Over the past twenty years, the field of plasmonics has been revolutionized with the isolation and utilization of two--dimensional materials, particularly graphene. Consequently there is significant interest in rapid, robust, and highly accurate computational schemes which can incorporate such materials. Standard volumetric approaches can be contemplated, but these require huge computational resources. Here we describe an algorithm which addresses this issue for nonlocal models of the electromagnetic response of graphene. Our methodology not only approximates the graphene layer with a surface current, but also reformulates the governing volumetric equations in terms of surface quantities using Dirichlet--Neumann Operators. We have recently shown how these surface equations can be numerically simulated in an efficient, stable, and accurate fashion using a High--Order Perturbation of Envelopes methodology. We extend these results to the nonlocal model mentioned above, and using an implementation of this algorithm, we study absorbance spectra of TM polarized plane--waves scattered by a periodic grid of graphene ribbons.

翻译：过去二十年间，随着二维材料（尤其是石墨烯）的分离与应用，等离激元学领域发生了革命性变化。因此，亟需开发能够整合此类材料的快速、稳健且高精度的计算方案。虽然可以考虑采用标准体方法，但这些方法需要巨大的计算资源。本文针对石墨烯电磁响应的非局域模型，提出一种解决该问题的算法。我们的方法不仅用表面电流近似石墨烯层，还利用Dirichlet-Neumann算子将控制体方程重新表述为表面量形式。我们近期已证明，通过高阶包络扰动方法，可以高效、稳定且精确地对这些表面方程进行数值模拟。本文将上述成果推广至前述非局域模型，并基于该算法的实现，研究了TM偏振平面波被石墨烯条带周期阵列散射后的吸收光谱。