Efficient mode-matching analysis of discontinuities in finite planar substrates using perfectly matched layers

A new method to determine the reflection of substrate modes in finite substrate planar circuits is proposed. The perfectly matched layer (PML) concept is used to transform the open problem into a closed one. The discrete set of substrate, evanescent, and Berenger modes of the resulting anisotropic waveguides are then used in a mode-matching scheme to deduce the scattering coefficients of the substrate modes for oblique incidence on the edge of the substrate. We show results for single- and double-layered substrates and compare with finite-difference time-domain (FDTD) results. The combined perfectly matched layer (PML) mode-matching technique turns out to be very efficient.