The propagation characteristics of the leaky TE mode in a two-dimensional photonic crystal waveguide is analyzed using the Fourier series expansion method combined with the Chew's perfectly matched layer (PML). The complex propagation constant and mode field profiles are numerically tested in detail. It is shown that the leakage phenomena can be well modeled by choosing the PML parameters in proper range.

In this paper, we developed the analytical method for the radiation field from a line current source placed in a stratified slab waveguide. This method is applicable to the analysis of excitation problem of inhomogeneous slab waveguide by increasing the number of layers. The numerical results are given for the cases of five layers, such as W and M type waveguides, and the inhomogeneous slab waveguide. The influence of guided and leaky modes on the radiation field are studied.