阵列波导传播常数的分析

在波导传输模中,涉及到一个基本的模式物理量传播常数。用紧束缚近似微扰法计算了阵列波导的传播常数与输入光角谱的关系,由此计算出传播常数的带宽。分析结果对器件的优化设计有一定的指导意义。     

用耦合波理论求解渐变折射率光纤的传播常数和模式场

本文应用耦合波理论来计算任意渐变折射李光纤的传播常数和模场分布.将无限伸展的抛物型折射率分布光纤作为一个理想波导,任意径向不均匀折射率分布光纤便可以视作该理想波导的微扰,其模场可以展开成一组完备的理想波导模的叠加.然后,模场和传播常数可以通过耦合波方程求得.进一步将一阶微分方程组形式的耦合波方程变换成线性方程组,使计算过程大大简化.文中给出了数值计算结果,并将其与准确值进行了比较.     

钛扩散LiNbO3单模波导场分布

给出了 Ti 扩散 LiNbO₃条波导任意阶导模场分布的近似解,通过逐点近似法确定待定常数,分析了它的物理意义,也给出了导模的传播常数和有效折射率的解析式,与变分法相比,这种方法物理概念明确,计算量小,寻优简单,为集成光学的设计提供了一种计算精度较高的计算方法.     

Ti：LiNbO3光波导导模的场分布

给出了Ti扩散LiNbO_3条波导任意阶导模场分布的试探解.通过变分法分析,不但可以合理地确定其中的待定参数,而且也得到了相应导模传播常数的近似值.与扩展的有效折射率方法比较:这种解不但在函数形式上简单,待定常数确定方便,而且具有精度高的优点.还可以得到等效一维波导折射率分布的解析表达式.     

钛扩散铌酸锂矩形波导中的双折射耦合对传播常数的影响

 从亥姆霍兹方程出发，得到了各向异性光波导在弱导近似下的耦合模理论。耦合系数包括偏振耦合项和双折射耦合项。并用马卡提里近似下的模式作为零级近似。用一级微扰法计算了折射率渐变分布的钛扩散铌酸锂矩形波导的传播常数。在给定参数的情况下，得到双折射项引起的传播常数的改变约为主微扰项的3%，因此双折射耦合对钛扩散铌酸锂矩形波导的性能影响不可忽略，这对设计和分析与它相关的光波导器件具有指导意义。     

有损耗波导中非线性TE波的数值模拟

本文发展了一种以有限元技术为基础的数值方法,用它分析有损耗波导中的非线性TE模。在这种方法中,非线性有损耗波导中TE波与功率有关的复传播常数和局城电场分布,可从这种波导直接得到,没有任何近似。作为这种方法的应用,计算了非线性有损耗波导系统中TE0模的功率色散关系和电场分布。     

局域波导模展开方法求解梯度型折射率光纤

将阶跃折射率光纤作为一个理想波导,以这个理想波导纤芯一包层的界面为界将横向平面分成两个区域,然后用局域波导模展开方法以及耦会波理论计算了梯度折射率光纤模式场和传播常数.     

基于变量变换伽辽金法光波导半矢量分析

基于变量变换伽辽金法(VTGM),建立了半矢量分析光波导本征值问题的数理模型;获得了矩形光波导、脊形光波导的本征模的模场分布及归一化传播常数,计算结果和已发表的结果非常接近.半矢量VTGM采用平面映射边界条件,避免了边界截断,又能反映模场的偏振特性,是一种较为理想的光子器件分析方法.     

金属包覆聚合物平板波导的微扰分析

用理想波导耦合是论为基础的微扰方法分析金属包覆聚合物平板波导,推理波导传播常数的近似解。经数值计算,分别求得传播常数的正确解与近似解,二者相比较,证明近似解具有较高的精确度。从而将求解金属包覆聚合物波导本征值方程的复杂复数运算简化成实数运算。     

一种基于多模干涉耦合器的模转换与合并器件的设计

多模波导干涉（MMI）耦合器在集成光路中被用来实现波导模式的转换或合并。对于实际的基于硅绝缘体（SOI）的三维波导，数值设计方法是必需的。采用有限差分波束传输法（FD-BPM）设计了一种66％模式转换、合并器。首先由FD-BPM求出MMI耦合器的输入、输出波导所支持的基模和一阶导模的模场分布，通过数值方法得到MMI耦合器的长度，然后将求得的模场作为输入波场，经过FD-BPM运算后在器件输出面上计算交叉积分得出实际的由基模转换为一阶模的功率百分比。对于算例中采用的SOI波导，器件长度为829μm，65．7％的功率由基模转换为一阶模。     

势阱中粒子能级与波函数微扰计算的代数递推公式

利用超位力定理（HVT）和Hellmann-Feynman定理（HFT）,导出了由有精确解的势阱的能级值用微扰法直接计算一维势阱的各级近似能级的普遍代数公式,并导出由能级近似值计算定态波函数近似表达式的代数公式,给出了代数公式具体应用的几个典型一维势阱实例,此法可推广到二维势阱与三维势阱的情形。     

克尔型非线性薄膜波导的TE模

对于芯区为克尔型非线性介质，覆盖层和衬底为线性介质的平板波导，用Ｋｒｙｌｏｖ－Ｂｏｇｏｌｉｕｂｏｖ－Ｍｉｔｒｏｐｏｌｓｋｙ的渐近法导出了色散方程及场分布的二阶近似数学表达式，计算量大为减少且结果精确。给出了对称和非对称情况的典型实例。     

多项式势阱中粒子能级的微扰计算

利用超位力定理(HVT)和Hellmann—Feynman定理(HFT)．可把势阱中粒子能级的微扰计算简化为代数公式．从而方便计算机编程．对于可展开为多项式的势阱,综合考虑势能多项展开式中截断近似和有限级次的递推计算二者引入的误差．我们重新定义了近似计算的阶次．作为例子,我们给出了高斯势的能级近似计算．     

Full-vectorial finite-difference beam propagation method based on the modified alternating direction implicit method

A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on $H$ fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.     

饱和光谱中带弛豫项的光学Bloch方程的微扰解法

本文利用微扰论方法,直接求解带弛豫项的光学Bloch方程,给出了计算各级微扰的递推公式,具体地给出了一级和二级微扰近似的解析表达式,并对所得结果做了物理解释。 关键词：     

Regular and singular perturbation expansions in the analysis of extensional vibrations of plates

The Kane-Mindlin differential equations appropriate for the study of low and high frequency extensional vibrations in elastic plate strips are solved by means of perturbation techniques. These procedures permit the development of simple expressions that can be used for the rapid calculation of the natural frequencies of vibration as a function of material and geometric parameters. A regular perturbation expansion yields an approximate form of the frequency relationship that is useful in the high frequency range, whereas in the low frequency range a singular perturbation procedure is used since the expansion parameter appears in the coefficient of the highest order derivative in the fundamental differential equation. Approximate formulas and some numerical results are presented for three types of boundary conditions.     

有振幅调制和相位畸变光束通过硬边光阑的M2因子

光束传输M^2因子是表征激光束的有用参量。利用矩形函数的复高斯函数的近似展开方法,给出部分相干光通过硬边光阑后强度二阶矩的近似计算公式,由此可得到部分相干光通过硬边光阑后的推广M^2因子。以有振幅调制和相位畸变光束为例,推导出相应的推广M^2因子的解析表达式,通过数值计算对提出的近似算法的计算精度进行了分析。研究结果表明,使用该近似方法计算得到的推广M^2因子的计算误差小于1％,且通过该方法可直接得到相应的近似解析计算公式,从而使计算得以简化,并有效地提高了计算效率。     

非线性声波方程二次谐波高阶近似解及实验验证

非线性声波方程的传统二次谐波二阶近似解不够精确,对测量材料的非线性系数造成较大误差。利用摄动法展开非线性声波方程得到一系列非齐次偏微分方程,根据低阶解的性质拟定高阶特解的形式,通过符号计算求出高次谐波特解,对所有二次谐波成分求和最终获得二次谐波的高阶近似解。在水中开展非线性声学实验验证高阶近似解,结果表明:二次谐波相对幅度随传播距离和输入信号均呈现先增加后减小的趋势,高阶近似解即使在传播距离不太短和输入信号不太弱的宽泛条件下也能更好地吻合实验结果。得到的高阶近似解不仅弥补了现有二次谐波幅度理论公式的不足,进行非线性声学实验时还可扩展测量范围,充分利用实验数据也能提高非线性系数的测量精度。      

Der Zerfall des Se71

The present paper starts form the original Ginzburg-Landau-equations of superconductivity and the linear theory of elasticity for internal stresses as well as the experimental fact that the specific volume and the elastic constants vary throughout the superconducting phase. With the aid of phenomenological expressions for the free energy and the spontaneous deformation (superconductive magnetostriction) of a deformable type II superconductor, a general method is given for the determination of the interaction between the field of the order parameter, the magnetic field, and the field of the elastic deformations. For an isolated straight vortex-line and for a straight vortex-line in the neighbourhood of a dislocation of arbitrary character, formulas for the internal stresses are derived using first order perturbation theory (corresponding to first powers in the changes of specific volume and elastic constants).     

Cookbook asymptotics for spiral and scroll waves in excitable media

Algebraic formulas predicting the frequencies and shapes of waves in a reaction-diffusion model of excitable media are presented in the form of four recipes. The formulas themselves are based on a detailed asymptotic analysis (published elsewhere) of the model equations at leading order and first order in the asymptotic parameter. The importance of the first order contribution is stressed throughout, beginning with a discussion of the Fife limit, Fife scaling, and Fife regime. Recipes are given for spiral waves and detailed comparisons are presented between the asymptotic predictions and the solutions of the full reaction-diffusion equations. Recipes for twisted scroll waves with straight filaments are given and again comparisons are shown. The connection between the asymptotic results and filament dynamics is discussed, and one of the previously unknown coefficients in the theory of filament dynamics is evaluated in terms of its asymptotic expansion. (c) 2002 American Institute of Physics.