Suppression of Collapse for Spiraling Elliptic Solitons

Desyatnikov, Anton S.; Buccoliero, Daniel; Dennis, Mark R.; Kivshar, Yuri S.

doi:10.1103/physrevlett.104.053902

Cited by 76 publications

(111 citation statements)

References 43 publications

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“…We can prove that f 2 ≥ 0 in equation (13). If f 1 is always positive or negative at any propagation distance z, the spiraling elliptic breathers will rotate anticlockwise or clockwise.…”

Section: Rotation Modementioning

confidence: 99%

“…Here, we give an example that [13], when b = 4.26, c = 2.13 the critical power P = 127.32π, the critical OAM σ = 0.35, and the rotational angular velocity ω = 0.17. The optical beam expressed in the xyz-coordinate frame (the laboratory frame) is of the form…”

Section: The Variational Solution Of the Spiraling Elliptic Breathersmentioning

confidence: 99%

“…The linear isotropy can also make the elliptic optical beams without the initial orbital angular momentum (OAM) rotate during the linear propagation [12], and the rotation angle will monotonously approach to the value determined by the media and the input parameters of the beam. It was predicted very recently that the spiraling elliptic solitons with the OAM can exist in isotropic saturable nonlinear media [13] and in isotropic nonlocal nonlinear media [14], where the OAM can bring in the effective linear anisotropy. The nonlinear propagation of elliptic optical beams in saturable nonlinear medium with the linear anisotropy is investigated in the paper.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of elliptic breathers in saturable nonlinear media with linear anisotropy

Liang¹,

Guo²,

Shou³

et al. 2014

J. Opt.

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We have introduced a class of spiraling elliptic breathers in saturable nonlinear media with linear anisotropy. Two kinds of evolution behaviors of the breathers, rotating and pendulum-like librating, are both predicted by the variational approach, and confirmed by the numerical simulation.The spiraling elliptic breathers can rotate even though they have no initial orbital angular momentum (OAM). Due to the linear anisotropy of the media, the OAM is no longer conserved. Therefore, the angular velocity is found to be not a constant but a periodic function of the propagation distance. When the linear anisotropy is large enough, the spiraling elliptic breathers can librate like the pendulum. The spiraling elliptic breathers exist in the media with not only the saturable nonlinearity but also the nonlocal nonlinearity, as a matter of fact, they are universal in the nonlinear media with the linear anisotropy. OCIS codes:(190.6135) Spatial solitons; (190.3270) Kerr effect. http://dx

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“…We can prove that f 2 ≥ 0 in equation (13). If f 1 is always positive or negative at any propagation distance z, the spiraling elliptic breathers will rotate anticlockwise or clockwise.…”

Section: Rotation Modementioning

confidence: 99%

Section: The Variational Solution Of the Spiraling Elliptic Breathersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamics of elliptic breathers in saturable nonlinear media with linear anisotropy

Liang¹,

Guo²,

Shou³

et al. 2014

J. Opt.

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“…For hyperelastic materials with strain energy given by (4.14), the generalized shear modulus S is given by 17) and so the wave amplitude equation (4.13) becomes…”

Section: Transverse Wave Propagation In Hyperelastic Materialsmentioning

confidence: 99%

“…They also arise in a spiralling elliptic soliton model of Ref. [17] and its extension in the Bose-Einstein setting in Ref. [1].…”

Section: Introductionmentioning

confidence: 99%

Ermakov-Modulated Nonlinear Schrödinger Models. Integrable Reduction

Rogers¹,

Saccomandi²,

Vergori³

2021

JNMP

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Nonlinear Schrödinger equations with spatial modulation associated with integrable Hamiltonian systems of Ermakov-Ray-Reid type are introduced. An algorithmic procedure is presented which exploits invariants of motion to construct exact wave packet representations with potential applications in a wide range of physical contexts such as, 'inter alia', the analysis of Bloch wave and matter wave solitonic propagation and pulse transmission in Airy modulated NLS models. A particular Ermakov reduction for Mooney-Rivlin materials is set in the broader context of transverse wave propagation in a class of higher-order hyperelastic models of incompressible solids.

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Influence of Transverse Cross‐Phases on Propagations of Optical Beams in Linear and Nonlinear Regimes

Liang

Zhang

Fang

et al. 2020

Laser & Photonics Reviews

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It is predicted that an orbital angular momentum (OAM) carried by an elliptic Gaussian beam (EGB) with a cross‐phase can induce an effective anisotropic diffraction (AD). At the so‐called critical OAM, such an OAM‐induced AD makes the spiraling elliptic Gaussian mode, which expands owing to the diffraction while keeping its elliptic degree changeless, exist in linearly isotropic media, where only the circular Gaussian mode is supposed to exist for a beam without an OAM. In this study, such a phenomenon is experimentally demonstrated via the propagations of the EGBs with the OAM in linearly and both‐linearly‐and‐nonlinearly isotropic media. In the former case, the spiraling elliptic Gaussian mode is observed at the critical OAM in the free space. In the latter case, the spiraling elliptic soliton predicted by Desyatnikov et al. is observed for the first time in cylindrical lead glass. The physics behind the spiraling elliptic soliton is the OAM‐induced AD, which preserves the elliptic degree of the EGB, whereas the nonlinearity only balances the diffraction of the EGB. The OAM‐induced AD is just a linear effect and has nothing to do with nonlinearity.

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Suppression of Collapse for Spiraling Elliptic Solitons

Abstract: We reveal that orbital angular momentum can suppress catastrophic self-focusing in nonlinear Kerr media supporting stable spiraling solitons with an elliptic cross section. We discuss the necessary requirements for observation of this effect with coherent optical and matter waves.

Cited by 76 publications

References 43 publications

Dynamics of elliptic breathers in saturable nonlinear media with linear anisotropy

Dynamics of elliptic breathers in saturable nonlinear media with linear anisotropy

Ermakov-Modulated Nonlinear Schrödinger Models. Integrable Reduction

Influence of Transverse Cross‐Phases on Propagations of Optical Beams in Linear and Nonlinear Regimes

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