非相干空间光孤子的理论研究及非相干矢量光束的传播演化特性
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摘要
空间光孤子是非线性光学领域中的一个重要研究分支，是光与物质相互作用中线性与非线性效应相互制衡的结果。经过近40年的研究，人们已取得了丰硕的研究成果，但一直以来，人们对于光孤子理论和实验上的研究绝大多数都采用相干光源，即得到相干光孤子。近年来，随着实验水平和材料研究的发展，人们已开始利用非相干光源来产生非相干光孤子。非相干空间光孤子的发现改变了人们对孤子的传统观念，为孤子科学、非线性光学以及其他非线性领域开辟了新的研究领域，在实用上也将大大推动基于光孤子的全光通讯器件的发展。
本文主要在理论上研究了非相干光束在非线性介质中的自陷行为，其中包括非相干光孤子的传播特性、非相干耦合孤子对、非相干双稳态孤子和非相干矢量光束在自由空间的传播演化特性。
论文主要包括以下四部分内容和结果：
一、利用相干密度法和互相干函数法分别研究了一维和二维非相干光束在对数型非线性介质中的自陷行为和传播特性。(1) 通过求解光束满足的非线性传播方程，得到了Gauss型非相干孤子的解析表达式；(2) 讨论了非相干孤子在介质中的传播演化形式，根据光束初始条件和介质非线性系数的选取，孤子可以存在多种不同的传播状态；(3) 研究了非相干孤子在传播过程中相干特性的变化，得到了相干长度的解析表达式，相干长度在传播过程中的演化与孤子束宽的变化成正比，孤子的演化决定相干性的变化，而相干性也同样影响到孤子的演化，二者相辅相成；(4) 分析比较了非相干孤子研究中的这两种研究方法，虽然两种方法的处理过程不同，但其本质是统一的，可以得到一致的结果，可以根据具体问题来选取适宜的方法。
二、研究了一种新型的非相干耦合孤子对在光折变介质中的传播特性，这种孤子对中的两束孤子分量光束波长相同，偏振方向相同，彼此不相干，且孤子分量光束本身也是空问非相干的。(1) 得到了亮—亮、暗—暗和亮—暗型耦合孤子对中非相干孤子分量光束的强度分布，发现耦合孤子对的形成与光束的非相干性无关，但耦合孤子对的存在形式与外加电场的偏置方向有关；(2) 在亮—暗型耦
2004年上海大学博士生毕业论文
合孤子对的研究中，在亮、暗孤子分量强度峰值近似相等的条件下，可以得到了
孤子对的解析表达式;(3)分析了构成孤子对非相干孤子分量光束的彼此无关的
各相干组份光束的传播演化特性，结果表明光束的非相干性仅影响到各相干组份
的强度分布，而与孤子对的强度分布无关。
三、非相干光孤子在高阶非线性介质中具有双稳态现象，即双稳态孤子。(1)
通过求解非线性薛定愕方程，得到了双稳态孤子的表达式，发现光束的非相干性
不影响双稳态孤子的产生，从而证明了高阶非线性介质中，可以存在宽度相同，
但其峰值功率不同的两种非相干孤子态;(2)讨论了介质的高阶非线性系数对双
稳态孤子存在范围的影响，并得到了双稳态孤子存在时光束的截止波长和最小宽
度;(3)根据稳定性条件，证明了所得到的双稳态孤子是一稳定解，可以不受微
扰的影响，保持稳定传播，并发现非相干双稳态孤子系统满足质量、动量及能量
守恒。
四、讨论了各向异性的非相干矢量光束一一角向偏振光束和偶极子光束在自
由空间中的传播特性。〔1)利用坡印亭矢量得到了角向偏振光束横截面上的能量
分布，各向异性的非相干性对光束能量的分布产生影响，相干角向偏振光束中心
处无能量传播，而非相干性使光束中心处的能量由无到有，并有可能形成能量峰
值;(2)非相干偶极子光束能量分布的讨论中，发现非相干性使光束能量主瓣两
侧的旁瓣位置发生移动，随着非相干性的增强，光束的能量旁瓣的位置由远离主
瓣到逐渐靠拢，最终合并为单峰结构;(3)在不同的非相干性条件下，光束具有
三种不同类型的演化行为，给出了具体的判断依据，利用均方宽度定量的描述了
光束在传播过程中的形状的变化。
The spatial soliton is one of major research fields in nonlinear optics, and its existence is correlated with the dynamic balance between the linear and nonlinear effects of the interactions between optical fields and media. Plenty of research achievements have been made in the last 40 years. But all along, attentions were mainly paid to coherent solitons in both theoretical and experimental investigations. With the recent developments in material science and experimental technology, incoherent solitons excited with incoherent light sources were experimentally observed. The findings of incoherent solitons have changed our traditional understanding of soliton phenomena and led to many new research topics. It's hopeful that the application of incoherent solitons shall improve the development of soliton-based all optical communication systems.
The aim of this thesis is to theoretically study the self-trapping behaviors of incoherent light beams in nonlinear media, including the dynamic evolution of incoherent solitons, incoherently coupled screening soliton pairs and incoherent bistable solitons, and the propagation characteristics of incoherent vector beams in free space.
The paper is arranged as follows:
(1) The self-trapping characteristics of one-dimensional and two- dimensional incoherent optical beams in logarithmically saturable photorefractive media are studied by means of the coherent density approach and the mutually coherent function approach, respectively, (a) The analytical expressions of Gaussian model incoherent solitons are obtained by resolving the nonlinear propagation equations for incoherent beams, (b) The propagating behaviors of the incoherent solitons are analyzed. It is shown that the solitons can propagate in a stationary or periodical way, depending on the initial beam conditions and the nonlinearity of the media, (c) The coherence length of incoherent soliton is given. Analysis shows that the coherence property of incoherent soliton
evolves diversely under different propagation conditions, (d) The coherent density approach and the mutually coherent function approach seem to be different, but they are in fact equivalent to each other.
(2) Incoherently coupled screening soliton pairs can be established in biased photorefractive media under steady-state conditions, each constituent of which is not only spatially incoherent with the other, but also with itself, (a) The properties of incoherently coupled soliton pairs in bright-bright, dark-dark and bright-dark configurations are studied with the coherent density approach, and the intensity expressions for these soliton pairs are given. The results show that the existence of coupled soliton pairs have nothing to do with the incoherence property of beams. However, the types of soliton pairs depend on the direction of external bias voltage, (b) The analytical solution of bright-dark soliton pair can be found when the intensity peaks of the two soliton constituents are approximately equal, (c) The propagation characteristics of coherent components that compose each constituent of coupled soliton pairs are discussed in detail. And their intensity distributions depend closely upon the incoherence property of beams.
(3) Incoherent bistable solitons can exist in high-order nonlinear media, (a) Using the coherent density method, I obtain the analytical expression for the spatially incoherent bistable soliton and find that the incoherence of the beam doesn't affect the existence of the incoherent bistable soliton. The widths of the two stable state solitons are the same, but their intensity peaks are different, (b) The high-order nonlinearity determines the existence and the intensity peak of the bistable soliton. The cut-off wavelength, the minimum width of incoherent beam and the nonlinearity of medium required for the existence of bistable soliton are found, (c) The incoherent bistable soliton is rigorously proven to keep propagating steadily against perturbation. It is also proven that the
本文主要在理论上研究了非相干光束在非线性介质中的自陷行为，其中包括非相干光孤子的传播特性、非相干耦合孤子对、非相干双稳态孤子和非相干矢量光束在自由空间的传播演化特性。
论文主要包括以下四部分内容和结果：
一、利用相干密度法和互相干函数法分别研究了一维和二维非相干光束在对数型非线性介质中的自陷行为和传播特性。(1) 通过求解光束满足的非线性传播方程，得到了Gauss型非相干孤子的解析表达式；(2) 讨论了非相干孤子在介质中的传播演化形式，根据光束初始条件和介质非线性系数的选取，孤子可以存在多种不同的传播状态；(3) 研究了非相干孤子在传播过程中相干特性的变化，得到了相干长度的解析表达式，相干长度在传播过程中的演化与孤子束宽的变化成正比，孤子的演化决定相干性的变化，而相干性也同样影响到孤子的演化，二者相辅相成；(4) 分析比较了非相干孤子研究中的这两种研究方法，虽然两种方法的处理过程不同，但其本质是统一的，可以得到一致的结果，可以根据具体问题来选取适宜的方法。
二、研究了一种新型的非相干耦合孤子对在光折变介质中的传播特性，这种孤子对中的两束孤子分量光束波长相同，偏振方向相同，彼此不相干，且孤子分量光束本身也是空问非相干的。(1) 得到了亮—亮、暗—暗和亮—暗型耦合孤子对中非相干孤子分量光束的强度分布，发现耦合孤子对的形成与光束的非相干性无关，但耦合孤子对的存在形式与外加电场的偏置方向有关；(2) 在亮—暗型耦
2004年上海大学博士生毕业论文
合孤子对的研究中，在亮、暗孤子分量强度峰值近似相等的条件下，可以得到了
孤子对的解析表达式;(3)分析了构成孤子对非相干孤子分量光束的彼此无关的
各相干组份光束的传播演化特性，结果表明光束的非相干性仅影响到各相干组份
的强度分布，而与孤子对的强度分布无关。
三、非相干光孤子在高阶非线性介质中具有双稳态现象，即双稳态孤子。(1)
通过求解非线性薛定愕方程，得到了双稳态孤子的表达式，发现光束的非相干性
不影响双稳态孤子的产生，从而证明了高阶非线性介质中，可以存在宽度相同，
但其峰值功率不同的两种非相干孤子态;(2)讨论了介质的高阶非线性系数对双
稳态孤子存在范围的影响，并得到了双稳态孤子存在时光束的截止波长和最小宽
度;(3)根据稳定性条件，证明了所得到的双稳态孤子是一稳定解，可以不受微
扰的影响，保持稳定传播，并发现非相干双稳态孤子系统满足质量、动量及能量
守恒。
四、讨论了各向异性的非相干矢量光束一一角向偏振光束和偶极子光束在自
由空间中的传播特性。〔1)利用坡印亭矢量得到了角向偏振光束横截面上的能量
分布，各向异性的非相干性对光束能量的分布产生影响，相干角向偏振光束中心
处无能量传播，而非相干性使光束中心处的能量由无到有，并有可能形成能量峰
值;(2)非相干偶极子光束能量分布的讨论中，发现非相干性使光束能量主瓣两
侧的旁瓣位置发生移动，随着非相干性的增强，光束的能量旁瓣的位置由远离主
瓣到逐渐靠拢，最终合并为单峰结构;(3)在不同的非相干性条件下，光束具有
三种不同类型的演化行为，给出了具体的判断依据，利用均方宽度定量的描述了
光束在传播过程中的形状的变化。
The spatial soliton is one of major research fields in nonlinear optics, and its existence is correlated with the dynamic balance between the linear and nonlinear effects of the interactions between optical fields and media. Plenty of research achievements have been made in the last 40 years. But all along, attentions were mainly paid to coherent solitons in both theoretical and experimental investigations. With the recent developments in material science and experimental technology, incoherent solitons excited with incoherent light sources were experimentally observed. The findings of incoherent solitons have changed our traditional understanding of soliton phenomena and led to many new research topics. It's hopeful that the application of incoherent solitons shall improve the development of soliton-based all optical communication systems.
The aim of this thesis is to theoretically study the self-trapping behaviors of incoherent light beams in nonlinear media, including the dynamic evolution of incoherent solitons, incoherently coupled screening soliton pairs and incoherent bistable solitons, and the propagation characteristics of incoherent vector beams in free space.
The paper is arranged as follows:
(1) The self-trapping characteristics of one-dimensional and two- dimensional incoherent optical beams in logarithmically saturable photorefractive media are studied by means of the coherent density approach and the mutually coherent function approach, respectively, (a) The analytical expressions of Gaussian model incoherent solitons are obtained by resolving the nonlinear propagation equations for incoherent beams, (b) The propagating behaviors of the incoherent solitons are analyzed. It is shown that the solitons can propagate in a stationary or periodical way, depending on the initial beam conditions and the nonlinearity of the media, (c) The coherence length of incoherent soliton is given. Analysis shows that the coherence property of incoherent soliton
evolves diversely under different propagation conditions, (d) The coherent density approach and the mutually coherent function approach seem to be different, but they are in fact equivalent to each other.
(2) Incoherently coupled screening soliton pairs can be established in biased photorefractive media under steady-state conditions, each constituent of which is not only spatially incoherent with the other, but also with itself, (a) The properties of incoherently coupled soliton pairs in bright-bright, dark-dark and bright-dark configurations are studied with the coherent density approach, and the intensity expressions for these soliton pairs are given. The results show that the existence of coupled soliton pairs have nothing to do with the incoherence property of beams. However, the types of soliton pairs depend on the direction of external bias voltage, (b) The analytical solution of bright-dark soliton pair can be found when the intensity peaks of the two soliton constituents are approximately equal, (c) The propagation characteristics of coherent components that compose each constituent of coupled soliton pairs are discussed in detail. And their intensity distributions depend closely upon the incoherence property of beams.
(3) Incoherent bistable solitons can exist in high-order nonlinear media, (a) Using the coherent density method, I obtain the analytical expression for the spatially incoherent bistable soliton and find that the incoherence of the beam doesn't affect the existence of the incoherent bistable soliton. The widths of the two stable state solitons are the same, but their intensity peaks are different, (b) The high-order nonlinearity determines the existence and the intensity peak of the bistable soliton. The cut-off wavelength, the minimum width of incoherent beam and the nonlinearity of medium required for the existence of bistable soliton are found, (c) The incoherent bistable soliton is rigorously proven to keep propagating steadily against perturbation. It is also proven that the
引文
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