Propagation dynamics of abruptly autofocusing circular Airy Gaussian vortex beams in the fractional Schrödinger equation

He, Shangling; Malomed, Boris A.; Mihalache, Dumitru; Peng, Xi; Yu, Xing; He, Yan; Deng, Dongmei

doi:10.1016/j.chaos.2020.110470

Cited by 55 publications

(22 citation statements)

References 56 publications

(29 reference statements)

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“…In addition to 1D and 2D TAWs, Airy waves were recently considered in generalized Schrödinger equations with fractional diffraction, characterized by the corresponding Lévy index [45,46]. This direction for the study of Airy waves may be quite promising too.…”

Section: The Three-wave Systemmentioning

confidence: 99%

Two-dimensional Airy waves and three-wave solitons in quadratic media

Prasatar¹,

Mayteevarunyoo²,

Malomed³

2022

Preprint

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We address the dynamics of two-dimensional (2D) truncated Airy waves and three-component solitons in the system of two fundamental-frequency and second-harmonic fields, coupled by quadratic (χ (2) ) terms. The system models second-harmonic-generating optical media and atomic-molecular mixtures in Bose-Einstein condensates. In addition to stable solitons, the system maintains truncated-Airy-waves states in either one of the fundamental-frequency components, represented by exact solutions, which are stable, unlike the Airy waves in the degenerate (two-component) χ ( 2) system. It is also possible to imprint vorticity onto the 2D Airy modes. By means of systematic simulations, we examine interactions between truncated Airy waves originally carried by different fundamental-frequency components, which are bending in opposite directions, through the secondharmonic field. The interaction leads to fusion of the input into a pair of narrow solitons. This is opposed to what happens in the 1D system, where the interacting Aity waves split into a large number of solitons. The interaction of truncated Aity waves carrying identical imprinted vorticities creates an additional pair of solitons, while opposite vorticities create a set of small-amplitude "debris" in the output. Slowly moving solitons colliding with a heavy truncated Airy wave bounce back, faster ones are absorbed by it, and collisions are quasi-elastic for fast solitons. Soliton-soliton collisions lead to merger into a single mode, or elastic passage, for lower and higher velocities, respectively.

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Section: The Three-wave Systemmentioning

confidence: 99%

Two-dimensional Airy waves and three-wave solitons in quadratic media

Prasatar¹,

Mayteevarunyoo²,

Malomed³

2022

Preprint

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“…The autofocusing of Airy beams in the framework of the linear FSE was recently studied in works [40] and [41]. However, the propagation of a radially polarized beams (including ones shifted off the center) governed by FSE, which is the subject of the present work, was not previously addressed.…”

Section: Introductionmentioning

confidence: 96%

Propagation dynamics of radially polarized symmetric Airy beams in the fractional Schrödinger equation

Malomed

Mihalache

et al. 2021

Physics Letters A

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“…[14][15][16] For certain applications, especially those involving trapping and guiding of microparticles, various types of vortex beams are widely used. These include beams with self-focusing property that can auto focus in the propagation, [17][18][19][20][21] perfect vortex beams with particles rotating at a constant speed [22][23][24][25] and optical vortex arrays with multiple singularities. [26] Although these vortex beams have exceptional and relevant functions, the range of their applications should be widened to advance the field of optical manipulation.…”

Section: Introductionmentioning

confidence: 99%

Modified Bessel–Gaussian Vortex Beam with an Adjustable Broken Opening

Yang

Zhang

et al. 2021

Annalen der Physik

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In this study, an open-ring controllable Bessel vortex beam is theoretically and experimentally constructed with a power-exponent-phase vortex. Its distribution in the far field after being blocked with obstacles is subsequently investigated. In the far field, the beam exhibits different degrees of the open-loop effect following adjustments in the phase term of the power exponent. For an obstructed beam, the direction of the open loop is offset by a certain value, and different open-loop angles can be achieved for different blocking angles. The developed beam can be used to guide particles and avoid obstacles.

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Propagation dynamics of abruptly autofocusing circular Airy Gaussian vortex beams in the fractional Schrödinger equation

Cited by 55 publications

References 56 publications

Two-dimensional Airy waves and three-wave solitons in quadratic media

Two-dimensional Airy waves and three-wave solitons in quadratic media

Propagation dynamics of radially polarized symmetric Airy beams in the fractional Schrödinger equation

Modified Bessel–Gaussian Vortex Beam with an Adjustable Broken Opening

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