Multimode Solitons Research Articles

Multi-mode solitons in a long-short range traffic lattice model with time delay

We consider a new form of solutions of a special lattice model for traffic system. By analyzing nearest sites’ interactions, time delay, and bumpy effects, we deduce the bifurcation lines and surfaces for stable and unstable regions and show how they vary as parameters vary. It shows that keeping other conditions unchanged, as the incoming flow increases, the traffic flow becomes unstable, opposite to when outgoing flow increases, it becomes stable. Besides, considering delayed optimal flow, multiple sites effect or artificial parameters can also help stabilize the traffic road condition. Moreover, by putting it into the framework of mKdV equations, we obtain the kink–antikink solitons involving all parameters, which show the feature of the traffic congestion. The result is original, and our model in differential or difference form can be reduced into the previous ones by choosing appropriate parameters. Since the optimal velocity function we considered involves finitely or infinitely many sites, the density waves can be in multi-mode and high dimension forms and can also be quasi-periodic, we show a new feature of the traffic lattice system.

Spatio-temporal control of dispersive waves trapping by solitons in graded-index multimode fibers

We investigate the impact of the spatial beam oscillations in a graded-index multimode fiber (MMF) upon the trapping and blue-shifting of dispersive pulses by a multimode soliton. We find that the dispersive pulses trapped by solitons can be controlled through adjusting the degree of compression of the spatial beam. This can provide an explanation for the enhanced blue spectral extension observed in the typical supercontinuum generation in graded-index MMFs. Besides, the spatial-temporal nonlinear effect may provide an additional degree of freedom for the spectrally tailored light generation and the ultrashort pulse generation with tunable wavelengths in the normal dispersion regime.

Spiraling interaction of multi-mode solitons in self-induced harmonic potentials

We investigate the propagation and spiraling interaction of multi-mode solitons in self-induced harmonic potentials. The general analytical propagation expression for the interaction of the multi-mode solitons is derived. The interaction characteristics, such as the evolution of the intensity of the combined optical field, the spacing of each constituent soliton to the longitudinal axis, the spiraling angle and velocity, the propagation trajectory, and the phase shift are discussed with detail. We show that it is possible to control the spiraling interacting trajectories of the solitons by carefully designing the input parameters. It is proved that the motion state of each soliton satisfies the conservation of mechanical energy. The results may have potential applications in all-optical information processing and particle control.

Nonlinear interactions in multimode optical fibers

Abstract The limitations of single-mode fibers incite multimode fibers to meet the technological demands and explore new physics. Multimode fibers support many spatial modes which can interact with each other through various nonlinear processes and give rise to complex spatiotemporal dynamics. In this review paper, we address intermodal coupling based nonlinear phenomena in short and long pulse regimes. Ultrashort femtosecond pulse regime is dominated by four-wave mixing, self and cross-phase modulation, interpulse as well as intrapulse Raman scattering and provides strong platform for the realization of multitude of nonlinear phenomena such as multimode soliton formation, generation of intense combs of dispersive waves from the multimode soliton, beam clean-up, geometric parametric instability, and optical event horizon. On the other hand, long pulse regime exhibits strong stimulated Raman processes and provides natural tool for the investigation of nonlinear phenomena such as, cascaded Raman scattering, intermodal four-wave mixing based wideband frequency generation, transient grating formation and many others. This article reviews the recent developments in intermodal nonlinear interactions in multimode fiber for both the short and long pulse regimes and provides a roadmap for future research directions in the area of multimode nonlinear fiber optics.

Accelerated nonlinear interactions in graded-index multimode fibers

Multimode optical fibers have recently reemerged as a viable platform for addressing a number of long-standing issues associated with information bandwidth requirements and power-handling capabilities. As shown in recent studies, the complex nature of such heavily multimoded systems can be effectively exploited to observe altogether novel physical effects arising from spatiotemporal and intermodal linear and nonlinear processes. Here, we study for the first time, accelerated nonlinear intermodal interactions in core-diameter decreasing multimode fibers. We demonstrate that in the anomalous dispersion region, this spatiotemporal acceleration can lead to relatively blue-shifted multimode solitons and blue-drifting dispersive wave combs, while in the normal domain, to a notably flat and uniform supercontinuum, extending over 2.5 octaves. Our results pave the way towards a deeper understanding of the physics and complexity of nonlinear, heavily multimoded optical systems, and could lead to highly tunable optical sources with very high spectral densities.

Spatial solitons in PT symmetric potential with competing gain and loss

The existence and stability of fundamental, dipole and tripole solitons are investigated in parity-time symmetric potential with competing gain and loss. The competing parameter decides both the width of potential and loss or gain region. All these solitons exist in the potential with a suitable width. It is easy to form a fundamental soliton when increasing the parameter k. To form a dipole and a tripole soliton, the values of k should locate in some region. The multimode solitons are unstable for a larger power while may be stable for a relatively small one. The effects of competing gain or loss profile on the stability of these solitons are investigated with a linear stability analysis corroborated by a beam propagation method.

Observation of multimode solitons in few-mode fiber.

We experimentally isolate and directly observe multimode solitons in few-mode graded-index fiber. We rely on Raman frequency shifts to spectrally isolate these multimode solitons. By varying the input energy and modal composition of the launched pulse, we observe a continuous variation of multimode solitons with different spatiotemporal properties. They exhibit an energy-volume relation that is distinct from those of single-mode and fully spatiotemporal solitons.

Spatiotemporal dynamics of multimode optical solitons.

As optical fiber communications and fiber lasers approach fundamental limits there is considerable interest in multimode fibers. In nonlinear science, they represent an exciting environment for complex nonlinear waves. As in single-mode fiber, solitons may be particularly important. Multimode solitons consist of synchronized, non-dispersive pulses in multiple spatial modes, which interact via the Kerr nonlinearity of the fiber. They are expected to exhibit novel spatiotemporal characteristics, dynamics and, like single-mode solitons, may provide a convenient intuitive tool for understanding more complex nonlinear phenomena in multimode fibers. Here we explore experimentally and numerically basic properties and spatiotemporal behaviors of these solitons: their formation, fission, and Raman dynamics.

Multisoliton complexes of Bose–Einstein condensates in nonlinear optical lattices

We theoretically study the role of the mode structure of a multicomponent Bose–Einstein condensate (BEC) in the potential created by a nonlinear optical lattice. We describe a multisoliton complex (MSC) as a superposition of different fundamental soliton modes in the matter-wave system. Using a similarity transformation, we solve the nonlinear evolution equation of the multimode coupled matter-wave field and construct a set of analytical bright soliton solutions. A perturbation method is used to examine the linear stability of the constructed solitons. Based on these particular solutions, we numerically analyze the mode structure of a MSC. The results show that the periodicity causes a Bloch modulation in the envelopes of the density distribution. When different fundamental modes collide with each other in the nonlinear lattice, the collision-induced shifts, and the space-dependent modulation of external potentials change the density profile of the multimode soliton complex. Therefore, the mode structure, which is absent in a one-mode BEC, provides the possible multiscale modeling of the matter-wave field with extra degrees of freedom.

Dynamics of the Manakov-typed bound vector solitons with random initial perturbations

Dynamics of the bound vector solitons with random initial perturbations is investigated for the Manakov model, which describes the propagation of the multimode soliton pulses in nonlinear fiber optics and two-component matter-wave solitons in the quasi-one-dimensional Bose–Einstein condensates (BECs) without confining potential. We review the analytic two-bound-vector-soliton solutions and give the three-bound-vector-soliton solutions. Breakup of the typical bound state is presented numerically when the symmetry and asymmetry random perturbations are added to the initial conditions. Relationship between the lifetime of the bound state and amplitude of the random perturbation is discussed. Meanwhile, existence of the symmetry-recovering is illustrated for the bound vector solitons with the asymmetry random perturbations. Discussions of this paper could be expected to be helpful in interpreting the dynamics of the Manakov-typed bound vector solitons when the random initial noises in nonlinear optical fibers or stochastic quantum fluctuations in the BECs are considered.

Bound vector solitons and soliton complexes for the coupled nonlinear Schrödinger equations

Dynamic features describing the collisions of the bound vector solitons and soliton complexes are investigated for the coupled nonlinear Schrödinger (CNLS) equations, which model the propagation of the multimode soliton pulses under some physical situations in nonlinear fiber optics. Equations of such type have also been seen in water waves and plasmas. By the appropriate choices of the arbitrary parameters for the multisoliton solutions derived through the Hirota bilinear method, the periodic structures along the propagation are classified according to the relative relations of the real wave numbers. Furthermore, parameters are shown to control the intensity distributions and interaction patterns for the bound vector solitons and soliton complexes. Transformations of the soliton types (shape changing with intensity redistribution) during the collisions of those stationary structures with the regular one soliton are discussed, in which a class of inelastic properties is involved. Discussions could be expected to be helpful in interpreting such structures in the multimode nonlinear fiber optics and equally applied to other systems governed by the CNLS equations, e.g., the plasma physics and Bose-Einstein condensates.

Multimode soliton dynamics in perturbed ladder lattices.

We investigate the interplay between the longitudinal and lateral solitonic modes in perturbed ladder lattices in regard to the transmission of soliton wave packet. (1) In a longitudinal uniform field the lateral and longitudinal solitonic modes are shown to be independent. However, unlike in the unperturbed case the dynamics of the soliton center of mass becomes confined within a finite spatial domain via the Bloch-Zener mechanism in the longitudinal direction and due to the transverse finiteness of the ladder in the lateral one. (2) The segment of on-site impurities causes the soliton mode-mode mixing. As a result the soliton exhibits rather complex two- or three-dimensional dynamics accompanied by wave radiation which may give rise to soliton trapping. Nevertheless, under some specific conditions the soliton is able to bypass even the strong impurities slaloming between them. In particular, the slalom soliton dynamics is possible on a ladder lattice with a segment of zigzig-distributed on-site impurities. We formulate the conditions favorable to the case and show that their violation gives rise to either soliton trapping on or soliton reflection from the impure segment. (3) Finally, we study the effect of the modified transverse bond on the longitudinal soliton dynamics and reveal that it might act on the soliton as either an attractive or a repulsive potential, depending on the sign of the transverse energy of the ingoing soliton. The effect is essentially a solitonic one and becomes strictly pronounced for heavy solitons, when imperfection-induced radiation effects are exponentially suppressed. We expect that transverse-bond imperfection could serve as a filter selecting the solitons with prescribed properties. A similar function is feasible for zigzag-distributed on-site impurities too.

Observation of two-dimensional multimode solitons

We present the first experimental observation of (2+1) -dimensional multimode (composite) solitons. A single-hump component and a double-hump (dipole-type) component are jointly self-trapped as a composite soliton in a biased photorefractive crystal.

Composite multihump vector solitons carrying topological charge

We propose composite solitons carrying topological charge: multicomponent two dimensional [ (2+1)D] vector (Manakov-like) solitons for which at least one component carries topological charge. These multimode solitons can have a single hump or exhibit a multihump structure. The "spin" carried by these multimode composite solitons suggests 3D soliton interactions in which the particlelike behavior includes spin, in addition to effective mass, linear, and angular momenta.

Observation of Multihump Multimode Solitons

We present the first experimental observation of multihump multimode solitons in nature. In a broader perspective, this is the first observation of a multihumped multimode self-trapped wave packet propagating in a dispersive nonlinear medium. Double- and triple-humped spatial profiles are found by incoherent population of two modes of the beams' self-induced waveguide (self-induced potential well).

Effects of the ion-beam density and velocity on the excitation of multimode soliton

Multimode solitons are observed to be excited in an ion-beam–plasma system. But, the excitation of some mode solitons of these is found to be suppressed under a certain condition depending on the density and velocity of a low-energy ion beam, produced by the applied negative pulse. Furthermore, weak interaction between the slow-beam soliton and ion-acoustic soliton is also observed to cause small time lags in their trajectories on the distance–time plane.

Ion-Beam-Plasma Systems 1. 2. Nonlinear Wave Phenomena in Beam-Plasma Systems. 2-1 Nonlinear Wave Phenomena in Ion-Beam-Plasma Systems.

Experimental studies on various types of nonlinear wave phenomena in ion-beam-plasma systems are reviewed.The phenomena include effects of ion-beams on solitons, excitation of multimode solitons, amplitude oscillations, frequency shifts, decay and explosive instabilities and the self-modulation of waves due to modulational instability.