Influence of gain saturation, gain asymmetry, and pump/probe depletion on wavelength conversion efficiency of FWM in semiconductor optical amplifiers

The effects of gain saturation, gain asymmetry, and pump/probe depletion on the conversion efficiency of four-wave mixing (FWM) in semiconductor optical amplifiers are studied analytically and numerically. The power dependence of FWM coupling coefficients and ultrafast relaxation-related gain mechanisms are included in the model. By studying the FWM efficiency in the transition from unsaturated to strongly saturated regions, it is seen that gain asymmetry results in deviation from small-signal models when the pump-probe detuning and pump powers are small. At high pump injection or gain conditions, it is also shown that the small-signal model breaks down even for relatively large detuning frequencies. Probe depletion is also seen to be critical under saturated conditions and an upper bound is derived for ranges of input pump power, pump-probe detuning, and gain for a given amplifier under which the small-signal model is valid.