Extreme events in optics: Challenges of the MANUREVA project

Dudley, John M.; Finot, Christophe; Millot, Guy; Garnier, Josselin; Genty, Goëry; Агафонцев, Д. С.; Dias, Frédéric

doi:10.1140/epjst/e2010-01243-x

Cited by 33 publications

(26 citation statements)

References 61 publications

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“…Following the pioneering work of Solli and coworkers [1] that have reported the observation of statistics analogous to hydrodynamic rogue waves in the formation of optical supercontinuum, most of the initial works have focused on the passive propagation of picosecond pulses in photonic crystal fibers [2]. Those different studies carried out in the anomalous dispersion regime have highlighted the specific role played by modulation instability, Akhmediev breathers [3,4] as well as Raman frequency shifted solitons that are also affected by third-order dispersion and resulting pulse-to-pulse interactions [5,6].…”

Section: Introductionmentioning

confidence: 99%

Experimental signatures of extreme optical fluctuations in lumped Raman fiber amplifiers

Hammani

Finot

2012

Optical Fiber Technology

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Abstract:In this work, we experimentally investigate several temporal and spectral methods to highlight extreme fluctuations which can develop during the Raman amplification of an ultrashort pulse train. Forward and backward pumping schemes are compared to dual pass configurations.Keywords: Fiber optics; Raman amplifiers; extreme statistics 2 IntroductionThe study of extreme statistics in nonlinear fiber optics is a topic that has recently stimulated much attention. Following the pioneering work of Solli and coworkers [1] that have reported the observation of statistics analogous to hydrodynamic rogue waves in the formation of optical supercontinuum, most of the initial works have focused on the passive propagation of picosecond pulses in photonic crystal fibers [2]. Those different studies carried out in the anomalous dispersion regime have highlighted the specific role played by modulation instability, Akhmediev breathers [3,4] as well as Raman frequency shifted solitons that are also affected by third-order dispersion and resulting pulse-to-pulse interactions [5,6]. However, observation of statistics that strongly deviate from a Gaussian distribution is absolutely not restricted to supercontinuum generation and can also be observed in telecommunication applications in the context of transmissions [7][8][9], Raman fiber lasers [10,11] as well as discrete amplification [12,13]. More precisely, in this latest field, it has been shown that under certain conditions, statistical distribution of an amplified signal can be strongly reshaped during the amplification process.Examples of this deleterious degradation have been discussed for parametric amplifiers [12,14,15] and for Raman amplifiers [13,16,17]: in both cases, a quasi-instantaneous gain and a low walk-off between the signal and a partially coherent pump lead to a dramatic transfer of fluctuations from the pump to the signal in a co-propagating configuration. In a previous work,we have numerically and analytically described the evolution of a continuous signal in a copropagating amplifier in the presence of a low walk-off and pump depletion [17]. We have also Experimental SetupOur experimental setup is sketched in Fig. 1a. An actively mode-locked erbium-doped fiber laser delivers a train of 2.9 ps pulses at a repetition rate of 10 GHz and with an initial average power of 10 mW (corresponding to a peak power of ~300 mW) at a wavelength of 1550 nm. Let us note that our previous works [13,16] or [19] involved much lower repetition rates as the signal source was a MHz passively mode-locked fiber laser. The pump is delivered by a Raman continuous wave fiber laser centered at 1455 nm with an average power up to 2 W. An essential point is that this pump is a partially incoherent wave (~20 GHz of spectral width) that exhibits high contrast, fast intensity fluctuations [19]. Indeed, its intensity autocorrelation signal (plotted in Fig. 1b) presents a characteristic contrast of one half [13,20] with a temporal width of 25 ps. This temporal duration is a characteristi...

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Section: Introductionmentioning

confidence: 99%

Experimental signatures of extreme optical fluctuations in lumped Raman fiber amplifiers

Hammani

Finot

2012

Optical Fiber Technology

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“…However a direct correspondence between nonlinear optics and hydrodynamics is provided by the one-dimensional nonlinear Schrödinger equation (1D-NLSE) (see Eq. (1)) that describes various wave systems [6,18]. In particular, the focusing 1D-NLSE describes at leading order the physics of deep-water wave trains and it plays a central role in the study of RW [6-8, 18, 19].…”

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Optical Rogue Waves in Integrable Turbulence

2015

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We report optical fiber experiments allowing to investigate integrable turbulence in the focusing regime of the one dimensional nonlinear Schrödinger equation (1D-NLSE). Our experiments are very similar in their principle to water tank experiments with random initial conditions (see M. Onorato et al. Phys. Rev. E 70 067302 (2004)). Using an original optical sampling setup, we measure precisely the probability density function (PDF) of optical power of partially coherent waves rapidly fluctuating with time. The PDF is found to evolve from the normal law to a strong heavy-tailed distribution, thus revealing the formation of rogue waves in integrable turbulence. Numerical simulations of 1D-NLSE with stochastic initial conditions reproduce quantitatively the experiments. Our investigations suggest that the statistical features experimentally observed rely on the stochastic generation of coherent analytic solutions of 1D-NLSE such as Peregrine solitons.The field of nonlinear optics has recently grown as a favorable laboratory to investigate both statistical properties of nonlinear random waves and hydrodynamic-like phenomena [1][2][3]. In particular, several recent works point out analogies between hydrodynamics and nonlinear fiber optics in the observation of supercontinuum generation [4], undular bores [2], optical turbulence, laminarturbulent transition [1] or oceanographic rogue waves (RW) [5,6].Rogue waves (RW), also called freak waves, are extremely large amplitude waves occurring more frequently than expected from the normal law [7,8] As stressed out in the recent review [6], there is no obvious analogy between most of the optical experiments on extreme events and oceanography. However a direct correspondence between nonlinear optics and hydrodynamics is provided by the one-dimensional nonlinear Schrödinger equation (1D-NLSE) (see Eq. (1)) that describes various wave systems [6,18]. In particular, the focusing 1D-NLSE describes at leading order the physics of deep-water wave trains and it plays a central role in the study of RW [6-8, 18, 19].Modulational instability (MI) is believed to be a fundamental mechanism for the formation of RW [8,20]. Moreover, analytical solutions of the integrable 1D-NLSE such a Akhmediev breathers (AB), Peregrine solitons or Kuznetsov-Ma solitons (KMs) are now considered as possible prototypes of RW [19,[21][22][23]. These coherent structures have been generated from very specific, carefullydesigned coherent initial conditions in optical fiber experiments [21,23,24].On the contrary, oceanic RW emerge from the interplay of incoherent waves in turbulent systems. The occurrence of RW in wave turbulence has been theoretically studied in optics [25,26] and in hydrodynamics [27]. In hydrodynamical experiments made with one-dimensional water tanks, non gaussian statistics of the wave height has been found to emerge from random initial conditions [20,28].The appropriate theoretical framework combining a statistical approach of random waves together with the 1D-NLSE is integrable turbulence...

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“…Recently, it is demonstrated that the Peregrine rogue wave spectrum in the standard NLSE features a triangular shape and gets dramatically broadened at the maximally-compressed peak, which is corresponding to the onset of supercontinuum generation [27][28][29][30]. Thus, it is meaningful to study the spectral property of the transition between the Peregrine rogue wave and the w-shaped traveling wave.…”

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State transition induced by higher-order effects and background frequency

et al. 2015

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State transition between the Peregrine rogue wave and w-shaped traveling wave induced by higherorder effects and background frequency is studied. We find that this intriguing transition, described by an exact explicit rational solution, is consistent with the modulation instability (MI) analysis that involves MI region and stability region in low perturbation frequency region. In particular, the link between the MI growth rate and transition characteristic analytically demonstrates that, the size characteristic of transition is positively associated with the reciprocal of zero-frequency growth rate. Further, we investigate the case for nonlinear interplay of multi-localized waves. It is interesting that the interaction of second-order waves in stability region features a line structure, rather than an elastic interaction between two w-shaped traveling waves. [7,8] of weakly modulated plane wave. More specifically, rogue waves exist only in the MI subregion where the instability frequency band is close to the vanishing frequency [9]. In this regard, rogue wave has a consistent structure in the standard nonlinear Schrödinger equation (NLSE) where the MI characteristic remains invariant in nature. Nevertheless, the MI often exhibits some interesting features when the additional physical effects are taken into consideration, such as cross-phase modulation [10, 11], higher-order perturbation terms [12], etc. Thus, it is important to study the rogue wave property induced by the features of MI growth rate distribution.Recent studies demonstrate that rogue wave can exhibit structural diversity beyond the reach of the standard NLSE in presence of higher-order effects [13][14][15][16][17][18][19][20][21][22][23][24]. However, to our knowledge, less attention has been paid to analyzing rogue wave property in combination with the distribution characteristic of corresponding MI growth rate. Here we find that, with some higher-order perturbation terms (the third-order dispersion and delayed nonlinear response term), the MI growth rate shows a non-uniform distribution characteristic in low perturbation frequency region, in particular, it opens up a stability region as background frequency changes (see Fig. 1). Thus we anticipate that there will be some interesting physical properties as a rogue wave evolves and approaches the stability region.As a starting point, we address the problem via a completely integrable higher-order NLSE-the Hirota equa- * Electronic address: zyyang@nwu.edu.cn † Electronic address: zhaolichen3@163.com tion (HE) [25]-which involves the higher-order perturbation effects. In dimensionless form, the HE readswhere z is the propagation variable, t is the retarded time in a moving frame with the group velocity, and E(t, z) is the slowly varying envelope of the wave field. The real parameter β is introduced to be responsible for the thirdorder dispersion and delayed nonlinear response term, respectively. If β = 0, it reduces to the standard NLSE. The existence of rogue waves in the HE has been recently dem...

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Extreme events in optics: Challenges of the MANUREVA project

Cited by 33 publications

References 61 publications

Experimental signatures of extreme optical fluctuations in lumped Raman fiber amplifiers

Experimental signatures of extreme optical fluctuations in lumped Raman fiber amplifiers

Optical Rogue Waves in Integrable Turbulence

State transition induced by higher-order effects and background frequency

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