Granularity and Inhomogeneity Are the Joint Generators of Optical Rogue Waves

Arecchi, F. T.; Bortolozzo, U.; Montina, Alberto; Residori, Stefania

doi:10.1103/physrevlett.106.153901

Cited by 163 publications

(128 citation statements)

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“…Conversely, if randomness mostly arises from the initial field, linear and nonlinear effects occurring inside the propagation medium interplay to modify the statistical properties of the incoherent wave launched as initial condition. This process, extensively studied during the past years, may result in the formation of extreme or rogue waves [2][3][4][5].In this context, the nonlinear Schrödinger equation (NLSE) plays a special role because it provides a universal model that rules the dynamics of many nonlinear wave systems. In the fields of oceanography and laser filamentation, numerical simulations of the NLSE with random initial conditions have been made in 2 þ 1 dimensions to study the emergence of rogue waves [6][7][8].…”

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confidence: 99%

Intermittency in Integrable Turbulence

et al. 2014

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We examine the statistical properties of nonlinear random waves that are ruled by the one-dimensional defocusing and integrable nonlinear Schrödinger equation. Using fast detection techniques in an optical fiber experiment, we observe that the probability density function of light fluctuations is characterized by tails that are lower than those predicted by a Gaussian distribution. Moreover, by applying a bandpass frequency optical filter, we reveal the phenomenon of intermittency; i.e., small scales are characterized by large heavy-tailed deviations from Gaussian statistics, while the large ones are almost Gaussian. These phenomena are very well described by numerical simulations of the one-dimensional nonlinear Schrödinger equation. DOI: 10.1103/PhysRevLett.113.113902 PACS numbers: 42.65.Sf, 05.45.-a The way through which nonlinearity and randomness interplay to influence the propagation of waves is of major interest in various fields of investigation, such as, e.g., hydrodynamics, wave turbulence, optics, or condensedmatter physics. If the spatiotemporal dynamics of the wave system is predominantly influenced by some disorder found inside the nonlinear medium, localized eigenmodes may emerge through the process of Anderson localization [1]. Conversely, if randomness mostly arises from the initial field, linear and nonlinear effects occurring inside the propagation medium interplay to modify the statistical properties of the incoherent wave launched as initial condition. This process, extensively studied during the past years, may result in the formation of extreme or rogue waves [2][3][4][5].In this context, the nonlinear Schrödinger equation (NLSE) plays a special role because it provides a universal model that rules the dynamics of many nonlinear wave systems. In the fields of oceanography and laser filamentation, numerical simulations of the NLSE with random initial conditions have been made in 2 þ 1 dimensions to study the emergence of rogue waves [6][7][8]. In the context of nonlinear fiber optics, the propagation of incoherent waves is often treated in 1 þ 1 dimensions from generalized NLSEs including high-order linear and nonlinear terms [2,[9][10][11]. Wave turbulence (WT) theory provides an appropriate framework for the statistical treatment of the interaction of random nonlinear waves that are described by these nonintegrable equations [12].If third-order nonlinearity and second-order (linear) dispersion dominate other physical effects in a onedimensional medium, wave propagation is ruled by the 1D NLSE, which is an integrable equation. In the focusing regime, the 1D NLSE possesses soliton and breather solutions that have been recently observed in various physical systems [13][14][15]. Considering a random input field, these breather solutions may exist embedded in random waves, thus behaving as prototypes of rogue waves that modify the statistical properties of the random input field [16,17]. In the defocusing regime, the 1D NLSE has dark or gray soliton solutions. These solutions have also bee...

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confidence: 99%

Intermittency in Integrable Turbulence

et al. 2014

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“…Since then, optical rogue waves have been observed in several systems [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], and their study has advanced the research in the field, in a way that has been compared to the introduction of optical systems to study chaos in the 1980s [26].…”

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Rogue waves in optically injected lasers: Origin, predictability, and suppression

et al. 2013

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Rogue waves are devastating extreme events that occur in many natural systems, and a lot of work has focused on predicting and understanding their origin. In optically injected semiconductor lasers rogue waves are rare ultra-high pulses that sporadically occur in the laser chaotic output intensity. Here we show that these optical rogue waves can be predicted with long anticipation time, that they are generated by a crisis-like process, and that noise can be employed to either enhance or suppress their probability of occurrence. By providing a good understanding of the mechanisms triggering and controlling the rogue waves, our results can contribute to improve the performance of injected lasers and can also enable new experiments to test if these mechanisms are also involved in other natural systems where rogue waves have been observed. Extreme events are often catastrophic ones, such as tsunamis, earthquakes, supernovas, stock market crashes, etc. [1][2][3][4][5]. Ocean rogue waves, also referred to as freak waves, are several times the average height of surrounding waves and have steep, fast rising, and fast falling sides, like "a wall of water" [6][7][8][9]. They are a topic of intensive research as they can develop suddenly even in calm and apparently safe seas and have been responsible for several boat accidents, representing a major challenge for the design of off-shore platforms for the oil and gas industry.In optics, Solli et al.[10] have shown that extremely broadband radiation can be generated from a narrow-band input, with a long-tailed distribution similar to that of ocean rogue waves. Since then, optical rogue waves have been observed in several systems [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], and their study has advanced the research in the field, in a way that has been compared to the introduction of optical systems to study chaos in the 1980s [26].In lasers, rogue waves occurring in the form of giant intensity pulses capable of producing catastrophic optical damage have been observed in pump-modulated [19], Raman [20], mode-locked [21][22][23], and optically injected lasers [24]. In Ref.[24] the rogue waves were studied in the framework of a simple and deterministic model that exhibits two types of chaos: one in which rogue waves do not appear consistently and one in which they are relatively frequent [24]. Since a deterministic chaotic system possesses some correlation length, the rogue waves in the system should have some degree of predictability.Here we show, experimentally and numerically, that these optical rogue waves can indeed be predicted with a long anticipation time as compared with the laser characteristic time scales. In addition, we show that an external crisis-like process [27,28], in the form of the crossing of the attractor, developed from one fixed point, with the stable manifold of another fixed point, gives rise to an expanded attractor that supports trajectories with rogue waves. We also show that noise can be exploited for either enhancing or suppressing ...

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“…Using third 6 harmonic generation microscopy we found that our LH have a prolate spheroid shape with dimensions of 2-3 μm for the transversal semi-principal axes while the longitudinal are approximately 8-10 μm. The lattices inscribed consist of five superposed layers of 400 LH for each layer.…”

Section: Methodsmentioning

confidence: 84%

“…Since sailors are well known story makers these monster, destructive waves that were in naval folklore perhaps for thousands of years penetrated the realm of science only recently and after quantitative observations [1,2]. Since then, they seem to spring up in many other fields including optics [3][4][5][6][7], BEC and matter waves, finance, etc [8][9][10][11][12]. Unique 2 features of rogue waves, contrary to other solitary waves, are both their extreme magnitude but also their sudden appearance and disappearance.…”

Section: Ocean Rogue Waves (Rw) -Huge Solitary Waves-have For Long Trmentioning

confidence: 99%

“…Intuitively, one may link the onset of a rogue wave to a resonant interaction of two or three solitary waves that may appear in the medium. However, large amplitude events may also appear in a purely linear regime [1,2,4,6]; a typical example is the generation of caustic surfaces in wave propagation [13,14].Propagation of electrons or light in a weakly scattering medium is a well-studied classical problem related to Anderson localization and caustic formation. Recent experiments in the optical regime [15] have shown clearly both the theoretically predicted light localization features as well as the localizing role of (focusing) nonlinearity in the propagation [15][16][17][18][19][20].…”

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Extreme events in complex linear and nonlinear photonic media

Mattheakis

Pitsios

Tsironis

et al. 2016

Chaos, Solitons & Fractals

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Ocean rogue waves (RW) -huge solitary waves-have for long triggered the interest of scientists. RWs emerge in a complex environment and it is still dubious the importance of linear versus nonlinear processes. Recent works have demonstrated thatRWs appear in various other physical systems such as microwaves, nonlinear crystals, cold atoms, etc. In this work we investigate optical wave propagation in strongly scattering random lattices embedded in the bulk of transparent glasses. In the linear regime we observe the appearance of RWs that depend solely on the scattering properties of the medium. Interestingly, the addition of nonlinearity does not modify the RW statistics, while as the nonlinearities are increased multiple-filamentation and intensity clamping destroy the RW statistics. Numerical simulations agree nicely with the experimental findings and altogether prove that optical rogue waves are generated through the linear strong scattering in such complex environments.Ocean rogue or freak waves are huge waves that appear in relatively calm seas in a very unpredictable way. Numerous naval disasters leading to ship disappearance under uncertain conditions have been attributed to these waves. Since sailors are well known story makers these monster, destructive waves that were in naval folklore perhaps for thousands of years penetrated the realm of science only recently and after quantitative observations [1,2]. Since then, they seem to spring up in many other fields including optics [3][4][5][6][7], BEC and matter waves, finance, etc [8][9][10][11][12]. Unique 2 features of rogue waves, contrary to other solitary waves, are both their extreme magnitude but also their sudden appearance and disappearance. In this regard they are more similar to transient breather events than solitons. Since the onset of both necessitates the presence of some form of nonlinearity in the equation of motion describing wave propagation, it has been tacitly assumed that extreme waves are due to nonlinearity. Intuitively, one may link the onset of a rogue wave to a resonant interaction of two or three solitary waves that may appear in the medium. However, large amplitude events may also appear in a purely linear regime [1,2,4,6]; a typical example is the generation of caustic surfaces in wave propagation [13,14].Propagation of electrons or light in a weakly scattering medium is a well-studied classical problem related to Anderson localization and caustic formation. Recent experiments in the optical regime [15] have shown clearly both the theoretically predicted light localization features as well as the localizing role of (focusing) nonlinearity in the propagation [15][16][17][18][19][20]. In these experiments a small (of the order of  10 3 ) random variation of the index of refraction in the propagation leads to eventual localization while at higher powers, where nonlinearity is significant, localization is even stronger. Thus, destructive wave interference due to disorder leads to Anderson localization that may be enhanced by self-...

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Granularity and Inhomogeneity Are the Joint Generators of Optical Rogue Waves

Cited by 163 publications

References 21 publications

Intermittency in Integrable Turbulence

Intermittency in Integrable Turbulence

Rogue waves in optically injected lasers: Origin, predictability, and suppression

Extreme events in complex linear and nonlinear photonic media

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