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.