The efforts to understand the physics of rogue waves have motivated the study of mechanisms that produce rare, extreme events, often through analogous optical setups. As many studies have reported nonlinear generation mechanisms, recent work has explored whether optical rogue events can be produced in linear systems. Here we report the observation of linear rogue events with tunable height, generated from light imprinted with a non-Markovian wavefront. Moreover, if the non-Markovian wavefront is allowed to propagate through a nonlinear medium, extraordinarily long-tailed intensity distributions are produced, which do not conform to the statistics previously observed in optical rogue wave experiments.
We unveil the relation between the linear Anderson localisation process and nonlinear modulation instability. Anderson localised modes are formed in certain temporal intervals due to the random background noise. Such localised modes seed the formation of solitary waves that will appear during the modulation instability process at those preferred intervals. Afterwards, optical-event horizon effects between dispersive waves and solitons produce an artificial collective acceleration that favours the collision of solitons, which could eventually lead to a rogue-soliton generation.
We advance a statistical theory of extreme event emergence in random nonlinear wave systems with self-similar intermediate asymptotics. We show, within the framework of a generic (1 + 1)D nonlinear Schrodinger equation with linear gain, that extreme events and even rogue waves in weakly nonlinear, statistical open systems emerge as parabolic-shape giant fluctuations in the self-similar asymptotic propagation regime. We analytically demonstrate the self-similar structure of the non-Gaussian statistics of emergent rogue waves and validate our results with numerical simulations. Our results shed …
Ocean rogue waves (RW) -huge solitary waves- have for long triggered the interest of scientists. RWs emerge in a complex environment and it is still dubious the importance of linear versus nonlinear processes. Recent works have demonstrated that RWs appear in various other physical systems such as microwaves, nonlinear crystals, cold atoms, etc. In this work we investigate optical wave propagation in strongly scattering random lattices embedded in the bulk of transparent glasses. In the linear regime we observe the appearance of RWs that depend solely on the scattering properties of the medium…
Random excitation of intense periodic highly-localized single-cycle light pulses in a stochastic background by continuous-wave stimulated Brillouin scattering in long optical fibers with weak feedback is found experimentally. Events with low period numbers are dominant and the optical feedback is crucial for the phenomenon. A three-wave coupling model for the phenomenon is proposed. The results are in good qualitative agreement with the observed phenomenon. The latter should be relevant to the understanding of similar rogue wave events in other nonlinear dissipative systems.
We explore extreme event occurrence in the integrable turbulence with self-similar asymptotics. We posit that rogue waves in such systems manifest themselves as giant fluctuations away from average self-similar dynamics of the system. We support our proposition with numerical simulations of rogue wave excitation in the self-similar regime of stimulated Raman scattering. We show that our results hold irrespective of a specific source correlation model, suggesting the universality of the proposed scenario.
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…
We report a theoretical study showing that rogue waves can emerge in whispering gallery mode resonators as the result of the chaotic interplay between Kerr nonlinearity and anomalous group-velocity dispersion. The nonlinear dynamics of the propagation of light in a whispering gallery-mode resonator is investigated using the Lugiato-Lefever equation, and we evidence a range of parameters where rare and extreme events associated with a non-gaussian statistics of the field maxima are observed.
Rogue waves in birefringent optical fibers are analyzed within the framework of the coupled nonlinear Schrödinger (CNLS) system. The generation of rogue waves is frequently associated with modulation instability (MI). It is commonly expected that since the CNLS equations exhibit larger growth rates they should also produce more rogue events than their scalar counterparts. This is found to occur only when both equations are focusing. When at least one component is defocusing, the CNLS equations may still exhibit larger growth rates, compared to the scalar system, but that does not necessarily r…
We present a spatio-temporal mechanism for producing 2D optical rogue waves in the presence of a turbulent state with creation, interaction and annihilation of optical vortices. Spatially periodic structures with bound phase lose stability to phase unbound turbulent states in complex Ginzburg- Landau and Swift-Hohenberg models with external driving. When the pumping is high and the external driving is low, synchronized oscillations are unstable and lead to spatio-temporal turbulence with high excursions in amplitude. Nonlinear amplification leads to rogue waves close to turbulent optical vorti…
We demonstrate a simple cascade mechanism that drives the formation and emergence of rogue waves in the generalized non-linear Schrödinger equation with third-order dispersion. This conceptually novel generation mechanism is based on inelastic collisions of quasi-solitons and is well described by a resonant-like scattering behaviour for the energy transfer in pair-wise quasi-soliton collisions. Our results demonstrate a threshold for rogue wave emergence and the existence of a period of reduced amplitudes - a "calm before the storm" - preceding the arrival of a rogue wave event. Comparing with…
Optical rogue waves are rare yet extreme fluctuations in the value of an optical field. The terminology was first used in the context of an analogy between pulse propagation in optical fibre and wave group propagation on deep water, but has since been generalized to describe many other processes in optics. This paper provides an overview of this field, concentrating primarily on propagation in optical fibre systems that exhibit nonlinear breather and soliton dynamics, but also discussing other optical systems where extreme events have been reported. Although statistical features such as long-t…
The generation of rogue waves is investigated via a nonlocal nonlinear Schrodinger (NLS) equation. In this system, modulation instability is suppressed and is usually expected that rogue wave formation would also be limited. On the contrary, a parameter regime is identified where the instability is suppressed but nevertheless the number and amplitude of the rogue events increase, as compared to the standard NLS (which is a limit of the nonlocal system). Furthermore, the nature of these waves is investigated; while no analytical solutions are known to model these events, numerically it is shown…
Soliton fusion is a fascinating and delicate phenomenon that manifests itself in optical fibers in case of interaction between co-propagating solitons with small temporal and wavelengths separation. We show that the mechanism of acceleration of trailing soliton by dispersive waves radiated from the preceding one provides necessary conditions for soliton fusion at the advanced stage of supercontinuum generation in photonic crystal fibers. As a result of fusion large intensity robust light structures arise and propagate over significant distances. In presence of small random noise the delicate c…
We investigate two types of nonlinear interaction between collinear femtosecond laser pulses with power slightly above the critical for self-focusing $P_{cr}$. In the first case we study energy exchange between filaments. The model describes this process through degenerate four-photon parametric mixing (FPPM) scheme and requests initial phase difference between the waves. When there are no initial phase difference between the pulses, the FPPM process does not work. In this case it is obtained the second type of interaction as merging between two, three or four filaments in a single filament wi…
Extremely large, rare events arise in various systems, often representing a defining character of their behavior. Another class of extreme occurrences, unexpected failures, may appear less important, but in applications demanding stringent reliability, the rare absence of an intended effect can be significant. Here, we report the observation of rare gaps in supercontinuum pulse trains, events we term rogue voids. These pulses of unusually small spectral bandwidth follow a reverse-heavy-tailed statistical form. Previous analysis has shown that rogue waves, the opposite extremes in supercontinuu…
Spontaneous emergence of self-organized patterns and their bifurcations towards a regime of complex dynamics in non-equilibrium dissipative systems is a paradigm of phase transition. Indeed, the behavior of these patterns in the highly nonlinear regime remains less explored, even in recent high-quality-factor resonators such as Kerr-nonlinear optical ones. Here, we investigate theoretically and experimentally the alteration of the resulting Kerr frequency combs from the weakly to the highly nonlinear regime, in the frameworks of spatiotemporal chaos, and dissipative phase transitions. We revea…
Numerical simulations are used to discuss various aspects of "optical rogue wave" statistics observed in noise-driven fiber supercontinuum generation associated with highly incoherent spectra. In particular, we consider how long wavelength spectral filtering influences the characteristics of the statistical distribution of peak power, and we contrast the statistics of the spectrally filtered SC with the statistics of both the peak power of the most red-shifted soliton in the SC and the maximum peak power across the full temporal field with no spectral selection. For the latter case, we show th…
We present numerical results of supercontinuum (SC) generation in the mid-IR spectral region, specifically addressing the molecular fingerprint window ranging from 2.5 to 25 um. By solving the Generalized Nonlinear Schrödinger Equation (GNLSE) in a chalcogenide waveguide, we demonstrate low-power SC generation beyond 10 um from a pump at 5 um. Further, we investigate the short-pulse and CW regimes, and show that a simple linear dispersion profile, applicable to a broad range of chalcogenide media, is sufficient to account for the broad SC generation, and yield rich pulse dynamics leading to th…
Light manifests extreme localized waves with long-tail statistics that seem analogous to the still little understood rogue waves in oceans, and optical setups promise to become laboratory test-beds for their investigation. However, to date there is no evidence that optical extreme events share the dynamics of their oceanic counterparts, and this greatly limits our ability to study rogue wave predictability using light. Using the Grassberger-Procaccia embedding method, we here demonstrate that optical spatial rogue wave data in photorefractive crystals has the same predictability and dynamic fe…
The famous demonstration of optical rogue wave (RW)-rarely and unexpectedly event with extremely high intensity-had opened a flourishing time for temporal statistic investigation as a powerful tool to reveal the fundamental physics in different laser scenarios. However, up to now, optical RW behavior with temporally localized structure has yet not been presented in random fiber laser (RFL) characterized with mirrorless open cavity, whose feedback arises from distinctive distributed multiple scattering. Here, thanks to the participation of sustained and crucial stimulated Brillouin scattering (…
In addition to deep-water rogue waves which develop from the modulation instability of an optical CW, wave propagation in optical fibers may also produce shallow water rogue waves. These extreme wave events are generated in the modulationally stable normal dispersion regime. A suitable phase or frequency modulation of a CW laser leads to chirp-free and flat-top pulses or flaticons which exhibit a stable self-similar evolution. Upon collision, flaticons at different carrier frequencies, which may also occur in wavelength division multiplexed transmission systems, merge into a single, high-inten…
We introduce a novel family of analytic solutions of the three-wave resonant interaction equations to the purpose of modeling unique events, i.e. "amplitude peaks" which are isolated in space and time. The description of these solutions is likely to be a crucial step in the understanding and forecasting of rogue-waves in a variety of multi-component wave dynamics, from oceanography to optics, from plasma physics to acoustics.
Caustics are natural phenomena in which nature concentrates the energy of waves. Although, they are known mostly in optics, caustics are intrinsic to all wave phenomena. For example, studies show that fluctuations in the profile of an ocean floor can generate random caustics and focus the energy of tsunami waves. Caustics share many similarities to rogue waves, as they both exhibit heavy-tailed distribution, i.e. an overpopulation of large events. Linear Schrödinger-type equations are usually used to explain the wave dynamics of caustics. However, in that the wave amplitude increases dramatica…
Rogue waves are intense and unexpected wavepackets ubiquitous in complex systems. In optics, they are promising as robust and noise-resistant beams for probing and manipulating the underlying material. Localizing large optical power is crucial especially in biomedical systems, where, however, extremely intense beams have not yet been observed. We here discover that tumor-cell spheroids manifest optical rogue waves when illuminated by randomly modulated laser beams. The intensity of light transmitted through bio-printed three-dimensional tumor models follows a signature Weibull statistical dist…
In analogy with ocean waves running up towards the beach, shoaling of prechirped optical pulses may occur in the normal group-velocity dispersion regime of optical fibers. We present exact Riemann wave solutions of the optical shallow water equations and show that they agree remarkably well with the numerical solutions of the nonlinear Schrödinger equation, at least up to the point where a vertical pulse front develops. We also reveal that extreme wave events or optical tsunamis may be generated in dispersion tapered fibers in the presence of higher-order dispersion.
Non-deterministic giant waves, denoted as rogue, killer, monster or freak waves, have been reported in many different branches of physics. Their origin is however still unknown: despite the massive numerical and experimental evidence, the ultimate reason for their spontaneous formation has not been identified yet. Here we show that rogue waves in optical fibres actually result from a complex dynamic process very similar to well known mechanisms such as glass transitions and protein folding. We describe how the interaction among optical solitons produces an energy landscape in a highly-dimensio…
We report the existence of stable dissipative light bullets in Kerr cavities. These three-dimensional (3D) localized structures consist of either an isolated light bullet (LB), or could occur in clusters forming well-defined 3D patterns. They can be seen as stationary states in the reference frame moving with the group velocity of light within the cavity. The number of LBs and their distribution in 3D settings are determined by the initial conditions while their maximum peak power remains constant for a fixed value of the system parameters. Their bifurcation diagram allows us to explain this p…
The extreme events are investigated for an $n$-component nonlinear Schrödinger ($n$-NLS) system in the focusing Kerr-like nonlinear media, which appears in many physical fields. We report and discuss the novel multi-parametric families of vector rational rogue wave (RW) solutions featuring the parity-time (PT) symmetry, which are characterized by non-identical boundary conditions for the components, and consistent with the degeneracy of $n$ branches of Benjamin-Feir instability. Explicit examples of PT-symmetric vector RWs are presented. Some parameter constraints can make some components gene…
Extreme or rogue waves are large and unexpected waves appearing with higher probability than predicted by Gaussian statistics. Although their formation is explained by both linear and nonlinear wave propagation, nonlinearity has been considered a necessary ingredient to generate superextreme waves, i.e., an enhanced wave amplification, where the wave amplitudes exceed by far those of standard rogue waves. Here we show, experimentally and theoretically, that superextreme optical waves emerge in the simple case of linear one-dimensional light diffraction. The underlying physics is a long-range c…
One of the open questions in the field of optical rogue waves is the relevance of the number of spatial dimensions in which waves propagate. Here we review recent results on extreme events obtained in 0, 1 and 2 spatial dimensions in the specific context of forced oscillatory media. We show that some dynamical scenarii can be relevant from 0 to 2D while others can take place only in sufficiently large number of spatial dimensions.
Optical rogue waves have been extensively studied in the past two decades. However, observations of multidimensional extreme wave events remain surprisingly scarce. In this work we present the experimental demonstration of the spontaneous generation of spatially localized two-dimensional beams in a quadratic nonlinear crystal, which are composed by twin components at the fundamental and the second-harmonic frequencies. These localized spots of light emerge from a wide background beam, and eventually disappear as the laser beam intensity is progressively increased.
The passively Q-switched, self-pulsing all-solid-state laser is a device of widespread use in many applications. Depending on the condition of saturation, which is easy to adjust, different dynamical phenomena are observed: continuous wave emission, stable oscillations, period doubling bifurcations, chaos and, in some chaotic regimes, extreme events in the form of pulses of extraordinary intensity. These pulses are also sometimes called "dissipative optical rogue waves". The mechanism of their formation is still unknown. Here, we report the direct observation of the pulse-to-pulse evolution of…
