GBC and Helmholtz-Galerkin Technique for the Analysis of Plane Wave Scattering from Graphene Covered Thin Dielectric Disk

The aim of this paper is the analysis of the plane wave scattering from a graphene covered thin dielectric disk. The formulation of the 3D problem at hand is deeply simplified by means of suitable generalized boundary conditions, involving the dielectric parameters and the graphene surface conductivity determined from the Kubo formalism, and using the Fourier series expansion. In this way, two sets of one-dimensional integral equations for the harmonics of the effective electric and magnetic currents are obtained. According to the Helmholtz decomposition, the currents are replaced by the corresponding surface curl-free and divergence-free contributions. A judicious choice of the sets of the expansion functions of these contributions in a Galerkin scheme leads to the Fredholm second-kind matrix equations for which the fast convergence is guaranteed.