Relationship between group velocity and symmetry of photonic crystals

Group velocity (GV) of eigenmode is a crucial parameter to explain the extraordinary phenomena about light propagation in photonic crystals (PhCs). To study relationships between group velocity and symmetry of PhCs, a new general expression of GV in PhCs made up of non-dispersive material is introduced. Based on this, the GVs of eigenmodes of PhCs, especially those of degenerate eigenmodes at highly symmetric points in the first Brillouin zone, are discussed. Some interesting results are obtained. For example, the summation of degenerate eigenmodes' GVs is invariant under the operations of wave vector K-group M_K. In addition, some numerical results are presented to verify them.