Optical rogue waves and dispersive shock waves

For more than a decade, I have been deeply involved with my colleagues in the study of new optical coherent structures arising from the combination of Kerr nonlinearity with dispersive effects. Several analogies with hydrodynamics have been drawn.

New coherent rogue structures in nonlinear focusing media

main collaborators : Dr. Kamal Hammani, Dr. Bertrand Kibler, Dr. Julien Fatome, Dr. Amin Chabcoub, Pr. John M. Dudley

main period : 2010-2020

Solitons over finite background have been a subject of intense investigations in the 2010s. In Dijon, with my colleagues, we have significantly contributed to a better knowledge of these structures by achieving the first experimental demonstration of the existence of the Peregrine soliton, a prototype of the infamous rogue wave that appears from nowhere and disappears without leaving a trace. Additional experimental studies have focused on optical Akhmediev breathers and have revealed applications to ultrashort high-repetitioin rate pulse trains.

main related publications :
B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, J.M. Dudley, The Peregrine soliton in nonlinear fibre optics, Nat Phys, 6 (2010) 790-795.
B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, J.M. Dudley, Observation of Kuznetsov-Ma soliton dynamics in optical fibre, Sci. Rep., 2 (2012) 463.
K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J.M. Dudley, G. Millot, Peregrine soliton generation and breakup in standard telecommunications fiber, Opt. Lett., 36 (2011) 112-114.
G. Xu, K. Hammani, A. Chabchoub, J.M. Dudley, B. Kibler, C. Finot, Phase evolution of Peregrine-like breathers in optics and hydrodynamics, Phys. Rev. E, 99 (2019) 012207.
A. Chabchoub, B. Kibler, C. Finot, G. Millot, M. Onorato, J.M. Dudley, A.V. Babanin, The nonlinear Schrödinger equation and the propagation of weakly nonlinear waves in optical fibers and on the water surface, Annals of Physics, 361 (2015) 490-500.
C. Finot, Optical pulse doublet resulting from the nonlinear splitting of a super-Gaussian pulse, Laser Phys. Lett., 17 (2020) 025103.
F. Audo, B. Kibler, J. Fatome, C. Finot, Experimental observation of the emergence of Peregrine-like events in focusing dam break flows, Opt. Lett., 43 (2018) 2864-2867.

Rogue waves in supercontinuum generation

main collaborators : Dr. Kamal Hammani, Dr. Bertrand Kibler, Pr. Arnaud Mussot, Dr. Antonio Picozzi, Pr. John M. Dudley

main period : 2009-2012

We also studied, mainly based on intensive numerical simulations, the statistical properties of optical supercontinua and how rogue coherent structures may influence the statistical behavior of the resulting expanding spectrum. We have therefore outlined the existence of Raman frequency-shifted solitons that strongly deviate from the average spectrum. We also identified the appearance of coherent structures in the middle of a turbulent field.

main related publications :
K. Hammani, C. Finot, B. Kibler, G. Millot, Soliton generation in a microstructured fiber by fourth order scalar modulation instability, IEEE Photon. J., 1 (2009) 205-212.
B. Kibler, C. Finot, J.M. Dudley, Soliton and rogue wave statistics in supercontinuum generation in photonic crystal fibre with two zero dispersion wavelengths, Eur. Phys. J. Special Topics, 173 (2009) 289-295.
K. Hammani, C. Finot, R. Habert, A. Mussot, A. Kudlinski, Active reduction of fluctuations in fourth-order modulation instability, Opt. Lett., 37 (2012) 4305-4307.
K. Hammani, B. Kibler, C. Finot, A. Picozzi, Emergence of rogue waves from optical turbulence, Phys. Lett. A, 374 (2010) 3585-3589.

Extreme fluctuations in fiber amplifiers

main collaborators : Dr. Kamal Hammani, Pr. John Dudley

main period : 2009-2013

In the context of the PhD work of Kamal Hammani, we intensively studied both analytically, numerically and experimentally the generation of extreme events in fiber-based amplifiers. In that case, the fluctuations of the pump are exponentially transferred to a week seed or a pulse train that then present statistical behaviors that strongly deviate from a Gaussian distribution.
We demonstrated and explained such an effect in Raman distributed amplifiers with a low level of dispersion as well as in parametric fiber amplifiers.

K. Hammani, C. Finot, G. Millot, Emergence of extreme events in fiber-based parametric processes driven by a partially incoherent wave, Opt. Lett., 34 (2009) 1138-1140.
K. Hammani, A. Picozzi, C. Finot, Extreme statistics in Raman fiber amplifier : from analytical description to experiments, Opt. Commun., 284 (2011) 2594-2603.
K. Hammani, C. Finot, Experimental signatures of extreme optical fluctuations in lumped Raman fiber amplifiers, Opt. Fiber. Technol., 18 (2012) 93-100.
K. Hammani, C. Finot, Extreme optical fluctuations in lumped Raman fibre amplifiers, J. Opt, 15 (2013) 064009.

Shock waves in defocusing media

main collaborators : Dr. Julien Fatome, Pr. Stefano Trillo, Pr. Stefan Wabnitz

main period : 2008-2020

We also took part in various studies investigating the optical wave-breaking effect that occurs upon nonlinear propagation in a normally dispersive fiber. Whereas this deleterious effect can be counteracted by the use of parabolic self-similar pulses, a fruitful analogy can once again be drawn with hydrodynamics and more specifically with the evolution of a wave in shallow waters. New phenomena such as collisions of optical undular bores or the new waveforms such as the flaticon pulses have been discussed. We also investigated the extension of those various concepts to include an additional dimension taking advantage of the vectorial nature of light.

main related publications :
C. Finot, B. Kibler, L. Provost, S. Wabnitz, Beneficial impact of wave-breaking on coherent continuum formation in normally dispersive nonlinear fibers, J. Opt. Soc. Am. B, 25 (2008) 1938-1948.
B. Varlot, S. Wabnitz, J. Fatome, G. Millot, C. Finot, Experimental generation of optical flaticon pulses, Opt. Lett., 38 (2013) 3899-3902.
S. Wabnitz, C. Finot, J. Fatome, G. Millot, Shallow water rogue wavetrains in nonlinear optical fibers, Phys. Lett. A, 377 (2013) 932-939.
J. Fatome, C. Finot, G. Millot, A. Armaroli, S. Trillo, Observation of Optical Undular Bores in Multiple Four-Wave Mixing, Phys. Rev. X, 4 (2014) 021022.
J. Nuno, C. Finot, G. Xu, G. Millot, M. Erkintalo, J. Fatome, Vectorial dispersive shock waves in optical fibers, Commun. Phys., 2 (2019) 138.

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