Generation Of Rogue Waves Research Articles

Rogue waves in birefringent optical fibers: elliptical and isotropic fibers

Rogue waves in elliptically polarized birefringent optical fibers are analyzed within the framework of a ‘non-integrable’ coupled nonlinear Schrödinger (CNLS) system, which can be used to describe pulse propagation in elliptically birefringent optical fibers. The modulation instability (MI) analysis of this system reveals that, in general, this coupled system is more unstable than its scalar (isotropic) counterpart. In fact, numerical simulations indicate that the generation of rogue events is comparable to the isotropic case. This implies that there is no 1-1 correspondence between rogue wave generation and MI, in these media. The birefringence angle for which the maximum number of rogue events is identified and the nature of the rogue wave is described for the different cases. Although the CNLS system is non-integrable in certain cases these rogue waves are well approximated by the rational solutions of the scalar integrable nonlinear Schrödinger (NLS) equation, while in other cases solitons of the scalar integrable NLS equation are better approximations of these rogue events. In every case, the relative solution of the isotropic system is found to be well suited to describe these waves.

Rogue waves in nonlocal media.

The generation of rogue waves is investigated in a class of nonlocal nonlinear Schrödinger (NLS) equations. In this system, modulation instability is suppressed as the effect of nonlocality increases. Despite this fact, there is a parameter regime where the number and amplitude of the rogue events increase as compared to the standard NLS equation, which is a limit of the system when nonlocality vanishes. Furthermore, the nature of these waves is investigated; while no analytical solutions are known to model these events, it is shown, numerically, that these rogue events differ significantly from the rational soliton (Peregrine) solution of the limiting NLS equation. The universal structure of the associated rogue waves is discussed and a local description is presented. These results can help in the experimental realization of rogue waves in these media.

Spontaneous excitations of low amplitude hole filaments, acoustic vortices, and rogue wave events in weakly disordered dust acoustic waves

In this work, we briefly review our recent experimental studies on the observations and waveform dynamics of spontaneous excitations of low and high amplitude singular objects: low amplitude hole filaments coinciding with the wiggling trajectories of topological defects surrounded by acoustic vortices with helical waveforms, and uncertain rogue wave events, in self-excited weakly disordered dust acoustic waves. The changes of waveform topology, caused by kinking, rupturing and reconnection of sequential wave crests surfaces, and the reversed process, are responsible for the chaotic creation, propagation, and annihilation of acoustic vortex pairs with opposite helicities winding around low amplitude hole filaments. The observed rogue wave events are preceded by a higher probability of surrounding defects. Particle focusing by the transverse electric forces from ruptured and tilted wave crests nearby defects are identified as the major cause for rogue wave generation.

Controlled generation of high-intensity optical rogue waves by induced modulation instability

Optical rogue waves are featured as the generation of high amplitude events at low probability in optical systems. Moreover, the formation of optical rogue waves is unpredictable and transient in photonic crystal fibers. In this paper, we put forward a method to generate high-intensity optical rogue waves in a more controlled way based on induced modulation instability, which can suppress the noise effect and hence play a leading role in the process of pulse evolution. Our numerical simulations indicate that the generation of rogue wave can be controlled when seeding at the optimal modulation frequency and the intensity of rogue wave can be enhanced with appropriate modulation depth. Further, high-intensity rogue wave can also be ejected in the fiber with a shorter propagation length by regulating the modulation depth. These results all provide a better understanding of optical rogue wave, which can contribute to the generation of tunable long-wavelength spectral components and selective excitation of mid-infrared supercontinuum.

Ion-acoustic waves in ultracold neutral plasmas: Modulational instability and dissipative rogue waves

Progress is reported on the modulational instability (MI) of ion-acoustic waves (IAWs) and dissipative rogue waves (RWs) in ultracold neutral plasmas (UNPs). The UNPs consist of inertial ions fluid and Maxwellian inertialess hot electrons, and the presence of an ion kinematic viscosity is allowed. For this purpose, a modified nonlinear Schrödinger equation (NLSE) is derived and then solved analytically to show the occurrence of MI. It is found that the (in)stability regions of the wavepacks are dependent on time due to of the existence of the dissipative term. The existing regions of the MI of the IAWs are inventoried precisely. After that, we use a suitable transformation to convert the modified NLSE into the normal NLSE whose analytical solutions for rogue waves are known. The rogue wave propagation condition and its behavior are discussed. The impact of the relevant physical parameters on the profile of the RWs is examined.

Generation of rogue waves in gyrotrons with high excess over the threshold

Generation of rogue waves in gyrotrons with high excess over the threshold

Graphene-Decorated Microfiber Photonic Device for Generation of Rogue Waves in a Fiber Laser

We reported on the rogue wave generation in a passively mode-locked fiber laser by utilizing a graphene-decorated microfiber photonic device (GMPD). The GMPD, which simultaneously possesses highly nonlinear and saturable absorption effects, provides the suitable condition for investigating rogue waves. With the proper pump power, the localized noise-like multi-pulse wave packet could be easily generated from the proposed fiber laser, which leads to generation of high-contrast fast intensity fluctuations of ultrashort pulse events, namely, rogue waves. Our findings indicate that the graphene-deposited microfiber waveguide structure indeed could be an excellent highly nonlinear photonic device for observing nonlinear dynamics such as rogue waves in optical systems.

Generation of Rogue Waves by Interaction of Relativistic Electron Beam with Unmagnetized Dusty Plasma Physical Consistency of Theories with Fermions in the Division Algebra Modules

Generation of Rogue Waves by Interaction of Relativistic Electron Beam with Unmagnetized Dusty Plasma Physical Consistency of Theories with Fermions in the Division Algebra Modules

Role of Multiple Soliton Interactions in the Generation of Rogue Waves: The Modified Korteweg-de Vries Framework.

The role of multiple soliton and breather interactions in the formation of very high waves is disclosed within the framework of the integrable modified Korteweg-de Vries (MKdV) equation. Optimal conditions for the focusing of many solitons are formulated explicitly. Namely, trains of ordered solitons with alternate polarities evolve to huge strongly localized transient waves. The focused wave amplitude is exactly the sum of the focusing soliton heights; the maximum wave inherits the polarity of the fastest soliton in the train. The focusing of several solitary waves or/and breathers may naturally occur in a soliton gas and will lead to rogue-wave-type dynamics; hence, it represents a new nonlinear mechanism of rogue wave generation. The discovered scenario depends crucially on the soliton polarities (phases), and is not taken into account by existing kinetic theories. The performance of the soliton mechanism of rogue wave generation is shown for the example of the focusing MKdV equation, when solitons possess "frozen" phases (certain polarities), though the approach is efficient in some other integrable systems which admit soliton and breather solutions.

Rogue waves generation via nonlinear soliton collision in multiple-soliton state of a mode-locked fiber laser.

We report for the first time, rogue waves generation in a mode-locked fiber laser that worked in multiple-soliton state in which hundreds of solitons occupied the whole laser cavity. Using real-time spatio-temporal intensity dynamics measurements, it is unveiled that nonlinear soliton collision accounts for the formation of rogue waves in this laser state. The nature of interactions between solitons are also discussed. Our observation may suggest similar formation mechanisms of rogue waves in other systems.

Characterization of optical rogue wave based on solitons' eigenvalues of the integrable higher-order nonlinear Schrödinger equation

The dynamics of the optical rogue wave phenomenon in the framework of integrable higher-order nonlinear Schrödinger equation (HNLSE) including the third order dispersion term is presented in this paper. When rogue waves generate through soliton collision, the colliding solitons' eigenvalues of the associated equation of HNLSE should be constant in the vicinity of rogue wave generation. Our results reveal that soliton collision is one of the generation mechanisms of optical rogue waves in anomalous dispersion fiber by taking the third order dispersion into consideration in the HNLSE based model.

Controllable rogue waves in Lugiato–Lefever equation with higher-order nonlinearities and varying coefficients

We report an analytical solutions of the Lugiato–Lefever equation with quintic nonlinearity, nonlinear dispersion effects and varying coefficients. With the help of the similarity transformation method, we describe rogue waves generation and its control in optical micro-resonators. Our results reveal how to control the trajectories of wave centers, the evolutions of wave peaks and the dynamical behavior of the first order rogue waves. Thus, we study the effect of the higher-order nonlinearities, external pump power of a continuous-wave laser, dispersion and dissipation parameters.

Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves

We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schrödinger (NLS) equation with the initial condition in the form of a rectangular barrier (a ‘box’). We use the Whitham modulation theory combined with the nonlinear steepest descent for the semi-classical inverse scattering transform, to describe the evolution and interaction of two counter-propagating nonlinear wave trains—the dispersive dam break flows—generated in the NLS box problem. We show that the interaction dynamics results in the emergence of modulated large-amplitude quasi-periodic breather lattices whose amplitude profiles are closely approximated by the Akhmediev and Peregrine breathers within certain space-time domain. Our semi-classical analytical results are shown to be in excellent agreement with the results of direct numerical simulations of the small-dispersion focusing NLS equation.

Effect of vorticity on the generation of rogue waves due to dispersive focusing

The kinematic and dynamic of steep two-dimensional focusing wave trains on a shearing flow in deep water are investigated analytically and numerically. In the absence of waves, the vorticity due to the vertical gradient of the horizontal current velocity is assumed constant. A linear kinematic model based on the spatio-temporal evolution of the frequency is derived, predicting the focusing distance and time of a chirped wave packet in the presence of constant vorticity. Furthermore, a linear model, based on a Fourier integral, is used to describe the evolution of the free surface on shearing current. To compute the fully nonlinear evolution of the wave group in the presence of vorticity, a new numerical model, based on a BIEM approach, is developed. On the basis of these different approaches, the role of constant vorticity on rogue wave occurrence is analysed. Two main results are obtained: (1) the linear behaviour expected in the presence of constant vorticity is significantly different from what is commonly expected in the presence of constant current and (2) the nonlinear effects are found to be of significant influence in the case at hand.

Influence of optical activity on rogue waves propagating in chiral optical fibers.

We derive the nonlinear Schrödinger (NLS) equation in chiral optical fiber with right- and left-hand nonlinear polarization. We use the similarity transformation to reduce the generalized chiral NLS equation to the higher-order integrable Hirota equation. We present the first- and second-order rational solutions of the chiral NLS equation with variable and constant coefficients, based on the modified Darboux transformation method. For some specific set of parameters, the features of chiral optical rogue waves are analyzed from analytical results, showing the influence of optical activity on waves. We also generate the exact solutions of the two-component coupled nonlinear Schrödinger equations, which describe optical activity effects on the propagation of rogue waves, and their properties in linear and nonlinear coupling cases are investigated. The condition of modulation instability of the background reveals the existence of vector rogue waves and the number of stable and unstable branches. Controllability of chiral optical rogue waves is examined by numerical simulations and may bring potential applications in optical fibers and in many other physical systems.

Numerical study of the generation and evolution of breather-type rogue waves

The behaviour of the Peregrine breather-type rogue waves is numerically studied based on the fourth-order nonlinear Schrödinger equation. The wavelet analysis method is adopted in order to analyse the time-frequency energy distribution during the generation and evolution of the Peregrine breather. It shows that the peak of the largest amplitudes of the resulting waves can be described in terms of the Peregrine breather-type solution and leads to the solution of the nonlinear Schrödinger (NLS) equation. Meanwhile, strong energy density is found to surge instantaneously and be seemingly carried over to the high-frequency components at the instant when the large, rogue wave occurs.

Rogue wave triggered at a critical frequency of a nonlinear resonant medium.

We consider a two-level atomic system interacting with an electromagnetic field controlled in amplitude and frequency by a high intensity laser. We show that the amplitude of the induced electric field admits an envelope profile corresponding to a breather soliton. We demonstrate that this soliton can propagate with any frequency shift with respect to that of the control laser, except a critical frequency, at which the system undergoes a structural discontinuity that transforms the breather in a rogue wave. A mechanism of generation of rogue waves by means of an intense laser field is thus revealed.

Statistical characterization of the internal structure of noiselike pulses using a nonlinear optical loop mirror

In this work we study statistically the internal structure of noiselike pulses generated by a passively mode-locked fiber laser. For this purpose, we use a technique that allows estimating the distribution of the amplitudes of the sub-pulses in the bunch. The technique takes advantage of the fast response of the optical Kerr effect in a fiber nonlinear optical loop mirror (NOLM). It requires the measurement of the energy transfer characteristic of the pulses through the NOLM, and the numerical resolution of a system of nonlinear algebraic equations. The results yield a strongly asymmetric distribution, with a high-amplitude tail that is compatible with the existence of extreme-intensity sub-pulses in the bunch. Following the recent discovery of pulse-energy rogue waves and spectral rogue waves in the noiselike pulse regime, we propose a new way to look for extreme events in this particular mode of operation of mode-locked fiber lasers, and confirm that rogue wave generation is a key ingredient in the complex dynamics of these unconventional pulses.

Generation of acoustic rogue waves in dusty plasmas through three-dimensional particle focusing by distorted waveforms

Rogue waves have been observed in fluids and other wave contexts. Experiments now show the formation of 3D acoustic rogue waves in dusty plasmas; they result from wave–particle interactions driving the dust particles into high-amplitude dynamics. Rogue waves—rare uncertainly emerging localized events with large amplitudes—have been experimentally observed in many nonlinear wave phenomena, such as water waves1,2,3,4,5,6, optical waves7,8, second sound in superfluid He II (ref. 9) and ion acoustic waves in plasmas10. Past studies have mainly focused on one-dimensional (1D) wave behaviour through modulation instabilities1,3,4,5,7,11, and to a lesser extent on higher-dimensional behaviour5,6,8,11,12. The question whether rogue waves also exist in nonlinear 3D acoustic-type plasma waves, the kinetic origin of their formation and their correlation with surrounding 3D waveforms are unexplored fundamental issues. Here we report the direct experimental observation of dust acoustic rogue waves in dusty plasmas and construct a picture of 3D particle focusing by the surrounding tilted and ruptured wave crests, associated with the higher probability of low-amplitude holes for rogue-wave generation.

Optical Dark Rogue Wave.

Photonics enables to develop simple lab experiments that mimic water rogue wave generation phenomena, as well as relativistic gravitational effects such as event horizons, gravitational lensing and Hawking radiation. The basis for analog gravity experiments is light propagation through an effective moving medium obtained via the nonlinear response of the material. So far, analogue gravity kinematics was reproduced in scalar optical wave propagation test models. Multimode and spatiotemporal nonlinear interactions exhibit a rich spectrum of excitations, which may substantially expand the range of rogue wave phenomena, and lead to novel space-time analogies, for example with multi-particle interactions. By injecting two colliding and modulated pumps with orthogonal states of polarization in a randomly birefringent telecommunication optical fiber, we provide the first experimental demonstration of an optical dark rogue wave. We also introduce the concept of multi-component analog gravity, whereby localized spatiotemporal horizons are associated with the dark rogue wave solution of the two-component nonlinear Schrödinger system.