Hybridization, degeneracy and polarization independence of modes in square array of graphene disk resonators with symmetry C4v

Hybridization of plasmonic eigenmodes belonging to different IRREPs of the point group of symmetry C4v is discussed. It is shown that the hybridization of the pair of 1D IRREPs modes A1 and B2 as well as the pair A2 and B1 can exist in this symmetry.

For the cell period p0 and the quadrumer period P, the relation P/p0 = 2 defines polarization independence of these pairs of modes. The discussed modes are dark ones and require for their excitation breaking the point symmetry of the quadrumer and, for breaking their degeneracy, i.e. separation in the two pairs, a modification of the discrete translation symmetry, i.e. change the parameter P/p0. The separated modes can be excited by normally incident plane wave with orthogonal polarizations.