Bright Vortex Research Articles

Transmission of Vortex Solitons in Three-Dimensional χ(2) Helical-Periodically Poled Ferroelectric Crystals

It is well known that bright vortex solitons are unstable in the χ2 nonlinear media due to the strong azimuthal modulation instability. To solve this problem, a quadratic (χ2) LiNbO3 ferroelectric crystal with a special kind of helical-periodically poled structure is proposed. The proposed structure is designed by embedding topological charges into the crystal with a quasi-phase matching technique. Simulation results indicate that vortex solitons containing fundamental-frequency and second-harmonic waves can robustly propagate over a distance. Two types of vortex states are obtained: double vortices state and vortex–antivortex state. The dependence of effective area, propagation constants, and maximum light intensity on the control parameters are presented. These results provide a new solution for robust transmission of bright vortex solitons in a χ2 nonlinear media.

Vortex Solitons in Quasi-Phase-Matched Photonic Crystals.

We report solutions for stable compound solitons in a three-dimensional quasi-phase-matched photonic crystal with the quadratic (χ^{(2)}) nonlinearity. The photonic crystal is introduced with a checkerboard structure, which can be realized by means of the available technology. The solitons are built as four-peak vortex modes of two types, rhombuses and squares (intersite- and onsite-centered self-trapped states, respectively). Their stability areas are identified in the system's parametric space (rhombuses occupy an essentially broader stability domain), while all bright vortex solitons are subject to strong azimuthal instability in uniform χ^{(2)} media. Possibilities for experimental realization of the solitons are outlined.

On vortex and dark solitons in the cubic–quintic nonlinear Schrödinger equation

We study topologically charged propagation-invariant eigenstates of the 1+2-dimensional Schrödinger equation with a cubic (focusing)–quintic (defocusing) nonlinear term. First, we revisit the self-trapped vortex soliton solutions. Using a variational ansatz that allows us to describe the solutions as a liquid with a surface tension, we derive a simple formula relating the inner and outer radii of the bright vortex ring. Then, using numerical and variational techniques, we analyse dark soliton solutions for which the wave function density asymptotes to a non-vanishing value. We find an eigenvalue cutoff for the propagation constant that depends on the topological charge l. The variational profile provides simple and very accurate results for l≥2. We also study the azimuthal stability of the eigenstates by a linear analysis finding that they are stable for all values of the propagation constant, at least for small l.

Functional Meta Lenses for Compound Plasmonic Vortex Field Generation and Control.

Surface plasmon polaritons carrying orbital angular momentum are of great fundamental and applied interest. However, common approaches for their generation are restricted to having a weak dependence on the properties of the plasmon-generating illumination, providing a limited degree of control over the amount of delivered orbital angular momentum. Here we experimentally show that by tailoring local and global geometries of vortex generators, a change in helicity of light imposes arbitrary large switching in the delivered plasmonic angular momentum. Using time-resolved photoemission electron microscopy we demonstrate pristine control over the generation and rotation direction of high-order plasmonic vortices. We generalize our approach to create complex topological fields and exemplify it by studying and controlling a "bright vortex", exhibiting the breakdown of a high-order vortex into a mosaic of unity-order vortices while maintaining the overall angular momentum density. Our results provide tools for plasmonic manipulation and could be utilized in lab-on-a-chip devices.

Solitary vortices supported by localized parametric gain

We demonstrate the existence and stability of bright vortex solitons sustained by a ring-shaped parametric gain, for both focusing and defocusing Kerr nonlinearities in lossy optical media. With the defocusing nonlinearity, the vortices are stable at all values of the detuning parameter, while under the focusing nonlinearity their stability region is limited to some positive values of the detuning. Unstable vortices in the focusing medium transform into stable rotating azimuthons.

Optical forces induced behavior of a particle in a non-diffracting vortex beam

An interaction between a light field with complex field spatial distribution and a micro-particle leads to forces that drag the particle in space and may confine it in a stable position or a trajectory. The particle behavior is determined by its size with respect to the characteristic length of the spatially periodic or symmetric light field distribution. We study theoretically and experimentally the behavior of a microparticle near the center of an optical vortex beam in a plane perpendicular to the beam propagation. We show that such particle may be stably trapped either in a dark spot on the vortex beam axis, or in one of two points placed off the optical axis. It may also circulate along a trajectory having its radius smaller or equal to the radius of the first bright vortex ring.

Stabilization of vortex-soliton beams in nematic liquid crystals

We study the interaction of two optical beams of different wavelengths (colors) in a nematic liquid crystal. We consider the case for which one component carries an optical vortex and the other component describes a localized beam. It is shown that a beam in one color can stabilize a vortex in the other color, the vortex being unstable in the absence of the second beam. We also show that the bright vortex can guide the beam in a stable manner, provided that the nonlocality is large enough. In this context we find that a different type of solitary wave (nematicon) instability can arise, one for which a ring structure develops at its peak. The results of approximate modulation solutions for the interaction between the vortex and the beam are found to be in good quantitative agreement with direct numerical simulations.

Dark and bright vortex solitons in electromagnetically induced transparent media

We show that dark and bright vortex solitons can exist in three-state electromagnetically induced transparent media under some appropriate conditions. We also analyse the stability of the dark and bright vortex solitons. This work may provide other research opportunities in nonlinear optical experiments and may result in a substantial impact on technology.

Two-dimensional solitons with hidden and explicit vorticity in bimodal cubic-quintic media

We demonstrate that two-dimensional two-component bright solitons of an annular shape, carrying vorticities (m,+/-m) in the components, may be stable in media with the cubic-quintic nonlinearity, including the hidden-vorticity (HV) solitons of the type (m,-m) , whose net vorticity is zero. Stability regions for the vortices of both (m,+/-m) types are identified for m=1 , 2, and 3, by dint of the calculation of stability eigenvalues, and in direct simulations. In addition to the well-known symmetry-breaking (external) instability, which splits the ring soliton into a set of fragments flying away in tangential directions, we report two new scenarios of the development of weak instabilities specific to the HV solitons. One features charge flipping, with the two components exchanging angular momentum and periodically reversing the sign of their spins. The composite soliton does not directly split in this case; therefore, we identify such instability as an intrinsic one. Eventually, the soliton splits, as weak radiation loss drives it across the border of the ordinary strong (external) instability. Another scenario proceeds through separation of the vortex cores in the two components, each individual core moving toward the outer edge of the annular soliton. After expulsion of the cores, there remains a zero-vorticity breather with persistent internal vibrations.

Bright Vortex Solitons in Bose Condensates

We suggest the possibility of observing and studying bright vortex solitons in attractive Bose-Einstein condensates in three dimensions with a radial trap. Such systems lie on the verge of critical stability and we discuss the conditions of their stability. We study the interaction between two such solitons. Unlike the text-book solitons in one dimension, the interaction between two radially trapped and axially free three-dimensional solitons is inelastic in nature and involves exchange of particles and deformation in shape. The interaction remains repulsive for all phase delta between them except for delta \approx 0.

Stable multicharged localized optical vortices in cubic–quintic nonlinear media

The stability of two-dimensional bright vortex solitons in a media with focusing cubic and defocusing quintic nonlinearities is investigated analytically and numerically. It is proved that above some critical beam powers not only one- and two-charged but also multiple-charged stable vortex solitons do exist. A vortex soliton occurs robust with respect to symmetry-breaking modulational instability in the self-defocusing regime provided that its radial profile becomes flattened, so that a self-trapped wave beam gets a pronounced surface. It is demonstrated that the dynamics of a slightly perturbed stable vortex soliton resembles an oscillation of a liquid stream having a surface tension. Using the idea of sustaining effective surface tension for spatial vortex soliton in a media with competing nonlinearities the explanation of a suppression of the modulational instability is proposed.

Mean-field model of interaction between bright vortex solitons in Bose–Einsteincondensates

Using the explicit numerical solution of the axially symmetric Gross–Pitaevskiiequation we study the dynamics of interaction among vortex solitons in a rotatingmatter-wave bright soliton train in a radially trapped and axially free Bose–Einsteincondensate to understand certain features of the experiment by Strecker et al (2002 Nature 417 150). In a soliton train, solitons of opposite phase (phaseδ = π)repel and stay apart without changing shape; solitons withδ = 0 attract, interact and coalesce, but eventually come out; solitons with a generalδ usually repel but interact inelastically by exchanging matter. We study this and suggestfuture experiments with vortex solitons.

Spinning solitons in cubic-quintic nonlinear media

We review recent theoretical results concerning the existence, stability and unique features of families of bright vortex solitons (doughnuts, or ‘spinning’ solitons) in both conservative and dissipative cubic-quintic nonlinear media.

Azimuthal instability of spinning spatiotemporal solitons

We find one-parameter families of three-dimensional spatiotemporal bright vortex solitons (doughnuts, or spinning light bullets), in dispersive quadratically nonlinear media. We show that they are subject to a strong instability against azimuthal perturbations, similarly to the previously studied (2+1)-dimensional bright spatial vortex solitons. The instability breaks the spinning soliton into several fragments, each being a stable nonspinning light bullet.

Three-dimensional spinning solitons in the cubic-quintic nonlinear medium.

We find one-parameter families of three-dimensional spatiotemporal bright vortex solitons (doughnuts, or spinning light bullets), in bulk dispersive cubic-quintic optically nonlinear media. The spinning solitons display a symmetry-breaking azimuthal instability, which leads to breakup of the spinning soliton into a set of fragments, each being a stable nonspinning light bullet. However, in some cases the instability is developing so slowly that the spinning light bullets may be regarded as virtually stable ones, from the standpoint of an experiment with finite-size samples.

Impact of imbalancing in the self-splitting of beams with nested vortices into solitons in quadratic non-linear crystals

We address the existence and instability of bright vortex solitary waves in quadratic non-linear media under conditions for Type II second-harmonic generation and study in detail the effects introduced by the presence of power imbalancing at the fundamental frequency. We find the families of solitary-wave solutions with different combinations of topological charges of the nested vortices and show their spontaneous azimuthal instability. The growth rates of the azimuthal perturbations are calculated as a function of the imbalancing. Experimental consequences are stressed and discussed.