Three-dimensional dispersive hybrid implicit-explicit finite-difference time-domain method for simulations of graphene

A dispersive hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method is presented in this paper. Surface conductivity of the graphene is incorporated into the HIE-FDTD method directly through an auxiliary difference equation. The time step size in proposed method has no relation with the fine spatial discretization, so it is very useful for the simulation of the graphene when it needs to be discretized across its thickness. The stability condition of this method is not only determined by the spatial cell sizes Δx and Δz, but also related with the surface conductivity of the graphene. The computational accuracy and efficiency of this method are demonstrated through numerical examples. The results show that with reasonable accuracy, the memory requirement and computation time of the dispersive HIE-FDTD method are both considerably reduced as compared with those of the conventional FDTD method and LOD-FDTD method.