Nonlinear-optical properties of biexcitons. II. Four-wave mixing

The nonperturbational treatment for the calculation of the nonlinear-optical susceptibility of an exciton-biexciton system near resonance, developed earlier, is extended to account for multibeam configurations; the case of forward degenerate four-wave mixing is examined in particular. Because of the mutual interactions among the beams, the propagation of each beam in a multibeam configuration is described by a different effective dielectric function: In a pump- and test-beam configuration the renormalization of the polariton dispersion relation near the two-photon biexciton resonance is manifested for the test beam by the opening of a pump-induced polariton gap, while for the strong pump beam itself the dispersion relation displays only a divergence, with no gap. For the parameters of CuCl, the nonperturbational treatment reproduces the main (asymmetric) features of the experimental four-wave-mixing spectrum well. This casts serious doubts on the Fano-interference model for the biexciton, which was previously invoked to reconcile the asymmetric appearance of the spectrum to the perturbational description of four-wave mixing in terms of the third-order susceptibility.