The dispersion properties of exciton polaritons in multiple-quantum-well based resonant photonic crystals are studied. In the case of structures with an elementary cell possessing a mirror symmetry with respect to its center, a powerful analytical method for deriving and analyzing dispersion laws of the respective normal modes is developed. The method is used to analyze band structure and dispersion properties of several types of resonant photonic crystals, which would not submit to analytical treatment by other approaches. These systems include multiple quantum well structures with an arbitrary periodic modulation of the dielectric function and structures with a complex elementary cell. Special attention was paid to determining conditions for superradiance (Bragg resonance) in these structures, and to the properties of the polariton stop band in the case when this condition is fulfilled (Bragg structures). The dependence of the band structure on the angle of propagation, the polarization of the wave, and the effects due to exciton homogeneous and inhomogeneous broadenings are considered, as well as dispersion properties of excitations in near-Bragg structures.
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