Z-Transform-Based FDTD Implementations of Biaxial Anisotropy for Radar Target Scattering Problems

Abstract

In this article, an efficient Z-transform-based finite-difference time-domain (Z-FDTD) is developed to implement and analyze electromagnetic scatterings in the 3D biaxial anisotropy. In terms of the Z-transform technique, we first discuss the conversion relationship between time- or frequency-domain derivative operators and the corresponding Z-domain operator, then build up the Z-transform-based iteration from the electric flux D converted to the electric field E based on dielectric tensor ε (and from the magnetic flux B converted to the magnetic field H in line with permeability tensor μ) by combining the constitutive formulations about the biaxial anisotropy. As a result, the iterative process about the Z-FDTD implementation can be smoothly carried out by means of combining with the Maxwell’s equations. To our knowledge, it is inevitably necessary for the absorbing boundary condition (ABC) to be considered in the electromagnetic scattering; hence, we utilize the unsplit-field complex-frequency-shifted perfectly matched layer (CFS-PML) to truncate the Z-FDTD’s physical region, and then capture time- and frequency-domain radiation with the electric dipole. In the 3D simulations, we select two different biaxial anisotropic models to validate the proposed formulations by using the popular commercial software COMSOL. Moreover, it is certain that those results are effective and available for electromagnetic scattering problems under the oblique incidence executed by the Z-FDTD method.