  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.
