Theory of exciton-exciton correlation in nonlinear optical response

We present a systematic theory of Coulomb interaction effects in the nonlin ear optical processes in semiconductors using a perturbation series in the exciting laser field. The third-order dynamical response consists of a phas e-space filling correction, a mean-field exciton-exciton interaction, and t wo-exciton correlation effects expressed as a force-force correlation funct ion. The theory provides a unified description of effects of bound and unbo und biexcitons, including memory effects beyond the Markovian approximation . In the degenerate four-wave-mixing experiments, correlation effects are s hown leading to polarization mixing, ringing, etc. The strong interaction, a nonperturbative theory of the correlation function, is numerically evalua ted for a one-dimensional model. Approximations for the correlation functio n are presented. [S0163-1829(98)03643-1].