负性向列相液晶中1+1维空间光孤子:微扰法

李迎兵; 梁果; 洪伟毅; 任占梅; 郭旗

doi:10.7498/aps.65.094204

摘要

利用微扰法对负性向列相液晶中的1+1维空间光孤子进行了系统性的研究, 得到了近似解析孤子解.通过数值迭代, 发现只有当非局域程度大于某一临界值时孤子才能存在.近似解析解即使在一般非局域程度下和数值解也符合得较好. 为讨论孤子的稳定性, 进行了线性稳定性分析, 发现孤子均是稳定的, 数值模拟进一步证实了线性稳定性分析的结果.

关键词:

In this paper, we systematically study the (1+1)-dimensional spatial optical solitons in nematic liquid crystals with negative dielectric anisotropy. Firstly, with the perturbation method, we obtain a (1+1)-dimensional soliton solution in the second approximation.Numerical simulations confirm the analytical soliton solution in the strongly nonlocal case, the critical power of a strongly nonlocal solition is directly proportional to wm2/w3, where wm is a characteristic length of the material response, and w is the soliton width. Secondly, the soliton solutions in nematic liquid crystal with negative dielectric anisotropy are obtained by numerical computation. It is found that the bright solitons exist only when the degree of nonlocality is above a critical value. The analytical solutions in the second approximation accord with the numerical ones very well even under the general degree of nonlocality. Finally, to investigate the stability, we conduct the linear stability analysis, and find that all the solitons are stable, which is also confirmed by the numerical simulations.

Keywords:

spatial optical solitons /
nematic liquid crystals with negative dielectric anisotropy /
perturbation method /
linear stability analysis

作者及机构信息

1.
华南师范大学, 广东省微纳光子功能材料与器件重点实验室, 广州 510006;

2.
商丘师范学院物理与电气信息学院, 商丘 476000

通信作者: 郭旗, guoq@scnu.edu.cn

基金项目: 国家自然科学基金(批准号: 11274125, 11474109)资助的课题.

Authors and contacts

1.
Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510006, China;

2.
School of Physics and Electrical Information, Shangqiu Normal University, Shangqiu 476000, China

Corresponding author: Guo Qi, guoq@scnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11274125, 11474109).

参考文献

[1]	Snyder A W, Mitchell D J 1997 Science 276 1538
[2]	Guo Q 2014 Advances in Nonlinear Optics (Shanghai: Shanghai Jiao Tong University Press) pp257-333 (in Chinese) [郭旗 2014 非线性光学研究前沿(上海: 上海交通大学出版社) 第257-333页]
[3]	Krolikowski W, Bang O 2001 Phys. Rev. E 63 016610
[4]	Buccoliero D, Desyatnikov A S, Krolikowski W, Kivshar Y S 2007 Phys. Rev. Lett. 98 053901
[5]	Deng D M, Guo Q 2007 Opt. Lett. 32 3206
[6]	Deng D M, Guo Q 2009 Opt. Lett. 34 43
[7]	Conti C, Peccianti M, Assanto G 2003 Phys. Rev. Lett. 91 073901
[8]	Assanto G 2013 Nematicons: Spatial Optical Solitons in Nematic Liquid Crystals (New York: John Wiley Sons, Inc.)
[9]	Rotschild C, Cohen O, Manela O, Segev M 2005 Phys. Rev. Lett. 95 213904
[10]	Conti C, Peccianti M, Assanto G 2004 Phys. Rev. Lett. 94 113902
[11]	Hu W, Zhang T, Guo Q, Li X, Lan S 2006 Appl. Phys. Lett. 89 071111
[12]	Peccianti M, Conti C, Assanto G 2005 Opt. Lett. 30 415
[13]	Wang J, Chen J Z, Liu J L, Li Y H, Guo Q, Hu W, Li D Y, Liu Y G, Xuan L 2014 arXiv: 1403.2154v2 [physics.optics]
[14]	Li Y H, Wang J, Hu W, Guo Q 2014 Acta Phys. Sin. 63 184207 (in Chinese) [李一亨, 王靖, 胡巍, 郭旗 2014 63 184207]
[15]	Nikolov N I, Dragomir N, Ole B, Krolikowski W Z 2003 Phys. Rev. E 68 036614
[16]	Esbensen B K, Bache M, Krolikowski W, Bang O 2012 Phys. Rev. A 86 023849
[17]	Quyang S, Guo Q, Hu W 2006 Phys. Rev. E 74 036622
[18]	Greiner W 2001 Quantum Mechanics An Introduction (4th Ed.) (New York: Springer)
[19]	Agrawal G P 2001 Nonlinear Fiber Optics Applications of Nonlinear Fiber Optics (USA: Elsevier Science)
[20]	Xu Z Y, Kartashov Y V, Torner L 2005 Opt. Lett. 30 3171
[21]	Yang J K, Taras L 2008 Stud. Appl. Math. 120 265
[22]	Haus H A 1984 Waves and Fields in Optoelectronics (Englewood Cliffs, NJ: Prentice-Hall) pp109-111, 159-160
[23]	Liang G, Hong W Y, Hu Y H, Wang J, Wang Z, Li Y B, Guo Q, Hu W, Lou S Y, Christodoulides D N 2015 Arxiv: 1510.05759v1 [physics.optics]

施引文献

[1]	Snyder A W, Mitchell D J 1997 Science 276 1538
[2]	Guo Q 2014 Advances in Nonlinear Optics (Shanghai: Shanghai Jiao Tong University Press) pp257-333 (in Chinese) [郭旗 2014 非线性光学研究前沿(上海: 上海交通大学出版社) 第257-333页]
[3]	Krolikowski W, Bang O 2001 Phys. Rev. E 63 016610
[4]	Buccoliero D, Desyatnikov A S, Krolikowski W, Kivshar Y S 2007 Phys. Rev. Lett. 98 053901
[5]	Deng D M, Guo Q 2007 Opt. Lett. 32 3206
[6]	Deng D M, Guo Q 2009 Opt. Lett. 34 43
[7]	Conti C, Peccianti M, Assanto G 2003 Phys. Rev. Lett. 91 073901
[8]	Assanto G 2013 Nematicons: Spatial Optical Solitons in Nematic Liquid Crystals (New York: John Wiley Sons, Inc.)
[9]	Rotschild C, Cohen O, Manela O, Segev M 2005 Phys. Rev. Lett. 95 213904
[10]	Conti C, Peccianti M, Assanto G 2004 Phys. Rev. Lett. 94 113902
[11]	Hu W, Zhang T, Guo Q, Li X, Lan S 2006 Appl. Phys. Lett. 89 071111
[12]	Peccianti M, Conti C, Assanto G 2005 Opt. Lett. 30 415
[13]	Wang J, Chen J Z, Liu J L, Li Y H, Guo Q, Hu W, Li D Y, Liu Y G, Xuan L 2014 arXiv: 1403.2154v2 [physics.optics]
[14]	Li Y H, Wang J, Hu W, Guo Q 2014 Acta Phys. Sin. 63 184207 (in Chinese) [李一亨, 王靖, 胡巍, 郭旗 2014 63 184207]
[15]	Nikolov N I, Dragomir N, Ole B, Krolikowski W Z 2003 Phys. Rev. E 68 036614
[16]	Esbensen B K, Bache M, Krolikowski W, Bang O 2012 Phys. Rev. A 86 023849
[17]	Quyang S, Guo Q, Hu W 2006 Phys. Rev. E 74 036622
[18]	Greiner W 2001 Quantum Mechanics An Introduction (4th Ed.) (New York: Springer)
[19]	Agrawal G P 2001 Nonlinear Fiber Optics Applications of Nonlinear Fiber Optics (USA: Elsevier Science)
[20]	Xu Z Y, Kartashov Y V, Torner L 2005 Opt. Lett. 30 3171
[21]	Yang J K, Taras L 2008 Stud. Appl. Math. 120 265
[22]	Haus H A 1984 Waves and Fields in Optoelectronics (Englewood Cliffs, NJ: Prentice-Hall) pp109-111, 159-160
[23]	Liang G, Hong W Y, Hu Y H, Wang J, Wang Z, Li Y B, Guo Q, Hu W, Lou S Y, Christodoulides D N 2015 Arxiv: 1510.05759v1 [physics.optics]

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