Dissipative Rogue Waves Research Articles

Transient dynamics of dissipative solitons formation in a net-normal dispersion mode-locked fiber laser based on nonlinear polarization evolution.

In mode-locked fiber lasers, the formation of ultrashort pulses from noisy or unstable states is a crucial area of research. Investigating these complex nonlinear dynamics can lead to valuable insights and new practical engineering techniques, particularly for the design and optimization of optical systems. Time-stretch dispersive Fourier transform, utilized in our study to investigate dissipative solitons formation in a net-normal dispersion nonlinear polarization evolution mode-locked fiber laser, provides a window into the intricate dynamics of such systems. In our experiments, the identification of five distinct transient stages in the formation process sheds light on the underlying mechanisms of dissipative soliton (DS) formation. The five distinct transient stages involved in the formation process include relaxation oscillation, modulation instability, spectral broadening, soliton explosions (SEs), and stable mode-locking. Notably, we also observed the generation of dissipative rogue waves during the SE stage. Our findings shed light on the intricate dynamics of DS formation and offer valuable insights for the design and optimization of mode-locked fiber lasers.

Dissipative rogue waves generated by multi-soliton explosions in an ultrafast fiber laser.

Derived from oceanography, nowadays the investigation of rogue waves (RWs) has been widely spread in various fields, particularly in nonlinear optics. Passively mode-locked fiber laser has been regarded as one of the excellent platforms to investigate the dissipative RWs (DRWs). Here, we report the observation of DRW generation induced by single and multi-soliton explosions in a passively mode-locked fiber laser. It was demonstrated that through the gain-mediated soliton interactions, one soliton could erupt because of the explosion of another soliton in the laser cavity. Meanwhile, the high-amplitude waves, which fulfill the DRWs criteria, could be detected in the multi-soliton explosion states. The DRWs were identified by characterizing the peak intensity statistics of the time-stretched soliton profiles. Particularly, it was found that the ratio between the highest recorded amplitudes and significant wave heights (SWHs) of DRWs induced by multi-soliton explosions is higher than that by single-soliton explosion case. Our findings will further contribute to the understanding of the physical mechanisms of DRWs in the soliton explosion regime.

Multi-Raman soliton self-frequency shifts and dissipative rogue wave trains induced by cubic-quintic-Raman contributions in a double-negative material

We examine the cubic-quintic-Raman influences on the system when the second-order dispersion and the cubic-quintic-nonlinearities act in a double-negative material. This research is done for both absorption and negative index regimes. Using the collective coordinates’ technique, the quintic-nonlinearity induces the generation of Kuznetsov-Ma breathers and Peregrine soliton. Thereafter, the cubic-Raman effect comes into play and breeds the chaotic Peregrine waves’ field, the complex rogue event, and the modified complex rogue event. Therefore, the quintic-Raman effect induces first-, second-, and third-forms of the dissipative rogue waves and the twin parallel wave trains. Some fascinating phenomena such as deletion of waves, damping effect, tree structure, and disintegration of the Raman soliton self-frequency shift leading to the multi-Raman soliton self-frequency shifts, are also scrutinized. Further, internal strife leading to these above-mentioned effects, are likewise presented in detail.

On the Analytical and Numerical Solutions of the Linear Damped NLSE for Modeling Dissipative Freak Waves and Breathers in Nonlinear and Dispersive Mediums: An Application to a Pair-Ion Plasma

In this work, two approaches are introduced to solve a linear damped nonlinear Schrödinger equation (NLSE) for modeling the dissipative rogue waves (DRWs) and dissipative breathers (DBs). The linear damped NLSE is considered a non-integrable differential equation. Thus, it does not support an explicit analytic solution until now, due to the presence of the linear damping term. Consequently, two accurate solutions will be derived and obtained in detail. The first solution is called a semi-analytical solution while the second is an approximate numerical solution. In the two solutions, the analytical solution of the standard NLSE (i.e., in the absence of the damping term) will be used as the initial solution to solve the linear damped NLSE. With respect to the approximate numerical solution, the moving boundary method (MBM) with the help of the finite differences method (FDM) will be devoted to achieve this purpose. The maximum residual (local and global) errors formula for the semi-analytical solution will be derived and obtained. The numerical values of both maximum residual local and global errors of the semi-analytical solution will be estimated using some physical data. Moreover, the error functions related to the local and global errors of the semi-analytical solution will be evaluated using the nonlinear polynomial based on the Chebyshev approximation technique. Furthermore, a comparison between the approximate analytical and numerical solutions will be carried out to check the accuracy of the two solutions. As a realistic application to some physical results; the obtained solutions will be used to investigate the characteristics of the dissipative rogue waves (DRWs) and dissipative breathers (DBs) in a collisional unmagnetized pair-ion plasma. Finally, this study helps us to interpret and understand the dynamic behavior of modulated structures in various plasma models, fluid mechanics, optical fiber, Bose-Einstein condensate, etc.

Adomian decomposition method for modelling the dissipative higher-order rogue waves in a superthermal collisional plasma

A reductive perturbation technique (the derivative expansion technique (DET)) is employed to derive a linear damped nonlinear Schrödinger equation (LDNLSE) for investigating the feature properties of the dissipative modulated nonlinear dust-acoustic wavepacket including rogue waves (RWs) in an electron-ion dusty plasma having superthermal electrons and ions. The modulational instability (MI) of the dissipative envelope structures is investigated and the (un)stable domain of the modulated structures is mapped precisely. The LDNLSE is solved numerically using Adomian decomposition method (ADM) in order to study the impact of the related plasma parameters on the features of the dissipative RWs. The influence of superthermal parameters and the dust-neutral collisional frequency on the profile of the dissipative dust-acoustic RWs is numerically investigated. Moreover, the accuracy of the numerical solutions is examined by estimating the global residual error in the whole space-time domain.

Three-dimensional dissipative ion-acoustic rogue waves in magnetized plasma with adiabatic ions and nonextensive electrons

ABSTRACT The modulational instability of ion-acoustic rogue waves in a three-dimensional magnetized, dissipative plasma consisting of inertial warm positive ions and nonextensive electrons has been theoretically investigated. Using the well-known reductive perturbation method, the (3+1)-dimensional modified nonlinear Schrödinger equation (mNLSE), i.e. the standard NLSE in addition to the dissipative term has been derived and then solved to obtained instability criteria, as well as first- and second-order rogue wave solutions. It is found that increasing viscosity results in dissipation of energy which makes the IARW shorter and thinner as was reported in the literature. Furthermore effects of relevant parameters such as nonextensive parameter, and magnetic field on growth rate and rogue waves solutions were discussed in detail. The results of the present investigation may be useful in understanding and predicting the nonlinear excitations that occur in space and laboratory dissipative plasma systems.

The Hybrid Finite Difference and Moving Boundary Methods for Solving a Linear Damped Nonlinear Schrödinger Equation to Model Rogue Waves and Breathers in Plasma Physics

In this paper, the dissipative and nondissipative modulated pulses such as rogue waves (RWs) and breathers (Kuznetsov-Ma breathers and Akhmediev breathers) that can exist and propagate in several fields of sciences, for example, plasma physics, have been analyzed numerically. For this purpose, the fluid dusty plasma equations with taking the kinematic dust viscosity into account are reduced to the linear damped nonlinear Schrödinger equation using a reductive perturbation technique. It is known that this equation is not integrable and, accordingly, does not have analytical solution. Thus, for modelling both dissipative RWs and breathers, the improved finite difference method is introduced for this purpose. It is found that FDM is a good numerical technique for small time interval but for large time interval it becomes sometimes unacceptable. Therefore, to describe these waves accurately, the new improved numerical method is considered, which is called the hybrid finite difference method and moving boundary method (FDM-MBM). This last and updated method gives an accurate and excellent description to many physical results, as it was applied to the dust plasma results and the results were good.

Breathing dissipative soliton explosions in a bidirectional ultrafast fiber laser

Soliton explosions, among the most exotic dynamics, have been extensively studied on parameter invariant stationary solitons. However, the explosion dynamics are still largely unexplored in breathing dissipative solitons as a dynamic solution to many nonlinear systems. Here, we report on the first observation of a breathing dissipative soliton explosion in a net-normal-dispersion bidirectional ultrafast fiber laser. The breathing soliton explosions could be stimulated by the soliton buildup process or alteration of polarization settings. Transient breathing soliton pairs with intensive repulsion that is sensitive to initial conditions can also be triggered by multiple soliton explosions in the soliton buildup process instead of being triggered by varying polarization settings. The high behavior similarity also exists in the breathing soliton buildup and explosion process owing to the common gain and loss modulation. In addition, dissipative rogue waves were detected in the breathing soliton explosion, and the collision of breathing soliton significantly enhanced the amplitude of rogue waves, which is characteristic of the breathing solitons in a bidirectional fiber laser. These results shed new insights into complex dissipative soliton dynamics.

Rogue waves of the dissipative Gross–Pitaevskii equation with distributed coefficients

By introducing a suitable ansatz and employing the similarity transformation technique, we construct the first- and second-order rational solutions for a quasi-one-dimensional (1D) dissipative Gross–Pitaevskii (GP) equation with a time-varying cubic nonlinearity and an external time-dependent potential. Then, by using these solutions, we engineer first- and second-order rogue waves in the Bose–Einstein condensate (BEC) contexts for the experimentally relevant systems when the gain/loss of atoms is taken into consideration. Our analysis shows that the control of the scattering length, the external harmonic, and the linear trapping potentials allows one to manage the motion and the background of dissipative rogue matter waves in BEC systems. We show that the wave amplitudes depend on the absolute value of s-wave scattering and the bias magnetic field, while its motion depends on the external trapping potentials. We show that unlike classical rogue waves, the nonzero continuous wave backgrounds of non-autonomous forced (damped) rogue matter waves in BECs with time-dependent complicated potential increases (decreases) during the wave motion. Our results also reveal that neither the gain nor the loss of the BEC atoms affects the amplitude of the rogue matter waves during their propagation. Our results may help to control and manage experimentally dissipative rogue waves in a BEC systems.

Control of dissipative rogue waves in nonlinear cavity optics: Optical injection and time-delayed feedback.

We investigate and review the formation of two-dimensional dissipative rogue waves in cavity nonlinear optics with transverse effects. Two spatially extended systems are considered for this purpose: the driven Kerr optical cavities subjected to optical injection and the broad-area surface-emitting lasers with a saturable absorber. We also consider a quasi-two-dimensional system (the two dimensions being space and time) of a fiber laser describing the complex cubic-quintic Ginzburg-Landau equation. We show that rogue waves are controllable by means of time-delayed feedback and optical injection. We show that without delayed feedback, transverse structures are stationary or oscillating. However, when the strength of the delayed feedback is increased, all the systems generate giant two-dimensional pulses that appear with low probability and suddenly appear and disappear. We characterize their formation by computing the probability distribution, which shows a long tail. Besides, we have computed the significant wave height, which measures the mean wave height of the highest third of the waves. We show that for all systems, the distribution tails expand beyond two times the significant wave height. Furthermore, we also show that optical injection may suppress the rogue wave formation in a semiconductor laser with a saturable absorber.

“Periodic” soliton explosions in a dual-wavelength mode-locked Yb-doped fiber laser

We report the “periodic” soliton explosions induced by intracavity soliton collisions in a dual-wavelength mode-locked Yb-doped fiber laser. Owing to the different group velocities of the two wavelengths, the mode-locked solitons centered at different wavelengths would periodically collide with each other. By using the dispersive Fourier transformation technique, it was found that each collision would induce soliton explosions, but none of them would be identical. Therefore, this phenomenon was termed as “periodic” soliton explosions. In addition, the dissipative rogue waves were detected in the dual-wavelength mode-locked state. The experimental results would be fruitful to the communities interested in soliton dynamics and dual-comb lasers.

Impact of dust kinematic viscosity on the breathers and rogue waves in a complex plasma having kappa distributed particles

In this paper, a numerical examination of propagating nonlinear dissipative dust-acoustic breathers and rogue waves (RWs) in electron depleted dusty plasmas having two superthermal ions of different temperature has been made. An important ingredient in this study is the inclusion of the dissipative effect due to the viscosity of the dust grains in the evolution wave equation. Accordingly, a damped/modified nonlinear Schrödinger equation (DNLSE), i.e. the standard nonlinear Schrödinger equation (NLSE) in addition to the damping term, is obtained using a reductive perturbation (the derivative expansion) method. Without taking into account the effect of dust viscosity, the standard NLSE is also examined, and the effect of relevant physical parameters on the breathers and rogue waves is examined. Moreover, the impact of dust kinetic viscosity on both breather structures and RWs is investigated by solving DNLSE numerically with the Dirichlet boundary conditions. This model may be useful to understand the excitation of dust-acoustic waves in the Earth's magnetotail.

Evolution of Dissipative Low-Frequency Rogue Waves in Superthermal Dusty Plasmas

The evolution of dissipative dust-ion acoustic (DIA) rogue waves is studied in a collisional dusty plasma with superthermal electrons. Multiple-time-scale reduction shows that the nonlinear dynamics of low-frequency waves reduces to a modified nonlinear Schrodinger (mNLS) equation. This equation captures the main features of modulated waves and shows a criterion in determining the maximum time for the occurrence of the modulational instability. It is found that the impact of such an energetic tail of electrons is to narrow the stability region in a dusty plasma with source and sink. Within the instability window, we have shown that the mNLS equation in a weakly dissipative plasma is responsible for the formation of DIA rogue waves. The possible region for the existence of dissipative rogue waves is precisely defined for physical parameters. It is shown that the rogue wave profile is very sensitive to any changes in the electron superthermality and dissipative parameters.

Rogue waves in a linear cavity Yb-fiber laser through spectral filtering induced pulse instability.

In this Letter, experimental observation of dissipative rogue waves (DRWs) due to spectral filtering induced pulse instabilities in a mode-locked ytterbium (Yb) fiber laser has been presented. A semiconductor saturable absorber mirror was used to mode-lock the linear cavity laser and a chirped fiber Bragg grating (CFBG) was used for dispersion management, which also acted as a spectral filter and output coupler. Under stable conditions, the cavity delivered dispersion managed dissipative solitons of 447fs duration and 0.69nJ pulse energy at 10.19MHz repetition rate with uniform intensity distribution over a long time span. As the spectral width increased with pump power, random intensity fluctuations were observed in the pulse train due to the filtering effect of the CFBG. Employing a dispersive Fourier transform by stretching the output pulse train in time allowed the existence of DRWs more than 4 times stronger than the significant wave height to be observed. Further increments of pump power led to a stable multi-pulsing state.

Numerical Investigation of the Dynamics of ‘Hot Spots’ as Models of Dissipative Rogue Waves

In this paper, the effect of gain or loss on the dynamics of rogue waves is investigated by using the complex Ginzburg-Landau equation as a framework. Several external energy input mechanisms are studied, namely, constant background or compact Gaussian gains and a ‘rogue gain’ localized in space and time. For linear background gain, the rogue wave does not decay back to the mean level but evolves into peaks with growing amplitude. However, if such gain is concentrated locally, a pinned mode with constant amplitude could replace the time transient rogue wave and become a sustained feature. By restricting such spatially localized gain to be effective only for a finite time interval, a ‘rogue-wave-like’ mode can be recovered. On the other hand, if the dissipation is enhanced in the localized region, the formation of rogue wave can be suppressed. Finally, the effects of linear and cubic gain are compared. If the strength of the cubic gain is large enough, the rogue wave may grow indefinitely (‘blow up’), whereas the solution under a linear gain is always finite. In conclusion, the generation and dynamics of rogue waves critically depend on the precise forms of the external gain or loss.

Dissipative Rogue Waves Among Noise-Like Pulses in a Tm Fiber Laser Mode Locked by a Monolayer MoS2 Saturable Absorber

We report on the experimental and numerical investigations of dissipative rogue waves (DRWs) among noise-like pulses, in a thulium-doped fiber laser mode locked by a monolayer MoS2 saturable absorber. By increasing the pumping power or weakening the effective cavity spectral filtering, the statistics distributions of the pulse events deviate from the Gaussian statistics to the L-shaped distributions with long tail, accompanied by the increase of the DRWs proportion. Our observations reveal the dissipat-ive nature of rogue waves in dissipative systems.

Extreme events and single-pulse spatial patterns observed in a self-pulsing all-solid-state laser.

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 of the absorber, which is easy to adjust, different dynamical regimes are observed: continuous-wave emission, stable oscillations, period doubling bifurcations, chaos, and, within some chaotic regimes, extreme events (EEs) in the form of pulses of extraordinary intensity. These pulses are sometimes called "dissipative optical rogue waves." The mechanism of their formation in this laser is unknown. Previous observations suggest they are caused by the interaction of a few transverse modes. Here we report a direct observation of the pulse-to-pulse evolution of the transverse pattern. In the periodical regimes, sequences of intensities are correlated with sequences of patterns. In the chaotic ones, a few different patterns alternate, and the EEs are related with even fewer ones. In addition, the series of patterns and the pulse intensities before and after an EE are markedly repetitive. These observations demonstrate that EEs follow a deterministic evolution, and that they can appear even in a system with few interacting modes. This information plays a crucial role for the development of a mathematical description of EEs in this laser. This would allow managing the formation of EE through control of chaos, which is of both academic and practical interest (laser rangefinder).

Drifting cavity solitons and dissipative rogue waves induced by time-delayed feedback in Kerr optical frequency comb and in all fiber cavities.

Time-delayed feedback plays an important role in the dynamics of spatially extended systems. In this contribution, we consider the generic Lugiato-Lefever model with delay feedback that describes Kerr optical frequency comb in all fiber cavities. We show that the delay feedback strongly impacts the spatiotemporal dynamical behavior resulting from modulational instability by (i) reducing the threshold associated with modulational instability and by (ii) decreasing the critical frequency at the onset of this instability. We show that for moderate input intensities it is possible to generate drifting cavity solitons with an asymmetric radiation emitted from the soliton tails. Finally, we characterize the formation of rogue waves induced by the delay feedback.

Spatiotemporal chaos and two-dimensional dissipative rogue waves in Lugiato-Lefever model

Driven nonlinear optical cavities can exhibit complex spatiotemporal dynamics. We consider the paradigmatic Lugiato-Lefever model describing driven nonlinear optical resonator. This model is one of the most-studied nonlinear equations in optics. It describes a large spectrum of nonlinear phenomena from bistability, to periodic patterns, localized structures, self-pulsating localized structures and to a complex spatiotemporal behavior. The model is considered also as prototype model to describe several optical nonlinear devices such as Kerr media, liquid crystals, left handed materials, nonlinear fiber cavity, and frequency comb generation. We focus our analysis on a spatiotemporal chaotic dynamics in one-dimension. We identify a route to spatiotemporal chaos through an extended quasiperiodicity. We have estimated the Kaplan-Yorke dimension that provides a measure of the strange attractor complexity. Likewise, we show that the Lugiato-Leferver equation supports rogues waves in two-dimensional settings. We characterize rogue-wave formation by computing the probability distribution of the pulse height.

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.