Observation of quadratic optical vortex solitons

We report on the generation of stable dark-vortex solitons in large-phase-mismatched second-harmonic generation of self-defocusing type, sustained by a combined effect of transverse walk-off and finite beam size.     

Observation of discrete vortex solitons in optically induced photonic lattices

We report on the first experimental observation of discrete vortex solitons in two-dimensional optically induced photonic lattices. We demonstrate strong stabilization of an optical vortex by the lattice in a self-focusing nonlinear medium and study the generation of the discrete vortices from a broad class of singular beams.     

Observation of second-band vortex solitons in 2D photonic lattices

We demonstrate second-band bright vortex-array solitons in photonic lattices. This constitutes the first experimental observation of higher-band solitons in any 2D periodic system. These solitons possess complex intensity and phase structures, yet they can be excited by a simple highly localized vortex-ring beam. Finally, we show that the linear diffraction of such beams exhibits preferential transport along the lattice axes.     

High-order polarization vortex spatial solitons

We investigate the formation of high-order polarization vortex spatial solitons. The high-order polarization vortex solitons have novel polarization states which are different from fundamental polarization vortex solitons and have rotational symmetry only in intensity. It is proved that the polarization vortex solitons cannot carry vortex phase. The existence domain and dynamical characteristic of these high-order polarization vortex solitons in Bessel optical lattices are discussed in detail.     

Two-dimensional higher-band vortex lattice solitons

We study self-localized second-band vortex states in two-dimensional photonic lattices and find stable ring solitons whose phase forms an array of counterrotating vortices. We also identify composite solitons in which a second-band vortex is jointly trapped with a mode arising from the first band and study their stability. When such a composite entity is unstable, it disintegrates while exchanging angular momentum between its constituents, eventually stabilizing into another form of composite soliton.     

Waveguiding properties of optical vortex solitons

An optical vortex soliton induces a graded-index waveguide over an extended propagation distance in a self-defocusing nonlinear optical medium. Using numerical techniques, we determine the waveguide dispersion and optimal size of the guided beam.     

Stability of solitons on vortex filaments

A vortex filament is a filament on which fluid vorticity is concentrated. This concept is particularly important in superfluidity and turbulence. This Letter focuses on the vortex filament equation (VFE), which is a model for the motion of a vortex filament in an incompressible and inviscid fluid. The VFE soliton solutions are considered and their spectral stability is proven by developing a straightforward method to solve the corresponding eigenvalue problem. A similar analysis is performed on the planar vortex filament equation. We discuss the applicability of the methods introduced in this Letter to other physically relevant curve equations and other types of solutions.     

Azimuthons: spatially modulated vortex solitons

We introduce a novel class of spatially localized self-trapped ringlike singular optical beams in nonlinear media, the so-called azimuthons, which appear due to a continuous azimuthal deformation of vortex solitons. We demonstrate that the azimuthons are characterized by two independent integer indices, the topological charge m and the number N of the intensity peaks along the ring. Each soliton family includes azimuthons with negative, positive, and zero angular velocity.     

Three-dimensional vortex solitons in self-defocusing media

We demonstrate that families of vortex solitons are possible in a bidispersive three-dimensional nonlinear Schr?dinger equation. These solutions can be considered as extensions of two-dimensional dark vortex solitons which, along the third dimension, remain localized due to the interplay between dispersion and nonlinearity. Such vortex solitons can be observed in optical media with normal dispersion, normal diffraction, and defocusing nonlinearity.     

非局域非线性介质中的拉盖尔-高斯涡旋呼吸子和涡旋光孤子

在圆柱坐标系下,利用分离变量的方法求得了非局域克尔介质中拉盖尔-高斯光束传输的精确解析解。当输入功率等于临界功率时,光束演变为拉盖尔-高斯涡旋光孤子,是一种旋转的多环光孤子;当输入功率接近于临界功率时,光束在传输过程中形成拉盖尔-高斯涡旋呼吸子。结果表明,低阶的拉盖尔-高斯孤子呈现中空多峰亮环分布。     

Asymmetric vortex solitons in nonlinear periodic lattices

We reveal the existence of asymmetric vortex solitons in ideally symmetric periodic lattices and show how such nonlinear localized structures describing elementary circular flows can be analyzed systematically using the energy-balance relations. We present the examples of rhomboid, rectangular, and triangular vortex solitons on a square lattice and also describe novel coherent states where the populations of clockwise and anticlockwise vortex modes change periodically due to a nonlinearity-induced momentum exchange through the lattice. Asymmetric vortex solitons are expected to exist in different nonlinear lattice systems, including optically induced photonic lattices, nonlinear photonic crystals, and Bose-Einstein condensates in optical lattices.     

Optical vortex solitons in parametric wave mixing

We analyze two-component spatial optical vortex solitons supported by parametric wave mixing processes in a nonlinear bulk medium. We study two distinct cases of such localized waves, namely, parametric vortex solitons due to phase-matched second-harmonic generation in an optical medium with competing quadratic and cubic nonlinear response, and vortex solitons in the presence of third-harmonic generation in a cubic medium. We find, analytically and numerically, the structure of two-component vortex solitons, and also investigate modulational instability of their plane-wave background. In particular, we predict and analyze in detail novel types of vortex solitons, a "halo-vortex," consisting of a two-component vortex core surrounded by a bright ring of its harmonic field, and a "ring-vortex" soliton which is a vortex in a harmonic field that guides a ring-like localized mode of the fundamental-frequency field.     

Rotating vortex solitons supported by localized gain

We show that ringlike 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.     

Stability of vortex solitons in the cubic-quintic model

We investigate one-parameter families of two-dimensional bright spinning solitons (ring vortices) in dispersive media combining cubic self-focusing and quintic self-defocusing nonlinearities. In direct simulations, the spinning solitons display a symmetry-breaking azimuthal instability, which leads to breakup of a soliton into a set of fragments, each being a stable nonspinning soliton. The fragments fly out tangentially to the circular crest of the original vortex ring. If the soliton’s energy is large enough, the instability develops so slowly that the spinning solitons may be regarded as virtually stable ones, in accord with earlier published results. Growth rates of perturbation eigenmodes with different azimuthal “quantum numbers” are calculated as a function of the soliton’s propagation constant κ from a numerical solution of the linearized equations. As a result, a narrow (in terms of κ) stability window is found for extremely broad solitons with values of the “spin” s=1 and 2. However, analytical consideration of a special perturbation mode in the form of a spontaneous shift of the soliton’s central “bubble” (core of the vortex embedded in a broad soliton) demonstrates that even extremely broad solitons are subject to an exponentially weak instability against this mode. In actual simulations, a manifestation of this instability is found in a three-dimensional soliton with s=1. In the case when the two-dimensional spinning solitons are subject to tangible azimuthal instability, the number of the nonspinning fragments into which the soliton splits is usually, but not always, equal to the azimuthal number of the instability eigenmode with the largest growth rate.     

Stabilization of dark and vortex parametric spatial solitons

We demonstrate that a weak defocusing Kerr effect in an optical medium with predominantly quadratic [or chi((2))] nonlinear response can eliminate the parametric modulational instability of plane waves, leading to the existence of stable two-wave dark and vortex spatial solitons.     

自散焦非局域非线性材料中的光学涡旋孤子

通过数值模拟的方法对非局域非线性自散焦材料中的光学 涡旋孤子的传输特性以及相互作用特性进行了研究. 研究表明, 拓扑荷|m|=1的非局域涡旋孤子是稳定的, 而拓扑荷|m|>1的非局域涡旋孤子均具有拓扑不稳定性. 在微扰存在的情况下以及在近距离相互作用的过程中, |m|>1的涡旋孤子会分裂成一系列的|m|=1的涡旋孤子. 非局域涡旋孤子与局域涡旋孤子具有相同的长距离相互作用模式, 即点涡旋相互作用模式. 但两者的短距离相互作用存在一些差别, 在相同的距离下, 两涡旋间的相互绕转的周期随着材料的非局域响应长度增大而增大. 关键词： 非局域非线性薛定谔方程 自散焦 涡旋孤子     

Algebraic bright and vortex solitons in defocusing media

We demonstrate that spatially inhomogeneous defocusing nonlinear landscapes with the nonlinearity coefficient growing toward the periphery as (1+|r|(α)) support one- and two-dimensional fundamental and higher-order bright solitons, as well as vortex solitons, with algebraically decaying tails. The energy flow of the solitons converges as long as nonlinearity growth rate exceeds the dimensionality, i.e., α>D. Fundamental solitons are always stable, while multipoles and vortices are stable if the nonlinearity growth rate is large enough.     

Stable ring-profile vortex solitons in bessel optical lattices

Stable ring-profile vortex solitons, featuring a bright shape, appear to be very rare in nature. However, here we show that they exist and can be made dynamically stable in defocusing cubic nonlinear media with an imprinted Bessel optical lattice. We find the families of vortex solitons and reveal their salient properties, including the conditions required for their stability. We show that the higher the soliton topological charge, the deeper the lattice modulation necessary for stabilization.