Theoretical study of the polarization dependence of third-order optical nonlinearities in semiconductor microcavities

We present a microscopic theory of the coherent third order (χ⁽³⁾) optical response of semiconductor quantum well microcavities, specialized to the four-wave-mixing configuration in the spectral vicinity of the lowest exciton frequency. The theory is that of a quantum mechanical many-electron system dipole-coupled to a classical radiation field. The many-electron dynamics is treated within the dynamics-controlled-truncation formalism restricted to the 1s-exciton subspace. Within this limitation, all Coulomb correlation effects are included, resulting in an effective theory of (virtual) exciton-polariton scattering. The theory is evaluated for various polarization configurations each of which depends differently on the underlying many-body effects, such as phase-space filling, Hartree-Fock exchange, and two-exciton correlations (including two-exciton continuum scattering and coherent biexciton formation).