Rotating optical soliton clusters

We introduce the concept of soliton clusters -- multi-soliton bound states in a homogeneous bulk optical medium, and reveal a key physical mechanism for their stabilization associated with a staircase-like phase distribution that induces a net angular momentum and leads to cluster rotation. The ringlike soliton clusters provide a nontrivial generalization of the concepts of two-soliton spiraling, optical vortex solitons, and necklace-type optical beams.Comment: 4 pages, 5 figure

Lattice topology and spontaneous parametric down-conversion in quadratic nonlinear waveguide arrays

We analyze spontaneous parametric down-conversion in various experimentally feasible 1D quadratic nonlinear waveguide arrays, with emphasis on the relationship between the lattice's topological invariants and the biphoton correlations. Nontrivial topology results in a nontrivial "winding" of the array's Bloch waves, which introduces additional selection rules for the generation of biphotons. These selection rules are in addition to, and independent of existing control using the pump beam's spatial profile and phase matching conditions. In finite lattices, nontrivial topology produces single photon edge modes, resulting in "hybrid" biphoton edge modes, with one photon localized at the edge and the other propagating into the bulk. When the single photon band gap is sufficiently large, these hybrid biphoton modes reside in a band gap of the bulk biphoton Bloch wave spectrum. Numerical simulations support our analytical results.Comment: 11 pages, 12 figure

Soliton dynamics in deformable nonlinear lattices

We describe wave propagation and soliton localization in photonic lattices which are induced in a nonlinear medium by an optical interference pattern, taking into account the inherent lattice deformations at the soliton location. We obtain exact analytical solutions and identify the key factors defining soliton mobility, including the effects of gap merging and lattice imbalance, underlying the differences with discrete and gap solitons in conventional photonic structures.Comment: 5 pages, 4 figure

Spin and orbital Hall effects for diffracting optical beams in gradient-index media

We examine the evolution of paraxial beams carrying intrinsic spin and orbital angular momenta (AM) in gradient-index media. A parabolic-type equation is derived which describes the beam diffraction in curvilinear coordinates accompanying the central ray. The center of gravity of the beam experiences transverse AM-dependent deflections -- the spin and orbital Hall effects. The spin Hall effect generates a transverse translation of the beam as a whole, in precise agreement with recent geometrical optics predictions. At the same time, the orbital Hall effect is significantly affected by the diffraction in the inhomogeneous medium and is accompanied by changes in the intrinsic orbital AM and deformations of the beam.Comment: 4 pages, 2 figures, to appear in Phys. Rev.

Optical Vortices during a Super-Resolution Process in a Metamaterial

We show that a super-resolution process with 100% visibility is characterized by the formation of a point of phase singularity in free space outside the lens in the form of a saddle with topological charge equal to -1. The saddle point is connected to two vortices at the end boundary of the lens, and the two vortices are in turn connected to another saddle point inside the lens. The structure saddle-vortices-saddle is topologically stable. The formation of the saddle point in free space explains also the negative flux of energy present in a certain region of space outside the lens. The circulation strength of the power flow can be controlled by varying the position of the object plane with respect to the lens

Effect of atmospheric turbulence on propagation properties of optical vortices formed by using coherent laser beam arrays

In this paper, we consider the effect of the atmospheric turbulence on the propagation of optical vertex formed from the radial coherent laser beam array, with the initially well-defined phase distribution. The propagation formula of the radial coherent laser array passing through the turbulent atmosphere is analytically derived by using the extended Huygens-Fresnel diffraction integral. Based on the derived formula, the effect of the atmospheric turbulence on the propagation properties of such laser arrays has been studied in great detail. Our main results show that the atmospheric turbulence may result in the prohibition of the formation of the optical vortex or the disappearance of the formed optical vortex, which are very different from that in the free space. The formed optical vortex with the higher topological charge may propagate over a much longer distance in the moderate or weak turbulent atmosphere. After the sufficient long-distance atmospheric propagation, all the output beams (even with initially different phase distributions) finally lose the vortex property and gradually become the Gaussian-shaped beams, and in this case the output beams actually become incoherent light fields due to the decoherence effect of the turbulent atmosphere.Comment: 10 pages, 5 figure

A topological charge selection rule for phase singularities

We present an study of the dynamics and decay pattern of phase singularities due to the action of a system with a discrete rotational symmetry of finite order. A topological charge conservation rule is identified. The role played by the underlying symmetry is emphasized. An effective model describing the short range dynamics of the vortex clusters has been designed. A method to engineer any desired configuration of clusters of phase singularities is proposed. Its flexibility to create and control clusters of vortices is discussed.Comment: 4 pages, 3 figure

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 $(m,\pm m)$ in the components, may be stable in media with the cubic-quintic nonlinearity, including the \textit{hidden-vorticity} (HV) solitons of the type $(m,-m)$, whose net vorticity is zero. Stability regions for the vortices of both $(m,\pm m)$ types are identified for $m=1$, 2, and 3, by dint of the calculation of stability eigenvalues, and in direct simulations. A novel feature found in the study of the HV solitons is that their stability intervals never reach the (cutoff) point at which the bright vortex carries over into a dark one, hence dark HV solitons can never be stable, contrarily to the bright ones. In addition to the well-known symmetry-breaking (\textit{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 \textit{charge flipping}, with the two components exchanging the angular momentum and periodically reversing the sign of their spins. The composite soliton does not split in this case, therefore we identify such instability as an \textit{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.Comment: 10 pages, 11 figure