| In this Masters thesis, the propagation of light in dielectric waveguides is studied. Using a finite difference spectral domain (FDSD) scheme with uniform discretization, the vectorial eigenmode equations representing propagation through a lossless, arbitrary index profile, longitudinally constant, waveguide, are derived. Also, a generalization of these FDSD equations for a broad category of anisotropic waveguides, namely those with a preferential axis aligned with the direction of propagation, is presented for the first time to our knowledge.; These equations are then solved using the Shifted Inverse Power Method (SIPM). A performance optimization study is performed on the resulting algorithm, using numerous control parameters. The algorithm is then tested on a wide variety of waveguides: multimode circular fibers, photonic bandgap fibers, fused-fibre couplers, rectangular anisotropic waveguides, and an imaginary waveguide, made of two anisotropic circular fibers fused in such a way that their transverse preferential axis are not aligned.; Comparison of the results with analytical solutions, whenever possible, yields excellent agreement for the effective indexes of the eigenmodes, with relative errors ranging from 7,5 · 10-7 to 4,7 - 10-10. When such analytical solutions are not available, results for the effective indexes are always found to be within the standard deviation of a set of previously reported results, except in one case where discretization was much finer in the reported results. Finally, an improvement is briefly discussed for fused-fibre coupler devices, based on simulation results. (Abstract shortened by UMI.)... |
