Hermite- elliptical Gaussian spatial optical soliton in strongly nonlocal media

Abstract

Abstract:

The propagation properties of paraxial Hermite-elliptical Gaussian light beam in a strongly nonlocal nonlinear media are studied. As the characteristic width of response function is much bigger than the beam width, the nonlocal nonlinear Schrödinger equation is simplified and the strongly nonlocal model with elliptic-symmetry medium response function is obtained. Using method of separation of variables, the analytic solution of Hermite- elliptical Gaussian spatial optical soliton and the conditions in which it forms are also derived. Further studies point out that with increasing of rank of Hermite- elliptical Gaussian spatial optical soliton, the light beam width increases, the degree of non-locality of medium relatively weakens; To get high-rank elliptical Gaussian spatial optical soliton, the degree of non-locality of nonlocal medium must be raised. The lowest-rank Hermite- elliptical Gaussian spatial optical soliton is just elliptical Gaussian spatial optical soliton.

Key words: nonlinear optics, Hermite-elliptical Gaussian spatial optical soliton, method of separation of variables, strongly nonlocal medium with elliptically symmetric response

CLC Number:

O437

WANG Qing, WANG Xing-hua, LI Dong-bo, LIU Meng-lian, LUO Xing-long. Hermite- elliptical Gaussian spatial optical soliton in strongly nonlocal media[J]. J4, 2012, 29(3): 349-352.

References

[1] Snyder A W , Mitchell D J. Accessible solitons[J].Science,1997, 276: 1538-1541.
[2] Peccianti M, Conti C, Assanto G，et al. All-optical switching and logic gating with spatial solitons in liquid crystals[J].Appl.Phys.Lett.,2002,81(18):3335-3337.
[3] Long Xuewen, Hu Wei, Guo Qi ,et al. Theoretical investigation of propagation of nonlocal spatial soliton in nematic liquid crystals[J]. Acta Physica Sinica(物理学报),2007,56 (3):1397-1403 (in Chinese). [龙学文, 胡巍，张涛,等. 向列相液晶中强非局域空间光孤子传输的理论研究[J]. 物理学报，2007, 56 (3): 1397-1403.]
[4] Rotschild C, Cohen O, Manela O，et al. Solitons in Nonlinear Media with an Infinite Range of Nonlocality: First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons[J]. Phys.Rev.Lett.2005，95（21）：213904-1～4.
[5] Huang Chunfu. Nonlocal polychromatic vector solitons[J]. Chinese Journal of Quantun Electronics(量子电子学报),2011,28（2）:168-171(in chinese). [黄春福. 非局域多色矢量孤子[J]. 量子电子学报, 2011, 28（2）:168-171]
[6] Bai Dongfeng, Guo Qi, Hu Wei. Variational investigation of Hermite-Gaussian beam propagation in nonlocal Kerr media[J]. Acta Physica Sinica(物理学报),2008, 57（9）: 5684-5689 (in Chinese) . [白东峰，郭旗，胡巍.非局域克尔介质中厄米高斯光束传输特性的变分研究.[J].物理学报, 2008, 57（9） 5684-5689]
[7] Zhang Xiaping, Guo Qi. Analytical solution in the Hermite Gaussian form of the beam propagating in the strong nonlocal media[J].Acta Physica Sinica(物理学报),2005,54(7):3178-3182 (in Chinese). [张霞萍, 郭旗. 强非局域非线性介质中光束传输的厄米高斯解[J] . 物理学报, 2005, 54( 7) :3178-3182.]
[8] Dai Jihui,Guo Qi. Optical beams in nonlocal nonlinear media: A variational solution of the Laguerre-Gauss form[J]. Acta Physica Sinica(物理学报), 2008,57(8):5001-5006 (in Chinese) . [戴继慧，郭旗. 非局域非线性介质中光束传输的拉盖尔-高斯变分解[J]. 物理学报, 2008,57(8) : 5001～5006.]
[9] Zhang Xiaping, Liu Youwen. Analytical solution in the Ince2Gaussian form of the beam propagating in the strong nonlocal media[ J] .Acta Physica Sinica(物理学报),2009,58(12):8332-8338 (in Chinese). [张霞萍，刘友文，强非局域非线性介质中光束传输的Ince-Gauss解[J]. 物理学报, 2009,58(12) : 8332～ 8338]
[10] Deng D M, ZhaoX, Guo Q, et al. Hermite–Gaussian breathers and solitons in strongly nonlocal nonlinear media[J]. J.Opt. Soc. Am. B, 2007, 24 (9):2537-2544.
[11] Hutsebaut X, Cambournac C, Haelterman M. et al. Singlecomponent higher-order mode solitons in liquid crystals [J]. Phys. Rev. E, 2004, 69(1): 016602-1～9.
[12] Wang Xinghua, Guo Qi .The propagation properties of the elliptically Gaussian beam in strongly nonlocal nonlinear media [J].Acta Physica Sinica(物理学报), 2005,54(7): 3183-3188 (in Chinese). [王形华，郭旗.椭圆高斯光束在强非局域非线性介质中的传输特性[J].物理学报,2005,54（7）: 3183～3188.]
[13] Qin Xiaojuan,Guo Qi, Hu Wei, lan Sheng.Strongly nonlocal elliptical spatial optical soliton[J].Acta Physica Sinica(物理学报),2006,55（3）:1237-1243(in Chinese). [秦晓娟，郭旗.椭圆强非局域空间光孤子[J].物理学报,2006,55（3）:1237～1243]
[14] Carmel R, Oren C. Solitons in Nonlinear Media with an Infinite Range of Nonlocality: First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons[J] phys.Rev.lett， 2005，95（21）：3904～3908
[15] Guo Qi, Luo B, Yi F,et al. Large phase shift of nonlocal optical spatial solitons [J]. Phys. Rev. E, 2004, 69(1): 016602-1~9
[16] Xie Yiqun ,Guo Qi. Interaction between optical spatial solitons in nonlocal Kerr media[J] .Acta Physica Sinica(物理学报),2004,53（9）: 3020～3024 (in Chinese) . [谢逸群，郭旗.非局域克尔介质中空间光孤子的相互作用[J].物理学报,2004,53（9）: 3020～3024.]
[17] Lu Yaxiong, Yu Xuecai, Zhang Xiaoxia. Laser Physics(激光物理) [M]. Beijing: Beijing University of Posts and Telecommunications Press，2005: 21 (in Chinese). [卢亚雄,余学才,张晓霞.激光物理[M].北京：北京邮电大学出版社，2005: 21.]
[18] Li Shaohua,Yang Zhenjun, Hu Wei, et al. Numerical study of Hermite-Gaussian beams in nonlocal thermal media[J]. Acta Physica Sinica . 2011, 60（2）: 024214-1～10(in Chinese). [李少华，杨振军，胡巍，等.厄米-高斯光束在热非局域介质中传输的数值模拟研究[J].物理学报,2011,60（2）: 024214-1～10.]