This work is concerned with the modeling and analysis of lossy planar dielectric optical waveguides. Loss mechanisms which affect propagation characteristics are reviewed, and various representations of the propagation constant in the lossy case are defined. Waveguide structures which are susceptable to absorption and/or to leakage loss, in particular silicon-based structures, are discussed. The modeling and analysis of these waveguides by various computational techniques is considered. Two computational methods, the commonly used transfer matrix method and the recently developed impedance boundary method of moments (IBMOM), are reviewed and extended to the complex domain. A third computational method, which offers improved convergence of the IBMOM for structures with large stepwise changes in refractive index, is formulated. In this approach, the regions containing refractive index discontinuities are replaced by equivalent extended impedance boundary conditions, and expansion of the transverse field in the remaining region of continuous refractive index profile is carried out. A significant increase in the rate of convergence is demonstrated for various waveguide structures, including an anti-resonant reflecting optical waveguide (ARROW) structure. Two applications of the IBMOM with extended impedance boundary conditions are presented. In the first, the method is applied to the design of a chemical sensor. The sensor, a silicon-based ARROW structure, is designed to measure the refractive index of certain chemical substances with a high degree of accuracy. In a second application, graded index SiON waveguides fabricated at Oregon State University are characterized and compared to the theoretical model. Excellent agreement between the theoretical and measured coupling angles is shown. / Graduation date: 1996

This dissertation includes three separate studies of related waveguide grating phenomena. These studies deal with a numerical improvement of the integral method of diffraction grating theory, the theoretical analysis of waveguide gratings, and fabrication techniques for photoresist grating masks. The first topic addresses the acceleration of the convergence of the integral kernels. To improve the performance of the integral method for calculating diffraction grating efficiencies, the convergence of the integral kernels is studied. A nonlinear sequence transformation, Levin's u-transformation, is successfully applied to accelerate the convergence of the integral kernels. The computer execution time saving is significant. The application details and many numerical examples are given. The second subject is the ray optics theory of waveguide grating analysis. To establish a linkage between the analysis of diffraction gratings and the analysis of waveguide gratings, a new rigorous ray optics theory is developed. It takes into account phase changes on diffraction, multiple diffraction processes, depletion of the incident guided wave, and lateral shifts. A general characteristic equation that determines the waveguide grating attenuation (coupling) coefficient is derived. The symmetry properties of grating diffraction are applied to waveguide grating analysis for the first time. Lateral shifts of optical rays at a periodically corrugated interface similar to the Goos-Haenchen shift at a planar interface are suggested. The third subject is the in situ control of the development of photoresist grating masks. The existing method for monitoring and modeling photoresist grating development are modified and extended to monitoring and modeling photoresist grating mask development. Experimental examples, detailed theoretical considerations, and computer simulations are presented.

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石墨烯，由單層碳原子緊密排列成蜂巢狀的晶體結構，擁有卓越的電學性能和光學性能。這些優異的性能包括：極高的電子遷移率，超寬的吸收光譜，栅電壓調控光躍遷性質，飽和吸收性質。石墨烯的獨特光學性質已經被用來製造多種高性能的光電器件，包括光電探測器， 飽和吸收器， 光調製器和四波混頻的介質。同時，石墨烯的製造工藝可以與現代半導體標準製造工藝相兼容， 加上它穩定的化學性質， 石墨烯非常有潛力在未來半導體工業發展中發揮重要作用。 / 單層石墨烯可以透過97.7% 垂直入射的光，吸收2.3% 左右，並且吸收的光頻非常寬。雖然對於單層碳原子結構，這個吸收率很大，但是在一些器件中，我們需要更高的光吸收率。爲了突破單層石墨烯光吸收的極限，一種可行的辦法是延長石墨烯與光相互作用的長度。將單層石墨烯轉移到長的硅波導上，可以延長石墨烯與光作用的長度。除了線性光吸收特性，石墨烯的飽和吸收特性也有廣泛的應用。很多脉衝激光發生器是利用被動鎖模的原理，即激光器中的飽和吸收器將連續的光波轉變成頻率固定的脉衝。石墨烯已經被證明是恢復速度快、調製範圍大的飽和吸收器。 但是，石墨烯和硅波導結合作為飽和吸收器的特性和它們的應用還從來沒有被研究過。 / 在論文中，我們研究了石墨烯轉移到硅波導后的線形光學性質和飽和吸收特性。首先我們討論了石墨烯轉移的方法，然後我們通過實驗調查了石墨烯在貴波導上的線形光學性質和飽和吸收特性。爲了研究石墨烯/硅波導在被動鎖模光纖激光器中的作用，我們利用石墨烯/硅波導作為飽和吸收器製造了一個光纖激光器。之後，通過在激光腔體中加入可调滤波器， 我們用成功的演示了波長可調製被動鎖模光纖激光器。 / 多脉衝激光光源在光纖通信，測量學和光學器件性能鑒定中有重要作用。所以研究緊湊、穩定並且價格實惠的多脉衝鎖模激光器非常有意義。爲了實現多脉衝鎖模光纖激光器，我們將硅基濾波器和石墨烯/硅波導集成在一起. 在論文中，我們設計并優化了能被應用於多脉衝鎖模激光器的寬帶寬濾波器凹凸光栅。 / Graphene, a single 2D sheet of carbon atoms arranged in a honeycomb lattice, has superior electrical and optical properties including extremely high charge-carrier mobility, broadband optical absorption, gate-variable optical transitions and saturable absorptions. Its unique optical properties have led to a range of promising optoelectronic devices, such as photo detectors, saturable absorbers, optical modulators and nonlinear media for four-wave mixing. Graphene’s complementary metal-oxide-semiconductor (CMOS) integration processes at wafer scale and its electrochemical stability make it a promising candidate for post CMOS electronics. / Monolayer grapheme transmits 97.7% of the normal incident light and absorbs 2.3%, independent of wavelength. In order to overcome the challenge of limited absorption of a monolayer and better exploit graphene optical properties, a long interaction length is needed. By integrating graphene directly on top of silicon waveguides, longer light/graphene interactions can be achieved. In addition to the linear optical properties of the graphene, its saturable absorption also finds useful applications. Many ultra-short pulse lasers are based on passive mode-locking, where a saturable absorber turns continuous wave output of the laser into a train of optical pulses. And graphene has been shown to make an excellent saturable absorber. However, the saturable absorption behavior of graphene-silicon wavguides and their applications have never been studied. / In this thesis, the linear and saturable absorption of monolayer graphene films transferred onto silicon waveguide are investigated. The transfer process of monolayer graphene to silicon waveguides is studied and linear and saturable absorption measurements are carried out. To investigate applications of graphene-silicon waveguides, a passive mode-lock fiber lasers in which graphene-silicon waveguides act as saturable absorbers to mode-lock pulses is constructed. By adding a tunable filter in cavity, a tunable mode-locked fiber laser based on graphene-silicon waveguide is demonstrated. / Multi-wavelength pulse sources are important for applications including optical fiber communication, instrumentation, and photonic component characterization. The availability of compact, reliable and cost effective multi-wavelength mode-locked lasers is of great importance. We also hope to build multiwavelength mode-locked fiber lasers by integrating CWDM silicon filters with graphene-silicon waveguides. The design process and optimization of a silicon filter called echelle grating is demonstrated. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Shi, Zerui. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references. / Abstracts also in Chinese. / Chapter Chapter 1: --- Introduction --- p.1 / Chapter 1.1 --- Photonic Integrated Circuit (PIC) --- p.1 / Chapter 1.2 --- Silicon on Insulator (SOI) Photonics --- p.3 / Chapter 1.2.1 --- SOI Waveguides --- p.5 / Chapter 1.2.2 --- SOI Waveguide Based Wavelength Division Multiplexing --- p.6 / Chapter 1.3 --- Graphene Photonics --- p.9 / Chapter 1.3.1 --- Band Structure of Monolayer Graphene --- p.9 / Chapter 1.3.2 --- Optical Absorption of Graphene --- p.13 / Chapter 1.3.3 --- Graphene Based Passive Mode-Locked Fiber Lasers --- p.18 / Chapter 1.4 --- Motivation --- p.22 / Chapter 1.5 --- Thesis Outline --- p.23 / Chapter 1.6 --- Reference --- p.24 / Chapter Chapter 2: --- Optical Properties of Graphene-Silicon Waveguides --- p.27 / Chapter 2.1 --- Fabrication and Transfer Process of Graphene-Silicon Waveguides --- p.28 / Chapter 2.1.1 --- Fabrication of SOI Waveguides --- p.28 / Chapter 2.1.2 --- Transfer Process of Monolayer Graphene onto SOI Waveguides --- p.29 / Chapter 2.2 --- Linear Optical Absorption of Graphene-Silicon Waveguides --- p.35 / Chapter 2.2.1 --- Introduction to Photoexcitation in Monolayer Graphene --- p.35 / Chapter 2.2.2 --- Experimental Results of Linear Absorption --- p.37 / Chapter 2.3 --- In-Plane Saturable Absorption of Graphene-Silicon Waveguides --- p.38 / Chapter 2.3.1 --- Experimental Result of In-Plane Saturable Absorption of Graphene-Silicon Waveguides --- p.39 / Chapter 2.3.2 --- Mechanism of Saturable Absorption of Graphene-Silicon Waveguides --- p.42 / Chapter 2.4 --- Summary --- p.44 / Chapter 2.5 --- Reference --- p.45 / Chapter Chapter 3: --- Hybrid Graphene-Silicon Waveguides Based Mode-Locked Fiber Lasers --- p.47 / Chapter 3.1 --- Background of Graphene Based Mode-Locked Fiber Lasers --- p.47 / Chapter 3.1.1 --- Passive Mode-Locked Lasers Fundamentals --- p.47 / Chapter 3.1.2 --- Review of Recent Works of Graphene Based Mode-Locked Fiber Lasers . --- p.52 / Chapter 3.2 --- Hybrid Graphene-Silicon Waveguides Based Mode-Locked Fiber Lasers --- p.55 / Chapter 3.2.1 --- Experimental Set Up and Results --- p.55 / Chapter 3.2.2 --- Discussion --- p.59 / Chapter 3.3 --- Tunable Graphene-Silicon Waveguides Based Mode-Locked Fiber Lasers --- p.62 / Chapter 3.4 --- Summary --- p.66 / Chapter 3.5 --- Reference --- p.66 / Chapter Chapter 4: --- Conclusion and Future Work --- p.68 / Chapter 4.1 --- Conclusion --- p.68 / Chapter 4.2 --- Future Work --- p.69 / Chapter 4.2.1 --- Design and Simulation Results of Echelle Grating --- p.69 / Chapter 4.2.2 --- Optimization and Experiment Results of Echelle Gratings --- p.77 / Chapter 4.2.3 --- Integration of Echelle Grating with SOI Waveguides --- p.82 / Chapter 4.3 --- Summary --- p.84 / Chapter 4.4 --- Reference --- p.85 / Chapter APPENDIX A: --- PUBLICATION LIST --- p.86 / Chapter APPENDIX B: --- LIST OF FIGURES --- p.87 / Chapter APPENDIX C: --- LIST OF TABLES --- p.91 / Chapter APPENDIX D: --- atlab Code of Simulation of Echelle Grating --- p.92

Numerical analysis of the electromagnetic fields in large, complex structures is very challenging due to the high computational overhead. Recently, it has been shown that a new method called Trefftz-FLAME ( Flexible Local Approximation MEthod) is suitable for problems where there exist a large number of similar structures. / This thesis develops Trefftz-FLAME in two areas. First, a novel 2D Trefftz-FLAME method incorporates the modal analysis and port boundary condition that are essential to an accurate calculation of reflection and transmission coefficients for photonic crystal devices. The new technique outperforms existing methods in both accuracy and computational cost. / The second area pertains to the 3D, vector problem of electromagnetic wave scattering by aggregates of identical dielectric particles. A methodology for the development of local basis functions is introduced, applicable to particles of any shape and composition. Boundary conditions on the surface of the finite FLAME domain are described, capable of representing the incident wave and absorbing the outgoing radiation. A series of problems involving dielectric spheres is solved to validate the new method. Comparison with exact solutions is possible in some cases and shows that the method is able to produce accurate near-field results even when the computational grid spacing is equal to the radius of the spheres.

Planar optical waveguides fabricated by K$ sp+$-Na$ sp+$ ion-exchange in soda-lime glass substrates are investigated. / Experimental characterizations of planar waveguide with respect to a wide range of fabrication conditions have been carried out, including detailed measurements of the refractive index anisotropy resulting from the large induced surface stresses. / Parallel to this, the non-linear diffusion process of ion-exchange was simulated numerically to provide, along with the results of the characterizations, a complete description of the refractive index profile from any set of fabrication conditions. / The magnitude of the maximum surface index change observed was shown theoretically to be almost entirely due to the induced stress at the surface of the substrate, arising from the presence of the larger potassium ions. / Finally, a novel class of single-mode channel waveguides, made by a "two-step" ion-exchange was analyzed. A simple model for these waveguides was developed and used in the design of two directional coupler structures which were fabricated and measured. / The two-step process was conceived because it relaxes waveguides' dimensional control, yielding single-mode guides of larger size, better suited for low-loss connections to optical fibers. It also provides an additional degree of freedom to adjust device properties.

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