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1、赣南师范学院 单位代码：10418硕 士 学 位 论 文论文题目：非局域空间损耗光孤子的传输特性及其相互作用 作者姓名 指导教师 学科(专业) 光 学 所在学院 物理与电子信息学院 提交日期 二 0 一一年四月二十日 赣南师范学院硕士学位论文i独创性声明本人声明所呈交的学位论文是本人在导师指导下进行的研究工作及取得的研究成果。除了文中特别加以标注和致谢的地方外，论文中不包含其他人已经发表或撰写过的研究成果，也不包含为获得赣南师范学院或其他教育机构的学位或证书而使用过的材料。与我一同工作的同志对本研究所做的任何贡献均已在论文中作了明确的说明并表示谢意。学位论文作者签名： 签字日期： 年 月 日学
2、位论文版权使用授权书本学位论文作者完全了解赣南师范学院有关保留、使用学位论文的规定，有权保留并向国家有关部门或机构送交论文的复印件和磁盘，允许论文被查阅和借阅。本人授权赣南师范学院可以将学位论文的全部或部分内容编入有关数据库进行检索，可以采用影印、缩印或扫描等复制手段保存、汇编学位论文。（保密的学位论文在解密后适用本授权书）学位论文作者签名： 导师签名：签字日期： 年 月 日 签字日期： 年 月 日摘 要赣南师范学院硕士学位论文ii现今，关于非局域非线性介质中光孤子的研究已经引起了人们的极大兴趣，在理论研究和实验研究所得结果都表明：非局域空间光孤子比局域孤子有着更为丰富的研究内容和广泛的潜在应
3、用价值。空间光束在非局域非线性介质中的传输满足非局域非线性薛定谔方程(Nonlocal Nonlinear Schrdinger Equation 简写为 NNLSE，下同)。本文针对弱非局域介质中 1+2 维 sech 型损耗空间光孤子以及对强非局域介质中损耗空间光孤子和 1+1 维高斯型损耗空间双光孤子相互作用分别进行研究并通过数值模拟的方法，得到了含小损耗情形下光束各参量的演化规律。在研究含有小损耗且具有 e 指数响应的弱非局域非线性介质中 1+2 维 sech 型光束传输时，得到了光束各参量的演化方程及演化规律和一个临界功率；并且在介质损耗足够小的前提下，得到了一个除了产生相移外，束宽
4、大小可近似保持不变的 1+2 维 sech 型损耗空间光孤子。在研究含小损耗椭圆对称强非局域非线性介质中傍轴椭圆高斯光束传输时，得到了光束各参量的演化方程和束宽的演化规律，当初始功率等于临界功率，并且介质损耗足够小时，傍轴椭圆高斯光束在传输中，其束宽持续缓慢展宽，得到了椭圆高斯型损耗空间光孤子。对 1+1 维高斯型单束损耗空间光孤子作了细致的分析后，得到其参量演化方程和光束束宽的演化规律，当光束从光腰处入射，且初始功率等于临界功率，并且损耗也足够小时，1+1 维高斯型单光束束宽将呈现非常缓慢的展宽过程，当 1+1 维高斯型单光束传输距离不远时，可以近似的得到其束宽缓慢展宽的准空间光孤子损耗光孤
5、子；当光束初始功率小于临界功率时，束宽将按准余弦函数作周期性展宽变化；当光束初始输入功率大于临界功率时，束宽将按准余弦函数先作周期压缩性变化再过度到作周期性展宽变化。对强非局域非线性介质中 1+1 维高斯光束在含小损耗时的相互作用进行了研究，得到了含小损耗强非局域非线性介质中 1+1 维高斯型双光束传输的模型，在此基础上运用解析的方法研究了双光束传输的演化规律，得到了准双孤子解；经过进一步分析发现在传输过程中两光束的中心轨迹呈艾里函数形式相互吸引；当损耗逐渐增大，传输的距离逐渐加长时，两光束的光强将逐渐减弱，相互吸引能力变小，两光束中心的轨迹越来越远离传输轴，两光束中心之间的距离越来越大。关键
6、词: 非线性光学；非局域介质；小损耗；损耗空间光孤子；孤子相互作用AbstractNowadays, more and more people are attracted to research the optical soliton in the nonlocal nonlinear 赣南师范学院硕士学位论文iiimedium. The results from experiment and theory studies show that: compared with local soliton, nonlocal spatial soliton has more research con
7、tents and wider potential application value. The propagation of the spatial beams in nonlocal nonlinear medium satisfied the nonlocal nonlinear Schrdinger equation (NNLSE). This dissertation would focus on the propagation properties of 1+2D Sech-type lossy spatial solitons in weak non-local medium a
8、nd the transmission characteristics of the lossy spatial solitons in strong nonlocal medium, numerically analyze the mutual reaction between the two beams both of which are 1+1D Gaussian-type spatial solitons.The evolution equations and rules of each beam parameter and critical power are obtained, w
9、hen analyzing the 1+2D Sech-type beams propagation in the weak nonlocal nonlinear medium with small loss and e index response. Furthermore, if the mediums loss is small enough, 1+2D Sech-type lossy spatial solitons which has a phase shift and remains almost the same beam width.The evolution equation
10、s of each beam parameter and the evolution rules of the beam width are gained, when researching the paraxial elliptical Gaussian type beams propagation in elliptical symmetry strong nonlocal nonlinear medium with small loss. The results show that: the beam width gets wide continuously and slowly, wh
11、en initial power equals critical power and the paraxial elliptical Gaussian beam propagates in medium with small enough loss, that is, the elliptical Gaussian type lossy spatial soliton is obtained in a way. Based on the detailed analysis of the 1+1D Gaussian type single beam loss spatial soliton, t
12、he evolution equations of each parameter and the evolution rules of the light beam width are obtained. When the light beam incidents at the light beam waist in the medium with small enough loss, and the initial power equals the critical power, the 1+1D Gaussian type single light beams beam width sho
13、ws a very slow getting-wide process. When the 1+1D Gaussian type single light beam propagates in a short distance, the quasi-spatial-optical-solition which is a lossy optical soliton whose beam width gets wide slowly is obtained approximately. When the initial power is smaller than critical power, t
14、he broadening change of the beam width will satisfy the quasi-periodic cosine function. When the initial power is bigger than critical power, beam width will be quasi-periodic cosine function first and then over-compression to make periodic changes of broadening change.The 1+1D Gaussian type double
15、beam propagation model is set up, when studying the mutual interaction of the 1+1D Gaussian type double beam in the nonlocal nonlinear medium with small loss. Using analytical method to study the evolution rules of two-beam transmission, quasi-soliton solution is obtained. Further analysis manifests that the center track of the two beams attracts each other in the form of AiryAi function during the transmission process. When the loss increases gradually, the transmission distance becomes gradually longer, and the two tracks are farther and farth
