0000000001186744
AUTHOR
Nail Akhmediev
Higher-order modulation instability in fiber optics
We report on analytical, numerical and experimental studies of higher-order modulation instability in fiber optics. This new form of instability arises from the nonlinear superposition of elementary instabilities and manifests as complex, yet deterministic temporal pulse break-up dynamics. We use the Darboux transformation to analytically describe the process and compare with experiments. In particular, we show how suitably low frequency modulation on a continuous wave field allows for the excitation of higher-order modulation instability through cascaded four-wave mixing.
Observation of Kuznetsov-Ma soliton dynamics in optical fibre
International audience; The nonlinear Schro¨dinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important serie…
Dissipative rogue wave generation from a mode-locked fiber laser experiment
Rare events of extremely high optical intensity are experimentally recorded at the output of a mode-locked fiber laser operating in a chaotic multiple-pulse regime. These fluctuations result from ceaseless nonlinear interactions between pulses.
The dynamics of a developing CW supercontinuum: Analytical predictions and experiments
International audience; We show that the development of the supercontinuum spectrum in the quasi-CW regime can be interpreted analytically in terms of Akhmediev Breathers. Theory and experiment are in excellent agreement.
Dissipative Rogue Waves Generated by Chaotic Pulse Bunching in a Mode-Locked Laser
Rare events of extremely high optical intensity are experimentally recorded at the output of a mode-locked fiber laser that operates in a strongly dissipative regime of chaotic multiple-pulse generation. The probability distribution of these intensity fluctuations, which highly depend on the cavity parameters, features a long-tailed distribution. Recorded intensity fluctuations result from the ceaseless relative motion and nonlinear interaction of pulses within a temporally localized multisoliton phase. © 2012 American Physical Society.
Optical bullets and "rockets" in nonlinear dissipative systems and their transformations and interactions
We demonstrate the existence of stable optical light bullets in nonlinear dissipative media for both cases of normal and anomalous chromatic dispersion. The prediction is based on direct numerical simulations of the (3+1)-dimensional complex cubic-quintic GinzburgLandau equation. We do not impose conditions of spherical or cylindrical symmetry. Regions of existence of stable bullets are determined in the parameter space. Beyond the domain of parameters where stable bullets are found, unstable bullets can be transformed into >rockets> i.e. bullets elongated in the temporal domain. A few examples of the interaction between two optical bullets are considered using spatial and temporal interact…
Interactions and transformations of dissipative optical bullets
Nonlinear dissipation provides distinctive dynamical properties to optical bullets. According to the system parameters, the dynamical properties of single bullets range from fully stable to pulsating and instable bullets. We are here interested in the following stage, namely the interaction between several optical bullets.
Kuznetsov-Ma Soliton Dynamics in Nonlinear Fiber Optics
The Kuznetzov-Ma (KM) soliton is a solution of the nonlinear Schrodinger equation derived in 1977 but never observed experimentally. Here we report experiments showing KM soliton dynamics in nonlinear breather evolution in optical fiber.
Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation
Numerical simulations of the onset phase of continuous wave supercontinuum generation from modulation instability show that the structure of the field as it develops can be interpreted in terms of the properties of Akhmediev Breathers. Numerical and analytical results are compared with experimental measurements of spectral broadening in photonic crystal fiber using nanosecond pulses
Higher-order modulation instability in optical fibers
International audience; We report on theoretical, numerical and experimental study of a new form of instability in a nonlinear fiber. This process of higher-order modulation instability arises from the nonlinear superposition of elementary instability dynamics.
Soliton collisions with shape change by intensity redistribution in mixed coupled nonlinear Schrodinger equations
International audience; A different kind of shape changing (intensity redistribution) collision with potential application to signal amplification is identified in the integrable N-coupled nonlinear Schrodinger (CNLS) equations with mixed signs of focusing- and defocusing-type nonlinearity coefficients. The corresponding soliton solutions for the N=2 case are obtained by using Hirota's bilinearization method. The distinguishing feature of the mixed sign CNLS equations is that the soliton solutions can both be singular and regular. Although the general soliton solution admits singularities we present parametric conditions for which nonsingular soliton propagation can occur. The multisoliton …
Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser
The multiple-period pulsations of the soliton parameters in a passively mode-locked fiber laser were discussed numerically and experimentally. It was found that the pulse acquired a periodic evolution that was not related to the round-trip time and consisted of many round trips. The macroperiodicity existed independently or in combination with other periodicity such as period doubling, tripling etc. Analysis shows that the new periods in the soliton modulation appear at bifurcation point related to certain points related to certain values of the cavity parameters.
Soliton complexes in dissipative systems: Vibrating, shaking and mixed soliton pairs
We show, numerically, that coupled soliton pairs in nonlinear dissipative systems modeled by the cubic-quintic complex Ginzburg-Landau equation can exist in various forms. They can be stationary, or they can pulsate periodically, quasiperiodically, or chaotically, as is the case for single solitons. In particular, we have found various types of vibrating and shaking soliton pairs. Each type is stable in the sense that a given bound state exists in the same form indefinitely. New solutions appear at special values of the equation parameters, thus bifurcating from stationary pairs. We also report the finding of mixed soliton pairs, formed by two different types of single solitons. We present …
Hydrodynamics of periodic breathers
We report the first experimental observation of periodic breathers in water waves. One of them is Kuznetsov–Ma soliton and another one is Akhmediev breather. Each of them is a localized solution of the nonlinear Schrödinger equation (NLS) on a constant background. The difference is in localization which is either in time or in space. The experiments conducted in a water wave flume show results that are in good agreement with the NLS theory. Basic features of the breathers that include the maximal amplitudes and spectra are consistent with the theoretical predictions.
Universal spectral dynamics of modulation instability : theory, simulation, experiment
A central process of nonlinear fibre optics is modulation instability (MI), where weak perturbations on a continuous wave are amplified to generate a parametric cascade of spectral sidebands. Although studied for many years, it has only been recently appreciated that MI dynamics can be described analytically by Akhmediev breather (AB) solutions to the nonlinear Schrodinger equation (NLSE) [1]. This has led to important results, including the first observation of the Peregrine Soliton [2]. AB theory has also shown that the spectral amplitudes at the peak of the MI gain curve yield a characteristic log-triangular spectrum, providing new insight into the initial phase of supercontinuum generat…
Supercontinuum to solitons: New nonlinear structures in fiber propagation
We review our recent work in the field of optical rogue wave physics and applications. Beginning from a brief survey of the well-known noise and incoherence processes in optical fiber supercontinuum generation, we trace the links to recent developments in studying the emergence of high contrast localised breather structures in both spontaneous and induced nonlinear instabilities. In the latter case, we discuss our recent measurements that have reported the experimental observation of the Peregrine soliton, a unique class of rational soliton predicted to exist over 25 years ago and never previously observed.
Dissipative soliton interactions inside a fiber laser cavity
We report our recent numerical and experimental observations of dissipative soliton interactions inside a fiber laser cavity. A bound state, formed from two pulses, may have a group velocity which differs from that of a single soliton. As a result, they can collide inside the cavity. This results in a variety of outcomes. Numerical simulations are based either on a continuous model or on a parameter-managed model of the cubic-quintic Ginzburg-Landau equation. Each of the models provides explanations for our experimental observations. © 2005 Elsevier Inc. All rights reserved.
Dissipative soliton resonance as a guideline for high-energy pulse laser oscillators
Dissipative soliton resonance (DSR) occurs in the close vicinity of a hypersurface in the space of parameters of the equation governing propagation in a dissipative nonlinear medium. Pulsed solutions can acquire virtually unlimited energies as soon as the equation parameters converge toward that specific hypersurface. Here we extend previous studies that have recently unveiled DSRs from the complex cubic-quintic Ginzburg-Landau equation. We clearly confirm the existence of DSR for a wide range of parameters in both regimes of chromatic dispersion, and we establish general features of the ultra-high-energy pulses that can be found close to a DSR. Application to high-energy mode-locked fiber …
Dissipative rogue waves out of fiber lasers
We study rogue waves in dissipative systems such as unidirectional fiber laser. We have found that the probability of producing extreme pulses in this setup is higher than in any other system considered so far.
Dissipative rogue wave generation in multiple-pulsing mode-locked fiber laser
Following the first experimental observation of a new mechanism leading to optical rogue wave (RW) formation briefly reported in Lecaplain et al (2012 Phys. Rev. Lett. 108 233901), we provide an extensive study of the experimental conditions under which these RWs can be detected. RWs originate from the nonlinear interactions of bunched chaotic pulses that propagate in a fiber laser cavity, and manifest as rare events of high optical intensity. The crucial influence of the electrical detection bandwidth is illustrated. We also clarify the observation of RWs with respect to other pulsating regimes, such as Q-switching instability, that also lead to L-shaped probability distribution functions.…
Roadmap on optical rogue waves and extreme events
Nail Akhmediev et al. ; 38 págs.; 28 figs.
Dissipative soliton pulsations with periods beyond the laser cavity round trip time
We review recent results on periodic pulsations of the soliton parameters in a passively mode-locked fiber laser. Solitons change their shape, amplitude, width and velocity periodically in time. These pulsations are limit cycles of a dissipative nonlinear system in an infinite-dimensional phase space. Pulsation periods can vary from a few to hundreds of round trips. We present a continuous model of a laser as well as a model with parameter management. The results of the modeling are supported with experimental results obtained using a fiber laser. © World Scientific Publishing Company.
Higher-Order Modulation Instability in Nonlinear Fiber Optics
International audience; We report theoretical, numerical, and experimental studies of higher-order modulation instability in the focusing nonlinear Schrödinger equation. This higher-order instability arises from the nonlinear superposition of elementary instabilities, associated with initial single breather evolution followed by a regime of complex, yet deterministic, pulse splitting. We analytically describe the process using the Darboux transformation and compare with experiments in optical fiber. We show how a suitably low frequency modulation on a continuous wave field induces higher-order modulation instability splitting with the pulse characteristics at different phases of evolution r…
Pulsating Dissipative Light Bullets
Finding domains of existence for (3+1)D spatio-temporal dissipative solitons, also called “dissipative light bullets”, by direct numerical solving of a cubic-quintic Ginzburg-Landau equation (CGLE) is a lengthy procedure [1,2]. Variational approaches pave the way for quicker soliton solution mapping, as long as tractable trial functions remain suitable approximations for exact solutions [3,4].
Optical rogue waves and localized structures in nonlinear fiber optics
We review our recent work in the field of optical rogue wave physics. Beginning from a brief survey of the well-known instabilities in optical fiber, we trace the links to recent developments in studying the emergence of high contrast localized breather structures in both spontaneous and induced nonlinear instabilities.
Complexes and Molecules of Dissipative Solitons in Mode-Locked Lasers
Pulse-pulse interaction is a major issue in the development of high-repetition rate fiber laser sources or soliton-based optical transmission lines. The design of a suitable level of nonlinear dissipation, through nonlinear filters or saturable absorbers for instance, is able to improve significantly the stability of multiple pulse operation. The concept of a dissipative soliton has become an important tool for the exploration and the analysis of the multiple pulse dynamics, with mode-locked lasers and regenerated transmission lines as important applications [1,2]. Above all, the study of dissipative solitons has become a fertile area of nonlinear science with multidisciplinary implications…
Nonlinear dynamics of temporal optical soliton molecules in lasers
Recent experiments demonstrate that fiber laser cavities are able to support various multisoliton complexes, analogous to soliton molecules. These advances, which could have impact on optical information transmission or storage, are guided by the concept of dissipative soliton and supported by numerical simulations. DOI: 10.2529/PIERS060828120520 As passively mode-locked lasers rely strongly on nonlinear dissipation, there is a growing interest in understanding various pulse dynamics in terms of the dynamics of dissipative solitons [1]. In particular, the interaction between dissipative temporal solitons can lead to the formation of stable multi-soliton complexes. The stability of multi-sol…
Superregular Breathers in Optics and Hydrodynamics: Omnipresent Modulation Instability beyond Simple Periodicity
Since the 1960s, the Benjamin-Feir (or modulation) instability (MI) has been considered as the self-modulation of the continuous “envelope waves” with respect to small periodic perturbations that precedes the emergence of highly localized wave structures. Nowadays, the universal nature of MI is established through numerous observations in physics. However, even now, 50 years later, more practical but complex forms of this old physical phenomenon at the frontier of nonlinear wave theory have still not been revealed (i.e., when perturbations beyond simple harmonic are involved). Here, we report the evidence of the broadest class of creation and annihilation dynamics of MI, also called superre…
Light bullets and dynamic pattern formation in nonlinear dissipative systems
In the search for suitable new media for the propagation of (3+1) D optical light bullets, we show that nonlinear dissipation provides interesting possibilities. Using the complex cubic-quintic Ginzburg-Landau equation model with localized initial conditions, we are able to observe stable light bullet propagation or higher-order transverse pattern formation. The type of evolution depends on the model parameters. ©2005 Optical Society of America.
Seeded and spontaneous higher-order modulation instability
International audience; We report on the dynamics of the higher-order modulation instability in optical fibers and show that it is the very same phenomenon that underpins the emergence of rogue waves in the early stage of supercontinuum generation.
Dissipative Solitons: present understanding, applications and new developments
Dissipative solitons form a new paradigm for the investigation of phenomena involving stable structures in nonlinear systems far from equilibrium. Basic principles can be applied to a wide range of phenomena in science. Recent results involving solitons and soliton complexes of the complex cubic-quintic Ginzburg–Landau equation are presented.
Quantized separations of phase-locked soliton pairs in fiber lasers
Quantized separations of phase-locked soliton pairs in fiber lasers were presented. The relation between the Kelly sidebands and the quantized separations between solitons was confirmed. Simulation results showed that the solitons can see each other at relatively larger distances than they would in the absence of radiation.
The Peregrine soliton in nonlinear fibre optics
International audience; The Peregrine soliton is a localized nonlinear structure predicted to exist over 25 years ago, but not so far experimentally observed in any physical system. It is of fundamental significance because it is localized in both time and space, and because it defines the limit of a wide class of solutions to the nonlinear Schrödinger equation (NLSE). Here, we use an analytic description of NLSE breather propagation to implement experiments in optical fibre generating femtosecond pulses with strong temporal and spatial localization, and near-ideal temporal Peregrine soliton characteristics. In showing that Peregrine soliton characteristics appear with initial conditions th…
Stationary and Pulsating Dissipative Optical Bullets
We demonstrate the existence of stable optical light bullets in nonlinear dissipative media. Beyond the domain where stable bullets are found, unstable bullets show unusual behaviors, like "optical rockets", pulsating solutions or pattern formation.
Regions of Existence and Transformations of (3+1)-D Dissipative Optical Solitons
We demonstrate the existence of stable optical light bullets in nonlinear dissipative media featuring both normal and anomalous chromatic dispersion. Beyond the domain where stable bullets are found, unstable bullets can be transformed into "rockets".
Dissipative solitons and their interactions
Coupled soliton pairs in nonlinear dissipative systems can exist in various forms. They can be stationary, or they can pulsate periodically, quasi-periodically or chaotically, as is the case for single solitons. Each type is stable in the sense that a given bound state exists in the same form inde.nitely. Single solitons can be perfectly stable for a given set of parameters. However, this does not mean that a bound state formed from them is either stationary or stable. Moreover, their relations can be highly complicated. Such is the life of dissipative solitons. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Vibrating and shaking soliton pairs in dissipative systems
We show that two-soliton solutions in nonlinear dissipative systems can exist in various forms. As with single solitons, they can be stationary, periodic or chaotic. In particular, we find new types of vibrating and shaking soliton pairs. Each type of pair is stable in the sense that the bound state exists in the same form indefinitely. © 2006 Elsevier B.V. All rights reserved.
Generating ultra-short high-energy pulses using dissipative soliton resonance: Pulse compression schemes
Dissipative soliton resonance (DSR) refers to a phenomenon where the energy of the stable soliton solution increases to extremely large values in a nonlinear dissipative system modeled by the complex cubic-quintic Ginzburg-Landau equation (CGLE) [1]. It occurs in the vicinity of a specific hyper-surface in the multi-dimensional space of the CGLE parameters. The phenomenon has applications in designing laser oscillators generating ultra-high energy pulses, since the dynamics of such lasers can be well-modeled by the CGLE. The DSR was first found in normally-dispersive media, in concordance with the current design trend for high-energy mode-locked laser oscillators [2–4]. However, we have sho…
Dissipative solitons for mode-locked fiber lasers
The concept of a dissipative optical soliton is applied to interpret various pulse dynamics either predicted numerically or observed experimentally in passively mode-locked fiber lasers. The recently discovered “dissipative soliton resonance” phenomenon and “soliton rain” dynamics are highlighted as prominent examples.
Dissipative rogue waves: extreme pulses generated by passively mode-locked lasers.
We study numerically rogue waves in dissipative systems, taking as an example a unidirectional fiber laser in a nonstationary regime of operation. The choice of specific set of parameters allows the laser to generate a chaotic sequence of pulses with a random distribution of peak amplitudes. The probability density function for the intensity maxima has an elevated tail at higher intensities. We have found that the probability of producing extreme pulses in this setup is higher than in any other system considered so far. © 2011 American Physical Society.
Dynamique des solitons de Kuznetsov-Ma observée en optique fibrée non-linéaire
International audience; Le soliton de Kuznetzov-Ma est une solution de l'équation de Schrödinger non-linéaire qui a été identifiée dès 1977 mais qui à ce jour n'avait encore jamais été observée expérimentalement. Nous décrivons ici une expérience mettant en évidence la dynamique du soliton KM à travers la propagation non-linéaire de breathers dans une fibre optique.
Spectral dynamics of modulation instability described using Akhmediev breather theory
International audience; The Akhmediev breather formalism of modulation instability is extended to describe the spectral dynamics of induced multiple sideband generation from a modulated continuous wave field. Exact theoretical results describing the frequency domain evolution are compared with experiments performed using single mode fiber around 1550 nm. The spectral theory is shown to reproduce the depletion dynamics of an injected modulated continuous wave pump and to describe the Fermi-Pasta Ulam recurrence and recovery towards the initial state. Realistic simulations including higher-order dispersion, loss and Raman scattering are used to identify that the primary physical factors that …
Spatiotemporal optical solitons in nonlinear dissipative media: From stationary light bullets to pulsating complexes
Nonlinear dissipative systems display the full (3+1) D spatiotemporal dynamics of stable optical solitons. We review recent results that were obtained within the complex cubic-quintic Ginzburg-Landau equation model. Numerical simulations reveal the existence of stationary bell-shaped (3+1) D solitons for both anomalous and normal chromatic dispersion regimes, as well as the formation of double soliton complexes. We provide additional insight concerning the possible dynamics of these soliton complexes, consider collision cases between two solitons, and discuss the ways nonstationary evolution can lead to optical pattern formation. © 2007 American Institute of Physics.
Optical rogue waves: Physics and impact
International audience; We review our recent work in the field of optical rogue wave physics and applications. Beginning from a brief survey of the well-known instabilities in optical fiber supercontinuum generation, we trace the links to recent developments in studying the emergence of high contrast localized breather structures in both spontaneous and induced nonlinear instabilities. We also discuss the precise nature of optical rogue wave statistics and examine the dynamics leading to the formation of extreme events in the context of noise-driven supercontinuum generation.
Optical bullets and double bullet complexes in dissipative systems
We show that optical light bullets can coexist with double bullet complexes in nonlinear dissipative systems. Coexistence occurs for a relatively large range of the system parameters, and is associated with either marginal stability or bistable existence of the two dissipative soliton species. In the case of marginal stability, spontaneous transformations of single bullets into double bullet complexes are observed. Among the bistable cases, we show how both clockwise and anticlockwise rotating double bullet complexes can be formed out of the phase-controlled interaction of two single bullets. The internal dynamics of pulsating double bullet complexes, with oscillations in both the spatial s…
Peregrine soliton in optical fiber-based systems
International audience; We report the first observation in optics of the Peregrine soliton, a novel class of nonlinear localized structure. Two experimental configurations are explored and the impact of non-ideal initial conditions is discussed.
Lumière sur les vagues scélérates : le soliton de Peregrine enfin observé !
National audience
Rediscovered dynamics of nonlinear fiber optics: from breathers to extreme localisation
International audience
Group interactions of dissipative solitons in a laser cavity: the case of 2+1.
What can be the outcome of the interaction between a dissipative soliton pair and a soliton singlet? We report an experimental observation of ???elastic??? collisions as well as ???inelastic??? formation of triplet soliton states in a fiber laser setup. These observations are supported with the numerical simulations based on the dispersion (parameter) managed cubic-quintic Ginzburg-Landau equation model.
Vibrating temporal soliton pairs
The study of temporal multisoliton complexes in dissipative systems is of potential interest for the development of new schemes of optical data transport and processing. In the present work, we thus consider pulsations of a soliton pair that consist mainly in the oscillations of the temporal separation and phase relationship between the two pulses, so that the relative motion of the two bound solitons resembles a vibrational motion.
Optical Soliton Molecules in Fiber Lasers
Recent experiments demonstrate that fiber laser cavities are able to support various multisoliton complexes, analogous to soliton molecules, which could have impact on optical information transmission or storage. These advances are guided by the concept of dissipative soliton.
Dissipative solitons for mode-locked lasers
International audience; Dissipative solitons are localized formations of an electromagnetic field that are balanced through an energy exchange with the environment in presence of nonlinearity, dispersion and/or diffraction. Their growing use in the area of passively mode-locked lasers is remarkable: the concept of a dissipative soliton provides an excellent framework for understanding complex pulse dynamics and stimulates innovative cavity designs. Reciprocally, the field of mode-locked lasers serves as an ideal playground for testing the concept of dissipative solitons and revealing their unusual dynamics. This Review provides basic definitions of dissipative solitons, summarizes their imp…
Stationary and pulsating dissipative light bullets from a collective variable approach
A collective variable approach is used to map domains of existence for (3+1) -dimensional spatiotemporal soliton solutions of a complex cubic-quintic Ginzburg-Landau equation. A rich variety of evolution behaviors, which include stationary and pulsating dissipative soliton dynamics, is revealed. Comparisons between the results obtained by the semianalytical approach of collective variables, and those obtained by a purely numerical approach show good agreement for a wide range of equation parameters. This also demonstrates the relevance of the semianalytical method for a systematic search of stability domains for spatiotemporal solitons, leading to a dramatic reduction of the computation tim…