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非局域高次非线性介质中的多极暗孤子

郑一帆 黄光侨 林机

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非局域高次非线性介质中的多极暗孤子

郑一帆, 黄光侨, 林机

Multi-pole dark solitons in nonlocal and cubic-quintic nonlinear medium

Zheng Yi-Fan, Huang Guang-Qiao, Lin Ji
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  • 研究一维非局域三-五次非线性模型下,暗孤子和多极暗孤子的新解和传输特性.发现非局域程度和非线性参量变化对暗孤子的峰值和束宽产生影响,并且在特定的竞争非局域非线性参数下存在稳定基态暗孤子和多极暗孤子的束缚态.另外,讨论了在局域自聚焦三次和非局域自散焦五次非线性介质中暗孤子和两极暗孤子的传输特性,发现孤子比在自散焦三次和自聚焦五次的非线性介质中传输更加稳定.进一步研究了单暗孤子和三极暗孤子的功率与传播常数和非局域程度的关系,并讨论了不同类型暗孤子的线性稳定性问题.
    In this paper, we mainly simulate the characteristics of the ground state dark soliton and the multipole dark soliton in the nonlocal and cubic-quintic nonlinear medium. Firstly, the influences of the degree of nonlocality on the amplitude and the width of the dark soliton in the self-defocusing cubic-and self-focusing quantic-nonlinear medium are studied. Secondly, we find the nonlinear parameters affecting the amplitude values of solitons, but the refractive index induced by the light beam is always a fixed value. The numerical results show that the ground state dark soliton can be propagated stably alone the z axis, and the stable states of the dipole soliton and the dark tri-pole and quadru-pole solitons are stable. However, some quadru-pole dark soliton is unstable after propagating the remote distance. Furthermore, we also discuss the characteristics of the ground state dark soliton and the dark dipole soliton in the local cubic-nonlinear and nonlocal quantic nonlinear media. Both the amplitude and the beam width of the dark ground state soliton and dark dipole soliton are also affected by the degree of nonlocality and nonlinearity. Two boundary values of the induced refractive index change with the variations of the three nonlinear parameters. The dark soliton and the dipole dark soliton are more stable in the self-focusing cubic nonlinear and the nonlocal self-defocusing quantic nonlinear medium than those in the self defocusing cubic nonlinear and nonlocal self-focusing quantic nonlinear medium. The powers of single dark soliton and dark tri-pole soliton decrease monotonically with the increase of propagation constant when the cubic-quintic nonlinearities are certain values and these degrees of nonlocalities are taken different values. Furthermore, we also analyze linear stabilities of various nonlocal spatial dark solitons. And we find that the dipole dark soliton is unstable when the propagation constant is in the region[-0.9,-1.0]. These properties of linear stabilities of other multi-pole dark solitons are the same as their propagation properties.
      通信作者: 林机, linji@zjnu.edu.cn
    • 基金项目: 浙江省自然科学基金(批准号:LZ15A050001)和国家自然科学基金(批准号:11675146,11835011)资助的课题.
      Corresponding author: Lin Ji, linji@zjnu.edu.cn
    • Funds: Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. LZ15A050001) and the National Natural Science Foundation of China (Grant Nos. 11675146, 11835011).
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    Doktorov E V, Molchan M A 2008 J. Phys. A: Math. Theor. 41 315101

    [3]

    Tsoy E N 2010 Phys. Rev. A 82 063829

    [4]

    Huang G Q, Lin J 2017 Acta Phys. Sin. 66 054208 (in Chinese)[黄光桥, 林机 2017 物理学报 66 054208]

    [5]

    Snyder A W, Mitchell D J 1997 Science 276 1538

    [6]

    Nikolov N I, Neshev D, Krolikowski W, Bang O, Rasmussen J J, Christiansen P L 2004 Opt. Lett. 29 286

    [7]

    Gao X H, Wang J, Zhou L H, Yang Z J, Ma X K, Lu D Q, Guo Q, Hu W 2014 Opt. Lett. 39 3760

    [8]

    Quyang S G, Guo Q 2009 Opt. Express 17 5170

    [9]

    Quyang S G, Hu W, Guo Q 2012 Chin. Phys. B 21 040505

    [10]

    Fischer R, Neshev D N, Krolikowski W, Kivshar Y S, Castillo D I, Cerda S C, Meneghetti M R, Caetano D P, Hickman J M 2006 Opt. Lett. 31 3010

    [11]

    Pu S Z, Hou C F, Zhan K Y, Yuan C X 2012 Phys. Scr. 85 015402

    [12]

    Bland T, Edmonds M J, Proukakis N P, Martin A M, O'Dell D H J, Parker N G 2015 Phys. Rev. A 92 063601

    [13]

    Kong Q, Wang Q, Bang O, Krolikowski W 2010 Opt. Lett. 35 2152

    [14]

    Kong Q, Wang Q, Bang O, Krolikowski W 2010 Phys. Rev. A 82 013826

    [15]

    Chen W, Shen M, Kong Q, Shi J L, Wang Q, Krolikowski W 2014 Opt. Lett. 39 1764

    [16]

    Xu Z Y, Kartashov Y V, Torner L 2005 Opt. Lett. 30 3171

    [17]

    Zhou L H, Gao X H, Yang Z J, Lu D Q, Guo Q, Cao W W, Hu W 2011 Acta Phys. Sin. 60 044208 (in Chinese)[周罗红, 高星辉, 杨振军, 陆大全, 郭旗, 曹伟文, 胡巍 2011 物理学报 60 044208]

    [18]

    Ghofraniha N, Amato L, Folli V, Trillo S, DelRe E, Conti C 2012 Opt. Lett. 37 2325

    [19]

    Pelinovsky D E, Kivshar Y S, Afanasjev V V 1996 Phys. Rev. E 54 2015

    [20]

    Kivshar Y S, Afansjev V V, Snyder A W 1996 Opt. Commun. 126 348

    [21]

    Zhou Z X, Du Y W, Hou C F, Tian H, Wang Y 2011 J. Opt. Soc. Am. B 28 1583

    [22]

    Hu Y H, Lou S Y 2015 Commun. Theor. Phys. 64 665

    [23]

    Gao X H, Zhang C Y, Tang D, Zheng H, Lu D Q, Hu W 2013 Acta Phys. Sin. 62 044214 (in Chinese)[高星辉, 张承云, 唐冬, 郑晖, 陆大全, 胡巍 2013 物理学报 62 044214]

  • [1]

    Mihalache D, Mazilu D, Lederer F, Crasovan L C, Kartashov Y V, Torner L, Malomed B A 2006 Phys. Rev. E 74 066614

    [2]

    Doktorov E V, Molchan M A 2008 J. Phys. A: Math. Theor. 41 315101

    [3]

    Tsoy E N 2010 Phys. Rev. A 82 063829

    [4]

    Huang G Q, Lin J 2017 Acta Phys. Sin. 66 054208 (in Chinese)[黄光桥, 林机 2017 物理学报 66 054208]

    [5]

    Snyder A W, Mitchell D J 1997 Science 276 1538

    [6]

    Nikolov N I, Neshev D, Krolikowski W, Bang O, Rasmussen J J, Christiansen P L 2004 Opt. Lett. 29 286

    [7]

    Gao X H, Wang J, Zhou L H, Yang Z J, Ma X K, Lu D Q, Guo Q, Hu W 2014 Opt. Lett. 39 3760

    [8]

    Quyang S G, Guo Q 2009 Opt. Express 17 5170

    [9]

    Quyang S G, Hu W, Guo Q 2012 Chin. Phys. B 21 040505

    [10]

    Fischer R, Neshev D N, Krolikowski W, Kivshar Y S, Castillo D I, Cerda S C, Meneghetti M R, Caetano D P, Hickman J M 2006 Opt. Lett. 31 3010

    [11]

    Pu S Z, Hou C F, Zhan K Y, Yuan C X 2012 Phys. Scr. 85 015402

    [12]

    Bland T, Edmonds M J, Proukakis N P, Martin A M, O'Dell D H J, Parker N G 2015 Phys. Rev. A 92 063601

    [13]

    Kong Q, Wang Q, Bang O, Krolikowski W 2010 Opt. Lett. 35 2152

    [14]

    Kong Q, Wang Q, Bang O, Krolikowski W 2010 Phys. Rev. A 82 013826

    [15]

    Chen W, Shen M, Kong Q, Shi J L, Wang Q, Krolikowski W 2014 Opt. Lett. 39 1764

    [16]

    Xu Z Y, Kartashov Y V, Torner L 2005 Opt. Lett. 30 3171

    [17]

    Zhou L H, Gao X H, Yang Z J, Lu D Q, Guo Q, Cao W W, Hu W 2011 Acta Phys. Sin. 60 044208 (in Chinese)[周罗红, 高星辉, 杨振军, 陆大全, 郭旗, 曹伟文, 胡巍 2011 物理学报 60 044208]

    [18]

    Ghofraniha N, Amato L, Folli V, Trillo S, DelRe E, Conti C 2012 Opt. Lett. 37 2325

    [19]

    Pelinovsky D E, Kivshar Y S, Afanasjev V V 1996 Phys. Rev. E 54 2015

    [20]

    Kivshar Y S, Afansjev V V, Snyder A W 1996 Opt. Commun. 126 348

    [21]

    Zhou Z X, Du Y W, Hou C F, Tian H, Wang Y 2011 J. Opt. Soc. Am. B 28 1583

    [22]

    Hu Y H, Lou S Y 2015 Commun. Theor. Phys. 64 665

    [23]

    Gao X H, Zhang C Y, Tang D, Zheng H, Lu D Q, Hu W 2013 Acta Phys. Sin. 62 044214 (in Chinese)[高星辉, 张承云, 唐冬, 郑晖, 陆大全, 胡巍 2013 物理学报 62 044214]

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出版历程
  • 收稿日期:  2018-04-23
  • 修回日期:  2018-07-30
  • 刊出日期:  2018-11-05

非局域高次非线性介质中的多极暗孤子

  • 1. 浙江师范大学物理系, 金华 321004
  • 通信作者: 林机, linji@zjnu.edu.cn
    基金项目: 浙江省自然科学基金(批准号:LZ15A050001)和国家自然科学基金(批准号:11675146,11835011)资助的课题.

摘要: 研究一维非局域三-五次非线性模型下,暗孤子和多极暗孤子的新解和传输特性.发现非局域程度和非线性参量变化对暗孤子的峰值和束宽产生影响,并且在特定的竞争非局域非线性参数下存在稳定基态暗孤子和多极暗孤子的束缚态.另外,讨论了在局域自聚焦三次和非局域自散焦五次非线性介质中暗孤子和两极暗孤子的传输特性,发现孤子比在自散焦三次和自聚焦五次的非线性介质中传输更加稳定.进一步研究了单暗孤子和三极暗孤子的功率与传播常数和非局域程度的关系,并讨论了不同类型暗孤子的线性稳定性问题.

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