High-Order Spectral Simulation of Dispersive Two-Dimensional Materials (Communications in Computational Physics, 2025)
Over the past twenty years, the field of plasmonics has been revolutionizedwith 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. Herewe describe an algorithm which addresses this issue for nonlocal models of the electromagnetic response of graphene. Our methodology not only approximates the graphenelayer with a surface current, but also reformulates the governing volumetric equationsin terms of surface quantities using Dirichlet-Neumann Operators. We have recentlyshown how these surface equations can be numerically simulated in an efficient, stable,and accurate fashion using a High-Order Perturbation of Envelopes methodology. Weextend these results to the nonlocal model mentioned above, and using an implementation of this algorithm, we study absorbance spectra of TM polarized plane-wavesscattered by a periodic grid of graphene ribbons.
Keywords: Two–dimensional materials; graphene; non–local current models; electromagnetic scattering; high–order spectral methods