Nonlinear dynamics of nonequilibrium exciton-polaritons in a periodic potential

An exciton-polariton condensate formed in a semiconductor microcavity coupled to an exciton reservoir in the strong coupling regime is studied. The condensate is trapped in onedimensional periodic potential, and we work in the centre of Brillouin zone. We develop a model for coupled three spatial harmonics of mean field. Using the simplified model we get important analytical relations for polaritonic eigenstates and band-structure. The analytical results are supported by numerical analysis. The strong influence of external potential and nonlinearity is discussed and the feedback induced by the inhomogeneity of the incoherent reservoir on the dynamics of coherent polaritons.