一种光折变扩散—漂移机制表面波的数值分析方法
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摘要
非线性光学是研究介质在强相干光作用下产生的非线性现象及其应用,非线性光学发展成为今天这样一门重要学科,应该说是从激光出现后才开始的。光致折射率变化效应,简称光折变效应,是指电光材料的折射率在空间调制光强或非均匀光强的辐照下发生了变化。光折变非线性光学领域的研究是沿两条途径发展的,一是研制高性能高质量的光折变材料,另一途径是研究光折变晶体的各种非线性特性及其在光学存储、光学信息处理和光计算机中的应用,还有光孤子通信,光开关。
现阶段,国内外对光折变晶体非线性表面波的研究主要集中于：扩散机制下的光折变晶体非线性表面波和扩散——漂移机制下的光折变晶体非线性表面波。文章从光折变表面波发生机制的基础上进行研究。首先是对光折变非线性表面波的形成机制加以分析,其次对扩散——漂移机制进行MATLAB模拟,模拟以实现光折变非线性表面波的产生条件,模拟实验所用的是材料是SBN晶体的物理和光学参数。重点分析了基于孤子自弯曲动态过程的光折变非线性表面波的非线性薛定谔方程,对扩散——漂移机制下的非线性薛定谔方程进行数值方法的求解,得到光折变非线性表面波方程的在数值方法下的解,并对得到的数值解进行说明和分析。
Nonlinear optics is to study the role of media in a strong coherent light and its effect of nonlinear phenomena and its application. It should be said that after the laser had been invented, the nonlinear optics has developed into such an important subject. Photo-induced refractive index change effect, called photorefractive effect for short, it refers to the electro-optic refractive index modulation in space or non-uniform light intensity of the radiation intensity, the occurrence of corresponding changes. Photorefractive nonlinear optics research in the field is developing into two ways, first, high quality development of photorefractive materials, another approach is to study the photorefractive crystal and its nonlinear characteristics in optical storage, optical information processing and optical computer application. And also optical soliton communication, optical switching.
At present. The research of photorefractive nonlinear crystal in demestic and abroad has focused on:the nonlinear surface wave under diffusion mechanism and diffusion-drift mechanism of nonlinear surface wave in the photorefractive crystal. In this article the further study is base on the mechanism of photorefractive surface waves. First, the analyze of formation mechanism of the photorefractive nonlinear surface wave, from the experiments we can verify whether the photorefractive nonlinear surface waves real indeed. Second, MATLAB simulation is based on the diffusion-drift mechanism, the simulation in order to achieve generation conditions of the photorefractive nonlinear surface wave, in the simulation we use SBN crystal material is the physical and optical parameters. Analyzed the dynamic process is based on the nonlinear Schrodinger equation about soliton self-bending photorefractive nonlinear surface waves, and diffusion-drift mechanism of nonlinear Schrodinger equation for solving with the numerical method. And obtain nonlinear photorefractive surface wave equation in the numerical solution, and gets the description and analysis of numerical solutions.
现阶段,国内外对光折变晶体非线性表面波的研究主要集中于：扩散机制下的光折变晶体非线性表面波和扩散——漂移机制下的光折变晶体非线性表面波。文章从光折变表面波发生机制的基础上进行研究。首先是对光折变非线性表面波的形成机制加以分析,其次对扩散——漂移机制进行MATLAB模拟,模拟以实现光折变非线性表面波的产生条件,模拟实验所用的是材料是SBN晶体的物理和光学参数。重点分析了基于孤子自弯曲动态过程的光折变非线性表面波的非线性薛定谔方程,对扩散——漂移机制下的非线性薛定谔方程进行数值方法的求解,得到光折变非线性表面波方程的在数值方法下的解,并对得到的数值解进行说明和分析。
Nonlinear optics is to study the role of media in a strong coherent light and its effect of nonlinear phenomena and its application. It should be said that after the laser had been invented, the nonlinear optics has developed into such an important subject. Photo-induced refractive index change effect, called photorefractive effect for short, it refers to the electro-optic refractive index modulation in space or non-uniform light intensity of the radiation intensity, the occurrence of corresponding changes. Photorefractive nonlinear optics research in the field is developing into two ways, first, high quality development of photorefractive materials, another approach is to study the photorefractive crystal and its nonlinear characteristics in optical storage, optical information processing and optical computer application. And also optical soliton communication, optical switching.
At present. The research of photorefractive nonlinear crystal in demestic and abroad has focused on:the nonlinear surface wave under diffusion mechanism and diffusion-drift mechanism of nonlinear surface wave in the photorefractive crystal. In this article the further study is base on the mechanism of photorefractive surface waves. First, the analyze of formation mechanism of the photorefractive nonlinear surface wave, from the experiments we can verify whether the photorefractive nonlinear surface waves real indeed. Second, MATLAB simulation is based on the diffusion-drift mechanism, the simulation in order to achieve generation conditions of the photorefractive nonlinear surface wave, in the simulation we use SBN crystal material is the physical and optical parameters. Analyzed the dynamic process is based on the nonlinear Schrodinger equation about soliton self-bending photorefractive nonlinear surface waves, and diffusion-drift mechanism of nonlinear Schrodinger equation for solving with the numerical method. And obtain nonlinear photorefractive surface wave equation in the numerical solution, and gets the description and analysis of numerical solutions.
引文
[1]李淳飞著《非线性光学》第二版,北京,电子工业出版社,2009，2
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[2]范琦康,吴存恺,毛少卿编著《非线性光学》第一版,江苏扬中,江苏科学技术出版社,电子工业出版社,1989,2
[3]李铭华,杨春晖,徐玉恒等著《光折变晶体材料科学导论》第一版,北京,科学出版社2003,iii
[4]Victor Aleshkevich, Yaroslav Kartashov, and Alexey Egorov
[5]张天浩,李坤,邵伟伟,宋伟,张博,王秉慧,胡志健,任相魁,朱宝刚,张力舟,许京军
[6]姜璐.非线性偏微分方程精确解与孤子相互作用问题的研究.北京邮电大学硕士毕业论文,2007,25
[7]李淳飞著《非线性光学》第二版,北京,电子工业出版社,2009，157-161
[8]刘思敏,郭儒,许京军,《光折变非线性光学及其应用》第一版,北京,科学出版社.2004,1,i
[9]Agraval,Govind P,
[10]李铭华,杨春晖,徐玉恒等著《光折变晶体材料科学导论》第一版,北京,科学出版社2003,2-8
[11]钱士雄,王恭明编著《非线性光学》第一版,上海,复旦大学出版社,2001，342-343
[12]Richard Fitzpatrick
[13]刘思敏,郭儒,许京军,《光折变非线性光学及其应用》第一版,北京,科学出版社.2004,1,2-8
[14]Ma SH (Ma Song-Hua), Fang JP (Fang Jian-Ping)
[15]N. V. Kukhtarev, V. B. Markov, S. G Odulov et al..
[16]王金来《光折变效应的物理过程及带输运模型》运城高等专科学校学报2000年18卷第03期
[17]M. Tiemann, T. Halfmann, T. Tschudi
[18]Carruthers J R, Grasso M J. Phase Equilibria Relations in the Ternary System BaO-SrO-Nb2O5. Electrochem. Soc.1970,117:1426
[19]刘世春《单模光纤色散与衰减系数的关系》光纤与电缆及其应用技术,2001年第05期
[20]Gerald Recktenwald,伍卫国,方群,张辉等译
[21]E. Alvarado-Mendez, J. A. Andrade-Lucio. et al.
[22]李晖,谢树森,陆祖康《色散、群速与群折射率》光子学报,1999年12期,2
[23]蒋志,范崇澄《光纤通信系统中色散与自相位调制作用下的频域传递函数》光学学报,2001年11期,1
[24]He X, Xie K, Xiang A
[26]石顺祥、陈国夫、赵卫、刘继芳《非线性光学》第一版,西安,西安电子科技大学出版社.348
[27]He JL, Yi J, He SL
[28]H.Gilles,S.Girard, and J.Hamel,Opt. Lett.27(2002) 1421.
[29]D.N. Christodoulides and M.I. Carvalho, Opt. Lett.19(1994)1714
[30]M.I. Carvalho,S.R. Singh,and D.N. Christodoulides,Opt. Comm.120(1995) 311
[31]M.. Seguev, G.C. Valley,B. Crosigniani, P. Diporto.and A.Yariv,phys. Rev.Lett.73(1994)3211
[32]E. Alvarado-Mendez, G. E. Torres-Ciseneros, M.Torres-Ciseneros.
[34]E. Alvarado-Mendez, G E. Torres-Ciseneros, M.Torres-Ciseneros.< Internal reflection of one-dimensional bright spatial solitons>. Optical and Quantum Electronics,1998,30:689
[35]Mark Cronin-Golomb.
[36]阎晓娜,董良威《光折变铌酸锂晶体电光、压电效应研究》上海大学学报(自然科学版)2005年03期,014
[37]王志斌,李志全《光孤子传输演化的分步傅里叶法研究》应用光学,2007-28-1
[38]A.V. Khomenko, Ervin Nippolainen, Alexei A. Kamshilin et al. Leaky photorefractive surface waves in Bil2TiO20 and Bil2SiO20 Crystals. Optics Communications.1998,150:175
[39]Q.Chang,E. Jia, and W.Sun,J. Comput.Phys.148.397(1999)
[40]Li Hua 1 Zhou Weikui 1 Deng Peizhi 2
[41]R. Ratowsky and J. A. Fleck, Opt.Lett.16,787(1991)
[42]Y.Chung and N. Dagli,IEEE J. Quantum Electron.26,1335(1990); IEEE J.Quantum Electron.27,2296(1991)
[43]P. Kacznuu'shi and P.E. Lagasse, Electron.Lett.24,675(1988)
[44]J. W. Cooley and J. W. Tukey,Math. Comput.19,297(1965)
[45]G. H. Weiss and A. A. Maradudin,J. Math. Phys.3,771(1962)
[46]M. Lax, J. H. Batteh, and G. P. Agrawal,J. Appl. Phys.52,109 (1981)
[47]B. Hermansson, D. Yevick, and P. Danielsen, IEEE J. Quantum Electron.19,1246(1983)
[48]A. Hasegawa and E Tappert, Appl. Phys. Lett.23,142(1973)
[49]R. H. Hardin and E D. Tappen, SIAM Rev. Chronicle 15,423(1973)
[50]D. Yevick and B. Hermansson, J. Appl. Phys.59,1769(1986);IEEEJ. Quan tum Electron.25,221(1989)