Soliton Pairs Research Articles

Evolutions of versatile wavelength-dependent bound solitons

Versatile structures of wavelength-dependent bound solitons are obtained based on nonlinear polarization rotation (NPR) mode-locked technology in an anomalous-dispersion fiber laser. After optimizing the intra-cavity birefringence and finely adjusting the operating wavelength of the laser, both the conventional soliton and loosely bound-state soliton pairs can be generated and switched under different operating wavelengths. With the evolution of bound state, the spectral interference fringes show significant changes and the temporal separation between bound solitons varies accordingly. Altering initial settings of laser parameters, wavelength-dependent multiple-soliton bound states are also found experimentally. Moreover, the formation and evolution mechanism of the bound states are explored and analyzed in this work.

Dissipative Kerr solitons in a photonic dimer on both sides of exceptional point

Exceptional points are a ubiquitous concept widely present in driven-dissipative coupled systems described by a non-Hermitian Hamiltonian. To date, exceptional points have been extensively examined in the systems supporting only a few optical modes, thereby leaving the observation of collective (multimode) effects outside of the scope of the study. In the present paper, we analyze the role of exceptional points in nonlinear multimode photonics. Specifically, we provide insights into the complex nonlinear dynamics arising in a continuous wave-driven pair of strongly coupled microresonators. Investigating this system, we demonstrate mechanisms of dissipative Kerr soliton formation in two fundamentally different regimes separated by a line of exceptional points. Highlighting the diversity of emergent nonlinear effects, we describe the on-demand generation of single-solitons, perfect soliton crystals and bright-dark soliton pairs on either side of exceptional points.

Separate coupled solitons in biased series photorefractive semiconductor circuit

We present, for the first time a theoretical foundation for separately coupled solitons in a biased series circuit consisting of semi-insulating photorefractive multiple quantum well (MQW) waveguides. As an example, a slab semiconductor waveguide based on a GaAs/AlGaAs structure is considered. The coupled steady state space charge field is derived for both the MQW structures using a bipolar band transport model. Hence, a system of two coupled equations is obtained for each MQW structure which governs the dynamical evolution of light beams. We then prove the existence of dark–dark, grey–grey and grey–dark separately coupled soliton pairs. We also see that the soliton propagating individually in one PR semiconductor can affect the other by the light-induced current. We investigate this coupling effect with respect to the soliton beam’s intensity profile and for each of the three cases, namely, dark–dark, grey–grey and grey–dark separately coupled solitons. Some potential applications are discussed.

Multiple double-pole bright-bright and bright-dark solitons and energy-exchanging collision in the M-component nonlinear Schrödinger equations.

Multiple double-pole bright-bright and bright-dark soliton solutions for the multicomponent nonlinear Schrödinger (MCNLS) system comprising three types of nonlinearities, namely, focusing, defocusing, and mixed (focusing-defocusing) nonlinearities, arising in different physical settings are constructed. An interesting type of energy-exchanging phenomenon during collision of these double-pole solitons is unraveled. To explore the objectives, we consider the general solutions of a set of generalized MCNLS equations and by taking the long-wavelength limit with proper parameter choices of single-pole bright-bright and bright-dark soliton pairs, the multiple double-pole bright-bright and bright-dark soliton solutions are constructed in terms of determinants. The regular double-pole bright-bright solitons exist in the focusing and focusing-defocusing MCNLS equations and undergo a particular type of energy-sharing collision for M≥2 in addition to the usual elastic collisions. A striking feature observed in the process of energy-sharing collisions is that the double-pole two-soliton possessing unequal intensities before collision indeed exactly exchange their intensities after collision. Further, the existence of double-pole bright-dark solitons in the MCNLS equations with focusing, defocusing, and mixed (focusing-defocusing) nonlinearities is analyzed by constructing explicit determinant form solutions, where the double-pole bright solitons exhibit elastic and energy-exchanging collisions while the double-pole dark solitons undergo mere elastic collision. The double-pole bright-dark solitons possess much richer localized coherent patterns than their counterpart double-pole bright-bright solitons. For particular choices of parameters, we demonstrate that the solitons would degenerate into the background, resulting in a lower number of solitons. Another important observation is the formation of doubly localized rogue waves with extreme amplitude, in the case of double-pole bright-dark four-solitons. Our results should stimulate interest in such special multipole localized structures and are expected to have ramifications in nonlinear optics.

Fate of soliton matter upon symmetry-breaking ferroelectric order

In a one-dimensional (1D) system with degenerate ground states, their domain boundaries, dubbed solitons, emerge as topological excitations often carrying unconventional charges and spins; however, the soliton excitations are only vital in the non-ordered 1D regime. Then a question arises; how do the solitons conform to a 3D ordered state? Here, using a quasi-1D organic ferroelectric, TTF-CA, with degenerate polar dimers, we pursue the fate of a spin-soliton charge-soliton composite matter in a 1D polar-dimer liquid upon its transition to a 3D ferroelectric order by resistivity, NMR and NQR measurements. We demonstrate that the soliton matter undergoes neutral spin-spin soliton pairing and spin-charge soliton pairing to form polarons, coping with the 3D order. The former contributes to the magnetism through triplet excitations whereas the latter carries electrical current. Our results reveal the whole picture of a soliton matter that condenses into the 3D ordered state.

General soliton and (semi-)rational solutions of the partial reverse space y-non-local Mel’nikov equation with non-zero boundary conditions

General soliton and (semi-)rational solutions to the y-non-local Mel’nikov equation with non-zero boundary conditions are derived by the Kadomtsev–Petviashvili (KP) hierarchy reduction method. The solutions are expressed in N × N Gram-type determinants with an arbitrary positive integer N. A possible new feature of our results compared to previous studies of non-local equations using the KP reduction method is that there are two families of constraints among the parameters appearing in the solutions, which display significant discrepancies. For even N, one of them only generates pairs of solitons or lumps while the other one can give rise to odd numbers of solitons or lumps; the interactions between lumps and solitons are always inelastic for one family whereas the other family may lead to semi-rational solutions with elastic collisions between lumps and solitons. These differences are illustrated by a thorough study of the solution dynamics for N = 1, 2, 3. Besides, regularities of solutions are discussed under proper choices of parameters.

Propagation of Optical Dark Solitons in Metamaterials

This paper studies the interaction between the formation of a single dark soliton and a pair of fundamental-order dark solitons. Based on the nonlinear Schrodinger’s equation combined with the lossless Drude model, the impacts of the nonlinearity, group velocity dispersion, third-order dispersion, and the self-steepening on the propagation of a dark soliton under the normal dispersion are studied using the distributed Fourier method. By selecting the ratio of group velocity dispersion length and the nonlinear length, the conditions for the stable transmission of dark solitons in metamaterials are obtained. On this basis, this paper also studies the interaction of a pair of fundamental-order dark soliton under the different conditions of the same amplitude with the same phase, the same amplitude with different phases, and different amplitudes with the same phase. In this paper, it is shown that the fundamental-order dark soliton pairs exhibit different characteristics of the interaction under the different conditions.

Annihilation and Control of Chiral Domain Walls with Magnetic Fields.

The control of domain walls is central to nearly all magnetic technologies, particularly for information storage and spintronics. Creative attempts to increase storage density need to overcome volatility due to thermal fluctuations of nanoscopic domains and heating limitations. Topological defects, such as solitons, skyrmions, and merons, may be much less susceptible to fluctuations, owing to topological constraints, while also being controllable with low current densities. Here, we present the first evidence for soliton/soliton and soliton/antisoliton domain walls in the hexagonal chiral magnet Mn1/3NbS2 that respond asymmetrically to magnetic fields and exhibit pair-annihilation. This is important because it suggests the possibility of controlling the occurrence of soliton pairs and the use of small fields or small currents to control nanoscopic magnetic domains. Specifically, our data suggest that either soliton/soliton or soliton/antisoliton pairs can be stabilized by tuning the balance between intrinsic exchange interactions and long-range magnetostatics in restricted geometries.

TaSe2-based mode-locked fiber laser with four switchable operating states

Transition metal dichalcogenides (TMDs) have attracted considerable attention in electronics and photonics. Tantalum diselenides (TaSe2) as a member of TMDs has been employed for field effect transistors and all-optical switching, and its nonlinear optical response has also been investigated. However, the applications of TaSe2 in ultrafast fiber lasers have not been exploited. Here, TaSe2 deposited on D-shaped fiber is used as saturable absorber (SA) in Er-doped fiber laser, and four switchable operating states (bright solitons, dark solitons, bright-dark soliton pairs and their HML counterparts, as well as bright-dark-bright soliton pairs) are realized successfully. To the best of our knowledge, this is the first presentation of a mode-locked fiber laser with the TaSe2-based SA, and also the first study of bright and dark soliton properties of a TaSe2-based fiber laser. It is foreseeable that TaSe2 will become an appealing candidate for bright and dark soliton fiber lasers.

Symmetry breaking solutions to nonlocal Alice-Bob Kadomtsev-Petviashivili system

Abstract The common Kadomtsev-Petviashivili (KP) system coupled with parity-time symmetry is studied. The bilinear form is introduced to the Alice-Bob Kadomtsev-Petviashivili(AB-KP) system with additional arbitrary constant a . The abundant solutions are discussed for various transformation function f , which are different from common KP system. As a result, a single soliton dependent on parameter a , breather, lump and the interaction between lump and a pair of stripe solitons are obtained. By choosing special parameters, the evolution plots of some breather and lump solutions are illustrated.

Tunable evolutions of bright beams in a separate spatial soliton pair due to the crystal temperature

We numerically investigate the temperature characteristics of the bright soliton and a Gaussian beam in a photorefractive crystal circuit, in which two photorefractive crystals are connected with an external voltage source. The results indicate that the dynamical evolution of the bright soliton and the Gaussian beam formed in one crystal depend strongly on the temperature of the other crystal, in which the dark soliton is formed. For the bright soliton, the full width at half maximum (FWHM) of the soliton increases and the center deflection decreases with the increase of the dark soliton crystal temperature. The Gaussian beam shows the similar evolution behaviors and experiences periodic compression and expansion during propagation. The deviation between the bright soliton and the Gaussian beam, however, becomes obvious as the increase of the temperature of the dark soliton crystal. A Gaussian beam that is mismatched with the bright soliton supported by the crystal could evolve into a bright solitary wave by tuning the temperature of the dark soliton crystal properly.

Observation of Soliton Molecules in a Robust All PM Mode-Locked Fiber Laser With Nonreciprocal Phase Bias

We report the first experimental observation, to the best of our knowledge, of soliton molecules in a robust all polarization-maintaining (PM) mode-locked fiber laser with a nonreciprocal phase bias that results in a low self-starting threshold and stable mode locking. Through elaborately tuning the waveplate in the cavity, calibrating the laser pulse from conventional soliton to soliton molecules is implemented, and versatile soliton molecules including harmonic soliton pairs, tightly or loosely bound soliton quartets, multipulse bound solitons are achieved and manipulated at different pump powers. Theoretical investigations are established to elucidate the soliton molecules spectral characteristics with various phase differences and time separations in the cavity that elicit good concurrence with achieved experimental results. The achieved results both rich the nonlinear dynamics in fiber lasers and pave the potential applications for this excellent architecture fiber laser.

Parallel dark-soliton pair in a bistable two-dimensional exciton-polariton superfluid

Collective excitations, such as vortex-antivortex and dark solitons, are among the most fascinating effects of macroscopic quantum states. However, 2D dark solitons are unstable and collapse into vortices due to snake instabilities. Making use of the optical bistability in exciton-polariton microcavities, we demonstrate that a pair of dark solitons can be formed in the wake of an obstacle in a polariton flow resonantly supported by a homogeneous laser beam. Unlike the purely dissipative case where the solitons are grey and spatially separate, here the two solitons are fully dark, rapidly align at a specific separation distance and propagate parallel as long as the flow is in the bistable regime. Remarkably, the use of this regime allows to avoid the phase fixing arising in resonant pumping regime and to circumvent the polariton decay. Our work opens very wide perspectives of studying new classes of phase-density defects which can form in driven-dissipative quantum fluids of light.

Interaction forces among solitons in external potentials

We demonstrate the possibility to generalize the Karpman and Solov’ev theory of interaction forces among solitons taking into account an external potential as a small perturbation. Closely following to the Karpman and Solov’ev adiabatic perturbation algorithm, we obtain analytical solutions completely describing the dynamics of two solitons trapped in the harmonic oscillator potential. Period of oscillations of two in-phase solitons decreases both with increasing the oscillator frequency and decreasing the initial separation between them, whereas two out-of-phase solitons can be found in the bound states of two practically noninteracting solitons. Analytical relations demonstrate a quite good qualitative and quantitative agreement with the numerical experiments. The main discrepancy between the generalized Karpman and Solov’ev perturbation theory and the results of direct computer experiments is explained by periodic perturbations of the soliton pair by the noise-like dispersive waves emitted by overlapped neighboring solitons.

Coupled propagation of two beams in cubic quintic nonlinear medium

In this paper, coupled propagation of two beams in cubic quintic nonlinear medium has been investigated. We have presented a complete understanding of spatial soliton pair formation, breather pair formation and their existence curves, for different coupling coefficients and also for different beam width of the co-propagating beams.

Characteristics of the interaction behavior between solitons in (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation

Starting with Hirota bilinear form of (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation, a class of lump solutions, a strip soliton, a pair of resonance solitons as well as the rogue wave have been obtained through symbolic computation. Firstly, two lump solutions are derived, consisting of six free parameters, while the other three accord with non-zero determinant condition which guarantee locality and analyticity for the solutions. Secondly, the interaction phenomenon between a lump wave and a stripe soliton is reflected. Interaction figures show that the lump wave can be absorbed by the stripe wave or separate from it. Thirdly, by a novel ansatz of hyperbolic function and quadratic function, a fresh transformation for the rogue wave and a pair of resonance solitons have been discovered, that a peak profiled rogue wave emerges from one of the resonance wave and transfers to another, and finally fades away. At the same time, numerical simulations are demonstrated to visualize the mechanism of the above solutions.

Investigation of the interaction of a pair of bright optical spatial pyroelectric solitons during their in-phase propagation in an undoped lithium niobate crystal at a wavelength of 532 nm

The formation of two-dimensional bright spatial solitons by in-phase laser beams with a wavelength of 532 nm propagating in the bulk of photorefractive lithium niobate crystal under the reversal of the sign of the nonlinear optical response of the material with the contribution of the pyroelectric effect has been experimentally demonstrated. It is shown that varying the distance between the beams at the input face of the crystal leads to the interaction of pyroelectric solitons, which allows the formation of non-rectilinear propagation paths of light beams.

Wavelength-Switchable Multiple Type Bound Solitons in a Passively Mode-Locked Er-Doped Fiber Laser

We report on the experimental observation of wavelength-switchable bound solitons in a passively mode-locked erbium-doped fiber ring laser based on a tapered graded-index multimode fiber. Due to the multimode interference filtering effect, by adjusting the polarization controller while maintaining the pump power of 158 mW at 1480 nm, the center wavelength of the fiber laser output can be switched between 1565 nm and 1595 nm. At the same time, bound soliton pairs and bound soliton triplets can be both observed in these two wavelengths. Such a simple, compact all-fiber mode-locked laser with switchable wavelength has great potential for high capacity optical communication.

Analysis of real-time spectral interference using a deep neural network to reconstruct multi-soliton dynamics in mode-locked lasers

The dynamics of optical soliton molecules in ultrafast lasers can reveal the intrinsic self-organized characteristics of dissipative systems. The photonic time-stretch dispersive Fourier transformation (TS-DFT) technology provides an effective method to observe the internal motion of soliton molecules real time. However, the evolution of complex soliton molecular structures has not been reconstructed from TS-DFT data satisfactorily. We train a residual convolutional neural network (RCNN) with simulated TS-DFT data and validate it using arbitrarily generated TS-DFT data to retrieve the separation and relative phase of solitons in three- and six-soliton molecules. Then, we use RCNNs to analyze the experimental TS-DFT data of three-soliton molecules in a passive mode-locked laser. The solitons can exhibit different phase evolution processes and have compound vibration frequencies simultaneously. The phase evolutions exhibit behavior consistent with single-shot autocorrelation results. Compared with autocorrelation methods, the RCNN can obtain the actual phase difference and analyze soliton molecules comprising more solitons and almost equally spaced soliton pairs. This study provides an effective method for exploring complex soliton molecule dynamics.

Collisions of Three-Component Vector Solitons in Bose-Einstein Condensates.

Ultracold gases provide an unprecedented level of control for the investigation of soliton dynamics and collisions. We present a scheme for deterministically preparing pairs of three-component solitons in a Bose-Einstein condensate. Our method is based on local spin rotations which simultaneously imprint suitable phase and density distributions. This enables us to observe striking collisional properties of the vector degree of freedom which naturally arises for the coherent nature of the emerging multicomponent solitons. We find that the solitonic properties in the quasi-one-dimensional system are quantitatively described by the integrable repulsive three-component Manakov model.