Femtosecond self- and cross-phase modulation in semiconductor laser amplifiers

We present detailed derivation of our new model for femtosecond pulse amplification in semiconductor laser amplifiers. The various dynamic nonlinear terms of gain compression and associated self-phase modulation are derived semiphenomenologically, and are discussed physically. Included are the effects of carrier depletion, carrier heating and spectral hole-burning, as well as linear and two photon absorption and the instantaneous nonlinear index. Additionally, we account for dynamically changing gain curvature and slope. We apply the theory to strong signal cross-phase-cross-gain modulation experiments with ~500 fs pulses in a broad area GaAs amplifier and show that the model accurately describes the observed complex phenomena. We also present experimental results on single beam strong signal amplification in two different quantum-well amplifiers using 150-200 fs duration pulses. For such pulse lengths, carrier heating becomes an integrating nonlinearity and its self-phase modulation is similar to that due to carrier depletion. Additionally, since the pulse spectrum is broad, the gain slope and curvature shift and narrow it. The resultant spectral distortions are very different than observed (and modeled) earlier for the ~500 fs pulses. The model is again able to correctly describe the evolution of these ultrashort pulses, indicating that it remains valid, even though pulse durations approach the intraband relaxation time