THz array of graphene disks: Classification of surface plasmon modes and their excitation

Abstract

We suggest a classification scheme for the eigenmodes in an array of graphene disks. The classification is based, first, on the division of the possible solutions in TE and TM modes and, second, on the irreducible representations (IRREPs) of the symmetry group of the unit cell. The last criterion classifies the possible modes in terms of the angular φ dependence of their corresponding currents. In the presented example of symmetry C4v of the square unit cell with the graphene disk, we show that the symmetry of the dipole mode is defined by two orthogonal subspaces of the 2D IRREP E. Two quadrupole modes described by IRREPs B1 and B2 are quasi-orthogonal and have different resonant frequencies. The angular resonances of the modes E, B1, and B2 are defined by the superposition of clockwise and anti-clockwise edge-guided surface plasmon-polariton waves. However, the modes described by IRREPs A1 and A2 can be considered the superposition of modes propagating along the radius. The radial TM mode A1 differs from the radial TE mode A2 by orientation of the graphene current with respect to the wavevector. We discuss the necessary symmetry and physical conditions for the excitation of the hybridized quasi-dark modes by plane waves with normal incidence. The theoretical results are illustrated by many numerical examples.