The Method of Analytical Preconditioning in the Analysis of the Propagation in Dielectric Waveguides with Wedges

The recent interest in dielectric waveguides with complicated structures and the improvement in the etching techniques frequently lead to a geometrical idealization in which the wedges cannot be ignored when accurate solutions are required. The aim of this paper is the introduction of a guaranteed-convergence method for the analysis of the propagation in dielectric waveguides with a polygonal cross section belonging to the class of methods of analytical preconditioning. A surface integral equation formulation in the spectral domain is discretized by means of Galerkin's method with analytical Fourier transformable expansion bases reconstructing the physical behavior of the fields even on the wedges. The obtained matrix equation has many symmetries due to reciprocity and the matrix coefficients are improper integrals of the oscillating functions efficiently computed by means of an analytical asymptotic acceleration technique and a vectorized C++ code implementation. Comparisons with the literature and the commercial software CST Microwave Studio are produced to show the effectiveness of the presented method.