Analytical theory of terahertz four-wave mixing in semiconductor-laser amplifiers

Four-wave mixing in bulk semiconductor-laser amplifiers is investigated for detunings up to 3 THz. Gain dispersion, i.e. the difference of the gain factors for pump, probe and signal waves as well as saturation effects are found to play a significant role in four-wave mixing with large detunings. To properly describe the saturation behavior, it is assumed that both differential gain and carrier density at transparency are different for different waves. Also, the nonlinear susceptibilities associated with different nonlinear effects are characterized by different dependencies on the carrier density. Generally, the carrier densities at the zero points of the nonlinear susceptibilities (if any) and those of the linear gain factors do not coincide. An analytical solution including these issues is given and a comparison with experimental data is presented.