Optical Rogue Waves in integrable turbulence

TL;DR

This study uses optical fiber experiments and simulations to explore integrable turbulence in the focusing regime of the 1D nonlinear Schrödinger equation, revealing the formation of rogue waves characterized by heavy-tailed power distributions.

Contribution

It provides the first experimental evidence of rogue waves in optical integrable turbulence and links their formation to stochastic Peregrine solitons.

Findings

Probability density function evolves from normal to heavy-tailed distribution.

Experimental results match numerical simulations of 1D-NLSE.

Rogue waves are linked to stochastic Peregrine solitons.

Abstract

We report optical fiber experiments allowing to investigate integrable turbulence in the focusing regime of the one dimensional nonlinear Schr\"odinger equation (1D-NLSE). Our experiments are very similar in their principle to water tank experiments with random initial conditions (see M. Onorato {\it et al.} Phys. Rev. E {\bf 70} 067302 (2004)). Using an original optical sampling setup, we measure precisely the probability density function (PDF) of optical power of partially coherent waves rapidly fluctuating with time. The PDF is found to evolve from the normal law to a strong heavy-tailed distribution, thus revealing the formation of rogue waves in integrable turbulence. Numerical simulations of 1D-NLSE with stochastic initial conditions reproduce quantitatively the experiments. Our investigations suggest that the statistical features experimentally observed rely on the stochastic generation of coherent analytic solutions of 1D-NLSE such as Peregrine solitons.