Active nonlinear spectroscopy of biexcitons in semiconductors: Propagation effects and Fano interferences

Four-wave degenerate-frequency mixing is used to study experimentally and theoretically the ${\Gamma }_1$ biexciton in CuCl and CdS. Propagation and polarization effects, which are particularly important in the case of CdS, are evidenced; giant oscillator strengths and autoionizing characters are also revealed. A formalism is sketched, which describes, for a coherent anti-Stokes Raman scattering-type experiment, the most general third-order susceptibility tensor in a solid where a three-nearly-equidistant-level system is distinguished amidst a large number of other, nonresonant, levels and where there is one two-photon-resonant autoionizing state. The propagation analysis accounts accurately on one side for the large shifts between the maxima of the spectra and the energetic position of the resonances, and on the other side for the severe nonlinearities and the highly structured profile of the observed line shapes. Thus, a very satisfactory agreement between experiment and theory is obtained and a number of biexciton parameters, including Fano's $q$ parameter, is determined.