【作者】 田晋平；

【导师】 周国生；

【作者基本信息】 山西大学 ， 光学， 2006， 博士

【摘要】 本文从解析的角度出发,利用求解高阶偏微分方程的几种不同方法,例如齐次平衡法、拟解法以及达布变换法,同时借助于各种微扰理论例如矩法、变分法和数值方法例如分步傅里叶方法、伦格—库塔积分法,深入系统地研究了皮秒、亚皮秒以及飞秒光脉冲在均匀与非均匀光纤及其放大介质中的无畸变传输特性,获得了各种情况下的经典的和新型的精确稳态孤波解。在此基础上,进一步考察光孤波脉冲的稳定性及其相互作用,为将来的大容量和超大容量光信息传输的实验和应用提供了比较全面的理论依据。我们的工作主要分为两大部分,首先就描述超短光脉冲在光纤系统中传输的高阶非线性薛定谔方程以及描述超短光脉冲在波分复用光通信系统中传输的耦合高阶非线性薛定谔方程展开理论研究,通过解析方法寻求其新型的组合孤波解,并利用数值方法进一步研究其稳定性。其次,对光脉冲在非均匀光纤中稳定传输特性进行了理论研究,获得了不同情况下的精确稳态孤波解,在此基础上,数值考察了皮秒和飞秒光脉冲在非均匀光纤中的稳定性及相互作用。 本文的主要创新点亦即具体内容分为如下几个系统连续的研究进程: 1) 通过行波变换法和齐次平衡法,在该领域首次获得了一般参数条件下描述超短光脉冲在光纤系统中传输的高阶非线性薛定谔方程的两种新型组合孤波解。同时通过数值模拟,我们发现在一定的参数条件下,这两种新型的组合孤波有很好的稳定性。然后进一步,也是首次获得了描述超短光脉冲在波分复用光通信系统中传输的耦合高阶非线性薛定谔方程的一组稳定的组合孤波解,这一结果对将来的超大容量光通信有一定的指导意义和参考价值。 2) 利用增益色散和非线性色散关系,首次从解析的角度完整地推更多还原

【Abstract】 Starting from the analytical point of view, we investigate picosecond, sub-picosecond and femtosecond optical pulses’ transmission characteristics in an optical fiber or an optical system, including bandwidth-limited gain and higher-order effects with the aid of different methods in solving higher-order derivative differential equation, such as homogenous balance method, anstaz method and Darboux transformation method, also with the aid of different types of perturbation methods, such as momentum method, variation method and numerical method such as symmetrical split-step Fourier transformation method and Lung-Kutta method. Some types of exact steady-state solitary wave solutions are obtained. Then, we further consider the stabilities and interactions of the optical pulses. Our results might provide a more comprehensive theoretical basis to the coming high and ultrahigh capacity of optical information transmitting in both experimental and applied studies. Our research works mainly consist of two parts. Firstly, we start our theoretical investigation from the nonlinear and higher-order nonlinear Schrodinger equations which describe optical pulses propagating in an optical fiber system as well as couple nonlinear and higher-order nonlinear Schroedinger equations which describe optical pulses propagating in a wavelength division multiplexing (WDM) system. Through analytical methods, we find new combined solitary wave solutions of the equations and then we studythe equations and then we study the solutions’ stability by numerical methods. Secondly, we theoretically investigate the steady state transmission of optical pulses in inhomogeneous optical fiber media, and also we obtain exact stable solutions. Based on the analytical results, we further consider the pulses interactions and the stabilities in the inhomogeneous optical fiber system. What we discussed in this paper may be helpful to achieve the undistorted transmission and high capacity communication of optical pulses in optical fiber systems. The detailed creative investigation results of this paper are as follows:1) By making use of traveling wave transformation method and homogeneous balance method, we firstly obtain two types of combined solitary wave solutions of higher-order nonlinear Schroed-inger equation. One of which is M-type and can be thought as a dark soliton with finite-width background. And the other one is wavy type. Then by employing the symmetrical split-step Fourier method, we find that these two types of combined solitary wave solutions are very stable during propagation in the optical fiber under the example parameter conditions. Furthermore, we find another steady state combined solitary wave solution of coupled higher-order nonlinear Schroedinger equation which describes the WDM optical communication system. Our results may have potential applications in the coming ultrahigh optical communications.2) By employing the evolution relations of gain dispersion and nonlinear dispersion, we firstly deduce detailedly the higher-order Ginzburg- Landau equation including fourth-order dispersion and other higher-order effects. And then we obtain an exact chirped solitary wave solution of the equation by anstaz method. Through momentum method and linear stability theory, we analyze the solution’s stability and obtain the relative parameter space. This result has its meaning not only on optical pulse transmission and optical laser designing, but also on some other physical area such as theapplication of surface waves in fluids, plasma physics, and Bose-Einstein condense (BEC).3) We solve the nonlinear and higher-order nonlinear Schroedigner equation with variable coefficients which govern the optical pulses propagating in inhomogeneous optical fiber media. This provides theoretical basis to the studies of the transmission characteristics of optical bright solitary waves in inhomogeneous optical fiber media and optical soliton control system. Then we firstly obtain the Lax pair of coupled nonlinear and higher-order nonlinear Schroedinger equation with variable coefficients. Based on the Lax pair, we obtain the exact iV-soliton solution of the system. This provide another theoretical basis to the studies of the propagation stabilities and interactions of optical bright solitary waves in inhomogeneous optical fiber systems.更多还原