A Homotopy Method for Locating All the Poles of a Parallel Plate Waveguide With the PML

In this paper, a homotopy method for locating all the poles of a parallel plate waveguide with the perfectly matched layer is proposed. As is well known, the Green's functions for an open multilayered medium can be approximated by those for a parallel plate waveguide with the perfectly matched layer, while the latter Green's functions can be theoretically expressed into series expansions of their own eigenmodes without involving any numerical integrations. The homotopy method here is applied for finding the desired mode poles. In this method, the Newton-Raphson iteration is employed to solve every node equation except the start node equation, while the dichotomy method is used to solve the start node equation. The roots of the end node equation are just the desired mode poles. With the proposed method, the Green's functions for a lossy or lossless multilayered medium can be efficiently calculated by the corresponding series expansions. Some numerical examples are provided to examine the robustness and accuracy of the proposed method.