Search results for "Rogue wave"
showing 10 items of 66 documents
Roadmap on optical rogue waves and extreme events
2016
Nail Akhmediev et al. ; 38 págs.; 28 figs.
Ondes scélérates et statistiques extrêmes dans les systèmes optiques fibrés
2011
This thesis deals with extremes statistics which has become an attractive subject in optics since a comparison with oceanic rogue waves has been proposed at the end of 2007. We report some potential mechanisms stimulating the rogue wave formation in the context of guided propagation of light in optical fibers. In a first part, we explore optical rogue waves in supercontinuums generated by fourth-order modulation instability and we propose a stabilization method based on the use of two continuous seeds. Then, we present a detailed study on Raman fiber amplifiers where we determine the conditions of emergence of giant structures : in presence of a partially incoherent pumping wave, a quasi-in…
Observation of Kuznetsov-Ma soliton dynamics in optical fibre
2012
International audience; The nonlinear Schro¨dinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important serie…
Dissipative rogue wave generation in multiple-pulsing mode-locked fiber laser
2013
Following the first experimental observation of a new mechanism leading to optical rogue wave (RW) formation briefly reported in Lecaplain et al (2012 Phys. Rev. Lett. 108 233901), we provide an extensive study of the experimental conditions under which these RWs can be detected. RWs originate from the nonlinear interactions of bunched chaotic pulses that propagate in a fiber laser cavity, and manifest as rare events of high optical intensity. The crucial influence of the electrical detection bandwidth is illustrated. We also clarify the observation of RWs with respect to other pulsating regimes, such as Q-switching instability, that also lead to L-shaped probability distribution functions.…
Optical Dark Rogue Wave
2016
AbstractPhotonics 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-parti…
Families of rational solutions to the KPI equation of order 7 depending on 12 parameters
2017
International audience; We construct in this paper, rational solutions as a quotient of two determinants of order 2N = 14 and we obtain what we call solutions of order N = 7 to the Kadomtsev-Petviashvili equation (KPI) as a quotient of 2 polynomials of degree 112 in x, y and t depending on 12 parameters. The maximum of modulus of these solutions at order 7 is equal to 2(2N + 1)2= 450. We make the study of the patterns of their modulus in the plane (x, y) and their evolution according to time and parameters a1, a2, a3, a4, a5, a6, b1, b2, b3, b4, b5, b6. When all these parameters grow, triangle and ring structures are obtained.
Rational solutions to the KPI equation of order 7 depending on 12 parameters
2018
We construct in this paper, rational solutions as a quotient of two determinants of order 2N = 14 and we obtain what we call solutions of order N = 7 to the Kadomtsev-Petviashvili equation (KPI) as a quotient of 2 polynomials of degree 112 in x, y and t depending on 12 parameters. The maximum of modulus of these solutions at order 7 is equal to 2(2N + 1) 2 = 450. We make the study of the patterns of their modulus in the plane (x, y) and their evolution according to time and parameters a1, a2, a3, a4, a5, a6, b1, b2, b3, b4, b5, b6. When all these parameters grow, triangle and ring structures are obtained.
Higher order Peregrine breathers solutions to the NLS equation
2015
The solutions to the one dimensional focusing nonlinear Schrödinger equation (NLS) can be written as a product of an exponential depending on t by a quotient of two polynomials of degree N (N + 1) in x and t. These solutions depend on 2N − 2 parameters : when all these parameters are equal to 0, we obtain the famous Peregrine breathers which we call PN breathers. Between all quasi-rational solutions of the rank N fixed by the condition that its absolute value tends to 1 at infinity and its highest maximum is located at the point (x = 0, t = 0), the PN breather is distinguished by the fact that PN (0, 0) = 2N + 1. We construct Peregrine breathers of the rank N explicitly for N ≤ 11. We give …
Hierarchy of solutions to the NLS equation and multi-rogue waves.
2014
The solutions to the one dimensional focusing nonlinear Schrödinger equation (NLS) are given in terms of determinants. The orders of these determinants are arbitrarily equal to 2N for any nonnegative integer $N$ and generate a hierarchy of solutions which can be written as a product of an exponential depending on t by a quotient of two polynomials of degree N(N+1) in x and t. These solutions depend on 2N-2 parameters and can be seen as deformations with 2N-2 parameters of the Peregrine breather P_{N} : when all these parameters are equal to 0, we recover the P_{N} breather whose the maximum of the module is equal to 2N+1. Several conjectures about the structure of the solutions are given.
Families of deformations of the thirteen peregrine breather solutions to the NLS equation depending on twenty four parameters
2017
International audience; We go on with the study of the solutions to the focusing one dimensional nonlinear Schrodinger equation (NLS). We construct here the thirteen's Peregrine breather (P13 breather) with its twenty four real parameters, creating deformation solutions to the NLS equation. New families of quasirational solutions to the NLS equation in terms of explicit ratios of polynomials of degree 182 in x and t multiplied by an exponential depending on t are obtained. We present characteristic patterns of the modulus of these solutions in the (x; t) plane, in function of the different parameters.