Photonic band gap enhancement in frequency-dependent dielectrics

We illustrate a general technique for evaluating photonic band structures in periodic d -dimensional microstructures in which the dielectric constant epsilon (omega) exhibits rapid variations with frequency omega . This technique involves the evaluation of generalized electromagnetic dispersion surfaces omega ( k--> ,epsilon) in a (d+1) -dimensional space consisting of the physical d -dimensional space of wave vectors k--> and an additional dimension defined by the continuous, independent, variable epsilon . The physical band structure for the photonic crystal is obtained by evaluating the intersection of the generalized dispersion surfaces with the "cutting surface" defined by the function epsilon (omega) . We apply this method to evaluate the band structure of both two- and three-dimensional (3D) periodic microstructures. We consider metallic photonic crystals with free carriers described by a simple Drude conductivity and verify the occurrence of electromagnetic pass bands below the plasma frequency of the bulk metal. We also evaluate the shift of the photonic band structure caused by free carrier injection into semiconductor-based photonic crystals. We apply our method to two models in which epsilon (omega) describes a resonant radiation-matter interaction. In the first model, we consider the addition of independent, resonant oscillators to a photonic crystal with an otherwise frequency-independent dielectric constant. We demonstrate that for an inhomogeneously broadened distribution of resonators impregnated within an inverse opal structure, the full 3D photonic band gap (PBG) can be considerably enhanced. In the second model, we consider a coupled resonant oscillator mode in a photonic crystal. When this mode is an optical phonon, there can be a synergetic interplay between the polaritonic resonance and the geometrical scattering resonances of the structured dielectric, leading to PBG enhancement. A similar effect may arise when resonant atoms that are coupled radiatively through resonance dipole-dipole interaction are placed in a photonic crystal.