The Theory of Non-Markovian Gain in Semiconductor Lasers

In this paper, non-Markovian optical gain of a semiconductor laser is derived from recently developed time convolutionless (TCL) quantum kinetic equations for electron-hole pairs, including the many body effects. Plasma screening and excitonic effects are taken into account using an effective Hamiltonian in the time-dependent Hartree–Fock approximation. To calculate the optical gain, equation of motion for the interband pair amplitude is integrated directly. It is shown that the line shape of optical gain spectra is Gaussian for the simplest, non-Markovian quantum kinetics, and the optical gain is enhanced by the excitonic effects caused by the attractive electron-hole Coulomb interaction and the interference effects (renormalized memory effects) between the external driving field and the stochastic reservoir of the system. Enhancement of optical gain by the memory effects suggests the violation of strict energy conservation on a very short time scale, as compared with the correlation time of the system governed by non-Markovian quantum kinetics.