Mesoscopic spatiotemporal theory for quantum-dot lasers

We present a mesoscopic theory for the spatiotemporal carrier and light-field dynamics in quantum-dot lasers. Quantum-dot Maxwell-Bloch equations have been set up that mesoscopically describe the spatiotemporal light-field and interlevel/intralevel carrier dynamics in each quantum dot (QD) of a typical QD ensemble in quantum-dot lasers. In particular, this includes spontaneous luminescence, counterpropagation of amplified spontaneous emission, and induced recombination as well as carrier diffusion in the wetting layer (quantum-well media) of the quantum-dot laser. Intradot scattering via emission and absorption of phonons, as well as scattering with the carriers and phonons of the surrounding wetting layer are dynamically included on a mesoscopic level. The spatiotemporal light-field dynamics reveals a characteristic interplay of spontaneous and stimulated emission in quantum-dot lasers that depends on typical spatial fluctuations in size and energy levels of the quantum dots and irregularities in the spatial distribution of the quantum dots in the active layer. Those effects are simulated via statistical methods. They are shown to directly affect the propagation of an ultrashort pulse in a quantum-dot waveguide. The strong influence of the localized carrier dynamics is seen in the selective depletion and refilling of quantum-dot energy levels.