Spatially structured multi-wave-mixing induced nonlinear absorption and gain in a semiconductor quantum well

We have studied two-dimensional absorption and gain spectrum in an asymmetric semiconductor triple-coupled-quantum-well (TCQW) nanostructure. Four subband transitions are coupled by using four coherent fields in a close-loop configuration to introduce cross-Kerr effect and four-wave-mixing (FWM) induced nonlinearity in achieving nonlinear absorption and gain profiles. Position-dependent absorption and gain are obtained by applying one, or two coherent fields in a variety of standing wave configurations including superposed field configuration in the standing-wave regime. In addition to the control parameters like Rabi frequency and detuning, the specialty of the model is to employ double-controlled spatial phase-coherence guided by the FWM-induced phase and the phases introduced by the standing wave formation. Our results highlight the high-precision electron localization in spatial domain. The evolution of spatially modulated gain without inversion may be a substitute for obtaining gain from a traditional quantum cascade laser. The importance of the present work is to find its application in designing electro-optic modulators in semiconductor nanostructures in near future.