NUMERICAL SIMULATION OF GRATING STRUCTURES INCORPORATING TWO-DIMENSIONAL MATERIALS: A HIGH-ORDER PERTURBATION OF SURFACES FRAMEWORK

The plasmonics of two-dimensional materials, such as graphene, has become an important field of study for devices operating in the terahertz to midinfrared regime where such phenomena are supported. The semimetallic character of these materials permits electrostatic biasing which allows one to tune their electrical properties, unlike the noble metals (e.g., gold, silver) which also support plasmons. In the literature there are two principal approaches to modeling two-dimensional materials: With a thin layer of finite thickness featuring an effective permittivity, or with a surface current. We follow this latter approach to not only derive governing equations which are valid in the case of curved interfaces, but also reformulate these volumetric equations in terms of surface quantities using Dirichlet--Neumann operators. Such operators have been used extensively in the numerical simulation of electromagnetics problems, and we use them to restate the governing equations at layer interfaces. Beyond this, we show that these surface equations can be numerically simulated in an efficient, stable, and accurate fashion using a High-Order Perturbation of Surfaces methodology. We present detailed numerical results which not only validate our simulation using the Method of Manufactured Solutions and by comparison to results in the literature, but also describe Surface Plasmon Resonances at the “wavy” (corrugated) interface of a dielectric-graphene-dielectric structure.