Enhanced multiwave mixing interactions in semiconductor optical amplifiers via pump modulation

It is demonstrated that, by modulating a semiconductor optical amplifier at a frequency determined by the detuning between the pump and probe in a collinear four wave mixing geometry, the enhancements in gain and reflectivity of two to three orders of magnitude are possible for remarkably small modulation depths (m=10^-2). The mechanism of frequency mixing using population pulsations in semiconductor laser amplifiers is summarized. In particular, the modification to the standard geometry to achieve enhancements is discussed. The appropriate four wave mixing equations including current modulation terms are solved analytically in the undepleted pump approximation. The analytic forms for transmission gain and phase conjugate reflectivity in several cases of interest are computed. In particular, the case in which four wave mixing is absent and energy transfer occurs solely as a result of the current modulation is examined