Controllable optical rogue waves: Recurrence, annihilation and sustainment

Tian, Qing; Yang, Qi; Dai, Chao-Qing; Zhang, Jie-Fang

doi:10.1016/j.optcom.2010.12.081

Cited by 30 publications

(15 citation statements)

References 28 publications

(50 reference statements)

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“…We underline that the transformation of the forced/damped NLS equation to the standard one has been possible only for 1/p(t) equal to a linear function in t. For other functional dependences, the transformation does not seem to be possible. Our result is consistent with ones reported in [18,19] where analytical solutions of the variable coefficient NLS equation are described.…”

Section: Reduction Of the Forced/damped Nls To The Standard Nlssupporting

confidence: 93%

Approximate rogue wave solutions of the forced and damped nonlinear Schrödinger equation for water waves

Onorato¹,

Proment²

2012

Physics Letters A

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We consider the effect of the wind and the dissipation on the nonlinear stages of the modulational instability. By applying a suitable transformation, we map the forced/damped Nonlinear Schrödinger (NLS) equation into the standard NLS with constant coefficients. The transformation is valid as long as |Γt| 1, with Γ the growth/damping rate of the waves due to the wind/dissipation. Approximate rogue wave solutions of the equation are presented and discussed. The results shed some lights on the effects of wind and dissipation on the formation of rogue waves.

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Section: Reduction Of the Forced/damped Nls To The Standard Nlssupporting

confidence: 93%

Approximate rogue wave solutions of the forced and damped nonlinear Schrödinger equation for water waves

Onorato¹,

Proment²

2012

Physics Letters A

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“…As well as controlling input conditions, other studies have shown that longitudinal variation in fibre dispersive and nonlinear properties can modify intensity fluctuations in both supercontinuum generation [84], and the dynamics of an evolving AB [85]. These studies are significant in that they show how a modified fibre propagation environment can mimic the way in which ocean topography influences water wave propagation [1].…”

Section: Controlling Rogue Waves In Fibre Systemsmentioning

confidence: 96%

Instabilities, breathers and rogue waves in optics

et al. 2014

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Optical rogue waves are rare yet extreme fluctuations in the value of an optical field. The terminology was first used in the context of an analogy between pulse propagation in optical fibre and wave group propagation on deep water, but has since been generalized to describe many other processes in optics. This paper provides an overview of this field, concentrating primarily on propagation in optical fibre systems that exhibit nonlinear breather and soliton dynamics, but also discussing other optical systems where extreme events have been reported. Although statistical features such as long-tailed probability distributions are often considered the defining feature of rogue waves, we emphasise the underlying physical processes that drive the appearance of extreme optical structures.Many physical systems exhibit behaviour associated with the emergence of high amplitude events that occur with low probability but that have dramatic impact. Perhaps the most celebrated examples of such processes are the giant oceanic "rogue waves" that emerge unexpectedly from the sea with great destructive power [1]. There is general agreement that 2 the emergence of giant waves involves physics different from that generating the usual population of ocean waves, but equally there is a consensus that one unique causative mechanism is unlikely. Indeed, oceanic rogue waves have been shown to arise in many different ways: from linear effects such as directional focusing or random superposition of independent wave trains, to nonlinear effects associated with the growth of surface noise to form localized wave structures [1,2].The analogous physics of nonlinear wave propagation in optics and in hydrodynamics has been known for decades, and the focusing nonlinear Schrödinger equation (NLSE) applies to both systems in certain limits (Box 1). The description of instabilities in optics as "rogue waves" is recent, however, first used in 2007 when shot-to-shot measurements of fibre supercontinuum (SC) spectra by Solli et al. yielded long-tailed histograms for intensity fluctuations at long wavelengths [3]. An analogy between this optical instability and oceanic rogue waves was suggested for two reasons. Firstly, highly skewed distributions are often considered to define extreme processes, since they predict that high amplitude events far from the median are still observed with non-negligible probability [4]. And secondly, the particular regime of SC generation being studied developed from modulation instability (MI), a nonlinear process associated with exponential amplification of noise that had previously been proposed as an ocean rogue wave generating mechanism [2].These pioneering results enabled for the first time a quantitative analysis of the fluctuations at the spectral edge of a broadband supercontinuum, and motivated many subsequent studies into how large amplitude structures could emerge in optical systems.These studies attracted broad interest and have essentially opened up a new field of "optical rogue wave physics". Although most...

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“…It is well known that the dynamics of ABs is strongly affected in the presence of varying dispersion and/or nonlinearity [11][12][13][14]. Yet, experimental studies have so far been restricted to the observation of AB propagation dynamics in nonlinear media with uniform dispersion and nonlinearity.…”

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confidence: 99%