本征不对称光纤法布里-珀罗干涉仪的理论模型

应用光学和数学理论导出本征不对称光纤法布里－珀罗干涉仪中反射光与透射光的数学模型及低反射率法布里－珀罗干涉腔长度的变化与干涉光光强的数学模型,半指出当ｒ１１＝ｔ１ｔ１ｒ２＝ｒ,且ｔ１ｔ１＝１－ｒ１＾２≈２。则法布里－珀罗腔反射光间的干涉近似为两束等幅光的干涉;文章还给出了光电转换器输出与法布里－珠罗干涉腔长度变化的数学模型。这些模型为不对称光纤法布里－珀罗干涉仪的使用提供理论依据。     

一种新的白光光纤传感系统波长解调方法

提出了一种新的白光非本征法布里-珀罗干涉（EFPI）光纤传感系统的干涉谱处理方法,在白光法布里-珀罗干涉光纤传感系统中,一个中心波长为850nm的发光二极管（LED）作为宽谱光源,HR2000高分辨力微型光谱仪用来测量返回的干涉光谱。通过跟踪干涉光谱中的特定谱峰点,法布里-珀罗干涉传感器的腔长值可以被解调出来。应用反向传播神经网络,解决了单峰测量方式的级次模糊问题。反向传播神经网络能够分辨出干涉谱中不同谱峰的干涉级次,因而可以进行多个谱峰的连续跟踪。从而实现了高精密度、大动态范围的测量。进行了基于这种干涉谱处理方法的白光法布里-珀罗干涉传感系统的应变测量实验。利用该传感系统实现了精密度达0．1με,500με范围的应变测量。     

高分辨率光纤应变传感技术的研究

介绍光纤应变传感器中光纤端面反射镜的制作方法,镀膜光纤的连接技术和构成不对称光纤法布里－珀罗干涉腔的方法。应用低反射率不对称光纤法布里－ 珀罗干涉腔与光纤连接构成的光纤应变传感器,以提高分辨率;重点导出此干涉腔反射光与应变的数学模型,论述其工作原理和测量方法,通过实验证明文中所述应变传感原理和测量方法是正确的,其分辨率优于０－００６８με。     

基于掺铒光纤的微型光纤法布里-珀罗干涉传感器

提出了一种化学腐蚀掺铒光纤制作微型光纤法布里-珀罗干涉传感器的方法。通过对掺铒光纤进行化学腐蚀,形成凹槽,再与单模光纤直接熔接制作而成。实验制作的微型法布里-珀罗干涉传感器干涉条纹光滑,对比度达到15dB。对该微型光纤法布里珀罗干涉腔进行了应变和温度传感实验。实验结果表明,在0-600με￡内,波谷移动随应变改变的灵敏度达到1．7pm／με,线性度为0．9998,从73～23℃,波谷移动随温度改变的灵敏度3．9pm／℃,线性度为0．9982。该方法制作的微型光纤法布里-珀罗传感器具有操作简单,一次成型,制作成本低的优点。     

光纤折射率传感器的设计与研究

基于菲涅耳反射及法布里-珀罗干涉原理设计的测量液体折射率的光纤传感器,该传感器可直接采用普通光纤裸纤端面作为传感器探头,探测系统具有结构简单,操作方便的特点,通过菲涅尔反射法和法布里-珀罗干涉法精确测量了水、甲苯和苯甲醚等样品的折射率,测量结果精确度较高。     

基于匹配光纤光栅法布里-珀罗干涉仪的应变解调方法

提出并实验验证了一种基于匹配光纤光栅法布里-珀罗干涉仪的应变传感器解调方法,该方法综合了光纤法布里-珀罗干涉技术和匹配光纤光栅滤波法的优点.通过半导体制冷片和压电陶瓷组成的闭环负反馈控制系统,精确调节匹配光栅法布里-珀罗干涉仪的温度和应变,有效解决了光栅法布里-珀罗干涉仪的失配问题,从而保证系统静态工作点处于最佳匹配位置,同时能够避免探头因环境温度波动导致的测量误差.实验结果表明,该系统能够响应50~800 Hz的输入信号,应变最小分辨力至少为0.4 nε/Hz^1/2,解调灵敏度高,且不受环境温度波动的影响,因而在动态应变或振动测量中具有较高的实用性.     

基于匹配光纤光栅法布里-珀罗干涉仪的应变解调方法

提出并实验验证了一种基于匹配光纤光栅法布里-珀罗干涉仪的应变传感器解调方法,该方法综合了光纤法布里-珀罗干涉技术和匹配光纤光栅滤波法的优点.通过半导体制冷片和压电陶瓷组成的闭环负反馈控制系统,精确调节匹配光栅法布里-珀罗干涉仪的温度和应变,有效解决了光栅法布里-珀罗干涉仪的失配问题,从而保证系统静态工作点处于最佳匹配位置,同时能够避免探头因环境温度波动导致的测量误差.实验结果表明,该系统能够响应50～800Hz的输入信号,应变最小分辨力至少为0.4nε/Hz1/2,解调灵敏度高,且不受环境温度波动的影响,因而在动态应变或振动测量中具有较高的实用性.     

用超薄金属膜和不对称法布里—珀罗干涉滤光片设计窄带高反膜

提出利用ｎ≈ｋ的金属膜层材料设计窄带反膜的一种新方法－用超薄金属膜与不对称法布里－珀罗干涉滤光组合设计法，给出了可光光区窄带高反膜的膜系结构，定量地分析了膜系的反射率，反射峰值，反射半波带宽光谱反射特性，实验证实了理论设计和分析，同时，也提供了设计非可见光波段的窄带高反滤光片的方法。     

光源谱宽对法布里-珀罗干涉式光纤传感器工作灵敏度的影响

对干涉式光纤传感器来说,光源的谱宽直接影响着传感器的工作特性。从法布里—珀罗干涉式光纤传感器出发,推导其灵敏度的理论表达式,并用MathCAD软件进行了数学分析。讨论了光源谱宽对传感器灵敏度的影响。介绍了具有温度反馈功能的法布里—珀罗光纤干涉实验系统,给出了用该实验系统拍摄的谐振曲线照片。从该系统进行的两个重要的实验(不同干涉腔长的灵敏度对比实验和不同干涉长度的光源实验)表明,法布里—珀罗干涉式光纤传感器的灵敏度与光源谱宽的理论表达式是正确的,理沦公式与实验结论能很好地吻合。最后指出了该方法可以用于分析其他类型的干涉式光纤传感器的灵敏度问题,为光源的选择提供了参考。     

用超薄金属膜和不对称法布里－珀罗干涉滤光片设计窄带高反膜

提出利用ｎ≈ｋ的金属膜层材料设计窄带高反膜的一种新方法用超薄金属膜与不对称法布里－珀罗干涉滤光片组合设计法。给出了可见光区的窄带高反膜的膜系结构；定量地分析了膜系的反射率、反射峰值、反射半波带宽等光谱反射特性。实验证实了理论设计和分析。同时，也提供了设计非可见光波段的窄带高反滤光片的方法     

Thermal diffusion in a sinusoidal temperature field

Separation of liquid mixtures in a thermal gradient, known as the Ludwig-Soret effect or thermal diffusion, is governed by a nonlinear, partial differential equation. It is shown here that the nonlinear differential equation for a binary mixture can be reduced to a Hamiltonian system of equations and that a solution can be obtained for the linear problem. The calculation gives a closed form expression for the space and time dependence of the concentration profile of the mixture, valid at short times.     

(2+1)维广义Calogero-Bogoyavlenskii-Schiff方程的无穷序列类孤子解

为了构造高维非线性发展方程的无穷序列类孤子新解, 研究了二阶常系数齐次线性常微分方程, 获得了新结论. 步骤一, 给出一种函数变换把二阶常系数齐次线性常微分方程的求解问题转化为一元二次方 程和Riccati方程的求解问题. 在此基础上, 利用Riccati方程解的非线性叠加公式, 获得了二阶常系数齐次线性常微分方程的无穷序列新解. 步骤二, 利用以上得到的结论与符号计算系统Mathematica, 构造了(2+1)维广义Calogero-Bogoyavlenskii-Schiff (GCBS)方程的无穷序列类孤子新解. 关键词： 常微分方程 非线性叠加公式 高维非线性发展方程 无穷序列类孤子新解     

电子在α-磁铁中的运动描述

 由于α-磁铁具有能量选择和束团脉宽压缩的功能，它是RF-gun注入器中一个非常重要的组成部分。描述了α-磁铁的结构特点，讨论了电子在α-磁铁中运动的归一化方程。采用数值计算的方法给出了与电子运动能量无关的理想轨道运动方程，并导出了α-磁铁的主要性质。     

电子在α-磁铁中的运动描述

由于α-磁铁具有能量选择和束团脉宽压缩的功能,它是RF-gun注入器中一个非常重要的组成部分。描述了α-磁铁的结构特点,讨论了电子在α-磁铁中运动的归一化方程。采用数值计算的方法给出了与电子运动能量无关的理想轨道运动方程,并导出了α-磁铁的主要性质。     

非线性演化方程椭圆函数解的一种简单求法及其应用

非线性演化方程的许多行波解可以写成满足投影Riccati方程的两个基本函数的多项式形式.利用这一性质，通过建立一般的椭圆方程与投影Riccati方程解之间的关系，导出了一个构造这些解的新方法.该方法对类型Ⅰ的方程和类型Ⅱ的方程均有效，同时也回答了如何求出非线性演化方程分式形式椭圆函数解的问题. 关键词： 非线性演化方程 椭圆函数解     

A Method for Solving Initial-value Problem and Finding Exact Solutions of Nonlinear Partial Differential Equations

Homogeneous balance method for solving nonlinear partial differential equation(s) is extended to solving initial-value problem and getting new solution(s) from a known solution of the equation(s) under consideration. The approximate equations for long water waves are chosen to illustrate the method, infinitely many simple-solitary-wave solutions and infinitely many rational function solutions, especially the closed form of the solution for initial-value problem, are obtained by using the extended homogeneous balance method given here.     

A new expansion method of first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term and its application to mBBM model

Based on a first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term which is extended from a type of elliptic equation, and by converting it into a new expansion form, this paper proposes a new algebraic method to construct exact solutions for nonlinear evolution equations. Being concise and straightforward, the method is applied to modified Benjamin-Bona-Mahony （mBBM） model, and some new exact solutions to the system are obtained. The algorithm is of important significance in exploring exact solutions for other nonlinear evolution equations.     

Canonical transformations and exact invariants for time‐dependent Hamiltonian systems

An exact invariant is derived for n‐degree‐of‐freedom non‐relativistic Hamiltonian systems with general time‐dependent potentials. To work out the invariant, an infinitesimalcanonical transformation is performed in the framework of the extended phase‐space. We apply this approach to derive the invariant for a specific class of Hamiltonian systems. For the considered class of Hamiltonian systems, the invariant is obtained equivalently performing in the extended phase‐space a finitecanonical transformation of the initially time‐dependent Hamiltonian to a time‐independent one. It is furthermore shown that the invariant can be expressed as an integral of an energy balance equation. The invariant itself contains a time‐dependent auxiliary function ξ (t) that represents a solution of a linear third‐order differential equation, referred to as the auxiliary equation. The coefficients of the auxiliary equation depend in general on the explicitly known configuration space trajectory defined by the system's time evolution. This complexity of the auxiliary equation reflects the generally involved phase‐space symmetry associated with the conserved quantity of a time‐dependent non‐linear Hamiltonian system. Our results are applied to three examples of time‐dependent damped and undamped oscillators. The known invariants for time‐dependent and time‐independent harmonic oscillators are shown to follow directly from our generalized formulation.     

Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

Using functional derivative technique in quantum field theory, the algebraic dynamics approach for solution of ordinary differential evolution equations was generalized to treat partial differential evolution equations. The partial differential evolution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynamics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new numerical algorithm—algebraic dynamics algorithm was proposed for partial differential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experiments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically. Supported by the National Natural Science Foundation of China (Grant Nos. 10375039, 10775100 and 90503008), the Doctoral Program Foundation of the Ministry of Education of China, and the Center of Nuclear Physics of HIRFL of China     

Internal Modes of Relativistic Solitons

We apply a linear perturbation analysis to investigate the relationship between soliton oscillations and the integrability of nonlinear PDEs in bi-dimensional spacetime. For this purpose, we consider a localized solution of the nonlinear differential equation, and study small amplitude fluctuations around it. The linearized equation is a Schrödinger-like, eigenvalue problem. By considering several nonlinear PDEs, which are known to have soliton and solitary wave solutions, we find that in systems which are integrable, this eigenvalue equation has one and only one bound state with zero frequency. Non-integrable equations—in contrast—show extra bound states. The time evolution of the oscillations are also calculated, using a numerical program to integrate the time-dependent equation. The behavior of the modes are studied, using the Fourier transform of the evolving solutions.