Spontaneous motion of cavity solitons in vertical-cavity lasers subject to optical injection and to delayed feedback

We consider a rate equation model describing broad area vertical-cavity surface-emitting lasers subject to injection and to time-delayed optical feedback. We show that the inclusion of an external cavity affects dramatically the space-time behavior of this system by modifying the instability threshold as well as the wavelength of the Turing instability. We show also that the delayed feedback is responsible for the appearance of traveling wave instability. Finally, we demonstrate that a single cavity soliton exhibits a spontaneous motion with a constant velocity. Without delayed feedback transition to the moving cavity soliton does not exist.