Theory of modulation instability in Kerr Fabry-Perot resonators beyond the mean field limit

We analyse the nonlinear dynamics of Fabry-Perot cavities of arbitrary finesse filled by a dispersive Kerr medium, pumped by a continuous wave laser or a synchronous train of flat-top pulses. The combined action of feedback, group velocity dispersion and Kerr nonlinearity leads to temporal instability with respect to perturbations at specified frequencies. We characterise the generation of new spectral bands by deriving the exact dispersion relation and we find approximate analytical expressions for the instabilities threshold and gain spectrum of modulation instability (MI). We show that, in contrast to ring-resonators, both the stationary solutions and the gain spectrum are dramatically affected by the duration of the pump pulse. We derive the extended Lugiato-Lefever equation for the Fabry-Perot resonator (FP-LLE) starting from coupled nonlinear Schr\"odinger equations (rather than Maxwell-Bloch equations) and we compare the outcome of the stability analysis of the two models. While FP-LLE gives overall good results, we show regimes that are not captured by the mean-field limit, namely the period-two modulation instability, which may appear in highly detuned or nonlinear regimes. We report numerical simulations of the generation of MI-induced Kerr combs by solving FP-LLE and the coupled Schr\"odinger equations

28 THz soliton frequency comb in a continuous-wave pumped fiber Fabry-Perot resonator

We report the generation of an optical frequency comb featuring 28 THz bandwidth, sustained by a single 80 fs cavity soliton recirculating in a fiber Fabry-Perot resonator. This large spectrum is comparable to frequency combs obtained with microresonators operating in the anomalous dispersion regime. Thanks to the compact design and the easy coupling of the resonator, cavity solitons can be generated in an all-fiber experimental setup with a continuous wave pumping scheme. We also observe the generation of a dispersive wave at higher frequencies which is supported by higher-order dispersion. These observations align remarkably well with both numerical simulations and the established theory of cavity solitons.Comment: 6 pages, 6 figure

Nonlinear localization and propagation of surface Plasmon modes in metallic nanostructures

La plasmonique non linéaire est un domaine largement inexploré et seules quelques interactions non linéaires dans les nanostructures métalliques ont été étudiées jusqu'à présent.Ces travaux de thèse portent sur l'apparition de modes plasmons de surface non linéaire dans des nanostructures métalliques (dimère, chaînes de nanoparticules) insérées dans une matrice diélectrique, et soumis à l'action d'une source électromagnétique externe de type onde plane.Une non-linéarité de type Kerr largement rencontré dans les milieux optiques est incluse dans la réponse du métal et le couplage dipôle-dipôle entre les nanoparticules est considérée.Dans le cas d'un nano-dimère, après avoir étudié la nature des solutions non linéaires ainsi que leur stabilité, nous avons mis en évidence l'émergence des dynamiques riches et complexes, et nous avons étudié en particulier l'apparition du chaos.Bien qu'il semble être aléatoire, il se produit dans un système déterministe non linéaire dans des conditions déterministes.L'existence de la route familière de dédoublement de période conduisant au chaos est mise en évidence, et les domaines correspondant à l'apparition de doublement de période et de chaos dans le plan des paramètres sont mis en évidence.Dans le cas d'une chaîne de nanoparticules métalliques unidimensionnelle, le mécanisme de l'instabilité modulationnelle, qui est responsable de l'amplification exponentielle de faibles perturbations et qui est due à la non-linéarité du métal, nous a permet d'observer plusieurs dynamiques spatio-temporelle.Le spectre de Lyapunov nous a permis d'identifier le comportement complexe observé comme chaos spatio-temporel.Nous avons montré que dans le régime hautement non linéaire, le chaos spatio-temporel est robuste et existe dans une large gamme de paramètres.Nonlinear plasmonics is a largely unexplored field and only a few nonlinear interactions in metal nanostructures have been investigated so far.This thesis work focuses on the appearance of nonlinear surface plasmon modes in metal nanostructures (dimer, chains of nanoparticles) inserted in a dielectric matrix, and subjected to the action of an external electromagnetic source of the plane wave type.A Kerr-type non-linearity widely encountered in optical media is included in the metal response and dipole-dipole coupling between nanoparticles is considered.In the case of a nano-dimer, after studying the nature of nonlinear solutions as well as their stability, we have highlighted the emergence of rich and complex dynamics, and we studied in particular the appearance of chaos.Although it appears to be random, it occurs in a nonlinear deterministic system under deterministic conditions.The existence of the familiar chaos-leading period-doubling route is reported, and the domains corresponding to the occurrence of period-doubling and chaos in the parameter plane are evidenced.In the case of a unidimensional metal nanoparticle chain, the mechanism of Modulational instability, which is responsible for the exponential amplification of low disturbances and which is due to the non-linearity of the metal, has allowed us to observe several spatiotemporal dynamics.The Lyapunov spectrum allowed us to identify the observed complex behavior as spatiotemporal chaos.We have shown that in the highly nonlinear regime, the spatiotemporal chaos is robust and exists in a wide range of parameters

Characterization of spatiotemporal chaos in arrays of nonlinear plasmonic nanoparticles

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Identification approaches for steel strip surface defects in hot rolling Process

In steel manufacturing process, flat products are greatly concerned with the surface quality and the possibilities of its on-line inspection. The visual control is obviously unable to continuously check the surface of the moving product, and the control at the ending stage remains not suitable although, it may provide information about process trends and parameters history. So, strip surface defects that are not detected yield to product downgrading or to costly rework operations for producer and/or end users. With such needed quality level, steel surface inspection systems are more and more implemented for detecting defects and allowing correction at appropriate time. Based on Computer vision, these applications make a use of detection and classification algorithms to identify these arising defects. The present work is related to a Project of a scientific and economic impact: The Development of an on-line inspection system for strip surface defects identification during the thermo-mechanical treatment in hot rolling process. We asses, in this work, some approaches in labeling each of the defects belonging to a database created for this aim. This Dataset is compound of five, among the most frequent, surface defect types and with 108 variants of each one. Obtained results shown the importance of the choice of a relevant image features extractor

Investigating Route to Chaos in Nonlinear Plasmonic Dimer

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Recent progresses in Fiber Fabry Perot resonators... in Lille

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Recent progresses in Fiber Fabry Perot resonators for frequency comb generation

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Unexpected Phase locked Brillouin assisted Kerr Combs

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Recent progresses in Fiber Fabry Perot resonators for frequency comb generation

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