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(1+2) dimensional spiraling elliptic spatial optical solitons in the media without anisotropy

Yu Ya-Dong Liang Guo Ren Zhan-Mei Guo Qi

(1+2) dimensional spiraling elliptic spatial optical solitons in the media without anisotropy

Yu Ya-Dong, Liang Guo, Ren Zhan-Mei, Guo Qi
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  • Starting from the nonlocal nonlinear Schrödinger equation in Cartesian coordinates, we also obtained nonlocal nonlinear Schrödinger equation in a rotating coordinate system.Assuming that the response function of media is Gaussian, we obtain the stable solutions of the solitons of nonlocal nonlinear Schrödinger equation in rotating coordinate system by means ot the imaginary-time evolution method. The propagation properties of the (1+2) dimensional spiraling elliptic spatial optical solitons in the media is discussed in different degrees of the nonlocality by using the split-step Fourier algorithm.The elliptic soliton profiles of the major and the minor axes are Gaussian shaped in a strongly nonlocal case, but not in a weakly nonlocal case. It is suggested that (1+2) dimensional elliptic solitons be highly dependent on the degree of nonlocality. The angular velocity for the change of the ellipticity is very sensitive when the nonlocality is strong,but in the weakly nonlocal case, the change of the angular velocity is very small.The angular velocity depends strongly on weakly nonlocal case to different degrees of ellipticity. Oppositely, in strongly nonlocal case, the value of the angular velocity is almost unchanged. In another way, the critical power for the solitons decreases as the nonlocality decreases in different degrees of ellipticity.Similarly,the critical power for the solitons decreases as the ellipticity decreases in different degrees of nonlocality.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11274125, 11474109).
    [1]

    Eugenieva E D, Christodoulides D N 2000 Opt.Lett. 25 972

    [2]

    Shen M, Wang Q, Shi J L 2007 Opt. Lett. 270 384

    [3]

    Krolikowski W, Bang O, Wyller J 2004 Phys. Rev. E 70 036617

    [4]

    Katz O, Carmon T, Schwartz T, Segev M, Christotoulides D N 2004 Opt. Lett. 29 1248

    [5]

    Ciattoni A, Palma C 2003 J. Opt. Soc. Am. 20 2163

    [6]

    Polyakov S V, Stegeman G I 2002 Phys. Rev. E 66 046622

    [7]

    Qin X J, Guo Q, Hu W, Lan S 2006 Acta Phys. Sin. 55 1237 (in Chinese) [秦晓娟, 郭旗, 胡巍, 兰胜 2006 物理学报 55 1237]

    [8]

    Rotschild C, Cohen O, Manela O, Segev M 2005 Phys.Rev.Lett. 95 213904

    [9]

    Zhang P, Zhao J L, Xiao F J, Lou C B, Xu J J, Chen Z G 2008 Opt.Express. 16 3865

    [10]

    Crosignani B, Porto P D 1993 Opt.Lett. 18 1394

    [11]

    Fibich G, Papnicolaou G 1999 SIAM J.Appl.Math. 60 183

    [12]

    Krolikowski W, Bang O, Nikolov N I, Neshev D, Wyller J, Rasmussen J J, Edmundson D 2004 J.Opt.B-Quantum S.O. 6 S288

    [13]

    Lopez A S, Desyatnikov A S, Kivshar S Y, Skupin S, Krolikowski W, Bang O 2006 Opt.Lett. 31 1100

    [14]

    Buccoliero D, Lopez A S, Skupin S, Desyatnikov A S, Bang O, Krolikowski W, Kivshar Y S 2007 Physica.B. 394 351

    [15]

    Briedis D, Petersen D E, Edmundson D, Krolikowski W, Bang O 2005 Opt.Express. 73 435

    [16]

    Liang G, Guo Q 2013 Phys. Rev. A 88 043825

    [17]

    Mitchell D J, Snyder A W 1999 J.Opt.Soc.Am.B 16 236

    [18]

    Krolikowski W, Bang O, Rasmussen J J, Wyller J 2001 Phys.Rev.E 64 016612

    [19]

    Guo Q, Chi S 2000 J.Opt.A:Pure Appl.Opt. 2 5

    [20]

    Yang J K, Lakoba T L 2008 Stud.Appl.Math. 120 265

    [21]

    Chiofalo M L, Succi S, Tosi M P 2000 Phys.Rev.E 62 7438

    [22]

    Carr L D, Castin Y 2002 Phys.Rev.A 66 063602

    [23]

    Cao J N, Guo Q 2005 Acta Phys.Sin. 54 3688 (in Chinese) [曹觉能, 郭旗 2005 物理学报 54 3688]

  • [1]

    Eugenieva E D, Christodoulides D N 2000 Opt.Lett. 25 972

    [2]

    Shen M, Wang Q, Shi J L 2007 Opt. Lett. 270 384

    [3]

    Krolikowski W, Bang O, Wyller J 2004 Phys. Rev. E 70 036617

    [4]

    Katz O, Carmon T, Schwartz T, Segev M, Christotoulides D N 2004 Opt. Lett. 29 1248

    [5]

    Ciattoni A, Palma C 2003 J. Opt. Soc. Am. 20 2163

    [6]

    Polyakov S V, Stegeman G I 2002 Phys. Rev. E 66 046622

    [7]

    Qin X J, Guo Q, Hu W, Lan S 2006 Acta Phys. Sin. 55 1237 (in Chinese) [秦晓娟, 郭旗, 胡巍, 兰胜 2006 物理学报 55 1237]

    [8]

    Rotschild C, Cohen O, Manela O, Segev M 2005 Phys.Rev.Lett. 95 213904

    [9]

    Zhang P, Zhao J L, Xiao F J, Lou C B, Xu J J, Chen Z G 2008 Opt.Express. 16 3865

    [10]

    Crosignani B, Porto P D 1993 Opt.Lett. 18 1394

    [11]

    Fibich G, Papnicolaou G 1999 SIAM J.Appl.Math. 60 183

    [12]

    Krolikowski W, Bang O, Nikolov N I, Neshev D, Wyller J, Rasmussen J J, Edmundson D 2004 J.Opt.B-Quantum S.O. 6 S288

    [13]

    Lopez A S, Desyatnikov A S, Kivshar S Y, Skupin S, Krolikowski W, Bang O 2006 Opt.Lett. 31 1100

    [14]

    Buccoliero D, Lopez A S, Skupin S, Desyatnikov A S, Bang O, Krolikowski W, Kivshar Y S 2007 Physica.B. 394 351

    [15]

    Briedis D, Petersen D E, Edmundson D, Krolikowski W, Bang O 2005 Opt.Express. 73 435

    [16]

    Liang G, Guo Q 2013 Phys. Rev. A 88 043825

    [17]

    Mitchell D J, Snyder A W 1999 J.Opt.Soc.Am.B 16 236

    [18]

    Krolikowski W, Bang O, Rasmussen J J, Wyller J 2001 Phys.Rev.E 64 016612

    [19]

    Guo Q, Chi S 2000 J.Opt.A:Pure Appl.Opt. 2 5

    [20]

    Yang J K, Lakoba T L 2008 Stud.Appl.Math. 120 265

    [21]

    Chiofalo M L, Succi S, Tosi M P 2000 Phys.Rev.E 62 7438

    [22]

    Carr L D, Castin Y 2002 Phys.Rev.A 66 063602

    [23]

    Cao J N, Guo Q 2005 Acta Phys.Sin. 54 3688 (in Chinese) [曹觉能, 郭旗 2005 物理学报 54 3688]

  • [1] Cao Jue-Neng, Guo Qi. Properties of spatial optical solitons to different degrees of nonlocality. Acta Physica Sinica, 2005, 54(8): 3688-3693. doi: 10.7498/aps.54.3688
    [2] Guo Qi, Wang Xing-Hua. The propagation properties of the elliptic Gaussian beam in strongly nonlocal nonlinear media. Acta Physica Sinica, 2005, 54(7): 3183-3188. doi: 10.7498/aps.54.3183
    [3] Zhou Jun, Ren Hai-Dong, Feng Ya-Ping. The pulsating propagation of spatial soliton in strongly nonlocal optical lattice. Acta Physica Sinica, 2010, 59(6): 3992-4000. doi: 10.7498/aps.59.3992
    [4] Zhu Ye-Qing, Long Xue-Wen, Hu Wei, Cao Long-Gui, Yang Ping-Bao, Guo Qi. The influence of nonlocality on solitons in nematic liquid crystals. Acta Physica Sinica, 2008, 57(4): 2260-2265. doi: 10.7498/aps.57.2260
    [5] Zheng Rui, Cao Wei-Wen, Chen Li-Xia, Lu Da-Quan, Guo Qi, Wu Li-Jun, Hu Wei, Gao Xing-Hui. Applications of spectral renormalization method to the research of nonlocal optical spatial soliton. Acta Physica Sinica, 2010, 59(2): 1063-1068. doi: 10.7498/aps.59.1063
    [6] Ouyang Shi-Gen. Optical vortex solitons in self-defocusing Kerr-type nonlocal medium. Acta Physica Sinica, 2013, 62(4): 040504. doi: 10.7498/aps.62.040504
    [7] Guo Qi, Xiao Yi. The mutually-trapped propagation of orthogonally polarized beam pair in plannar waveguides. Acta Physica Sinica, 2005, 54(11): 5201-5209. doi: 10.7498/aps.54.5201
    [8] Gong Lun-Xun. Some new exact solutions of the Jacobi elliptic functions of NLS equation. Acta Physica Sinica, 2006, 55(9): 4414-4419. doi: 10.7498/aps.55.4414
    [9] RUAN HANG-YU, CHEN YI-XIN. RING SOLITONS, DROMIONS, BREATHERS AND INSTANTONS OF THE NLS EQUATION. Acta Physica Sinica, 2001, 50(4): 586-592. doi: 10.7498/aps.50.586
    [10] Dai Ji-Hui, Guo Qi. Rotating azimuthon in strongly nonlocal nonlinear media. Acta Physica Sinica, 2009, 58(3): 1752-1757. doi: 10.7498/aps.58.1752
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Publishing process
  • Received Date:  27 November 2014
  • Accepted Date:  13 February 2015
  • Published Online:  05 August 2015

(1+2) dimensional spiraling elliptic spatial optical solitons in the media without anisotropy

  • 1. Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510006, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 11274125, 11474109).

Abstract: Starting from the nonlocal nonlinear Schrödinger equation in Cartesian coordinates, we also obtained nonlocal nonlinear Schrödinger equation in a rotating coordinate system.Assuming that the response function of media is Gaussian, we obtain the stable solutions of the solitons of nonlocal nonlinear Schrödinger equation in rotating coordinate system by means ot the imaginary-time evolution method. The propagation properties of the (1+2) dimensional spiraling elliptic spatial optical solitons in the media is discussed in different degrees of the nonlocality by using the split-step Fourier algorithm.The elliptic soliton profiles of the major and the minor axes are Gaussian shaped in a strongly nonlocal case, but not in a weakly nonlocal case. It is suggested that (1+2) dimensional elliptic solitons be highly dependent on the degree of nonlocality. The angular velocity for the change of the ellipticity is very sensitive when the nonlocality is strong,but in the weakly nonlocal case, the change of the angular velocity is very small.The angular velocity depends strongly on weakly nonlocal case to different degrees of ellipticity. Oppositely, in strongly nonlocal case, the value of the angular velocity is almost unchanged. In another way, the critical power for the solitons decreases as the nonlocality decreases in different degrees of ellipticity.Similarly,the critical power for the solitons decreases as the ellipticity decreases in different degrees of nonlocality.

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