【作者】 杨荣草；

【导师】 周国生； 李录；

【作者基本信息】 山西大学 ， 光学， 2005， 博士

【摘要】 本文分别以变系数非线性薛定谔方程和变系数高阶非线性薛定谔方程为模型,从解析和数值两方面对皮秒和飞秒光脉冲在非均匀光纤系统中的传输特性进行比较深入的理论研究,给出不同情况下的精确稳定孤波解。在此基础上,我们进一步考察孤波解的稳定性和孤波间的相互作用。为研究实际非均匀光纤或孤子控制系统中光脉冲的稳定传输提供一定的理论依据。最后,我们考虑新型光纤——光子晶体光纤的传输特性。运用有限差分法分析空气孔形状对光子晶体光纤特性的影响,由定量的计算给出一些定性的结果,这对设计实用的光子晶体光纤有一定的参考价值。本文的主要内容如下: 1) 仿照理想光纤中描述光脉冲传输的基本方程,给出非均匀光纤中描述皮秒脉冲传输的变系数非线性薛定谔方程和描述飞秒脉冲传输的变系数高阶非线性薛定谔方程,并简单介绍数值模拟方法。 2) 研究皮秒光脉冲在非均匀光纤中的稳定传输特性。从变系数非线性薛定谔方程入手,讨论非均匀光纤中皮秒亮孤子的传输特性。在已有工作的基础上,利用适当的变换,给出变系数非线性薛定谔方程的暗N-孤子解,并详细讨论非均匀光纤中皮秒暗孤子的传输特性及孤子间的相互作用。 3) 研究飞秒光脉冲在非均匀光纤中的稳定传输特性。为了对照起见,我们首先介绍非均匀光纤中飞秒亮孤子的传输特性。然后,利用拟解法解析求解变系数高阶非线性薛定谔方程,得到非均匀光纤中飞秒暗孤子解。借助于数值方法,进一步分析飞秒暗孤子的稳定性和非均匀光纤中飞秒暗孤子间的相互作用。 4) 研究飞秒组合孤立波在非均匀光纤中的稳定传输特性。通过解析求解变系数高阶非线性薛定谔方程,得到不同参数条件下的三类组合孤波解,这些解可以描述飞秒亮、暗孤波在非均匀光纤中同时传输的特性。另外,我们数值模拟飞秒组合孤波间的相互作用,结果发现飞秒组合孤波间的相互作用完全不同于亮的或暗的飞秒孤波间的相互作用,组合孤波间的相互作用要弱的多。更多还原

【Abstract】 Based on the nonlinear Schrodinger equation with varying coefficients and the higher-order nonlinear Schrodinger equation with varying coefficients, we investigate, analytically and numerically, the transmission of pico- and femto-second optical pulses in inhomogeneous fiber systems. And some types of exact stable solitary wave solutions under different conditions are obtained. Furthermore, the stability and the interaction of the solitary waves are studied by employing the symmetrized split-step Fourier method. This may be helpful to provide some theoretical bases for studying the stable transmission of optical pulses in real fiber or soliton control systems. The main contents are as follows:1) Following the nonlinear Schrodinger equation governing the propagation of optical pulses in ideal fiber, we introduce the nonlinear Schrodinger equation with varying coefficients and the higher-order nonlinear Schrodinger equation with varying coefficients to describe the propagation of optical fiber in inhomogeneous fiber system.2) Starting from the nonlinear Schrodinger equation with varying coefficients, we study the stable transmission of picosecond pulses in inhomogeneous fiber. We discuss the propagation of picosecond bright solitons in inhomogeneous fiber. On the basis of previous work, we present the exact dark N-soliton solution by using an appropriate mapping, and discuss the propagation properties and the interaction of picosecond dark solitons in a soliton control system in detail.3) We investigate the transmission of femtosecond pulses in inhomogeneous fiber. To compare, we first introduce the propagation of femtosecond bright solitons in inhomogeneous fiber system. Then, we solve analytically the higher-order nonlinear Schrodinger equation with varying coefficients and obtain the exact dark soliton solution. With the aid of the numerical method, we analyze the stability and the更多还原