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 delta of the dielectric component is assumed to be small, whereas its permittivity epsilon is large. The spectrum of the photonic crystal is studied as delta --> 0 while epsilon delta = n(-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 lm, we carry out a thorough analytical and numerical analysis of the spectrum of the photonic crystal. In particular, for small n we obtain the linear and quadratic approximations of the spectral bands and, given delta, we estimate the minimum value of epsilon for which at least one spectral gap opens up.