Vector Solitons Research Articles

Dynamics of fundamental solitons and rogue waves on the mixed backgrounds

On the mixed nonzero–zero backgrounds, the vector fundamental breathers, solitons and rogue waves of the coupled higher-order nonlinear Schrodinger system with sign-alternating nonlinearity are investigated. Using the Lax pair and Darboux transformation, we produce a family of vector solutions on the mixed backgrounds. Via the breather-to-soliton conversion, we show the vector solitons on the mixed backgrounds. We show the vector fundamental rogue waves of ultra-high peak amplitude on the mixed backgrounds.

Modulation of dark vector bisolitons

In the manuscript, we report the theoretical simulation results about modulating dark vector bisolitons in 1064 nm wavelength band, when input soliton state is polarization-locking or group-velocity-locking. Varieties of pulse shapes and corresponding optical spectra in orthogonally polarized directions can be achieved by changing orthogonally polarized modes’ pulse parameters. When input soliton state is polarization-locking, one dip always occurs for orthogonally polarized modes regardless of pulse parameters’ changes. While for input soliton state of group-velocity-locking, “1 + 2″/“2 + 1″ pseudo-high-order dark vector soliton, vector solitons with chirp-like structures can be achieved. The theoretical simulation results give reference for studying the modulation of vector multi-solitons and vector bisolitons at other wavelengths.

Multihumped nondegenerate fundamental bright solitons in N-coupled nonlinear Schrödinger system

In this letter we report the existence of nondegenerate fundamental bright soliton solution for coupled multi-component nonlinear Schrödinger equations of Manakov type. To derive this class of nondegenerate vector soliton solutions, we adopt the Hirota bilinear method with appropriate general class of seed solutions. Very interestingly the obtained nondegenerate fundamental soliton solution of the N-coupled nonlinear Schrödinger (CNLS) system admits multi-hump natured intensity profiles. We explicitly demonstrate this specific property by considering the nondegenerate soliton (NDS) solutions for 3 and 4-CNLS systems. We also point out the existence of a special class of partially NDS solutions by imposing appropriate restrictions on the wavenumbers in the already obtained completely NDS solution. Such class of soliton solutions can also exhibit multi-hump profile structures. Finally, we present the stability analysis of nondegenerate fundamental soliton of the 3-CNLS system as an example. The numerical results confirm the stability of triple-humped profile nature against perturbations of 5% and 10% white noise. The multi-hump nature of nondegenerate fundamental soliton solution will be useful in multi-level optical communication applications with enhanced flow of data in multi-mode fibers.

Some Results on Ricci Almost Solitons

We find three necessary and sufficient conditions for an n-dimensional compact Ricci almost soliton (M,g,w,σ) to be a trivial Ricci soliton under the assumption that the soliton vector field w is a geodesic vector field (a vector field with integral curves geodesics). The first result uses condition r2≤nσr on a nonzero scalar curvature r; the second result uses the condition that the soliton vector field w is an eigen vector of the Ricci operator with constant eigenvalue λ satisfying n2λ2≥r2; the third result uses a suitable lower bound on the Ricci curvature S(w,w). Finally, we show that an n-dimensional connected Ricci almost soliton (M,g,w,σ) with soliton vector field w is a geodesic vector field with a trivial Ricci soliton, if and only if, nσ−r is a constant along integral curves of w and the Ricci curvature S(w,w) has a suitable lower bound.

Vector NLS solitons interacting with a boundary* *Supported by NSFC No. 11601312, 11875040.

We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions (BCs): the homogeneous Robin BCs and the mixed Neumann/Dirichlet BCs. The construction is based on the so-called dressing the boundary, which generates soliton solutions by preserving the integrable BCs at each step of the Darboux-dressing process. Under the Robin BCs, examples, including boundary-bound solitons, are explicitly derived; under the mixed Neumann/Dirichlet BCs, the boundary can act as a polarizer that tunes different components of the vector solitons. Connection of our construction to the inverse scattering transform is also provided.

XPM‐Induced Vector Asymmetrical Soliton with Spectral Period Doubling in Mode‐Locked Fiber Laser

AbstractCross phase modulation (XPM) can induce soliton trapping in nonlinear medium, which has been employed to achieve vector soliton, optical switching, and optical analog of gravity‐like potentials. Here, the first observation of a novel soliton operation is reported whose wavelength exhibits redshift and blueshift periodically in a mode‐locked fiber laser under appropriate birefringence and dispersion map. XPM dominates the dynamics by inducing and sustaining the vector asymmetrical soliton (VAS) with spectral period doubling, and exhibits a unique trajectory of pulse trapping. The XPM‐induced VAS is an idiosyncratic steady state featured with asymmetry in the model based on the coupled Ginzburg–Landau equation, which depicts the distinct pulse features in comparison with vector soliton, soliton molecule, and traditional period‐doubling evolutions. The two orthogonal polarized directions of mode‐locked fiber laser can be regarded as the XPM‐coupled dissipative resonators guiding the further study of the optical nonlinear dynamics and chaos for soliton, which is helpful to laser design and brings useful insights into nonlinear science and applications.

Real-time collision dynamics of vector solitons in a fiber laser

Particle-like structures of solitons, as a result of the balance between dispersion and nonlinearity, enable remarkable elastic and inelastic soliton collisions in many fields. Despite the experimental observation of temporal vector-soliton collisions in birefringent fibers, collision dynamics of vector solitons in fiber lasers have not been revealed before, to the best of our knowledge. Here, the real-time spectral evolutions of vector solitons during collisions in a dual-comb fiber laser, which generates vector solitons with slightly different repetition rates, are captured by a time-stretch dispersive Fourier transform technique. We record the whole process of vector-soliton collisions, including the formation of weak pulses induced by cross-polarization coupling, opposite central wavelength shifts of both vector solitons, distinct intensity redistribution and dissipative energy, and gradual recovery to initial states. Furthermore, extreme collisions with strong four-wave mixing sidebands are observed by virtue of coherent coupling between the orthogonal polarization components of vector solitons. Numerical simulations match well with the experimental observations. The experimental and numerical evidences of vector-soliton collision dynamics could give insight into the understanding of nonlinear dynamics in fiber lasers and other physical systems, as well as the improvement of laser performance for application in dual-comb spectroscopy.

Vector solitons in nonlocal optical media with pseudo spin-orbit-coupling.

We numerically investigate the existence and stability of nonlocal vector solitons with pseudo spin-orbit-coupling (SOC). The pseudo SOC is realized by a framework based on the spatial-domain copropagation of two beams with mutually orthogonal polarizations and opposite transverse components of the carrier wave vectors in nonlocal optical media. The numerical results show that there are two kinds of solutions for vector solitons, one is central symmetric, and the other is noncentral symmetric. The solitons may exist below a certain threshold value of the effective SOC strength in the system.

Vector quartic solitons in birefringent fibers.

We theoretically investigated the vector properties of quartic solitons in a pure fourth-order-dispersion birefringent fiber and a quartic-dispersion-dominant mode-locked fiber laser. We found that, compared with scalar pure quartic solitons, a vector quartic soliton (VQS) in the birefringent fiber still preserves the Gaussian shape, except for the distinctions of reduced peak power, central frequency offset, slight frequency chirp, and mitigated oscillatory tails. We also demonstrated that pulse shaping in the mode-locked laser cavity could explicitly facilitate the formation of Kelly sidebands and distortion of oscillatory tails. Furthermore, dynamical evolutions of quartic group-velocity-locked and polarization-rotating vector solitons were obtained to enrich the nonlinear community of VQSs. We believe that our elaborate findings will bring insights into both the fundamental understanding and potential applications of VQSs.

Manipulation of Soliton Bunches Generated From a Polarization-Route-Assisted Vector Fiber Laser

In this article, we report robust vector soliton bunches arising in a passively mode-locked fiber laser based on carbon nanotube (CNT). By introducing a polarization-route-assisted module (PRAM) and finely adjusting the cavity birefringence, the soliton bunches can be flexibly manipulated to operate with controllable soliton numbers and positions. Moreover, the potential bandwidth resource provided by the concept of soliton bunches for the ease of breaks a new path for the enhancement of data-carrying capacity. Our research is helpful to extend the theory of vector soliton dynamics in fiber lasers and promotes the promising application in optical communication systems.

Polarization-dependent dissipative soliton intensity modulation enabled repetition-rate-switchable CPA system

We report a watt-level, repetition-rate-switchable all-fiber chirped pulse amplification (CPA) system by using polarization-dependent dissipative soliton intensity modulation effect. The intensity modulation for pulse repetition rate tuning is realized by combination of the polarization discrimination device (i.e., polarizer) and the polarization-rotating vector soliton (PRVS). Up to ~100% intensity modulation depth with a period of two cavity roundtrips for the PRVS seed was obtained by adjusting the dissipative soliton polarization state that was injected into the polarizer. Relying on this mechanism, the repetition rate of the output pulse from the CPA system can be dynamically switched between 1.37 MHz and 2.74 MHz. The pulse energy of ~2.0 μJ and ~2.2 μJ were achieved for the repetition rates of 1.37 MHz and 2.74 MHz, corresponding to 1.12 ps and 970 fs pulse duration, respectively. These findings would provide an alternative method for dynamic tuning of pulse repetition rate in high power laser systems, which also underpins the significance of fundamental research of vector dissipative solitons in practical applications such as flexible high-energy pulse laser systems.

Vector soliton generation from a compact all-polarization-maintaining fiber laser

We investigate polarization-locked vector solitons (PLVSs) arising in an all-polarization-maintaining (PM) soliton fiber laser mode-locked by a carbon nanotube. The laser can operate stably in both Q-switched and mode-locked states with different pump power. Under the PLVS condition, we observe a string of peak-dip-pair sidebands after polarization-resolving measurement, indicating the strong and regular energy exchange between the two polarized orthogonal components, which evidently distinguishes this all-PM fiber laser from conventional single-mode fiber-based vector cavities. By dispersion compensating, vector dissipative solitons are also successfully obtained. The cavity structure is greatly simplified and stabilized by a hybrid fiber component and shows excellent long-term stability.

Vector dynamics of ultrafast cylindrical vector beams in a mode-locked fiber laser

The vector dynamics of solitons are crucial but easily neglected for realizing vortex solitons. In this Letter, we investigate the effect of vector dynamics on cylindrical vector beams (CVBs) implementation and propose a novel technical method to realize femtosecond CVBs based on vector-locked solitons, which are presented as group-velocity-locked vector solitons (GVLVSs) in the experiment. The outstanding vector properties of GVLVSs not only greatly improve the efficiency of solitons converted into CVBs and output power of CVBs (2.4 times and 4.1 times that of scalar solitons and vector change periodical solitons, with the purity of 97.2%), but also relax the obstacle of ultrafast CVBs from the fundamental frequency to the harmonic regime (up to 198 MHz) for the first time, to the best of our knowledge. This is the highest repetition rate reported for ultrafast CVBs based on passive mode-locking. The investigation of the influence of solitons vector dynamics evolution on the realization of CVBs provides guidance for the excellent performance of ultrafast CVBs.

Almost Riemann solitons and gradient almost Riemann solitons on Lp-Sasakian manifolds

The upcoming article aims to investigate almost Riemann solitons and gradient almost Riemann solitons in a LP-Sasakian manifoldM3. At first, it is proved that if (1,Z,?) be an almost Riemann soliton on a LP-Sasakian manifold M3, then it reduces to a Riemann soliton, provided the soliton vector Z has constant divergence. Also, we show that if Z is pointwise collinear with the characteristic vector field ?, then Z is a constant multiple of ?, and the ARS reduces to a Riemann soliton. Furthermore, it is proved that if a LP-Sasakian manifold M3 admits gradient almost Riemann soliton, then the manifold is a space form. Also, we consider a non-trivial example and validate a result of our paper.

Certain results of conformal and *-conformal Ricci soliton on para-cosymplectic and para-Kenmotsu manifolds

The goal of the paper is to deliberate conformal Ricci soliton and *-conformal Ricci soliton within the framework of paracontact geometry. Here we prove that if an ?-Einstein para-Kenmotsu manifold admits conformal Ricci soliton and *-conformal Ricci soliton, then it is Einstein. Further we have shown that 3-dimensional para-cosymplectic manifold is Ricci flat if the manifold satisfies conformal Ricci soliton where the soliton vector field is conformal. We have also constructed some examples of para-Kenmotsu manifold that admits conformal and *-conformal Ricci soliton and verify our results.

Polarization manipulation of bright-dark vector bisolitons* *Project supported by National Key Research and Development Program of China (Grant No. 2018YFB0504500), the National Natural Science Foundation of China (Grant No. 51672177), and Shanghai Sailing Program (Grant No. 20YF1447500).

We simulate the polarization manipulation of bright-dark vector bisolitons at 1-μm wavelength regime. Through changing the pulse parameters, different kinds of pulse shapes and optical spectra are generated in output orthogonal polarization directions. When the input vector bisoliton is polarization-locked with 1064 nm central wavelength, “1+1” fundamental dark-dark and “2+1” pseudo-high-order bright-dark group-velocity-locked vector solitons can be achieved through changing the projection angle. When the input vector bisoliton is group-velocity-locked with 1063 nm and 1065 nm central wavelengths, “2+1” and “2+2” pseudo-high-order bright-dark group-velocity-locked vector solitons, bright-dark group-velocity-locked vector solitons with chirp-like temporal oscillations are generated. Our simulation results can provide beneficial conduct for polarization manipulation of vector multi-solitons, and have promising applications in quantum information register, optical communications, nanophotonics, and all-optical switching.

Solitons in [formula omitted] symmetric Manakov system

Parity-time (PT)-symmetric Manakov system including four cases are discussed in this paper, which is used to depict the nonlinear waves in optical fibers. Via constructing the generalized Manakov system, soliton/soliton-like solutions of PT-symmetric Manakov system are attained: First and second cases are the solitons and periodic solutions, respectively; Third and fourth cases are the soliton-like solutions. Loss and gain of the soliton-like propagation is not balanced in the third and fourth cases, which is consistent with the experimental result. Time frequency-spectrum of the fourth case are analyzed: Phase spectrum of the one-order soliton-like and amplitude spectrum of the two-order soliton-like both have periodic perturbation. Besides, bilinear forms of the M(M>2)-coupled PT-symmetric Manakov system are also attained, which can help us to obtain the M-dimension vector solitons and discuss the nonlinear waves in multi-mode optical fibers. At the end of this paper, we display the rogue waves of generalized Manakov system and discuss the relations between the linear turbulence and rogue-wave's shape. Amplitude of the rogue wave is increased with a phase-shift parameter (δ1). Time frequency-spectrum of the rogue wave are analyzed.

New general extended direct algebraic approach for optical solitons of Biswas-Arshed equation through birefringent fibers

In this paper, the new general extended direct algebraic method is applied to achieve optical solitons of Biswas-Arshed equation with birefringent fiber involving two component vector soliton. Family of semi-bright soliton, dark singular soliton, singular soliton of Type 1 as well as 2, trigonometric, mixed hyperbolic and rational solitons are constructed and also verified by the aid of modern technical computing package program. The observed findings demonstrate that the approach is straightforward and easy, offers analytical results in generalized manner also these findings may help to address the challenges and predicaments that exist in the optical fibers and telecommunications sector. The solutions encountered with this model are completely latest to the academic literature. Some randomly chosen solutions are illustrated graphically for the physical interpretation. At the end, conclusions are announced.

Vector bright soliton interactions of the two-component AB system in a baroclinic fluid

A two-component AB system, which describes the wave-packets in a baroclinic fluid, is investigated in this paper. Bright one- and two-soliton solutions are constructed via the Hirota method. We derive the degenerate and nondegenerate vector solitons associated with the one and two wave numbers, respectively, and the latter admit both the single- and double-hump profiles. Effects of the supercritical / subcritical coefficient μ and nonlinearity coefficient σ in that system on the wave packets A 1 and A 2 are analysed: Velocities of A 1 , A 2 and the wave-induced modification of the basic flow, B , are proportional to μ , amplitudes of A 1 and A 2 are inversely proportional to σ , and amplitude of B is proportional to μ . Via the asymptotic analysis, we find that (1) the interactions between the two degenerate solitons or two nondegenerate solitons can be elastic under certain conditions, otherwise the interactions are shape-changing with the total energy in each soliton (consisting of all the components) being conserved; (2) the interactions between the nondegenerate and degenerate solitons are shape-changing, and the nondegenerate solitons can remain the double-hump shape or change to the periodic oscillation after the interactions; (3) the energy redistribution between the A 1 and A 2 components occurs when the two degenerate solitons undergo the shape-changing interaction, and the nondegenerate soliton undergoes the interaction without any intensity redistribution.

Ricci soliton vector fields of spherically symmetric static spacetimes

In this paper, we focused our attention to find Ricci solitons of spherically symmetric static spacetimes. It is shown that special classes of such spacetime metrics admit shrinking, expanding or steady Ricci solitons. It is found that the dimensions of the Ricci soliton vector fields are four, five, eight, ten or eleven. It is observed that non-Einstein metrics also exist with shrinking or expanding Ricci soliton vector fields. In all the cases, the obtained Ricci soliton vector fields are proved to be gradient and concircular potential fields.