Runge-Kutta Exponential Time Differencing Scheme for Incorporating Graphene Dispersion in the FDTD Simulations

Abstract

In this paper, the Runge-Kutta exponential time differencing (RK-ETD) scheme is used for incorporating Graphene dispersion in the finite difference time domain (FDTD) simulations. The Graphene dispersion is described in the gigahertz and terahertz frequency regimes by Drude model, and the stability of the implementation is studied by means of the von Neumann method combined with the Routh-Hurwitz criterion. It is shown that the presented implementation retains the standard nondispersive FDTD time step stability constraint. In addition, the RK-ETD scheme is used for the FDTD implementation of the complex-frequency shifted perfectly matched layer (CFS-PML) to truncated open region simulation domains. A numerical example is included to validate both the stability and accuracy of the given implementation.

A Unified View of DI- and ETD-FDTD Methods for Drude Media

“…in by a firstdegree polynomial, the TRETD integrator is obtained as (18) This scheme has been used for modeling plasma and graphene in [5] and [20], respectively.…”

“…It is worth noting that replacing the exponential function by the Padé approximant (20) any of the above ETD integrators leads to its DI counterpart. Hence, DI and ETD schemes are equivalent for…”