Group-theoretical classification of eigenmodes in three-dimensional photonic lattices

General relations concerned with the irreducible representations of the radiation field in arbitrary three-dimensional photonic lattices are derived. Based on this relation, an efficient method for the mode assignment that excludes unphysical quasilongitudinal eigenmodes is presented. This method is applied to a simple cubic lattice with ${\mathrm{O}}_{\mathrm{h}}$ symmetry as an example, and its uncoupled modes that cannot be excited by an incident plane wave are identified.