Maxwell-Bloch equations for spatially inhomogeneous semiconductor lasers .1. Theoretical formulation

Space-dependent Maxwell-Bloch equations are derived for the description of spatiotemmporal dynamics of spatially inhomogeneous semiconductor lasers. The dynamics of the charge carriers is described in a density-matrix approach using a Wigner function representation. On this basis, the coupled set of equations of motion for the active medium and the space-dependent light field is derived. Based on typical length and time scales, approximations are performed to obtain a numerically tractable problem. The many-body interactions give rise to space-dependent energy renormalizations, Coulomb enhancement: and scattering processes. The latter ones are considered in the form of momentum- and density-dependent microscopic relaxation rates due to carrier-carrier and carrier-phonon interaction for the carrier distribution functions and the polarization. For the spatial transport or the carriers an ambipolar diffusion model is derived.