Quantifying optical rogue waves

TL;DR

This paper introduces two improved methods for estimating the distribution exponent of optical rogue waves in supercontinuum generation, revealing insights into their statistical behavior and physical effects like pump depletion and fiber refractive index changes.

Contribution

It presents a generalized Hill estimator and a multi-parameter model for more accurate rogue wave distribution analysis, validated with experimental data.

Findings

Consistent estimation results from two methods.

Identification of power-law breakdown due to pump depletion and saturation.

Detection of weak memory effects linked to refractive index changes.

Abstract

This work presents two distinct approaches to estimating the exponent related to the distribution of optical rogue waves observed in supercontinuum generated in a single-mode fiber, that is, to quantifying the rogueness. The first is a generalization of the well-known Hill estimator, and the second relies on estimating all parameters of a multi-parameter model. We show that the model shows a good correspondence with experimental data, and that the two estimating approaches provide consistent results, which are significantly more accurate than those obtained with earlier methods of estimation. Furthermore, alternative visualization through the tail function revealed the presence of pump depletion as well as detector saturation leading to the breakdown of power-law behavior for the largest observations. We characterized this breakdown via a combination of an exponential and a generalized Pareto distribution. Additionally, we have uncovered a weak memory effect in the data, which can be attributed to changes of the refractive index in the single-mode fiber.