Spatio-temporal dynamics and fluctuations in quantum dot lasers: Mesoscopic theory and modeling

We present a mesoscopic theory for the spatio-temporal carrier- and light field dynamics in quantum dot lasers based on spatially resolved semiconductor Bloch equations describing the dynamics of electrons and holes in each quantum dot. The Bloch equations are dynamically coupled to spatially resolved wave equations for the counterpropagating light fields and to a diffusion equation describing the carrier dynamics in the wetting layer of the quantum dot laser. These quantum dot Maxwell-Bloch equations (QD-MBEs) self-consistently consider the dynamic changes in the carrier distributions and the inter-level dipoles together with the spatially varying carrier-light field dynamics. Intradot scattering via emission and absorption of phonons, as well as the scattering with the carriers and phonons of the surrounding wetting layer are dynamically included on a mesoscopic level. Spatial fluctuations in size and energy levels of the quantum dots and irregularities in the spatial positioning of the quantum dots in the laser structure are simulated via statistical methods. Numerical simulations on the basis of the QD-MBEs reveal a complex carrier dynamics and a characteristic interplay of spontaneous and stimulated emission. For a specific set of QD-parameters the results of the modeling allow an analysis and interpretation of e.g. saturation effects and dynamic pulse shaping in quantum dot lasers.