Theory of single-mode lasing in coherent quantum cascade lasers

Abstract

A theory is developed for steady-state single-mode lasing in coherent quantum-well cascade lasers. This laser model is an example of a strictly quantum mechanical problem in which approximate kinetic approaches are not used to account for dissipative scattering processes. Exact wave functions are found for the system in weak and strong electromagnetic fields, so that the output power and frequency can be determined as functions of the coherent pump current and system parameters. It is shown that for pumping by monoenergetic electrons the power has a nonlinear (root) dependence and tends to saturate in strong fields. It is predicted that the coherent pumping efficiency may be increased by adjusting the energy of the pump electrons, which will lead to a linear power dependence, a high efficiency, and low threshold currents. A population inversion is found not be a necessary condition for lasing in the coherent laser. In particular, in the high field regime the population of the lower level exceeds that of the upper, while in the optimally adjusted regime they are the same.