Accurate location of all the mode poles of the Green's functions for a parallel plate waveguide with a PML

Abstract

The theoretical basis of the PML technique for calculating the Green's functions for a microstrip structure is that after adding a PML with a PEC upward boundary above the microstrip structure, the spatial Green's function on the original medium-air interface will not be changed. The implementation of this method strongly relies on precisely locating all the mode poles of the spectral Green's function (i.e., surface mode poles, evanescent mode poles and Berenger mode poles). In this paper, the imaginary part of the PML's complex thickness is first selected to be zero, and then all the mode poles of the spectral domain Green's function for this ordinary parallel plate waveguide are found. After this, the imaginary part of the PML's complex thickness is successively increased, and at every step, the Newton-Raphson iteration method is employed to find the current mode poles. This process continues until the imaginary part of the PML's complex thickness reaches the predetermined value. The proposed method can, without frequency limitations, accurately locate all the mode poles of the spectral domain Green's function for a parallel plate waveguide with a PML. Provided numerical examples in this paper demonstrate the efficiency and accuracy of the proposed method.