Resonant three-dimensional photonic crystals

The theory of the exciton-polariton band structure of a resonant three-dimensional photonic crystal is developed for an arbitrary dielectric contrast and an arbitrary effective mass of an exciton excited in a composite material. The calculation is performed for a periodic array of semiconductor balls embedded in a dielectric matrix. The position of the lower polariton dispersion branches is shown to depend monotonically on the exciton effective mass and to be governed by the interaction of light with the first several states of a mechanical exciton quantum-confined within each ball. The effect of excitonic states on the band gap of a photonic crystal in the [001] direction is considered analytically in terms of a two-wave approximation.