Graphene has transformed the fields of plasmonics and photonics, and become an indispensable component for devices operating in the terahertz to mid-infrared range. Here, for instance, graphene surface plasmons can be excited, and their extreme interfacial confinement makes them vastly effective for sensing and detection. The rapid, robust, and accurate numerical simulation of optical devices featuring graphene is of paramount importance and many groups appeal to Black-Box Finite Element solvers. While accurate, these are quite computationally expensive for problems with simplifying geometrical features such as multiple homogeneous layers, which can be recast in terms of interfacial (rather than volumetric) unknowns. In either case, an important modeling consideration is whether to treat the graphene as a material of small (but non-zero) thickness with an effective permittivity, or as a vanishingly thin sheet of current with an effective conductivity. In this contribution we ponder the correct relationship between the effective conductivity and permittivity of graphene, and propose a new relation which is based upon a concrete mathematical calculation that appears to be missing in the literature. We then test our new model both in the case in which the interface deformation is non-trivial, and when there are two layers of graphene with non-flat interfacial deformation.

中文翻译：

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关于模拟石墨烯的有效介电常数和电导率的一致选择

石墨烯已经改变了等离子体和光子学领域，并成为在太赫兹到中红外范围内运行的设备不可或缺的组件。例如，在这里，石墨烯表面等离子体可以被激发，它们极端的界面限制使它们对于传感和检测非常有效。以石墨烯为特征的光学设备的快速、稳健和准确的数值模拟至关重要，许多团体都对黑盒有限元求解器提出了要求。虽然准确，但对于简化几何特征（例如多个同质层）的问题而言，这些计算成本非常高，可以根据界面（而不是体积）未知数进行重铸。在任一情况下，一个重要的建模考虑是将石墨烯视为具有有效介电常数的小（但非零）厚度材料，还是将其视为具有有效电导率的极薄电流片。在这篇文章中，我们思考了石墨烯的有效电导率和介电常数之间的正确关系，并提出了一种新的关系，该关系基于文献中似乎缺少的具体数学计算。然后，我们在界面变形非平凡的情况下以及当有两层石墨烯具有非平坦界面变形的情况下测试我们的新模型。在这篇文章中，我们思考了石墨烯的有效电导率和介电常数之间的正确关系，并提出了一种新的关系，该关系基于文献中似乎缺少的具体数学计算。然后，我们在界面变形非平凡的情况下以及当有两层石墨烯具有非平坦界面变形的情况下测试我们的新模型。在这篇文章中，我们思考了石墨烯的有效电导率和介电常数之间的正确关系，并提出了一种新的关系，该关系基于文献中似乎缺少的具体数学计算。然后，我们在界面变形非平凡的情况下以及当有两层石墨烯具有非平坦界面变形的情况下测试我们的新模型。