ... Drop n Figure 6.1: Schematic of the proposed dual-channel design of AR contra- DCs. • A number of such dual-channel contra-DCs can be cascaded to con- struct a multiplexer/demultiplexer for WDM networks. Fig. 6.2 shows the schematic of such a multiplexer/demultiplexer. For applications in coarse WDM, the ideal spectral response of this multiplexer/demultiplexer is shown in Fig. 6.3, in which each channel is located at a CWDM wave- length, defined by ITU-T G.694.2. The channel bandwidth is chosen 88 6.2. Future Work to be 5 to 10 nm, depending on system specifications, which enables athermal operation within a large temperature range. ... ... Through Drop 1 Input Add 1 Λ Perturbation ...... ...... ... ... Drop 2 Add 2 Input ... Through...... ...... ... ... Drop 1 ... ... Drop 2 ... ... ...... ... ... Drop 3 ... ... Drop 4 ... ... ...... ... ... Drop n-3 ... ... Drop n-2 ... ... ...... ... ... Drop n-1 ... ... Drop n Figure 6.2: Proposed multiplexer/demultiplexer using AR contra-DCs. 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