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This paper presents a parametric study of the stresses in a matrix near a cylindrical inclusion. The Texas Grain Analysis Program (TEXGAP), a finite element approach, is used to model the problem. Eight different models are investigated which establish the stress effects of varying interlayer thickness, varying modulus of elasticity of inclusions and interlayers, and element size. The results, presented as plots of axial stresses, show a definite lowering of the stress in the area of inclusion termination as the interlayer thickness is increased from zero. A further stress decrease is noted with the addition of some inclusion elasticity. Similarly, the stresses also decrease as the interlayer becomes more elastic.

<p>Optical waveguide is a very important component in numerous optical structures, devices and photonic circuits. With the rapid development of fabrication technologies, increasing integrated complexity and different materials characteristics, there is higher demand on high-index contrast waveguide with arbitrary cross section and anisotropic material, which indicates the need to develop an efficient, high-performance mode solver to analyze optical waveguides to reduce the fabrication cycle and total cost. Modeling and simulation methods, including Finite Difference Time-Domain (FDTD) method, Finite Element Method (FEM), Beam Propagating Method (BPM), Mode Matching Method (MMM) and Couple Mode Theory (CMT), etc, have been popular for years. Among those methods, FEM is a good and efficient method, especially for its superiority on arbitrary meshes.</p> <p>In this thesis, both scalar and vectorial FEM mode solvers are implemented with an emphasis on dealing with the radiation and evanescent modes by enclosing the whole region with the Perfect Matched Layer (PML) and Perfect Reflecting Boundary (PRB). Thus, the unbounded and continuous radiation modes together with evanescent modes are replaced by what we called "complex modes", but still keeping the completeness and orthogonality properties.</p> / Master of Applied Science (MASc)