Fluctuations and correlations in modulation instability

Solli, Daniel R.; Herink, Georg; Jalali, Bahram; Ropers, Claus

doi:10.1038/nphoton.2012.126

Cited by 204 publications

(176 citation statements)

References 34 publications

Supporting

Mentioning

172

Contrasting

Unclassified

Order By: Relevance

“…In spatial experiments, the speckle fields are localized [45,46] and the dynamics of random waves is confined in a way comparable to the one found in pulsed experiments [47]. Our experiments with "non-decaying" continuous waves widen the perspective by providing new information about nonlinear interactions among unbounded random waves in integrable turbulence.…”

Section: B)supporting

confidence: 56%

Optical Rogue Waves in Integrable Turbulence

2015

View full text Add to dashboard Cite

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...

show abstract

Section: B)supporting

confidence: 56%

Optical Rogue Waves in Integrable Turbulence

2015

View full text Add to dashboard Cite

show abstract

“…We investigated the coherence of the PI gain lobes based on the statistical analysis of spectral correlations [2]. The background-free correlations of the first Stokes region (0.9 THz) for different PC states are shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…Here, we demonstrate a new pattern formation process in partially mode-locked fiber laser (PML), where the laser redistributes its energy from center wavelength to sidebands through parametric instability (PI), and subsequently longitudinal modes are populated via cascaded four-wave-mixing (FWM). We find that the PI, which exhibits great fluctuations when it is spontaneously grown from noise in conservative systems [2], may possess a high degree of coherence in dissipative laser system with gain, and quasi-periodic cooperative and competitive cascade FWM-activated mode interactions are obtained. The polarization of each filtered wavelength of PML tends to dithering/vibrating, indicating that the well-defined state of polarization (SOP) of conventional dissipative solitons is also broken in PML.…”

Section: Introductionmentioning

confidence: 90%

“…Stochastically driven nonlinear processes limit the number of amplified modes in a natural system due to competitive mode interaction, which is accompanied by loss of coherence when increasing the complexity of system [1][2][3]. Here, we demonstrate a new pattern formation process in partially mode-locked fiber laser (PML), where the laser redistributes its energy from center wavelength to sidebands through parametric instability (PI), and subsequently longitudinal modes are populated via cascaded four-wave-mixing (FWM).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Coherence manipulation of partially mode-locked fiber laser

Zhu

Gao

Wabnitz

et al. 2016

The 8th International Symposium on Ultrafast Phenomena and Terahertz Waves

View full text Add to dashboard Cite

show abstract

“…Solli and co-workers are currently exploring modulational instability, a nonlinear phenomenon that is ubiquitous in nature and can influence the shapes of sand ripples, cloud formations and heart rhythms and play an important role in the generation of broadband optical supercontinuua 8 .…”

mentioning

confidence: 99%

The power of analogies

2013

Nature Photon

View full text Add to dashboard Cite

editorialAs one would expect, Nature Photonics strives to publish findings that represent important conceptual insights or technological advances in the field of optics. However, we have also been publishing studies in which photonics proves to be a useful platform for mimicking and gaining a better understanding of other physical systems, such as those found in astrophysics and hydrodynamics.Photonics is particularly suitable for such studies as it can often allow largescale, highly inaccessible and rare events in the natural world to be recreated on demand and explored on a lab bench using modest equipment. For example, optical metamaterials can now be engineered to behave in an analogous fashion to black holes 1 and gravitational lensing has recently been mimicked on an optical polymer chip 2 . Furthermore, fibre optics is being extensively used to generate and explore complex nonlinear wave phenomena found in fluid flows, including turbulence 3 , rogue waves 4 , modulational instability 5 , solitons 6 and chaos 7 ."Research in optics is interesting in its own right, but it also has the potential to model other systems on a table-top scale and under ambient conditions, " comments Daniel Solli, an expert in nonlinear systems from the University of California at Los Angeles in the USA and the University of Göttingen in Germany. "The timescales of optical experiments are also often short, and by employing devices such as megahertz-rate mode-locked lasers it is possible accumulate large data sets in a short period of time. "Solli says that photonics experiments have helped explain the origin of rogue waveslarge freak waves that occasionally occur in the ocean. "We've narrowed it down to a set of specific input noise conditions, and made measurements that would never have been possible in hydrodynamics. "Solli points out another benefit of photonics -the very high level of control it offers. For example, it is possible to tailor the frequency, shape, strength, duration and timing of light pulses. Optical measurement technologies are also well developed in optics, with a plethora of high-performance instruments available. They include ultrafast, highly sensitive detectors and high-resolution spectrum analysers, which make it possible to capture single-shot dynamics and collect a wealth of information.Solli and co-workers are currently exploring modulational instability, a nonlinear phenomenon that is ubiquitous in nature and can influence the shapes of sand ripples, cloud formations and heart rhythms and play an important role in the generation of broadband optical supercontinuua 8 .Dentcho Genov at Louisiana Tech University in the USA is another researcher who has been using photonics to model physical systems. He uses unique optical structures (in particular, custom-designed metamaterials and microstructured waveguides) to mimic astrophysical phenomena such as celestial mechanics, Einstein's field equations, gravitational lensing and the event horizons of black holes.Genov explains that an equivalence exists betw...

show abstract

Fluctuations and correlations in modulation instability

Cited by 204 publications

References 34 publications

Optical Rogue Waves in Integrable Turbulence

Optical Rogue Waves in Integrable Turbulence

Coherence manipulation of partially mode-locked fiber laser

The power of analogies

Contact Info

Product

Resources

About