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

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Abstract
Space-dependent Maxwell-Bloch equations are derived for the description of spatiotemporal 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. © 1996 The American Physical Society.