Theory of photon bands in three-dimensional periodic dielectric structures

Recent experiments have found the existence of ``photon bands'' in periodic dielectric structures analogous to the electron bands in the solid. Using a plane-waves method, we study in the scalar-wave approximation the nature of the photon bands in structures where spherical ``atoms'' of dielectric constant εₐ are periodically arranged in a background dielectric εb. The scalar-wave calculation predicts gaps in the spectrum for εₐ/εb or εb/εₐ{}3 or so. The nature and symmetry of the wave functions is also discussed.