Photonic bands using vector spherical waves .3. Group-theoretical treatment

The group-theoretical treatment for photonic bands is given. The symmetry-adapted planewave bases are given for the eigenvectors of the electric fields and the transformation properties of the vector spherical-waves are clarified. For a fcc array of dielectric spheres, the group-theoretical band assignment is presented and the result is used to clarify the origins of the difference from band to band, concerning the mixing between transverse and longitudinal components, the activity to an incident light in the reflectivity, the mutual orthogonality of the eigenvectors and so on. Promising application of photonic crystal as a useful polarizer of light is proposed.