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Design and characterization of a dumbbell micro-ring resonator reflector Yun, Han 2013

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Design and Characterization of a Dumbbell Micro-Ring Resonator Reflector by Han Yun  B.A.Sc., The University of British Columbia, 2009  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in The Faculty of Graduate Studies (Electrical and Computer Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) May 2013 c Han Yun 2013  Abstract A dumbbell shape micro-ring resonator reflector fabricated using the siliconon-insulator (SOI) technology for use as a reflective notch filter is presented. The development of this dumbbell micro-ring reflector is motivated by the increasing demand for highly confined resonant structures as integrated optical components in modern optical communication and sensor applications. In this thesis, we have analyzed and simulated the reflection properties of dumbbell micro-ring reflectors based on SOI strip waveguides. We have optimized our design based on the analytic modeling and simulation results and had our devices fabricated at a foundry. An automated optical probe station has been developed for characterizing the performance of the fabricated dumbbell micro-ring reflectors. Measurement results on the reflection spectrum showed an extinction ratio of 20 dB with a quality factor of ∼11,000. Thermal tuning responses showed the potential for those resonators in sensor applications.  ii  Preface I am the main author of the conference publications titled, “Design of a Microring Reflector with a Dumbbell Structure”[29] and “Dumbbell MicroRing Reflector”[30]. I proposed the design of the dumbbell micro-ring reflector, modeled and simulated the device using analytic and numerical methods, and optimized its performance for fabrication. I then created a design mask layout that was fabricated by Imec in Belgium. I characterized the device using an automated measurement system, implemented and developed by Charlie Lin and me. Dr. Nicolas Jaeger, my supervisor, and Dr. Lukas Chrostowski guided my research by providing important insights into the design of the device as well as editing drafts of the conference paper and poster. I am one of the co-authors in numerous conference and journal papers. Collaborating with other colleagues, I have been involved in many research projects during my Master’s studies. In these projects, I participated in various photonic device designs including waveguide Bragg grating filters, micro-disk reflectors, grating-assisted micro-ring filters, contra-directional couplers, vernier racetrack resonators, CWDM demultiplexers, and adiabatic 3-dB couplers. The list of publications as main author includes: 1. H. Yun, W. Shi, Y. Wang, L.Chrostowski, and N. A. F. Jaeger, “2x2 iii  Preface Adiabatic 3-dB Coupler on Silicon-on-Insulator Rib Waveguides”, Photonics North 2013, Ottawa, Canada, accepted. 2. H. Yun, W. Shi, X. Wang, L. Chrostowski, and N. A. F. Jaeger, “Dumbbell Micro-Ring Reflector”, Proc. SPIE, Photonics North 2012, vol. 8412, pp. 84120P, 10/2012. 3. H. Yun, W. Shi, X. Wang, L. Chrostowski, and N. A. F. Jaeger, “Design of a Microring Reflector with a Dumbbell Structure”, The 15th Canadian Semiconductor Science and Technology Conference, 06/2011. The list of publications as co-authors include: 1. X. Wang, H. Yun, and L. Chrostowski, “Integrated Bragg Gratings in Spiral Waveguides”, CLEO (Conference on Lasers and Electro-Optics): 2013, San Jose, US, accepted. 2. W. Shi, H. Yun, C. Lin, X. Wang, J. Flueckiger, N. A. F. Jaeger, and L. Chrostowski, “Silicon CWDM Demultiplexers Using Contra-Directional Couplers”, CLEO (Conference on Lasers and Electro-Optics): 2013, San Jose, US, accepted. 3. W. Shi, H. Yun, C. Lin, M. Greenberg, X. Wang, Y. Wang, S. T. Fard, J. Flueckiger, N. A. F. Jaeger, and L. Chrostowski, “Ultra-compact, attop demultiplexer using anti-reection contra-directional couplers for CWDM networks on silicon”, Opt. Express, Vol. 21, No. 6, pp. 6733-6738, 03/2013. 4. R. Boeck, J. Flueckiger, H. Yun, L. Chrostowski, N. A. F. Jaeger, ”High Performance Vernier Racetrack Resonators”, Opt. Letters, Vol. 37, No. 24, pp. 5199-5201, 12/2012 5. W. Shi, X. Wang, C. Lin, H. Yun, Y. Liu, T. Baehr-Jones, M. Hochberg, N. A. F. Jaeger, L. Chrostowski,, ”Electrically tunable resonant iv  Preface filters in phase-shifted contra-directional couplers”, IEEE Group IV Photonics Conference, pp. 78-80, 09/2012 6. W. Shi, H. Yun, W. Zhang, C. Lin, T. K. Chang, Y. Wang, N. A. F. Jaeger, and L. Chrostowski, “Ultra-compact, high-Q silicon microdisk reflectors”, Opt. Express, Vol. 20, Issue 20, pp. 21840-21846, 09/2012. 7. X. Wang, W. Shi, H. Yun, S. Grist, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band waveguide Bragg gratings on SOI wafers with CMOScompatible fabrication process”, Opt. Express, Vol. 20, Issue 14, pp. 1554715558, 07/2012. 8. W. Shi, T. K. Chang, H. Yun, W. Zhang, C. Lin, N. A. F. Jaeger, and L. Chrostowski, “Differential measurement of transmission losses of integrated optical components using waveguide ring resonators”, Photonics North, Montreal, Canada, 06/2012. 9. W. Shi, X. Wang, W. Zhang, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Integrated microring add-drop filters with contradirectional couplers ”, CLEO (Conference on Lasers and Electro-Optics) 2012, San Jose, US, pp. JW4A.91 , 05/2012. 10. W. Shi, X. Wang, H. Yun, W. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Integrated silicon contradirectional couplers: modeling and experiment”, SPIE Photonics Europe, Brussels, Belgium, pp. 8424-82, 04/2012. 11. W. Shi, X. Wang, H. Yun, W. Zhang, L. Chrostowski, and N. A. F. Jaeger, “Add-drop filters in silicon grating-assisted asymmetric couplers ”, OFC/NFOEC, Los Angeles, US, pp. OTh3D.3 , 04/2012. 12. W. Shi, X. Wang, W. Zhang, H. Yun, C. Lin, L. Chrostowski, and N. A. F. Jaeger, “Grating-coupled silicon microring resonators”, Applied v  Preface Physics Letters, Vol. 100, Issue 12, pp. 121118 - 121118-4, 03/2012. 13. L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, S. A. Schmidt, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices”, Proceedings of SPIE Volume 8236; Laser Resonators, Microresonators, and Beam Control XIV, 01/2012. 14. X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-Band Transmission Filter using Phase-Shifted Bragg Gratings in SOI Waveguide”, IEEE Photonics Conference, pp. ThZ1, 10/2011.  vi  Table of Contents Abstract Preface  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ii  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  iii  Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii List of Tables  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  x  List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xi  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Dedication  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv  1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1  1  Silicon Photonics in Optical Communications and Optical Interconnects . . . . . . . . . . . . . . . . . . . . . . . . . . . .  1  1.2  Thesis Objective . . . . . . . . . . . . . . . . . . . . . . . . .  3  1.3  Thesis Organization . . . . . . . . . . . . . . . . . . . . . . .  6  2 Design, Analysis, and Simulation . . . . . . . . . . . . . . . .  7  2.1  Design Approach . . . . . . . . . . . . . . . . . . . . . . . . .  8  vii  Table of Contents 2.2  Theoretical Analysis . . . . . . . . . . . . . . . . . . . . . . .  11  2.2.1  Transfer-Matrix Method for the Directional Coupler .  11  2.2.2  Analytic Model of Single Ring Resonator Add-drop Filter . . . . . . . . . . . . . . . . . . . . . . . . . . .  16  Analytic Model of Dumbbell Micro-ring Reflector  . .  20  . . . . . . . . . . . . . . . . . . . . . . . . . . . .  25  2.3.1  Silicon-on-Insulator Strip Waveguides . . . . . . . . .  26  2.3.2  Directional Coupler . . . . . . . . . . . . . . . . . . .  28  2.3.3  Effects of Coupling Coefficients  . . . . . . . . . . . .  31  2.3.4  Design Optimization  . . . . . . . . . . . . . . . . . .  33  2.2.3 2.3  Simulation  3 Automated Optical Measurement System  . . . . . . . . . .  36  Fibre-to-Fibre Automated Measurement Setup . . . . . . . .  38  3.1.1  Nano-positioned Optical Probes  . . . . . . . . . . . .  38  3.1.2  Motion Control Rack System . . . . . . . . . . . . . .  41  3.1.3  Sample Stage with Thermal Control System  . . . . .  41  3.1.4  Tunable Laser System . . . . . . . . . . . . . . . . . .  42  3.1.5  Monitoring System  . . . . . . . . . . . . . . . . . . .  42  System Operation . . . . . . . . . . . . . . . . . . . . . . . .  43  3.2.1  Measurement Principle  . . . . . . . . . . . . . . . . .  43  3.2.2  Operation Modes  . . . . . . . . . . . . . . . . . . . .  45  24-Hour Alignment Testing . . . . . . . . . . . . . . . . . . .  49  4 Implementation of Dumbbell Micro-ring Reflector . . . . .  52  3.1  3.2  3.3  4.1  Design and Analysis . . . . . . . . . . . . . . . . . . . . . . .  53  4.1.1  53  Design Scheme . . . . . . . . . . . . . . . . . . . . . .  viii  Table of Contents 4.1.2 4.2  4.3  Theoretical Analysis . . . . . . . . . . . . . . . . . . .  53  Simulation and Optimization . . . . . . . . . . . . . . . . . .  57  4.2.1  Parameters . . . . . . . . . . . . . . . . . . . . . . . .  57  4.2.2  Optimization . . . . . . . . . . . . . . . . . . . . . . .  59  Fabrication and Characterization . . . . . . . . . . . . . . . .  61  4.3.1  Fabrication . . . . . . . . . . . . . . . . . . . . . . . .  61  4.3.2  Reflection Spectra . . . . . . . . . . . . . . . . . . . .  62  4.3.3  Loss Measurement of Y-branch Splitters Using Microring Resonators  4.3.4  . . . . . . . . . . . . . . . . . . . . .  64  Thermal Tuning Responses . . . . . . . . . . . . . . .  69  5 Summary, Conclusions, and Suggestions for Future Work  71  5.1  Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  71  5.2  Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . .  72  5.3  Suggestions for Future Work  . . . . . . . . . . . . . . . . . .  73  Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  75  ix  List of Tables 2.1  List of Simulation Parameters . . . . . . . . . . . . . . . . . .  25  4.1  Parameters for Curve-fitting . . . . . . . . . . . . . . . . . . .  67  x  List of Figures 1.1  Schematics of micro-ring reflectors . . . . . . . . . . . . . . .  5  2.1  Schematic drawing of dumbbell micro-ring reflector. . . . . .  9  2.2  Optical paths in dumbbell micro-ring reflector . . . . . . . . .  10  2.3  Schematics of a directional coupler . . . . . . . . . . . . . . .  12  2.4  Schematic drawing of single micro-ring resonator add-drop filter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  2.5  2D schematic drawing of dumbbell micro-ring reflector with device dimensions, field components, and couplers labeled . .  2.6  21  SOI strip waveguide and wavelength-dependent effective refractive index . . . . . . . . . . . . . . . . . . . . . . . . . . .  2.7  17  27  Perspective view of directional coupler and symmetric mode distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . .  30  2.8  Effective index of the even and odd mode. . . . . . . . . . . .  30  2.9  Coupling coefficients effect on reflection . . . . . . . . . . . .  32  2.10 Reflectivity difference scanning result . . . . . . . . . . . . . .  34  2.11 Reflectivity extinction ratio scanning result . . . . . . . . . .  35  3.1  37  Schematic diagrams of automated measurement system . . .  xi  List of Figures 3.2  Automated fibre alignment measurement setup . . . . . . . .  39  3.3  Custom-designed mechanical components . . . . . . . . . . .  40  3.4  System control GUI . . . . . . . . . . . . . . . . . . . . . . .  44  3.5  Automated Measurement Flowchart . . . . . . . . . . . . . .  46  3.6  24-hours Alignment Test Measurement Results . . . . . . . .  51  4.1  Schematic drawings of dumbbell micro-ring reflector . . . . .  54  4.2  Trimetric view of a directional coupler and cross-sectional symmetric mode distribution. . . . . . . . . . . . . . . . . . .  4.3  Reflectivity scanning as functions of |κ12 | and |κ56 | when |κ34 | = 0.94 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  4.4  58  60  Optical image of fabricated dumbbell micro-ring reflector with dimensions labeled and with inset SEM image of the directional coupler. . . . . . . . . . . . . . . . . . . . . . . . . . . .  61  4.5  Dumbbell micro-ring reflector measurement schematics . . . .  62  4.6  Reflective response result . . . . . . . . . . . . . . . . . . . .  63  4.7  Micro-ring resonators with and without integrated Y-branch splitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  65  4.8  Measured and fit transmission spectra of micro-ring resonators. 68  4.9  Reflection spectra versus temperature . . . . . . . . . . . . .  69  4.10 Resonant wavelength shift versus temperature . . . . . . . . .  70  xii  Acknowledgements I would like to thank my parents and fianc´ee for their continuous support, encouragement, and faith throughout my education. I would like to express my gratitude to my supervisor, Dr. Nicolas A. F. Jaeger, for suggesting this project, and to Drs. Nicolas A.F. Jaeger and Lukas Chrostowski for providing continual guidance and support during my research. My thanks extend to those individuals in the Electrical and Computer Engineering Department who have helped me during my research, specially ´ Dr. Wei Shi, Xu Wang, Charlie Lin, Miguel Angel Guill´en Torres, Jonas Flueckiger, and Dr. Mark Greenberg. I gratefully acknowledge the support of the Natural Sciences and Engineering Research Council (NSERC) of Canada. Furthermore, I would also like to acknowledge CMC Microsystems for the provision of services that facilitated this research, Lumerical Solutions, Inc. and Design Workshop Technologies for the design tools.  xiii  Dedication To my father, Qinglong Yun, my mother, Gexin Jin, and my fianc´ee, Xiaoran Ma, whose unconditional love, continuous support, encouragement, and faith have given me the strength to overcome obstacles and to succeed in so many aspects and areas of my life.  xiv  Chapter 1  Introduction 1.1  Silicon Photonics in Optical Communications and Optical Interconnects  The implementation of photonic integrated circuits demonstrates the convergence of technological sophistication and economics of scale made possible by using silicon substrates. More specifically, in them, silicon is used as an optical waveguide medium as well as an active medium[9, 10]. The low cost of high crystal quality silicon wafers, and its high compatibility with mature silicon IC manufacturing techniques, have greatly promoted the rapid growth of silicon photonics in recent years. The strong optical confinement, offered by the high refractive index contrast between silicon and silicon dioxide, scales down the feature size of photonic circuits, which are implemented on the silicon-on-insulator (SOI) platform, to the sub-micrometer level and thus provides for highly compact photonic circuits and devices [9, 10]. Fabricated using CMOS (Complementary Metal-Oxide-Semiconductor) compatible processes, silicon photonic circuits have the potential to be integrated with CMOS VLSI (Very Large Scale Integration) chips, for added electronicphotonic functionality.  1  1.1. Silicon Photonics in Optical Communications and Optical Interconnects The potential for integrating silicon photonic circuits with CMOS VLSI microelectronic chips has drawn great interest from some of the world’s leading companies, such as IBM and Intel, who see silicon photonics as a means to satisfy the increasing demands for ultra-fast data transfer between and within microchips, while being able to be fabricated using established CMOS facilities[12, 15]. In 2012, for the first time, IBM demonstrated single-die multichannel wavelength-mulitplexed 25Gbps transceivers by integrating optical silicon modulators and germanium photodetectors into NMOS (n-type metal-oxide-semiconductor) circuitry using standard 90nm semiconductor fabrication processes[2]. This technology breakthrough illustrates the advantages of integrating silicon photonics with electronics and offers great potential for delivering ultra-high rates data in optical interconnect applications. Furthermore, silicon is well suited for the fabrication of photonic devices. Many applications have been demonstrated in the 1.3 - 1.6 µm wavelength range including discrete optical components, such as splitters, directional couplers, and ring resonators. Also, optical systems based on these components, such as wavelength-division multiplexing (WDM) systems, have been demonstrated within that wavelength range.  2  1.2. Thesis Objective  1.2  Thesis Objective  The excellent performance given by highly confined resonant structures has drawn great interest for integrated optical components in modern optical communication systems[1]. Micro-ring reflectors (MRRs), with the advantages of easy fabrication and monolithic integration with other photonic devices, can serve as alternative components for distributed Bragg reflectors (DBRs) in applications such as, reflective filters, sensors, and optical switches[6, 13, 17]. Under special circumstances, MRRs, as reflective filters, have the advantage in applications in which a single input/output fibre is preferred[17, 20]. Functioning as wavelength-selective reflectors, MRRs can be fabricated using SOI technology and be integrated into photonic integrated circuits. The concept of wavelength-selective reflectors using micro-ring resonators was first proposed by Poon et al. in 2004[13]. They investigated the reflection properties of a circular array of coupled micro-ring resonators and showed that a micro-ring array consisting of an odd number (N≥3) of rings, and with one ring coupled to the input/output (I/O) waveguide exhibited narrow bandwidth reflection, whereas an array consisting of an even number (N≥4) of rings had no reflection (see Fig. 1.1a). Poon et al. simulated the micro-ring structures with radii of 125 µm. Chremmos et al.[4] and Chung et al.[6] analyzed and discussed the double-ring/coupled-ring reflector using two parallel-coupled circular micro-rings. In their papers, two parallel-coupled micro-rings were both coupled to the I/O waveguide and showed narrow bandwidth reflective behavior (see Fig. 1.1b). Chung et al.  3  1.2. Thesis Objective demonstrated an MRR with two rings with radii of 50 µm. Shi et al.[17], in 2009, demonstrated an MRR using a micro-ring resonator integrated with a waveguide crossing structure, with low-loss and low-crosstalk, but which required a double-etch scheme in the fabrication (see Fig. 1.1c). Here, we present a “dumbbell” shape micro-ring resonator reflector which has a dumbbell shape racetrack micro-ring structure coupled to a strip waveguide to achieve reflection (see Fig. 1.1d). Our device, without the need for additional complex lithography and processing steps, but with a small foot-print containing rings with radii of 30 µm, shows high reflectivity and high extinction ratio, and has the potential to be used as a wavelengthselective notch filter in optical communication systems or as various types of sensors in sensing systems.  4  1.2. Thesis Objective  (a)  Reflection  Input  Transmission  (b)  Input  Transmission  (c)  Reflection  Reflection  Input  Transmission  Input  Transmission  (d)  Reflection Input  Transmission  Figure 1.1: Schematics of micro-ring reflectors: (a) circular array of coupled micro-rings; (b) parallel-coupled micro-ring reflector; (c) micro-ring reflector with a waveguide cross; (b) dumbbell micro-ring reflector.  5  1.3. Thesis Organization  1.3  Thesis Organization  This thesis consists of five chapters. In Chapter 1, we introduce and review the development of silicon photonics in modern optical communication systems and optical interconnect applications. The motivation of this thesis is also presented. In Chapter 2, we show the background theory as well as the analytic modeling of directional couplers. Single ring resonator adddrop filters and dumbbell micro-ring resonator reflectors are analyzed using the transfer-matrix method. Also, simulation results of the reflection properties of the dumbbell micro-ring reflectors are presented in this chapter. In Chapter 3, the automated measurement system developed for characterizing on-chip silicon photonic circuits is described, and its performance is shown. In Chapter 4, the implementation of dumbbell micro-ring reflectors is provided. Experimental results of an optimized dumbbell micro-ring notch reflector are presented. Lastly, in Chapter 5, conclusion and some suggestions for future research are given.  6  Chapter 2  Design, Analysis, and Simulation In this chapter, we present the design, analysis, and simulation of dumbbell micro-ring reflectors. We describe the mechanisms that result in the reflection properties of the device. Since waveguide directional couplers are important components in our device, we use a transfer-matrix method derived from supermode theory to analyze the light transfer between the two parallel coupled waveguides comprising the directional couplers. We show the derivation of the transfer functions of single ring resonator add-drop filters in forms of 2x2 matrices using the transfer-matrix method. We expand the transfer matrices, and apply the transfer-matrix method to obtain an analytic model for dumbbell micro-ring reflectors. We then calculate the reflectivities of the dumbbell micro-ring reflector and do numerical simulations in MATLAB to characterize the reflection properties of the device.  7  2.1. Design Approach  2.1  Design Approach  Our device, which contains three directional couplers, has the shape of a dumbbell (see Fig. 2.1). The reflector consists of a dual-coupler micro-ring resonator with an additional directional coupler located at the “handle” of the dumbbell structure. The reflected signal consists of traveling waves from various reflection and resonant paths (see Fig. 2.2) within the dumbbell structure. For example, for one reflection path, which is shown in Fig. 2.2a, the input light injected into the port on the left is coupled to a counter-clockwise wave via directional coupler 1. After propagating through waveguide L2 , where L2 is also the length of waveguide, the light is coupled into a clockwise wave via directional coupler 2 and propagates through the length of waveguide L4 . Thus the light is coupled into a backward traveling wave via directional coupler 3, and becomes a portion of the reflected signal at the left port after passing through directional coupler 1. Figure 2.2b shows another reflection path within the device. In this case, after coupling into a clockwise traveling wave via directional couplers 1 and 2, the light propagates through the lengths of waveguide L4 , L3 , and L2 and then passes through directional couplers 3 and 2 in sequence and becomes a portion of the reflected signal after coupling into a backward traveling wave via directional coupler 1. There are two types of resonant path inside the dumbbell micro-ring structure. One type of resonant path enables the light to resonate inside the dumbbell with no effects from the directional couplers. For example, as shown in Fig. 2.2c, the light travels along the dumbbell micro-ring and passes  8  2.1. Design Approach  L5  L4  L2  Ein Er  Coupler 1  Coupler 2  L1  L3  Et Coupler 3  Figure 2.1: Schematic drawing of dumbbell micro-ring reflector. through the three directional couplers and thus forms a counter-clockwise resonant wave. The other type of resonant path is shown in Fig. 2.2d as an example. The clockwise wave propagating through the left “head” of the dumbbell shape is coupled into a counter-clockwise wave via directional coupler 2. After traveling along the right “head”, the wave is coupled back to a clockwise wave via directional coupler 2. The reflected traveling waves combined with the resonant waves form the total reflected signal for the dumbbell micro-ring reflector.  9  2.1. Design Approach  Ein Er  (a)  Ein Er  (b)  (c)  (d) Figure 2.2: paths.  Optical paths: (a), (b): Reflection paths; (c), (d): Resonant  10  2.2. Theoretical Analysis  2.2 2.2.1  Theoretical Analysis Transfer-Matrix Method for the Directional Coupler  The coupling of optical power between two parallel waveguides occurs when the two waveguides are placed in close proximity to each other. Directional couplers, consisting of such waveguide structures, can be designed to allow certain amount of light to transfer from one waveguide to the other, depending on the design requirement. Here, we use a transfer-matrix method to model the directional couplers. As shown in Fig. 2.3, we assume that two identical, loss-less waveguides with lengths, L, are placed near to each other with a waveguide separation, d, to allow coupling to occur. The electric field distribution of each waveguide, within the directional coupler, can be written in terms of the superposition of the even and odd eigenmodes (supermodes) of the directional coupler, which gives: ψ1 (x, z) = Ce ψe (x)e−jβe ·z + Co ψo (x)e−jβo ·z −jβe ·z  ψ2 (x, z) = Ce ψe (x)e  ,  (2.1)  −jβo ·z  − Co ψo (x)e  where ψe (x) and ψo (x) are the normalized even and odd mode electric fields (see Fig. 2.3a), respectively, Ce and Co are the respective eigenmode electric field amplitudes, and βe and βo are the respective eigenmode propagation constants. Thus, the electric fields at the input ports of the coupler, i.e., at  11  2.2. Theoretical Analysis  e (x)   1 ( x,0)   1 ( x, L)  x0  d   2 ( x, L)   2 ( x,0)  o (x) x  L  z0  zL  (a) y  z  A1  B1  t1  1  x0 A2  d  2  t2  B2  L  z0  zL  (b)  Figure 2.3: Schematic diagrams of a directional coupler z = 0, can be written as: ψ1 (x, 0) = Ce ψe (x) + Co ψo (x)  .  (2.2)  ψ2 (x, 0) = Ce ψe (x) − Co ψo (x) After propagating along the coupler, the electric fields at the output ports, i.e., at z = L, can be expressed as: ψ1 (x, L) = Ce ψe (x)e−jβe ·L + Co ψo (x)e−jβo ·L −jβe ·L  ψ2 (x, L) = Ce ψe (x)e  − Co ψo (x)e  .  (2.3)  −jβo ·L  Referring to Fig. 2.3b, the electric fields at the output ports of the coupler  12  2.2. Theoretical Analysis can also be written in terms of the input electric fields: ψ1 (x, L) = t1 · ψ1 (x, 0) + κ1 · ψ2 (x, 0)  ,  (2.4)  ψ2 (x, L) = t2 · ψ2 (x, 0) + κ2 · ψ1 (x, 0) where t1 is the “straight-through” field coupling coefficient for waveguide 1, and κ1 is the “cross” field coupling coefficient from waveguide 1 to waveguide 2. t2 and κ2 are the “straight-through” and “cross” coupling coefficients for waveguide 2, respectively. Substituting Eq. (2.2) into Eq. (2.4) gives: ψ1 (x, L) = t1 [Ce ψe (x) + Co ψo (x)] + κ1 [Ce ψe (x) − Co ψo (x)]  ,  ψ2 (x, L) = t2 [Ce ψe (x) − Co ψo (x)] + κ2 [Ce ψe (x) + Co ψo (x)] which can be rearranged as: ψ1 (x, L) = (t1 Ce + κ1 Ce )ψe (x) + (t1 Co − κ1 Co )κo (x)  .  (2.5)  ψ2 (x, L) = (t2 Ce + κ2 Ce )ψe (x) − (t2 Co − κ2 Co )κo (x) Noticing that Eq. (2.5) is equivalent to Eq. (2.3), the following relationships can be obtained: t1 Ce + κ1 Ce = Ce e−jβe ·L t1 Co − κ1 Co = Co  e−jβo ·L  and  t2 Ce + κ2 Ce = Ce e−jβe ·L t2 Co − κ2 Co = Co  .  (2.6)  e−jβo ·L  13  2.2. Theoretical Analysis From Eq. (2.6), the coupling coefficients can be solved as: κ1 = κ2 = 12 (e−jβe ·L − e−jβo ·L )  (2.7)  t1 = t2 = 21 (e−jβe ·L + e−jβo ·L ) Further simplifying Eq. (2.7) gives: o · L) · e−j( κ1 = κ2 = −j · sin( βe −β 2 o · L) · e−j( t1 = t2 = cos ( βe −β 2  βe +βo )·L 2  (2.8)  βe +βo )·L 2  Now we can redefine the “cross” and the “straight-through” field coupling coefficients as: −jβc ·L κ = sin ( ∆β 2 · L) · e  ,  (2.9)  −jβc ·L t = cos ( ∆β 2 · L) · e  where ∆β = βe − βo and βc = (βe + βo )/2. Thus, we can express the electric fields at the output ports in terms of the electric fields at the input ports as: ψ1 (x, L) = t · ψ1 (x, 0) − jκ · ψ2 (x, 0)  .  (2.10)  ψ2 (x, L) = t · ψ2 (x, 0) − jκ · ψ1 (x, 0) Relabeling the ports in Fig. 2.3a to Fig. 2.3b, Eq. (2.10) is also rewritten in matrix form as:       −jκ A1  B1   t   =  . B2 −jκ t A2  (2.11)  We would like to express A1 and B1 in terms of A2 and B2 , which gives:  14  2.2. Theoretical Analysis      A −t 1 1   1   A2    =    −jκ −κ2 − t2 t B1 B2   (2.12)  Hence, the field components in waveguide 1, E1 , can be expressed in terms of the product of the field components in waveguide 2, E2 , and the coupling transfer-matrix, C, i.e.,  E1 = CE2 , where C =  1  −t  −jκ −κ2 − t2   1  t  (2.13)  15  2.2. Theoretical Analysis  2.2.2  Analytic Model of Single Ring Resonator Add-drop Filter  The transfer-matrix method is often used to investigate the optical properties of complex optical circuits. The matrix formulation can be conveniently employed to determine the transfer functions of optical resonators when multiple couplings are involved [27]. Since we will be looking at the reflection properties of the dumbbell micro-ring reflector, which consists of three directional couplers in a dumbbell shape micro-ring structure, the transfermatrix method enables us to determine the behaviour of the device simply using the matrix manipulations, without the need for solving each reflected signal separately. The following shows the derivation of the through port and drop port transfer functions of single ring resonator add-drop filters using the transfermatrix method. Referring to Fig. 2.4, the single ring resonator add-drop filter consists of a micro-ring resonator with two directional couplers. The field components of the directional couplers are defined as:      ai  Ei =  , bi  i = 1, 2, 3, 4,  (2.14)  where ai and bi represent the field components for the waves traveling along the waveguides. Assuming that each directional coupler consists of two identical waveguides, we define the cross-coupling coefficients for the couplers as κ1 and κ2 and the straight-through coupling coefficients as t1 and t2 (see Fig.2.4).  16  2.2. Theoretical Analysis  Coupler 1  Coupler 2  1 1 t2  t1  t1  t2  2  2  Edrop  Ein L a1  a4 a2  a3  b2  b3  b1  Ethr Figure 2.4: filter.  b4 L  Eadd  Schematic drawing of single micro-ring resonator add-drop  17  2.2. Theoretical Analysis According to Eq. (2.13), the coupling transfer-matrix of the couplers can be defined as:  Cm =    1 1  −tm  , −jκm −t2 − κ2 t m m m  m = 1, 2,  (2.15)  where κm = |κm |e−(jβc +α/2)LC and tm = |tm |e−(jβc +α/2)LC are the cross field coupling and the straight-through field coupling coefficients, respectively, of the directional coupler, βc is the propagation constant of the waveguides, as defined in Eq. (2.9), inside the coupler, and LC is the coupling length. We note that the propagation in the micro-ring introduces phase shifts and propagation losses to the traveling waves. Hence, we define P as the propagation matrix in sections of the ring, between the couplers, of lengths, L, which can be expressed as:  0  P = e(jβ+α/2)L  e−(jβ+α/2)L 0    .  (2.16)  where β is the propagation constant of the mode of a single, unperturbed waveguide. Using Equations (2.14), (2.15), and (2.16), the relationships between the ports of the ring can be written as:      b4  a1    = C1 P C2   . b1 a4  (2.17)  18  2.2. Theoretical Analysis Referring to the port labels in Fig. 2.4, Eq. (2.17) can also be written as:               Ein   Eadd   Eadd  M1,1 M1,2   Eadd    = C1 P C2  ≡M  ≡  (2.18) Ethr Edrop Edrop M2,1 M2,2 Edrop   where the matrix M is the transfer matrix of the device. Assuming that the light is only injected from the input port, i.e., a1 = Ein and b4 = Eadd = 0, the transfer functions, for the power, of the through and drop ports are given by:  Gthr =  |M2,2 |2 |Ethr |2 = |Ein |2 |M1,2 |2  (2.19)  Gdrop =  |Edrop |2 1 = 2 |Ein | |M1,2 |2  (2.20)  The transfer functions in Equations (2.19) and (2.20) show the convenience and simplicity of using the transfer-matrix method to characterize the transmission and reflection properties of optical circuits. Thus, we will analyze and characterize our device using this approach.  19  2.2. Theoretical Analysis  2.2.3  Analytic Model of Dumbbell Micro-ring Reflector  The transfer-matrix method, introduced in the previous section, has been used to analyze the reflection properties of our device. The field components of the directional couplers are defined as:   ai         bi    Ei =  ,    ci    di  i = 1, 2, 3, ..., 6,  (2.21)  where ai and bi represent the field components for the forward traveling waves along the waveguides and ci and di represent the field components for the backward traveling waves (see Fig. 2.5). Assuming that there is no mixing between the forward and backward traveling waves, we can express the coupling relationships for both the forward and backward traveling waves within the directional coupler using a 4 × 4 coupling matrix[6, 13]:   −t  1  0  0        2 2  0 0 1 −t − κ t  C=  ,  −jκ  0 0 −t 1    2 2 0 0 −t − κ t  (2.22)  where κ = |κ|e−(jβc +α/2)LC and t = |t|e−(jβc +α/2)LC are the cross field coupling and the straight-through field coupling coefficients, respectively, of the directional coupler, βc is the propagation constant of the waveguides inside  20  2.2. Theoretical Analysis  L5  L4 d 4 c4 a 4 b4 d 2 c2 a 2 b2  Ein  Er  a1 b1 d1 c1  L2 C12  a3 b3 d 3 c3  L1  C34  L3  d 5 c5 a5 b5  C56  a6 b6 d 6 c6  Et  Figure 2.5: 2D schematic drawing of dumbbell micro-ring reflector with device dimensions, field components, and couplers labeled. the coupler, α is the propagation loss coefficient, and LC is the coupling length. Within one directional coupler, the power transmission ratio, TC , can be expressed as TC = |κ|2 + |t|2 . Using Equations (2.21) and (2.22), the field components within each directional coupler can be expressed as:  E1 = C12 E2 , E3 = C34 E4 , and E5 = C56 E6  (2.23)  where C12 , C34 , and C56 (see Fig. 2.5) are the coupling matrices, respectively, between the fields Ei and Ei+1 (i = 1, 3, and 5) within the directional couplers. We define Pm (m = 1, 2, ..., 5) to be the propagation transfer matrices for light propagating through the length of waveguides Lm between the directional couplers. The propagation matrix, for each waveguide that bridges  21  2.2. Theoretical Analysis the directional couplers, is given by   0  0 0    0     −1  P  0 0 0  L2  P2 =     0 0 PL2   0   0 0 0 0    0 PL3    0  P3 =   0  0  0  0  0  0  PL−1 3  0  0  0      0    0  0 (2.24)    0 0   0 0  P4 =    0 PL4  0 0  0 PL−1 4 0 0  0      0    0  0    0    0  P5 =    0  PL−1 5  0 0 PL5 0 0 0 0 0 0      0     0   0  where PLm = e−(jβ+α/2)Lm . The relationships of the field components between the couplers are thus give by  E2 = P2 E3 + P5 E4 and E5 = P3 E3 + P4 E4  (2.25)  Using Equations 2.23 and 2.25, the relationship between the left port and the right port of the device is given by E1 = C12 (P2 C34 + P5 )(P3 C34 + P4 )−1 C56 E6 .  (2.26)  Since the transfer matrices in Eq. (2.26) are 4 × 4 matrices, the result of the multiplication of transfer matrices can also be written in terms of an  22  2.2. Theoretical Analysis equivalent 4 × 4 matrix M , i.e. M = C12 (P2 C34 + P5 )(P3 C34 + P4 )−1 C56  (2.27)  Substituting the field components defined in Eq. (2.21) into Eq. (2.26), we can express Eq. (2.26) as:    a M  1   1,1     b1      ..  = .     c1      M4,1 d1  ··· ..  .  ···    a M1,4   6     ..   b6    .      c6    M4,4 d6  (2.28)  where Mi,j represents the elements in matrix M . Assuming that light is only injected into the left port, i.e., the input signal a1 = Ein and c6 = 0, and knowing that the connection between the two couplers via waveguide L1 can be expressed as: a6 = PL1 b1 and d6 = PL−1 c . 1 1  (2.29)  Thus, we can rewrite Eq. (2.28) as:    a M  1   1,1     b1      ..  = .     c1      M4,1 d1  ··· ..  .  ···      P b   L1 1      ..   b6   . .     0    M4,4 PL−1 c 1 1  M1,4  (2.30)  We can solve Eq. (2.30) and express the field components b1 and b6 in 23  2.2. Theoretical Analysis terms of c1 :  b1 =  M2,2 + (M3,2 M2,4 − M2,2 M3,4 )PL−1 1 · c1 M3,2 + (M2,2 M3,1 − M3,2 M2,1 )PL1  (2.31)  and  b6 =  1 − M3,4 PL1 −  M3,1 PL1 [M2,2 + (M3,2 M2,4 −M2,2 M3,4 )PL1 ] M3,2 + (M2,2 M3,1 −M3,2 M2,1 )PL1  M3,2  · c1 .  (2.32)  Substituting Eq. (2.31) and Eq. (2.32) into Eq. (2.30), we can calculate the reflectivity of the device:  R=  |Er |2 d1 = 2 |Ein | a1  2  =  M4,1 PL1 · r1 + M4,2 · r2 + M4,4 PL−1 1  (2.33)  M1,1 PL1 · r1 + M1,2 · r2 + M1,4 PL−1 1  where r1 and r2 are the ratios of the field components b1 and b6 to c1 respectively, i.e.,  r1 =  M2,2 + (M3,2 M2,4 − M2,2 M3,4 )PL−1 b1 1 = c1 M3,2 + (M2,2 M3,1 − M3,2 M2,1 )PL1  (2.34)  and 1 − M3,4 PL1 − b6 r2 = = c1  M3,1 PL1 [M2,2 + (M3,2 M2,4 −M2,2 M3,4 )PL1 ] M3,2 + (M2,2 M3,1 −M3,2 M2,1 )PL1  M3,2  .  (2.35)  24  2.3. Simulation  2.3  Simulation  In this section, we present the simulations of the reflection properties of the dumbbell micro-ring reflector, based on the analytic model described in previous section, to verify our design approach. We defined the geometry of the SOI photonic waveguide and calculated its effective refractive index and group index for a single TE mode using a 2-D Finite-Difference eigenmode solver[8, 19]. We then used a curve-fitting model, introduced by Rouger et al.[14], to calculate the coupling lengths of the couplers, which give us the required coupling coefficients, for our device. In Sections 2.3.3 and 2.3.4, we investigated the effects of the coupling coefficients, which determine our device performance, and then optimized our design based on numerical simulations in MATLAB. Table 2.1 lists the definitions of the parameters that were used in our simulation. Symbol α β κ t λ nef f ng LC G TC  Significance Propagation loss Propagation constant Cross-coupling coefficient Straight-through coupling coefficient Optical wavelength Effective refractive index Group refractive index Coupling length Coupler gap distance Power transfer ratio  Unit /m rad/cm  nm  µm nm  Table 2.1: List of Simulation Parameters.  25  2.3. Simulation  2.3.1  Silicon-on-Insulator Strip Waveguides  We designed the dumbbell shape micro-ring reflector based on 500-nm-wide, 220-nm-high, silicon photonic nano-wires laying on top of a silicon dioxide layer which has a thickness greater than 1 µm (see Fig. 2.6a). The high refractive index contrast between silicon and silicon dioxide enables strong confinement of the optical mode[3]. The waveguide geometry was chosen to ensure single mode propagation for TE polarization, while still having low propagation loss[3]. Assuming that the ambient temperature was 25◦ C, we calculated the waveguide effective refractive index, nef f , using a 2-D Finite-Difference eigenmode solver[8, 19]. This eigenmode solver calculates the optical modes of the waveguide by solving Maxwell’s equations on a cross-sectional mesh of the waveguide using a finite difference algorithm, assuming that the waveguide is infinitely long along the direction of propagation and its cross-section is invariant. nef f , as shown in Fig. 2.6b, is wavelength dependent. Hence, the propagation constant of the guided mode at a single wavelength can be calculated as β = 2πnef f /λ. Given that nef f is highly dispersive, the group index, ng , was used in our calculation of the optical phase for predicting the resonator’s free spectrum range. We calculated ng using the equation[27]  ng = nef f − λ  dnef f , dλ  (2.36)  in our simulations.  26  2.3. Simulation  Cladding  500 nm 220 nm  Si > 1 μm  SiO2  SiO2 Si  (a)  (b) Figure 2.6: (a) Perspective view of SOI strip waveguide with insets showing the waveguide geometry and TE mode distribution; (b) Wavelengthdependent effective index of SOI strip waveguide. 27  2.3. Simulation  2.3.2  Directional Coupler  In our device, the directional coupler consists of two identical parallelcoupled SOI waveguides with 200 nm gap distance (see Fig. 2.7). The power behavior within a directional coupler can be expressed as a function of the structure of the coupler, the position in the coupler, the coupling coefficients, and the power transmission ratio[14]. The field coupling coefficients, κ and t, can be expressed as: κ2 = sin2 (B · LC · e−A·G )  (2.37)  t2 = cos2 (B · LC · e−A·G ) where A and B are coefficients obtained by curve-fitting the exponential behavior of the coupling coefficients as functions of the coupler gas distance, G, and coupling length, LC [14]. In this case, given G, κ, and the power transmission ratio, TC , we can calculate LC from the following equation: |κ| LC = arcsin( √ ) · (B · e−A·G )−1 , TC  (2.38)  where A = 9.0842834 · 10−3 nm−1 and B = 1.8670660 · 10−4 nm−1 are extracted from Ref. 14 at T = 298K and λ = 1550 nm. In our simulation, we assume that the coupling between the straight waveguide and the ring structure is only due to the coupling between the parallel section of the coupler. Since βc , defined in Equations (2.9), (2.15), and (2.22) is given by βc =  28  2.3. Simulation (βe + βo )/2, we can calculate βc using:  βc =  2π 2π ne + no · nc = ·( ) λ λ 2  where ne and no are the effective indices of the even and odd modes of the directional coupler, respectively, and nc is taken to be the effective index of the directional coupler and is equal to the average of the even and odd mode effective indices. ne and no can be calculated using the 2-D FD mode solver and, thus, nc can be obtained. As shown in Fig. 2.8, nc (labeled as Neffc ) is approximately equal to the effective index of a single, unperturbed waveguide, nef f (labeled as NeffSWG ), i.e., nc  nef f . Hence, βc  β, where  β is the propagation constant of a single, unperturbed waveguide. From now on we use β as the propagation constant for the waveguides inside and outside of the directional couplers in our simulations. To take the real situation into account, we also include waveguide propagation loss and coupling loss in our transfer-matrix equation. We use a waveguide power propagation loss of α[/m] = 115.12/m, converted from α[dB/cm] = 5 dB/cm. We use a power transmission ratio of TC = 0.9, which is based on our fabrication and measurement experience, in our simulations. Therefore, the straight-through coupling coefficients t can be expressed as  t=  0.9 − |κ|2 · e−(jβ+α/2)LC .  (2.39)  29  2.3. Simulation  200 nm  Cladding Si  Si SiO2  SiO2 Si  Figure 2.7: Perspective view of directional coupler with gap distance labeled and an inset showing symmetric TE mode distribution profile.  Even-mode  Odd-mode  Figure 2.8: Effective indices of the even and odd modes in directional coupler and the effective index of a single waveguide, with insets showing the even and odd TE mode electric field distributions of the directional couplers. 30  2.3. Simulation  2.3.3  Effects of Coupling Coefficients  Referring to the parameters defined in Equations (2.22), (2.24), (2.36), (2.38), and (2.39), and substituting them into Eq. (2.33), the reflectivity of the device, R, can be expressed as a function of wavelength and the magnitudes of the cross-coupling coefficients of the three directional couplers of the device, i.e., R = f (λ, |κ12 |, |κ34 |, |κ56 |).  (2.40)  Hence, the cross-coupling coefficients, κ12 , κ34 , and κ56 , of the device are key factors in determining the performance of the dumbbell micro-ring reflector and, as shown in Fig. 2.9, can significantly affect the magnitude of the reflectivity spectrum as well as the values of the free spectral range and the quality factor. The curves in Fig. 2.9 indicate that the reflectivity spectrum with different selections of the three coupling coefficients may have either high reflectivity with high extinction ratio, or high reflectivity with low extinction ratio, or low reflectivity with high extinction ratio, or low reflectivity with low extinction ratio. Since the device is designed for use as a reflector, the reflection spectrum should have high reflectivity with high extinction ratio. In this case, κ12 , κ34 , and κ56 should be carefully chosen to meet this requirement.  31  2.3. Simulation  0 −5  Reflection, dBm  −10 −15 −20 −25 −30 −35 −40 −45 −50 1546  κ12 κ12 κ12 κ12  = = = =  0.86, κ34 0.94, κ34 0.50, κ34 0.94, κ34  1547  = = = =  0.94, κ56 0.92, κ56 0.10, κ56 0.01, κ56  1548  = = = =  0.81 0.65 0.05 0.02  1549  1550  1551  1552  1553  Wavelength, nm Figure 2.9: Simulated reflectivity responses for several sets of coupling coefficients that give (a) high reflectivity, high extinction ratio, or (b) high reflectivity, low extinction ratio, or (c) low reflectivity, high extinction ratio, or (d) low reflectivity, low extinction ratio[30]. Copyright 2012 Society of Photo-Optical Instrumentation Engineers.  32  2.3. Simulation  2.3.4  Design Optimization  To optimize the performance of the reflector, we need to find the proper values for the coupling coefficients of our device. In this case, we define Rp to be the maximum reflectivity and Rv to be the minimum reflectivity for the various possible combinations of cross-coupling coefficients of the three couplers. We scan the reflection spectrum and calculate the reflectivity difference Rp − Rv and the reflectivity extinction ratio 10 log10 (Rp /Rv ) as functions of the three cross-coupling coefficients of the couplers. The simulation results are shown in Fig. 2.10 and Fig. 2.11 using hot colormaps, where brighter colors correspond to higher values. Figure. 2.10 shows the simulation results of the reflectivity differences as a function of |κ12 |, |κ34 |, and |κ56 |, and Figure. 2.11 shows the simulation results of the reflectivity extinction ratio as a function of |κ12 |, |κ34 |, and |κ56 |. Based on our simulation results, we choose the values for the three cross-coupling coefficients, which are |κ12 | = 0.84, |κ34 | = 0.94, and |κ56 | = 0.77, to meet the requirements of high reflectivity and high extinction ratio.  33  2.3. Simulation  (a)  (b) Figure 2.10: Reflectivity differences as functions of κ12 , κ34 , and κ56 : (a) Perspective volume view; (b) Perspective view with cross-sectional slices.  34  2.3. Simulation  (a)  (b) Figure 2.11: Reflectivity extinction ratios as functions of κ12 , κ34 , and κ56 : (a) Perspective volume view; (b) Perspective view with cross-sectional slices.  35  Chapter 3  Automated Optical Measurement System To characterize fabricated devices, an automated optical measurement setup has been developed for measuring on-chip nanophotonic circuits. This automated system has been designed to perform high speed and high resolution wavelength-swept measurements with accurate fibre alignment. In this chapter, we introduce the hardware setup as well as the system operation of the automated setup. Measurement results of a strip waveguide are also presented to show the system performance including system stability, measurement repeatability, and measurement flexibility.  36  Chapter 3. Automated Optical Measurement System  PC GPIB  Agilent 8164A Lightwave Measurement System Agilent 81682A  Agilent 81635A  Optical Fibre 50/50 Coupler  USB 50/50 Coupler  Pin  Holding Arm  Pout Rotation Platform  NanoMAX 341 Stage  NanoMAX 341 Stage  Sample Stage  LDC-501 TEC Controller  MST601  MNA601  MMR601 Motion Control Rack System  Figure 3.1: Schematic diagram of automated measurement system.  37  3.1. Fibre-to-Fibre Automated Measurement Setup  3.1  Fibre-to-Fibre Automated Measurement Setup  We have developed an automated optical probe station for characterizing on-chip nanophotonic circuits. We assembled the entire measurement setup on top of an optical table, supported by pneumatic vibration isolators with automatic re-leveling, to minimize environmental disturbances during the measurements. The schematic diagram of the automated probe station, as shown in Fig. 3.1, consists of two sets of micro/nano-positioners independently controlled to position two optical fibres (input and output), a motion control rack system, a sample stage with temperature control, a tunable laser system, and other peripherals to measure the optical responses of the devices. This measurement system has been modularized so that its subsystems can be extended and changed easily for innovative experiments. Figure 3.2 shows the implemented setup.  3.1.1  Nano-positioned Optical Probes  In the setup, two side-loading fibre chucks[25], installed with two cleaved optical fibres, were used as the input and output probes. The fibre chucks, as shown in Fig. 3.2 1 , were held by two aluminum arms. These arms were installed, respectively, on two rotation platforms that were mounted to the automated stages via aluminum adapter plates. The aluminum arms and adapter plates were custom-designed using 3D CAD software to fit other hardware components (see Fig. 3.3). The rotation platforms gave flexibility for tuning the incident angle of the probes from 0◦ to 90◦ by rotating the 38  3.1. Fibre-to-Fibre Automated Measurement Setup  ⑤ ④ ③  ① ⑥  ② ⑦  ⑧  Figure 3.2: Automated optical probe station setup with parts labeled: 1 Fibre chuck; 2 Holding arm; 3 Rotation platform; 4 Adapter plate; 5 MAX341 Stage; 6 Heat sink; 7 Thermoelectric cooler; 8 Sample stage. holding arms, which helps to maximize the coupling efficiency and to match the grating peak transmission wavelength. The probe motions were automated by two NanoMax MAX341 stages[26] which give sub-micron resolution positioning to accurately align the input/output fibres to the periodic grating couplers integrated on the chip. The NanoMax MAX341 stages, purchased from Thorlabs, Inc., are 3-axis flexure stages with a stepper motor and a closed-loop internal piezoelectric actuator on each axis. The stepper motors are able to provide the stage 4mm-travel-distance per axis with 0.06 µm minimum step size, an accuracy  39  3.1. Fibre-to-Fibre Automated Measurement Setup  (a)  (b) Figure 3.3: Custom-designed mechanical components: (a) 3D CAD model and manufactured arm; (b) 3D CAD model and manufactured adapter plate.  40  3.1. Fibre-to-Fibre Automated Measurement Setup of 1.0 µm, a repeatability of 0.5 µm, and a backslash of <7 µm. The closedloop internal piezoelectric actuators give the stages 20 µm travel range with a positional resolution of 20 nm on each axis.  3.1.2  Motion Control Rack System  The automated stages were driven and controlled by an APTTM MMR601 Rack System[24] containing three plug-in dual-channel stepper motor controller modules (MST601) and two plug-in Nanotrak control modules (MNA601). The rack system was connected to the computer via a USB cable. The three MST601 modules, which contain six channels in total, were connected, respectively, to the stepper motors of the two NanoMax MAX341 stages. The two MNA601 modules were connected to the output fibre via single-mode fibres and 50/50 benchtop couplers for fibre auto-alignment. Connecting to the motorized stages, the MNA601 modules drove the built-in piezoelectric actuators through coaxial SMC cables and received the feedback signals through 7-pin LEMO cables for closed-loop piezoelectric actuation.  3.1.3  Sample Stage with Thermal Control System  We used a 3-axis linear translation manual stage as the sample stage that held our optical chips. We attached a thermoelectric cooler and a thermistor to a copper heat sink using thermal adhesive. The copper heat sink was mounted to the sample stage. The thermoelectric cooler and the thermistor were connected to the TEC controller module of the Stanford Research Systems LDC-501. The LDC-501 maintained the copper heat sink at a stabilized operating temperature and was able to be program-controlled by 41  3.1. Fibre-to-Fibre Automated Measurement Setup the computer via a GPIB (General Purpose Interface Bus) connection.  3.1.4  Tunable Laser System  For the tunable laser system, we used an Agilent 8164A Lightwave Measurement System mainframe[23] with an Agilent 81682A tunable laser source (TLS) module[21] and an Agilent 81635A power sensor module[22] installed. The Agilent 81628A TLS module covered the wavelength range from 1460 nm to 1580 nm, and provided up to 8 dBm of power with a wavelength resolution of 0.1 pm. The built-in wavelength meter of the TLS module provided a wavelength accuracy of ±10 pm, which was necessary to accurately and reproducibly characterize the devices. The Agilent 81635A power sensor measured the power in the wavelength range from 800 nm to 1650 nm over a power range from +10 dBm to -80 dBm. The Agilent 8164A mainframe communicated with the computer via a GPIB connection and controlled both the TLS module and the power sensor during wavelengthswept measurements.  3.1.5  Monitoring System  A monitoring system, including microscope and CMOS USB camera, was also implemented to simultaneously view the input/output fibre alignment. The camera, which was attached to the microscope, was connected to the computer and the video is displayed on the computer monitor.  42  3.2. System Operation  3.2 3.2.1  System Operation Measurement Principle  The input optical fibre, connected to the output the TLS module, was moved by the motorized NanoMax MAX341 stage to inject light into the input port of the optical circuits. The optical responses of the device were collected by the output fibre, and were then split into two identical signals via a 50/50 benchtop coupler connected to the output fibre. One of the two signals is delivered to the power sensor module for wavelength-swept measurements. The other signal was split, again, into two identical signals by a second 50/50 benchtop coupler. These two signals, with one quarter of the output power in each of them, were delivered, respectively, to the two MNA601 modules of the rack system for auto-alignment. The plugged-in MNA601 modules installed in the MMR601 main rack system were provided with ActiveX control components from Thorlabs, Inc. Each ActiveX control component provided a graphical user interface (GUI) and a programmable interface. We integrated all of the ActiveX control components of the control modules into a system control GUI [11]. This GUI, as shown in Fig. 3.4, integrates the functionalities from both the MST601 modules and the MNA601 modules and thus enables us to control the movements of the automated stage and to perform the embedded fibre auto-alignment function.  The system control GUI was developed and programmed by Charlie Lin using Matlab.  43  3.2. System Operation  Figure 3.4: System control GUI. 44  3.2. System Operation  3.2.2  Operation Modes  As shown in Fig. 3.5, the setup supports two operation modes, fully-automatic mode and semi-automatic mode. To start with, for each mode, we initialize the system GUI and move all of the motors to their “Home” positions, which are set during manufacture and taken to be the zero offset positions. The system GUI then establishes a horizontal coordinate system for each stage, which uses the “Home” position and the 4mm×4mm travel range of the stage as the origin and the first quadrant, respectively, of the coordinate system. We call the coordinates in this coordinate system as “motor coordinates”, which give the distances that the motorized stages need to move to the required positions. We use fully-automatic mode to characterize multiple on-chip optical devices having constant input/output fibre incident angles. The measurements in fully-automatic mode require the motor coordinates of the integrated grating couplers of the devices to automatically align the input/output fibres. In this case, we align the input/output fibres to the grating couplers of the first device using piezoelectric auto-alignment and save the corresponding motor coordinates of the stages in the system GUI. We then move the fibres and repeat the above procedures on the last device. We extract the coordinates of the grating couplers of all of the devices from the mask layout GDS file, and save them in an Excel file. These coordinates, also called as the “layout coordinates”, are used for mapping the motor coordinates of the rest of the devices. Using the Excel file, the system GUI matches the layout coordinates of the grating couplers of the first and last devices to  45  3.2. System Operation  Load Chip  Initiate System GUI  Semi-automatic Mode No  Move I/O fibres to Device  Fully Automated Yes  Adjust Fibre Angle Piezoelectric Auto-alignment Wavelength Sweep  Move I/O fibres to 1st Device  Fully-automatic Mode  1st Device Motor Coordinates  Adjust Fibre Angle Piezoelectric Auto-alignment  Output Files  Move I/O fibres to Last Device  End  Piezoelectric Auto-alignment  Layout Coordinates  Last Device Motor Coordinates  Motor Coordinates Move I/O fibres to Device Piezoelectric Auto-alignment Wavelength Sweep  Output Files Next Device  Yes  No End  Figure 3.5: Automated Measurement Flowchart.  46  3.2. System Operation their motor coordinates, and then calculates the relative chip rotation angles along with the “magnitude scaling constants”, which are the ratios of the moving distances calculated from the layout coordinates to those calculated from the motor coordinates of each axis, and thus extrapolates the motor coordinates of rest of the devices based on the assumption that the system errors of the stage movements along each axis have uniform distributions. Hence, the travel paths of the fibres are mapped for auto-alignment. The system GUI then controls the stages to move the fibres, according to the motor coordinates, from one device to another. After moving the fibres to a device, the piezoelectric auto-alignment function is performed to optimize the coupling efficiency between the fibres and the grating couplers. The system GUI then latches the piezoelectric actuators and locks the stepper motors and performs a wavelength sweep of the optical response of the device. The measurements results are then saved to the computer before the system GUI aligns the fibres to the next device. The measurements in semi-automatic mode have fewer degrees of automation, but have more flexibility and simpler procedures for characterizing devices with various measurement requirements, as compared to those in fully-automatic mode measurements (see Fig. 3.5). In semi-automatic mode, we are able to adjust the incident angles of the input/output fibres for each device to maximize the coupling efficiency for the intended wavelength range. For example, if the output signal of the device is designed to be maximum at shorter wavelengths, then we increase the incident angles of the input/output fibres so that the output power will be maximized at shorter wavelengths. We are also able to set the wavelength range, reso47  3.2. System Operation lution, and sweep-speed of the tunable laser source on a device-by-device basis. For example, we usually measure a device with a 10 pm wavelength resolution, at a wavelength sweep-speed of 40 nm/s, over the wavelength range from 1480 nm 1580 nm, for high speed wavelength-swept measurements. We can also measure a device with a 1 pm wavelength resolution, at a wavelength sweep-speed of 5 nm/s, over the same wavelength range, for high resolution wavelength-swept measurements.  48  3.3. 24-Hour Alignment Testing  3.3  24-Hour Alignment Testing  We performed a 24-hour alignment test to evaluate the system stability and measurement repeatability of the automated setup. A single strip waveguide integrated with two grating couplers was chosen for this test. The fibre chucks, loaded with input/output fibres, were rotated to match the polarization of the grating couplers. The incident angles of the fibres were adjusted to maximize the coupling efficiency. The LDC-501 temperature controller was set to keep the experiment operating at 25◦ C. The 24-hour alignment test was performed in fully-automatic mode. At the beginning of each hour, during the test, the system GUI aligned the input/output fibres to the strip waveguide using piezoelectric auto-alignment. After the alignment, the stepper motors and the piezoelectric actuators were locked to keep the fibres from moving. The system GUI then performed ten wavelength-swept measurements, with 5 minute intervals between measurements, and saved the measurement results. The system GUI kept locking the motors and the piezoelectric actuators until the end of the tenth measurement. The system GUI then unlocked the motors and piezoelectric actuators and moved the stages back to their “Home” positions at the end of each hour. The system GUI repeated the above procedures every hour during the 24-hour alignment test. The wavelength-swept measurements covered the wavelength range from 1480 nm to 1580 nm with the wavelength resolution of 10 pm at the sweepspeed of 20 nm/s. Figure. 3.6a shows the power transmission spectrum of the strip waveguide (obtained from the fifth measurement during Hour 1)  49  3.3. 24-Hour Alignment Testing with a boxplot showing the power variation of the ten measurements at λ = 1550 nm. During the 24-hour test, the transmission power, as shown in Fig. 3.6b, drifted between -23.35 dBm and -22.59 dBm at λ = 1550 nm. This suggests that the automated measurement setup had relatively stable performance and could provide repeatable measurement results for long duration experiments.  50  3.3. 24-Hour Alignment Testing  Strip Waveguide Power at Hour 1 -20  Power [dBm]  -25  -30 -23.12  -23.14  -35  -23.16  -23.18  -40  1550  -45 1480  1490  1500  1510  1520  1530  1540  1550  1560  1570  1580  Wavelength [nm]  (a) Power at λ = 1550nm within 24 hours −22.5 −22.6 −22.7  Power [dBm]  −22.8 −22.9 −23 −23.1 −23.2 −23.3 −23.4 −23.5  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24  Time [hr]  (b) Figure 3.6: 24-hours alignment test results: (a) Transmission spectrum of a strip waveguide with a boxplot showing the power variation at λ = 1550nm of ten successive measurements; (b) Power vs. Time at λ= 1550 nm. 51  Chapter 4  Implementation of Dumbbell Micro-ring Reflector In this chapter, we present the implementation of a dumbbell shape microring resonator designed for use as a reflective notch filter. The device is designed and analyzed using the transfer-matrix method. We simulated the analytic model of the device and optimized its notch reflection properties. The dumbbell micro-ring reflector was fabricated using the silicon-oninsulator technology and its response measured using the automated optical measurement system. The measurement result showed a reflective response with a quality factor of ∼11,000 and an extinction ratio of 20 dB. We measured and characterized the excess optical loss from the 6-degree Y-branch power splitter that had been integrated into the dumbbell micro-ring reflector. The thermal responses of our device have also been presented.  Sections 4.1 and 4.2 and subsections 4.3.1 and 4.3.2 have been published in Yun et al.[30]. For the convenience of the reader, Sections 4.1 and 4.2 repeat the approach introduced in Chapter 2 for analyzing, modeling, and simulating the dumbbell micro-ring reflector.  52  4.1. Design and Analysis  4.1 4.1.1  Design and Analysis Design Scheme  Our device, which contains three directional couplers, has the shape of a dumbbell (see Fig. 4.1a). As shown in Fig. 4.1b, the reflector consists of a dual-coupler micro-ring resonator with an additional directional coupler located at the “handle” of the dumbbell structure to achieve the reflection. The reflected signal consists of the traveling waves from various optical paths within the dumbbell shape structure. For example, for one such path, the input light injected into the port on the left is coupled to a counter-clockwise wave via directional coupler 1. After propagating through waveguide L2 , where L2 is also the length of waveguide, the light is coupled into a clockwise wave via directional coupler 2 and propagates through the length of waveguide L4 . Thus the light is coupled into a backward traveling wave via directional coupler 3 and becomes a portion of the reflected signal at the left port after passing through directional coupler 1. The reflected traveling wave from the optical path described above is combined with the waves from other reflection paths and resonant paths to form the total reflected signal for the dumbbell micro-ring reflector.  4.1.2  Theoretical Analysis  We use the transfer-matrix method to analyze the reflection properties of the device[27, 28]. We define the field components (labeled in Fig. 4.1b) of  53  4.1. Design and Analysis  (a)  (b) Figure 4.1: Schematic drawings of dumbbell micro-ring reflector: (a) 3-D schematic on an SOI platform and (b) 2-D schematic with transfer-matrix elements labeled[30]. Copyright 2012 Society of Photo-Optical Instrumentation Engineers.  54  4.1. Design and Analysis the directional couplers as: T  Ei =  ai bi ci di  ,  i = 1, 2, 3, ..., 6,  (4.1)  where ai and bi represent the field components for the forward traveling waves along the waveguide and ci and di represent the field components for the backward traveling waves. Assuming that there is no mixing between the forward and backward traveling waves, we can express the coupling relationships for both the forward and backward traveling waves within the directional coupler using a 4 × 4 coupling matrix[6, 13]:   −t  1  0  0        2 2 0 0 1  −t − κ t  C=  ,  −jκ  0 0 −t 1    2 2 0 0 −t − κ t  (4.2)  where κ = |κ|e−(jβ+α/2)LC and t = |t|e−(jβ+α/2)LC are the cross-coupling and the straight-through coupling coefficients, respectively, of the directional coupler, β is the propagation constant, α is the propagation loss coefficient, and LC is the coupling length. Within one directional coupler, the power transmission ratio TC can be expressed as TC = |κ|2 + |t|2 . We define Pm (m = 1, 2, ..., 5) as the propagation transfer matrices for light propagating through lengths of waveguides Lm between the directional couplers. With the above expressions and definitions, the relationship between  55  4.1. Design and Analysis the left port and the right port of the device is given by E1 = C12 (P2 C34 + P5 )(P3 C34 + P4 )−1 C56 E6 .  (4.3)  C12 , C34 , and C56 (see Fig. 4.1b) are the coupling matrices, respectively, between the fields Ei and Ei+1 (i = 1, 3, and 5) within the directional couplers. The propagation matrix in Eq. (4.3), for each waveguide that bridges the directional couplers, is given by   0  0 0    0     −1  P   L2 0 0 0  P2 =     0 0 0 P  L2    0 0 0 0    0 0   0 0  P4 =    0 PL4  0 0  0 PL−1 4 0 0  0      0    0  0    0 PL3    0  P3 =   0  0  0  0  0  0  PL−1 3  0  0    0    0  P5 =    0  PL−1 5  0    0    0  0  0 0 PL5 0 0 0 0 0 0    ,   (4.4)    0     0   0  where PLm = e−(jβ+α/2)Lm . Assuming that the light is injected only into the left port, i.e., the input signal a1 = Ein and c6 = 0, we can calculate the reflected signal, Er = d1 , by solving Eq. (4.3) with the following additional relationships, which take into account the effect of connecting the two bottom couplers via waveguide L1 :  a6 = PL1 b1 and d6 = PL−1 c . 1 1  (4.5) 56  4.2. Simulation and Optimization  4.2 4.2.1  Simulation and Optimization Parameters  We designed the dumbbell shape micro-ring reflector based on 500-nm-wide, 220-nm-high, SOI nano-wires (see Fig. 4.2a). The gap distance in all of the directional couplers was 200 nm. We calculated the effective refractive indices using 2-D simulation method[8, 19] (see Fig. 4.2b). The power behavior within a directional coupler can be expressed as a function of the structure of the coupler, the position in the coupler, the coupling coefficient, and the power transmission ratio[14]. In this case, given the coupling gap distance, G, the coupling coefficient, and the power transmission ratio, TC , we can calculate the coupling length, LC , of the directional coupler from the following equation: |κ| LC = arcsin( √ ) · (B · e−A·G )−1 , TC  (4.6)  where A = 9.0842834 · 10−3 nm−1 and B = 1.8670660 · 10−4 nm−1 were obtained using Ref. 14. To take the real situation into account, we also include waveguide propagation loss and coupling loss in our transfer-matrix equation. We use a waveguide propagation loss α = 5 dB/cm and a power transmission ratio TC = 0.9, extracted from measurement and experiment data [5, 14] , in our simulations.  57  4.2. Simulation and Optimization  (a)  (b) Figure 4.2: (a) Trimetric view of a directional coupler, with the dimensions labeled ; (b) Mode distribution profile of the symmetric mode in two coupled waveguides[30]. Copyright 2012 Society of Photo-Optical Instrumentation Engineers. 58  4.2. Simulation and Optimization  4.2.2  Optimization  The cross-coupling coefficients, κ12 , κ34 , and κ56 , are key factors in determining the performance of the dumbbell micro-ring resonator reflector and, as shown in Fig. 2.9, can significantly affect the magnitude of the reflectivity spectrum as well as the values of the free spectral range and the quality factor. In this case, we defined Rp to be the maximum reflectivity and Rv to be the minimum reflectivity for the various possible combinations of the cross-coupling coefficients of the three couplers. We scanned the reflection spectrum and calculated the reflectivity difference, Rp − Rv , and the reflectivity extinction ratio, 10 log10 (Rp /Rv ), as functions of the three cross-coupling coefficients. The simulation plots in Fig. 4.3 show reflectivity differences and reflectivity extinction ratio values as functions of |κ12 | and |κ56 | for a fixed value of |κ34 |. Based on our simulation results, we chose the values for the three crosscoupling coefficients, which were |κ12 | = 0.84, |κ34 | = 0.94, and |κ56 | = 0.77, to meet the requirements of high reflectivity and high extinction ratio.  59  4.2. Simulation and Optimization  (a)  (b) Figure 4.3: Reflectivity scanning as functions of |κ12 | and |κ56 | when |κ34 | = 0.94: (a) Reflectivity differences; (b) Reflectivity extinction ratio[30]. Copyright 2012 Society of Photo-Optical Instrumentation Engineers.  60  4.3. Fabrication and Characterization  4.3 4.3.1  Fabrication and Characterization Fabrication  We drew the mask layout using the DW-2000 physical layout and verification software from Design Workshop Technologies[7], and generated the mask layout GDSII file, after passing the DRC (Design Rule Checking), for fabrication. The devices were fabricated at ePIXfab by Imec in Belgium using 193 nm deep UV lithography on SOI platform. Figure. 4.4 shows the fabricated dumbbell micro-ring reflector which has bending radii of 30 µm at the “heads” of the dumbbell, 15 µm in all other bends, and coupler gap distances of 200 nm in the three directional couplers. The coupling lengths of the directional couplers, which are respectively 35.83 µm, 47.30 µm, and 31.20 µm, are also labeled in Fig. 4.4b.  500 nm 200 nm  47.30µm 35.83µm  31.20µm  Figure 4.4: Optical image of fabricated dumbbell micro-ring reflector with dimensions labeled and with inset SEM image of the directional coupler.  61  4.3. Fabrication and Characterization  4.3.2  Reflection Spectra  The schematic for measuring the dumbbell micro-ring reflector using the automated probe station is shown in Fig. 4.5. We used TE-mode periodic grating couplers to couple the light into and out of our optical circuit. A 6degree Y-branch power splitter[17] was used and integrated into the circuit to split and isolate the reflected signal from the input light. A single-mode, polarization-maintaining fibre was used as the input fibre, and a multi-mode fibre was used as the output fibre to collect all of the light coming out of the output grating coupler. The incident angles of the fibres were adjusted to maximize the coupling efficiency at λ0 = 1550 nm. The fibre chucks were rotated to align the polarization to match the grating couplers. The chip was placed on top of the copper heat sink with an operating temperature setting of 25◦ C during the measurements.  Figure 4.5: Measurement schematic of dumbbell micro-ring reflector with an inset SEM image showing the Y-branch power splitter[30]. Copyright 2012 Society of Photo-Optical Instrumentation Engineers. 62  4.3. Fabrication and Characterization Measurements were taken on the reflection port of the device with incident angles of 12◦ on the input/output fibres (see Fig. 4.6). The reflected power response measured at the reflection port, after calibrating out the loss introduced by the straight waveguide and the two grating couplers between the input port and the reflection port, gave an extinction ratio of 20 dB, a free spectrum range (FSR) of 0.889 nm, and a quality factor (Q) of ∼11,000, which was calculated using Qλ/∆λ = where  fr ≈ f  λr λ3dB  (4.7)  λ3dB = 0.14 nm is the 3dB wavelength bandwidth as shown in  Fig. 4.6.  −10  0.14nm  Reflectivity, dBm  −20  20 dB  −30  −40  −50 Experiment −60  1542.5  Simulation  1543  1543.5  1544  1544.5  1545  Wavelength, nm  Figure 4.6: Measured and simulated reflection spectra at 25◦ C (an estimated loss of 7.4 dB from the Y-branch power splitter is included in the simulation data, and the optical paths are tuned to fit the free spectral range and the resonance peaks).  63  4.3. Fabrication and Characterization  4.3.3  Loss Measurement of Y-branch Splitters Using Micro-ring Resonators  The integrated Y-branch power splitter introduces excess losses to the reflector. Here we used a micro-ring-based method to characterize the optical losses from the integrated Y-branch power splitter, which was independent of the grating coupler insertion losses[16, 18]. The Y-branch power splitter, as shown in Fig. 4.7a, is 20-µm-long with a 6-degree opening angle between its two branch arms and is designed to have a 3 dB optical loss when light travels from its stem waveguide to either of its two branch waveguides. We designed and fabricated all-pass racetrack micro-ring resonators (not our designed micro-ring reflectors) with several 6-degree Y-branch power splitters integrated inside the ring cavity, as well as a reference micro-ring resonator without any Y-branch splitter (see Fig. 4.7b). Two Y-branch splitters were combined back-to-back to form a symmetric Mach-Zehnder interferometer (MZI) with short arms (6 µm), which avoided the impact of the intrinsic 3 dB loss on the transmission spectrum of the micro-ring. We then inserted various numbers of such MZIs into the ring. The reference micro-ring resonator had a round-trip length of ∼544.25 µm with a coupling length of 15 µm and a coupler gap distance of 200 nm. The micro-ring resonators with Y-branch splitters had the same coupler design as the reference micro-ring. We used the automated setup to measure the transmission spectra of the Y-branch splitter integrated micro-ring resonators, as well as the reference micro-ring resonator. We calculated the coupling coefficient of the 15-µm-  64  4.3. Fabrication and Characterization  (a)  (b) Figure 4.7: Micro-ring resonators with and without integrated Y-branch splitters: (a) 6-degree Y-branch power splitter mask layout and SEM image; (b) Optical image of fabricated micro-ring resonators with and without Ybranch.  65  4.3. Fabrication and Characterization long directional coupler using the 2D FD mode solver. Then we extracted the waveguide loss of the reference micro-ring resonator by curve fitting the measured power transmission spectrum using the following equation[16, 27]:  T =  a2 + t2 − 2at cos δ |Et |2 = |Ein |2 1 + a2 t2 − 2at cos δ  (4.8)  where a is the round-trip loss, t is the straight-through coupling coefficient, and δ is the round-trip phase shift. The round-trip phase shift is wavelength dependent and is given by  δ=  2π · l · nef f λ  where l, nef f , and λ are the round-trip length, the effective index, and the wavelength, respectively[27]. Using the same method, we were also able to extract the total round-trip loss of the micro-ring resonator integrated with Y-branch splitters. Thus we could obtain the insertion loss of the Y-branch splitter by subtracting the waveguide loss from the total round-trip loss. The measured and fit spectra of the reference micro-ring resonator are shown in Fig. 4.8a, for which the round-trip loss is determined to be 0.511 dB. Figure 4.8b shows the measured and fit spectra of the micro-ring resonator with two pairs of Y-branch splitters inserted in the optical cavity, for which the round-trip loss was determined to be 3.322 dB. Table 4.1 lists the values of the parameters that were used for curve-fitting the measured spectra. The excess loss induced by the Y-branch splitters was then extracted and found to be 2.801 dB, which implies an excess loss of  0.7 dB  per Y-branch splitter. Thus, the Y-branch power splitter integrated in the 66  4.3. Fabrication and Characterization dumbbell micro-ring reflector introduced 7.4 dB optical loss to the reflection response of the reflector, in total. Including this 7.4 dB loss in our simulation, as shown in Fig. 4.6, we fit the simulation results to the measured reflection spectrum. Reference Micro-ring Resonator  Micro-ring Resonator with two Y-branch pairs  Round-trip Length l [µm]  544.25  547.57  Coupling Coefficient t  0.8982  0.8982  Group Index ng  4.1989  4.1989  Round-trip Loss α [dB/cm]  9.3963  60.6680  Device  Table 4.1: Parameters for Curve-fitting.  67  4.3. Fabrication and Characterization  −38 −40  Power [dBm]  −42 −44 −46 −48 −50 −52 1544.5  Curve Fit Measured 1545  1545.5  1546  1546.5  Wavelength [nm]  (a) −23.5 −24  Power [dBm]  −24.5 −25 −25.5 −26 −26.5 −27 1544.5  Curve Fit Measured 1545  1545.5  1546  1546.5  Wavelength [nm]  (b) Figure 4.8: Measured and fit transmission spectra of: (a) a micro-ring resonator; (b) a micro-ring resonator with 2 pairs of Y-branch splitters. 68  4.3. Fabrication and Characterization  4.3.4  Thermal Tuning Responses  We have also investigated the thermal responses of the dumbbell micro-ring reflector. We controlled the TEC controller to tune the operating temperature. As shown in Fig. 4.9, the resonance peak shifted from ∼1527.50 nm to ∼1528.01nm when the operating temperature was tuned from 22◦ C to 28◦ C. To characterize the thermal responses of the device, we tracked the changes of the resonant peak wavelengths by tuning the temperature from 20◦ C to 40◦ C in 1◦ C increment. As shown in Fig. 4.10, curve fitting gives a 0.082 nm/K wavelength shift.  Figure 4.9: Reflection spectra versus temperature tuning at 25±3◦ C.  69  4.3. Fabrication and Characterization  1529.2  1529  1528.8  Wavelength [nm]  1528.6  1528.4  λ = 0.082031 · T + 1525.7024 → 1528.2  1528  1527.8 Experiment Data Curve Fitting  1527.6  1527.4  1527.2 20  22  24  26  28  30  32  34  36  38  40  Temperature [◦ C]  Figure 4.10: Resonant wavelength shift vs. Temperature with curve fitting.  70  Chapter 5  Summary, Conclusions, and Suggestions for Future Work 5.1  Summary  The design and characterization of an SOI dumbbell micro-ring resonator reflector has been presented in this thesis. Directional couplers were analyzed using the transfer-matrix method, developed from the eigenmode (supermode) theory, to describe the power coupling behavior between the two waveguides and thus to determine the amount of the power that can be coupled from one waveguide to the other. The transfer functions of the add and drop ports of single micro-ring resonator add-drop filters were then derived using the transfer-matrix method, which showed the convenience and simplicity of this matrix formulation. We then applied the transfermatrix method to obtain the analytic model of the dumbbell micro-ring reflector, and, thus, calculated the reflectivity of the device. We characterized the optical mode of the SOI strip waveguide using a 2-D Finite-Difference eigenmode solver and calculated the coupling lengths of directional couplers using a curve-fit method. We determined the parameters that were used in  71  5.2. Conclusions the analytic model of the dumbbell micro-ring reflector and optimized our design, base on numerical simulations in MATLAB, for fabrication. We also designed and assembled a fibre-to-fibre automated optical measurement system. This measurement setup was implemented to automatically characterize on-chip nanophotonic circuits for high speed and high resolution wavelength-swept measurements with accurate fibre alignment. System testing results showed that the setup had relatively stable performance and could provide repeatable measurement results. We have fabricated an SOI dumbbell micro-ring reflector at ePIXfab by Imec. We measured the reflective responses of the device using the automated measurement setup. Integrated 6-degree Y-branch power splitters were also fabricated and characterized using a micro-ring-based method for calibrating out the optical losses introduced to the dumbbell micro-ring reflector by the Y-branch. The thermal responses of the dumbbell micro-ring reflector were also measured.  5.2  Conclusions  In conclusion, we have demonstrated a wavelength-selective reflector based on a dumbbell shape micro-ring resonator structure. We designed and fabricated the reflector based on silicon nanophotonic waveguides using SOI technology. The measured reflection spectra of the fabricated device showed notch reflective responses. A reflectivity extinction ratio of 20 dB with a Q factor of ∼11,000 and a FSR of 0.889 nm have been achieved when the three directional couplers of the reflector have their respective cross-coupling co-  72  5.3. Suggestions for Future Work efficients of 0.84, 0.94, and 0.77. A 0.082 nm/K wavelength shift has also been obtained from the thermal measurement results. Functioning as a reflective notch filter, this reflector geometry can be used for implementing reflective-type electro-optical modulators when carrier injection or depletion mechanisms are incorporated. By monitoring the shift of a resonant wavelength or variation of the reflected light intensity of a fixed wavelength, the dumbbell reflector can be used for either thermal sensing, biochemical sensing, or radio-frequency (RF) electric field detection[20]. Combined with a single optical fiber or integrated with a single strip waveguide for delivering both the input light and reflected signal, the device can be used in remote sensing applications.  5.3  Suggestions for Future Work  The performance of the dumbbell micro-ring reflector, as a notch reflective filter, can be tunned by adjusting the coupling coefficients of the three couplers. Since our simulation optimized the coupling coefficients to two decimal places, higher reflectivity extinction ratios could be achieved by optimizing the coupling coefficients a higher degree. Another approach might be to use the fabrication processes with less waveguide sidewall roughness, and, thus, to improve the device performance by having lower scattering losses. The measured thermal responses also suggest that local thermal heaters can be integrated on the chips to ensure that the device resonates at the designed wavelength. For the fibre-to-fibre automated measurement setup, following improve-  73  5.3. Suggestions for Future Work ments can be made: integrating the functions of the fibre chuck, the holding arm, and the rotation plate into one mechanical part to reduce system errors; using lensed fibres or using manufacture-cleaved fibres to reduce the insertion loss between the fibre and grating coupler; using a two-axis linear long travel motorized stage as the sample stage to increase the measurement range from die-scale to chip-scale, or even to wafer-scale; integrating electric RF/DC probes into the setup for electro-optic measurements.  74  Bibliography [1] V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson. Alloptical control of light on a silicon chip. Nature, 431:1081–1084, 2004. [2] S. Assefa, S. Shank, W. Green, M. Khater, E. Kiewra, C. Reinholm, S. Kamlapurkar, A. Rylyakov, C. Schow, F. Horst, H. Pan, T. Topuria, P. Rice, D. M. Gill, J. Rosenberg, T. Barwicz, M. Yang, J. Proesel, J. Hofrichter, B. Offrein, W. Haensch X. Gu, J. Ellis-Monaghan, and Y. Vlasov. 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Murphy. Vector Finite Difference Modesolver for Anisotropic Dielectric Waveguides. J. Lightwave Technol., 26:1423–1431, 2008. [9] B. Jalali and S. Fathpour. Silicon Photonics. J. Lightwave Technol., 24:4600–4615, 2006. [10] I. P. Kaminow, T. Li, and A. E. Willner. Optical Fiber Telecommunications V A (Fifth Edition): Components and Subsystems. Academic Press, 2008. [11] C. Lin. Photonic device design flow : from mask layout to device measurement. Thesis, page 97, 2012. [12] J. D. Meindl. Beyond Moore’s law: the interconnect era. Computing in Science and Engineering, 5:20–24, 2003. [13] J. K. S. Poon, J. Scheuer, and A. Yariv. Wavelength-Selective Reflector Based on a Circular Array of Coupled Microring Resonators. IEEE Photonics Technol. Lett., 16:1331–1333, 2004.  76  Bibliography [14] N. Rouger, L. Chrostowski, and R. Vafaei. Temperature Effects on Silicon-on-Insulator (SOI) Racetrack Resonators: A Coupled Analytic and 2D Finite Difference Approach. J. Lightwave Technol., 28:1380– 1392, 2010. [15] W. Shi. Silicon Photonic Filters for Wavelength-Division Multiplexing and Sensing Applications. Thesis, page 121, 2012. [16] W. Shi, T. K. Chang, H. Yun, W. Zhang, C. Lin, Y. Wang, N. A. F. Jaeger, and L. Chrostowski. Differential Measurement of Transmission Losses of Integrated Optical Components Using Waveguide Ring Resonators. Proc. SPIE, Photonics North 2012, 8412:84120R, 2012. [17] W. Shi, R. Vafaei, M. A. Torres, N. A. F. Jaeger, and L. Chrostowski. Design and characterization of microring reflectors with a waveguide crossing. Opt. Lett., 35:2901–2903, 2010. [18] W. Shi, H. Yun, W. Zhang, C. Lin, T. K. Chang, Y. Wang, N. A. F. Jaeger, and L. Chrostowski. Ultra-compact, high-Q silicon microdisk reflectors. Opt. Express, 20:21840–21846, 2012. [19] MODE Solutions.  http://www.lumerical.com/tcad-products/mode/.  Lumerical Solutions, Inc. [20] H. Sun, A. Chen, and L. R. Dalton. A reflective microring notch filter and sensor. Opt. 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