Photoinduced Kerr rotation by more than $pi /2$ radians is demonstrated in planar quantum well microcavity in the strong coupling regime. This result is close to the predicted theoretical maximum of $pi $. It is achieved by engineering microcavity parameters such that the optical impedance matching condition is reached at the smallest negative detuning between exciton resonance and the cavity mode. This ensures the optimum combination of the exciton induced optical non-linearity and the enhancement of the Kerr angle by the cavity. Comprehensive analysis of the polarization state of the light in this regime shows that both renormalization of the exciton energy and the saturation of the excitonic resonance contribute to the observed optical nonlinearities.
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