Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations

We examine the propagation of electromagnetic waves in periodic dielectric structures by solving the vector Maxwell equations with the plane-wave method. Contrary to experimental reports, as well as results of scalar-wave calculations, we do not find a true gap extending throughout the Brillouin zone in the fcc structure. However, there is a depletion in the photon density of states, seemingly a remnant of the Mie resonance, giving rise to a pseudogap in the spectrum that is quite strong for dielectric-sphere packing fraction β∼0.3–0.4. An effect analogous to the Borrmann effect in x-ray diffraction is predicted, where certain photon modes will propagate an anomalously long distance before getting absorbed.