  We have developed a theory of exciton-polariton band structure of resonant
three-dimensional photonic crystals for arbitrary dielectric contrast and
effective mass of the exciton that is excited in one of the compositional
materials. The calculation has been carried out for a periodic array of spheres
embedded in a dielectric matrix. It has been shown that the position of the
lower branches of the polariton dispersion curve monotonously depends on the
exciton effective mass and is determined by the coupling of light with the
first few states of the mechanical exciton quantum confined inside each sphere.
Particularly, we have studied the role of excitonic effects on the
photonic-crystal band gap along the [001] direction of the Brillouin zone and
presented an analytic description of the polariton dispersion in terms of the
two-wave approximation.
