Mathematics

Plasmonic structures are made of dielectrics and metals, and at optical frequencies metals exhibit unusual electromagnetic properties like a negative dielectric permittivity whereas dielectrics have a positive one. This change of sign allows the propagation of electromagnetic surface waves at the metal-dielectric interface, where strange phenomena appear if it presents corners. Recently theoretical studies have been carried out, combining results of the T-coercivity approach and the analysis of corner singularities : it has been shown the existence of two states, depending on the problem's parameters. In this presentation we present the theory of T-coercivity and a stable numerical method adapted to each state, with a specific treatment at the corners. In the first state (the solutions are of "classical energy”, H^1) we develop meshing rules adapted to the geometry to guarantee the convergence’s optimality of the approximation with the finite element method. For the second state (the solutions are no longer in H^1), we propose an original numerical method using Perfectly Matched Layers at corners to capture the singularities. These techniques will be applied to a 2D plasmonic scattering problem.