Solutions of the Vector Nonlinear Schrödinger Equations: Evidence for Deterministic Rogue Waves

Baronio, Fabio; Degasperis, A.; Conforti, Matteo; Wabnitz, Stefan

doi:10.1103/physrevlett.109.044102

Cited by 538 publications

(485 citation statements)

References 35 publications

(44 reference statements)

Supporting

Mentioning

464

Contrasting

Unclassified

Order By: Relevance

“…For instance, consider a system of coupled nonlinear Schrödinger equations (NLSEs) to describe the nonlinear interaction between wave packets in dispersive conservative media. Such coupled systems are of physical relevance in various domains such as nonlinear optics, hydrodynamics, plasma physics, multicomponent Bose-Einstein condensates, and financial systems [1][2][3][4][5]. The first multicomponent NLSE type of model with applications to physics is the well-known Manakov model [6].…”

Section: Introductionmentioning

confidence: 99%

Polarization modulation instability in a Manakov fiber system

et al. 2015

View full text Add to dashboard Cite

The Manakov model is the simplest multicomponent model of nonlinear wave theory: It describes elementary stable soliton propagation and multisoliton solutions, and it applies to nonlinear optics, hydrodynamics, and Bose-Einstein condensates. It is also of fundamental interest as an asymptotic model in the context of the widely used wavelength-division-multiplexed optical fiber transmission systems. However, although its physical relevance was confirmed by the experimental observation of Manakov (vector) solitons in a planar waveguide in 1996, there have in fact been no quantitative experiments confirming its validity for nonlinear dynamics other than soliton formation. Here, we report experiments in optical fiber that provide evidence of passband and baseband polarization modulation instabilities in a defocusing Manakov system. In the spontaneous regime, we also reveal a unique saturation effect as the pump power increases. We anticipate that such observations may impact the application of this minimal model to describe and understand more complicated phenomena in nature, such as the formation of extreme waves in multicomponent systems.

show abstract

Section: Introductionmentioning

confidence: 99%

Polarization modulation instability in a Manakov fiber system

et al. 2015

View full text Add to dashboard Cite

show abstract

“…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].…”

mentioning

confidence: 99%

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

et al. 2013

View full text Add to dashboard Cite

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 ...

show abstract

“…Recent developments have taken into account dissipative effects [11,15,16], included higher-order nonlinear terms [17][18][19], or considered the coupling between several fields [20][21][22][23][24][25]. The latter investigations have led to the discovery of intricate rogue wave structures that are generally unattainable in the scalar models.…”

mentioning

confidence: 99%

Coexisting rogue waves within the (2+1)-component long-wave–short-wave resonance

2014

View full text Add to dashboard Cite

The coexistence of two different types of fundamental rogue waves is unveiled, based on the coupled equations describing the (2+1)-component long-wave-short-wave resonance. For a wide range of asymptotic background fields, each family of three rogue wave components can be triggered by using a slight deterministic alteration to the otherwise identical background field. The ability to trigger markedly different rogue wave profiles from similar initial conditions is confirmed by numerical simulations. This remarkable feature, which is absent in the scalar nonlinear Schrödinger equation, is attributed to the specific three-wave interaction process and may be universal for a variety of multicomponent wave dynamics spanning from oceanography to nonlinear optics. [4,5], these extreme wave events were also observed in a wide class of physical systems, including capillary waves and surface ripples [6,7], plasmas [8], optical fibers [9,10], mode-locked lasers [11], and filaments [12]. These studies have uncovered general features of nonlinearity and complexity shared by rogue waves, e.g., they are extremely large and steep compared with typical events, occur in a nonlinear medium, and follow an unusual L-shaped statistics [9,[11][12][13]. Despite these diverse features, mathematical solutions of rogue waves can be expressed as rational functions localized in both space and time. One typical example is the Peregrine soliton [14], a well-known rogue wave prototype in various experimental fields [4,8,10], which is the lowest-order rational solution to the nonlinear Schrödinger (NLS) equation.Following the need to model complex physical systems more precisely, it has become important to study rogue wave phenomena beyond the framework of the NLS equation. Recent developments have taken into account dissipative effects [11,15,16], included higher-order nonlinear terms [17][18][19], or considered the coupling between several fields [20][21][22][23][24][25]. The latter investigations have led to the discovery of intricate rogue wave structures that are generally unattainable in the scalar models. In particular, we showed in Ref.[25] that the long-wave-short-wave (LWSW) resonance interaction can result in stable dark and bright rogue waves in spite of the onset of modulational instability (MI). This finding brings about the possibility to observe dark rogue waves in LWSW resonance systems such as negative index media [26] and capillary-gravity waves [6,27].Basically, the LWSW resonance is a general parametric process that manifests when the group velocity of the short wave matches the phase velocity of the long wave [28]. It has been predicted in different disciplines such as fluid dynamics [27], plasma physics [29], oceanography [30], and nonlinear optics [26,31]. Early works showed that both the LWSW and the NLS equations could be obtained from the same Davey-Stewartson system under the appropriate parameter conditions [27,32,33], although the former is currently less popular in use than the latter.In fact, it is possible to co...

show abstract

Solutions of the Vector Nonlinear Schrödinger Equations: Evidence for Deterministic Rogue Waves

Cited by 538 publications

References 35 publications

Polarization modulation instability in a Manakov fiber system

Polarization modulation instability in a Manakov fiber system

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

Coexisting rogue waves within the (2+1)-component long-wave–short-wave resonance

Contact Info

Product

Resources

About