Dynamic modeling of a terahertz quantum cascade laser based on difference frequency generation

In this paper, we consider a terahertz quantum cascade laser based on difference frequency generation and investigate theoretically the transient dynamics of its quantum cascade laser mid-infrared pumps and terahertz wave generated via intra-cavity difference frequency generation. The mid-infrared pumps operate simultaneously and have a common upper level. Our mathematical treatment uses an approach based on adiabatic elimination and leads to analytical solutions for the time-dependent nonlinear susceptibility as well as the terahertz difference frequency generation power. In addition, the equation that allows for the determination of the buildup time of the terahertz difference frequency generation is derived within our model and compared with those for the two mid-infrared pumps.