Control of spatiotemporal rogue waves by harmonic pump modulation in a semiconductor laser with a saturable absorber

Through numerical simulations, statistical and dynamical properties of extreme events in a broad-area semiconductor laser with intracavity saturable absorber are investigated. By inclusion of a diffusion coefficient for the field, formation of rogue waves in a state of extended turbulence is studied and shown to be affected by harmonic perturbations. In particular, we propose a control technique based on periodic modulation of the pump parameter which can either drive the state of the system closer to or away from the chaotic attractors respectively enhancing or suppressing the generation of rogue waves. By statistical and dynamical analysis of the events in terms of intensity and optical gain, we show that when the system is under resonant modulation with frequency close to that of the dominant oscillations in the turbulent state (which is equal to the relaxation oscillation frequency typical of semiconductor lasers), more rogue waves are triggered with larger intensities and shorter lifetimes. On the other hand, off-resonant modulations restrain the formation of rogue waves where they appear in lower intensities and longer lifetimes. An example of special cases where the proposed scheme can completely forbid or allow the emission of rogue waves is also presented.