非线性光孤子传输方程的研究

本文在从描述光孤子在单模光纤中的非线性传输方程（ＮＬＳ，即非线性薛定谔方程）出发，利用Ｍａｘｗｅｌｌ方程和慢变包络近似性，导出ｐｓ量级光孤子高阶修正的非线性薛定谔方程（ＨＭＮＬＳ）可进一步研究色散，损耗等高价效应对孤子传输造成的影响。     

光纤色散补偿后的非线性研究

研究了色散补偿后光纤链路的非线性对脉冲波形及频谱演化的影响。首次得出了非线性薛定谔ＮＬＳ方程的适用于弱或强非线性色散光纤的两种级数解，可分别描述在弱非线性色散光纤中的频谱演化，和在强非线性色散光纤中脉冲波形的演化。首次得出正负色散完全抵消时，适用于任意波形的输出信号的频域表达式、非线性噪声系数、无啁啾高斯脉冲展宽因子表达式和计算结果。     

非线性薄介质中的激光相移研究

应用克尔介质中的动力学方程，根据薄介质近似，分别研究了三种情况下激光穿过薄介质后的相移。尤其研究了考虑非线性吸收和折射情况下对用求解贝努里方程的方法研究非线性相移的结果，该方法与以往的幂曳数方法相比，具有数学模型直观，物理意义清晰求解过程简便的特点。     

弥散非线性信道自适应均衡器

提出一种基于非线性差分方程模型的弥散非线信道自适应均衡器，在弥散非线性信道上传高速数据信号时，根据正交估计原理和快速正交算法，利用接收信号序列和训练序列可以迅速估计出该差分方程的基向量和权系数，所提出的自适应非线性均衡器的结构使其具有较好的自适应功能。模拟结果表明，采用这种自适应均衡器可使高速音带数据传输系统的误码性能改善３个数量级。     

恒压源驱动下的扬声器低频跳跃

通过能量法求解扬声器非线性振动系统的非线性微分方程的一阶近似解，得出幅频关系方程和幅频关系曲线，并着重分析讨论磁场的非线性对扬声器低频跳跃的影响，得出一些结论。     

五次非线性对光纤反常色散区调制不稳定性的影响

从带五次非线性项的扩展非线性薛定谔方程出发,重点考虑了五次非线性对常用的自聚焦光纤中反常色散区调制不稳定性的影响.研究结果表明,当入射功率较小时,五次非线性对调制不稳定性的影响并不明显,这说明了当入射功率很小时,忽略非线性薛定谔方程中五次非线性项的做法是合理的;随着入射功率的增加,五次非线性对调制不稳定性的影响越来越大,这种影响主要表现为五次非线性增大了调制不稳定性频谱的范围及增益值,并最终减小了使调制不稳定性发生的入射功率范围;当入射功率继续增加,超过一定的阈值条件时,调制不稳定性不能发生.     

变形的非线性Schrodinger方程的孤子解及其特征

本文用广田法给出了变形非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程的孤子解，讨论子孤子解的特征。结果表明，立方导数项的存在可使形成飞秒光孤子脉冲所需的峰值功率明显地低于由非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程所预期的值。     

一类非线性矩阵方程对称解的双迭代算法

传统的方程求解办法并不能算出非线性矩阵方程的对称解,故文章给出一类非线性矩阵方程对称解的双迭代算法,先以牛顿迭代算法求解方程对称解,然后,借助MCG,即修正梯度共轭法经由牛顿迭代后算得的每一步线性矩阵方程的对称解进行计算。研究结果表明,文章所提出的非线性矩阵方程的对称解是有效可取的。     

三光子吸收情况下的激光相移研究

对三光子吸收情况下的非线性相移进行研究 ,由它的耦合方程研究非线性相移在介质出射面处的横向分布。由此比较与双光子吸收情况下的非线性相移的不同。     

利用(G'/G) 展开法求解广义变系数Burgurs方程

近年来，变系数非线性发展方程受到越来越多的被关注。2008年王明亮等提出了一种新的方法，即(G'/G)展开法。将(G'/G)展开法首次尝试应用到变系数非线性发展方程中，并以广义变系数Burgers方程为例，最终成功得到了在系数满足一定条件时新的精确解；然后又尝试将该展开法进行新的扩展，再一次对广义变系数Burgers方程求解，又成功得到了一些新解。实践证明，该展开法不仅易于求解常系数非线性发展方程，而且对变系数非线性发展方程仍很高效、简洁、实用，并且具有广泛的应用前景。     

光纤中随时间变化的三阶非线性对类明孤子传输特性的影响

从MNLS方程出发,考虑三阶非线性微扰的作用,采用变分法,求得拉格朗日密度函数表达式。在此基础上,推出了类明孤子脉冲参数随传输距离的演化方程组,讨论了三阶非线性微扰对类明孤子传输特性的影响。     

Eigenvalue communication

The authors propose a communication method for a nonlinear and dispersive medium such as an optical fiber that is based on eigenvalues of associated equations for the wave amplitude. In optical communications, the communication distance measured by the carrier wavelength reaches the order of 10/sup 11/-10/sup 13/. As a result, dispersive and nonlinear effects, even if small, contribute significantly to the distortion of signal information contained in waveforms or in frequency spectra. Thus, it is desirable to use other parameters which remain unaltered. The eigenvalues of the associated equation for the nonlinear Schrodinger equation which describes the lightwave envelope in fibers constitute such parameters. Soliton-based communication corresponds to the case of one eigenvalue.<>     

An analytical treatment of the effect of axial inhomogeneity onfemtosecond solitary waves near the zero dispersion point

A perturbed nonlinear Schrodinger equation, valid for femtosecond pulse propagation in axially inhomogeneous optical fibers near the zero dispersion point, is considered. It is found that for a weak axial nonuniformity, and under certain conditions, this equation can be treated analytically. Exact bright and dark solitary wave solutions are derived and their behavior in the presence of the inhomogeneity is analyzed. The nonuniformity induced time shift of the solitary waves is also obtained. The potential use of this parameter as a diagnostic tool for estimating characteristic parameters of the axial variations is discussed and its range of values is investigated     

应用改进的试探函数法求非线性数学物理方程精确解

应用改进的试探函数法求得Jimbo-Miwa方程和非线性传输线电位方程的精确解,这些解包括双曲函数解、三角函数解。当对双曲函数解中的参数取特殊值时,可以得到了孤立波解。当对三角函数解中的参数取特殊值时,可以得到对应的周期波函数解。实践证明,试探函数法对于研究非线性数学物理方程具有非常广泛的应用意义。     

Nonlinear dynamics of femtosecond optical solitary wave propagationat the zero dispersion point

A perturbed nonlinear Schrodinger equation, describing nonlinear pulse propagation of femtosecond duration in optical fibers at the zero dispersion point, is considered. This equation is reduced to an ordinary differential equation, which is treated by means of Hamiltonian dynamics techniques. Conditions for solitary wave formation, as well as the solutions themselves, namely, a bright soliton, a rarefaction soliton, and a pair of dark solitons, are derived analytically. The shifts of the solitary wave velocity, the angular frequency, and the wavenumber, as well as the peak power required to launch a bright soliton are also obtained. The connection among the point initial conditions of the pulse and the type of solitary wave that can be excited is finally presented     

光纤放大器中孤子的量子效应

利用含时Hartree近似法得到光孤子在含光纤损耗、双光子吸收、三阶色散效应的光纤放大器中传输时的量子非线性薛定谔方程,在一定条件下,有量子态的孤子解,并由此方程讨论了经典和量子效应对孤子在光纤放大器中传输时的影响,由此进一步发现,光场算符的量子力学平均值是一系列修正的经典孤子的叠加。     

光学孤子在单模光纤中的非线性传输方程

人们熟知,由非线性薛定谔(NLS)方程描述的光学孤子可以在单模光纤中稳定地传输。本文在准单色近似和慢变包络近似条件下,利拥泰勒级数展开推出了这一非线性传输方程。由于推出的方程包含着高阶线性色散和光纤损耗项,因而可以用来研究短光脉冲(皮秒量级)在单模光纤传输过程中相关的非线性光学孤子效应,比如光学孤子分裂和光学孤子损耗等。     

The Quantum Theory of Optical Pulses Amplification

The propagation of optical signals in optical fiber amplifier is treated with fully quantum mechanics method in this paper. The micro-Hamiltonian of the system with nonlinear effect is derived by combining spatial mode and temporal mode, and propagation equation of optical pulses in a optical fiber amplifier is derived with dispersion relation. The characteristic parameters such as gain, output power and noise figure of the amplifier are analyzed and their quantum mechanics formulas are obtained.     

Some study on dark and bright optical solitons in a real system with periodically distributed dispersion and nonlinearity

We study the dynamics of short optical pulses in a real system with periodically distributed dispersion and the nonlinearity is governed by the higher order nonlinear Schrödinger equation (HNLSE) with linear and nonlinear gain (loss). Under specific parametric circumstances, where the dark and bright solitary waves are combined, a set of entirely new types of solitary waves with nonlinear chirp have emerged. For a properly intense optical pulse in the combined solitary waves, the binding of the bright and dark solitary waves is very strong. It is seen that by numerical simulation, these pooled types of solitary-like solutions show a high degree of stability while propagating over an extremely long distance in the considering system, even in the presence of a high degree of perturbation of the amplitude and white noise. All constraint relations on the physical parameters are explicitly shown to be related to the development and to the dynamical study of the chirped solitary like solution in the considering medium.     

强非局域介质中高斯光束参量演化规律的分析

光束存非局域非线性介质中传输时遵循非局域非线性薛定谔方程（NNLSE）。对应用变分法得到的傍轴高斯光束存强非局域非线性介质中的束宽演化方程进行了简化，消除了由于强非局域非线性介质响应函数作泰勒级数展开产生的势函数假根的影响；求出了傍轴高斯光束各参量的演化表达式。结果表明，傍轴高斯光求存强非局域非线性介质中传输时束宽的近似演化规律为正弦函数和余弦函数，并存在一个临界功率。当初始功率等于临界功率时，可以得到空间光孤子。对于一般情形，束宽作周期性压缩或展宽变化。当束宽比α≤0．3时，所得结果与非局域非线性薛定谔方程的数值解基本一致。