High-Order Spectral Simulation of Graphene Ribbons (Communications in Computational Physics, 2019)
The plasmonics of graphene and other two-dimensional materials has attracted enormous amounts of attention in the scientific literature over the past decade.Both the possibility of exciting plasmons in the terahertz to midinfrared regime, andthe active tunability of graphene via electrical gating or chemical doping has generateda great deal of excitement among engineers seeking sensing devices which operate inthis regime. Consequently, there is significant demand for robust and highly accuratecomputational capabilities which can incorporate such materials. Standard volumetricapproaches can answer this demand, but require vast computational resources in exchange. Here we describe an algorithm which addresses this issue in two ways, first,we model the graphene layer with a surface current which is applicable to a wide classof two-dimensional materials. In addition, we reformulate the governing volumetricequations in terms of surface quantities using Dirichlet-Neumann Operators. Thesesurface equations can be numerically simulated in an efficient, stable, and accuratefashion using a novel High-Order Perturbation of Envelopes methodology. We utilize an implementation of this algorithm to study absorbance spectra of TM polarizedplane-waves scattered by a periodic grid of graphene ribbons.
Keywords: Layered media; two-dimensional materials; graphene; electromagnetic scattering; high-order spectral methods; high-order perturbation of envelopes methods.