# Statistical properties of nonlinear stage of modulation instability in fiber optics

## TL;DR

This paper experimentally investigates the nonlinear stage of modulation instability in optical fibers, revealing breather formation, statistical decay patterns, and oscillatory autocorrelation features characteristic of integrable turbulence.

## Contribution

It provides the first single-shot experimental observation of breather development and detailed statistical analysis of the nonlinear modulation instability in fiber optics.

## Key findings

- Observation of breather structures evolving from initial noise
- Decaying oscillations of the second-order moment over time
- Oscillatory features in the autocorrelation function g^{(2)}( au)

## Abstract

We present an optical fiber experiment in which we examine the space-time evolution of a modulationally unstable plane wave initially perturbed by a small noise. Using a recirculating fiber loop as experimental platform, we report the single-shot observation of the noise-driven development of breather structures from the early stage to the long-term evolution of modulation instability. Performing single-point statistical analysis of optical power recorded in the experiments, we observe decaying oscillations of the second-order moment together with the exponential distribution in the long term evolution, as predicted in [D.\,S. Agafontsev and V.\,E. Zakharov, Nonlinearity {\bf 28}, 2791 (2015)]. Finally, we demonstrate experimentally and numerically that the autocorrelation of the optical power $g^{(2)}(\tau)$ exhibits some unique oscillatory features typifying the nonlinear stage of the noise-driven modulation instability and of integrable turbulence