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 ${\mathrm{\epsilon }}_{\mathit{a}}$ are periodically arranged in a background dielectric ${\mathrm{\epsilon }}_{\mathit{b}}$. The scalar-wave calculation predicts gaps in the spectrum for ${\mathrm{\epsilon }}_{\mathit{a}}$/${\mathrm{\epsilon }}_{\mathit{b}}$ or ${\mathrm{\epsilon }}_{\mathit{b}}$/${\mathrm{\epsilon }}_{\mathit{a}}$≳3 or so. The nature and symmetry of the wave functions is also discussed.