Various families of charge-one vortex solitons in two-dimensional periodic media are reported. These vortices reside either in the semi-infinite gap or higher band gaps of the media. For both Kerr and saturable nonlinearities (either focusing or defocusing), infinite vortex families are found. All these families do not bifurcate from Bloch bands; rather, they turn around before reaching edges of Bloch bands. It is further revealed that vortices with drastically different topological shapes can belong to the same vortex family, which is quite surprising.
Nonlocality is a key feature of many physical systems since it prevents a catastrophic collapse and a symmetry-breaking azimuthal instability of intense wave beams in a bulk self-focusing nonlinear media. This opens up an intriguing perspective for stabilization of complex topological structures such as higher-order solitons, vortex rings and vortex ring-on-line complexes. Using direct numerical simulations, we find a class of cylindrically-symmetric $n$-th order spatial solitons having the intensity distribution with a central bright spot surrounded by $n$ bright rings of varying size. We inv…
We report the numerical realization and demonstration of robustness of certain 2-component structures in Bose-Einstein Condensates in 2 and 3 spatial dimensions with non-trivial topological charge in one of the components. In particular, we identify a stable symbiotic state in which a higher-dimensional bright soliton exists even in a homogeneous setting with defocusing interactions, as a result of the effective potential created by a stable vortex in the other component. The resulting vortex-bright solitary waves, which naturally generalize the recently experimentally observed dark-bright sol…
We investigate the formation and propagation of vector vortex solitons (VS) and unipolar soliton (US) in a cold atomic gas with Bessel lattices (BLs). The system we consider is a cold, coherent atomic gas with a tripod or multipod level configuration. Dueing to the giant enhancement of Kerr nonlinearity contributed by electromagnetically induced transparency (EIT), a vector weak vortex soliton can be effectively formed with ultraslow propagating velocity. Furthermore, we demonstrate that the characteristics of 2D VS and US can be controlled and manipulated via adjusting BLs. The results predic…
We derive the nonlinear equations governing the dynamics of three-dimensional (3D) disturbances in a nonuniform rotating self-gravitating fluid under the assumption that the characteristic frequencies of disturbances are small compared to the rotation frequency. Analytical solutions of these equations are found in the form of the 3D vortex dipole solitons. The method for obtaining these solutions is based on the well-known Larichev-Reznik procedure for finding two-dimensional nonlinear dipole vortex solutions in the physics of atmospheres of rotating planets. In addition to the basic 3D x-anti…
We show, by means of numerical and analytical methods, that media with a repulsive nonlinearity which grows from the center to the periphery support a remarkable variety of previously unknown complex stationary and dynamical three-dimensional solitary-wave states. Peanut-shaped modulation profiles give rise to vertically symmetric and antisymmetric vortex states, and novel stationary hybrid states, built of top and bottom vortices with opposite topological charges, as well as robust dynamical hybrids, which feature stable precession of a vortex on top of a zero-vorticity base. The analysis rev…
Vortex solitons (dark solitons) are described in self-defocusing Kerr media whose phase line singularity is not parallel to the propagation direction, but is perpendicular or tilted almost arbitrary angles, depending on the medium linear dispersion. These solitons broaden the so-called spatiotemporal optical vortices recently observed in experiments to the nonlinear realm, opening new perspectives in practical applications of optical vortices.
We use the cubic complex Ginzburg-Landau equation coupled to a dissipative linear equation as a model of lasers with an external frequency-selective feedback. It is known that the feedback can stabilize the one-dimensional (1D) self-localized mode. We aim to extend the analysis to 2D stripe-shaped and vortex solitons. The radius of the vortices increases linearly with their topological charge, $m$, therefore the flat-stripe soliton may be interpreted as the vortex with $m=\infty$, while vortex solitons can be realized as stripes bent into rings. The results for the vortex solitons are applicab…
The emergence of vortex-bright soliton dipoles in two-component Bose-Einstein condensates through bifurcations from suitable eigenstates of the underlying linear system is examined. These dipoles can have their bright solitary structures be in phase (symmetric) or out of phase (anti-symmetric). The dynamical robustness of each of these two possibilities is considered and the out-of-phase case is found to exhibit an intriguing symmetry-breaking instability that can in turn lead to tunneling of the bright wavefunction between the two vortex "wells". We interpret this phenomenon by virtue of a vo…
We demonstrate a robust, stable, mobile, two-dimensional (2D) spatial and three-dimensional (3D) spatiotemporal optical soliton in the core of an optical vortex, while all nonlinearities are of the cubic (Kerr) type. The 3D soliton can propagate with a constant velocity along the vortex core without any deformation. Stability of the soliton under a small perturbation is established numerically. Two such solitons moving along the vortex core can undergo a quasi-elastic collision at medium velocities. Possibilities of forming such a 2D spatial soliton in the core of a vortical beam are discussed…
We discover that a spatially localized gain supports stable vortex solitons in media with cubic nonlinearity and two-photon absorption. The interplay between nonlinear losses and gain in amplifying rings results in suppression of otherwise ubiquitous azimuthal modulation instabilities of radially symmetric vortex solitons. We uncover that the topology of the gain profile imposes restrictions on the maximal possible charge of vortex solitons. Symmetry breaking occurs at high gain levels resulting in the formation of necklace vortex solitons composed of asymmetric bright spots.
We investigate propagating dark soliton solutions of the two-dimensional defocusing nonlinear Schrödinger / Gross-Pitaevskii (NLS/GP) equation that are transversely confined to propagate in an infinitely long channel. Families of single, vortex, and multi-lobed solitons are computed using a spectrally-accurate numerical scheme. The multi-lobed solitons are unstable to small transverse perturbations. However, the single-lobed solitons are stable if they are sufficiently confined along the transverse direction, which explains their effective one-dimensional dynamics. The emergence of a transvers…
The properties of vector vortex beams in vertical-cavity-surface emitting lasers with frequency-selective feedback is investigated. They are interpreted as high-order vortex solitons with a spatially non-uniform, but locally linear polarization state. In contrast to most schemes to obtain vector vortex beams relying on imprinting the polarization structure, vector vortex solitons form spontaneously due to the near polarization degeneracy in vertical-cavity devices. We observe radially, hyperbolic and spiral polarization configurations depending on small residual anisotropies in the system and …
We demonstrate stable and metastable vortex-bright solitons in a three-dimensional spin-orbit-coupled three-component hyperfine spin-1 Bose-Einstein condensate (BEC) using numerical solution and variational approximation of a mean-field model. The spin-orbit coupling provides attraction to form vortex-bright solitons in both attractive and repulsive spinor BECs. The ground state of these vortex-bright solitons is axially symmetric for weak polar interaction. For a sufficiently strong ferromagnetic interaction, we observe the emergence of a fully asymmetric vortex-bright soliton as the ground s…
We demonstrate a stable, mobile, dipolar or nondipolar three-dimensional matter-wave soliton in the vortex core of a uniform nondipolar condensate. All intra- and inter-species contact interactions can be repulsive for a strongly dipolar soliton. For a weakly dipolar or nondipolar soliton, the intra-species contact interaction in the soliton should be attractive for the formation of a compact soliton. The soliton can propagate with a constant velocity along the vortex core without any deformation. Two such solitons undergo a quasi-elastic collision at medium velocities. We illustrate the findi…
Helical and Straight Solitons Induced by Vortex Beams with Off-Axis Pivots in Cubic-Quintic Nonlinear Media
College of Physics and Electronics Engineering, Shanxi University（山西大学物理电子工程学院）；Shanxi Key Laboratory of Wireless Communication and Detection（山西省无线通信与探测重点实验室）；Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University（特拉维夫大学电气工程学院物理电子系）；Instituto de Alta Investigación, Universidad de Tarapacá（塔拉帕卡大学高级研究所）
We present a numerical solution in the form of a three-dimensional (3D) vortex soliton in unmagnetized plasma in the model of the generalized Zakharov equations with saturating exponential nonlinearity. To find the solution with a high accuracy we use two-step numerical method combining the Petviashvili iteration procedure and the Newton-Kantorovich method. The vortex soliton with the topological charge $m=1$ turns out to be stable provided the nonlinear frequency shift exceeds a certain critical value. The stability predictions are verified by direct simulations of the full dynamical equation…
A vortex-bright soliton can precess around a fix point. Here, we find numerically that the fixed point and the associated precessional orbits can be shifted by applying a constant driving force on the bright component, the displacement is proportional to the force with a minus sign. This robust dynamics is then discussed theoretically by treating the vortex-bright soliton as an effective point particle, explaining the observed dynamics and predicting new ones that are subsequently confirmed. By appropriately tuning the force, the vortex-bright soliton can be guided following an arbitrary traje…
We predict that a photonic crystal fiber whose strands are filled with a defocusing nonlinear medium can support stable bright and also vortex solitons if the strength of the defocusing nonlinearity grows toward the periphery of the fiber. The domains of soliton existence depend on the transverse growth rate of the filling nonlinearity and nonlinearity of the core. Remarkably, solitons exist even when the core material is linear.
Stable vortex soliton arrays in disclination-fractal systems
Xi'an Jiaotong University（西安交通大学）；Hamad Bin Khalifa University（哈马德·本·哈利法大学）；Aerospace Information Research Institute, Chinese Academy of Sciences（中国科学院空天信息创新研究院）
By numerical and variational analysis of the three-dimensional Gross-Pitaevskii equation we study the formation and dynamics of bright and vortex-bright solitons in a cigar-shaped dipolar Bose-Einstein condensate for large repulsive atomic interactions. Phase diagram showing the region of stability of the solitons is obtained. We also study the dynamics of breathing oscillation of the solitons as well as the collision dynamics of two solitons at large velocities. Two solitons placed side-by-side at rest coalesce to form a stable bound soliton molecule due to dipolar attraction.
By using different continuation methods, we unveil a wide region in the parameter space of the discrete cubic-quintic complex Ginzburg-Landau equation, where several families of stable vortex solitons coexist. All these stationary solutions have a symmetric amplitude profile and two different topological charges. We also discover the dynamical formation of a variety of 'bound-state' solutions, composed of two or more of these vortex solitons. All of these stable composite structures persist in the conservative cubic limit, for high values of their power content.
We examine the existence and stability of nonlinear discrete vortex solitons in a square lattice when the standard discrete Laplacian is replaced by a fractional version. This creates a new, effective site-energy term, and a coupling among sites, whose range depends on the value of the fractional exponent $α$, becoming effectively long-range at small $α$ values. At long-distance, it can be shown that this coupling decreases faster than exponential: $\sim \exp(- |{\bf n}|)/\sqrt{|\bf{n}|}$. In general, we observe that the stability domain of the discrete vortex solitons is extended to lower pow…
We show the existence of stable two- and three-dimensional vortex solitons carrying multiple, spatially separated, single-charge topological dislocations nested around a vortex-ring core. Such new nonlinear states are supported by elliptical gain landscapes in focusing nonlinear media with two-photon absorption. The separation between the phase dislocations is dictated mostly by the geometry of gain landscape and it only slightly changes upon variation of the gain or absorption strength.
We analyze numerically the formation and the subsequent dynamics of two-dimensional matter wave dark solitons in a Thomas-Fermi rubidium condensate using various techniques. An initially imprinted sharp phase gradient leads to the dynamical formation of a stationary soliton as well as very shallow grey solitons, whereas a smooth gradient only creates grey solitons. The depth and hence, the velocity of the soliton is provided by the spatial width of the phase gradient, and it also strongly influences the snake-instability dynamics of the two dimensional solitons. The vortex dipoles stemming fro…
We show that ring-like localized gain landscapes imprinted in focusing cubic (Kerr) nonlinear media with strong two-photon absorption support new types of stable higher-order vortex solitons containing multiple phase singularities nested inside a single core. The phase singularities are found to rotate around the center of the gain landscape, with the rotation period being determined by the strength of the gain and the nonlinear absorption.
