Hybrid implicit-explicit FDTD implementation of graphene using generalized dispersive model

Abstract

This paper presented a general approach for the hybrid implicit-explicit finite difference time domain (HIE-FDTD) implementation of Graphene. In the presented implementation the Graphene dispersion is described by a generalized dispersive model (GDM) that unifies in a simple form the commonly used dispersion models. In addition, the stability of the implementation is studied by means of the root-locus method from the discrete-control theory. It is shown that by incorporating the material dispersion into the HIE-FDTD algorithm by means of central difference and average operators, approximated over one time step, the standard non-dispersive HIE-FDTD time step stability constraint will be preserved. This finding is confirmed by using the von Neumann method combined with the Routh-Hurwitz criterion. Numerical simulation is included to show the validity of the presented implementation.