Analytical investigation of the dynamics behaviors of quantum cascade laser

In this paper, we investigate analytically and numerically the transient dynamics of the mid-infrared quantum cascade laser operating in a single mode. The approach is based on using adiabatic elimination in the rate equations model. Analytical solutions are derived for steady-state and time-dependent number of electrons in the various levels, population inversion and number of photons in the cavity. In addition, the equation that allows for the determination of time for steady-state establishment is derived within the premises of our analytical model in the most general case. The results are compared with numerical calculations. The dependence of the buildup time on current injection is also examined and compared with our other existing model.