(1+2)维各向同性介质中的旋转椭圆空间光孤子

余亚东; 梁果; 任占梅; 郭旗

doi:10.7498/aps.64.154202

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摘要

从(1+2)维非局域非线性薛定谔方程出发, 通过坐标变换得到了旋转坐标系下的非局域非线性薛定谔方程. 假设响应函数为高斯型, 用虚时间法数值求解了旋转坐标系下的非局域非线性薛定谔方程的静态孤子解, 迭代出了不同非局域程度条件下的静态椭圆孤子数值解. 最后采用分步傅里叶算法, 以迭代的孤子解作为初始输入波形, 模拟了在不同的非局域程度条件下, (1+2)维椭圆空间光孤子的旋转传输特性. 强非局域时, 椭圆光孤子的长轴方向和短轴方向波形都是高斯型, 其他的非局域程度下, 不是高斯型. 由此表明：(1+2)维椭圆光孤子对非局域程度依赖性很强. 旋转角速度和功率均与非局域程度以及孤子的椭圆度有关.

关键词:

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

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

参考文献

[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]

施引文献

[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]

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(1+2)维各向同性介质中的旋转椭圆空间光孤子

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

基金项目:

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

收稿日期: 2014-11-27

修回日期: 2015-02-13

刊出日期: 2015-08-05

摘要: 从(1+2)维非局域非线性薛定谔方程出发, 通过坐标变换得到了旋转坐标系下的非局域非线性薛定谔方程. 假设响应函数为高斯型, 用虚时间法数值求解了旋转坐标系下的非局域非线性薛定谔方程的静态孤子解, 迭代出了不同非局域程度条件下的静态椭圆孤子数值解. 最后采用分步傅里叶算法, 以迭代的孤子解作为初始输入波形, 模拟了在不同的非局域程度条件下, (1+2)维椭圆空间光孤子的旋转传输特性. 强非局域时, 椭圆光孤子的长轴方向和短轴方向波形都是高斯型, 其他的非局域程度下, 不是高斯型. 由此表明：(1+2)维椭圆光孤子对非局域程度依赖性很强. 旋转角速度和功率均与非局域程度以及孤子的椭圆度有关.

关键词:

(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).

Received Date: 27 November 2014

Accepted Date: 13 February 2015

Published Online: 05 August 2015

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.

Keywords:

nonlocal nonlinear Schrodinger equation /
spiraling elliptic solitons /
critical power /
rotation velocity

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