Theory of polariton parametric interactions in semiconductor microcavities

We review some fascinating aspects of the nonlinear optical properties of semiconductor microcavities in the strong exciton-photon coupling regime. Our theoretical discussion is mainly focused on the angle-resolved experiments with resonant optical excitation. Within a model of interacting bosons, we describe the stimulated parametric amplification, luminescence as well as the existence of peculiar collective excitations due to the anomalous coupling between polaritons.