【作者】 王浩；

【导师】 宋叔尼；

【作者基本信息】 东北大学 ， 基础数学， 2020， 硕士

【摘要】 随着光纤孤子理论的发展,及其光孤子通信系统的实用性,光纤非线性光学的研究引起了人们的广泛关注.在非线性光学中,光脉冲传输的基本理论模型通常由耦合非线性薛定谔方程来描述.本文以光纤通信为背景,利用Hirota双线性方法研究了两个变系数耦合非线性薛定谔方程.1.变系数耦合高阶非线性薛定谔方程描述了超短脉冲在非均匀光纤系统中的传播演化.本文首先利用Hirota双线性方法求得了方程的亮单孤子解以及亮双孤子解.其次对解的特征参数进行赋值得到相应的强度函数,并用Maple软件画出相对应的孤子强度函数图像.最后分析了光束的传输特性以及群速度色散、三阶色散效应和色散增益对孤子传输的影响,特别是对单孤子脉冲和双孤子脉冲的波形的影响.2.(2+1)-维变系数耦合非线性薛定谔方程描述了连续波光束在长周期光栅折射率非线性波导放大器内的传输问题.本文首先利用Hirota双线性方法求得了方程的亮单孤子解和亮双孤子解.其次利用Maple软件画出孤子强度图像,并借助图像直观分析了光束的传输特性和衍射效应、非线性效应以及光纤损耗对孤子传输的影响.最后给出了 Kuznetsov-Ma孤子解的演化图像,并对Kuznetsov-Ma孤子的传输特性进行了分析.更多还原

【Abstract】 With the development of fiber soliton theory and the practicality of optical soliton communication system,the research of optical fiber nonlinear optics has attracted much attention.In nonlinear optics,the basic theoretical model of optical pulse propagation is usually described by coupled nonlinear Schrodinger equation.In this paper,two coupled nonlinear Schrodinger equations with variable coefficients are studied by Hirota bilinear method in the background of optical fiber communication.1.The propagation of ultra-short pulses in an inhomogeneous fibers is described by coupled higher-order nonlinear Schrodinger equation with variable coefficients.Firstly,in this paper,the bright one-soliton solutions and two-soliton solutions are obtained by the Hirota bilinear method.Secondly,intensity functions are obtained by assigning the characteristic parameters of solutions,and the corresponding intensity images of soliton are drawn by Maple software.Finally,the propagation characteristics of the beam and the effects of the group-velocity dispersion,third-order dispersion and dispersion gain on soliton transmission,especially on the waveform of one-soliton pulse and two soliton pulse,are analyzed.2.(2+1)-dimensional variable coefficients coupled nonlinear Schrodinger equation describes the propagation of a continuous-wave beam inside a graded-index nonlinear waveguide amplifier with an additional long-period grating.Firstly,in this paper,bright one-soliton and two-soliton solutions are obtained by Hirota bilinear method.Secondly,intensity images of soliton are drawed by Maple software.Propagation characteristics of the beam,diffraction effect,nonlinear effect and fiber loss on soliton transmission are visually analyzed by the image.Finally,the evolution images of Kuznetsov-Ma solitons solution are obtained and the propagation characteristics of Kuznetsov-Ma solitons are analyzed.更多还原