Extension of the contour‐path effective‐permittivity finite‐difference time‐domain method to three‐dimensional problems for the analysis of arbitrarily shaped dielectric media

Abstract

AbstractThe conventional finite‐difference time‐domain (FDTD) method has been formulated in the Cartesian coordinate system. In this case, the staircase approximation should be used even for the analysis of arbitrarily shaped dielectric media. As a result, small meshes are required to accurately model these media. In this letter, we extend the contour‐path effective‐permittivity (CP‐EP) technique to three‐dimensional (3D) problems in which a reasonably accurate solution can be obtained with larger meshes for arbitrarily shaped dielectric media. The formulation is performed with the position of the dielectric medium being considered in each cell, leading to its effective permittivity. We compare the result from the present method with the Mie solution and that from the conventional staircase FDTD method to confirm the effectiveness of the 3D CP‐EP technique. The relative error of the scattering cross‐section is reduced to about half that of the staircase FDTD method.