The Theory of Spiral Laser Beams in Nonlinear Media

Kruglov, V. I.; Logvin, Yu. A.; Волков, В. М.

doi:10.1080/09500349214552301

Cited by 131 publications

(114 citation statements)

References 10 publications

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“…(13) provides an explanation for the numerical findings that were first reported in Ref. [40] and later considered in many works, but never reproduced in an analytical form. The stability of the self-trapped modes has been systematically tested by real-time simulations of Eqs.…”

Section: The Resultsmentioning

confidence: 99%

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Stable giant vortex annuli in microwave-coupled atomic condensates

2016

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Stable self-trapped vortex annuli (VAs) with large values of topological charge S (giant VAs) are not only a subject of fundamental interest, but are also sought for various applications, such as quantum information processing and storage. However, in conventional atomic Bose-Einstein condensates (BECs) VAs with S > 1 are unstable. Here, we demonstrate that robust self-trapped fundamental solitons (with S = 0) and bright VAs (with the stability checked up to S = 5), can be created in the free space by means of the local-field effect (the feedback of the BEC on the propagation of electromagnetic waves) in a condensate of two-level atoms coupled by a microwave (MW) field, as well as in a gas of MW-coupled fermions with spin 1/2. The fundamental solitons and VAs remain stable in the presence of an arbitrarily strong repulsive contact interaction (in that case, the solitons are constructed analytically by means of the Thomas-Fermi approximation). Under the action of the attractive contact interaction with strength β, which, by itself, would lead to collapse, the fundamental solitons and VAs exist and are stable, respectively, at β < β max (S) and β < β st (S), with β st (S = 0) = β max (S = 0) and β st (S ≥ 1) < β max (S ≥ 1). Accurate analytical approximations are found for both β st and β max , with β st (S) growing linearly with S. Thus, higher-order VAs are more robust than their lower-order couterparts, on the contrary to what is known in other systems that may support stable self-trapped vortices. Conditions for the experimental realizations of the VAs are discussed.

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Section: The Resultsmentioning

confidence: 99%

“…[41], for S = 0, and in Ref. [40] for 1 ≤ S ≤ 5 , i.e., β max does not depend of the LFE strength, γ. To explain this fact, we note that, at the limit stage of the collapse, when the shrinking 2D annulus becomes extremely narrow, the equation for the wave function becomes asymptotically tantamount to Eq.…”

Section: The Resultsmentioning

confidence: 99%

Stable giant vortex annuli in microwave-coupled atomic condensates

2016

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“…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: 93%

Theory of singular vortex solutions of the nonlinear Schrödinger equation

Fibich

Gavish

2008

Physica D: Nonlinear Phenomena

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“…In particular, the first ever example of solitons which was introduced theoretically in nonlinear optics, viz., the Townes solitons [16], i.e., 2D self-trapped modes supported by the cubic selffocusing nonlinearity (in fact, these solutions were discovered before term "soliton" had been coined) are subject to the instability caused by the critical collapse, therefore they have never been observed in the experiment. Multidimensional solitons with embedded vorticity, alias 2D vortex rings and 3D vortex tori, which also exist in cubic media (in particular, there are higher-order versions of Townes solitons with embedded vorticity [17]), are vulnerable to a still stronger splitting instability initiated by modulational perturbations in the azimuthal direction; usually, the modulational instability splits the vortex ring into a few fragments, which resemble fundamental (zero-vorticity) solitons and suffer the destruction via the intrinsic collapse or decay into small-amplitude waves ("radiation") [1].…”

Section: Introductionmentioning

confidence: 99%

Multidimensional solitons: Well-established results and novel findings

Malomed

2016

Eur. Phys. J. Spec. Top.

125

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A brief review is given of some well-known and some very recent results obtained in studies of two-and three-dimensional (2D and 3D) solitons. Both zero-vorticity (fundamental) solitons and ones carrying vorticity S = 1 are considered. Physical realizations of multidimensional solitons in atomic Bose-Einstein condensates (BECs) and nonlinear optics are briefly discussed too. Unlike 1D solitons, which are typically stable, 2D and 3D ones are vulnerable to the instability induced by the occurrence of the critical and supercritical collapse, respectively, in the same 2D and 3D models that give rise to the solitons. Vortex solitons are subject to a still stronger splitting instability. For this reason, a central problem is looking for physical settings in which 2D and 3D solitons may be stabilized. The review addresses one well-established topic, viz., the stabilization of the 3D and 2D states, with S = 0 and 1, trapped in harmonic-oscillator (HO) potentials, and another topic which was developed very recently: the stabilization of 2D and 3D free-space solitons, which mix components with S = 0 and ±1 (semi-vortices and mixed modes), in a binary system with the spinorbit coupling (SOC) between its components. In both cases, the generic situations are drastically different in the 2D and 3D geometries. In the former case, the stabilization mechanism creates a stable ground state (GS, which was absent without it), whose norm falls below the threshold value at which the critical collapse sets in. In the 3D geometry, the supercritical collapse does not allow to create a GS, but metastable solitons can be constructed.

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The Theory of Spiral Laser Beams in Nonlinear Media

Cited by 131 publications

References 10 publications

Stable giant vortex annuli in microwave-coupled atomic condensates

Stable giant vortex annuli in microwave-coupled atomic condensates

Theory of singular vortex solutions of the nonlinear Schrödinger equation

Multidimensional solitons: Well-established results and novel findings

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