SYMMETRY, DEGENERACY, AND UNCOUPLED MODES IN 2-DIMENSIONAL PHOTONIC LATTICES

The photonic bands of two-dimensional triangular and square lattices c omposed of circular rods were classified by means of the group theory based on the symmetry of the lattice structure. According to this clas sification, it was shown that the uncoupled mode, or the mode that can not be excited by an external plane wave, which we previously found fo r the triangular lattice by the numerical calculation of the transmitt ance, is an antisymmetric mode under the relevant mirror reflection, a nd this fact is consistent with the observation by Robertson et al. It was also shown that triangular and square lattices with C-6v or C-4v symmetry have many other uncoupled modes with relatively low eigenfreq uencies and some of them can be easily identified as the spectral rang es of total reflection in spite of their nonzero state density.