A four-wave interaction between consecutive ultrashort light pulses propagating in a medium

The interaction between a medium and two ultrashort light pulses passing through it consecutively is investigated. The frequencies of the pulses are assumed to satisfy the conditions of two-photon resonance with some transition in the matter. It is shown that despite the nonsynchronism of the pulses there is a region for such resonant four-photon interactions in which the phase of the generated wave is locked, and hence the process is also coherent spatially. It is also found that at large distances a proportional subpulse whose area tends to be 0 or 2 pi stands out sharply against the subpulse of the trigger field at the second pulse. The conditions for attainment of maximal conversion efficiency are found by approximate solutions for the initial stage and the area theorem; finally, it is demonstrated that a wave which is absent at the input cannot arise in systems with a high wave mismatch, but an increase in energy of the second pulse is possible if it contains both frequency components at the input.