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

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 Schrödinger 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.

References in corpus (8)

• Instabilities, breathers and rogue waves in optics
• Non-Gaussian statistics and extreme waves in a nonlinear optical cavity
• The laminar-turbulent transition in a fibre laser
• Optical Rogue Waves in integrable turbulence
• Real-time full bandwidth measurement of spectral noise in supercontinuum generation
• Integrable turbulence and formation of rogue waves
• Free-energy transition in a gas of non-interacting nonlinear wave-particles
• Nonlinear propagation of an optical speckle field

Cited by in corpus (25)

• Rogue waves and analogies in optics and oceanography
• Direct observation of Rogue Waves in optical turbulence using Time Microscopy
• Bound state soliton gas dynamics underlying the noise-induced modulational instability
• Experimental evidence of a hydrodynamic soliton gas
• Statistical properties of nonlinear stage of modulation instability in fiber optics
• Nonlinear spectral analysis of Peregrine solitons observed in optics and in hydrodynamic experiments
• Spontaneous emergence of rogue waves in partially coherent waves: a quantitative experimental comparison between hydrodynamics and optics
• Soliton gas in bidirectional dispersive hydrodynamics
• Optical Random Riemann Waves in Integrable Turbulence
• Wave condensation with weak disorder versus beam self-cleaning in multimode fibers
• Statistics of extreme events in integrable turbulence
• Effect of local Peregrine soliton emergence on statistics of random waves in the 1-D focusing Nonlinear Schrödinger equation
• Prediction and manipulation of hydrodynamic rogue waves via nonlinear spectral engineering
• Direct scattering transform: catch soliton if you can
• Experimental study of integrable turbulence in shallow water
• Early stage of integrable turbulence in 1D NLS equation: the semi-classical approach to statistics
• Modulation property of flexural-gravity waves on a water surface covered by a compressed ice sheet
• Obstruction to ergodicity in nonlinear Schrödinger equations with resonant potentials
• On the origins of spectral broadening of incoherent waves:Catastrophic process of coherence degradation
• Bound-state soliton gas as a limit of adiabatically growing integrable turbulence
• Growing of integrable turbulence
• Properties of synchronous collisions of solitons in the Korteweg - de Vries equation
• Rigorous criteria for anomalous waves induced by abrupt depth change using truncated KdV statistical mechanics
• Observation of a generalized Gibbs ensemble in photonics
• Coexistence of solitons and extreme events in deep water surface waves