Auto-waveguide propagation and the collapse of spiral light beams in non-linear media

Kruglov, V. I.; Волков, В. М.; Vlasov, R. A.; Drits, V V

doi:10.1088/0305-4470/21/23/020

Cited by 38 publications

(26 citation statements)

References 7 publications

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“…As early as 1988, it was found that saturation in the form of CQ nonlinearity stabilize optical vortices against collapse, and "the data from the computer experiment show that these beams are stable" (after Kruglov, Volkov, Vlasov, and Drits [1988]). Further study, however, reveal that the azimuthal instability of CQ vortices may take place (Kruglov, Logvin, and Volkov [1992]).…”

Section: Cubic-quintic Nonlinearitymentioning

confidence: 99%

Optical vortices and vortex solitons

2005

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Optical vortices are phase singularities nested in electromagnetic waves that constitute a fascinating source of phenomena in the physics of light and display deep similarities to their close relatives, quantized vortices in superfluids and Bose-Einstein condensates. We present a brief overview of the major advances in the study of optical vortices in different types of nonlinear media, with emphasis on the properties of vortex solitons. Self-focusing nonlinearity leads, in general, to the azimuthal instability of a vortex-carrying beam, but it can also support novel types of stable or meta-stable self-trapped beams carrying nonzero angular momentum, such as ring-like solitons, necklace beams, and soliton clusters. We describe vortex solitons created by multi-component beams, by parametrically coupled beams in quadratic nonlinear media, and in partially incoherent light, as well as discrete vortex solitons in periodic photonic lattices.

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Section: Cubic-quintic Nonlinearitymentioning

confidence: 99%

Optical vortices and vortex solitons

2005

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“…We now consider vortex solutions ψ = A(t, r )e imθ of the two-dimensional critical NLS (4). In this case, Eq.…”

Section: Conservation Lawsmentioning

confidence: 99%

“…More generally, the k-ring profile is the k-ring solution of (29) with the minimal value of c G . 4 Fig. 4 shows a graph of the tail magnitude c G as a function of g 0 for m = 2 and f c = 0.35.…”

Section: Substitution Of ψ a M Into The Critical Nls (4) Gives The Fomentioning

confidence: 99%

“…1 However, almost all of this research effort has been on non-collapsing vortices. In fact, to the best of our knowledge, the only studies of collapsing vortex solutions are those of Kruglov and co-workers [3,4] and of Vuong et al [5]. Therefore, there is a huge gap between the available theory on non-vortex and vortex singular NLS solutions.…”

Section: Introductionmentioning

confidence: 99%

“…In Section 4.2 we show that as in the vortex-free case, there are two types of explicit blowup solutions of the critical NLS (4) , these singular vortex ring solutions are identically zero at the singularity point r = 0. In Section 4.3 we consider the critical power (L 2 norm) for collapse in the critical NLS (4). Recall that in the non-vortex case the critical power is equal to P cr = |R 0,0 | 2 r dr , where R 0,0 is the ground state solution of…”

Section: Introductionmentioning

confidence: 99%

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