Spatio-temporal dynamics of semiconductor lasers: Theory, modelling and analysis

The spatio-temporal dynamics of semiconductor lasers is studied theoretically on the basis of semiclassic laser theory. The carrier dynamics is described in a density-matrix approach and the coupled set of equations of motion for the active medium and the light field are derived. Several approximations related to separations of length and time scales are discussed, resulting in a hierarchy of model equations leading from microscopic to macroscopic levels of description. By numerically solving space-dependent coupled partial differential equations for the (complex) optical fields, the interband polarization and the charge carrier distribution functions on the various levels of the hierarchy the formation and longitudinal propagation of unstable transverse optical filamentary structures is analyzed in a model configuration for typical double-heterostructure multi-stripe and broad-area lasers. Spectral and spatial hole burning which is observed in the simulated carrier distributions reflects the interplay between stimulated emission and the relaxation dynamics of the carrier distributions as well as the polarization. Its details are strongly influenced by the momentum and density dependence of the microscopic relaxation rates. The transverse hole burning leads to complex spatio-temporal patterns in the macroscopic intensity picture. This complex spatio-temporal dynamic behavior in multi-stripe and broad-area lasers is analyzed by various theoretical tools which allows one to quantify the degree of complexity.