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Explosion induced rogue waves and chaotic multi-pulsing in a passively mode-locked all-normal dispersion fiber laser
摘要： In this work, an experimental study of non-stationary pulse dynamics consisting of explosion events and chaotic multi-pulsing from an all-normal dispersion Yb-fiber laser operating in noise-like pulse (NLP) state have been reported. During explosion in NLP state, which resembled soliton explosion, dispersive Fourier transform measurements revealed large, intermittent amplitude fluctuations in the real-time spectrum indicative of rogue waves. The fluctuations either appeared randomly at the lasing wavelength within the Yb-gain spectra or at the frequency downshifted Raman Stokes wavelength. It was also observed that such fluctuation at the Raman wavelength could even exceed the amplitude of the spectral components at the main lasing wavelength. With suitable adjustments, the laser operation could be switched to chaotic multi-pulsing state where the acquisition of a large number of consecutive roundtrips revealed inter-pulse motion with unique trajectories occurring over millisecond time scales.
关键词： optical rogue waves,multi-pulsing,non-stationary pulse dynamics,noise-like pulse,fiber lasers,mode-locked fiber lasers,non-linear dynamics
更新于2025-09-23 15:21:01
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Characteristics of higher-order vector rogue waves to a coupled fourth-order nonlinear Schr??dinger system in a two-mode optical fiber
摘要： Optical ?ber communication serves a signi?cant role in recent communication. Investigated in the work is a coupled fourth-order nonlinear Schr?dinger system for the ultrashort optical pulses in a two-mode optical ?ber. For the complex envelopes of two ?eld polarization components, we work out the Darboux transformation and higher-order vector rogue-wave solutions. The second-order vector rogue waves with the triangle structure, each component of which is composed of three four-petaled rogue waves, are shown. With the strength of the higher-order linear and nonlinear effects increasing, width of the triangle structure along the distance axis decreases, while width of the triangle structure along the time axis increases. We obtain the second-order vector rogue waves with the merged structure and the third-order vector rogue waves with the triangle and pentagon structures. We expect that our results could be helpful in studying the rogue-wave phenomena in the nonlinear optics.
关键词： Nonlinear Schr?dinger system,Optical ?ber communication,Darboux transformation,Rogue waves,Higher-order effects
更新于2025-09-23 15:19:57
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Vector rational and semi-rational rogue waves for the coupled cubic-quintic nonlinear Schr??dinger system in a non-Kerr medium
摘要： Non-Kerr media possess certain applications in photonic lattices and optical fibers. Studied in this paper are the vector rational and semi-rational rogue waves in a non-Kerr medium, through the coupled cubic-quintic nonlinear Schr?dinger system, which describes the effects of quintic nonlinearity on the ultrashort optical pulse propagation in the medium. Applying the gauge transformations, we derive the N th-order Darboux transformtion and N th-order vector rational and semi-rational rogue wave solutions, where N is a positive integer. With such solutions, we present three types of the second-order rogue waves with the triangle structure: the one with each component containing three four-petalled rogue waves, the one with each component containing three eye-shaped rogue waves, and the other with one component containing three anti-eye-shaped rogue waves and the other component containing three eye-shaped rogue waves. We exhibit the third-order vector rogue waves with the merged, triangle and pentagon structures in each component. Moreover, we show the first- and second-order vector semi-rational rogue waves which display the coexistence of the rogue waves and the breathers.
关键词： Rational rogue waves,Coupled cubic-quintic nonlinear Schr?dinger system,Darboux transformation,Semi-rational rogue waves,Non-Kerr medium
更新于2025-09-19 17:13:59
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Breather waves, high-order rogue waves and their dynamics in the coupled nonlinear Schr?dinger equations with alternate signs of nonlinearities
摘要： We consider the analytic vector breather and high-order rogue wave solutions for the coupled nonlinear Schr?dinger (NLS) equations with alternate signs of nonlinearities via Darboux dressing transformation. By adjusting spectral parameters, we indicate that the breather wave solutions contain temporally periodic nonlinear waves and spatially periodic nonlinear waves, respectively. The vector rogue wave solutions include the bright one-peak-two-valleys rogue wave and the bright rogue wave without valleys. Additionally, we successfully show different types of the distributions for the second-order vector rogue waves. The existence condition for the rogue waves is discussed. For the coupled NLS equations with alternate signs of nonlinearities, the rogue wave solutions exist if the baseband modulation instability (MI) is present.
关键词： Darboux dressing transformation,high-order rogue waves,modulation instability,coupled nonlinear Schr?dinger equations,breather waves
更新于2025-09-19 17:13:59
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On the role of four-wave mixing effect in the interactions between nonlinear modes of coupled generalized nonlinear Schr?dinger equation
摘要： In this paper, we investigate the effect of four-wave mixing in the interactions among nonlinear waves such as solitons, breathers, and rogue waves of a coupled generalized nonlinear Schr?dinger equation. We explore several interesting results including superposition of breather pulses, increment in the number of breather pulses and in amplitudes of breathers, and rogue waves. By strengthening the four-wave mixing parameter, we observe different transformations that occur between different localized structures. For instance, we visualize a transformation from bright soliton to breather form, bright and dark rogue wave to four-petaled rogue wave structures, four-petaled rogue wave to other rogue wave forms, and so on. Another important observation that we report here is that the interaction of a bright soliton with a rogue wave in the presence of the four-wave mixing effect provides interaction between a dark oscillatory soliton and a rogue wave.
关键词： solitons,coupled generalized nonlinear Schr?dinger equation,breathers,four-wave mixing,rogue waves,nonlinear waves
更新于2025-09-12 10:27:22
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Numerical study of complex dynamics and extreme events within noise-like pulses from an erbium figure-eight laser
摘要： Some complex dissipative dynamics associated with the noise-like pulse (NLP) regime of a passively mode-locked erbium-doped ?ber laser are studied numerically. By means of a convenient 3D mapping of the spatio-temporal pulse evolution, for properly chosen dispersion parameters, several puzzling dissipative dynamics of NLPs are identi?ed, including the expelling of sub-packets that move away from the main bunch, the sudden extinction of isolated sub-pulses, the collision between di?erent internal fragments travelling at di?erent speeds, the rising of sub-pulses, the formation of complex trajectories by substructures that ?rst move away and then return to the main bunch, and so on. In addition, the emergence of optical rogue waves (ORWs) within NLPs is also demonstrated numerically; to help understand these behaviors evidenced in the time domain, spectral analyzes were also performed that show, among other things, that the spectrum of a NLP is notoriously distorted when it hosts an ORW phenomenon. These numerical results are consistent with previously published experimental results.
关键词： erbium-doped ?ber laser,dissipative dynamics,noise-like pulse,optical rogue waves
更新于2025-09-12 10:27:22
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The Physics of the one-dimensional nonlinear Schr?dinger equation in fiber optics: rogue waves, modulation instability and self-focusing phenomena
摘要： We review the different dynamical mechanisms leading to the emergence of coherent structures in physical systems described by the integrable one-dimensional nonlinear Schr?dinger equation (1DNLSE) in the focusing regime. In this context, localized and coherent structures are very often associated to rogue wave events. We focus on one-dimensional optical experiments and in particular on (single mode) optical fibers experiments. In the focusing regime of 1DNLSE, the so-called modulation instability (MI), arising from nonlocal perturbation of the plane waves, is the most common phenomenon. Alongside the standard MI, other mechanisms are responsible for the emergence of rogue waves. We classify the different scenarios by considering those induced by small perturbations of unstable stationary state (the plane waves) and the ones arising from the self-focusing of large pulses without any perturbation. In the former case, the perturbations can be local, global, random or deterministic. In the latter case, the self-focusing dynamics can be observed both with isolated pulses or with large initial fluctuations of the optical power. We review the dynamics of emergence of localized structures in all these different scenarios.
关键词： modulation instability,nonlinear Schr?dinger equation,self-focusing phenomena,rogue waves,fiber optics
更新于2025-09-12 10:27:22
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Rare events in mixed-mode oscillations from weakly coupled lasers
摘要： We study a dynamical system consisting of two mutually coupled molecular lasers, each of which shows mixed-mode oscillations and chaos when uncoupled. The type of coupling, incoherent laser interaction via saturable absorbers is an example of inhibitory nonlinear coupling, which is also found in Hodgkin-Huxley models that describe action potentials in neurons. We have carried out extensive numerical bifurcation analysis and numerical simulations to show that for small-enough coupling, well below the chaotic synchronization threshold, the presence of distinctive resonances in a symmetric mirror con?guration of the system generates a type of rare events characterized by very small amplitudes. When this symmetry is broken by introducing a relatively small difference between the lasers pump parameters near an in-phase Hopf bifurcation, we observe extreme rare events (rogue waves) in one of the lasers. In this case the outliers deviate from power-law distributions and are reminiscent of those known as dragon kings. We consider the conditions for both types of rare events to occur, their origin, as well as relevant statistical features.
关键词： mixed-mode oscillations,dragon kings,rogue waves,weakly coupled lasers,rare events
更新于2025-09-12 10:27:22
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[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Generation of Rogue-Like Pulses via Stimulated Soliton Collision in Dispersion Oscillating Optical Fiber
摘要： In the case of optical supercontinuum generation, rogue waves can appear as rare solitons, possessing anomalously large peak intensity [1]. To stimulate the generation of high-intensity pulses, the use of the modulation of the fiber dispersion is proposed. The propagation of optical soliton in a fiber with variable dispersion is described by nonlinear Schr?dinger equation [2] ????/???? + ??(??(cid:2870)/2)[1 + 0.2sin(2????/??(cid:3040))](??(cid:2870)??/????(cid:2870)) = ??????(??)|??(??, ??)|(cid:2870), where ??(??, ??) is the electric field amplitude, z is the propagation distance, t is the local time, ??(cid:2870) is the group- velocity dispersion parameter, zm is the modulation period, ?? is the nonlinear coefficient, ??(??) = (1 ? ??(cid:3019))??(??) + ??(cid:3019)?(cid:3019)(??) is the nonlinear response function, which includes both instantaneous Kerr nonlinearity and stimulated Raman scattering, ??(cid:3019) = 0.18 [3]. The initial field was assumed as superposition of two in-phase fundamental solitons ??(0, ??) = ??(cid:2868)sech(??/??(cid:2868) ? ??/2) + ??(cid:2868)sech(??/??(cid:2868) + ??/2), where ??(cid:2868) = 1.13 ps is the initial pulse width, ?? = 6 is the initial pulse separation. In a fiber without dispersion modulation (zm=∞) the collision of two in- phase solitons is suppressed due to effect of stimulated Raman scattering. Dispersion modulation with zm=0.85 km induces fusion of the solitons into high-intensity pulse at z=5 km (fig.1a). The peak power (fig.1a, top) is two times higher than the same for unperturbed case (zm=∞). The high-intensity pulse propagates up to z=10 km before fission onto two solitons propagating with different group velocities. The eigenvalue analysis of the soliton propagation in the fig.1b is shown. Each of the discrete eigenvalue λ of Zakharov-Shabat spectral problem is associated with fundamental soliton [3]. The real part Re(λ) and imaginary part Im(λ) give the soliton frequency shift and soliton energy correspondingly. Initial field ??(0, ??) has two imaginary eigenvalues λ1= i0.502 and λ2= i0.497. At the initial state of propagation (z<5 km) these eigenvalues are changed synchronously (fig.1b). The high intensity pulse (5 km<z<10 km) is formed by two-soliton breather. Nonlinear interference between these solitons gives high-intensity oscillations (fig.1a, top). In the process of the soliton fusion the energy of the first soliton increases while the energy of the second is suppressed. At z=7.5 km we have Im(λ1)=0.6 (curve 1, fig.1b) and Im(λ2)=0.04 (curve 2, fig.1b). Due to stimulated Raman scattering, the solitons acquire different group velocities, which are defined by Re(λ) (fig.1b, bottom). As a result, the breather splits into two separate solitons (z>10 km). The dispersion oscillation fibers rearranges eigenvalues in the complex plane [Re(λ), Im(λ)]. This phenomenon can be used for all-optical encoding in fiber-optics eigenvalue communication links.
关键词： stimulated Raman scattering,soliton collision,nonlinear Schr?dinger equation,rogue waves,dispersion oscillating optical fiber
更新于2025-09-12 10:27:22
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[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Topological Control of Optical Nonlinear Waves
摘要： Controlling nonlinear optical processes is a signi?cant challenge in photonics. Shock waves, rogue waves, and solitons are widespread, from optics to hydrodynamics. Intense research is dedicated to advanced techniques for tailoring extreme waves and ?nding the conditions to induce transitions from one kind of wave to another. We develop a new strategy to supervise, modify or tune a laser beam in third-order nonlinear materials, when light propagation is ruled by the nonlinear Schr¨odinger equation (NLSE). We denote our approach topological control (TC). TC is based on the one-to-one correspondence between the number of wave packet oscillating phases and the genus of toroidal surfaces associated with the NLSE solutions by the Riemann theta function [1]. For a box-shaped wave in a focusing Kerr medium, TC allows to control transitions from dispersive shock waves (DSWs), to rogue waves (RWs) and soliton gases (SGs). We prove that our method is experimentally realizable in a photorefractive crystal [2]. Speci?cally, we use the parametric time-dependence of photorefractive nonlinearity to shape the asymptotic wave pro?le. We tailor time-dependent propagation coef?cients, as nonlinearity and dispersion, to explore each region in the state-diagram [Fig. 1(a)] and observe all the phases in the nonlinear wave evolution [Fig. 1(b)]. This new technique casts light on focusing DSWs and RW generation, and can be extended to many other nonlinear phenomena, from classical to quantum ones.
关键词： photorefractive crystal,nonlinear Schr¨odinger equation,topological control,nonlinear optical processes,shock waves,rogue waves,solitons
更新于2025-09-11 14:15:04