An Unconditionally Stable FDTD Method for Simulating Graphene

An unconditionally stable FDTD method is proposed in this paper to simulate graphene. By transforming the third-order equation of the electric field to the first-order equation and applying the backward-difference discretization to the time-derivation, the time step size can be selected arbitrarily. Both the theoretical analysis and numerical example validate the unconditional stability of this method. The simulation of the infinite graphene sheet also shows that as long as the time step size is chosen satisfied the accuracy requirement, this proposed method can observably speed up the whole simulation with high accuracy, even the time step discretization is orders of magnitude larger than that permitted by the CFL condition.