Saturation effects in nondegenerate four-wave mixing between short optical pulses in semiconductor laser amplifiers

We present a simple, yet powerful method for calculating nonlinear pulse propagation and pulse interaction in active semiconductor waveguides. The model is based on the density matrix equations, which under realistic operation conditions are shown to lead to an accurate description of the material gain, that includes the dynamics of carrier heating and spectral-hole burning (SHB). A very general and compact description of the amplifier dynamics in terms of an integral equation is derived. The model is used to analyze saturation effects in short pulse amplification and nondegenerate four-wave mixing. An analytical expression for the four-wave mixing response is derived, which extends previous results to the case of short and intense pulses. Saturation of the four-wave mixing signal is shown to be strongly pulsewidth dependent due to ultrafast gain dynamics, and self-phase modulation is shown to give excessive broadening of the conjugate pulse. Finally, the impacts on the noise characteristics are calculated and shown to explain recent experimental results.