Extreme-Event Statistics of Raman-Shifted Optical Solitons

Extreme-event statistics provide a framework for understanding the occurrence of rare, high-impact phenomena in complex physical systems. We report an experimental study of extreme-event behavior in optical solitons undergoing Raman-induced self-frequency shifts in highly nonlinear fibers. At the fiber output, the soliton peak-power distribution extends beyond five standard deviations from the mean, whereas the input statistics remain confined within this range, motivating an extreme-value analysis of the outliers. Using the block-maxima approach, we find that the statistics of the frequency-shifted solitons closely follow the Gumbel distribution, consistent with predictions of extreme-value theory. Small deviations from the ideal Gumbelian form indicate an enhanced likelihood of rare, high-intensity events arising from nonlinear dynamics. These results show that nonlinear fiber systems serve as an effective platform for exploring universal aspects of extreme-event statistics and for examining how nonlinearity reshapes the probability landscape of rare optical phenomena.