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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 ₀ are periodically arranged in a background dielectric ₁. The scalar-wave calculation predicts gaps in the spectrum for ₀/₁ or ₁/₀3 or so. The nature and symmetry of the wave functions is also discussed.
Satpathy et al. (Mon,) studied this question.