Theory of the third-order nonlinear optical response of exciton-microcavity coupled system

A microscopic semi-classical theory for the self-consistent calculation of the nonlinear response field is applied to the exciton-microcavity coupled systems. Our results show that the respective spectral features of the degenerated four wave mixing (DFWM) signal in both the weak (Omega less than or equal to Gamma) and the strong coupling (Omega >> Gamma) regimes, where Omega is the Rabi splitting and Gamma is the width of the modes, can be clearly described with a single framework. In the weak coupling regime, the nonlinear signal is strongest at the bare excitonic resonance, and its enhancement due to cavity effect is remarkable. In the strong coupling regime, our framework very well reproduces the polarization dependent DFWM spectra in a recent experiment.