FEMTOSECOND SELF-PHASE 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 n onlinear terms of gain compression and associated self-phase modulatio n are derived semiphenomenologically, and are discussed physically. In cluded are the effects of carrier depletion, carrier heating and spect ral hole-burning, as well as linear and two photon absorption and the instantaneous nonlinear index. Additionally, we account for dynamicall y changing gain curvature and slope. We apply the theory to strong sig nal cross-phase-cross-gain modulation experiments with similar to 500 fs pulses in a broad area GaAs amplifier and show that the model accur ately describes the observed complex phenomena. We also present experi mental results on single beam strong signal amplification in two diffe rent quantum-well amplifiers using 150-200 fs duration pulses. For suc h pulse lengths, carrier heating becomes an integrating nonlinearity a nd its self-phase modulation is similar to that due to carrier depleti on. Additionally, since the pulse spectrum is broad, the gain slope an d curvature shift and narrow it. The resultant spectral distortions ar e very different than observed (and modeled) earlier for the similar t o 500 fs pulses. The model is again able to correctly describe the evo lution of these ultrashort pulses, indicating that it remains valid, e ven though purse durations approach the intraband relaxation time.