Observation of Multivortex Solitons in Photonic Lattices

Terhalle, Bernd; Richter, Tobias; Desyatnikov, Anton S.; Neshev, Dragomir N.; Królikowski, Wiesław; Kaiser, F.; Denz, Cornélia; Kivshar, Yuri S.

doi:10.1103/physrevlett.101.013903

Cited by 84 publications

(56 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, more recently both in optics [28,29] and in BEC [30,31] (so far in the absence of the lattice for the latter case), the study of higher charge vortices has been of interest. In particular, in the emerging area of hexagonal [21,32] and honeycomb [20] lattices, it has been predicted [33,34] and experimentally observed [35] very recently that a higher-order vortex with topological charge S = 2 is more stable than a fundamental vortex with unit charge (S = 1) when self-trapped with a focusing nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

Geometric stabilization of extendedS=2vortices in two-dimensional photonic lattices: Theoretical analysis, numerical computation, and experimental results

et al. 2009

View full text Add to dashboard Cite

In this work, we focus our studies on the subject of nonlinear discrete self-trapping of S = 2 (doubly-charged) vortices in two-dimensional photonic lattices, including theoretical analysis, numerical computation and experimental demonstration. We revisit earlier findings about S = 2 vortices with a discrete model, and find that S = 2 vortices extended over eight lattice sites can indeed be stable (or only weakly unstable) under certain conditions, not only for the cubic nonlinearity previously used, but also for a saturable nonlinearity more relevant to our experiment with a biased photorefractive nonlinear crystal. We then use the discrete analysis as a guide towards numerically identifying stable (and unstable) vortex solutions in a more realistic continuum model with a periodic potential. Finally, we present our experimental observation of such geometrically extended S = 2 vortex solitons in optically induced lattices under both self-focusing and self-defocusing nonlinearities, and show clearly that the S = 2 vortex singularities are preserved during nonlinear propagation.

show abstract

Section: Introductionmentioning

confidence: 99%

Geometric stabilization of extendedS=2vortices in two-dimensional photonic lattices: Theoretical analysis, numerical computation, and experimental results

et al. 2009

View full text Add to dashboard Cite

show abstract

“…A number of groups have been studying the diffraction of OV through the photonic lattices to generate solitons [7][8][9][10][11][12]. Terhalle et al [7] reported the generation of multivortex solitons when vortex beam diffract from laser-induced photonic lattice in a strontium barium niobate crystal.…”

Section: Introductionmentioning

confidence: 99%

“…Terhalle et al [7] reported the generation of multivortex solitons when vortex beam diffract from laser-induced photonic lattice in a strontium barium niobate crystal. Alexander et al [11] used triangular photonic lattice to demonstrate the self-trapped states of light in the form of multivortex localised states.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Propagation of vortex beams through self-assembled photonic crystal

Kedia

Kumar

Singh

2013

Journal of Experimental Nanoscience

View full text Add to dashboard Cite

This study describes a new and simple approach to produce multiple optical vortices (OVs) using three-dimensional polymeric photonic crystal (PhC). The crystals are fabricated by well-known inward-growing self-assembly technique using polystyrene micro-particles of particle sizes 990 and 1900 nm. This fabrication technique provides the cubic lattice arrangement to the spheres with the h1 1 1i plane parallel to the substrate. When a Gaussian beam from a He-Ne laser at 633 nm is diffracted through the crystal of particle size 990 nm, six bright spots along with a central spot are observed on the screen. Diffractions are observed up to third-order in the case of 1900 nm particle size PhC. Multiple OVs arise when vortex beam with topological charge 1 is diffracted through such a crystal. The diffraction pattern shows similar arrangement of bright spots as for the Gaussian beam except now the diffracted spots contain the property of incident OV, i.e. the central dark core. The diffraction is recorded using a charge coupling device camera.

show abstract

“…Further experimental studies in two-dimensional square lattices include DVSs that bifurcate from the second linear band [110,111], and with topological charge equal to two [112]. DVSs have also been observed in hexagonal lattices, including discrete multivortex solitons (several vortices inside the cluster of excited waveguides) [113], DVSs with topological charge two [114], and single DVSs [115]. Some of the observed discrete vortex solitons in Refs.…”

Section: Vorticesmentioning

confidence: 99%

Theoretical studies of Bose-Hubbard and discrete nonlinear Schrödinger models : Localization, vortices, and quantum-classical correspondence

Jason¹

View full text Add to dashboard Cite

This thesis is mainly concerned with theoretical studies of two types of models: quantum mechanical Bose-Hubbard models and (semi-)classical discrete nonlinear Schrödinger (DNLS) models.Bose-Hubbard models have in the last few decades been widely used to describe Bose-Einstein condensates placed in periodic optical potentials, a hot research topic with promising future applications within quantum computations and quantum simulations. The Bose-Hubbard model, in its simplest form, describes the competition between tunneling of particles between neighboring potential wells ('sites') and their on-site interactions (can be either repulsive or attractive). We will also consider extensions of the basic models, with additional interactions and tunneling processes.While Bose-Hubbard models describe the behavior of a collection of particles in a lattice, the DNLS description is in terms of a classical field on each site. DNLS models can also be applicable for Bose-Einstein condensates in periodic potentials, but in the limit of many bosons per site, where quantum fluctuations are negligible and a description in terms of average values is valid. The particle interactions of the Bose-Hubbard models become nonlinearities in the DNLS models, so that the DNLS model, in its simplest form, describes a competition between on-site nonlinearity and tunneling to neighboring sites. DNLS models are however also applicable for several other physical systems, most notably for nonlinear waveguide arrays, another rapidly evolving research field.The research presented in this thesis can be roughly divided into two parts: 1) We have studied certain families of solutions to the DNLS model. First, we have considered charge flipping vortices in DNLS trimers and hexamers. Vortices represent a rotational flow of energy, and a charge flipping vortex is one where the rotational direction (repeatedly) changes. We have found that charge flipping vortices indeed exist in these systems, and that they belong to continuous families of solutions located between two stationary solutions.Second, we have studied discrete breathers, which are spatially localized and time-periodic solutions, in a DNLS models with the geometry of a ring coupled to an additional, central site. We found under which parameter values these solutions exist, and also studied the properties of their continuous solution families. We found that these families undergo different bifurcations, and that, for example, the discrete breathers which have a peak on one and two (neighboring) sites, respectively, belong to the same family below a critical value of the ring-to-centralv vi site coupling, but to separate families for values above it.2) Since Bose-Hubbard models can be approximated with DNLS models in the limit of a large number of bosons per site, we studied signatures of certain classical solutions and structures of DNLS models in the corresponding Bose-Hubbard models.These studies have partly focused on quantum lattice compactons. The corresponding classical lattice compac...

show abstract

Observation of Multivortex Solitons in Photonic Lattices

Cited by 84 publications

References 23 publications

Geometric stabilization of extendedS=2vortices in two-dimensional photonic lattices: Theoretical analysis, numerical computation, and experimental results

Geometric stabilization of extendedS=2vortices in two-dimensional photonic lattices: Theoretical analysis, numerical computation, and experimental results

Propagation of vortex beams through self-assembled photonic crystal

Theoretical studies of Bose-Hubbard and discrete nonlinear Schrödinger models : Localization, vortices, and quantum-classical correspondence

Contact Info

Product

Resources

About