Experimental and numerical study of the predictability of rogue waves in semiconductor lasers

Experimentally rogue waves in a commercial vertical cavity surface emitting laser (VCSEL) under cw optical injection were studied. Extreme intensity pulses were observed in the chaotic amplitude regime and the phenomenon was explained in terms of a simple and deterministic model. A sudden change in the maximum Lyapunov exponent and a simultaneous expansion of the amplitude distribution characterized a well defined parameter region where rogue waves were observed. It is determined that they occurred after an external crisis-like event in the form of the crossing of a chaotic attractor with the stable 2D manifold of a fixed point. The mechanism involved in the occurrence of deterministic rogue waves (involving an attractor, a barrier, and a saddle point) is very generic and thus one can expect that this type of extreme event can be observed in other systems.Extreme intensity pulses occur after a well defined precursor that is related with the local convergence of the trajectories in the phase space just before a rogue wave. Furthermore, we also show that, in the parameter region where deterministic rogue waves occur, a noise source modeling spontaneous emission can substantially reduce their probability of occurrence; on the other hand, noise can also induce the rogue waves, for parameters close to the external crisis.