Revisiting the stability of the HIE-FDTD technique for modeling graphene dispersion

Abstract

Recently, the stability of the dispersive hybrid implicit–explicit finite difference time domain (HIE-FDTD) scheme has been studied for the time domain simulations of infinite-thin graphene structures. It has been shown that the time step stability limit is a function of the graphene parameters and more restrictive than the classical HIE-FDTD constraint. In this communication, the stability of this numerical scheme is revisited, and based on the Routh–Hurwitz criterion, alternative time step stability condition is derived. To retain the classical HIE-FDTD stability constraint, stability improved implementation of the graphene dispersion is introduced. These findings are validated by using the root-locus method from the discrete-control theory. In addition, the stability is verified numerically and the accuracy of the presented implementation is demonstrated by studying the transmission coefficient of a thin two-dimensional (2D) graphene sheet placed in a 3D domain and excellent agreement with the analytical result is observed.