Rogue Breather Structures in Nonlinear Systems with an Emphasis on Optical Fibers as Testbeds

Kibler, Bertrand

doi:10.1002/9781119088134.ch10

Cited by 5 publications

(9 citation statements)

References 84 publications

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“…The nonlinear spectral analysis of the SFB observed both in the optical fiber experiment and in the water tank experiment reveals that they represent general genus 4 solutions of the 1D-NLSE that may exhibit a space-time evolution that is much more complex than a simpler degenerate genus 2 solution like PS or ABs, as shown in the recent experiments reported in ref. [82,84,85]. Moreover, nonlinear spectral analysis reveals that the spectrum of the observed SFB slowly changes with the propagation distance, thus confirming a clear evidence of the influence of perturbative higher order effects like dissipation in the experiments [86,87].…”

Section: Discussionmentioning

confidence: 54%

“…[80] and [83]. Such observations are also known to be related to the phenomenon of higher modulation instability recently observed in optics and in hydrodynamics [82,[84][85][86], wherein non-ideal excitation of first-order breathers (ABs, PS...) or propagation losses were identified as perturbations that introduce deviations from the expected nonlinear dynamics on longer propagation distances (simply due the unstable nature of NLS breathers). In particular, it was shown that higher order modulation instability arises from perturbations on breathers close to the PS limit, thus resulting in a nonlinear superposition (i.e., complex arrangement) of several elementary breathers.…”

Section: Nonlinear Spectral Analysis Of the Peregrine Soliton Obmentioning

confidence: 83%

“…The impact of an asymetric initial excitation of ABs has been analyzed in Refs. [24,81,82]. We note that exact analytical description of the formation of ABs and related structures in the initial value problem (1), (12) was also developed in the recent work [49] using the finite-gap theory.…”

Section: Nonlinear Spectral Analysis Of the Peregrine Soliton Obmentioning

confidence: 93%

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Nonlinear spectral analysis of Peregrine solitons observed in optics and in hydrodynamic experiments

et al. 2018

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The data recorded in optical fiber and in hydrodynamic experiments reported the pioneering observation of nonlinear waves with spatiotemporal localization similar to the Peregrine soliton are examined by using nonlinear spectral analysis. Our approach is based on the integrable nature of the one-dimensional focusing nonlinear Schrödinger equation (1D-NLSE) that governs at leading order the propagation of the optical and hydrodynamic waves in the two experiments. Nonlinear spectral analysis provides certain spectral portraits of the analyzed structures that are composed of bands lying in the complex plane. The spectral portraits can be interpreted within the framework of the so-called finite gap theory (or periodic inverse scattering transform). In particular, the number N of bands composing the nonlinear spectrum determines the genus g=N-1 of the solution that can be viewed as a measure of complexity of the space-time evolution of the considered solution. Within this setting the ideal, rational Peregrine soliton represents a special, degenerate genus 2 solution. While the fitting procedures previously employed show that the experimentally observed structures are quite well approximated by the Peregrine solitons, nonlinear spectral analysis of the breathers observed both in the optical fiber and in the water tank experiments reveals that they exhibit spectral portraits associated with more general, genus 4 finite-gap NLSE solutions. Moreover, the nonlinear spectral analysis shows that the nonlinear spectrum of the breathers observed in the experiments slowly changes with the propagation distance, thus confirming the influence of unavoidable perturbative higher-order effects or dissipation in the experiments.

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Section: Discussionmentioning

confidence: 54%

Section: Nonlinear Spectral Analysis Of the Peregrine Soliton Obmentioning

confidence: 83%

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Nonlinear spectral analysis of Peregrine solitons observed in optics and in hydrodynamic experiments

et al. 2018

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“…The two evolution scenarios are determined solely by the input relative phase of the MI sidebands and are characterized by successive shifted versus unshifted temporal patterns at the points of maximum compression, respectively [5]. To this end, using an ultra-low loss optical fiber appears the most natural choice since it is known from the numerics [15] and experiments [16] that too large linear losses have the detrimental effect to induce all evolutions to become of the shifted type, regardless of the initial condition. Nevertheless, due to the long fiber span considered here, even the residual ultra-low losses are critical thereby requiring adequate compensation.…”

Section: Introductionmentioning

confidence: 99%

Observation of four Fermi-Pasta-Ulam-Tsingou recurrences in an ultra-low-loss optical fiber

Vanderhaegen¹,

Szriftgiser²,

Kudlinski³

et al. 2020

Opt. Express

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“…For this reason it is an appropriate advantageous formulation in the case where we aim to rely just on one point measurement (over time) in order to predict the occurrence of a rogue wave downstream of the wave propagation. We emphasize that the proposed time-domain analysis and prediction can be also applied to electromagnetic waves [46].…”

Section: Evolution Of Isolated Localized Groupsmentioning

confidence: 99%

Predicting ocean rogue waves from point measurements: An experimental study for unidirectional waves

et al. 2019

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Rogue waves are strong localizations of the wave field that can develop in different branches of physics and engineering such as water or electromagnetic waves. Here, we experimentally quantify the prediction potentials of a comprehensive rogue-wave reduced-order precursors tool that has been recently developed to predict extreme events due to spatially localized modulation instability. The laboratory tests have been conducted in two different water wave facilities and they involve unidirectional water waves; in both cases we show that the deterministic and spontaneous emergence of extreme events is well-predicted through the reported scheme. Due to the interdisciplinary character of the approach, similar studies may be motivated in other nonlinear dispersive media, such nonlinear optics, plasma and solids governed by similar equations allowing the early stage of extreme wave detection.

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Rogue Breather Structures in Nonlinear Systems with an Emphasis on Optical Fibers as Testbeds

Cited by 5 publications

References 84 publications

Nonlinear spectral analysis of Peregrine solitons observed in optics and in hydrodynamic experiments

Nonlinear spectral analysis of Peregrine solitons observed in optics and in hydrodynamic experiments

Observation of four Fermi-Pasta-Ulam-Tsingou recurrences in an ultra-low-loss optical fiber

Predicting ocean rogue waves from point measurements: An experimental study for unidirectional waves

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