Degenerate four-wave mixing for arbitrary pump and probe intensities

An analytical expression is derived for the degenerate four-wave mixing signal produced by pump and probe input fields of arbitrary intensity appropriate for stationary media and for situations of negligible absorption or depletion. By retaining all higher-order phase-matched terms in the nonlinear polarization, the signal amplitude is found to be the sum of an infinite series. An extension of the Abrams-Lind standard perturbation theory in the limit of weak probes is used for validation. Based on analytical results, the maximum signal strength is found to be obtained for zero detuning and equal pump and probe field amplitudes of approximately 1.204 ESAT