Abstract

Self-pumped oscillation and instability of the degenerate four-wave mixing (DFWM) process have, and are presently, being investi- gated^[1]. Degenerate n-wave mixing have in various media, based on a generalization of DFWM, has been experimentally studied so far^[2,3,4] but no work has been done neither on the oscillation nor on instability of this process. We have performed a theoretical analysis of the oscillation behavior and of the instability of the degenerate six-wave mixing (DSWM). Pump depletion and self and cross-phase modulation have been considered. The gain of both probe and signal waves are studied against the coupling constant, the self and cross-phase modulation terms, the ratio of the third and fifth order nonlinearities, and the initial probe intensity. Unlike DFWM case, the oscillation threshold of DSWM depends on the initial probe intensity. Below the threshold, the computed gain is small. Above it, more tha 90% of the pump beams energy can be transferred to the probe and signal beams. Hence, the system acts as a binary switch for the gain of both probe and signal waves. Near threshold, the system has an instable behavior. The domain of instability depends strongly on the ratio of the third and fifth order non-linearities. Following these results, we will also present the non degenerate six-wave mixing geometry as an exemple of a parametric oscillator with a large bandwidth. The choice of the nonlinear medium and the experimenteal conditions required to observe these behaviors will also be discussed.

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