Analysis of Inhomogeneous Dielectric Waveguides in Plane-Stratified Media.

A rigorous formulation which combines the finite element method (FEM) and the surface integral equation method (SIEM) is developed for the analysis of inhomogeneous anisotropic waveguides of arbitrary cross-section embedded in plane-stratified dielectric media or in a homogeneous cladding. In this approach, the waveguide interior (guiding core) is modeled by the FEM based on the vectorial electric field formulation. The waveguide exterior (layered medium environment) is modeled by the combined field integral equation method (CFIEM) utilizing the mixed-potential field representation. The interior and exterior problems are coupled by enforcing the continuity conditions on the tangential fields across the surface of the waveguide cross-section. The resulting hybrid formulation is discretized by the Galerkin's approach, leading to a sparse system of linear equations. The modal propagation constants are found as the zeros of the system matrix determinant. The slowly-convergent spectral integrals that arise in the layered medium Green's functions are efficiently evaluated by the discrete complex image method (DCIM). The DCIM is extended to the case of leaky modes on microstrip transmission lines. To validate the developed computer code and to illustrate its capabilities, sample dispersion curves and modal field distributions are presented and, where possible, compared with published results. The approach developed here incorporates the strengths of some of the existing methods. It results in a sparse matrix and rigorously takes into the account of layered medium environment.