Spectral Properties of Thin-Film Photonic Crystals

We study spectral properties of three-dimensional photonic crystals formed by a periodic array of air cubes separated by a thin film of optically dense dielectric material. The thickness δ of the dielectric component is assumed to be small, whereas its permittivity ε is large. The spectrum of the photonic crystal is studied as δ → 0 while εδ = η-1 is kept constant. Under the additional condition of a vanishing normal component of the magnetic field on the surface of the optically dense dielectric film, we carry out a thorough analytical and numerical analysis of the spectrum of the photonic crystal. In particular, for small η we obtain the linear and quadratic approximations of the spectral bands and, given δ, we estimate the minimum value of ε for which at least one spectral gap opens up.