A simple analytic approach to degenerate four-wave mixing by comparison with real-time holography

A simple analytic theory for degenerate four-wave mixing (DFWM) is presented. From the fundamental relationship between real-time holography and DFWM simple expressions for the DFWM signal are developed. The basic assumption in our approach is that the four waves are coupled only by the grating created by the forward-probe interference and that the intensities of the forward beam and the probe beam are not affected by the four-wave interaction. In general, this is only true when the backward pump beam intensity is much smaller than both the forward beam intensity and the probe beam intensity. However, within this restricted parameter range we obtain simple analytic expressions for the DFWM signal including the effects of linear losses in the nonlinear medium. For thin nonlinear media the signal intensity is determined by a squared Bessel-function of first order, and for thick nonlinear media the signal intensity is determined by a squared sine-function. The theory is restricted to small values of the signal reflectivity. Finally, we have investigated the DFWM signal from a CdS-sample with a
Q
-switched frequency doubled Nd:YAG laser. At a sample temperature of 375 K we obtain a third-order susceptibility of
\chi^{(3)} = 4.4 \cdot 10^{-7}
ESU. We apply the theory to these experiments.