Four-photon parametric mixing in optical fibers: effect of pump depletion

The analytical solutions to differential equations governing nonlinear four-photon mixing in optical fibers are presented for the general case of depleted pump power. The expressions reduce to those derived earlier with the assumption of nondepleted pump power. We find that the maximum power available for conversion from the pump waves to the signal waves resulting from a third-order nonlinearity depends on the index mismatch and that the index mismatch required for achieving maximum possible power transfer is a function of the frequency shift.