BCC-Grid versus SC-Grid in the modeling of a sheet of graphene as a surface boundary condition in the context of ADE-FDTD

Abstract

Here, we model a thin layer of graphene located above a metal surface by means of a surface boundary condition in two different stencils, namely, a simple cubic grid (SC-Grid) and a body centered cubic grid (BCC-Grid). We extend the methodology described in the literature by taking into account the interband contribution of the graphene’s conductivity in addition to the intraband contribution. The mathematical description of the presented developments is explained. Besides this, the metal in contact with the graphene sheet is considered as a dispersive medium; therefore, we deal with the problem by using the auxiliary differential equation finite-difference time-domain (ADE-FDTD) method. In this context, we compared the two stencils and demonstrated that BCC-Grid does not present discontinuities in the normal components of the electric and magnetic fields located on the graphene surface; in this respect, BCC-Grid is also more appropriate than the traditional Yee’s cell for these type of applications.