Failure of the \alpha-factor in describing QD laser dynamical instabilities and chaos

We show that the long-established concept of a linewidth-enhancement factor \alpha to describe carrier-induced refractive index changes in semiconductor lasers breaks down in quantum dot (QD) lasers when describing complex dynamic scenarios, found for example under high-excitation or optical injection. By comparing laser simulations using a constant \alpha-factor with results from a more complex non-equilibrium model that separately treats gain and refractive index dynamics, we examine the conditions under which an approximation of the amplitude-phase coupling by an \alpha-factor becomes invalid. The investigations show that while a quasi-equilibrium approach for conventional quantum well lasers is valid over a reasonable parameter range, allowing one to introduce an \alpha-factor as a constant parameter, the concept is in general not applicable to predict QD laser dynamics due to the different timescales of the involved scattering processes.