Nonlinear random optical waves: integrable turbulence, rogue waves and intermittency

TL;DR

This paper investigates how nonlinear optical waves evolve statistically in integrable systems, revealing phenomena like spectral broadening, rogue waves, and intermittency through simulations and experiments.

Contribution

It provides new insights into the statistical behavior of nonlinear waves in optical fibers, highlighting the emergence of intermittency and heavy-tailed distributions in integrable turbulence.

Findings

Spectral broadening with exponential wings occurs in both regimes.

Heavy-tailed deviations are observed in focusing regime.

Intermittency manifests as scale-dependent statistical deviations.

Abstract

We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we specifically focus on optical fiber systems accurately described by the integrable one-dimensional nonlinear Schr\"odinger equation. We consider random complex fields having a gaussian statistics and an infinite extension at initial stage. We use numerical simulations with periodic boundary conditions and optical fiber experiments to investigate spectral and statistical changes experienced by nonlinear waves in focusing and in defocusing propagation regimes. As a result of nonlinear propagation, the power spectrum of the random wave broadens and takes exponential wings both in focusing and in defocusing regimes. Heavy-tailed deviations from gaussian statistics are observed in focusing regime while low-tailed deviations from gaussian statistics are observed in defocusing regime. After some transient evolution, the wave system is found to exhibit a statistically stationary state in which neither the probability density function of the wave field nor the spectrum change with the evolution variable. Separating fluctuations of small scale from fluctuations of large scale both in focusing and defocusing regime, we reveal the phenomenon of intermittency; i.e., small scales are characterized by large heavy-tailed deviations from Gaussian statistics, while the large ones are almost Gaussian.