Polaritons in a nonideal periodic array of microcavities

The virtual crystal approximation is employed to numerically model the propagation of localized electromagnetic excitations through a two-dimensional array of coupled microcavities containing atomic clusters (quantum dots). The constructed model allows for the presence of defects (absence of cavities and/or quantum dots) at certain sites of the supercrystal. We derive the dispersion relations for polaritonic modes as functions of defect concentrations. This permits to evaluate the densities of states of polaritons and their effective masses as well as the band gaps for any prescribed values of defect concentrations.