Upper limits on terahertz difference frequency generation power in quantum well heterostructures

There is currently considerable interest in terahertz (THz) difference frequency generation (DFG) utilizing near-resonant intersubband nonlinearity in quantum cascade lasers and other quantum well heterostructures. Such devices were shown to operate at room temperature, but their power demonstrated so far has been rather low. In all previous works the intracavity configuration was studied, in which the nonlinear mixing region was placed inside a pump laser cavity. Here we obtain the upper limits on the THz DFG power that can be achieved in intersubband quantum well systems under external optical pumping. We consider strong optical fields and include all resonant absorption or pump depletion, and nonlinear saturation effects by self-consistently solving three coupled wave equations, the Poisson equation, and density matrix equations. Although we use a GaInAs/AlInAs double quantum well heterostructure as an example, our analysis is applicable to any material system possessing resonant second-order optical nonlinearity. The maximal THz DFG power is reached for intermediate pump intensities of the order of the saturation intensity. Further increase of the pump intensity results in the decrease of the maximum THz DFG power. We analyze the dependence of THz power on the length and doping of the nonlinear mixing region, and present the design of the optimal structures.