Fermi-Pasta-Ulam Recurrence in Nonlinear Fiber Optics: The Role of Reversible and Irreversible Losses

Mussot, Arnaud; Kudlinski, Alexandre; Droques, Maxime; Szriftgiser, Pascal; Akhmediev, Nail

doi:10.1103/physrevx.4.011054

Cited by 65 publications

(76 citation statements)

References 34 publications

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“…Contrary to the so-called cutback technique [32,[43][44][45], the technique used here (and similar for example to the one used in [31]) allows to explore various normalized propagation lengths with only one optical fiber having a fixed length. The key point is to adjust the spectral width and the optical power in order to change proportionally the number of linear lengths and of nonlinear lengths experienced by the waves.…”

Section: B the Optical Experimentsmentioning

confidence: 99%

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Spontaneous emergence of rogue waves in partially coherent waves: A quantitative experimental comparison between hydrodynamics and optics

et al. 2018

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Rogue waves are extreme and rare fluctuations of the wave field that have been discussed in many physical systems. Their presence substantially influences the statistical properties of an incoherent wave field. Their understanding is fundamental for the design of ships and offshore platforms. Except for very particular meteorological conditions, waves in the ocean are characterised by the so-called JONSWAP (Joint North Sea Wave Project) spectrum. Here we compare two unique experimental results: the first one has been performed in a 270-meter wave tank and the other in optical fibers. In both cases, waves characterised by a JONSWAP spectrum and random Fourier phases have been launched at the input of the experimental device. The quantitative comparison, based on an appropriate scaling of the two experiments, shows a very good agreement between the statistics in hydrodynamics and optics. Spontaneous emergence of heavy tails in the probability density function of the wave amplitude is observed in both systems. The results demonstrate the universal features of rogue waves and provide a fundamental and explicit bridge between two important fields of research. Numerical simulations are also compared with experimental results.

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Section: B the Optical Experimentsmentioning

confidence: 99%

“…In particular this allowed us to study the statistics as a function of the propagation distance without the use of the so-called "cut-back" technique [32,[43][44][45].…”

Section: Introductionmentioning

confidence: 99%

Spontaneous emergence of rogue waves in partially coherent waves: A quantitative experimental comparison between hydrodynamics and optics

et al. 2018

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“…After several decades of research and a plethora of works, see for instance Ref. [22][23][24][25][26][27][28], the question concerning the energy sharing mechanism in a chain of nonlinear oscillators, and, therefore, in a many-body system, can be considered still an open question. Furthermore, in references [17][18][19] the energy flow in a linear chain of interacting rotating dipoles and in a two-dipole system are explored.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the classical phase space and energy transfer for two rotating dipoles with and without external electric field

González‐Férez¹,

Iñarrea²,

Salas³

et al. 2017

Phys. Rev. E

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We explore the classical dynamics of two interacting rotating dipoles that are fixed in the space and exposed to an external homogeneous electric field. Kinetic energy transfer mechanisms between the dipoles are investigated varying both the amount of initial excess kinetic energy of one of them and the strength of the electric field. In the field-free case, and depending on the initial excess energy an abrupt transition between equipartition and non-equipartition regimes is encountered.The study of the phase space structure of the system as well as the formulation of the Hamiltonian in an appropriate coordinate frame provide a thorough understanding of this sharp transition.When the electric field is turned on, the kinetic energy transfer mechanism is significantly more complex and the system goes through different regimes of equipartition and non-equipartition of the energy including chaotic behavior.

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“…The first experimental demonstration in optical fibers of the FPU recurrence was presented by Van Simaeys et al [12] showing that the dynamics of optical fields in the region of small third dispersion is described with a good accuracy by the NLSE and connected with modulation instability (MI). For current experimental situation, see [13] and references therein.The main aim of this paper is to explain how the recurrence phenomenon appears within the one-dimensional NLSE iψ t + ψ xx + 2|ψ| 2 ψ = 0.It is well-known that in many physical applications this equation can be derived from the averaging of the equations of motion for solutions in the form of quasimonochromatic waves in a weakly nonlinear regime (see, e.g. [23]).…”

mentioning

confidence: 99%

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confidence: 99%

Fermi–Pasta–Ulam recurrence and modulation instability

Kuznetsov

2017

Jetp Lett.

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We give a qualitative explanation of the analog of the Fermi-Pasta-Ulam (FPU) recurrence in a one-dimensional focusing nonlinear Schrodinger equation (NLSE). That recurrence can be considered as a result of the nonlinear development of modulation instability. All known exact localized solitonstype solutions describing propagation on the background of the modulationally unstable condensate show the recurrence to the condensate state after its interaction with solitons. The condensate state locally recovers its original form with the same amplitude but a different phase after soliton leave its initial region. This is the analog of the FPU recurrence for the NLSE. Based on the integrability of the NLSE, we demonstrate that the FPU recurrence takes place not only for condensate but for more general solution in the form of the cnoidal wave. This solution is periodic in space and can be represented as a solitonic lattice. That lattice reduces to isolated soliton solution in the limit of large distance between solitons. The lattice transforms into the condensate in the opposite limit of dense soliton packing. The cnoidal wave is also modulationally unstable due to soliton overlapping. This instability at the linear stage does not provide the cnoidal wave recurrence. The recurrence happens at the nonlinear stage of the modulation instability. From the practical point of view the latter property is very important, especially for the fiber communication systems which use soliton as an information carrier.1. The phenomenon of recurrence in nonlinear systems with many degrees of freedom was first observed in numerical experiment by Fermi, Pasta and Ulam [1] in 1954. The idea of Fermi was to address how randomization due to the nonlinear interaction leads to the energy equipartition between large number of degrees of freedom in the mechanical chain. The chain in [1] had a quadratic nonlinearity and included 64 oscillators supplemented with long-wave initial conditions. Instead of the energy equipartition, numerical experiments showed that after a finite time a recurrence to the initial data was achieved accompanied by a quasi-periodic energy exchange between several initially exited modes. That recurrence phenomenon became known as the Fermi-PastaUlam (FPU) problem and has been one of the most attractive subjects for numerous investigations. Later, mainly by efforts of N. Zabusky, these results were reproduced by means of more powerful computers. Besides, there were observed many other peculiarities in this problem (for details, see the original papers by Zabusky Since the discovery of the Inverse Scattering Transform (IST), which was first applied to the KDV equation by Gardner, Greene, Kruskal and Miura [5], and later to the nonlinear Schrodinger equation (NLSE) by Zakharov and Shabat [6], many aspects of the FPU recurrence became more clear. In 1971 Zakharov and Faddeev [7] proved that the KDV equation, which, in particular, can be obtained from the FPU system in the continuous limit for waves propagated in one direction...

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Fermi-Pasta-Ulam Recurrence in Nonlinear Fiber Optics: The Role of Reversible and Irreversible Losses

Cited by 65 publications

References 34 publications

Spontaneous emergence of rogue waves in partially coherent waves: A quantitative experimental comparison between hydrodynamics and optics

Spontaneous emergence of rogue waves in partially coherent waves: A quantitative experimental comparison between hydrodynamics and optics

Analysis of the classical phase space and energy transfer for two rotating dipoles with and without external electric field

Fermi–Pasta–Ulam recurrence and modulation instability

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