Degenerate four-wave mixing for arbitrary pump and probe intensities

An analytical expression for the degenerate four-wave mixing signal produce d in a medium composed of two-level atoms by pump and probe lasers of arbit rary intensities and parallel linear polarization, suffering negligible abs orption and depletion, has been derived. The Abrams-Lind approach [Opt. Let t. 2, 94 and 3, 205 (1978)] for deriving the phase-matched polarization has been extended to find all the other higher-order polarization terms contri buting to the signal. The signal field amplitude is expressed as an infinit e series whose convergence rate depends on the intensity of the input field s and their detuning from resonance. The solution is successfully verified by comparison with a full numerical nonperturbative calculation and is foun d to be equivalent to the Abrams-Lind result in the limit of weak probe int ensity. The result is used to calculate the saturation effects on spectral line shape that are relevant to simulation of molecular spectra obtained by degenerate four-wave mixing with saturating pump and probe fields. The res ult is extended to treat atomic motion in the case of forward geometry of t he input beams. (C) 1999 Optical Society of America [S0740-3224(99)00805-X] OCIS codes: 190.1900, 190.0190, 190.4380, 300.6290, 300.6420.