  A general theory of polariton parametric photoluminescence in spatially
inhomogeneous systems is developed. The quantum Langevin equations are solved
in a generalized Bogoliubov de Gennes approximation. We apply the formalism to
the specific case of a disordered microcavity. In this case, we numerically
solve the equations for the coherent emission and the photoluminescence. We
describe the effect of the exciton and photon disorder on the photoluminescence
pattern exhibited in momentum space, finding a good agreement with the
experimental observations.
