arXiv subjects

Stefano Trillo

Publications and source records attributed to Stefano Trillo.

At least 19 recordsLinked to original sources

arXiv2026

Pseudovorticity of 2+1D optical solitons

In the hydrodynamic representation of a quantum fluid or optical field, vorticity vanishes wherever the phase is well defined, and is instead localized at phase singularities, or quantum vortices. Pseudovorticity, by contrast, characterizes local rotational structures, even in regions without singularities or net orbital angular momentum. We study both experimentally and numerically pseudovorticity in photorefractive solitons and show that a detailed phase and amplitude analysis unveils a complex rotational flow dynamic: bright 2+1D solitons are found to carry a pseudovorticity dipole, while quadrupoles emerge in soliton fusion. The phenomenon, also explained using geometrical considerations, suggests a general picture according to which stable high-dimensional solitons naturally carry a hierarchy of pseudovorticity multipoles, encoded in the local perturbed phase and amplitude.

physics.optics↗

arXiv2025

Recurrent nonlinear modulational instability via down-conversion in quadratic media

We investigate the induced modulation instability in second-harmonic generation beyond the early stage of the linearized growth of the modulation. We find a regime of recurrence (quasi-periodic conversion and back-conversion between the pump and the modulation) which is genuine of the parametric conversion process in quadratic media. Such recurrence is mainly driven by a process of non-degenerate downconversion, showing no analogy to the cascading regime which mimics the cubic (Kerr) nonlinearities. We consider two different steady states, i.e., a pure second-harmonic and a mixed fundamental/second-harmonic state. Both exhibit this dynamics, which we show to be amenable to a description in terms of reduced frequency-truncated models. The comparison with full numerical simulations of the starting model prove the validity and robustness of the reduced models in characterizing in a simple and elegant way a wide range of modulationally-unstable steady states.

physics.optics↗

arXiv2024

Peregrine solitons and resonant radiation in cubic and quadratic media

We present the fascinating phenomena of resonant radiation emitted by transient rogue waves in cubic and quadratic nonlinear media, particularly those shed from Peregrine solitons, one of the main wavepackets used today to model real-world rogue waves. In cubic media, it turns out that the emission of radiation from a Peregrine soliton can be attributed to the presence of higher-order dispersion, but is affected by the intrinsic local longitudinal variation of the soliton wavenumber. In quadratic media, we reveal that a two-color Peregrine rogue wave can resonantly radiate dispersive waves even in the absence of higher-order dispersion, subjected to a phase-matching mechanism that involves the second harmonic wave, and to a concomitant difference-frequency generation process. In both cubic and quadratic media, we provide simple analytic criteria for calculating the radiated frequencies in terms of material parameters, showing excellent agreement with numerical simulations.

physics.optics↗

arXiv2024

Evidence of 1+1D photorefractive stripe solitons deep in the Kerr limit

The Kerr nonlinearity allows for exact analytic soliton solutions in 1+1D. While nothing excludes that these solitons form in naturally-occurring real-world 3D settings as solitary walls or stripes, their observation has previously been considered unfeasible because of the strong transverse instability intrinsic to the extended nonlinear perturbation. We report the observation of solitons that are fully compatible with the 1+1D Kerr paradigm limit hosted in a 2+1D system. The waves are stripe spatial solitons in bulk copper doped potassium-lithium-tantalate-niobate (KLTN) supported by the unsaturated photorefractive screening nonlinearity. The parameters of the stripe solitons fit well, in the whole existence domain, with the 1+1D existence curve that we derive for the first time in closed form starting from the saturable model of propagation. Transverse instability, that accompanies the solitons embedded in the 3D system, is found to have a gain length much longer than the crystal. Findings establish our system as a versatile platform for investigating exact soliton solutions in bulk settings and in exploring the role of dimensionality at the transition from integrable to non-integrable regimes of propagation.

nlin.PS↗

arXiv2024

Gain-controlled taming of recurrent modulation instability

We show how the recurrence phenomenon characteristic of the nonlinear stage of induced modulational instability in a passive fiber is affected by forcing. An additional linear amplification, even if extremely weak, induces separatrix crossing in correspondence of critical values of the gain around which the recurrence process considerably slows down, switching between dynamical orbits of different kind. We present evidence for such phenomenon in a fiber optics experiment where the gain is finely tuned by means of Raman amplification. A theoretical explanation is also provided that matches almost perfectly with our experimental results.

physics.optics↗

arXiv2022

Extreme wave excitation from localized phase-shift perturbations

The modulation instability is a focusing mechanism responsible for the formation of strong wave localizations not only on the water surface, but also in a variety of nonlinear dispersive media. Such dynamics is initiated from the injection of side-bands, which translate into an amplitude modulation of the wave field. The nonlinear stage of unstable wave evolution can be described by exact solutions of the nonlinear Schr\"odinger equation (NLSE). In that case, the amplitude modulation of such coherent extreme wave structures is connected to a particular phase-shift seed in the carrier wave. In this letter, we show that phase-shifts localization applied to the background, excluding any amplitude modulation excitation, can indeed trigger extreme events. Such rogue waves can be for instance generated by considering the parametrization of fundamental breathers and thus, by seeding only the local phase-shift information to the regular carrier wave. Our wave tank experiments show an excellent agreement with the expected NLSE hydrodynamics and confirm that even though delayed in their evolution, breather-type extreme waves can be generated from a purely regular wave train. Such novel focusing mechanism awaits experimental confirmation in other nonlinear media, such optics, plasma, and Bose-Einstein condensates.

physics.flu-dyn↗

arXiv2022

Multiple symmetry breaking induced by weak damping in the Fermi-Pasta-Ulam-Tsingou recurrence process

We show that even small dissipation can strongly affect the Fermi-Pasta-Ulam-Tsingou recurrence phenomenon. Taking the fully nonlinear stage of modulational instability as an experimentally accessible example, we show that the linear attenuation induces the symmetry of the recurrence to be broken through separatrix crossing occurring at multiple critical values of the attenuation. We provide experimental evidence for this phenomenon in a fiber optics experiment designed in such a way that the effective losses can be carefully tailored by techniques based on Raman amplification.

nlin.PS↗

arXiv2021

Stochastic modulational instability in the nonlinear Schr\"odinger equation with colored random dispersion

We study modulational instability (MI) in optical fibers with random group-velocity dispersion (GVD). We consider Gaussian and dichotomous colored stochastic processes. We resort to different analytical methods (namely, the cumulant expansion and the functional approach) and assess their reliability in estimating the MI gain of stochastic origin. If the power spectral density (PSD) of the GVD fluctuations is centered at null wavenumber, we obtain low-frequency MI sidelobes which converge to those given by a white noise perturbation when the correlation length tends to 0. If instead the stochastic processes are modulated in space, one or more MI sidelobe pairs corresponding to the well-known parametric resonance (PR) condition can be found. A transition from small and broad sidelobes to peaks nearly indistinguishable from PR-MI is predicted, in the limit of large perturbation amplitudes and correlation lengths of the random process. We find that the cumulant expansion provides good analytical estimates for small PSD values and small correlation lengths, when the MI gain is very small. The functional approach is rigorous only for the dichotomous processes, but allows us to model a wider range of parameters and to predict the existence of MI sidelobes comparable to those observed in homogeneous fibers of anomalous GVD

nlin.PS↗

arXiv2020

Stabilization of unsteady nonlinear waves by phase space manipulation

We introduce a dynamic stabilization scheme universally applicable to unidirectional nonlinear coherent waves. By abruptly changing the waveguiding properties, the breathing of wave packets subject to modulation instability can be stabilized as a result of the abrupt expansion a homoclinic orbit and its fall into an elliptic fixed point (center). We apply this concept to the nonlinear Schr\"odinger equation framework and show that an Akhmediev breather envelope, which is at the core of Fermi-Pasta-Ulam-Tsingou recurrence and extreme wave events, can be frozen into a steady periodic (dnoidal) wave by a suitable variation of a single external physical parameter. We experimentally demonstrate this general approach in the particular case of surface gravity water waves propagating in a wave flume with an abrupt bathymetry change. Our results highlight the influence of topography and waveguide properties on the lifetime of nonlinear waves and confirm the possibility to control them.

physics.flu-dyn↗

arXiv2020

Phase-suppressed hydrodynamics of solitons on constant-background plane wave

Soliton and breather solutions of the nonlinear Schrödinger equation (NLSE) are known to model localized structures in nonlinear dispersive media such as on the water surface. One of the conditions for an accurate propagation of such exact solutions is the proper generation of the exact initial phase-shift profile in the carrier wave, as defined by the NLSE envelope at a specific time or location. Here, we show experimentally the significance of such initial exact phase excitation during the hydrodynamic propagation of localized envelope solitons and breathers, which modulate a plane wave of constant amplitude (finite background). Using the example of stationary black solitons in intermediate water depth and pulsating Peregrine breathers in deep-water, we show how these localized envelopes disintegrate while they evolve over a long propagation distance when the initial phase shift is zero. By setting the envelope phases to zero, the dark solitons will disintegrate into two gray-type solitons and dispersive elements. In the case of the doubly-localized Peregrine breather the maximal amplification is considerably retarded; however locally, the shape of the maximal focused wave measured together with the respective signature phase-shift are almost identical to the exact analytical Peregrine characterization at its maximal compression location. The experiments, conducted in two large-scaled shallow-water as well as deep-water wave facilities, are in very good agreement with NLSE simulations for all cases.

nlin.PS↗

arXiv2020

"Extraordinary" modulation instability in optics and hydrodynamics

The classical theory of modulation instability (MI) attributed to Bespalov-Talanov in optics and Benjamin-Feir for water waves is just a linear approximation of nonlinear effects and has limitations that have been corrected using the exact weakly nonlinear theory of wave propagation. We report results of experiments in both, optics and hydrodynamics, which are in excellent agreement with nonlinear theory. These observations clearly demonstrate that MI has wider band of unstable frequencies than predicted by the linear stability analysis. The range of areas where the nonlinear theory of MI can be applied is actually much larger than considered here.

nlin.PS↗

arXiv2020

Phase transitions of photon fluid flows driven by a virtual all-optical piston

The piston problem, i.e. the dynamics in a uniform gas at rest under the action of a moving piston is fundamental problem of physics and a canonical case study in shock wave physics. We investigate theoretically and experimentally the analogous problem for a photon fluid, which turns out to be strongly influenced by the dispersive character of the problem. The experiment makes use of a fiber optics setup where an all-optically controlled quasi instantaneous change of frequency of the input light mimics the piston action. We show that the flow exhibits phase transitions which involve cross-over from regimes characterized by 2-shocks (pushing piston) to 2-rarefaction waves (retracting piston), with the appearance of cavitating states at critical amplitudes of the jump. Importantly, the appearance of vacuum points into the 2-shock marks the transition to a regime which is unique to the photon fluid. Our observations allow for the extensive and quantitative test of the state of the art description of the dispersive Riemann problem, i.e. Whitham modulation theory, applied to the universal defocusing nonlinear Schrödinger equation.

physics.optics↗

arXiv2019

Doubly periodic solutions of the focusing nonlinear Schrödinger equation: recurrence, period doubling and amplification outside the conventional modulation instability band

Solitons on a finite a background, also called breathers, are solutions of the focusing nonlinear Schrödinger equation, which play a pivotal role in the description of rogue waves and modulation instability. The breather family includes Akhmediev breathers (AB), Kuznetsov-Ma (KM), and Peregrine solitons (PS), which have been successfully exploited to describe several physical effects. These families of solutions are actually only particular cases of a more general three-parameter class of solutions originally derived by Akhmediev, Eleonskii and Kulagin [Theor. Math. Phys. {\bf 72}, 809--818 (1987)]. Having more parameters to vary, this significantly wider family has a potential to describe many more physical effects of practical interest than its subsets mentioned above. The complexity of this class of solutions prevented researchers to study them deeply. In this paper, we overcome this difficulty and report several new effects that follow from more detailed analysis. Namely, we present the doubly periodic solutions and their Fourier expansions. In particular, we outline some striking properties of these solutions. Among the new effects, we mention (a) regular and shifted recurrence, (b) period doubling and (c) amplification of small periodic perturbations with frequencies outside the conventional modulation instability gain band.

nlin.SI↗

arXiv2018

Auto-modulation versus breathers in the nonlinear stage of modulational instability

The nonlinear stage of modulational instability in optical fibers induced by a wide and easily accessible class of localized perturbations is studied using the nonlinear Schrodinger equation. It is showed that the development of associated spatio-temporal patterns is strongly affected by the shape and the parameters of the perturbation. Different scenarios are presented that involve an auto-modulation developing in a characteristic wedge, possibly coexisting with breathers which lie inside or outside the wedge.

nlin.PS↗

arXiv2017

Recurrence due to periodic multi-soliton fission in the defocusing nonlinear Schrodinger equation

We address the degree of universality of the Fermi-Pasta-Ulam recurrence induced by multisoliton fission from a harmonic excitation by analysing the case of the semiclassical defocusing nonlinear Schrodinger equation, which models nonlinear wave propagation in a variety of physical settings. Using a suitable Wentzel-Kramers-Brillouin approach to the solution of the associated scattering problem we accurately predict, in full analytical way, the number and the features (amplitude and velocity) of soliton-like excitations emerging post-breaking, as a function of the dispersion smallness parameter. This also permits to predict and analyse the near-recurrences, thereby inferring the universal character of the mechanism originally discovered for the Korteweg-deVries equation. We show, however, that important differences exist between the two models, arising from the different scaling rules obeyed by the soliton velocities.

nlin.SI↗

arXiv2017

Universal behavior of modulationally unstable media

Evidence is presented of universal behavior in modulationally unstable media. An ensemble of nonlinear evolution equations, including three partial differential equations, an integro-differential equation, a nonlocal system and a differential-difference equation, is studied. Collectively, these systems arise in a variety of applications in the physical and mathematical sciences, including water waves, optics, acoustics, Bose-Einstein condensation, and more. All these models exhibit modulational instability, namely, the property that a constant background is unstable to long-wavelength perturbations. In this work, each of these systems is studied analytically and numerically for a number of different initial perturbations of the constant background, and it is shown that, for all systems and for all initial conditions considered, the dynamics gives rise to a remarkably similar structure comprised of two outer, quiescent sectors separated by a wedge-shaped central region characterized by modulated periodic oscillations. A heuristic criterion that allows one to compute some of the properties of the central oscillation region is also given.

nlin.PS↗

arXiv2017

Dispersive dam-break flow of a photon fluid

We investigate the temporal photonic analogue of the dam-break phenomenon for shallow water by exploiting a fiber optics setup. We clearly observe the decay of the step-like input (photonic dam) into a pair of oppositely propagating rarefaction wave and dispersive shock wave. Our results show evidence for a critical transition of the dispersive shock into a self-cavitating state. The detailed observation of the cavitating state dynamics allows for a fully quantitative test of the Whitham modulation theory applied to the universal defocusing nonlinear Schroedinger equation.

physics.optics↗

arXiv2016

Competing Turing and Faraday instabilities in longitudinally modulated passive resonators

We experimentally investigate the interplay of Turing and Faraday (modulational) instabilities in a bistable passive nonlinear resonator. The Faraday branch is induced via parametric resonance owing to a periodic modulation of the resonator dispersion. We show that the bistable switching dynamics is dramatically affected by the competition between the two instability mechanisms, which dictates two completely novel scenarios. At low detunings from resonance switching occurs between the stable stationary lower branch and the Faraday-unstable upper branch, whereas at high detunings we observe the crossover between the Turing and Faraday periodic structures. The results are well explained in terms of the universal Lugiato-Lefever model.

physics.optics↗