An FDTD Method for Fully Anisotropic Periodic Structures Impinged by Obliquely Incident Plane Waves

A finite-difference time-domain (FDTD) method is developed to analyze electromagnetic scattering from 3-D fully anisotropic periodic structures impinged by obliquely incident plane waves. Starting from Maxwell's curl equations, we employ material transformation matrices to link the update of the electric and magnetic fields in the FDTD method. The problem under consideration is Bloch-Floquet periodic in the horizontal directions but finite in the vertical direction. At the FDTD truncation boundaries in the horizontal directions, the Bloch-Floquet periodic boundary conditions (BPBCs) are applied, while the perfectly matched layer (PML) absorbing boundary condition is implemented for the vertical direction. We design three different anisotropic models in 3-D simulations to validate our method with a commercial software package COMSOL. These examples show the accuracy and efficiency of the FDTD method for analyzing the propagation characteristics, including reflectance, transmittance, absorptance, and complex reflection and transmission coefficients for the fully anisotropic periodic structures.