Observation of double-charge discrete vortex solitons in hexagonal photonic lattices

Terhalle, Bernd; Richter, Tobias; Law, Kody J. H.; Göries, Dennis; Rose, Patrick; Alexander, Tristram J.; Kevrekidis, P. G.; Desyatnikov, Anton S.; Królikowski, Wiesław; Kaiser, F.; Denz, Cornélia; Kivshar, Yuri S.

doi:10.1103/physreva.79.043821

Cited by 71 publications

(47 citation statements)

References 26 publications

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“…It is exactly opposite to the Table I in [25], which was derived by the group-theory and is valid in the focusing cubic media. This finding also verifies the very recent reports [55,57] in which the stability of discrete vortex solitons supported by hexagonal photonic lattices in focusing media is proved to be opposite to the stability in the defocusing ones. We note that our conclusion is more general since the above two studies are restricted to the single-and double-charge discrete vortex solitons.…”

Section: Lattice Ordersupporting

confidence: 91%

Stable Higher-Charged Vortex Solitons in Optically-Induced Lattices

Dong¹,

Li²

2012

Optical Communication

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Section: Lattice Ordersupporting

confidence: 91%

Stable Higher-Charged Vortex Solitons in Optically-Induced Lattices

Dong¹,

Li²

2012

Optical Communication

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“…This is true for soft nonlinearities and positive coupling (or hard nonlinearities and negative coupling), while the results are reversed if either the nature of the nonlinearity or the sign of the coupling are changed. It is interesting to note that similar findings have been reported not only in DNLS type chains [32] but also in continuum photorefractive crystals [34] (where they have recently been confirmed experimentally [35]). Furthermore, inphase and out-of-phase structures are also examined.…”

Section: Introductionsupporting

confidence: 81%

Existence and stability of multisite breathers in honeycomb and hexagonal lattices

Koukouloyannis¹,

Law²,

Kourakis³

et al. 2010

J. Phys. A: Math. Theor.

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Abstract. We study the existence and stability of multisite discrete breathers in two prototypical non-square Klein-Gordon lattices, namely a honeycomb and a hexagonal one. In the honeycomb case we consider six-site configurations and find that for soft potential and positive coupling the out-of-phase breather configuration and the charge-two vortex breather are linearly stable, while the in-phase and charge-one vortex states are unstable. In the hexagonal lattice, we first consider three-site configurations. In the case of soft potential and positive coupling, the in-phase configuration is unstable and the charge-one vortex is linearly stable. The out-of-phase configuration here is found to always be linearly unstable. We then turn to six-site configurations in the hexagonal lattice. The stability results in this case are the same as in the six-site configurations in the honeycomb lattice. For all configurations in both lattices, the stability results are reversed in the setting of either hard potential or negative coupling. The study is complemented by numerical simulations which are in very good agreement with the theoretical predictions. Since neither the form of the on-site potential nor the sign of the coupling parameter involved have been prescribed, this description can accommodate inverse-dispersive systems (e.g., supporting backward waves) such as transverse dust-lattice oscillations in dusty plasma (Debye) crystals or analogous modes in molecular chains.Existence and stability of multisite breathers in honeycomb and hexagonal lattices 2

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“…It is interesting to explore whether stable doubly charged gap vortex soliton exists in self-defocusing square photonic lattices without "decaying" into a quadrupole soliton, although such stable high-order discrete vortex solitons have been observed in hexagonal photonic lattices under a selffocusing nonlinearity [20]. Indeed, we find that when the input vortex ring is expanded to cover eight lattice sites as shown in Figure 4(a), under appropriate nonlinear conditions, the phase singularity can maintain and it can evolve into a "true" stable gap vortex soliton.…”

Section: Discrete Gap Vortexmentioning

confidence: 99%

“…On the other hand, DCV propagation in isotropic square photonic lattice leads to periodic charge flipping with a quadrupole-like mediate states [18]. Stable SCV, DCV, and multivortex solitons in hexagonal lattices have also been experimentally demonstrated [19][20][21].…”

Section: Introductionmentioning

confidence: 98%

Experiments on Linear and Nonlinear Localization of Optical Vortices in Optically Induced Photonic Lattices

Song

Lou

Tang

et al. 2012

International Journal of Optics

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We provide a brief overview on our recent experimental work on linear and nonlinear localization of singly charged vortices (SCVs) and doubly charged vortices (DCVs) in two-dimensional optically induced photonic lattices. In the nonlinear case, vortex propagation at the lattice surface as well as inside the uniform square-shaped photonic lattices is considered. It is shown that, apart from the fundamental (semi-infinite gap) discrete vortex solitons demonstrated earlier, the SCVs can self-trap into stable gap vortex solitons under the normal four-site excitation with a self-defocusing nonlinearity, while the DCVs can be stable only under an eight-site excitation inside the photonic lattices. Moreover, the SCVs can also turn into stable surface vortex solitons under the four-site excitation at the surface of a semi-infinite photonics lattice with a self-focusing nonlinearity. In the linear case, bandgap guidance of both SCVs and DCVs in photonic lattices with a tunable negative defect is investigated. It is found that the SCVs can be guided at the negative defect as linear vortex defect modes, while the DCVs tend to turn into quadrupole-like defect modes provided that the defect strength is not too strong.

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Observation of double-charge discrete vortex solitons in hexagonal photonic lattices

Cited by 71 publications

References 26 publications

Stable Higher-Charged Vortex Solitons in Optically-Induced Lattices

Stable Higher-Charged Vortex Solitons in Optically-Induced Lattices

Existence and stability of multisite breathers in honeycomb and hexagonal lattices

Experiments on Linear and Nonlinear Localization of Optical Vortices in Optically Induced Photonic Lattices

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