The Second-order Condition of FDTD Method at Sloped Dielectric Interfaces by Averaging the Permittivities along Surface Normal

The second-order conditions of the Yee-grid based FDTD method at sloped planar dielectric interfaces are studied. The theoretical analysis is performed for TE waves. It is found that second-order accuracy can be achieved if the averaging process for the effective permittivities is taken along the normal direction to the dielectric interface. The length of average depends on the relative orientation of the interface in the FDTD mesh. The proposed line average scheme is more accurate than the traditional cell average scheme, and is validated for the scattering by a dielectric cylinder. Due to its simplicity, the proposed line average scheme needs much less time in the preprocessing stage of the FDTD calculation to get the proper values of effective permittivities, as compared with the traditional cell average scheme. The proposed line average scheme is also applied to TM waves, and gives at least 3.3 dB better results than other methods.