On the Derivation of the Numerical Permittivity and Stability of the CDS-FDTD Implementation of High-Order Constitutive Relations

Abstract

Recently, the derivation of the numerical permittivity and stability of the finite-difference time-domain (FDTD) implementation of a 4-pole complex rational function by using the central difference scheme (CDS) have been studied. In this communication, the accuracy and the stability limitation of this scheme are investigated. In addition, alternative FDTD implementation based on the Mobius transformation (MT) is presented. It is observed that the CDS implementation is less accurate and more stability restrictive than the MT counterpart.