A new density matrix theory for semiconductor lasers, including non-Markovian intraband relaxation and its application to nonlinear gain

A density matrix equation for semiconductor lasers is derived from the microscopic equation of motion for electrons using a projection operator method. The effect on non-Markovian intraband relaxation is described by the autocorrelation functions of electron scattering terms in the microscopic interaction Hamiltonian. The obtained density matrix equation provides a systematic treatment for dynamical properties of semiconductor lasers, and the treatment can be performed by calculating the autocorrelation functions from available material parameters. A gain formula for arbitrary light output power is derived from a single-mode steady-state nonperturbative solution. A simplified estimation using a stochastic model shows that non-Markovian intraband relaxation enhances both linear gain and nonlinear gain. The reduction of nonlinear gain effects is discussed