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. 2017 Jun 23;7(1):4198.
doi: 10.1038/s41598-017-04095-9.

Suppression of collapse for two-dimensional Airy beam in nonlocal nonlinear media

Qian Kong  1 , Ning Wei  1 , Cuizhi Fan  1 , Jielong Shi  1 , Ming Shen  2
Affiliations

Suppression of collapse for two-dimensional Airy beam in nonlocal nonlinear media

Qian Kong et al. Sci Rep. .

Abstract

Dynamics and collapse of two-dimensional Airy beams are investigated numerically in nonlocal nonlinear media with split step Fourier transform method. In particular, the stability and self-healing properties of the Airy beams depend crucially on the location and topological charge of the vortex when the beams carry angular momentum. The propagation of abruptly autofocusing Airy beams is also demonstrated in local and nonlocal media. In strongly self-focusing regime, with the help of nonlocality, stationary propagation of two-dimensional Airy beams can be obtained, which always collapse in local nonlinear media.

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Conflict of interest statement

The authors declare that they have no competing interests.

Figures

Figure 1
Figure 1
The profile of the Gaussian nonlocal response function (a) and its Fourier transform in (b).
Figure 2
Figure 2
The intensity distributions of two-dimensional fundamental Airy beam at different propagation distances in (a) free space, (b,c) local self-focusing nonlinear media (σ = 0), and (d) nonlocal nonlinear media, respectively. The initial parameters are m = 0, x 0 = y 0 = 0, A = 5 (a,b), and A = 10 (c,d). The degree of nonlocality of Fig. 2(d) is σ = 2.
Figure 3
Figure 3
The intensity distributions of a vortex Airy beam at different propagation distances in local self-focusing nonlinear media (σ = 0). The initial parameters are x 0 = y 0 = 0, A = 2 (a), A = 0.2 (b), and A = 0.01 (c). The topological charges are m = 1 (a), m = 2 (b), and m = 3 (c), respectively.
Figure 4
Figure 4
The intensity distributions of a vortex Airy beam at different propagation distances in local self-focusing nonlinear media (σ = 0). The amplitude and the topological charge of the beam are A = 2 and m = 1. The location of the vortex are (a)x 0 = 0, y 0 = 2, (b)x 0 = 2, y 0 = 2, and (c)x 0 = 2, y 0 = 0, respectively.
Figure 5
Figure 5
The intensity distributions of a vortex Airy beam at different propagation distances in (a) local nonlinear (σ = 0) and (b) nonlocal nonlinear media, respectively. The initial parameters are m = 1, x 0 = y 0 = 0, and A = 8, respectively. The degree of nonlocality of Fig. 5(b) is σ = 1.
Figure 6
Figure 6
The intensity distributions of inward accelerating abruptly autofocusing Airy beam at different propagation distances in (a–c) local (σ = 0), and (d) nonlocal nonlinear media, respectively. The initial parameters are m = 0, r 0 = 0.5, A = 1 (a,b), and A = 12 (c,d). The degree of nonlocality of Fig. 6(d) is σ = 5.
Figure 7
Figure 7
The intensity distributions of outward accelerating abruptly autofocusing Airy beam at different propagation distances in (a–c) local (σ = 0), and (d) nonlocal nonlinear media, respectively. The initial parameters are m = 0, r 0 = 5, A = 1 (a,b), and A = 12 (c,d). The degree of nonlocality of Fig. 7(d) is σ = 5.
Figure 8
Figure 8
The intensity distributions of inward accelerating abruptly autofocusing Airy beam at different propagation distances in (a–c) local (σ = 0), and (d) nonlocal nonlinear media, respectively. The initial parameters are m = 1, r 0 = 0.5, A = 0.5 (a,b), and A = 3 (c,d). The degree of nonlocality of Fig. 8(d) is σ = 5.
Figure 9
Figure 9
The intensity distributions of outward accelerating abruptly autofocusing Airy beam at different propagation distances in (a–c) local (σ = 0), and (d) nonlocal nonlinear media, respectively. The initial parameters are m = 1, r 0 = 5, A = 0.5 (a,b), and A = 2 (c,d). The degree of nonlocality of Fig. 9(d) is σ = 5.
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