  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.
