若干新型材料中光学空间孤子的研究
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摘要
研究目前人们比较感兴趣的几种新型光学材料中的光学空间孤子,包括光致异构有机聚合物中非自发的空间孤子；强非局域非线性介质中的贝塞尔孤立波及管理系统Gross-Pitaevskii方程的椭圆函数孤立波解。主要研究内容和取得的成果如下：
1.研究在背景光环境中光致异构空间孤子的形成及特性,提出了光控光的新方案。发现外加背景光能影响暗孤子和灰孤子的传播,特别重要而有趣的发现是外加背景光能实现光致异构暗-亮孤子的转换。理论预言可以用背景光控制信号光的传播。这一方案对单光子异构化和双光子异构化都适用。
2.研究光致异构有机聚合物中的非相干耦合亮-暗孤子对,提出另一个光控光的方案。研究结果表明,虽然单光束只能自发形成光致异构灰孤子和光致异构暗孤子,但是如果通过耦合一个暗孤子来形成亮-暗矢量孤子的形式可以得到亮孤子成分。于是预言可用暗光束来控制亮光束的传播。
3.研究管理系统强非局域非线性介质中高维贝塞尔孤立波的传播。这是继我们小组获得强非局域非线性薛定谔方程的厄米-高斯孤立波解,拉盖尔-高斯孤立波解和库玛-高斯孤立波解之后所得到的另一解析形式的孤立波解,即贝塞尔孤立波解。把这种孤立波的特性和其他孤立波的特性进行了详细的对比研究。
4.利用椭圆函数展开法研究三维广义非线性薛定谔方程(或G-P方程),得到该方程的精确解析解,即雅克比椭圆函数解。该解析解包含单函数解和混合函数解。标准的双曲正割亮孤子解和双曲正切暗孤子解正是单一椭圆函数解的特例,单一椭圆函数还包含了三角函数解等周期函数解。混合椭圆函数解则是与以前所获得的解完全不同的解,一般也表现为周期函数。
第3条和第4条中涉及到管理系统(或参数可变系统)中的空间孤子研究,这是我们首次在管理系统中研究空间孤子,有望促进对管理系统中光学空间孤子的研究。
5.研究了基本空间孤子的形成条件,首次得到类暗亮孤子不能在单调非线性介质中形成的结论,有望加深人们对孤子基本概念的理解。
Optical spatial solitons supported by some presently new optical materials are investigated, which include non-spontaneous optical solitons in organic polymers that experience photoisomerization, Bessel solitary wave in strongly nonlocal nonlinear media and Jacobian elliptical function solution to Gross-Pitaevskii (G-P) equation governing the evolution of matter wave in management system. The research contents and the obtained results are as follows:
1. The formation and characters of spatial solitons associated with photoisomerization are studied, and a new method of light-controlling-light is put forward. It is found that a background light can greatly effect the propagation of dark solitons and gray solitons. The most important and interesting find is the presentation of background light can realize the dark soliton-bright soliton transformation. And then it is predicted that the propagation of a signal light can be controlled by adding a background light. This idea is applicable to both the cases of single-photon-isomerization and two-photon-isomerization.
2. Incoherently-coupled bright-dark soliton pairs in organic polymer that experience photoisomerization are investigated, and another idea of light-controlling-light is proposed. Research results show that a bright soliton can be obtained by coupling a dark soliton and forming a bright-dark vector soliton although a single beam can only spontaneously form a gray soliton or a dark soliton through photoisomerization. Therefore it is predicted that the propagation of a bright light beam can be controlled using a dark light beam.
3. The propagation of Bessel solitary wave in strongly nonlocal nonlinear media with distributed parameters is researched. This is a new analytical solution to the strongly nonlocal nonlinear Schrodinger equation, prior to which Hermite-Gaussian solitary wave solution; Laguerre-Gaussian solitary wave solution and Kummar-Gaussian solitary wave solution were obtained by our group. The characters of this solitary wave are compared with that of the other solitary waves.
4. The general nonlinear Schrodinger equation (or G-P equation) is investigated using the method of Jacobian elliptic function expandation, and the analytical solutions of such equations, namely elliptical function solutions are obtained. These precise solutions include single-function solutions and hybrid-function solutions. The standard hyperbolic secant bright soliton solution and the hyperbolic tangent dark soliton solution are just the special cases of single-elliptic function solutions. Some periodic functions such as trigonometric functions are also included in single-elliptic function solutions. Hybrid elliptic function solutions, which are always periodic functions, are totally different from the previously obtained solutions.
5. Issues 3 and 4 involve with the research of spatial solitons in a management system or a system with varying coefficients. It is for the first time for us to study spatial solitons in a management system, which is expected to stimulate the investigation on optical spatial solitons in management systems.
6. The necessary conditions for elementary solitons to be formed are studied, and the conclusion is derived for the first time to our knowledge that dark-like bright solitons cannot be formed in media with monotonic nonlinearities, which is expected to help comprehending the notion of elementary solitons.
1.研究在背景光环境中光致异构空间孤子的形成及特性,提出了光控光的新方案。发现外加背景光能影响暗孤子和灰孤子的传播,特别重要而有趣的发现是外加背景光能实现光致异构暗-亮孤子的转换。理论预言可以用背景光控制信号光的传播。这一方案对单光子异构化和双光子异构化都适用。
2.研究光致异构有机聚合物中的非相干耦合亮-暗孤子对,提出另一个光控光的方案。研究结果表明,虽然单光束只能自发形成光致异构灰孤子和光致异构暗孤子,但是如果通过耦合一个暗孤子来形成亮-暗矢量孤子的形式可以得到亮孤子成分。于是预言可用暗光束来控制亮光束的传播。
3.研究管理系统强非局域非线性介质中高维贝塞尔孤立波的传播。这是继我们小组获得强非局域非线性薛定谔方程的厄米-高斯孤立波解,拉盖尔-高斯孤立波解和库玛-高斯孤立波解之后所得到的另一解析形式的孤立波解,即贝塞尔孤立波解。把这种孤立波的特性和其他孤立波的特性进行了详细的对比研究。
4.利用椭圆函数展开法研究三维广义非线性薛定谔方程(或G-P方程),得到该方程的精确解析解,即雅克比椭圆函数解。该解析解包含单函数解和混合函数解。标准的双曲正割亮孤子解和双曲正切暗孤子解正是单一椭圆函数解的特例,单一椭圆函数还包含了三角函数解等周期函数解。混合椭圆函数解则是与以前所获得的解完全不同的解,一般也表现为周期函数。
第3条和第4条中涉及到管理系统(或参数可变系统)中的空间孤子研究,这是我们首次在管理系统中研究空间孤子,有望促进对管理系统中光学空间孤子的研究。
5.研究了基本空间孤子的形成条件,首次得到类暗亮孤子不能在单调非线性介质中形成的结论,有望加深人们对孤子基本概念的理解。
Optical spatial solitons supported by some presently new optical materials are investigated, which include non-spontaneous optical solitons in organic polymers that experience photoisomerization, Bessel solitary wave in strongly nonlocal nonlinear media and Jacobian elliptical function solution to Gross-Pitaevskii (G-P) equation governing the evolution of matter wave in management system. The research contents and the obtained results are as follows:
1. The formation and characters of spatial solitons associated with photoisomerization are studied, and a new method of light-controlling-light is put forward. It is found that a background light can greatly effect the propagation of dark solitons and gray solitons. The most important and interesting find is the presentation of background light can realize the dark soliton-bright soliton transformation. And then it is predicted that the propagation of a signal light can be controlled by adding a background light. This idea is applicable to both the cases of single-photon-isomerization and two-photon-isomerization.
2. Incoherently-coupled bright-dark soliton pairs in organic polymer that experience photoisomerization are investigated, and another idea of light-controlling-light is proposed. Research results show that a bright soliton can be obtained by coupling a dark soliton and forming a bright-dark vector soliton although a single beam can only spontaneously form a gray soliton or a dark soliton through photoisomerization. Therefore it is predicted that the propagation of a bright light beam can be controlled using a dark light beam.
3. The propagation of Bessel solitary wave in strongly nonlocal nonlinear media with distributed parameters is researched. This is a new analytical solution to the strongly nonlocal nonlinear Schrodinger equation, prior to which Hermite-Gaussian solitary wave solution; Laguerre-Gaussian solitary wave solution and Kummar-Gaussian solitary wave solution were obtained by our group. The characters of this solitary wave are compared with that of the other solitary waves.
4. The general nonlinear Schrodinger equation (or G-P equation) is investigated using the method of Jacobian elliptic function expandation, and the analytical solutions of such equations, namely elliptical function solutions are obtained. These precise solutions include single-function solutions and hybrid-function solutions. The standard hyperbolic secant bright soliton solution and the hyperbolic tangent dark soliton solution are just the special cases of single-elliptic function solutions. Some periodic functions such as trigonometric functions are also included in single-elliptic function solutions. Hybrid elliptic function solutions, which are always periodic functions, are totally different from the previously obtained solutions.
5. Issues 3 and 4 involve with the research of spatial solitons in a management system or a system with varying coefficients. It is for the first time for us to study spatial solitons in a management system, which is expected to stimulate the investigation on optical spatial solitons in management systems.
6. The necessary conditions for elementary solitons to be formed are studied, and the conclusion is derived for the first time to our knowledge that dark-like bright solitons cannot be formed in media with monotonic nonlinearities, which is expected to help comprehending the notion of elementary solitons.
引文
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