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Momentum-dependent and independent intraband relaxation time effects on a non-Markovian (Gaussian line shape) many-body optical gain spectrum are presented. Our theoretical results are compared with experimental data as well as those obtained from a many-body gain model with a conventional Lorentzian line shape function. We show that a Gaussian line shape gain model with a constant intraband relaxation time gives good agreement with experimental gain spectra and the inclusion of k-dependent intraband relaxation time yields slightly improved agreement. In the case of a Lorentzian line shape function, it is found that the inclusion of the k-dependent carrier-carrier scattering in the intraband relaxation time is important to obtain good agreement with the experiment. This is because the Gaussian line shape function is steeper than the Lorentzian for a constant intraband relaxation time. The Gaussian line shape function with a constant intraband relaxation time requires less computational time than that with a k-dependent intraband relaxation time; therefore, it is an efficient model for comparison with experimental data.

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We present a detailed study of four-wave mixing in a long-wavelength distributed-feedback (DFB) laser for both nearly degenerate and nondegenerate pump-probe detunings. We characterize scaling laws of the power dependence of multiple conjugate waves on the pump and probe power levels for the nearly degenerate case. We also measure the output ratio of the probe and conjugate waves up to a detuning of 500 GHz and report the cavity enhancement of the DFB laser on this output ratio.

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