Unconditionally Stable Bilinear Transformation FDTD Algorithm for Modeling Double-Negative Meta-material Electromagnetic Problems

Abstract

Accurate and unconditionally stable finite difference time domain (FDTD) algorithm is presented for modeling electromagnetic wave propagation in double-negative (DNG) meta-material domains. The proposed algorithm is based on incorporating the Bilinear transformation technique into the FDTD implementations of Maxwell's equations. The stability of the proposed approach is studied by combining the von Neumann method with the Routh-Huwitz criterion and it has been observed that the proposed algorithm is free from the Courant-Friedrichs-Lewy (CFL) stability limit of the conventional FDTD scheme. Furthermore, the proposed algorithm is incorporated with the split-step FDTD scheme to model two-dimensional problems. Numerical examples carried out in one and two dimensional domains are included to show the validity of the proposed algorithm.