Abstract
Optical fibres are favourable tabletop laboratories to investigate both coherent and incoherent nonlinear waves. In particular, exact solutions of the one-dimensional nonlinear Schrödinger equation such as fundamental solitons or solitons on finite background can be generated by launching periodic, specifically designed coherent waves in optical fibres. It is an open fundamental question to know whether these coherent structures can emerge from the nonlinear propagation of random waves. However the typical sub-picosecond timescale prevented—up to now—time-resolved observations of the awaited dynamics. Here, we report temporal ‘snapshots' of random light using a specially designed ‘time-microscope'. Ultrafast structures having peak powers much larger than the average optical power are generated from the propagation of partially coherent waves in optical fibre and are recorded with 250 femtoseconds resolution. Our experiment demonstrates the central role played by ‘breather-like' structures such as the Peregrine soliton in the emergence of heavy-tailed statistics in integrable turbulence.
Highlights
Optical fibres are favourable tabletop laboratories to investigate both coherent and incoherent nonlinear waves
Observations performed with the time microscope (TM) at the output of the fibre immediately reveals the emergence of intense peaks, with powers frequently exceeding the average power hPi by factors of 10–50
The random waves used as initial conditions in our experiments are partially coherent light waves emitted by a high power Amplified Spontaneous Emission (ASE) light source at a wavelength lB1560 nm
Summary
Optical fibres are favourable tabletop laboratories to investigate both coherent and incoherent nonlinear waves. It is conjectured by some authors that breather solutions of the 1D-NLSE such as the Peregrine soliton (PS) may represent prototypes of RWs20,22,24,26–28 This has motivated nice experiments in which these solitons on finite background (SFB) have been generated in optical fibres[29,30,31,32] and in a one-dimensional water tank[32,33]. Heavy-tailed deviations from Gaussianity reported in previous experiments possibly arise from the stochastic generation of SFB that are localized in space and time, such as the PS This conjecture is supported by numerical simulations of the 1D-NLSE that have shown that some highamplitude coherent structures compatible with some breather solutions of the 1D-NLSE like the PS can spontaneously emerge from a stochastic background[25,28,36,38]
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