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

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.