Theory of non-Markovian gain in strained-layer quantum-well lasers with many-body effects

A non-Markovian model for the optical gain of strained-layer quantum-well lasers is developed taking into account the valence-band mixing, strain effects, many-body effects, and the non-Markovian relaxation using the time-convolutionless reduced-density operator formalism given in previous papers for an arbitrary driven system coupled to a stochastic reservoir. Many-body effects are taken into account within the time-dependent Hartree-Fock approximation and the valence-band structure is calculated from the 6 x 6 Luttinger-Kohn Hamiltonian. The optical gain with Coulomb (or excitonic) enhancement is derived by integrating the equation of motion for the interband polarization. It is shown that the vertex function for the interband polarization can be obtained exactly without relying on the Fade approximation. As a numerical example, an InxGa1-xAs-InP quantum well (QW) is chosen for its wide application in optical communication systems. It is predicted that the Coulomb enhancement of gain is pronounced in the cases of compressive and unstrained QW's while it is negligible in the case of tensile strained QW.