Theory of resonant Doppler-broadened backward four-wave mixing in the pump saturation regime

Abstract

We analyze the properties of phase-conjugate (PC) emission via resonant, Doppler-broadened, backward four-wave mixing in the saturation regime, when both counterpropagating pump waves are arbitrarily intense. One considers two atomic situations, either a four-level system modeled as a pair of uncoupled transitions, or a three-level system. The first case leads to an analytical expression of the PC field, for arbitrary pump intensities, in the Doppler limit. The second case, in general, necessitates a numerical solution, except in the asymptotic regime when one pump is very intense compared to the other one. One finds that both cases lead to quite similar predictions: (i) two-peaked or four-peaked emission line shape, depending on the forward to backward pump intensity ratio; (ii) the maximum of PC reflectivity is obtained for infinite backward saturation, but for a fi-p nite value of the forward pump intensity; (iii) for backward saturation, the emission line shape is practically independent of the forward pump intensity. Finally, the theoretical analysis is extended to the case of a saturating probe and its effect on emission line shape and PC reflectivity, as well as its application to the properties of emission processes involving higher-order optical susceptibilities (degenerate multiwave mixing).