Gain recovery modeling of quantum cascade lasers

We present a model to estimate the gain recovery of quantum cascade lasers (QCLs). We implement the model for two QCLs with different quantum mechanical designs. It is found that both incoherent scattering and coherent tunnelling are important for gain recovery, however, their relative importance depends on the quantum mechanical design and the operating conditions. Though the details of the gain recovery vary for the two QCLs, a complete gain recovery takes ~ 2 ps in both cases. The results are consistent with the results found in pump-probe experiments.