We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schrödinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance.
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 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 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…
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.
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…
Stabilization of Interband Phase Solitons in Two-Band Noncentrosymmetric Superconducting Rings
Centro de Física de Materiales (CFM-MPC), Centro Mixto CSIC-UPV/EHU（材料物理中心）；Tel Aviv University（特拉维夫大学）；Instituto de Alta Investigación, Universidad de Tarapacá（塔拉帕卡大学高等研究所）；Institute for Theoretical Solid State Physics, IFW Dresden（德累斯顿IFW固体物理理论研究所）；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）
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…
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）
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 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…
Multi-ring necklace vortex solitons in Kerr nonlinear media with azimuthally modulated Bessel potentials
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学系）；Instituto de Alta Investigación, Universidad de Tarapacá（塔拉帕卡大学高等研究院）
