拉曼增益对双折射光纤中孤子传输特性的影响

本文采用考虑拉曼增益的耦合非线性薛定谔方程,利用分步傅里叶方法求解并仿真模拟了光孤子脉冲在不同性质的双折射光纤中传输时的演化过程.结果表明,拉曼增益可以有效抑制非线性耦合导致的孤子漂移,同时会导致光孤子脉冲峰值在传输时不断增大,产生拉曼放大效应.拉曼增益也可以有效抑制双折射光纤中传输的相邻光孤子之间的相互作用.     

非均匀光纤系统中高阶效应对拉曼脉冲产生的影响

从含三阶效应和自陡峭效应的变系数耦合非线性薛定谔方程(CNLS)出发,采用分步傅里叶数值算法,仿真模拟了光孤子在光纤中传输时的演变,探析三阶效应以及自陡峭效应对拉曼脉冲产生的影响。结果表明自陡峭效应改变了孤子的传输特性,破坏孤子的传输周期,导致孤子随着传输距离的增加而衰减,使得大部分能量从泵浦脉冲前沿转移到拉曼脉冲,使拉曼脉冲变为孤子脉冲在光纤中传输。     

拉曼增益对高双折射光纤中孤子俘获的影响

从高双折射光纤中含有拉曼效应和自陡峭效应的非线性薛定谔方程出发,利用快速分步傅里叶变换,模拟了孤子的两个正交偏振分量的演化,分析了拉曼增益和自陡峭效应对孤子俘获的影响。结果发现:当群速度失配较小时,拉曼增益增大了孤子俘获的阈值;当群速度失配较大时,拉曼增益破坏了孤子传输。自陡峭在群速度失配较大时才有明显的影响,此时快轴向慢轴发生能量转移,且当输入脉冲振幅N较大时,两脉冲彼此俘获。     

高阶非线性薛定谔方程的一个新型孤波解

给出了高阶非线性薛定谔方程的一个新型孤波解, 该解描述了满足一定参数条件时光纤中超短光脉冲的传输, 解的表达式可以表示为亮孤子和暗孤子和的形式. 同时利用分步傅里叶方法在一定微扰条件下对脉冲传输进行了数值模拟.     

拉曼散射与自陡峭效应对皮秒孤子传输特性的影响

通过求解包含拉曼增益和自陡峭效应的高阶非线性薛定谔方程, 运用MATLAB模拟了拉曼增益和自陡峭效应共同作用对孤子脉冲在各向同性光纤中传输特性的影响, 结果表明, 自陡峭效应会导致孤子产生时域位移, 而且会使高阶孤子产生孤子分裂现象. 与此同时, 拉曼增益改变了孤子的传输特性, 抑制了自陡峭效应, 从而导致脉冲宽度增大、脉冲偏移程度减弱、高阶孤子分裂成基阶孤子所需的传输距离增大.     

色散条件下各向同性光纤中拉曼增益对光脉冲自陡峭的影响

基于光脉冲所满足的慢变函数,详细推导了包含拉曼增益的高阶非线性薛定谔方程,在考虑色散的条件下,运用分步傅里叶方法对其数值分析,进而模拟仿真了拉曼增益对高斯脉冲在各向同性光纤中传播时自陡峭效应的影响,并与不考虑拉曼增益的自陡峭效应作比较,从而得出拉曼增益在不同条件下对高斯脉冲自陡峭效应的具体影响方式.结果表明,拉曼增益会影响高斯脉冲的展宽、脉冲峰值衰减以及在前后沿的振荡,其影响程度与具体的自陡峭参数、脉冲功率和色散系数的大小有关.     

光孤子对的振幅比与相位差对传输的影响

利用分步傅里叶变换法分别求解含三阶色散效应和不考虑三阶色散情况下的光孤子非线性薛定谔（NLS）方程,通过数值求解发现三阶色散效应会使孤子对脉冲发生单边振荡,并在振荡侧逐级产生次脉冲。讨论孤子对的两束孤子脉冲之间的振幅比与相位差对传输的影响,发现在不考虑三阶色散的情况下,振幅比与相位差均对孤子对的传输有显著影响,在考虑三阶色散效应时,只有相位差对孤子对的传输产生影响,并可以导致脉冲能量转移。     

超高斯型光脉冲在零色散区传输特性的研究

根据超短脉冲在光纤中传输所遵从的高阶非线性薛定谔方程,采用分步傅里叶方法模拟了超高斯型超短脉冲在光纤中的传输演化.在零色散区对损耗、高阶色散、高阶非线性、啁啾等因素对光脉冲传输的影响进行分析并得出了一些结论:损耗对传输脉冲的形状影响比较小基本上可以忽略,对脉冲的幅度影响比较大.一阶孤子传输一段距离后稳定时的幅度和脉宽在传输时基本不变,是进行光孤子通信的理想载体,而高阶孤子在开始传输和传输过程中的幅度和脉宽变化较大.当这些因素共同作用时,对脉冲的传输特性有较大的影响.但通过合理的选择各个影响因素的参量,能得到一个比较适于信息传输的高阶孤子脉冲.这对通过提高入射光脉冲功率使光脉冲在光纤中形成高阶孤子来提高两光中继器之间的中继距离的研究有一定的参考意义.     

光脉冲传输数值模拟的分步小波方法

从信号的多尺度小波分解和正交小波变换出发，将描述光学介质中脉冲传输的非线性薛定谔 方程（NLSE）表示为小波域中的分步算符形式，给出了分步小波算法的迭代公式，导出了线 性算符在小波域中的具体表式，并讨论微分算符的矩阵结构.作为一个例子，用分步小波方 法（SSWM）解NLSE，给出了超短高斯脉冲在光纤中线性和非线性传输的波形演化，并与解析 解和分步傅里叶方法的结果作了比较.结果表明，分步小波方法是研究脉冲在光学介质中传 输的一种有效的数值计算方法. 关键词： 分步小波方法 光脉冲传输 非线性薛定谔方程 多尺度小波分解     

拉曼增益对高双折射光纤中暗孤子俘获的影响

从高双折射光纤中含有拉曼增益的耦合非线性薛定谔方程出发, 利用拉格朗日方法, 推导出了暗孤子俘获的阈值, 并利用快速分步傅里叶变换, 模拟了孤子的两个正交偏振分量的演化, 对比了两种方法得到的阈值, 探究了暗孤子俘获受拉曼增益的影响. 研究发现解析解所得阈值比数值解偏小, 且群速度失配越小时, 二者符合得越好; 并且拉曼增益减小了暗孤子的俘获阈值, 当平行拉曼增益增大时, 俘获阈值减小加快.     

Numerical simulation of propagation of a femtosecond optical soliton in a single-mode fiber with allowance for the imaginary part of Raman response

We consider the effect of Raman inertial response of a medium on the stability of a first-order femtosecond soliton. Numerical solution to the high-order nonlinear Schrödinger equation, with the complex Raman term, describing propagation of a femtosecond optical soliton in a single-mode fiber, is obtained. It is shown that a soliton solution of the high-order nonlinear Schrödinger equation exists under certain conditions imposed on the equation coefficients. These conditions lead to limitations on the wavelength, fiber type, and the highest energy. Results of numerical solutions are in agreement with available experimental data.     

Exact Solutions to Extended Nonlinear Schrödinger Equation in Monomode Optical Fiber

By using the generally projective Riccati equation method, more new exact travelling wave solutions to extended nonlinear Schrödinger equation (NLSE), which describes the femtosecond pulse propagation in monomode optical fiber, are found, which include bright soliton solution, dark soliton solution, new solitary waves, periodic solutions, and rational solutions. The finding of abundant solution structures for extended NLSE helps to study the movement rule of femtosecond pulse propagation in monomode optical fiber.     

Dark solitons in optical fiber with inhomogeneous effects

We study the nonlinear wave propagation in an inhomogeneous optical fiber core in the normal dispersive regime. In order to include the inhomogeneous physical effects, the nonlinear Schrödinger equation (NLSE), which governs the solitary pulse propagation in optical fiber, is modified by adding terms for phase modulation and power gain or loss. The modified NLSEs are bilinearized and exact dark soliton solutions are obtained. The results are discussed.     

The Hamiltonian dynamics of the soliton of the discrete nonlinear Schrödinger equation

Hamiltonian equations are formulated in terms of collective variables describing the dynamics of the soliton of an integrable nonlinear Schrödinger equation on a 1D lattice. Earlier, similar equations of motion were suggested for the soliton of the nonlinear Schrödinger equation in partial derivatives. The operator of soliton momentum in a discrete chain is defined; this operator is unambiguously related to the velocity of the center of gravity of the soliton. The resulting Hamiltonian equations are similar to those for the continuous nonlinear Schrödinger equation, but the role of the field momentum is played by the summed quasi-momentum of virtual elementary system excitations related to the soliton.     

Optical soliton solutions of the generalized higher-order nonlinear Schrödinger equations and their applications

The propagation of the optical solitons is usually governed by the higher order nonlinear Schrödinger equations (NLSE). In optics, the NLSE modelizes light-wave propagation in an optical fiber. In this article, modified extended direct algebraic method with add of symbolic computation is employed to construct bright soliton, dark soliton, periodic solitary wave and elliptic function solutions of two higher order NLSEs such as the resonant NLSE and NLSE with the dual-power law nonlinearity. Realizing the properties of static and dynamic for these kinds of solutions are very important in various many aspects and have important applications. The obtaining results confirm that the current method is powerful and effectiveness which can be employed to other complex problems that arising in mathematical physics.     

1D Solitons in Saturable Nonlinear Media with Space Fractional Derivatives

Two decades ago, standard quantum mechanics entered into a new territory called space-fractional quantum mechanics, in which wave dynamics and effects are described by the fractional Schrödinger equation. Such territory is now a key and hot topic in diverse branches of physics, particularly in optics driven by the recent theoretical proposal for emulating the fractional Schrödinger equation. However, the light-wave propagation in saturable nonlinear media with space fractional derivatives is yet to be clearly disclosed. Here, such nonlinear optics phenomenon is theoretically investigated based on the nonlinear fractional Schrödinger equation with nonlinear lattices—periodic distributions of either focusing cubic (Kerr) or quintic saturable nonlinearities—and the existence and evolution of localized wave structures allowed by the model are addressed. The model upholds two kinds of one-dimensional soliton families, including fundamental solitons (single peak) and higher-order solitonic structures consisting of two-hump solitons (in-phase) and dipole ones (anti-phase). Notably, the dipole solitons can be robust stable physical objects localized merely within a single well of the nonlinear lattices—previously thought impossible. Linear-stability analysis and direct simulations are executed for both soliton families, and their stability regions are acquired. The predicted solutions can be readily observed in optical experiments and beyond.