Colloque en l`honneur de Jérôme Léon

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 Colloque en l’honneur de Jérôme Léon Université Montpellier 2 -­‐ 15 et 16 Novembre 2011 Polytech, bâtiment 31 – Salles 101 et 102 Mardi 15 Novembre : Matinée : chairman F. Geniet 9h20 V. Lorman Accueil du directeur du département de physique théorique du L2C. 9h30 M. Boiti – F. Pempinelli Jérôme Léon a true friend and a clever coworker. A short overview on joint scientific results (Flora Pempinelli) Main successive developments (Marco Boiti) 10h10 P.C. Sabatier Le parcours de J. Léon en Physique Mathématique Appliquée. 10h30 Pause Café 11h10 T. Dauxois Non-­‐linear Internal Waves. 12h00 Déjeuner restaurant administratif UM2 Après-­‐midi : chairman M. Boiti 14h G. Martel Role of saturable absorber & dispersion to generate high powers directly from
mode-locked fiber-based dissipative soliton chirped pulse oscillators. In this contribution, we will make a review on various experimental and numerical results – based on the extended nonlinear Schrodinger Equation – of Er-­‐doped fiber lasers passively mode-­‐locked by different saturable absorber mirrors (SAM). Different laser configurations have been studied vs. total cavity dispersion in order to explore power scalability. Systematic characterization has been performed through pulse energy, RF and optical spectra, chirped and dechirped pulse durations measurements. For each regime we will compare the properties of the SAM requested to self-­‐start and sustain pure mode-­‐locking operation from CW. In particular, self-­‐Q-­‐switch avoidance and optical damage threshold properties of these SAMs will be discussed. Common tendencies to extract maximum pulse energies with close-­‐to-­‐
Fourier-­‐Transform-­‐limit dechirpable pulses are obtained at 1.5 µm wavelength and relied generally on operating within the Chirped Pulse Oscillator (CPO) regime. Comparatively to a pure solitonic regime where pulse stabilization occurs through compensation of anomalous dispersion by Kerr effect, the CPO stability takes place thanks to gain vs. losses competition and spectral filtering effects. Very important key parameters deduced from our experimental results as well as from our simulations will be given for power scaling of such lasers. A stringent discussion will focus on SAM parameters influencing the spectral shaping of such regimes with typical very pronounced steep-­‐edges profiles. Analytical solutions describing our results are still under progress and strongly requested in order to obtain reliable predictive models. 14h20 C. Montes Coherence transfer in a counterpropagating mirrorless optical parametric
oscillator
Distributed positive feedback established by a counterpropagating three-­‐wave mixing process in a submicrometer structured second-­‐order nonlinear crystal leads to mirrorless parametric oscillation with remarkable spectral properties. It has been experimentally demonstrated that the phase modulation of the pump is coherently transferred to the co-­‐propagating parametric wave, while the counterpropagating wave retains a narrow bandwidth and high coherence. The main mechanisms responsable for these properties are the maximized convective separation between the pump and the counterpropagating wave and the associated phase-­‐locking between the pump and the co-­‐propagating parametric wave. This suggests that mirrorless optical parametric oscillators can be pumped with incoherent light and still generate highly coherent backward-­‐propagating radiation. To this purpose we have developed a new numerical scheme that combines two standard methods: the method of the trajectories, usually employed to solve the nonlinear three-­‐wave interaction for the large convection involved in the counterpropagating configuration, together with the spectral method for realizing the intraband group velocity dispersion effect. Simulations prove a coherence transfer of several orders of magnitude between a highly incoherent pump and the backward wave, the co-­‐propagating wave absorbing the pump incoherence. 14h40 P. Emplit Experimental study of the 1D Kerr Cavity Soliton Temporal cavity solitons are packets of light persisting in a continuously driven nonlinear resonator. They are robust attracting states, readily excited through a phase-­‐insensitive and wavelength-­‐insensitive process. As such, they constitute an ideal support for bits in an optical buffer that would seamlessly combine three critical telecommunication functions, namely all-­‐optical storage, all-­‐optical reshaping and wavelength conversion. In this talk we report the first experimental observation of temporal cavity solitons, in a standard silica optical fibre loop. 15h Pause Café 15h30 G. Montemezzani Photoinduced structures for the control of spatial modulation instabilities and for discrete optics Photoinduced periodic lattices in photorefractive materials can influence the optical patterns arising as a result of modulation instability in a nonlinear optical system with feedback. For instance, a control of such patterns can be achieved by properly choosing the lattice periodicity, strength and orientation, as confirmed experimentally and theoretically. On the other hand, periodic or quasi-­‐periodic photoinduced structures created by a proper lateral illumination of a nonlinear crystal can guide an optical wave and lead to discrete propagation of light. The output distribution of the propagating waves can be easily reconfigured, for instance by introducing a photoinduced "defect" or by a longitudinal modulation of the characteristics of the photoinduced structures. 15h50 G. Renversez Solitons spatiaux avec une nonlinéarité Kerr : au delà du soliton de Townes Par une approche numérique en utilisant une méthode que nous avons développée, nous généralisons le soliton spatial de Townes au cas de milieux structurés pour une nonlinéarité de type Kerr optique dans le cadre d'un modèle scalaire. Nous retrouvons alors le soliton de Townes comme le cas limite des courtes longueurs d'onde. Dans le cadre d'un modèle vectoriel et pour une nonlinéarité de type Kerr isotrope, nous pouvons exhiber numériquement un soliton spatial vectoriel. La question cruciale de la stabilité des solutions obtenues n'est pas traitée en l'état actuel de nos travaux. 16h10 R. Khomeriki All optical Transistors and Diodes with subwavelength linear waveguides We consider the possibility of amplification of optical signals by side illumination of dielectric-­‐metal combined subwavelength waveguide when the side driving helps the beam to pass through the waveguide. The problem is linear with no need in high power fields and this makes suggested scenario very promising in experimental and technological realizations. Mercredi 16 Novembre : Matinée : chairman A. Taki 9h00 S. Aubry KAM Tori and Absence of Diffusion of a Wave Packet in the 1D Random DNLS Model Abstract : When nonlinearity is added to an infinite system with purely discrete linear spectrum, the Anderson modes become coupled one with each other by terms of higher order than linear allowing energy exchange between them. It is generally believed, on the basis of numerical simulations in such systems, that any initial wave-­‐packet with finite energy spreads down chaotically to zero amplitude with second moment diverging as a power law of time, slower than standard diffusion (sub-­‐diffusion). We present results which suggest that the interpretation of spreading cannot described as initially believed and that new questions arise and still remain opened. 9h40 S. Ruffo Linear response theory for a long-­‐range interacting system in a quasistationary state Long-­‐range interacting systems, while relaxing to equilibrium, often get trapped in long-­‐lived quasistationary states which have lifetimes that diverge with system size. In this talk I will address the question of how a long-­‐range system in a quasistationary state responds to an external perturbation.
10h00 J. Dorignac Non linear supratransmission revisited. Nonlinear Supratransmission (NST) was discovered by J. Léon and F. Geniet [Phys. Rev. Lett. 89, 134102 (2002)] in a chain of coupled pendula forced at one end with a frequency lying within the forbidden band gap: when the forcing amplitude is low enough, an evanescent wave is formed that becomes unstable at a critical value above which a sudden energy transfer occurs through the emission of gap solitons. This phenomenon has since been observed in many different contexts and in particular in some continuous non integrable multicomponent Nonlinear Schrödinger like models used in Optics. For such models, the NST threshold is a surface whose dimension is equal to the number of fields involved. I shall present an asymptotic method that permits the determination of the NST threshold and a monomer approach that provides simple and reliable analytical expressions for NST manifolds. 10h20 Pause Café 10h40 F. Ginovart La diffusion stimulée de Raman : une longue histoire cette présentation retracera les travaux réalisés sur la diffusion stimulée de Raman depuis son démarrage en 1992 à Montpellier. 11h00 G. Reinisch Vortex-­‐nucleation in a rotating Bose-­‐Einstein condensate (BEC): a macroscopic Zeeman effect. By adding to the 2D parabolically-­‐confined "nonlinear-­‐Schrödinger" Hamiltonian a quadratic term for the uniform angular-­‐velocity field defining the BEC rotation, we show by use of a simple quantum rotator model that the first vortex appears for that critical BEC rotation which corresponds to the discrete energy gap beween the vortexless BEC ground state and its first excited vortex eigenstate. Such a transition in a simple macroscopique two level quantum system can be described in the BEC rotating frame by a vector-­‐
potential Hamiltonian which is identical to the Zeeman Hamiltonian when keeping both its paramagnetic and diamagnetic terms. Therefore, by use of Larmor's theorem, vortex-­‐nucleation in a rotating BEC actually appears as a macroscopic Zeeman effect . This picture is in excellent agreement with the experimental data provided by the three pioneering ENS-­‐Paris, JILA-­‐Boulder and MIT rotating-­‐BEC groups [G. Reinisch, PRL 99, 120402 (2007)]. 11h20 A. Degasperis Nonlocal wave interaction and solvable models We describe a simple model of two wave interaction in chi2 media. The amplitude equations have a Lax pair but the dynamics may not be solvable by the spectral method. This unusual feature is displayed by the behavior of simple soliton solutions. 12h00 Déjeuner restaurant administratif UM2 Après-­‐midi : chairman J. Dorignac 14h00 T. Taliercio Nanostructured arrays of doped semiconductors for IR nanophotonics: a linear point of view. The main idea developed by Jérôme and I was to identify a system which should present supra-­‐
transmission to obtain bi-­‐stability. One system which should present the expected characteristics is the surface plasmon polariton (SPP). The SPP results from the coupling of the electromagnetic wave with the collective oscillation of the electrons supported by the metal/dielectric interface. Unfortunately SPP is 2D system, so quite difficult to investigate by free space optic. In this work, we have imagined a 3D system composed of an array of doped and un-­‐doped semiconductors of which the optical properties are governed by SPP. We have developed an analytic model which describe their optical properties. This analytic model highlights a strong coupling between the incident light and the free electrons of the doped semiconductor, that is a huge photonic band gap. By modifying the period, the ratio between materials and the doping level of the doped semiconductor, it is possible to adjust the frequency and the broadening of the photonic band gap. These linear optical properties give the possibility to develop potential applications in the mid infra-­‐red range (filtering) and define the first step before studying nonlinear optical properties. 14h20 D. Felbacq second harmonic generation in a random medium We study the possibility of an efficient emission of second harmonic in a 1D random medium. The randomness prevents the possibility of a phase matching condition but it appears that by taking advantage of the structure of the modes it is possible to couple a necklace state to an Anderson localized state to obtain an efficient conversion. The extension to a 2D random medium will be discussed. 14h40 Pause Café 15h10 A. Taki Les ondes scélérates en optique (Rogue Waves in Optics) De récentes observations ont montré que la probabilité de rencontrer une vague gigantesque en plein milieu de l'océan, connue sous le nom d'onde scélérate ou "rogue wave", est plus importante que celle prédite par les modèles statistiques classiques. Même si de nombreux efforts ont été consentis pour comprendre et prédire l'avènement de ces phénomènes potentiellement destructeurs, de nombreuses zones d'ombres subsistent. Une avancée majeure a été récemment apportée à ce sujet très complexe permettant une comparaison directe entre ces gigantesques ondes hydrauliques et des ondes optiques particulières, très puissantes, se propageant dans des fibres optiques. Ces ondes solitaires, dans leur manifestation fondamentale, résultent de la compensation de la dispersion chromatique (dépendance de l'indice de réfraction de la longueur d'onde) de la fibre optique par sa non linéarité (Effet Kerr : dépendance de l'indice de réfraction de l'intensité de l'onde). Elles possèdent des caractéristiques proches de celles des solitons optiques qui sont capables de se déplacer sur d'importantes distances sans se déformer. Il est donc désormais possible d'étudier les propriétés de ces vagues de plusieurs dizaines de mètres de hauteur au sein même d'un laboratoire d'optique... 16h Fin du colloque 
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