We construct and discuss a semirational, multiparametric vector solution of coupled nonlinear Schrödinger equations (Manakov system). This family of solutions includes known vector Peregrine ...solutions, bright- and dark-rogue solutions, and novel vector unusual freak waves. The vector rogue waves could be of great interest in a variety of complex systems, from optics and fluid dynamics to Bose-Einstein condensates and finance.
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We report and discuss analytical solutions of the vector nonlinear Schrödinger equation that describe rogue waves in the defocusing regime. This family of solutions includes bright-dark and dark-dark ...rogue waves. The link between modulational instability (MI) and rogue waves is displayed by showing that only a peculiar kind of MI, namely baseband MI, can sustain rogue-wave formation. The existence of vector rogue waves in the defocusing regime is expected to be a crucial progress in explaining extreme waves in a variety of physical scenarios described by multicomponent systems, from oceanography to optics and plasma physics.
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Optical Dark Rogue Wave Frisquet, Benoit; Kibler, Bertrand; Morin, Philippe ...
Scientific reports,
02/2016, Volume:
6, Issue:
1
Journal Article
Peer reviewed
Open access
Photonics enables to develop simple lab experiments that mimic water rogue wave generation phenomena, as well as relativistic gravitational effects such as event horizons, gravitational lensing and ...Hawking radiation. The basis for analog gravity experiments is light propagation through an effective moving medium obtained via the nonlinear response of the material. So far, analogue gravity kinematics was reproduced in scalar optical wave propagation test models. Multimode and spatiotemporal nonlinear interactions exhibit a rich spectrum of excitations, which may substantially expand the range of rogue wave phenomena, and lead to novel space-time analogies, for example with multi-particle interactions. By injecting two colliding and modulated pumps with orthogonal states of polarization in a randomly birefringent telecommunication optical fiber, we provide the first experimental demonstration of an optical dark rogue wave. We also introduce the concept of multi-component analog gravity, whereby localized spatiotemporal horizons are associated with the dark rogue wave solution of the two-component nonlinear Schrödinger system.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
We formulate a non-recursive Darboux transformation technique to obtain the general
th-order rational rogue wave solutions to the coupled Fokas-Lenells system, which is an integrable extension of the ...noted Manakov system, by considering both the double-root and triple-root situations of the spectral characteristic equation. Based on the explicit fundamental and second-order rogue wave solutions, we demonstrate several interesting rogue wave dynamics, among which are coexisting rogue waves and anomalous Peregrine solitons. Our solutions are generalized to include the complete background-field parameters and therefore helpful for future experimental study.
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We investigate the spatial nonlinear localization of light on a quasi-plane-wave background with a harmonic perturbation induced by modulation instability in a quadratic nonlinear optical medium. In ...particular, we demonstrate experimentally the excitation of deterministic Akhmediev breathers and thus the growth-decay dynamics of modulation instability in a LiNbO_{3} slab waveguide. The results should stimulate new interest in modulation instability, extreme events, turbulence, recurrence, and supercontinuum generation in quadratic nonlinear optics.
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The resonant interaction of an optical field with two-level doping ions in a cryogenic optical fiber is investigated within the framework of nonlinear Schrödinger and Maxwell-Bloch equations. We ...present explicit fundamental rational rogue wave solutions in the context of self-induced transparency for the coupled optical and matter waves. It is exhibited that the optical wave component always features a typical Peregrine-like structure, while the matter waves involve more complicated yet spatiotemporally balanced amplitude distribution. The existence and stability of these rogue waves is then confirmed by numerical simulations, and they are shown to be excited amid the onset of modulation instability. These solutions can also be extended, using the same analytical framework, to include higher-order dispersive and nonlinear effects, highlighting their universality.
We study the existence and properties of rogue-wave solutions in different nonlinear wave evolution models that are commonly used in optics and hydrodynamics. In particular, we consider the ...Fokas-Lenells equation, the defocusing vector nonlinear Schrödinger equation, and the long-wave-shortwave resonance equation. We show that rogue-wave solutions in all of these models exist in the subset of parameters where modulation instability is present if and only if the unstable sideband spectrum also contains cw or zero-frequency perturbations as a limiting case (baseband instability). We numerically confirm that rogue waves may only be excited from a weakly perturbed cw whenever the baseband instability is present. Conversely, modulation instability leads to nonlinear periodic oscillations.
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We investigate the coexisting rogue wave dynamics associated with two fundamental-frequency optical waves interacting in a quadratic nonlinear medium. Using the vector Chen-Lee-Liu nonlinear ...Schrödinger equation model, we obtain exact rogue wave solutions at first and higher orders on the more general periodic backgrounds. We unveil that the inherent self-steepening effect may allow an omnipresent rogue wave coexistence over a broad range of parameters in both the normal and anomalous dispersion regimes, in addition to allowing ultrastrong peak amplitudes. We also demonstrate that such universality of coexistence can be anticipated by the appearance of two peaks in the modulation instability spectrum. We numerically confirm the robustness of the coexisting Peregrine solitons against initial noise as well as their excitation from a turbulent wave field caused by modulation instability. We expect that these findings will shed light on the generation of extreme wave events resulting from the interference of multiple continuous-wave fields.
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Abstract
The bulk-boundary correspondence is a key feature of topological physics and is universally applicable to Hermitian and non-Hermitian systems. Here, we report a similar universal ...correspondence intended for the rogue waves in integrable systems, by establishing the relationship between the fundamental rogue wave solutions of integrable models and the baseband modulation instability of continuous-wave backgrounds. We employ an
N
-component generalized nonlinear Schrödinger equation framework to exemplify this modulation instability-rogue wave correspondence, where we numerically confirm the excitation of three coexisting Peregrine solitons from a turbulent wave field, as predicted by the modulation instability analysis. The universality of such modulation instability-rogue wave correspondence has been corroborated using various integrable models, thereby offering an alternative way of obtaining exact rogue wave solutions from the modulation instability analysis.
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