Estimation of heavy tails in optical non-linear processes

In optical non-linear processes, rogue waves can be observed, which can be mathematically described by heavy-tailed distributions. These distributions are special since the probability of registering extremely high intensities is significantly higher than for the exponential distribution, which is most commonly observed in statistical and quantum optics. Our work provides a practical overview of the generic statistics toolkit concerning heavy-tailed distributions and proposes methods to deal with issues specific to non-linear optics. We take a closer look at supercontinuum generation, where rogue waves were already observed. We propose modifications to the Hill estimator to deal with detector saturation as well as corrections introduced by pumping the process by bright squeezed vacuum. The suggested methodology facilitates statistically reliable observation of heavy-tailed distribution in non-linear optics, nano-optics, atomic, solid-state processes, and optomechanics.

Automated summary

This paper discusses the observation of rogue waves in optical non-linear processes and their mathematical description using heavy-tailed distributions. The focus is on supercontinuum generation, proposing modifications to the Hill estimator to handle issues specific to detector saturation and bright squeezed vacuum. The suggested methodology facilitates reliable observation of heavy-tailed distribution in various optical and solid-state processes.