留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

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

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

downloadPDF
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]. , 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]. , 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 ofα=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 indexesαand linear potential coefficientsa.

    Figure 3.Peak intensities and their positions of SG beams with a linear potential for different Lévy indexesαand linear potential coefficientsaduring 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 indexesα(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 ofw0=10 for different Lévy indexes (x0=20)

  • [1] KIRK N P, CONNOR J N L, CURTIS P R,et al. Theory of axially symmetric cusped focusing: numerical evaluation of a Bessoid integral by an adaptive contour algorithm[J].Journal of Physics A:Mathematical and General, 2000, 33(26): 4797-4808.doi:10.1088/0305-4470/33/26/306
    [2] BERRY M V, UPSTILL C. IV catastrophe optics: morphologies of caustics and their diffraction patterns[J].Progress in Optics, 1980, 18: 257-346.
    [3] SIVILOGLOU G A, CHRISTODOULIDES D N. Accelerating finite energy Airy beams[J].Optics Letters, 2007, 32(8): 979-981.doi:10.1364/OL.32.000979
    [4] RING J D, LINDBERG J, MOURKA A,et al. Auto-focusing and self-healing of Pearcey beams[J].Optics Express, 2012, 20(17): 18955-18966.doi:10.1364/OE.20.018955
    [5] CHEN ZH G, MORANDOTTI R.Nonlinear Photonics and Novel Optical Phenomena[M]. New York: Springer, 2012.
    [6] ZANNOTTI A, DIEBEL F, DENZ C. Dynamics of the optical swallowtail catastrophe[J].Optica, 2017, 4(10): 1157-1162.doi:10.1364/OPTICA.4.001157
    [7] ZANNOTTI A, DIEBEL F, BOGUSLAWSKI M,et al. Optical catastrophes of the swallowtail and butterfly beams[J].New Journal of Physics, 2017, 19(5): 053004.doi:10.1088/1367-2630/aa6ecd
    [8] CHENG K, LU G, ZHONG X Q. The Poynting vector and angular momentum density of Swallowtail-Gauss beams[J].Optics Communications, 2017, 396: 58-65.doi:10.1016/j.optcom.2017.03.038
    [9] CHENG K, LU G, ZHOU Y,et al. The Poynting vector and angular momentum density of the autofocusing Butterfly-Gauss beams[J].Optics & Laser Technology, 2018, 105: 23-34.
    [10] CHENG K, LIANG M T, SHU L Y,et al. Polarization states and Stokes vortices of dual Butterfly-Gauss vortex beams with uniform polarization in uniaxial crystals[J].Optics Communications, 2022, 504: 127471.doi:10.1016/j.optcom.2021.127471
    [11] TENG H A, QIAN Y X, LAN Y P,et al. Abruptly autofocusing circular swallowtail beams[J].Optics Letters, 2021, 46(2): 270-273.doi:10.1364/OL.415709
    [12] TENG H A, QIAN Y X, LAN Y P. Swallowtail-type diffraction catastrophe beams[J].Optics Express, 2021, 29(3): 3786-3794.doi:10.1364/OE.416134
    [13] TENG H A, HU J T, CAI Y M,et al. Caustics and wavefront of Swallowtail-Gauss catastrophe beams[J].Results in Physics, 2022, 42: 105991.doi:10.1016/j.rinp.2022.105991
    [14] JIANG J J, XU D L, MO ZH W,et al. Generation and control of tornado waves by means of ring swallowtail vortex beams[J].Optics Express, 2022, 30(7): 11331-11344.doi:10.1364/OE.453165
    [15] ZHANG N CH, SONG J Q, LI D M,et al. Multi-focus autofocusing circular hyperbolic umbilic beams[J].Optics Express, 2022, 30(18): 32978-32989.doi:10.1364/OE.467601
    [16] LASKIN N. Fractional Schrödinger equation[J].Physical Review E, 2002, 66(5): 056108.doi:10.1103/PhysRevE.66.056108
    [17] LONGHI S. Fractional Schrödinger equation in optics[J].Optics Letters, 2015, 40(6): 1117-1120.doi:10.1364/OL.40.001117
    [18] ZANG F, WANG Y, LI L. Dynamics of Gaussian beam modeled by fractional Schrödinger equation with a variable coefficient[J].Optics Express, 2018, 26(18): 23740-23750.doi:10.1364/OE.26.023740
    [19] ZHANG Y Q, LIU X, BELIĆ M R,et al. Propagation dynamics of a light beam in a fractional Schrödinger equation[J].Physical Review Letters, 2015, 115(18): 180403.doi:10.1103/PhysRevLett.115.180403
    [20] ZHANG Y Q, BELIĆ M R, ZHANG L,et al. Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential[J].Optics Express, 2015, 23(8): 10467-10480.doi:10.1364/OE.23.010467
    [21] ZHANG Y Q, LIU X, BELIĆ M R,et al. Automatic Fourier transform and self-Fourier beams due to parabolic potential[J].Annals of Physics, 2015, 363: 305-315.doi:10.1016/j.aop.2015.10.006
    [22] ZHANG Y Q, LIU X, BELIĆ M R,et al. Anharmonic propagation of two-dimensional beams carrying orbital angular momentum in a harmonic potential[J].Optics Letters, 2015, 40(16): 3786-3789.doi:10.1364/OL.40.003786
    [23] ZENG L W, ZENG J H. Preventing critical collapse of higher-order solitons by tailoring unconventional optical diffraction and nonlinearities[J].Communications Physics, 2020, 3(1): 26.doi:10.1038/s42005-020-0291-9
    [24] LI L, LI H G, RUAN W,et al. Gap solitons in parity-time-symmetric lattices with fractional-order diffraction[J].Journal of the Optical Society of America B, 2020, 37(2): 488-494.doi:10.1364/JOSAB.376975
    [25] CHE W W, YANG F W, CAO SH L,et al. Gray solitons in parity-time-symmetric localized potentials with fractional-order diffraction[J].Physics Letters A, 2021, 413: 127606.doi:10.1016/j.physleta.2021.127606
    [26] MALOMED B A. Optical solitons and vortices in fractional media: a mini-review of recent results[J].Photonics, 2021, 8(9): 353.doi:10.3390/photonics8090353
    [27] LIU X Y, MALOMED B A, ZENG J H. Localized modes in nonlinear fractional systems with deep lattices[J].Advanced Theory and Simulations, 2022, 5(4): 2100482.doi:10.1002/adts.202100482
    [28] ZHONG M, YAN ZH Y. Spontaneous symmetry breaking and ghost states in two-dimensional fractional nonlinear media with non-Hermitian potential[J].Communications Physics, 2023, 6(1): 92.doi:10.1038/s42005-023-01212-1
    [29] XU CH J, WU J H, WU Y,et al. Propagation of the Pearcey Gaussian beams in a medium with a parabolic refractive index[J].Optics Communications, 2020, 464: 125478.doi:10.1016/j.optcom.2020.125478
    [30] LIN Z J, XU C J, HUANG H Q,et al. Accelerating trajectory manipulation of symmetric Pearcey Gaussian beam in a uniformly moving parabolic potential[J].Optics Express, 2021, 29(11): 16270-16283.doi:10.1364/OE.424489
    [31] GAO R, GUO T, REN SH M,etal. Periodic evolution of the Pearcey-Gaussian beam in the fractional Schrödinger equation under Gaussian potential[J].JournalofPhysicsB:Atomic,MolecularandOpticalPhysics, 2022, 55(9): 095401.
    [32] GAO R, REN SH M, GUO T,et al. Propagation dynamics of chirped Pearcey-Gaussian beam in fractional Schrödinger equation under Gaussian potential[J].Optik, 2022, 254: 168661.doi:10.1016/j.ijleo.2022.168661
    [33] ZHANG X, ZHANG J, CHEN CH SH,et al. Controllable focusing behavior of chirped Pearcey-Gaussian pulses under time-dependent potentials[J].Optics Express, 2022, 30(19): 34835-34847.doi:10.1364/OE.471329
    [34] LIU SH L, ZHANG Y W, MALOMED B A,et al. Experimental realisations of the fractional Schrödinger equation in the temporal domain[J].Nature Communications, 2023, 14(1): 222.doi:10.1038/s41467-023-35892-8
    [35] HUANG X W, SHI X H, DENG ZH X,et al. Potential barrier-induced dynamics of finite energy Airy beams in fractional Schrödinger equation[J].Optics Express, 2017, 25(26): 32560-32569.doi:10.1364/OE.25.032560
    [36] HUANG X W, DENG ZH X, FU X Q. Dynamics of finite energy Airy beams modeled by the fractional Schrödinger equation with a linear potential[J].Journal of the Optical Society of America B, 2017, 34(5): 976-982.doi:10.1364/JOSAB.34.000976
  • 加载中
图(7)
计量
  • 文章访问数:138
  • HTML全文浏览量:58
  • PDF下载量:55
  • 被引次数:0
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

目录

    /

      返回文章
      返回

        重要通知

        2024年2月16日科睿唯安通过Blog宣布,2024年将要发布的JCR2023中,229个自然科学和社会科学学科将SCI/SSCI和ESCI期刊一起进行排名!《 》作为ESCI期刊将与全球SCI期刊共同排名!

        Baidu
        map