非局域表面暗孤子及其稳定性分析

高星辉; 唐冬; 张承云; 郑晖; 陆大全; 胡巍

doi:10.7498/aps.63.024204

摘要

非局域体介质中的暗孤子及表面亮孤子由于在光通信领域的潜在应用而受到极大关注，然而到目前为止却没有对非局域表面暗孤子的研究. 在线性介质和非局域非线性介质的分界面上，数值模拟得到了1+1维非局域基态和二阶表面暗孤子，研究了它们的波形与传播常数和介质非局域程度的关系，基于它们的稳定性分析进行了理论推导和数值模拟. 稳定性分析结果表明：1+1维非局域基态表面暗孤子在其存在区域总是稳定的，而二阶表面暗孤子是区域不稳定的，其不稳定区域的宽度与传播常数以及介质的非局域程度有关系，且受传播常数的影响更大. 加噪声的初始输入传输图验证了稳定性分析结果的正确性.

关键词:

非局域 /
表面暗孤子 /
稳定性

Abstract

Due to their future applications in optical communication, nonlocal dark solitons in bulk medium and surface bright solitons have received much attention recently. However, nonlocal surface dark solitons have not been investigated till now. In this paper, 1+1 dimensional nonlocal fundamental and second-order surface dark solitons have been found numerically at the interface between thermal nonlinear medium and linear medium. The relation between the wave shape of nonlocal surface dark soliton and propagation constant and nonlocality degree is investigated. Moreover, the stability of them is analyzed theoretically. The numerical simulation results show that 1+1 dimensional nonlocal fundamental surface dark Solitons are always stable in the domain of their existence, while second-order surface dark solitons are oscillatorily unstable and the width of unstable domain depends more greatly on propagation constant than nonlocality degree of nonlocal nonlinear medium. The figure showing the propagation, with the initial input of noise added, confirms the correctness of stability analysis results.

Keywords:

作者及机构信息

1.
广州大学机械与电气工程学院, 广州 510006;

2.
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 510631

基金项目: 国家自然科学基金（批准号：11174090，11174091）资助的课题.

Authors and contacts

1.
College of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, China;

2.
Guangdong Key Laboratory of Micro-Nano Photonic Materials and Devices, South China Normal University, Guangzhou 510631, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11174090, 11174091).

参考文献

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[11]	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]
[12]	Dreischuh A, Neshev D N, Petersen D E, Bang O, Krolikowski W 2006 Phys. Rev. Lett. 96 043901
[13]	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]
[14]	Stegeman G I, Seaton C T 1985 J. Appl. Phys. 58 R57
[15]	Mihalache D, Bertolotti M, Sibilia C 1989 Prog. Opt. 27 229
[16]	Alfassi B, Rotschild C, Manela O, Segev M, Christ-odoulides D N 2007 Phys. Rev. Lett. 98 213901
[17]	Alfassi B, Rotschild C, Manela O, Segev M 2009 Phys. Rev. A 80 041808
[18]	Ye F, Kartashov Y V, Torner L 2008 Phys. Rev. A 77 033829
[19]	Kartashov Y V, Vysloukh V A, Torner L 2009 Opt. Lett. 34 283
[20]	Kartashov Y V, Vysloukh V A, Torner L 2007 Opt. Express 15 16216
[21]	Kartashov Y V, Ye F, Vysloukh V A, Torner L 2007 Opt. Lett. 32 2260
[22]	Skinner S R, Andersen D R 1991 J. Opt. Soc. Am. B 8 759
[23]	Chen Y J 1992 Phys. Rev. A 45 4974
[24]	Yang Z J, Ma X K, Lu D Q, Zheng Y Z, Gao X H, Hu W 2011 Opt. Express 19 4890

施引文献

[1]	Mitchell M, Segev M, Christodoulides D N 1998 Phys. Rev. Lett. 80 4657
[2]	Mamaev A V, Zozulya A A, Anderson D Z, Saffman M 1997 Phys. Rev. A 56 R1110
[3]	Peccianti M, Brzdakiewicz K A, Assanto G 2002 Opt. Lett. 27 1460
[4]	Peccianti M, Conti C C, Assanto G 2005 Opt. Lett. 30 415
[5]	Derrien F, Henninot F, Warenghem M, Abbate G 2000 J. Opt. A: Pure Appl. Opt. 2 332
[6]	Litvak A G, Mironov V A, Fraiman G M, Yunakovskii A D 1975 Sov. J. Plasmas Phys. 1 31
[7]	Krolikowski W, Bang O, Nikolov N I, Neshev D, Wyller J, Rasmussen J J, Edmundson D 2004 J. Opt. B 6 S288
[8]	Nikolov N I, Neshev D, Krolikowski W, Bang O, Rasmussen J J, Christiansen P L 2004 Opt. Lett. 29 286
[9]	Ouyang S, Guo Q 2009 Opt. Express 17 5170
[10]	Armaroli A, Trillo S, Fratalocchi A 2009 Phys. Rev. A 80 053803
[11]	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]
[12]	Dreischuh A, Neshev D N, Petersen D E, Bang O, Krolikowski W 2006 Phys. Rev. Lett. 96 043901
[13]	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]
[14]	Stegeman G I, Seaton C T 1985 J. Appl. Phys. 58 R57
[15]	Mihalache D, Bertolotti M, Sibilia C 1989 Prog. Opt. 27 229
[16]	Alfassi B, Rotschild C, Manela O, Segev M, Christ-odoulides D N 2007 Phys. Rev. Lett. 98 213901
[17]	Alfassi B, Rotschild C, Manela O, Segev M 2009 Phys. Rev. A 80 041808
[18]	Ye F, Kartashov Y V, Torner L 2008 Phys. Rev. A 77 033829
[19]	Kartashov Y V, Vysloukh V A, Torner L 2009 Opt. Lett. 34 283
[20]	Kartashov Y V, Vysloukh V A, Torner L 2007 Opt. Express 15 16216
[21]	Kartashov Y V, Ye F, Vysloukh V A, Torner L 2007 Opt. Lett. 32 2260
[22]	Skinner S R, Andersen D R 1991 J. Opt. Soc. Am. B 8 759
[23]	Chen Y J 1992 Phys. Rev. A 45 4974
[24]	Yang Z J, Ma X K, Lu D Q, Zheng Y Z, Gao X H, Hu W 2011 Opt. Express 19 4890

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