Single-shot observation of optical rogue waves in integrable turbulence using time microscopy

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.

Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation

“…Recent theoretical studies, however, have shown that it actually appears more generally as a universal structure emerging during intensity localisation of high power pulses in the semi-classical (zero dispersion) limit of the NLSE [10]. Some evidence for this universality has already been seen in experiments that have characterised Peregrine soliton-like structures emerging during partially coherent nonlinear wave propagation in optical fibers [11]. But all other experimental studies of Peregrine solitons have been restricted only to the regime of plane wave modulation instability.…”

“…Although techniques do exist which can reduce or suppress this pedestal to some degree [16], our results suggest that -at least for nonlinear N-soliton compression scenarios described by the NLSE -its presence is inevitable. Finally, we anticipate application of these results in studies of extreme events and rogue waves in integrable turbulence [11,26,29,30] where the problem of nonlinear localisation mechanisms remains a challenging open problem. …”

Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation

“…It has also been understood that rogue waves play important role in the characterization of the nonlinear stage of modulational instability [41], [17] and particularly, in the development of integrable turbulence [40], [1], [37], [33]. One of the universal mathematical models for the rogue wave description is the one-dimensional focusing Nonlinear Schrödinger (fNLS) equation,…”

Formation of rogue waves from a locally perturbed condensate

“…Later, J.M. Soto-Crespo, N. Devine and N. Akhmediev have demonstrated that in the case of higher condensate disturbances, the tails of the probability density function of wave amplitudes increases [38] (see also the works [38][39][40] where the non-Gaussian statistics was observed for the development of strongly fluctuating initial conditions). They concluded that only initial perturbations of significant amplitude can contain spatially localized breathers, that is consistent with the theory suggested here (the minimal amplitude of SLCP generated by breathers is determined by the perturbation width, see the second paragraph).…”