<p>The main contributions of this thesis include two points: firstly, we originally establish Complex STM to semi-analytically calculate the mode profiles of multi-layer planar waveguide terminated with both PML and PRB ; secondly, although CMMM has been generally applied to the simulation of waveguide facets, Bragg gratings, etc[52-53], we for the first time demonstrate that CMMM can also be utilized for the modeling of couplings of radiation field outgoing perpendicularly to the waveguide axis with an incident wave launched in the examples of high-index-contrast waveguide crossings and corners. CMMM is proved to be able to estimate the field profiles and power flows accurately through the validation with FDTD.</p> / <p>Optical waveguides are basic building blocks of high-density photonic integrated circuits and play crucial roles in optical access networks, biomedical system, sensors and so on. Various kinds of dielectric waveguides apply the total internal reflection condition to transmit optical field [9] and even more complicated structures based on waveguide interconnects, Bragg grating, photonic crystals are actively developed by corporations and academic institutes. Especially, the fast developing pace of Metal-Organic Chemical Vapor Deposition (MOCVD), Molecular Beam Epitaxy (MBE) and other fabrication techniques has predicted the increasing complication and thus more advanced function of modern optics integrated circuits. Under such circumstances, convenient and accurate modeling and simulation schemes are necessary for the exploration, designing and optimization of photonic devices, systems and networks before the time-consuming and expensive fabrication process.</p> <p>The thesis summarizes several frequency-domain modeling schemes for the calculation of mode profile or beam propagation in 2D dielectric waveguide. The thesis mainly covers conventional Smooth Transition Method (STM), High Order Finite Difference (HOFD) scheme, Complex STM, and Complex Mode Matching Method (CMMM) based on the 2D waveguide model terminated with Perfect Matching Layer (PML) and Perfect Reflection Boundary (PRB). The mode spectrums and modal patterns obtained from Complex STM are compared with those of HOFD, and the simulation of waveguide crossings and corners with CMMM is validated with Finite-Difference-Time-Domain (FDTD) Method.</p> <p><strong> </strong></p> / Master of Applied Science (MASc)