Determination of the signal polarization state in four-wave mixing experiments on semiconductors

Based on symmetry considerations, we develop a simple model for the determination of the polarization state of the four-wave mixing (FWM) response on semiconductors depending on the polarization of incoming photons. The model describes interactions within the system of polaritons taking into account their composite character and thus the correct symmetry. We separate the FWM response into three main contributions which may differ in symmetry. They are: polariton-polariton scattering, bipolariton-mediated scattering and scattering due to phase space filling. We then derive algebraic equations for each of the channels for calculation of the respective FWM response polarizations. Compared to microscopic theories, solution of these equations is much faster and therefore the theory becomes very useful if one wants to determine the polarization state of the response in a particular experiment. Thanks to the correct description of symmetries of various types of interactions, our model is more accurate in predictions than the optical Bloch equations.