On analyticity of scattered fields in layered structures with interfacial graphene

Abstract

Two‐dimensional materials such as graphene have become crucial components of most state‐of‐the‐art plasmonic devices. The possibility of not only generating plasmons in the terahertz regime, but also tuning them in real time via chemical doping or electrical gating make them compelling materials for engineers seeking to build accurate sensors. Thus, the faithful modeling of the propagation of linear waves in a layered, periodic structure with such materials at the interfaces is of paramount importance in many branches of the applied sciences. In this paper, we present a novel formulation of the problem featuring surface currents to model the two‐dimensional materials which not only is free of the artificial singularities present in related approaches, but also can be used to deliver a proof of existence, uniqueness, and analytic dependence of solutions. We advocate for a surface integral formulation which is phrased in terms of well‐chosen Impedance–Impedance Operators that are immune to the Dirichlet eigenvalues which plague the Dirichlet–Neumann Operators that appear in classical formulations. With a High‐Order Perturbation of Surfaces approach we are able to give a straightforward demonstration of this new well‐posedness result which only requires the verification that a finite collection of explicitly stated transcendental expressions be nonzero. We further illustrate the utility of this formulation by displaying results of a High‐Order Spectral numerical implementation which is flexible, rapid, and robust.