LAUSR

Abstract The plasmonics of two–dimensional materials, such as graphene, has become an important field over the past decade. The active tunability of graphene via electrical gating or chemical doping has generated a great deal of excitement among engineers seeking sensing devices. Consequently there is significant demand for robust and highly accurate computational capabilities which can simulate such materials. The class of High–Order Perturbation of Surfaces methods have proven to be particularly appropriate for this purpose. In this contribution we describe our recent efforts to utilize both Dirichlet–Neumann Operators and Impedance–Impedance Operators in these schemes. In addition, we present detailed numerical results which not only validate our simulations using the Method of Manufactured Solutions, but we also describe Localized Surface Plasmon Resonances in graphene nanotubes enclosing rod–shaped dielectric materials.