Electromagnetic Eigenvalue Problem for Twin Dielectric Rods Covered with Graphene: Symmetry Classes of the H-Polarized Supermodes

The electromagnetic eigenvalue problem for two identical circular dielectric nanowires with graphene covers is investigated. In particular, we consider the splitting of the optically coupled nanowire modes to independent symmetry classes. In our analysis, we use the Kubo formalism for the graphene conductivity, the resistive boundary conditions, the separation of variables in the local coordinates, and the addition theorems for the cylindrical functions. As a result, we derive eigenvalue equations for four different classes of symmetry for the natural modes of twin dielectric nanowires covered with graphene. Our analysis can be used in the modelling of the laser modes of such structures, since graphene is known as a possible material for plasmonic resonance elements of nanolasers.