Perfectly matched layer absorbing boundary conditions for a vectorial BPM based on the Fourier series expansion

Abstract

A new formulation of the vectorial-BPM with Perfectly Matched Layer absorbing boundary conditions of coordinate stretching-type has been developed. It is shown that, if the resulting wave equations are discretized by a Fourier series expansion method based on the Galerkin's strategy, the obtained results are clearly superior to those obtained with the classical FFT-BPM (based on the collocation strategy). Both the formulation and the proposed discretization scheme were tested in 2D situations, homogeneous and guided-wave media, showing in all cases excellent results. Also, in this work, a variable transformed Fourier series expansion method is used to analyze the propagation in 2D structures and the problems involved with reflections in the transformed coordinates are pointed out.