Complex Dynamics of semiconductor Quantum dot Lasers subject to delayed Optical Feedback

We study a five variable electron-hole model for a quantum dot (QD) laser subject to optical feedback. The model includes microscopically computed Coulomb scattering rates. We consider the case of a low linewidth enhancement factor and a short external cavity. We determine the bifurcation diagram of the first three external cavity modes and analyze their bifurcations. The first Hopf bifurcation marks the critical feedback rate below which the laser is stable. We derive an analytical approximation for this critical feedback rate that is proportional to the damping rate of the relaxation oscillations (ROs) and inversely proportional to the linewidth enhancement factor. The damping rate is described in terms of the carrier lifetimes. They depend on the specific band structure of the QD device and they are computed numerically.