A theory of degenerate four-wave mixing in absorbing media is developed in terms of a general nonlinear susceptibility. The predictions of the theory are examined in both high and low reflectivity regimes and the specific nonlinearity-inducing mechanisms of thermally induced refractive index changes, the Kerr effect, and saturable absorption are considered. Such a theory is of particular relevance to degenerate four-wave mixing experiments in the ultraviolet and the predictions of the theory are compared with results obtained from such experiments.
Intracavity nearly degenerate four-wave mixing in amplifying media has been demonstrated to be a powerful technique to get very high conjugated reflectivities. A physical interpretation of this process is given in terms of interactions among pump (ω), probe (\omega- \delta\omega), or conjugated (\omega + \delta\omega) waves with optically induced refractive index modulations or gratings. Mixing experiments performed at the milliwatt level inside a (GaAl)As semiconductor laser operating above or below threshold have demonstrated very high conjugated reflectivities (a factor of 103-104) together with a 10 percent energy conversion efficiency. The appearance of additional peaks related to the ac Stark effect and observation of bistability on probe and conjugated beams also make this mixing process interesting for the study of instabilities occurring in lasers.