  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.
