  In this paper, we investigate theoretically the stabilization of a
free-running vertical-cavity surface-emitting laser exhibiting polarization
chaos dynamics. We report the existence of a boundary isolating the chaotic
attractor on one side and a steady-state on the other side, and identify the
unstable periodic orbit playing the role of separatrix. In addition, we
highlight a small range of parameters where the chaotic attractor passes
through this boundary, and therefore where chaos only appears as a transient
behaviour. Then, including the effect of spontaneous emission noise in the
laser, we demonstrate that, for realistic levels of noise, the system is
systematically pushed over the separating solution. As a result, we show that
the chaotic dynamics cannot be sustained unless the steady-state on the other
side of the separatrix becomes unstable. Finally, we link the stability of this
steady-state to a small value of the birefringence in the laser cavity and
discuss the significance of this result on future experimental work.
