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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.
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Keywords:
- spatial optical solitons /
- nematic liquid crystals with negative dielectric anisotropy /
- perturbation method /
- linear stability analysis
[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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[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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