Energy band of photons and low-energy photon diffraction

For a model system composed of identical dielectric spheres ordered in a three-dimensional lattice, the secular equation of the energy band of photons is derived and the diffraction of uv or visible light is formulated. The model simulates void lattices in irradiated metals or ordered lattices in polystyrene latexes, in which the large lattice constants and hence the low frequency of the diffracted electromagnetic waves give rise to a Bragg reflection orders of magnitude stronger than that involved in the x-ray diffraction. The present formulation is an extension of the theory of Mie and Debye. Also, it is an extension of the Korringa-Kohn-Rostoker formalism for energy-band calculations to Maxwell's equations or to the vector Helmholtz equation. Although the present paper is restricted to developing a formulation, some characteristic aspects anticipated in low-energy photon diffraction are discussed in relation to low-energy electron diffraction.