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由于变系数非线性Schrödinger方程的增益、色散和非线性项都是变化的, 根据方程这一特点可以研究光脉冲在非均匀光纤中的传输特性. 本文利用Hirota方法, 得到非线性Schrödinger方程的解析暗孤子解. 然后根据暗孤子解对暗孤子的传输特性进行讨论, 并且分析各个物理参量对暗孤子传输的影响. 经研究发现, 通过调节光纤的损耗、色散和非线性效应都能有效的控制暗孤子的传输, 从而提高非均匀光纤中的光脉冲传输质量. 此外, 本文还得到了所求解方程的解析双暗孤子解, 最后对两个暗孤子相互作用进行了探讨. 本文得到的结论有利于研究非均匀光纤中的孤子控制技术.The terms of gain(or absorption), dispersion, and nonlinearity in the nonlinear Schrödinger equation are usually variables, which can be used to study the propagation of optical pulses in inhomogeneous optical fibers. In this paper, with the aid of the Hirota method, the bilinear forms of the Schrödinger equation are derived. Based on the bilinear form, the analytic dark soliton solutions to the nonlinear Schrödinger equation are obtained. The properties of dark solitons are discussed. Stable dark solitons are observed in the normal dispersion regime. In addition, corresponding parameters for controlling the propagation of dark solitons are analyzed. Results of our reflearch show that the propagation route of solitons can be effectively controlled by the gain(or absorption), dispersion, and nonlinearity, which can improve the quality of signal transmission in optical communications. When the amplitude of the loss coefficient increases, the amplitude of the dark soliton increases suddenly during the transmission process.By means of changing the type of dispersion, the purpose of controlling the dark soliton phase and phase oscillation is achieved. The possibly applicable soliton control techniques, which are used to design dispersion and nonlinearity-managed systems, are proposed. The proposed techniques may find applications in soliton management communication links, like soliton control.In addition, two-soliton solution is obtained. With the dark two-soliton solution, the interaction between two solitons is discussed in the paper. The result may be of potential application in the ultralarge capacity transmission systems.
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Keywords:
- dark soliton /
- inhomogeneous optical fiber /
- soliton control /
- nonlinear Schrö /
- dinger equation
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[2] Kuznetsov E A, Rubenchik A M, Zakharov V E 1986 Phys. Rep. 142 103
[3] Frantzeskakis D J 2010 J. Phys. A 43 213001
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[5] Kivshar Y S, Agrawal G 2003 Optical Solitons: from Fibers to Photonic Crystals (San Diego: Academic Press)
[6] Li Z J, Hai W H, Deng Y 2013 Chin. Phys. B 22 090505
[7] Tang B, Li D J, Tang Y 2014 Chaos 24 023113
[8] Zhao W, Bourkoff E 1989 Opt. Lett. 14 703
[9] Zhao W, Bourkoff E 1992 JOSA B 9 1134
[10] Hamaide J P, Emplit P, Haelterman M 1991 Opt. Lett. 16 1578
[11] Uzunov I M, Gerdjikov V S 1993 Phys. Rev. A 47 1582
[12] Agrawal G P 2007 Nonlinear Fiber Optics (San Diego: Academic Press)
[13] Mollenauer L, Gordon J P 2006 Solitons in Optical Fibers (Burlington: Academic Press)
[14] Liu W J 2011 Ph. D. Dissertation (Beijing: Beijing University of Posts and Telecommunications) (in Chinese) [刘文军 2011 博士学位论文 (北京: 北京邮电大学)]
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[16] SerkinV N, Hasegawa A 2000 JETP Lett. 72 89
[17] SerkinV N, Hasegawa A 2002 IEEEJ. Sel. Top. Quant. 8 418
[18] LiL, Li Z H, Li S Q, Zhou G S 2004 Opt. Commun. 234 169
[19] HaoRY, Li L, Li Z H, Xue W R, Zhou G S 2004 Opt. Commun. 236 79
[20] HaoRY, Li L, Li Z H, Yang R C, Zhou G S 2005 Opt. Commun. 245 383
[21] Wang L Y, Li L, Li Z H, Zhou G S, Mihalache D 2005 Phys. Rev. E 72 036614
[22] SerkinV N, Hasegawa A, Belyaeva TL 2007 Phys. Rev. Lett. 90 113902
[23] Wang J F, Li L, Jia S T 2008 JOSAB 25 1254
[24] Zolotovskii I O, Novikov S G, Okhotnikov O G 2012 Opt. Spectr. 112 893
[25] Li S C, Wu L H, Lin M M, Duan W S 2007 Chin. Phys. Lett. 24 2312
[26] Sun Q H, Pan N, Lei M, Liu W J 2014 Acta Phys. Sin. 63 150506 (in Chinese) [孙庆华, 潘楠, 雷鸣, 刘文军 2014 63 150506]
[27] Luo H G, Zhao D, He X G 2009 Phys. Rev. A 79 063802
[28] Gao Y T, Tian B 2007 Phys. Lett. A 361 523
[29] Liu W J, Lei M 2013 J. Electromagnet. Wave. 27 884
[30] Liu W J, Tian B, Zhang H Q, Xu T, Li H 2009 Phys. Rev. A 79 063810
[31] Liu W J, Tian B, Zhang H Q, Li L L, Xue Y S 2008 Phys. Rev. E 77 066605
[32] Liu W J, Tian B, Zhang H Q 2008 Phys. Rev. E 78 066613
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[1] Hasegawa A, Tappert F 1973 Appl. Phys. Lett. 23 142
[2] Kuznetsov E A, Rubenchik A M, Zakharov V E 1986 Phys. Rep. 142 103
[3] Frantzeskakis D J 2010 J. Phys. A 43 213001
[4] Wang W B, Yang H, Tang P H, Han F 2013 Acta Phys. Sin. 62 184202 (in Chinese) [王威彬, 杨华, 唐平华, 韩芳 2013 62 184202]
[5] Kivshar Y S, Agrawal G 2003 Optical Solitons: from Fibers to Photonic Crystals (San Diego: Academic Press)
[6] Li Z J, Hai W H, Deng Y 2013 Chin. Phys. B 22 090505
[7] Tang B, Li D J, Tang Y 2014 Chaos 24 023113
[8] Zhao W, Bourkoff E 1989 Opt. Lett. 14 703
[9] Zhao W, Bourkoff E 1992 JOSA B 9 1134
[10] Hamaide J P, Emplit P, Haelterman M 1991 Opt. Lett. 16 1578
[11] Uzunov I M, Gerdjikov V S 1993 Phys. Rev. A 47 1582
[12] Agrawal G P 2007 Nonlinear Fiber Optics (San Diego: Academic Press)
[13] Mollenauer L, Gordon J P 2006 Solitons in Optical Fibers (Burlington: Academic Press)
[14] Liu W J 2011 Ph. D. Dissertation (Beijing: Beijing University of Posts and Telecommunications) (in Chinese) [刘文军 2011 博士学位论文 (北京: 北京邮电大学)]
[15] Serkin V N, Hasegawa A 2000 Phys. Rev. Lett. 85 4502
[16] SerkinV N, Hasegawa A 2000 JETP Lett. 72 89
[17] SerkinV N, Hasegawa A 2002 IEEEJ. Sel. Top. Quant. 8 418
[18] LiL, Li Z H, Li S Q, Zhou G S 2004 Opt. Commun. 234 169
[19] HaoRY, Li L, Li Z H, Xue W R, Zhou G S 2004 Opt. Commun. 236 79
[20] HaoRY, Li L, Li Z H, Yang R C, Zhou G S 2005 Opt. Commun. 245 383
[21] Wang L Y, Li L, Li Z H, Zhou G S, Mihalache D 2005 Phys. Rev. E 72 036614
[22] SerkinV N, Hasegawa A, Belyaeva TL 2007 Phys. Rev. Lett. 90 113902
[23] Wang J F, Li L, Jia S T 2008 JOSAB 25 1254
[24] Zolotovskii I O, Novikov S G, Okhotnikov O G 2012 Opt. Spectr. 112 893
[25] Li S C, Wu L H, Lin M M, Duan W S 2007 Chin. Phys. Lett. 24 2312
[26] Sun Q H, Pan N, Lei M, Liu W J 2014 Acta Phys. Sin. 63 150506 (in Chinese) [孙庆华, 潘楠, 雷鸣, 刘文军 2014 63 150506]
[27] Luo H G, Zhao D, He X G 2009 Phys. Rev. A 79 063802
[28] Gao Y T, Tian B 2007 Phys. Lett. A 361 523
[29] Liu W J, Lei M 2013 J. Electromagnet. Wave. 27 884
[30] Liu W J, Tian B, Zhang H Q, Xu T, Li H 2009 Phys. Rev. A 79 063810
[31] Liu W J, Tian B, Zhang H Q, Li L L, Xue Y S 2008 Phys. Rev. E 77 066605
[32] Liu W J, Tian B, Zhang H Q 2008 Phys. Rev. E 78 066613
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