Microscopic VECSEL modeling

This tutorial gives an overview of the microscopic approach developed to describe equilibrium and nonequilibrium effects in optically excited semiconductor systems with an emphasis to the application for VECSEL modelling. It is outlined how nonequilibrium quantum theory is used to derive dynamic equations for the relevant physical quantities, i.e. The optically induced polarization and the dynamical carrier occupation probabilities. Due to the Coulombic many-body interactions, polarization and populations couple to expectation values of higher-order quantum correlations. With the help of a systematic correlation expansion and truncation approach, we arrive at a closed set of equations. Formally these can be combined with Maxwell's equations for the classical light field, yielding the Maxwell-semiconductor Bloch equations (MSBE). However, instead of the more traditional approach where losses and dissipative processes are treated phenomenologically and/or through coupling to external reservoirs, we derive fully microscopic equations for the carrier-carrier and carrier-phonon scattering as well as the effective polarization dephasing. Due to their general nature, the resulting equations are fully valid under most experimentally relevant conditions. The theory is applied to model the high-intensity light field in the VECSEL cavity coupled to the dynamics of the optical polarization and the nonequilibrium carrier distributions in the quantum-well gain medium.