High-Order FDTD With Exponential Time Differencing Algorithm for Modeling Wave Propagation in Debye Dispersive Materials

Abstract

Abstract-A high-order (HO) finite-difference time-domain (FDTD) method with exponential time differencing (ETD) algorithm is proposed to model electromagnetic wave propagation in Debye dispersive material in this paper. The proposed method introduces an auxiliary difference equation (ADE) technique which establishes the relationship between the electric displacement vector and electric field intensity with a differential equation in Debye dispersive media. The ETD algorithm is applied to the displacement vector and auxiliary difference variable in time domain, and the fourth-order centraldifference discretization is used in space domain. One example with plane wave propagation in a Debye dispersive media is calculated. Compared with the conventional ETD-FDTD method, the results from our proposed method show its accuracy and efficiency for Debye dispersive media simulation.

ADE-TLM Algorithm for Modeling Wave Propagation in Biological Tissues with Debye Dispersion

“…The numerical solutions proposed for modeling such dispersive media could be grouped in three main categories: recursive convolution methods based on a recursive computation of a convolution integral between the frequencydependent susceptibility and the electric field [1] [2], the Z-transform method [3] [4], and the auxiliary differential equation method (ADE) [5]. The latter is of particular interest owing to its easier arithmetic implementation [6], first introduced by Kishawa to model Debye media, Lorentz media, and media obeying to the Cole-Cole circular relaxation arc model [7] [8]. It was then extended to cover non linear dispersive media by Goorjian and Taflove [9],and more recently extended to cover 2-D Kerr and Raman nonlinear dispersive media response to an optical pulse [10].…”