Nonequilibrium theory for gain in quantum cascade lasers

A nonequilibrium theory for gain in quantum cascade lasers is presented. Optical absorption /spl alpha/ at a given photon energy is calculated from the imaginary part of the optical susceptibility. The occupation functions for each electronic subband are calculated from the diagonal terms in the carrier Green's functions (which are expanded in terms of Wannier-Stark states), and obtained by self-consistent solutions of Dyson equations. Scattering with phonons and impurities are included in the relevant self-energies. The resulting integral equation and gain spectra is shown.