0000000000764176
AUTHOR
Amin Chabchoub
The nonlinear Schrodinger equation and the propagation of weakly nonlinear waves in optical fibres and on the water surface
International audience; The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose–Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin–Feir index, i.e. a nondimensional par…
Longitudinal phase evolution of Peregrine-like breathers
International audience; We report the first experimental study of the longitudinal evolution of breather pulses during nonlinear fiber propagation. Gerchberg-Saxton phase retrieval reveals a large phase shift across the point of maximum compression.
Hydrodynamics of periodic breathers
We report the first experimental observation of periodic breathers in water waves. One of them is Kuznetsov–Ma soliton and another one is Akhmediev breather. Each of them is a localized solution of the nonlinear Schrödinger equation (NLS) on a constant background. The difference is in localization which is either in time or in space. The experiments conducted in a water wave flume show results that are in good agreement with the NLS theory. Basic features of the breathers that include the maximal amplitudes and spectra are consistent with the theoretical predictions.
Two-stage linear-nonlinear shaping of an optical frequency comb as rogue nonlinear-Schrödinger-equation-solution generator
International audience; We report a wave generator of complex solutions of the nonlinear Schrödinger equation (NLSE) combining both intensity and phase spectral shaping of an initial optical frequency comb with subsequent nonlinear propagation in an optical fiber. We apply the explicit analytical form of the two-breather solutions of the NLSE as a linear spectral filter to shape ideal modulation of a continuous wave. The additional nonlinear propagation of the tailored wave provides experimental evidence of both the growth and decay of the fundamental second-order periodic breather solution. The temporal and spectral profiles of the higher-order breather are in excellent agreement with the …
Phase evolution of Peregrine-like solitons in nonlinear fiber optics
Optical fiber systems are well-known to provide convenient platforms in which one may investigate a large variety of fascinating fundamental nonlinear coherent structures such as solitons or self-similar patterns. Interestingly, one of the major conclusions of the studies dealing with extreme-value fluctuations is that the temporal and spectral characteristics of localization processes can be well described in terms of solitons over finite background and in particular in terms of Peregrine soliton (PS) [1]. Whereas the longitudinal evolution of the temporal and spectral intensity of the PS have been characterized in detail [2], much less attention has been experimentally devoted to the evol…
Le soliton Peregrine, une onde fondamentale des dynamiques non-linéaires
National audience; Des ondes très variées sont régies par l’équation de Schrödinger non-linéaire : la lumière dans les fibres optiques, les vagues océaniques, les ondes dans les plasmas, les condensats de Bose-Einstein… Quand la non-linéarité compense la dispersion, un soliton peut se propager tout en maintenant ses caractéristiques temporelles et spectrales inchangées. En présence d’une onde continue, une autre onde non-linéaire existe : le soliton Peregrine (PS), prédit dès 1983 [1] mais démontré expérimentalement seulement en 2010 [2]. Au contraire du soliton usuel, le PS apparait de nulle part, concentre temporellement et spatialement son énergie, puis disparait sans laisser de trace.Le…
Superregular Breathers in Optics and Hydrodynamics: Omnipresent Modulation Instability beyond Simple Periodicity
Since the 1960s, the Benjamin-Feir (or modulation) instability (MI) has been considered as the self-modulation of the continuous “envelope waves” with respect to small periodic perturbations that precedes the emergence of highly localized wave structures. Nowadays, the universal nature of MI is established through numerous observations in physics. However, even now, 50 years later, more practical but complex forms of this old physical phenomenon at the frontier of nonlinear wave theory have still not been revealed (i.e., when perturbations beyond simple harmonic are involved). Here, we report the evidence of the broadest class of creation and annihilation dynamics of MI, also called superre…