分数薛定谔方程中燕尾高斯光束的可控反转与聚焦特性

黄宏伟; 程科; 杨嶒浩; 姚纳

doi:10.37188/CO.EN-2023-0018

Volume 17 Issue 2

Mar. 2024

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Chinese Optics > 2024 > 17(2): 481-492.

HUANG Hong-wei, CHENG Ke, YANG Ceng-hao, YAO Na. Controllable inversion and focusing behaviors of Swallowtail-Gaussian beams in fractional Schrödinger equations[J]. Chinese Optics, 2024, 17(2): 481-492. doi: 10.37188/CO.EN-2023-0018

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HUANG Hong-wei, CHENG Ke, YANG Ceng-hao, YAO Na. Controllable inversion and focusing behaviors of Swallowtail-Gaussian beams in fractional Schrödinger equations[J]. Chinese Optics, 2024, 17(2): 481-492. doi: 10.37188/CO.EN-2023-0018

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Controllable inversion and focusing behaviors of Swallowtail-Gaussian beams in fractional Schrödinger equations

doi: 10.37188/CO.EN-2023-0018

1.
College of Optoelectronic Engineering, Chengdu University of Information Technology, Chengdu 610225, China
2.
School of Aeronautics & Astronautics, University of Electronic Science and Technology of China, Chengdu 610054, China

Funds: Supported by Natural Science Foundation of Sichuan Province, China (No. 2023NSFSC0049)

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Author Bio:
HUANG Hong-wei (1998—), male, born in Changshou, Chongqing City. M.E, College of Optoelectronic Engineering, Chengdu University of Information Technology. His research interests focus on the propagation of catastrophe beams. E-mail: 985919155@qq.com

CHENG Ke (1979—), male, born in Jianli, Hubei province. Ph.D., Professor, College of Optoelectronic Engineering, Chengdu University of Information Technology. His research interests focus on the propagation and control of High-Power Lasers. E-mail: ck@cuit.edu.cn
Corresponding author: ck@cuit.edu.cn
Received Date: 16 Aug 2023
Rev Recd Date: 07 Oct 2023
Accepted Date: 25 Oct 2023

Available Online: 04 Nov 2023

Abstract

Abstract

By transferring a one-dimensional swallowtail catastrophe to an optical field, the evolution dynamics of the Swallowtail-Gaussian (SG) beams in fractional Schrödinger equations (FSE) with different potentials, which include the linear, parabolic, and Gaussian potential and non-potential cases, were investigated using the split-step Fourier method. In a non-potential case, the SG beams split into two sub-beams, and their splitting trajectories along straight lines can be curved with a larger Lévy index in FSE. In a linear potential case, periodic inversion and focusing behaviors are found, and a larger Lévy index can strengthen their peak intensities at focusing points and curve trajectories. However, the period distance of inversion and focusing is only affected by linear potentials rather than the Lévy index. In a parabolic potential case, the beams evolve from chaos interference into an apparent period in inversion and focusing of main and side lobes with a larger Lévy index, where the inversion and focusing position are combined and determined by parabolic potential and the Lévy index. In a Gaussian potential case, the evolution dynamics are evidently constrained within potential barriers. In a narrow barrier, the periodic inversion and focusing display chaotic behavior because of the interference of both the reflected main and side lobes. In contrast, the periodic evolution in a wider barrier becomes more prominent owing to the attenuation of the side lobes. The study of the SG beam in FSE offers the possibility of optical modulators and switches through the utilization of the higher-order swallowtail catastrophe wave fields.
- Swallowtail-Gaussian beam,
- Fractional Schrödinger equation,
- Lévy index

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References(36)

References

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