Estimation of heavy tails in optical non-linear processes

TL;DR

This paper provides practical statistical methods to identify and analyze heavy-tailed distributions associated with rogue waves in optical non-linear processes, enhancing the reliability of such observations across various fields.

Contribution

It introduces modified estimators and correction techniques for heavy-tailed distribution analysis in non-linear optics, addressing detector saturation and pumping effects.

Findings

Modified Hill estimator for detector saturation

Correction methods for bright squeezed vacuum pumping

Reliable detection of heavy tails in non-linear optical data

Abstract

In optical non-linear processes rogue waves can be observed, which can be mathematically described by heavy-tailed distributions. These distributions are special due to the fact that 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. The current manuscript gives 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, nanooptics, atomic, solid-state processes and optomechanics.