A rigorous and simple method is proposed for analyzing guided modes of metallic electromagnetic crystal waveguides. The method is a combination of generalized reflection and transmission matrices and the mode-matching technique. Fast convergence, low computer cost, and high calculating precision are main advantages of the proposed method. This method can easily avoid the relative convergence phenomena than a classical mode-matching method, and the proposed formulation is very suitable to analyzing multilayered problems with very low computer cost. The existence of H-polarized modes in metallic electromagnetic crystal waveguides has been verified.

A novel inverse scattering approach is developed to the reconstruction of electrical property distributions of a two-dimensional biaxial anisotropic object using time-domain scattering data. The approach is an extension of the forward-backward time-stepping (FBTS) algorithm previously described for an isotropic object. Synthetic examples of inversion are given to assess the effectiveness of the proposed method.

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.

Electromagnetic crystals formed by vertical full posts stacked in a rectangular waveguide are analyzed using the image theory and the lattice sums technique. It is shown that the frequency response of the crystals consisting of circular posts can be obtained by a simpler matrix calculus based on the one-dimensional lattice sums, the T-matrix of a circular cylinder in free space, and the generalized reflection and transmission matrices.