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从非线性薛定谔方程和热扩散的泊松方程出发, 采用分步傅里叶算法以及多重网格法, 对两束光在(1+2)维热非局域介质中的相互作用规律进行了研究.结果表明, 在传输过程中, 两束光以互相缠绕的方式前进.如果选择适当的入射功率、光束间距和倾斜参量, 两束光的传输轨迹在(X, Y)平面上的投影近似为圆形; 而在保持入射功率和倾斜参量的大小不变的情况下, 如果仅改变光束入射时的间距, 两束光中心的轨迹在(X, Y) 平面上的投影依然近似成圆形. 由于在热非局域介质中存在特殊的非线性折射率形成机制, 所以尽管两束光离边界很远, 但是仍然能够感受到边界的影响; 在输入光整体偏离介质中心或两光束倾斜参量的绝对值不相等时, 它们整体做振荡传输.According to the nonlinear Schrödinger equation and Poisson equation of thermal diffusion, we investigate the interaction of double beams in (1+2)-dimension thermal nonlocal medium, using the slip-step Fourier algorithm and multi-grid method. The results show that the two beams intertwine with each other during propagation. If the power and the tilt parameter are appropriate, the projections of the trajectories of the beams in (X, Y) plane are approximately circle, even if the incident distance between the beams is changed. Because of the strongly nonlocal property of thermal medium, the influences of boundaries and initial transverse momentum can be felt when beams are far from the boundaries; there will be an oscillatory propagation when the mass center of the input field deviates from sample center or the initial transverse momentum is unequal to zero.
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Keywords:
- double beams /
- thermal nonlocal media /
- interaction
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[21] Teukolsky S A, Vetterling W T, Flannery B P (Translated by Fu Z Y, Zhao M N, Ding Y) 1995 Numerical Recips in C: The Art of Scientific Computing (Beijing: Electronic Industry Press) pp734-749 (in Chinese) [Teukosky S A, Vetterling W T, Flannery B P 著, 傅祖芸, 赵梅娜, 丁 岩 译 1995 C语言数值算法程序大全 (北京: 电子工业出版社) 第734–749页]
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[1] Snyder A W, Mitchell D J 1997 Science 276 1538
[2] Guo Q, Luo B, Yi F H, Chi S, Xie Y Q 2004 Phys. Rev. E 69 016602
[3] Yang Z J, Li S H, Lu D Q, Hu W 2010 Acta Phys. Sin. 59 4707 (in Chinese) [杨振军, 李少华, 陆大全, 胡巍 2010 59 4707]
[4] Yang Z J, Lu D Q, Hu W, Zheng Y Z, Gao X H 2010 Chin. Phys. B 19 124212
[5] Zheng Y J, Xuan W T, Lu D Q, Ouyang S G, Hu W, Guo Q 2010 Acta Phys. Sin. 59 1075 (in Chinese) [郑亚建, 宣文涛, 陆大全, 欧阳世根, 胡巍, 郭旗 2010 59 1075]
[6] Chen L X, Lu D Q, Hu W, Yang Z J, Cao W W, Zheng R, Guo Q 2010 Acta Phys. Sin. 59 327 (in Chinese) [陈利霞, 陆大全, 胡巍, 杨振军, 曹伟文, 郑睿, 郭旗 2010 59 327]
[7] Liang Y B, Zheng Y J, Yang P B, Cao L G, Lu D Q, Hu W, Guo Q 2008 Acta Phys. Sin. 57 5690 (in Chinese) [梁炎斌, 郑亚建, 杨平保, 曹龙贵, 陆大全, 胡 巍, 郭 旗 2008 57 5690]
[8] Jiang Q, Shou Q, Zheng Y J, Liang Y B, Hu W, Guo Q 2010 Acta Phys. Sin. 59 329 (in Chinese) [江群, 寿倩, 郑亚建, 梁炎斌, 胡巍, 郭旗 2010 59 329]
[9] Lu D Q, Hu W 2009 Phys. Rev. A 80 053818
[10] Lu K Q, Li K H, Zhao W, Zhang Y Q, Zhang M Z, Zhang Y H, Cheng G H, Li K H 2010 Chin. Phys. B 19 024211
[11] Rotschild C, Segev M, Xu Z, Kartashov Y V, Torner L, Cohen O 2006 Opt. Lett. 31 3312
[12] Dreischuh A, Neshev D N, Petersen D E, Bang O, Krolikowski W 2006 Phys. Rev. Lett. 96 043901
[13] Rotschild C, Cohen O, Manela O, Segev M, Carmon T 2005 Phys. Rev. Lett. 95 213904
[14] Alfassi B, Cohen O, Manela O, Segev M 2007 Opt. Lett. 32 154
[15] Rotschild C, Alfassi B, Cohen O, Segev M 2006 Nature Phys. 2 769
[16] Alfassi B, Rotschild C, Manela O, Segev M 2007 Phys. Rev. Lett. 98 213901
[17] Barak A, Rotschild C, Alfassi B, Segev M, Christodoulides D N 2007 Opt. Lett. 32 2450
[18] Li S H, Yang Z J, Lu D Q, Hu W 2011 Acta Phys. Sin. 60 024214 (in Chinese) [李少华, 杨振军, 陆大全, 胡巍 2011 60 024214]
[19] Iturbe Castillo M D, Stepanov S, Sanchz-Mondragon J J 1996 Opt. Lett. 21 1622
[20] Agrawal G P (Translated by Jia D F, Yu Z H, Tan B, Hu Z Y) 2002 Nonlinear Fiber Optics and Application of Nonlinear Fiber Optic (Beijing: Electronic Industry Press) pp34, 35 (in Chinese) [ Agrawal G P 著, 贾东方, 余震虹, 谈 斌, 胡智勇 译 2002 非线性光纤光学原理及应用 (北京: 电子工业出版社) 第34, 35页]
[21] Teukolsky S A, Vetterling W T, Flannery B P (Translated by Fu Z Y, Zhao M N, Ding Y) 1995 Numerical Recips in C: The Art of Scientific Computing (Beijing: Electronic Industry Press) pp734-749 (in Chinese) [Teukosky S A, Vetterling W T, Flannery B P 著, 傅祖芸, 赵梅娜, 丁 岩 译 1995 C语言数值算法程序大全 (北京: 电子工业出版社) 第734–749页]
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