Dynamics of the nonlinear four-wave mixing interaction

Abstract

We present an analysis of the impulse response of four-wave mixing, in the case where the “two-photon term” of the nonlinear susceptibility is dominant. The nonlinear interaction itself will be considered to be steady state. The conditions of negligible pump depletion are considered first. It is shown that the reflected beam has only the character of perfect phase conjugation if the pulse length is longer than the medium length, and the latter is short compared to the characteristic distance of the problem. The “weak-pulse” approximation involving only two coupled equations is compared to the exact four-wave solution, when the medium thickness approaches the critical oscillation threshold. Finally, the stability and existence of steady-state solutions is analyzed for very long media (compared with the oscillation length).