Rogue waves are large ocean surface waves that occur more often than predicted by Gaussian statistics in a given sea state. Originally confined to research in hydrodynamics, the science of rogue waves ventured into optics in 2007 with the observation of long tail statistics in the spectral wings of a supercontinuum generated in an optical fiber. This observation and a possible connection with ocean waves have then spread the research on extreme statistical behavior to a much wider range of optical systems.

What make optical systems convenient for research into the science of extreme events are the data acquisition time, typically much faster than in other systems (time series in excess of a million points can be recorded in less than one second), and the wide range of dynamics (both linear and nonlinear) that can lead to the emergence of optical waves with extreme intensities. For example, random collisions of breathers in noise-seeded modulation instability or collisions of solitons in the incoherent regime of supercontinuum generation have been identified as mechanisms for the emergence of optical rogue waves in fiber systems.
Extreme events in dissipative systems where energy exchange with the environment play a significant role in the dynamics have also been investigated and in particular rogue-like behavior and extreme statistics in laser cavities and amplifiers have been reported. Examples of dynamics underlying the long tail statistics in these cases include the exponential amplification of Gaussian fluctuations due to an intensity-dependent gain element in the system or the coincidence in time of chaotic bursts of noise that give rise to pulses with abnormally large intensities.

Here, using a time-to-spectrum transformation measurement technique, Runge et al. analyze a new type of highly dissipative system and report on the observation of extreme energy fluctuations. Specifically, they quantify in real-time the energy variations between consecutive cavity round-trips at the output of an Ytterbium fiber laser operating in the regime of partial mode-locking where noise-like Raman pulses are randomly emitted. In the low gain regime, it is shown that the energy fluctuations associated with the Raman pulses are highly skewed with the outliers fulfilling the statistical criterion commonly used to define rogue waves. On the other hand, for high gain, the shot-to-shot pulse energy variations are reduced and follow a near-normal distribution. Of course, previous studies on the amplification of pump intensity fluctuations in a Raman amplifier or in cascaded Raman supercontinuum have highlighted rogue-like statistics so that the results reported here may not be completely surprising. However, the originality of the work of Runge et al. is two-fold: (i) the laser operates in the all-normal dispersion regime where generally no soliton-like structures are present; and (ii) the results highlight for the first time the central role that the nonlinear transmission of a passive element (in the form of an amplifying loop mirror) may play in the emergence and selection of extreme optical pulses.

A detailed analysis of the causative mechanism has yet to be performed, but the results shown here confirm the presence of extreme fluctuations that are linked to the nonlinear amplification of noise in a dissipative optical system where gain and feedback are coupled through a nonlinear passive element. Even more generally, the experiments performed here (along with previously published studies) suggest that nonlinear systems driven near-threshold may exhibit long tail intensity statistics as a result of noise amplification.

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