All the modes in a layered medium background truncated by a PML backed with a PEC

In this paper, an accurate method for determining all the modes in a layered medium background truncated at top by a perfectly matched layer (PML) backed with a perfectly electric conductor (PEC) is proposed. Adding a PML backed with a PEC makes the Green´s functions for a layered medium background can be expanded with the discrete set of the eigenmodes, avoiding numerically calculating the Sommerfeld integrals when the spectral Green´s functions are inversed into the spatial domain. However, it is essential to accurately determine the desired modes and to accurately calculate the corresponding residues. In this paper, the tracking all the mode poles by using consecutive perturbation on the PML´s complex thickness is established. With this method, all the mode poles in a layered medium parallel plate waveguide with a PML can be accurately located, and the corresponding residues can also be accurately calculated without any contour integral. Some numerical examples are provided in the paper to demonstrate the efficiency and accuracy of the proposed method.