Pump depletion effects in thermal degenerate four-wave mixing

Characteristics such as a large magnitude of nonlinearity, fast response, broadband operation, and easy availability make absorbing liquids attractive candidates for performing phase conjugation of optical beams by degenerate four-wave mixing. The coupled-wave equations describing the interaction of four optical fields in an absorbing medium have been solved previously for the case of no pump depletion and no self-action of any of the beams. When studying phase conjugation oscillation, however, the effect of depletion of the pump beams on the phase conjugate reflectivity must be considered. Moreover, in absorbing media the self-action effects are always present. The coupled-wave equations, including the self-action terms for all four waves involved, are derived here for the first time to the authors' knowledge. For the case of small absorption, these equations are solved analytically, and the effect of pump depletion on phase conjugate reflectivity R is determined. In the absence of the pump depletion, R is proportional to tan2(Ql), where Ql is a dimensionless gain parameter characterizing the nonlinear medium and the input pump power. When pump depletion and self-action are included, R does not go to infinity when Ql equals odd multiples of π2. Instead R takes on values dependent on the probe ratio q1, which is the ratio of the input probe irradiance to the input pump irradiance. The authors find that the maximum value for R is 1q1. They also find that for Ql close to odd multiples of π2, the reflectivity is significantly reduced from the value obtained by ignoring pump depletion, even for probe ratios as small as one-tenth of 1%. Experimental confirmation of this theory, using an argon-ion laser as the pump and carbon tetrachloride mixed with a dye as the absorbing medium, is in progress and is reported