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1、华中科技大学 博士学位论文 全息空间光孤子的理论研究 姓名：张绘蓝 申请学位级别：博士 专业：物理电子学 指导教师：刘劲松 20070427 I 摘 要 在光学介质中，横相位调制一度被认为只能伴随着自相位调制出现，不能单独存 在，直到一种新型的空间光孤子全息空间光孤子在光折变介质中提出才给出了一种 横相位调制单独存在的方式。对全息光孤子，两束相干光之间由于干涉在介质中形成 折射率光栅，两束光在通过该光栅时发生布拉格衍射产生横相位调制，使得两束光同 时被捕获形成空间光孤子。每束光都是全息孤子的一个必不可少的分量，因为单独一 束光是不可能形成孤子的。 由于全息光孤子的独特性，它吸引了人们越来越多的
2、研究兴趣。在本论文中，我 们主要研究了哈密顿系统中全息明孤子所诱导波导的特性，耗散系统中全息孤子的稳 定性以及哈密顿系统和耗散系统中的全息孤子解的问题。 根据哈密顿系统中全息孤子的理论模型，我们考察了哈密顿系统中两分量相同的 全息明孤子所形成波导的特性，发现波导可能的导模数主要依赖于孤子的峰值强度和 背景光之间的强度比，导模数随着比值的增加而单调增加。我们对导模以及正弦波、 余弦波在波导中的动态演化做了数值模拟。结果显示，由这种明全息孤子所诱导的波 导可以用来实现对某一维上有周期性并具有慢变包络振幅的探测波的导引。 在已有的关于耗散系统全息空间光孤子的理论模型中，一束光输出能量给另一束 光，输
3、出能量的光为泵浦光，能量流入的光为信号光，并认为泵浦光的强度为常数并 忽略它的演化。对由该模型所得到的耗散全息孤子解，我们通过用数值模拟的方法研 究系统参数，如介质的吸收、外电场等，对孤子的稳定传播的影响，考察了这种孤子 解的稳定性。同时也用理论分析的方法研究了这种孤子解的稳定性。数值分析和理论 分析的结果都显示泵浦光强为常数的耗散全息孤子模型所给出的信号光孤子解对微 扰具有稳定性。但是进一步的研究表明当泵浦光强为常数时系统会出现泵浦光清空以 及泵浦光调制不稳定性，这两种效应又会极大的影响信号孤子光的稳定传播。因此需 要在考虑忽略泵浦光演化的基础上寻找更合适的耗散全息孤子解。 为了得到哈密顿系
4、统中两分量不同的全息孤子解，我们通过两个模式耦合的方法 得到了哈密顿系统中两分量显著不同的全息孤子解以及任意振幅的全息孤子解。我们 II 发现两个同阶模式之间的耦合可以得到单峰单峰、双峰双峰、多峰多峰组合的 任意振幅的全息孤子解，两个不同阶数模式之间的耦合可以得到单峰双峰，单峰 多峰，双峰多峰组合的全息孤子解。同时在每一个组合中又包括了很多可能的孤子 解，涵盖了从一般到特殊的很多种的情况，极大的丰富了全息孤子解的形式，也扩大 了全息孤子解参数的取值范围。另一方面，模式耦合的方法可以推广到耗散系统中， 得到不存在调制不稳定性的耗散全息孤子解。而且，在这样一种模式耦合的过程中可 以看到模式以及峰值
5、强度对横相位调制的影响，从而横相位调制有更深的了解。 关键词关键词: 耗散系统 全息孤子 波导 导模 III ABSTRACT In optically materials, cross-phase modulation (XPM) has been traditionally believed to be always accompanied by self-phase modulation (SPM). However, a new kind of spatial solitons, holographic solitons, has been suggested theoreticall
6、y in photorefractive media and can be supported by strong XPM but lack SPM altogether. For holographic solitons, the interference of two mutually coherent beams will induce a grating in refractive index and lead to simultaneous trapping of the two beams in a form of spatial solitons via XPM, arising
7、 from Bragg diffraction from the induced grating. The presence of both beams is required and each beam is a necessary component of a holographic soliton, since each beam alone cannot survive as a soliton if the other beam is absent. A considerable research interest has been invested in the study of
8、holographic solitons due to its specialty. In this dissertation we investigate theoretically the properties of waveguide induced by holographic solitons in Hamiltonian system, and the stability of holographic soliton solutions in dissipative system (DHS), and holographic soliton solutions with two s
9、ignificantly different components in both Hamiltonian system and dissipative system. Based on the theoretical model of holographic solitons in Hamiltonian system, we analyze the properties of waveguided induced by bright holographic solitons with two identical components. We find that the number of
10、possible guided modes in such waveguide is solely dependent on the intensity ratio of the soliton, which is the ratio between the soliton max intensity and the sum of background illumination. The number of guided modes increases monotonically with increasing intensity ratio. We perform numerical sim
11、ulation of the wave guiding in such waveguide for guided mode beams and cosine waves and sine waves. The results imply that it is possible to realize the wave guiding in the bright holographic soliton-induced waveguide for a probe beam periodic in one dimension and with slowly varying amplitude. In
12、a proposed model for DHS, one beam can act as pump beam to supply energy for the other beam, which behaves as the signal beam. And the intensity of pump beam has been considered as constant so that the evolution of pump beam is ignored. Based on such model, a numerical study is performed on the stab
13、ility property of DHS solutions through IV analyzing the role of every single system parameter, such as the linear loss of the crystal, the external biased field. For comparison, a theoretic analysis on the stability of DHS solutions is presented. Both numerical result and theoretic result indicate
14、the signal soliton beam is stable against small perturbation under the assumption that the evolution of pump beam is ignored. However, further investigation reveals that the assumption of constant pump beam intensity will bring the depleted effect and the modulational instability (MI) on pump beam,
15、which can greatly influence the stable propagation of signal beam. Proper DHS solutions should be obtained in the model with the evolution of pump beam. In order to obtain the holographic soliton solutions with two constituents significantly dissimilar, a mode coupling method is applied in Hamiltoni
16、an system. The coupling between two modes of the same mode-order will give rise to single hump-single hump, two humps-two humps, and multihumps-multihumps holographic soliton solutions with arbitrary amplitude. And the coupling between two modes of different mode-order can generate single hump-two humps, two humps-multihumps, and single hump-two humps holographic soliton solutions. These results will lead to the enormously various shapes for holographic solitons and greatly enriches
