Stable Second-Order Explicit Runge-Kutta Finite Difference Time Domain Formulations for Modeling Graphene Nano-Material Structures

Abstract

In this paper, stable second-order Runge-Kutta finite difference time domain (RK-FDTD) formulations are introduced for modeling graphene nano-material structures. In this respect, a differencing scheme in which the electric field and the associated current density are collocated in time and space is used for incorporating graphene’s dispersion into the FDTD algorithm. The stability of the formulations is studied by using the root-locus method, and it is shown that the given formulations maintain the conventional Courant-Friedrichs-Lewy (CFL) time-step stability limit. The stability and the accuracy of the formulations are validated through a numerical test that investigates the tunneling phenomena of electromagnetic wave propagation through an infinite free-standing graphene layer. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.