Individual Solitons Research Articles

Stability and Chirp of Tightly Bunched Solitons From Nonlinear Polarization Rotation Mode-Locked Erbium-Doped Fiber Lasers

Investigation of tightly bunched solitons generated from the nonlinear polarization rotation (NPR) governed mode-locked erbium-doped fiber laser (ML-EDFL) is demonstrated. By changing the intra-cavity polarization, the solitons can be switched from the tightly bunched state to coarse bunched state. In the tightly bunched state (stable state), the energy fluctuation of soliton is substantially suppressed to ΔE/E = 2.5 × 10 −3 with a timing jitter of Δt = 16 ps. In addition, the dynamic evolution of bunched solitons in the NPRML-EDFL is also explored by configuring two output ports at different positions. As compared to the output node before the EDF, the tightly bunched solitons delivered from the output node after the EDF performs the shorter pulsewidth of 380 fs with the lower noises with ΔE/E = 1.6 × 10−3 (timing jitter Δt = 12 ps). Enlarging pump power promotes the split number of bunched solitons within one mode-locked pulse envelope. The individual soliton of different orders experiences different amounts of long-range attractive force from solitons, which leads to an unequalized spacing between the adjacent solitons occurred within bunched pulse envelope. The chirp parameter of C = −0.022 is dominated by the cooperation of group-delay dispersion and self-phase modulation effects, which can further compress the EDFL pulse to <400 fs.

Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation

A variety of methods for examining the properties and solutions of nonlinear evolution equations are explored by using the Vakhnenko equation (VE) as an example. The VE, which arises in modelling the propagation of high-frequency waves in a relaxing medium, has periodic and solitary traveling wave solutions some of which are loop-like in nature. The VE can be written in an alternative form, known as the Vakhnenko-Parkes equation (VPE), by a change of independent variables. The VPE has anN-soliton solution which is discussed in detail. Individual solitons are hump-like in nature whereas the corresponding solution to the VE comprisesN-loop-like solitons. Aspects of the inverse scattering transform (IST) method, as applied originally to the KdV equation, are used to find one- and two-soliton solutions to the VPE even though the VPE’s spectral equation is third-order and not second-order. A Bäcklund transformation for the VPE is used to construct conservation laws. The standard IST method for third-order spectral problems is used to investigate solutions corresponding to bound states of the spectrum and to a continuous spectrum. This leads toN-soliton solutions andM-mode periodic solutions, respectively. Interactions between these types of solutions are investigated.

Marine seismic observation of internal solitary wave packets in the northeast South China Sea

AbstractRecently the novel seismic oceanography method has been reported to be an effective way to study the energetic internal solitary waves (ISWs) in the northern South China Sea. An optimized seismic‐oceanographic cruise was carried out to observe such near‐surface ISWs on Dongsha Plateau in July 2014. Several soliton trains rather than single solitons were captured using the seismic technique. After seismic data processing, one prototypical rank‐ordered ISW packet on northeast side of Dongsha Island was clearly identified for further analysis. This included waveforms, propagation velocities, and vertical velocities for individual solitons. In this study, an improved scheme was applied to derive the transient phase velocities from the seismic data which is verified from independent satellite and hydrographic data. Analytical predictions from Korteweg‐de Vries equation fit better than the extended Korteweg‐de Vries equation ignoring background currents. Our results show that the seismic method can be successfully used to image targets in shallow water below 40 m and that seismic oceanography is a promising technique for studying near‐surface phenomena with high spatial resolution.

Generation of χ(2) solitons from the Airy wave through the parametric instability.

Spontaneous creation of solitons in quadratic media by the downconversion (i.e., parametric instability against the generation of fundamental-frequency excitations) from the truncated Airy-wave (AW) mode in the second-harmonic component is studied. Parameter regions are identified for the generation of one, two, and three solitons, with additional small-amplitude "jets." Shares of the total power carried by individual solitons are found. Also considered are soliton patterns generated by the downconversion from a pair of AWs bending in opposite directions.

Influence of gain dynamics on dissipative soliton interaction in the presence of a continuous wave

We investigate the effect of the gain dynamics on the motion and interactions of solitons in the frame of a complex Ginzburg-Landau-type model, which accounts for dissipative soliton formation and propagation in a ring fiber laser. It is shown that the gain dynamics modifies the soliton velocity and their interactions. In the presence of an injected continuous wave, an initial crystal of a few solitons gets broken, either into bunches or into individual solitons. Quasielastic collisions analogous to Newton's cradle have been seen. The soliton set may evolve into gas, solitons, or harmonic mode-locked patterns. The time jitter present in the last situation has been considered.

Harmonic passive mode locking of bound-soliton structures in fiber lasers

It has been shown by numerical simulation that additional inertial nonlinearity of the refractive index results in repulsion of solitons in multi-pulse passive mode-locked fiber lasers if the intersoliton distance is sufficiently large. At the same time, closely spaced solitons are attracted to each other. It has been found that the combination of these properties of soliton interaction can lead to harmonic passive mode locking of identical structures of bound solitons (generation with an equidistant arrangement of soliton structures in the laser cavity). These properties of soliton interaction are caused by the asymmetry of the wings of an individual soliton, which manifests itself as the asymmetry of Kelly's spectral peaks and is due to the inertial nonlinearity of the refractive index. Other possible mechanisms of this asymmetry are also discussed.

Vibration spectrum of a two-soliton molecule in dipolar Bose–Einstein condensates

We study the vibration of soliton molecules in dipolar Bose–Einstein condensates by variational approach and numerical simulations of the nonlocal Gross–Pitaevskii equation. We employ the periodic variation of the strength of dipolar atomic interactions to excite oscillations of solitons near their equilibrium positions. When the parametric perturbation is sufficiently strong the molecule breaks up into individual solitons, like the dissociation of ordinary molecules. The waveform of the molecule and resonance frequency, predicted by the developed model, are confirmed by numerical simulations of the governing equation.

Mathematical and computer modeling of seismic processes based on a soliton approach

In this paper we consider a mathematical model of seismic process, taking into account the role of solitary waves as a shocks trigger. Methods of forecasting are based on evaluating trajectories of individual solitons and clarification of shocks probability. We allocate among the entire set of shocks individual subsets caused by the same soliton and construct of hypothetical trajectory of the solitons. The probability of a shock can be verified taking into account the soliton components of seismic process. The information system for the analysis of soliton component seismic processes was developed. We show the effectiveness of soliton approach and the possibility of its application to the analysis of seismic processes in several regions of the Earth by using this information system.

Stabilizing the false vacuum: Mott skyrmions.

Topological excitations keep fascinating physicists since many decades. While individual vortices and solitons emerge and have been observed in many areas of physics, their most intriguing higher dimensional topological relatives, skyrmions (smooth, topologically stable textures) and magnetic monopoles emerging almost necessarily in any grand unified theory and responsible for charge quantization remained mostly elusive. Here we propose that loading a three-component nematic superfluid such as 23Na into a deep optical lattice and thereby creating an insulating core, one can create topologically stable skyrmion textures. The skyrmion's extreme stability and its compact geometry enable one to investigate the skyrmion's structure, and the interplay of topology and excitations in detail. In particular, the superfluid's excitation spectrum as well as the quantum numbers are demonstrated to change dramatically due to the skyrmion, and reflect the presence of a trapped monopole, as imposed by the skyrmion's topology.

Direct observation of single-electron solitons and Friedel oscillations in a quasi-one dimensional material with incommensurate charge-density waves

We have performed scanning tunneling microscopy experiments in the quasi-one dimensional charge density wave (CDW) system NbSe3, where we could image and study in detail individual solitons corresponding to the self-trapping of a single electron. Our analysis shows that the type of soliton we observed is an “Amplitude Soliton”, characterized by a vanishing CDW amplitude at the soliton center and by a π-shift of its phase along the chain direction. Pairs of solitons or multiple solitons were also observed. Such observations could be made only in the high-temperature CDW phase. Additionally, one-dimensional Friedel oscillations around charged defects could also be imaged and are found to be superimposed to the CDW. The distinction between amplitude solitons and Friedel oscillations can be made without any ambiguity.

Monopole-vortex complex at large distances and nonAbelian duality

We discuss the large-distance approximation of the monopole-vortex complex soliton in a hierarchically broken gauge system, SU(N+1) - > SU(N) x U(1) - > 1, in a color-flavor locked SU(N) symmetric vacuum. The ('t Hooft-Polyakov) monopole of the higher-mass-scale breaking appears as a point and acts as a source of the thin vortex generated by the lower-energy gauge symmetry breaking. The exact color-flavor diagonal symmetry of the bulk system is broken by each individual soliton, leading to nonAbelian orientational CP^{N-1} zeromodes propagating in the vortex worldsheet, well studied in the literature. But since the vortex ends at the monopoles these fluctuating modes endow the monopoles with a local SU(N) charge. This phenomenon is studied by performing the duality transformation in the presence of the CP^{N-1} moduli space. The effective action is a CP^{N-1} model defined on a finite-width worldstrip.

Dark soliton fiber lasers.

Dark soliton formation and soliton dynamics in all-normal dispersion cavity fiber ring lasers without an anti-saturable absorber in cavity is studied both theoretically and numerically. It is shown that under suitable conditions the dark solitons formed could be described by the nonlinear Schrödinger equation. The dark soliton formation in an all-normal-dispersion cavity erbium-doped fiber ring laser without an anti-saturable absorber in cavity is first experimentally demonstrated. Individual dark solitons are experimentally identified. Excellent agreement between theory and experiment is observed.

Acoustic mode coupling induced by nonlinear internal waves: evaluation of the mode coupling matrices and applications.

This paper applies the mode coupling equation to calculate the mode-coupling matrix for nonlinear internal waves appearing as a train of solitons. The calculation is applied to an individual soliton up to second order expansion in sound speed perturbation in the Dyson series. The expansion is valid so long as the fractional sound speed change due to a single soliton, integrated over range and depth, times the wavenumber is smaller than unity. Scattering between the solitons are included by coupling the mode coupling matrices between the solitons. Acoustic fields calculated using this mode-coupling matrix formulation are compared with that obtained using a parabolic equation (PE) code. The results agree very well in terms of the depth integrated acoustic energy at the receivers for moving solitary internal waves. The advantages of using the proposed approach are: (1) The effects of mode coupling can be studied as a function of range and time as the solitons travel along the propagation path, and (2) it allows speedy calculations of sound propagation through a packet or packets of solitons saving orders of magnitude computations compared with the PE code. The mode coupling theory is applied to at-sea data to illustrate the underlying physics.

Head-on collision of dust-acoustic solitons in a strongly coupled dusty plasma

The collision between two counterpropagating dust acoustic solitary waves in a strongly coupled dusty plasma has been observed. The measured velocity and width of the solitary wave agree with the solution of the Korteweg-de Vries equation derived by using the generalized hydrodynamic model. The two counterpropagating solitary waves of equal amplitude merge into a single pulse with twice the individual soliton amplitude and then pass through each other. The solitons suffer a small time delay in propagation after collision. The measured delay time obtained from their trajectories is also presented.

Soliton pair generation in the interactions of Airy and nonlinear accelerating beams

We investigate numerically the interactions of two in-phase and out-of-phase Airy beams and nonlinear (NL) accelerating beams in Kerr and saturable NL media, in one transverse dimension. We find that bound and unbound soliton pairs, as well as single solitons, can form in such interactions. If the interval between two incident beams is large relative to the width of their first lobes, the generated soliton pairs just propagate individually and do not interact. However, if the interval is comparable to the widths of the maximum lobes, the pairs interact and display varied behavior. In the in-phase case, they attract each other and exhibit stable bound, oscillating, and unbound states, after shedding some radiation initially. In the out-of-phase case, they repel each other and, after an initial interaction, fly away as individual solitons. While the incident beams display acceleration, the solitons or soliton pairs generated from those beams do not.

Soliton switching in inhomogeneous nonlocal media

We address a simple way to achieve routing of optical spatial solitons via soliton interactions in the inhomogeneous nonlocal media. We reveal that the variation of the nonlocality disturbs the solitons pairs and splits them into two individual solitons which have the same escape angle but opposite deflection directions. In particular, the escape angle monotonically increases with the increase of the nonlocality variation rate. We demonstrate that the soliton pairs could form self-consistent waveguides that are able to controllably guide a weak signal by any output positions.

Hydrodynamic Supercontinuum

We report the experimental observation of multi-bound-soliton solutions of the nonlinear Schrödinger equation (NLS) in the context of hydrodynamic surface gravity waves. Higher-order N-soliton solutions with N=2, 3 are studied in detail and shown to be associated with self-focusing in the wave group dynamics and the generation of a steep localized carrier wave underneath the group envelope. We also show that for larger input soliton numbers, the wave group experiences irreversible spectral broadening, which we refer to as a hydrodynamic supercontinuum by analogy with optics. This process is shown to be associated with the fission of the initial multisoliton into individual fundamental solitons due to higher-order nonlinear perturbations to the NLS. Numerical simulations using an extended NLS model described by the modified nonlinear Schrödinger equation, show excellent agreement with experiment and highlight the universal role that higher-order nonlinear perturbations to the NLS play in supercontinuum generation.

Anomalous interaction of nonlocal solitons in media with competing nonlinearities

We theoretically investigate properties of individual bright spatial solitons and their interaction in nonlocal media with competing focusing and defocusing nonlinearities. We consider the general case with both nonlinear responses characterized by different strengths and degrees of nonlocality. We employ a variational approach to analytically describe soliton properties. In particular, we prove analytically that the interplay of focusing and defocusing nonlocal nonlinearities leads to attraction or repulsion of solitons depending on their separation distance. We then study the propagation and interaction of solitons using numerical simulations of the full model of beam propagation. The numerical simulations fully confirm our analytical results.

Beam steering in a nonlocal medium with inhomogeneous nonlinearity

We address the dynamics of out-of-phase soliton pairs and dipole solitons in a nonlocal medium with inhomogeneous nonlinearity, and demonstrate their self-splitting into two individual solitons. We reveal that this self-splitting strongly depends on the variation of the longitudinal nonlinearity and it can be employed for efficient control of the soliton trajectories. We also demonstrate that the index waveguide, which is induced by the soliton pairs and the dipole soliton bound state, yields a family of special waveguides and beam splitters for trapped linear beams. Interestingly, the switching efficiency of this beam splitter could be controlled by adjustment of the longitudinal nonlinearity.

Soliton molecules in dipolar Bose-Einstein condensates

Dipolar interactions support the formation of intersite soliton molecules in a stack of quasi-one-dimensional (quasi-1D) traps. We show that the stability and properties of individual solitons and soliton molecules in such a geometry crucially depend on the interplay between contact and dipolar interactions. In particular, two different quasi-1D soliton regimes are possible: a one-dimensional (1D) soliton characterized by purely repulsive dipole-dipole interactions (DDI) and a three-dimensional (3D) soliton for which a sufficiently large dipole moment renders the DDI attractive. Furthermore, we find that in contrast to the dimers of polar molecules the soliton dimers exhibit a nontrivial behavior of the elementary excitations that stems from the competition between onsite and intersite DDI. Finally, we prove the existence of soliton trimers in a regime where molecular trimers do not occur. We demonstrate that the soliton molecules that we report are well feasible under realistic experimental conditions.