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

HUANG Hong-wei CHENG Ke YANG Ceng-hao YAO Na

黄宏伟, 程科, 杨嶒浩, 姚纳. 分数薛定谔方程中燕尾高斯光束的可控反转与聚焦特性[J]. 中国光学(中英文), 2024, 17(2): 481-492. doi: 10.37188/CO.EN-2023-0018
引用本文: 黄宏伟, 程科, 杨嶒浩, 姚纳. 分数薛定谔方程中燕尾高斯光束的可控反转与聚焦特性[J]. 中国光学(中英文), 2024, 17(2): 481-492. doi: 10.37188/CO.EN-2023-0018
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
Citation: 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

分数薛定谔方程中燕尾高斯光束的可控反转与聚焦特性

详细信息
  • 中图分类号: O437.5

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

doi: 10.37188/CO.EN-2023-0018
Funds: Supported by Natural Science Foundation of Sichuan Province, China (No. 2023NSFSC0049)
More Information
    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
  • 摘要:

    在光场中引入一维燕尾突变函数,利用分步傅立叶方法研究了燕尾高斯(SG)光束在分数薛定谔方程(FSE)中的演化动力学,详细讨论了线性势、抛物线势、高斯势及无势的情况。在无势情况下,SG光束会因群延迟的变化而分裂成两个子光束,并且分裂轨迹会随着Lévy指数的增大出现弯曲。在线性势下,SG光束出现了周期性反转和聚焦行为,Lévy指数和线性势系数分别影响聚焦点峰值强度和反转及聚焦的演化周期,其反转和聚焦周期距离只受线性势影响而与Lévy指数无关。在抛物线势情况下,具有较大Lévy指数的SG光束的主瓣和旁瓣反转和聚焦从杂乱转变为周期性演化,其反转聚焦位置由抛物线势系数和Lévy指数共同决定。在高斯势中,光束的演化在势垒的约束下由于反射主瓣和旁瓣的干扰,窄势垒的周期性反转和聚焦出现杂乱混沌现象,而对于宽势垒,由于旁瓣减弱,周期性演化变得清晰。本文研究结果为利用高阶燕尾光波场实现光调制器和光开关提供了可能。

     

  • Figure 1.  Group delay and intensity split of one-dimensional Swallowtail-Gaussian beam without potentials for different Lévy indexes of α=1, 1.4, 1.8, and 2. White dotted lines: the evolutions of the main lobe

    Figure 2.  (Color online) Intensity and spectral distributions of SG beams with a linear potential for different Lévy indexes α and linear potential coefficients a.

    Figure 3.  Peak intensities and their positions of SG beams with a linear potential for different Lévy indexes α and linear potential coefficients a during propagation. (a) a = 8, (b) a = 4, (c) the peak intensity (Max) of the longitudinal coordinate in transmission varies with the change of the Lévy indexes α(a = −4, +4, −8, +8)

    Figure 4.  Intensity evolution of the SG beams with parabolic potential for different Lévy indexes and parabolic potential coefficients. White solid lines in (j)−(l): evolution trajectories of main lobes; Red and white dotted circles: inversion and focus positions of main lobes

    Figure 5.  (a) Peak intensities of SG beams for different parabolic potential coefficients during propagation; (b) peak intensity in reversal positions versus parabolic potentials

    Figure 6.  The evolution dynamics of SG beams for different Gaussian potentials and Lévy indexes. (a)−(c): α=1, w0=1; (d)−(f): α=1, x0=20; (g)−(i): x0=20, w0=1

    Figure 7.  The evolution dynamics of SG beams in a larger Gaussian potential width of w0=10 for different Lévy indexes (x0=20)

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出版历程
  • 收稿日期:  2023-08-16
  • 修回日期:  2023-10-07
  • 录用日期:  2023-10-25
  • 网络出版日期:  2023-11-04

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