Journal of Quantum Optics, Volume. 28, Issue 2, 149(2022)

Propagation Characteristics of the Gaussian Beam in the Fractional Inhomogeneous Media

SONG Li-jun*, LIU Xiao-qi, and LIU Shu-jie
Author Affiliations
  • [in Chinese]
  • show less
    References(35)

    [1] [1] EISENBERG H S, SILBERBERG Y, MORANDOTTI R, et al. Diffraction Management[J]. Physical Review Letters, 2000, 85(9): 1863. DOI: 10.1103/PhysRevLett.85.1863.

    [2] [2] STALIUNAS K, HERRERO R. Nondiffractive propagation of light in photonic crystals[J]. Physical Review E, 2006, 73(1): 016601. DOI: 10.1103/PhysRevE.73.016601.

    [3] [3] HUANG C, YE F, CHEN X. Diffraction control of subwavelength structured light beams in Kapitza media[J]. Optics Express, 2015, 23(10): 12692-12699. DOI: 10.1364/OE.23.012692.

    [4] [4] LONGHI S, MARANGONI M, LOBINO M, et al. Observation of dynamic localization in periodically curved waveguide arrays[J]. Physical Review Letters, 2006, 96(24): 243901. DOI: 10.1103/PhysRevLett.96.243901.

    [5] [5] SZAMEIT A, KARTASHOV Y V, DREISOW F, et al. Inhibition of light tunneling in waveguide arrays[J]. Physical Review Letters, 2009, 102(15): 153901. DOI: 10.1103/PhysRevLett.102.153901.

    [6] [6] ABLOWITZ M J, MUSSLIMANI Z H. Discrete diffraction managed spatial solitons[J]. Physical Review Letters, 2001, 87(25): 254102. DOI: 10.1103/PhysRevLett.87.254102.

    [7] [7] CHRISTODOULIDES D N, EUGENIEVA E D. Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays[J]. Physical Review Letters, 2001, 87(23): 233901. DOI: 10.1103/PhysRevLett.87.233901.

    [8] [8] ROSBERG C R, GARANOVICH I L, SUKHORUKOV A A, et al. Demonstration of all-optical beam steering in modulated photonic lattices[J]. Optics Letters, 2006, 31(10): 1498-1500. DOI: 10.1364/ol.31.001498.

    [9] [9] KARTASHOV Y V, VYSLOUKH V A. Switching management in couplers with biharmonic longitudinal modulation of refractive index[J]. Optics Letters, 2009, 34(22): 3544-3546. DOI: 10.1364/OL.34.003544.

    [10] [10] MUSSLIMANI Z H, MAKRIS K G, El-GANAINY R, et al. Optical Solitons in PT Periodic Potentials[J]. Physical Review Letters, 2008, 100(3): 030402. DOI: 10.1103/PhysRevLett.100.030402.

    [11] [11] KARTASHOV Y V, KONOTOP V V, VYSLOUKH V A. Dissipative surface solitons in periodic structures[J]. Europhysics Letters, 2010, 91(3): 34003. DOI: 10.1209/0295-5075/91/34003.

    [12] [12] WU J, YANG X. Ultrastrong extraordinary transmission and reflection in PT-symmetric Thue-Morse optical waveguide networks[J]. Optics Express, 2017, 25(22): 27724-27735. DOI: 10.1364/OE.25.027724.

    [13] [13] LAUGHLIN R B. Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionall Charged Excitations[J]. Physical Review Letters, 1983, 50(18): 1395-1398. DOI: 10.1103/PhysRevLett.50.1395.

    [14] [14] WEN J, ZHANG Y, XIAO M. The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics[J]. Advances in Optics & Photonics, 2013, 5(1): 83-130. DOI: 10.1364/AOP.5.000083.

    [15] [15] ROKHINSON L P, LIU X, FURDYNA J K. The fractional a.c. Josephson effect in a semiconductor-superconductor nanowire as a signature of Majorana particles[J]. Nature Physics, 2012, 8: 795-799. DOI: 10.1038/nphys2429.

    [16] [16] OLIVAR-ROMERO F, ROSAS-ORTIZ O. Factorization of the Quantum Fractional Oscillator[J]. Journal of Physics Conference Series, 2016, 698: 012025. DOI: 10.1088/1742-6596/698/1/012025.

    [17] [17] LASKIN N. Fractional Quantum Mechanics and Lévy Path Integrals[J]. Physics Letters A, 2000, 268(4-6): 298-305. DOI: 10.1016/s0375-9601(00)00201-2.

    [18] [18] LASKIN N. Fractional Schrdinger equation[J]. Physical Review E, 2002, 66(5): 056108. DOI: 10.1103/PhysRevE.66.056108.

    [19] [19] LONGHI S. Fractional Schrdinger equation in optics[J]. Optics Letters, 2015, 40(6): 1117-1120. DOI: 10.1364/OL.40.001117.

    [20] [20] ZHANG Y Q, LIU X, BELIC M R. Propagation Dynamics of a Light Beam in a Fractional Schrdinger Equation[J]. Physical Review Letters, 2015, 115(18): 180403. DOI: 10.1103/PhysRevLett.115.180403.

    [21] [21] ZHANG Y, ZHONG H, BELIC M R, et al. PT symmetry in a fractional Schrdinger equation[J]. Laser & Photonics Reviews, 2016, 10(3): 526-531. DOI: 10.1002/lpor.201600037.

    [22] [22] ZHANG Y, ZHONG H, BELIC M R, et al. Diffraction-free Beams in Fractional Schrdinger Equation[J]. Scientific Reports, 2015, 6(1): 23645. DOI: 10.1038/srep23645.

    [23] [23] LIEMERT A, KIENLE A. Fractional Schrdinger Equation in the Presence of the Linear Potential[J]. Mathematics, 2016, 4(2): 31. DOI: 10.3390/math4020031.

    [24] [24] HUANG X, FU X, DENG Z. Dynamics of finite energy Airy beams modeled by the fractional Schrdinger 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.

    [25] [25] HUANG C, DONG L. Beam propagation management in a fractional Schrdinger equation[J]. Scientific Reports, 2017, 7(1): 5442. DOI: 10.1038/s41598-017-05926-5.

    [26] [26] ZHANG L, LI C, ZHONG H, et al. Propagation dynamics of super-Gaussian beams in fractional Schrdinger equation: from linear to nonlinear regimes[J]. Optics Express, 2016, 24(13): 14406-14418. DOI:10.1364/OE.24.014406.

    [27] [27] HUANG C, DONG L. Gap solitons in the nonlinear fractional Schrdinger equation with an optical lattice[J]. Optics Letters, 2016, 41(24): 5636-5639. DOI: 10.1364/OL.41.005636.

    [28] [28] DONG L, HUANG C. Double-hump solitons in fractional dimensions with a PT symmetric potential[J]. Optics Express, 2018, 26(8): 10509-10518. DOI: 10.1364/OE.26.010509.

    [29] [29] RAY S S. Dispersive optical solitons of time-fractional Schrdinger-Hirota equation in nonlinear optical fibers[J]. Physica A: Statistical Mechanics and its Applications, 2019, 537: 122619. DOI: 10.1016/j.physa.2019.122619.

    [30] [30] WANG Q, ZHANG L, MALOMED B A, et al. Transformation of multipole and vortex solitons in the nonlocal nonlinear fractional Schrdinger equation by means of Lévy-index management[J]. Chaos, Solitons & Fractals, 2022, 157: 111995. DOI: 10.1016/j.chaos.2022.111995.

    [31] [31] CHEN M, ZENG S, LU D, et al. Optical solitons, self-focusing, and wave collapse in a space-fractional Schrdinger equation with a Kerr-type nonlinearity[J]. Physical Review E, 2018, 98(2): 022211. DOI: 10.1103/PhysRevE.98.022211.

    [32] [32] ZENG L, ZENG J. One-dimensional solitons in fractional Schrdinger equation with a spatially modulated nonlinearity: nonlinear lattice[J]. Optics Letters, 2019, 44(11): 2661-2664. DOI: 10.1364/OL.44.002661.

    [33] [33] GUNDOGDU H, GOZUKIZIL O F. Cubic nonlinear fractional Schrdinger equation with conformable derivative and its new travelling wave solutions[J]. Journal of Applied Mathematics and Computational Mechanics, 2021, 20(2): 29-41. DOI: 0.17512/jamcm.2021.2.03.

    [34] [34] HUANG C, DONG L. Dissipative surface solitons in a nonlinear fractional Schrdinger equation[J]. Optics Letters, 2019, 44(22): 5438-5441. DOI: 10.1364/OL.44.005438.

    [35] [35] WANG R R, WANG Y Y, DAI C Q. Dissipative solitons of the nonlinear fractional Schrdinger equation with PT-symmetric potential[J]. Optik, 2022, 254: 168639. DOI: 10.1016/j.ijleo.2022.168639.

    Tools

    Get Citation

    Copy Citation Text

    SONG Li-jun, LIU Xiao-qi, LIU Shu-jie. Propagation Characteristics of the Gaussian Beam in the Fractional Inhomogeneous Media[J]. Journal of Quantum Optics, 2022, 28(2): 149

    Download Citation

    EndNote(RIS)BibTexPlain Text
    Save article for my favorites
    Paper Information

    Category:

    Received: Oct. 25, 2021

    Accepted: --

    Published Online: Oct. 14, 2022

    The Author Email: SONG Li-jun (songlij@sxu.edu.cn)

    DOI:10.3788/jqo20222802.0602

    Topics