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.

中文翻译：

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BCC-Grid 与 SC-Grid 在 ADE-FDTD 背景下作为表面边界条件的石墨烯片建模

摘要 在这里，我们通过两种不同模板中的表面边界条件对位于金属表面上方的薄层石墨烯进行建模，即简单立方网格 (SC-Grid) 和体心立方网格 (BCC-Grid)。除了带内贡献之外，我们还通过考虑石墨烯电导率的带间贡献来扩展文献中描述的方法。解释了所呈现的发展的数学描述。除此之外，与石墨烯片接触的金属被认为是分散介质；因此，我们通过使用辅助微分方程有限差分时域（ADE-FDTD）方法来处理该问题。在这种情况下，我们比较了两个模板，并证明 BCC-Grid 在位于石墨烯表面的电场和磁场的正常分量中不存在不连续性；在这方面，BCC-Grid 也比传统的 Yee 单元更适合这些类型的应用。