Microcavity polaritons in disordered exciton lattices

We investigate the interaction of excitons in a two dimensional lattice and photons in a planar cavity in the presence of disorder. The strong exciton-photon coupling is described in terms of polariton quasi-particles, which are scattered by a disorder potential. We consider three kinds of disorder: (a) inhomogeneous exciton energy, (b) inhomogeneous exciton-photon coupling and (c) deviations from an ideal lattice. These three types of disorder are characteristic of different physical systems, and their separate analysis gives insight on the competition between randomness and light-matter coupling. We consider conventional planar polariton structures (with excitons resonant to photon modes emitting normal to the cavity) and Bragg polariton structures, in which excitons in a lattice are resonant with photon modes at a finite angle satisfying the Bragg condition. We calculate the absorption spectra in the normal direction and at the Bragg angle by a direct diagonalization of the exciton-photon Hamiltonian. We found that in some cases weak disorder increases the light-matter coupling and leads to a larger polariton splitting. Moreover, we found that the coupling of excitons and photons is less sensitive to disorder of type (b) and (c). This suggests that polaritonic structures realized with impurities in a semiconductor or with atoms in optical lattices are good candidate for the observation of some of the Bragg polariton features.