The object of this study is to quantitatively elucidate the laser-power dependence in transient degenerate four-wave mixing (DFWM) with an emphasis on the high laser-pump intensity region. We discuss our investigation on the power dependence of transient DFWM by taking gas-phase iodine (
I2) molecules as a testing example. The distinct physical feature is that in the high-power laser pump, where both laser-pulse duration and the inverse of pump rate are much shorter than the molecular population relaxation time, the steady-state DFWM theory of Abrams and Lind [Optical Phase Conjugation, edited by R. A. Fisher (Academic, New York, 1983), Chap. 8, pp. 211--284; Opt. Lett. 2, 94 (1978); 3, 205 (1978)] is not appropriate. The prediction by the steady-state theory has shown the DFWM to decrease with increasing laser-pump intensity as a function of 1/
Ilaser, which disagrees with the saturation behavior observed in the experiment. To elucidate the dependence of DFWM on the laser pump intensity, a non-steady-state extension of the nonperturbative theory of Abrams and Lind is required. The non-steady-state theoretical result will be shown to be in good agreement with the experimental power dependence at resonance transient DFWM especially in the high-power pump region.
A set of coupled equations is derived and used to analyze transient coherent degenerate four-wave mixing (DFWM) in a two-level system. The numerical results show that in the case of near-resonance, intense pumping, and short pulses, the properties of degenerate four-wave mixing have interesting coherent interaction characteristics, such as quasi-periodicity in the pump pulse area, probe pulse areas, and energy reflectivity, oscillatory behavior of the DFWM pulse, and generation of a DFWM signal in the case of delayed incidence, where the three incident pulses do not overlap in the medium.>