Periodical self-focusing and self-accelerating of a finite-energy Airy beam in a gradient-index fiber

Hanmou Zhang; Wenyu Fu; Xingrong Zheng

doi:10.3788/COL201513.S21406

Journals >Chinese Optics Letters >Volume 13 >Issue Suppl. >Page S21406 > Article

Chinese Optics Letters
Vol. 13, Issue Suppl., S21406 (2015)

Periodical self-focusing and self-accelerating of a finite-energy Airy beam in a gradient-index fiber

Hanmou Zhang^*, Wenyu Fu, and Xingrong Zheng

Author Affiliations

Department of Physics, Long-Dong University, Qingyang 745000, China

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DOI: 10.3788/COL201513.S21406 Cite this Article Set citation alerts

Hanmou Zhang, Wenyu Fu, Xingrong Zheng. Periodical self-focusing and self-accelerating of a finite-energy Airy beam in a gradient-index fiber[J]. Chinese Optics Letters, 2015, 13(Suppl.): S21406 Copy Citation Text

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Abstract

We investigate propagation of a finite energy Airy beam in a gradient-index fiber analytically and numerically, and find that the beam not only repeats its intensity features, but also has the phenomenon of self-focusing and self-accelerating periodically. The numerical results show that the beam centroid position and beam width evolve periodically. The radial gradient of the refractive index determines the propagation period for the beam and the truncated parameter affects the amplitude of both the centroid position and beam width.

E (x_{0}, y_{0}, 0) = A i (\frac{x_{0}}{w_{0}}) \exp (a_{x} \frac{x_{0}}{w_{0}}) A i (\frac{y_{0}}{w_{0}}) \exp (a_{y} \frac{y_{0}}{w_{0}}),

(1)

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n^{2} (x, y, ω) = {\begin{matrix} n_{0}^{2} (ω) [1 - α^{2} (ω) (x^{2} + y^{2})] & x^{2} + y^{2} \leq R_{0}^{2} \\ n_{0}^{2} (ω) [1 - α^{2} (ω) R_{0}^{2}] & x^{2} + y^{2} \geq R_{0}^{2} \end{matrix},

(2)

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α (ω) = \frac{1}{R_{0}} {[1 - \frac{n_{1}^{2} (ω)}{n_{0}^{2} (ω)}]}^{1 / 2} .

(3)

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[\begin{matrix} A & B \\ C & D \end{matrix}] = [\begin{matrix} \cos (α z) & \sin (α z) / n α \\ - n α \sin (α z) & \cos (α z) \end{matrix}] .

(4)

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E (x, y, z) = - \frac{i k}{2 π B} \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} E (x_{0}, y_{0}, 0) \times \exp {\frac{i k}{2 B} [A (x_{0}^{2} + y_{0}^{2}) - 2 (x x_{0} + y y_{0}) + D (x^{2} + y^{2})]} d x_{0} d y_{0} .

(5)

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W (x, y, z) = \frac{1}{A} \prod_{j = x, y} A i (\frac{j}{A w_{0}} - \frac{B^{2}}{4 k^{2} A^{2} w_{0}^{4}} - \frac{a_{j} B}{i k A w_{0}^{2}}) \times \exp (\frac{i k D}{2 B} j^{2}) \exp (\frac{a_{j} j}{A w_{0}} - \frac{a_{x} B^{2}}{2 k^{2} A^{2} w_{0}^{4}} - \frac{i k j^{2}}{2 A B} + \frac{i a_{j}^{2} B}{2 k A w_{0}^{2}} - \frac{i B^{3}}{12 k^{2} A^{3} w_{0}^{6}}) .

(6)

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I (x, y, z) = E (x, y, z) \cdot E^{*} (x, y, z),

(7)

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W (z) = 2 \sqrt{〈 x^{2} 〉 - {〈 x 〉}^{2}},

(8)

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n^{2} (ω) = 1 + \sum_{j = 1}^{3} \frac{C_{j} ω_{j}^{2}}{ω_{j}^{2} - ω^{2}} .

(9)

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Hanmou Zhang, Wenyu Fu, Xingrong Zheng. Periodical self-focusing and self-accelerating of a finite-energy Airy beam in a gradient-index fiber[J]. Chinese Optics Letters, 2015, 13(Suppl.): S21406

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