Since its discovery in seventies, the degenerate four-wave mixing (DFWM) technique has been widely used in atomic, molecular and solid-state spectroscopy. It has been demonstrated by a number of authors that the implementation of various kinds of DFWM results in the striking improvement in spectral resolution and signal-to-noise ratio.

The existing experimental and theoretical works on DFWM are mostly concerned with the steady-state regime where the laser pulse duration is longer than the electronic relaxation rate of the medium, and the short-pulse case where the pulse duration is too short to create a substantial change in the electronic population. Recently, we have generalized the well-known steady-state two-level model of DFWM by Abrams and Lind with the following features.

A. The non-stationary evolution of the excited state is taken into account for the casewhere the optical pump rate is comparable to or faster than the excited state decay rate.

B. The effect of quantum state degeneracy (magnetic sub-levels) is considered.

C. The effect of atomic/molecular motion is discussed.

D. Contrary to the existing theoretical works these results are obtained with the non-  perturbative approach.

We have used our transient DFWM theoretical results for the interpretation of experimental data of iodine molecules obtained in our laboratory. The theoretical calculations have demonstrated a good agreement with experimental data on the laser-pump intensity, the rotational quantum number and the iodine pressure dependences of DFWM signal. We have also compared the predictions of our transient DFWM model with the existing theoretical results (and classical Abrams-Lind model in particular).

In this paper, we shall review and compare in details the theoretical treatments of the steady-state and transient DFWM. The experimental results of DFWM will also be reviewed.