Spontaneous emergence of rogue waves in partially coherent waves: a quantitative experimental comparison between hydrodynamics and optics

Rogue waves are extreme and rare fluctuations of the wave field that have been discussed in many physical systems. Their presence substantially influences the statistical properties of an incoherent wave field. Their understanding is fundamental for the design of ships and offshore platforms. Except for very particular meteorological conditions, waves in the ocean are characterised by the so-called JONSWAP (Joint North Sea Wave Project) spectrum. Here we compare two unique experimental results: the first one has been performed in a 270-meter wave tank and the other in optical fibers. In both cases, waves characterised by a JONSWAP spectrum and random Fourier phases have been launched at the input of the experimental device. The quantitative comparison, based on an appropriate scaling of the two experiments, shows a very good agreement between the statistics in hydrodynamics and optics. Spontaneous emergence of heavy tails in the probability density function of the wave amplitude is observed in both systems. The results demonstrate the universal features of rogue waves and provide a fundamental and explicit bridge between two important fields of research. Numerical simulations are also compared with experimental results

Ultra-fast statistics and dynamics in nonlinear fiber optics experiments

Le travail de thèse présenté dans ce manuscrit est consacré à l’étude de la statis-tique et de la dynamique d’ondes partiellement cohérentes se propageant dans un milieunon linéaire, la fibre optique. Les études effectuées durant ce travail de thèse se placentprincipalement dans le champ de la turbulence intégrable qui examine la propagationnon linéaire d’ondes partiellement cohérentes dans des systèmes physiques décrits par deséquations intégrables telles que l’équation de Schrödinger non linéaire à une dimension.Nous avons reproduit en optique une expérience déjà réalisée en hydrodynamique.Nous comparons ainsi les déviations de la statistique gaussienne résultant de la propaga-tion non linéaire d’ondes lumineuses dans une fibre optique et de vagues dans un canalunidirectionnel. Afin d’observer la dynamique des ondes partiellement cohérentes se propageant dans unefibre optique en régime de dispersion anormale, nous avons construit un microscope tem-porel qui a permis d’observer des structures cohérentes particulières présentant des pro-priétés de localisation dans l’espace et dans le temps similaires à celles des ondes scélérates.Finalement, nous avons étudié le régime de propagation très faiblement non linéaire. Lathéorie cinétique des ondes (appelée encore théorie de la Turbulence d’ondes) prédit quel’élargissement spectral ne dépend pas du signe de la dispersion et nous avons présentédans ce manuscrit la preuve expérimentale de cette hypothèse.The work presented in this thesis is related to the statistical and dynamical propertiesof partially coherent waves propagating inside an optical fiber. Our work mainly enterswithin the field of Integrable Turbulence that deals with nonlinear partially coherentwaves described by integrable equations, such as the one-dimensional nonlinear Shcrödin-ger equation. We have reproduced an experiment in optics that has been done some years ago inhydrodynamics. We compare the statistics of optical waves propagating inside an opticalfiber to the the statistics of waves propagating inside a water tank. Moreover we have built a time microscope in order to observe the real-time evolution of partially coherent waves. The soliton-like structures that have been observed in our expe-riments have localization properties in space and time that are similar to those typifyingrogue waves found in the field of oceanography. We have also examined the weakly nonlinear regime that can be described by using the so-called wave turbulence (WT) theory. WT theory states that the spectral broadening insuch a weakly nonlinear regime does not depend on the sign of the second-order dispersioncoefficient. In this thesis, we presented an experimental result confirming this theoreticalprediction