Polarization of light emitted by a semiconductor microcavity in the regime of a resonant parametric scattering of the exciton polaritons shows extremely strong and unusual dependence on the polarization of pumping light. This dependence is interpreted here using the pseudospin model and in the framework of a quasiclassical formalism where the parametric scattering is described as resonant four-wave mixing. We show that the optically induced splitting of the exciton-polariton eigenstate, both in linear and circular polarizations, is responsible for the observed polarization effects. The splitting in circular polarizations, achieving 0.5 meV, has been detected experimentally, while the splitting in linear polarizations, which is much weaker, only manifests itself in the pseudospin dynamics of the exciton polaritons
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