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

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  • He, Shangling
  • Malomed, Boris A.
  • Mihalache, Dumitru
  • Peng, Xi
  • Yu, Xing
  • He, Yingji
  • Deng, Dongmei

Abstract

We introduce axisymmetric Airy-Gaussian vortex beams in a model of an optical system based on the (2+1)-dimensional fractional Schrödinger equation (FSE), characterized by its Lévy index (LI), 1<α⩽2. By means of numerical methods, we explore propagation dynamics of the beams with vorticities from 0 to 4. The propagation leads to abrupt autofocusing, followed by its reversal (rebound from the center). It is shown that LI, the relative width of the Airy and Gaussian factors, and the vorticity determine properties of the autofocusing dynamics, including the focusing distance, radius of the focal light spot, and peak intensity at the focus. A maximum of the peak intensity is attained at intermediate values of LI, close to α=1.4. Dynamics of the abrupt autofocusing of Airy-Gaussian beams carrying vortex pairs (split double vortices) is considered too.

Suggested Citation

  • He, Shangling & Malomed, Boris A. & Mihalache, Dumitru & Peng, Xi & Yu, Xing & He, Yingji & Deng, Dongmei, 2021. "Propagation dynamics of abruptly autofocusing circular Airy Gaussian vortex beams in the fractional Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920308626
    DOI: 10.1016/j.chaos.2020.110470
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    References listed on IDEAS

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    1. P. Panagiotopoulos & D.G. Papazoglou & A. Couairon & S. Tzortzakis, 2013. "Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets," Nature Communications, Nature, vol. 4(1), pages 1-6, December.
    2. Li, Pengfei & Malomed, Boris A. & Mihalache, Dumitru, 2020. "Symmetry breaking of spatial Kerr solitons in fractional dimension," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. Li, Pengfei & Malomed, Boris A. & Mihalache, Dumitru, 2020. "Vortex solitons in fractional nonlinear Schrödinger equation with the cubic-quintic nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    4. Qiu, Yunli & Malomed, Boris A. & Mihalache, Dumitru & Zhu, Xing & Peng, Xi & He, Yingji, 2020. "Stabilization of single- and multi-peak solitons in the fractional nonlinear Schrödinger equation with a trapping potential," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Qiu, Yunli & Malomed, Boris A. & Mihalache, Dumitru & Zhu, Xing & Zhang, Li & He, Yingji, 2020. "Soliton dynamics in a fractional complex Ginzburg-Landau model," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
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    1. Wu, Zhenkun & Yang, Kaibo & Ren, Xijun & Li, Peng & Wen, Feng & Gu, Yuzong & Guo, Lijun, 2022. "Conical diffraction modulation in fractional dimensions with a PT-symmetric potential," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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