Quantum Maxwell-Bloch equations for spatially inhomogeneous semiconductor lasers

We present quantum Maxwell-Bloch equations (QMBE) for spatially inhomogeneo us semiconductor laser devices. The QMBE are derived from fully quantum mec hanical operator dynamics describing the interaction of the light field wit h the quantum states of the electrons and the holes near the band gap. By t aking into account field-field correlations and field-dipole correlations, the QMBE include quantum noise effects, which cause spontaneous emission an d amplified spontaneous emission. Tn particular, the source of spontaneous emission is obtained by factorizing the dipole-dipole correlations into a p roduct of electron and hole densities. The QMBE are formulated for general devices, for edge emitting lasers and for vertical cavity surface emitting lasers, providing a starting point for the detailed analysis of spatial coh erence in the near-field and far-field patterns of such laser diodes. Analy tical expressions are given for the spectra of gain and spontaneous emissio n described by the QMBE. These results are applied to the case of a broad a rea laser, for which the frequency and carrier density dependent spontaneou s emission factor beta and the evolution of the far-held pattern near thres hold are derived. [S1050-2947(99)02803-6].