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Journal ArticleDOI

The Peregrine soliton in nonlinear fibre optics

TL;DR: The Peregrine soliton was observed experimentally for the first time by using femtosecond pulses in an optical fiber as mentioned in this paper, which gave some insight into freak waves that can appear out of nowhere before simply disappearing.
Abstract: The Peregrine soliton — a wave localized in both space and time — is now observed experimentally for the first time by using femtosecond pulses in an optical fibre. The results give some insight into freak waves that can appear out of nowhere before simply disappearing.

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Citations
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Journal ArticleDOI
TL;DR: This work presents the first experimental results with observations of the Peregrine soliton in a water wave tank, and proposes a new approach to modeling deep water waves using the nonlinear Schrödinger equation.
Abstract: The conventional definition of rogue waves in the ocean is that their heights, from crest to trough, are more than about twice the significant wave height, which is the average wave height of the largest one-third of nearby waves. When modeling deep water waves using the nonlinear Schr\"odinger equation, the most likely candidate satisfying this criterion is the so-called Peregrine solution. It is localized in both space and time, thus describing a unique wave event. Until now, experiments specifically designed for observation of breather states in the evolution of deep water waves have never been made in this double limit. In the present work, we present the first experimental results with observations of the Peregrine soliton in a water wave tank.

950 citations

Journal ArticleDOI
TL;DR: In this paper, the authors introduce the concept of rogue waves, which is the name given by oceanographers to isolated large amplitude waves, that occur more frequently than expected for normal, Gaussian distributed, statistical events.

851 citations


Cites background or methods from "The Peregrine soliton in nonlinear ..."

  • ...The Peregrine solution has been recently reproduced experimentally in wave tank laboratories [59] and in optical fibers [60]....

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  • ...Direct analogies for this type of soliton solutions can be established with the Peregrine solitons observed in wave tank experiments [59] and in optical fibers [60]....

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  • ...Envelope solitons have been experimentally identified in this context, in particular, the Peregrine soliton has been observed in nonlinear optical fibers [60] and more recently the Ma–Kuznetsov breather has also been reproduced experimentally [78]....

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Journal ArticleDOI
TL;DR: Curious wave phenomena that occur in optical fibres due to the interplay of instability and nonlinear effects are reviewed in this article, where the authors propose a method to detect such phenomena.
Abstract: Curious wave phenomena that occur in optical fibres due to the interplay of instability and nonlinear effects are reviewed.

735 citations

Journal ArticleDOI
07 Apr 2017-Science
TL;DR: Spectral interferometry images the formation, binding, and internal dynamics of optical soliton complexes as they propagated in a laser cavity and tracks two- and three-soliton bound states over hundreds of thousands of consecutive cavity roundtrips, implying that its dynamics may be topologically protected.
Abstract: Solitons, particle-like excitations ubiquitous in many fields of physics, have been shown to exhibit bound states akin to molecules. The formation of such temporal soliton bound states and their internal dynamics have escaped direct experimental observation. By means of an emerging time-stretch technique, we resolve the evolution of femtosecond soliton molecules in the cavity of a few-cycle mode-locked laser. We track two- and three-soliton bound states over hundreds of thousands of consecutive cavity roundtrips, identifying fixed points and periodic and aperiodic molecular orbits. A class of trajectories acquires a path-dependent geometrical phase, implying that its dynamics may be topologically protected. These findings highlight the importance of real-time detection in resolving interactions in complex nonlinear systems, including the dynamics of soliton bound states, breathers, and rogue waves.

464 citations

Journal ArticleDOI
TL;DR: Akhmediev et al. as mentioned in this paper derived general high-order rogue waves in the nonlinear Schrodinger equation using the bilinear method and showed that the general N − 1 free irreducible complex parameters have the highest peak amplitudes among all rogue waves of the same order.
Abstract: General high-order rogue waves in the nonlinear Schrodinger equation are derived by the bilinear method. These rogue waves are given in terms of determinants whose matrix elements have simple algebraic expressions. It is shown that the general N -th order rogue waves contain N −1 free irreducible complex parameters. In addition, the specific rogue waves obtained by Akhmediev et al. (Akhmediev et al. 2009 Phys. Rev. E 80 , 026601 (doi:10.1103/PhysRevE.80.026601)) correspond to special choices of these free parameters, and they have the highest peak amplitudes among all rogue waves of the same order. If other values of these free parameters are taken, however, these general rogue waves can exhibit other solution dynamics such as arrays of fundamental rogue waves arising at different times and spatial positions and forming interesting patterns.

424 citations


Cites background from "The Peregrine soliton in nonlinear ..."

  • ...Recently, an optical analogue of rogue waves — optical rogue waves, was observed in optical fibres [1, 2]....

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References
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Journal ArticleDOI
04 Oct 2006
TL;DR: In this paper, a review of numerical and experimental studies of supercontinuum generation in photonic crystal fiber is presented over the full range of experimentally reported parameters, from the femtosecond to the continuous-wave regime.
Abstract: A topical review of numerical and experimental studies of supercontinuum generation in photonic crystal fiber is presented over the full range of experimentally reported parameters, from the femtosecond to the continuous-wave regime. Results from numerical simulations are used to discuss the temporal and spectral characteristics of the supercontinuum, and to interpret the physics of the underlying spectral broadening processes. Particular attention is given to the case of supercontinuum generation seeded by femtosecond pulses in the anomalous group velocity dispersion regime of photonic crystal fiber, where the processes of soliton fission, stimulated Raman scattering, and dispersive wave generation are reviewed in detail. The corresponding intensity and phase stability properties of the supercontinuum spectra generated under different conditions are also discussed.

3,361 citations

Journal ArticleDOI
13 Dec 2007-Nature
TL;DR: This work reports the observation of rogue waves in an optical system, based on a microstructured optical fibre, near the threshold of soliton-fission supercontinuum generation—a noise-sensitive nonlinear process in which extremely broadband radiation is generated from a narrowband input.
Abstract: Recent observations show that the probability of encountering an extremely large rogue wave in the open ocean is much larger than expected from ordinary wave-amplitude statistics. Although considerable effort has been directed towards understanding the physics behind these mysterious and potentially destructive events, the complete picture remains uncertain. Furthermore, rogue waves have not yet been observed in other physical systems. Here, we introduce the concept of optical rogue waves, a counterpart of the infamous rare water waves. Using a new real-time detection technique, we study a system that exposes extremely steep, large waves as rare outcomes from an almost identically prepared initial population of waves. Specifically, we report the observation of rogue waves in an optical system, based on a microstructured optical fibre, near the threshold of soliton-fission supercontinuum generation--a noise-sensitive nonlinear process in which extremely broadband radiation is generated from a narrowband input. We model the generation of these rogue waves using the generalized nonlinear Schrodinger equation and demonstrate that they arise infrequently from initially smooth pulses owing to power transfer seeded by a small noise perturbation.

2,173 citations


"The Peregrine soliton in nonlinear ..." refers methods in this paper

  • ...We anticipate applications in establishing links between optical and hydrodynamic extreme event...

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Journal ArticleDOI
TL;DR: In this paper, a theoretical analysis of the stability of periodic wave trains to small disturbances in the form of a pair of side-band modes is presented, where the wave train becomes highly irregular far from its origin, even when the departures from periodicity are scarcely detectable at the start.
Abstract: The phenomenon in question arises when a periodic progressive wave train with fundamental frequency ω is formed on deep water—say by radiation from an oscillating paddle—and there are also present residual wave motions at adjacent side-band frequencies ω(1 ± δ), such as would be generated if the movement of the paddle suffered a slight modulation at low frequency. In consequence of coupling through the non-linear boundary conditions at the free surface, energy is then transferred from the primary motion to the side bands at a rate that, as will be shown herein, can increase exponentially as the interaction proceeds. The result is that the wave train becomes highly irregular far from its origin, even when the departures from periodicity are scarcely detectable at the start.In this paper a theoretical investigation is made into the stability of periodic wave trains to small disturbances in the form of a pair of side-band modes, and Part 2 which will follow is an account of some experimental observations in accord with the present predictions. The main conclusion of the theory is that infinitesimal disturbances of the type considered will undergo unbounded magnification if \[ 0 < \delta \leqslant (\sqrt{2})ka, \] where k and a are the fundamental wave-number and amplitude of the perturbed wave train. The asymptotic rate of growth is a maximum for δ = ka.

2,109 citations

Journal ArticleDOI
TL;DR: In this article, a number of ases in which these equations reduce to a one dimensional nonlinear Schrodinger (NLS) equation are enumerated, and several analytical solutions of NLS equations are presented, with discussion of their implications for describing the propagation of water waves.
Abstract: Equations governing modulations of weakly nonlinear water waves are described. The modulations are coupled with wave-induced mean flows except in the case of water deeper than the modulation length scale. Equations suitable for water depths of the order the modulation length scale are deduced from those derived by Davey and Stewartson [5] and Dysthe [6]. A number of ases in which these equations reduce to a one dimensional nonlinear Schrodinger (NLS) equation are enumerated.Several analytical solutions of NLS equations are presented, with discussion of some of their implications for describing the propagation of water waves. Some of the solutions have not been presented in detail, or in convenient form before. One is new, a “rational” solution describing an “amplitude peak” which is isolated in space-time. Ma's [13] soli ton is particularly relevant to the recurrence of uniform wave trains in the experiment of Lake et al.[10].In further discussion it is pointed out that although water waves are unstable to three-dimensional disturbances, an effective description of weakly nonlinear two-dimensional waves would be a useful step towards describing ocean wave propagation.

1,318 citations

Book
01 Jan 1997
TL;DR: In this article, the influence of higher-order dispersion on solitons was studied in the presence of gain, loss, and spectral filtering in a birefringent media.
Abstract: Basic equations. The nonlinear Schroedinger equation. Exact solutions. Non-Kerr-law nonlinearities. Normal dispersion regime. Multiple-port linear devices made from solitons. Nonlinear pulses in birefringent media. Pulses in nonlinear couplers. Multi-core nonlinear fiber arrays. The influence of higher-order dispersion on solitons. Beam dynamics. Planar nonlinear guided waves. Nonlinear pulses in presence of gain, loss and spectral filtering. References. Index.

1,030 citations