Fundamental Limitations on Gain of THz QCL

We analyze the main physical processes in quantum cascade lasers with spatial separation between the region of photon radiation and LO phonon emission providing depopulation of the lower level of the optical transition. Our purpose is to find reasons of reduction of the population inversion at low photon energy and search for ways of its increase. The expression for the population inversion is obtained from equation for simplified density matrix. This allows us, on one hand, to take into account coherence of tunneling between different levels and, on the other hand, to understand its role in transition probabilities in a simple way. We come to the conclusion that population inversion in THz lasers can be significantly increased by optimization of tunneling matrix element between the two regions and LO phonon emission time. The optimal value of the matrix element is smaller than its maximal possible value. As well, the optimal LO phonon emission time is larger than the time reached at LO phonon resonant emission.