Existence of a photonic gap in periodic dielectric structures

Using a plane-wave expansion method, we have solved Maxwell's equations for the propagation of electromagnetic waves in a periodic lattice of dielectric spheres (dielectric constant ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{a}}$) in a uniform dielectric background (${\mathrm{\ensuremath{\epsilon}}}_{\mathit{b}}$). Contrary to experiment, we find that fcc dielectric structures do not have a ``photonic band gap'' that extends throughout the Brillouin zone. However, we have determined that dielectric spheres arranged in the diamond structure do possess a full photonic band gap. This gap exists for refractive-index contrasts as low as 2.