Finite-difference time-domain methods for anisotropic media with total-field/scattered-field formulation

Abstract

Analysis of electromagnetic (EM) wave phenomena in complex media has attracted considerable interest over recent years, particularly due to applications such as biomedical, environmental remote sensing and photonic bandgap. In such applications, EM wave can interact with arbitrary geometries composed of anisotropic, dispersive and inhomogeneous media. In such cases, the use of analytical methods to obtain EM solutions may not be possible, thus, numerical methods that discretize Maxwell’s equations on a volumetric mesh are often sought. The finite-difference time-domain (FDTD) method is one such numerical method that is conceptually simple yet robust in handling complex media. However, several intrinsic problems persist, such as the time step size limitation as well as accurate incident wave source. In this research, we investigate such issues in FDTD and propose developments specifically for complex media. Here, the complex media refer to materials that are characterized by anisotropic constitutive relations.