Simulation of a longitudinally electron-beam-pumped nanoheterostructure semiconductor laser

A three-dimensional numerical model of a vertical-cavity surface-emitting laser (VCSEL) containing a resonance grating of quantum wells (QWs) is developed. The Helmholtz equation for a field and the diffusion equation for a medium, in which an electron beam is the source of charge carriers, aresolved self-consistently, which allowed us to find the longitudinal and radial profiles of the generated field, its frequency, and the threshold pump current. The characteristics of the higher-order modes are calculated against the background of the frozen medium formed by the generated mode. The stability limit of the single-mode regime and the type of a mode at which lasing begins to develop with increasing pump power are found from calculations of the gain balance and losses for higher-order modes. An iteration algorithm is developed for calculating the parameters of a VCSEL with many QWs, the calculation time increasing linearly with the number of QWs. The profiles of the resonator modes and their frequency spectrum are calculated for a cylindrically symmetric VCSEL. The stability limits of single-mode lasing are determined. The results are compared qualitatively with experiments.