Thirty years ago, Coullet et al. proposed that a special optical field exists in laser cavities bearing some analogy with the superfluid vortex. Since then, optical vortices have been widely studied, inspired by the hydrodynamics sharing similar mathematics. Akin to a fluid vortex with a central flow singularity, an optical vortex beam has a phase singularity with a certain topological charge, giving rise to a hollow intensity distribution. Such a beam with helical phase fronts and orbital angular momentum reveals a subtle connection between macroscopic physical optics and microscopic quantum optics. These amazing properties provide a new understanding of a wide range of optical and physical phenomena, including twisting photons, spin-orbital interactions, Bose-Einstein condensates, etc., while the associated technologies for manipulating optical vortices have become increasingly tunable and flexible. Hitherto, owing to these salient properties and optical manipulation technologies, tunable vortex beams have engendered tremendous advanced applications such as optical tweezers, high-order quantum entanglement, and nonlinear optics. This article reviews the recent progress in tunable vortex technologies along with their advanced applications.

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Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

Chapter 5 - Optical vortices and vortex solitons

The Theory of Space, Time and Gravitation. By V. Fock. Pp. 411. 100s. 1959. (Pergamon Press)

We review the properties of optical spatial dissipative solitons (SDS). These are stable, self‐localized optical excitations sitting on a uniform, or quasi‐uniform, background in a dissipative environment like a nonlinear optical cavity. Indeed, in optics they are often termed “cavity solitons.” We discuss their dynamics and interactions in both ideal and imperfect systems, making comparison with experiments. SDS in lasers offer important advantages for applications. We review candidate schemes and the tremendous recent progress in semiconductor‐based cavity soliton lasers. We examine SDS in periodic structures, and we show how SDS can be quantitatively related to the locking of fronts. We conclude with an assessment of potential applications of SDS in photonics, arguing that best use of their particular features is made by exploiting their mobility, for example in all‐optical delay lines.

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Fundamentals and Applications of Spatial Dissipative Solitons in Photonic Devices

We present the experimental observation of scalar multipole solitons in highly nonlocal nonlinear media, including dipole, tripole, quadrupole, and necklace-type solitons, organized as arrays of out-of-phase bright spots. These complex solitons are metastable, but with a large parameters range where the instability is weak, permitting their experimental observation.

http://www.icfo.eu/images/publications/J06-063.pdf

Two-dimensional multipole solitons in nonlocal nonlinear media.

We reveal the existence of stable dissipative soliton complexes with curvilinear motion of their center of mass. This type of motion results from the field distribution asymmetry and is well pronounced for asymmetric complexes of laser solitons with strong coupling. We present results of numerical simulations of such complexes in a model of wide-aperture lasers or laser amplifiers with saturable gain and absorption. The complex consists of a pair of strongly coupled vortex solitons weakly coupled with a number of other vortex solitons. Similar complexes are expected to exist in different spatially distributed nonlinear dissipative systems, including schemes with discrete dissipative solitons.

Curvilinear motion of multivortex laser-soliton complexes with strong and weak coupling.

We analyze the existence, stability, and propagation of dissipative discrete localized modes in one- and two-dimensional nonlinear lattices composed of weakly coupled split-ring resonators (SRRs) excited by an external electromagnetic field. We employ the near-field interaction approach for describing quasi-static electric and magnetic interaction between the resonators, and demonstrate the crucial importance of the electric coupling, which can completely reverse the sign of the overall interaction between the resonators. We derive the effective nonlinear model and analyze the properties of nonlinear localized modes excited in one-and two-dimensional lattices. In particular, we study nonlinear magnetic domain walls (the so-called switching waves) separating two different states of nonlinear magnetization, and reveal the bistable dependence of the domain wall velocity on the external field. Then, we study two-dimensional localized modes in nonlinear lattices of SRRs and demonstrate that larger domains may experience modulational instability and splitting.

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Discrete dissipative localized modes in nonlinear magnetic metamaterials

The reflection of monochromatic and quasi-monochromatic pulsed light incident on a moving inhomogeneity in the optical characteristics of a medium having plasma-type dispersion has been analyzed. The velocity V of the inhomogeneity, induced in the medium by an intense laser pulse, has been changed by varying its carrier frequency. It has been shown that the usual back-reflection mode, when the reflected radiation pulse moves in the direction opposite the direction of incident radiation, is implemented only if the velocity V is less than the critical value V
 min, which depends on the carrier frequency of the incident radiation pulse. It has been found that reflected radiation moves in the same direction as the incident radiation in a certain range of the velocity V
 min < V < V
 max (forward reflection). In this case, the reflected radiation pulse begins to lag behind a fast-moving inhomogeneity. When V
 max < V < c, where c is the speed of light in vacuum, the group velocity of the incident radiation pulse is less than the speed of inhomogeneity, and there is no reflection. Analytical treatment is supported by numerical simulation.

Forward light reflection from a moving inhomogeneity

We demonstrate that nonlinear magnetic metamaterials comprised of a lattice of weakly coupled split-ring resonators driven by an external electromagnetic field may support entirely new classes of spatially localized modes---knotted solitons, which are stable self-localized dissipative structures in the form of closed knotted chains. We demonstrate different topological types of stable knots for the subcritical coupling between resonators and instability-induced breaking of the chains for the supercritical coupling.

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Knotted Solitons in Nonlinear Magnetic Metamaterials

An analysis of clusters of weakly coupled two-dimensional spatial optical solitons in a large-aperture class A laser with a saturable absorber is developed. The symmetries that control the transverse motion of the clusters are described. Numerical solutions of the governing generalized complex Ginzburg-Landau equation demonstrate the existence of four types of clusters of weakly coupled cavity solitons that correspond to symmetries of transverse intensity distributions and energy flows: (1) stationary (with two mirror symmetry axes), (2) rotating about a stationary center of mass (invariant under rotation), (3) translating without rotation (with a single mirror symmetry axis), and (4) asymmetric ones rotating about a center of mass that moves around a circle (with equal periods of rotation and circular motion).

A. N. Shatsev

Papers

Curvilinear motion of multivortex laser-soliton complexes with strong and weak coupling.

Discrete dissipative localized modes in nonlinear magnetic metamaterials

Forward light reflection from a moving inhomogeneity

Knotted Solitons in Nonlinear Magnetic Metamaterials

Motion of clusters of weakly coupled two-dimensional cavity solitons