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

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.