Caustics and Rogue Waves in an Optical Sea

There are many examples in physics of systems showing rogue wave behaviour, the generation of high amplitude events at low probability. Although initially studied in oceanography, rogue waves have now been seen in many other domains, with particular recent interest in optics. Although most studies in optics have focussed on how nonlinearity can drive rogue wave emergence, purely linear effects have also been shown to induce extreme wave amplitudes. In this paper, we report a detailed experimental study of linear rogue waves in an optical system, using a spatial light modulator to impose random phase structure on a coherent optical field. After free space propagation, different random intensity patterns are generated, including partially-developed speckle, a broadband caustic network, and an intermediate pattern with characteristics of both speckle and caustic structures. Intensity peaks satisfying statistical criteria for rogue waves are seen especially in the case of the caustic network, and are associated with broader spatial spectra. In addition, the electric field statistics of the intermediate pattern shows properties of an optical sea with near-Gaussian statistics in elevation amplitude, and trough-to-crest statistics that are near-Rayleigh distributed but with an extended tail where a number of rogue wave events are observed.Comment: 10 pages, 5 figures, to be published in Scientific Report

Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability

Modulation instability is a fundamental process of nonlinear science, leading to the unstable breakup of a constant amplitude solution of a physical system. There has been particular interest in studying modulation instability in the cubic nonlinear Schrödinger equation, a generic model for a host of nonlinear systems including superfluids, fibre optics, plasmas and Bose–Einstein condensates. Modulation instability is also a significant area of study in the context of understanding the emergence of high amplitude events that satisfy rogue wave statistical criteria. Here, exploiting advances in ultrafast optical metrology, we perform real-time measurements in an optical fibre system of the unstable breakup of a continuous wave field, simultaneously characterizing emergent modulation instability breather pulses and their associated statistics. Our results allow quantitative comparison between experiment, modelling and theory, and are expected to open new perspectives on studies of instability dynamics in physics

On the origin of heavy-tail statistics in equations of the Nonlinear Schrödinger type

We study the formation of extreme events in incoherent systems described by the Nonlinear Schrödinger type of equations. We consider an exact identity that relates the evolution of the normalized fourth-order moment of the probability density function of the wave envelope to the rate of change of the width of the Fourier spectrum of the wave field. We show that, given an initial condition characterized by some distribution of the wave envelope, an increase of the spectral bandwidth in the focusing/defocusing regime leads to an increase/decrease of the probability of formation of rogue waves. Extensive numerical simulations in 1D+1 and 2D+1 are also performed to confirm the results

ASE narrow‐band noise pulsing in erbium‐doped fiber amplifier and its effect on self‐phase modulation

In this paper, we report a study of the features of polarized and unpolarized narrow-band amplified spontaneous emission (ASE) in a low-doped erbium fiber at 976-nm pumping. We demonstrate that ASE noise can be treated as a train of Gaussian-like pulses with random magnitudes, widths, and inter-pulse intervals. ASE noise can also provide a statistical analysis of these three parameters. We also present the data that reveal ASE noise’s role in optical spectrum broadening through self-phase modulation of light propagating in a communication fiber. In particular, the data show that the ASE noise derivative defines the broadening’s spectral shape

Vagues scélérates linéaire et non-linéaire dans les systèmes optiques

This thesis describes the study of several different classes of linear and nonlinear effects in optics that generatelarge amplitude extreme events with properties analogous to the destructive “rogue waves” on the surface of theocean. The thesis begins with a brief overview of the analogous physics of wave localisation in hydrodynamicand optical systems, where we describe linear and nonlinear rogue wave generating mechanisms in bothcases. We then present numerical and experimental results for rogue wave generation in a linear opticalsystem consisting of free space propagation of a spatial optical field with random phase. Computed statisticsbetween experiment and modelling are in good agreement, and we interpret the results obtained in termsof the properties of localised optical caustics. We then consider rogue waves in the nonlinear system ofmodulation instability described by the Nonlinear Schrodinger Equation (NLSE), and a detailed numericalstudy is presented comparing the spatio-temporal characteristics of localised structures seen from numericalsimulations with different known analytic solutions to the NLSE. Two experimental studies of modulationinstability are then reported. In the first, we present experimental results studying the properties of modulationinstability using a time-lens magnifier system; in the second, we report experimental results studying thefrequency-domain properties of modulation instability using real-time spectral measurements. The latter studyexamines the effect of a weak seed field on spectral bandwidth and stability. All experimental results arecompared with the NLSE simulations and discussed in terms of the qualitative properties of modulationinstability, in order to gain new insights into the complex dynamics associated with nonlinear pulse propagation.In all of these studies, different statistical properties are analised in relation to the emergence of rogue waves.Ces travaux de thèse présentent l’étude des différentes classes d’effets linéaires et non-linéaires en optiquequi génèrent des événements extrêmes dont les propriétés sont analogues à celles des « vagues scélérates » destructrices qui apparaissent à la surface des océans. La thèse commence avec un bref aperçu de l’analogie physique entre la localisation d’onde dans les systèmes hydrodynamique et les systèmes optique, pour lesquels nous décrivons les mécanismes de génération de vagues scélérates linéaire et non-linéaire. Nous présentons ensuite quelques résultats numérique et expérimentaux de la génération de vagues scélérates dans un système optique linéaire dans le cas d’une propagation spatiale d’un champ optique qui présenteune phase aléatoire, où nous interprétons les résultats obtenus en terme de caustiques optiques localisées.Nous considérons ensuite les vagues scélérates obtenues dans des systèmes non-linéaires qui présentent une instabilité de modulation décrite par l’équation de Schrödinger non-linéaire (ESNL). Nous présentons une étude numérique détaillée comparant les caractéristiques spatio-temporelles des structures localisées obtenues dans les simulation numérique avec les différentes solutions analytiques obtenues à partir de l’ESNL.Deux études expérimentales d’instabilités de modulation sont ensuite effectuées. Dans la première, nous présentons des résultats expérimentaux qui étudient les propriétés d’instabilité de modulation en utilisant un système d’agrandissement temporel par lentille temporelle; dans la deuxième, nous rapportons des résultats expérimentaux sur les propriétés des instabilités de modulation dans le domaine fréquentiel en utilisant une technique de mesure spectrale en temps-réel. Cette dernière étude examine l’effet sur la bande spectrale et surla stabilité d’un faible champ perturbateur. Tous les résultats expérimentaux sont comparés avec la simulation d’ESNL et abordés en termes des propriétés qualitatives d’instabilité de modulation. Dans toutes ces études,différentes propriétés statistiques sont analysées en rapport avec l’apparition des vagues scélérates

Pusat kebudayaan populer dan eksibisi teknologi jepang di Surabaya

Pusat Kebudayaan Populer dan Eksibisi Teknologi Jepang ini merupakan proyek yang dilatarbelakangi kebutuhan atas suatu wadah untuk menampung aspirasi dan ekspresi khususnya masyarakat Surabaya mengenai perkembangan kebudayaan populer dan tren, disamping menghadirkan kemajuan teknologi yang berlangsung di Jepang melalui eksibisi. Dalam upaya mewadahi sebagian besar kegiatan yang berhubungan dengan kebudayaan populer, maka fungsi ruang di dalamnya didesain menjadi beberapa area yang meliputi area animasi, video-game, musik, fashion, cafe dan resto, hobby shop, komik, pendidikan dan cross culture, serta area eksibisi yang cukup luas. Konsep desain dari bangunan ini sendiri berusaha mengekspresikan ciri budaya populer Jepang yang didalamnya meliputi sifat-sifat "keterbukaan" terhadap budaya asing, "transformasi" atau perubahan itu sendiri yang terus-menerus berlangsung, serta "ketidak-menentuan" arah pola perubahan itu

Breathers Emergence in Spontaneous Modulation Instability

International audienceModulation instability (MI) is one of the most fundamental processes in nonlinear fiber optics, underlying energy exchange dynamics in parametric amplification and dominating the initial stages of noise-seeded long pulse supercontinuum generation [1]. MI is also linked with the emergence of large amplitude optical rogue wave structures with long-tailed statistics [2]. In particular, numerical simulations of noise-seeded MI show a chaotic pattern of localized peaks that are potential candidates for rogue wave events, but the exact nature of these peaks remains a subject of active study. Although previous studies have shown that the highest-intensity events can be fitted with particular spatio-temporally localized solutions of the nonlinear Schrödinger equation (NLSE) [3], the characteristics over the full intensity range remain unclear. Here we report extensive numerical simulations of the NLSE, iψξ + 1/2ψττ + |ψ|2 ψ = 0, showing that the spontaneously emergent peaks due to MI can in fact be globally described by analytic soliton on finite background (SFB) or “breather” solutions and their superpositions. We also report on a detailed statistical analysis, revealing how the Peregrine soliton is not – as widely believed – statistically rare enough to be considered as a rogue wave prototype

Statusrapport Elkas en Fresnelkas : openbare rapportage

In dit rapport worden de belangrijkste materialen en omzettingsmethoden, meetresultaten, aanvullende meetresultaten, economische kengetallen en een transitie scenario van de elektriciteit leverende kassen beschreve

Interferometric autocorrelation measurements of supercontinuum based on two-photon absorption

International audienceWe report on interferometric autocorrelation measurements of broadband supercontinuum light in the anomalous dispersion regime using two-photon absorption in a GaP photodetector. The method is simple and low-cost and provides a direct measure of second-order coherence properties, including quantitative information on coherence time and average duration of the supercontinuum pulses as well as on the presence of temporally coherent sub-structures. We report measurements in regimes where the supercontinuum is coherent and incoherent. In the former case, the interferometric measurements are similar to what is observed for mode-locked laser pulses, while in the latter case, the interferometric measurements and coherence properties are shown to have characteristics similar to those of a stationary chaotic light source

Emergent rogue wave structures and statistics in spontaneous modulation instability

International audienceThe nonlinear Schrödinger equation (NLSE) is a seminal equation of nonlinear physics describing wave packet evolution in weakly-nonlinear dispersive media. The NLSE is especially important in understanding how high amplitude " rogue waves " emerge from noise through the process of modulation instability (MI) whereby a perturbation on an initial plane wave can evolve into strongly-localised " breather " or " soliton on finite background (SFB) " structures. Although there has been much study of such structures excited under controlled conditions, there remains the open question of how closely the analytic solutions of the NLSE actually model localised structures emerging in noise-seeded MI. We address this question here using numerical simulations to compare the properties of a large ensemble of emergent peaks in noise-seeded MI with the known analytic solutions of the NLSE. Our results show that both elementary breather and higher-order SFB structures are observed in chaotic MI, with the characteristics of the noise-induced peaks clustering closely around analytic NLSE predictions. A significant conclusion of our work is to suggest that the widely-held view that the Peregrine soliton forms a rogue wave prototype must be revisited. Rather, we confirm earlier suggestions that NLSE rogue waves are most appropriately identified as collisions between elementary SFB solutions. The terminology of " rogue wave " in physics describes events with high amplitude that emerge randomly in the dynamical behaviour of a particular system with low probability. This label was initially applied to describe the unexpected appearance of large and destructive waves on the ocean 1,2 but has now been generalized to describe large amplitude rare events in many other systems 3,4. Particular interest in rogue waves emerging during propagation in systems described by the nonlinear Schrödinger equation (NLSE) or its extensions has led to studies of rogue wave behaviour for deep water wave groups, pulse propagation in optical fibres, plasmas and cold atoms 5–7. The NLSE has particular significance in the context of rogue wave behaviour because it exhibits the Benjamin-Feir or modulation instability (MI), where a weak modulation on a plane wave will undergo exponential growth with propagation 8,9. After this initial exponential growth, the subsequent dynamics sees periodic growth and decay in a form of Fermi-Pasta-Ulam (FPU) recurrence 10. Because rapid growth and decay of a weakly modulated pulse envelope would also increase the amplitude and steep-ness of an underlying carrier wave, MI has long been considered a primary candidate for a rogue wave generating mechanism 11–13. Although the initial mathematical studies of MI were performed using linear stability analysis 9 , MI and FPU dynamics in the NLSE can also be described using various types of " breather " or soliton on finite background (SFB) solutions to the NLSE 14–17. The possibility to describe these dynamics analytically has motivated much research to obtain possible insights into the particular initial conditions tha