Symmetries of the eigenstates in an anisotropic photonic crystal

Abstract

We present a group theory analysis of the symmetries of the eigenmodes and eigenvalues of photonic crystals with either materially or geometrically anisotropic motif. Irreducible Brillouin zone of such a photonic crystal varies with the parameters of the anisotropic motif. By using coset decomposition of a group, we have identified the irreducible Brillouin zones of such photonic crystals. We have shown the existence of a fundamental zone in the orientations of a motif for which the eigenvalues are found to be unique, and such a zone is fully described by a set of symmetry elements, which form a new group. In addition, by using a two-dimensional photonic crystal with hexagonal lattice as an example, we present a full description of the eigenmode symmetry in the photonic crystal with an anisotropic motif. A classification of degenerate states, which is in the absence of a spatial modulation and in the absence of an anisotropy, is shown by using a properly derived integer system, and the eigenstate splitting (and evolution) in the presence of the anisotropy and the spatial modulation are described in detail.