Real-time capture of rogue waves emerging from spontaneous modulation instability
Modulation instability (MI) is one of the most fundamental processes of nonlinear science . In nonlinear fiber optics, MI develops when a weak perturbation on top of a continuous wave field experiences exponential amplification and evolves into strongly-localized breather structures with large intensity. Although MI has been studied for decades, there continues to be intense interest in understanding its dynamics because when triggered from noise, it generates high amplitude and statistically-rare “rogue waves” of importance in hydrodynamics and optics . Due to experimental limitations, however, the ultrafast instability dynamics of noise-driven spontaneous MI in optics have never been directly observed experimentally. Using a time-lens magnifier system, we report for the first time the measurement of both the statistics and intensity profiles of transient breather structures emerging from spontaneous modulation instability. Our measurements are in excellent agreement with numerical simulations. The technique has tremendous potential as a laboratory tool in the study of nonlinear instabilities.
 V. E. Zakharov and L. A. Ostrovsky, Phys. D 238, 540-548 (2009)
 J. M. Dudley, F. Dias, M. Erkintalo, G. Genty, Nature Photon. 8, 755–764 (2014)