Efficient and stable generalized auxiliary differential equation FDTD implementation of graphene dispersion

Abstract

Purpose

The purpose of this paper is to present efficient and stable generalized auxiliary differential equation finite difference time domain (G-ADE-FDTD) implementation of graphene dispersion.

Design/methodology/approach

A generalized dispersive model is used for describing the graphene’s intraband and interband conductivities in the terahertz and infrared frequencies. In addition, the von Neumann method combined with the Routh-Hurwitz criterion are used for studying the stability of the given implementation.

Findings

The presented G-ADE-FDTD implementation allows modeling graphene’s dispersion using the minimal number of additional auxiliary variables, which will reduce both the CPU time and memory storage requirements. In addition, the stability of the implementation retains the standard non-dispersive Courant–Friedrichs–Lewy (CFL) constraint.

Practical implications

The given implementation is conveniently applicable for most commonly used dispersive models, such as Debye, Lorentz, complex-conjugate pole residue, etc.

Originality/value

The presented G-ADE-FDTD implementation not only unifies the implementation of both graphene’s intraband and interband conductivities, with the minimal computational requirements but also retains the standard non-dispersive CFL time step stability constraint.

Citation

Ramadan, O. (2019), "Efficient and stable generalized auxiliary differential equation FDTD implementation of graphene dispersion", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 38 No. 6, pp. 2070-2083. https://doi.org/10.1108/COMPEL-03-2019-0115