| In this thesis work, the Method of Lines (MOL), which is based on eigenpair calculation, is modified using Pade approximants (PBPM). Because the use of Pade approximants decreases the numerical demand of the MOL from N3 to N, where N is the number of discretizations, the PBPM is far more efficient than the MOL. Various numerical experiments which are reported in this thesis work confirm that the PBPM is much more efficient than the MOL when the number of transverse mesh points is large. The PBPM has been applied in the analysis of a variety of integrated optical devices. This includes a beam expander, which connects two wave guides of different core widths, using a linearly tapered junction. In addition, a waveguide crossing with a resonant cavity at the center has been studied. Finally a novel three-way 90° beam splitter as proposed and its operation has been verified using the developed PBPM approach. This type of beam splitter utilizes a rectangular cavity at the center. |
