Optical Random Riemann Waves in Integrable Turbulence

Abstract

We examine integrable turbulence (IT) in the framework of the defocusing cubic one-dimensional nonlinear Schrödinger equation. This is done theoretically and experimentally, by realizing an optical fiber experiment in which the defocusing Kerr nonlinearity strongly dominates linear dispersive effects. Using a dispersive-hydrodynamic approach, we show that the development of IT can be divided into two distinct stages, the initial, pre-breaking stage being described by a system of interacting random Riemann waves. We explain the low-tailed statistics of the wave intensity in IT and show that the Riemann invariants of the asymptotic nonlinear geometric optics system represent the observable quantities that provide new insight into statistical features of the initial stage of the IT development by exhibiting stationary probability density functions.

References in corpus (4)

• Emergence of a Turbulent Cascade in a Quantum Gas
• Direct observation of Rogue Waves in optical turbulence using Time Microscopy
• Optical Rogue Waves in integrable turbulence
• Observation of nonlinear dispersion relation and spatial statistics of wave turbulence on the surface of a fluid

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• From modulational instability to focusing dam breaks in water waves
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• Integrable turbulence developing from strongly nonlinear partially coherent waves
• Experimental study of integrable turbulence in shallow water
• Early stage of integrable turbulence in 1D NLS equation: the semi-classical approach to statistics
• Nonlinear interactions between solitons and dispersive shocks in focusing media
• Soliton gas of the integrable Boussinesq equation and its generalised hydrodynamics
• Phase and Amplitude single-shot measurement by using heterodyne time-lens and ultrafast digital time-holography
• One-dimensional wave kinetic theory