Soliton Pairs Research Articles

Generation of bright-dark soliton pairs based on a ferromagnetic insulator Cr2Si2Te6 as a modulator in an Er-doped fiber laser.

In this work, a saturable absorber (SA) based on Cr2Si2Te6 (CST), with a modulation depth of 14.90% and saturation intensity of 4.81MW/cm2, was prepared by a liquid phase stripping method. Its nonlinear optical properties and application in obtaining mode-locked pulse output of bright-dark solitons are studied. When the pump power was 1250 mW, the maximum output power was 26.60 mW; the energy of the single pulse was 15.02 nJ, and the repetition rate was 1.77 MHz. Our results provided evidence that CST can be used as an excellent SA for a mode-locked laser and demonstrated that ferromagnetic insulators can be used for the study of bright-dark soliton pairs.

Dynamics of breathing dissipative soliton pairs in a bidirectional ultrafast fiber laser.

The breathing dissipative soliton as a dynamic solution to many nonlinear systems has induced substantial interest in nonlinear photonics and ultrafast laser science. However, the exotic breathing multi-soliton dynamics are still largely unexplored in the bidirectional fiber laser compared to the unidirectional laser. Here, we reveal nonequilibrium dynamics of a breathing soliton pair (BSP) with energy transfer in a bidirectional laser; in particular, the dissociation and annihilation of the BSP was triggered by control over intra-cavity polarization. Optical rogue waves were detected simultaneously, and the collision of breathers significantly increased the intensity of rogue waves, which is characteristic of the bidirectional laser. Further, the buildup dynamics of the BSP with nanosecond pulse separation and a breathing soliton molecule were observed. Multiple single soliton explosions and transient pulse splitting are distinct features of soliton molecule buildup compared to the soliton pair. These findings shed new insights into the multiple breather dynamics of nonlinear systems.

Singular soliton, shock-wave, breather-stripe soliton, hybrid solutions and numerical simulations for a (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada system in fluid mechanics

In this paper, a (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada system is investigated in fluid mechanics via the symbolic computation. With the help of the Hirota method, we derive some singular soliton, shock-wave, breather-stripe soliton and hybrid solutions. Based on the finite difference method, we get some numerical one-soliton solutions. We graphically show the singular and shock-wave solutions, and observe that the singular one-soliton solutions are explosive and unstable, but the shock-wave solutions are non-singular and stable. We observe that the breather-stripe soliton moves along the negative direction of the y axis, where y is a variable, and the amplitude and shape of the breather-stripe soliton remain invariant during the propagation. We graphically demonstrate the interaction among a rogue wave, a periodic wave and a pair of the stripe solitons: the rogue wave arises from the one stripe soliton; the rogue wave interacts with the periodic wave, the rogue wave splits into two waves and then the two waves merge into a wave; the rogue wave fuses with the other stripe soliton. We graphically present the numerical one-soliton solutions which agree with the analytic one-soliton solutions.

Two-dimensional Airy waves and three-wave solitons in quadratic media

We address the dynamics of two-dimensional (2D) truncated Airy waves (TAWs) and three-component solitons in the system of two fundamental-frequency (FF) and second-harmonic (SH) fields, coupled by quadratic () terms. The system models second–harmonic-generating optical media and atomic-molecular mixtures in Bose–Einstein condensates. In addition to stable solitons, the system maintains truncated-Airy-waves states in either one of the FF components, represented by exact solutions, which are stable, unlike the Airy waves in the degenerate (two-component) system. It is also possible to imprint vorticity onto the 2D Airy modes. By means of systematic simulations, we examine interactions between TAWs originally carried by different FF components, which are bending in opposite directions, through the SH field. The interaction leads to fusion of the input into a pair of narrow solitons. This is opposed to what happens in the 1D system, where the interacting Aity waves split into a large number of solitons. The interaction of truncated Aity waves carrying identical imprinted vorticities creates an additional pair of solitons, while opposite vorticities create a set of small-amplitude ‘debris’ in the output. Slowly moving solitons colliding with a heavy TAW bounce back, faster ones are absorbed by it, and collisions are quasi-elastic for fast solitons. Soliton-soliton collisions lead to merger into a single mode, or elastic passage, for lower and higher velocities, respectively.

Generation of bound solitons in a mode- locked Tm-doped fiber laser based on a graded-index multimode fiber saturable absorber

In this work, we report on the experimental observations of bound solitons in a Tm-doped passively mode-locked fiber laser by using an all-fiber saturable absorber, structured by a stretched graded index multimode fiber. Stable out-of-phase soliton pairs are obtained, with a temporal separation of 4.36 ps between the two ∼1.88 ps pulses, while the central wavelength can be continuously tuned from 1959 nm to 1962 nm. Meanwhile, some different pulse separations from 16 ps to 18.02 ps of tightly bound soliton pairs have also been realized by cautiously adjusting the PC. The results are helpful for us to understand the nonlinear dynamics in fiber lasers and further explore high-capacity fiber communication.

Hamiltonian approach to the soliton-soliton interaction and for a classical solitonic gas

The known stationary solutions of the parametrically driven and damped nonlinear Schrödinger equation (PDDNLS) have been used to calculate the interaction potential and the interaction law of pairs of solitons from a strictly theoretical point of view. In agreement with the numerical simulations reported in the literature, our results reveal that the phase difference between solitons plays an important role in their dynamics (this can be either zero or π), and that the two-soliton interaction is very weak and exponential type. Finally, the model was applied to a solitonic gas to find its thermodynamics and numerical simulations were also performed to study the dynamics of this gas.

Oscillation properties of matter-wave bright solitons in harmonic potentials

We investigate the oscillation periods of bright soliton pair or vector bright soliton pair in harmonic potentials. We demonstrate that periods of low-speed solitons are greatly affected by the position shift during their collisions. The modified oscillation periods are described by defining a characterized speed, with the aid of asymptotic analysis on related exact analytic soliton solutions in integrable cases. The oscillation period can be used to distinguish the inter- and intra-species interactions between solitons. However, a bright soliton cannot oscillate in a harmonic trap, when it is coupled with a dark soliton (without any trapping potentials). Interestingly, it can oscillate in an anti-harmonic potential, and the oscillation behavior is explained by a quasi-particle theory. The modified period of two dark-bright solitons can be also described well by the characterized speed. These results address well the effects of position shift during soliton collision, which provides an important supplement for previous studies without considering phase shift effects.

Dark-Bright Soliton Bound States in a Microresonator.

Dissipative Kerr solitons in microresonators have facilitated the development of fully coherent, chip-scale frequency combs. In addition, dark soliton pulses have been observed in microresonators in the normal dispersion regime. Here, we report bound states of mutually trapped dark-bright soliton pairs in a microresonator. The soliton pairs are generated seeding two modes with opposite dispersion but with similar group velocities. One laser operating in the anomalous dispersion regime generates a bright soliton microcomb, while the other laser in the normal dispersion regime creates a dark soliton via Kerr-induced cross-phase modulation with the bright soliton. Numerical simulations agree well with experimental results and reveal a novel mechanism to generate dark soliton pulses. The trapping of dark and bright solitons can lead to light states with the intriguing property of constant output power while spectrally resembling a frequency comb. These results can be of interest for telecommunication systems, frequency comb applications, and ultrafast optics.

Breathing Dissipative Soliton Molecule Switching in a Bidirectional Mode‐Locked Fiber Laser

Breathing optical solitons propagating in a dissipative nonlinear system can interact and bind stably, forming an optical soliton molecule that presents striking molecule‐like dynamics. To date, the breathing soliton pair has been mainly observed in the microcavity platform, and the peculiar dynamic evolution of breathing soliton molecules (BSMs) remains largely unexplored in mode‐locked fiber lasers. Herein, the transient switching dynamics of BSMs in a bidirectional ultrafast fiber laser is revealed, specifically triggered at different parameter spaces of saturable absorption with manipulation polarizations that maintain constant pulse separation or undergo strong repulsion and kink after switching. All‐optical switching of breather molecules and significantly increasing multiple soliton molecules’ switching of two or three solitons between states with different binding separations by applying a strong stimulus with periodic pump modulation is demonstrated. The instantaneous pulse breakup can be induced by the collision of bidirectional breathing solitons in each switching, which is characteristic of the breathing solitons in a bidirectional fiber laser and further corroborated by numerical simulation. The study unveils new perspectives into the ultrafast transient process of BSMs in various dissipative systems.

Chirped optical soliton propagation in birefringent fibers modeled by coupled Fokas-Lenells system

The propagation of ultrashort light pulses in a birefringent optical fiber exhibiting spatiotemporal dispersion, cross- and self-phase modulation, self-steepening, and group-velocity dispersion effects is addressed. The evolution of light pulses in such system is described by the coupled Fokas-Lenells equations which offer an accurate description of pulse dynamics in the femtosecond range when certain terms of the next asymptotic order beyond those necessary for the nonlinear Schrödinger equation are sustained. We report the first analytical demonstration of the propagation of chirped solitons in a birefringent fiber medium governed by the coupled Fokas-Lenells equations. The formation of those nonlinearly chirped solitons in the optical material may be attributed to the presence of self-steepening process. The results show that the frequency chirp associated with each of the two field components is directly proportional to the total intensity of the pulse. The chirped solitons for the system including the dark-dark and bright-bright soliton pairs in the presence of all fiber parameters are retrieved. The chirps accompanying the soliton pairs are also determined. The existence constraints of these chirped solitons are presented. In addition, the stability of the chirped solutions with respect to the finite perturbations is studied numerically.

Higher-order algebraic soliton solutions of the Gerdjikov–Ivanov equation: Asymptotic analysis and emergence of rogue waves

In this paper, we derive the determinant representation of higher-order algebraic soliton solutions of the Gerdjikov–Ivanov equation by using the Darboux transformation and some limit technique. Based on the asymptotic balance between different algebraic terms, we obtain the asymptotic expressions of algebraic soliton solutions with the order 2≤N≤4. It turns out that all the asymptotic solitons have the same amplitudes, most of them are located in the parabolic curves and thus have the varying velocities with the rate O(|t|−12) (except that one pair of asymptotic solitons are located in the straight lines for the odd-order cases), and they exhibit the elastic interactions of the attractive type. In addition, we reveal that the transient rogue waves are generated in the soliton-interaction region and the peak value is exactly N times the amplitude of individual soliton.

Bright Soliton and Bright–Dark Soliton Pair in an Er-Doped Fiber Laser Mode-Locked Based on In2Se3 Saturable Absorber

The output power in ultrafast fiber lasers is usually limited due to the lack of a versatile saturable absorber with high damage threshold and large modulation depth. Here we proposed a more efficient strategy to improve the output energy of erbium-doped fiber laser based on indium selenide (In2Se3) prepared by using the physical vapor deposition (PVD) method. Finally, stable mode-locked bright pulses and triple-wavelength dark–bright pulse pair generation were obtained successfully by adjusting the polarization state. The average output power and pulse energy were 172.4 mW/101 nJ and 171.3 mW/100 nJ, which are significantly improved compared with the previous work. These data demonstrate that the PVD-In2Se3 can be a feasible nonlinear photonic material for high-power fiber lasers, which will pave a fresh avenue for the high-power fiber laser.

Deep learning based pulse prediction of nonlinear dynamics in fiber optics

The initial state of a nonlinear optical fiber system plays a vital role in the ultrafast pulse evolution dynamic. In this work, a data-driven compressed convolutional neural network, named inverse network, is proposed to predict initial pulse distribution through a series of discrete power profiles at different propagation distances. The inverse network is trained and tested based on two typical nonlinear dynamics: (1) the pulse evolution in a fiber optical parametric amplifier system and (2) soliton pair evolution in high-nonlinear fibers. Great prediction accuracy is reached when the epoch grows to 5000 in both cases, with the normalized root mean square errors below 0.01 on the entire testing set. Meanwhile, the lightweight network is highly effective. In this work, it takes approximately 30 seconds for 5,000 epochs training with a dataset size of 900. The inverse network is further tested and analyzed on the dataset with different signal-to-noise ratios and input sizes. The results show fair stability at the deviation on the testing set. The proposed inverse network demonstrates a promising approach to optimizing the initial pulse of fiber optics systems.

Stern-Gerlach deflection of vector spatio-temporal soliton pairs in cold Rydberg gases

We propose a scheme to investigate vector spatio-temporal soliton pairs via double Rydberg electromagnetically induced transparency (EIT). We show that three dimensional (3D) vector monopole and vortex solitons, with ultralow generation power and ultraslow speed, have been found under three response regions. In particular, these spatio-temporal soliton pairs experience a significant Stern-Gerlach deflection when a gradient magnetic field is applied to the system. The results reported here are useful not only for extending the research realm of nonlinear magneto-optics but also for the application in the detection of microgradient magnetic fields.

Interaction of Airy beams modeled by the fractional nonlinear cubic-quintic Schrödinger equation

We investigate theoretically and numerically the interaction of Airy beams modeled by fractional nonlinear cubic-quintic Schrödinger equation. By considering fractional diffraction effect, when the initial beam interval between the two Airy beams is large enough, it is found that two in-phase Airy beams attract and repel each other, and two out-of-phase beams repel each other. This is different from the interaction of two Airy beams with large interval in standard nonlinear Schrödinger equation, where the two beams display a weak interaction. For smaller interval, single breathing soliton and symmetric breathing soliton pairs are formed in the in-phase and out-of-phase cases, respectively. As the Lévy index decreases, for the single breathing soliton, the oscillation becomes stronger, the mean peak intensity increases, and the soliton width decreases, for the symmetric breathing soliton pair, the width becomes narrower, and the repulsion between the two Airy components becomes stronger. Besides, the quintic defocusing strength will modulate the interaction of Airy beams. When the strength coefficient increases, the width of the breathing soliton formed in the in-phase case becomes wider, the repulsion between the two beams in the out-of-phase case increases, as well as the width of the soliton pair becomes wider. The work may provide new control methods on the interaction of Airy beams.

Periodic attraction and repulsion within the tight-bound π-phase soliton molecule.

In the over-pumped dissipative system, the single pulse is prone to split into multi-soliton modes, among which the soliton molecule (SM) comprising two pulses has attracted much interest recently. In this Letter, the tight-bound SM with the π-phase-difference, a soliton pair predicted to be unstable observed in fiber lasers, is found to have oscillating separation with excellent stability. For the first time, to the best of our knowledge, we reveal the mechanism of the π-phase SM to circumvent the irreversible repulsion and the role of dispersive waves on the SM. During the periodic propagation, the destructive interference between solitons produces the repulsion while the dispersive waves give rise to the attractive force, leading to the dynamic oscillating behavior of the SM. The numerical simulation reproduces the experimental observation and offers panoramic insights into the nonlinear interactions between multiple components in dissipative systems.

Parameter regulation for periodic wave pair and photovoltaic soliton pair excitations in the bias photovoltaic-photorefractive crystal

In the bias photovoltaic-photorefractive crystal, the two-component nonlinear Schrödinger equation can portray the dynamics of periodic wave pair and photovoltaic soliton pair. These excitations are analytically revealed including the Jacobian sn-cn type and sn-dn type periodic wave pair and their related dark-bright soliton pair, the mixed elliptic function pair excitation and their related bi-peaked soliton and bright soliton pair. In view of these results, the formation conditions of these periodic wave and soliton pairs are related to parameters of the photovoltaic field, the space charge electric field, irradiance and nonlinearity. Moreover, the excitation regulation of soliton pairs including amplitudes, widths and the change of propagation constants based on the parameter related to the photovoltaic field and space charge electric field is investigated in the bias photovoltaic-photorefractive LiNbO3 crystal.

Strain manipulation of vortex core in bi-component magnetic nanodisks

Magnetic vortex as one of the quintessentially non-uniform magnetic structure that can be found to commonly exist in micrometer or submicrometer sized ferromagnetic thin films. Here, we present that the vortex core can be efficiently expelled from the central region and excited into gyrotropic motion by using a voltage induced strain in bi-component magnetic nanodisks. In particular, the polarity can be deterministic switched by proper modulation the amplitude and frequency of applied voltage. The related results of micromagnetic simulations indicated that the magnetic vortex polarity is reversed through the nucleation-annihilation process of topological vortex-antivortex pairs or rotation-fusion edge soliton pairs. This voltage-controlled low-power vortex polarity switching scheme has the ability to accurately address individual magnets in dense arrays and also is compatible with integrated circuit techniques, which provides an additional route for the design of vortex-based on-chip devices.

Nonlinear self-accelerating beam in atomic ensembles: Mathematical models and numerical calculations

The eigenmodes based on paraxial accelerating beams in nonlinear atomic vapors with Kerr and cubic-quintic nonlinearities are demonstrated from mathematical models and numerical simulations. Upon adjusting the generation and propagation conditions, these nonlinear accelerating beams exhibit different evolution properties. We show numerically that the adopted beams can propagate robustly in the medium regardless of its absorption properties. The shape and peak intensity of the main lobes of these beams, based on the fact that they are the eigenmodes of the nonlinear Schrödinger equation in atomic media, are preserved for a significantly long propagation distance. If such beams are not the modes of the system, they are subject to the under-healing or over-healing effect, which damages the shape of the self-accelerating beams. In a numerical investigation, we also discuss the interactions between truncated accelerating beams, which readily generate non-accelerating solitons and soliton pairs.

Breather pair formation in holographic medium

In this paper, we have investigated 2-D spatial breather pair formation in a holographic medium, wherein the beams are solely affected by cross action effect, self action effect is absent. We have shown coupled propagation, by plotting an existence surface for soliton pairing in the parameter space of power and width ratio of the two beams. The parameter space of power and width ratio of the two beams away from an existence surface provides “breather pairs”. It is seen that, in contrast to coupled breather pair propagation in a Kerr medium or in an electromagnetically induced transparent (EIT) medium, a holographic medium offers quite stable propagation to these breathers.