全矢量有限元模型及其在光波导中的应用

为了研究光波导和光子晶体光纤的模式特性和传输特性,从矢量波动方程出发,推导出了各向异性介质中场微分方程复数泛函表达式,利用棱边/节点混合元离散了该泛函,加入了各向异性介质匹配层边界条件,得到关于传播常量的广义特征值方程.以矩形波导为例,对各向异性介质匹配层边界条件的吸收特性进行了研究,得到了基模以及几个高阶模的场分布、色散曲线和损耗曲线.结果表明该方法可靠有效.对正六边形晶格光子晶体光纤进行了分析.数据表明：光纤有效折射率随空气孔直径或波长的增大而减小,但与空气孔圈数无关;光纤限制损耗(confinement loss)随波长增大近似成指数增大,而增加空气孔直径或者空气孔圈数则可使之显著降低.     

光子晶体光纤的弯曲损耗振荡特性分析

综合运用弯曲光纤的等效直光纤模型、全矢量频域有限差分法及各向异性完全匹配层吸收边界,计算了两种类型(折射率引导型和带隙型)光子晶体光纤(PCF)的弯曲损耗.通过数值模拟弯曲损耗随弯曲半径的变化关系,证实了两种光子晶体光纤均具有弯曲损耗振荡特性.进而分析了两种光子晶体光纤弯曲损耗振荡的产生机理并给出了与损耗峰对应的包层模式.结果表明,振荡的产生源于基模与包层模式的耦合,其中,折射率引导型光子晶体光纤的弯曲损耗振荡机理类似于传统双包层光纤,带隙型光子晶体光纤弯曲损耗振荡的产生则是两种不同类型的包层模式共同作用的结果.     

基于表面等离子体共振和定向耦合的D形光子晶体光纤折射率和温度传感器

利用光子晶体光纤结构的灵活性和性能的优越性, 设计了一种基于D形光子晶体光纤的折射率和温度传感器. 在D形光子晶体光纤表面抛磨并镀上金纳米薄膜, 作为表面等离子体共振传感通道用来测量液体折射率; 在包层的一个空气孔中填充温敏液体甲苯, 作为定向耦合通道实现对温度的测量. 进一步的数值计算发现, 基于定向耦合效应的温度传感和基于表面等离子体共振的折射率传感相互独立, D形光子晶体光纤同时进行折射率和温度传感检测. 在各向异性的完美匹配层边界条件下利用全矢量有限元法对该传感器特性进行了数值研究, 发现D形光子晶体光纤的空气孔直径决定了定向耦合吸收峰的中心波长和温度传感的灵敏度, 金薄膜的厚度和D形结构的抛磨深度仅影响表面等离子体共振峰的相对强度. 结果表明: 该传感器在-10–80 ℃的温度范围内具有11.6 nm/℃的温度灵敏度, 在1.34–1.44折射率范围内折射率灵敏度最高可达26000 nm/RIU.     

利用超格子模型对布拉格光纤的研究

为了研究布拉格光纤的模式特征和传输特性,提出了超格子模型,利用傅里叶级数表示光纤横向折射率分布,利用平面波展开法分析布拉格光纤的能带结构,基于厄米-主斯函数的局域正交函数展开法,从全矢量耦合波动方程出发,得到关于模式传播常量和电场展开系数的本征方程,从而分析布拉格光纤的模式特征。以高折射率芯布拉格光纤为例,实现了该算法,得到基模与二次模的横向电场分布、基模色散曲线和模式双折射。基模的模式双折射可用于衡量算法的精度,结果表明该算法精度较高。超格子模型不仅可以用于研究高折射率芯布拉格光纤,而且同样可以研究低折射率区域导光的布拉格光纤。     

压缩型双缺陷椭圆孔光子晶体光纤

提出了一种通过横向压缩普通圆孔光子晶体光纤,得到双缺陷椭圆孔光子晶体光纤的方法.所提出的双缺陷光子晶体光纤具有高双折射率,采用全矢量有限元方法和各向异性介质完美匹配层方法对该光子晶体光纤的双折射特性和约束损耗特性进行了研究.理论模拟结果表明所提出的光子晶体光纤的双折射率可以达到10－2量级.     

小尺度表面粗糙度与介质吸收对介质折射率测量的影响

将介质表面的小尺度粗糙度等效为覆盖在理想光滑表面上的多层等厚折射率渐变的薄膜,并通过特征矩阵计算多层等效膜模型的P光反射率与入射角的关系.将吸收介质的折射率虚部带入菲涅尔公式进行计算.运用COMSOL Mutiphysics软件对表面粗糙度和介质吸收进行建模和仿真计算.计算结果表明,小尺度表面粗糙度与介质吸收都会导致折射率测量产生误差.分别考虑以布儒斯特角和全反角作为折射率测量的手段,为了得到优于10-5的测量准确度,测量表面粗糙介质的折射率时,采用全反角进行判定;测量具有吸收效应的介质折射率时,采用布儒斯特角进行判定.     

小尺度表面粗糙度与介质吸收对介质折射率测量的影响（英文）

将介质表面的小尺度粗糙度等效为覆盖在理想光滑表面上的多层等厚折射率渐变的薄膜,并通过特征矩阵计算多层等效膜模型的P光反射率与入射角的关系.将吸收介质的折射率虚部带入菲涅尔公式进行计算.运用COMSOL Mutiphysics软件对表面粗糙度和介质吸收进行建模和仿真计算.计算结果表明,小尺度表面粗糙度与介质吸收都会导致折射率测量产生误差.分别考虑以布儒斯特角和全反角作为折射率测量的手段,为了得到优于10~(-5)的测量准确度,测量表面粗糙介质的折射率时,采用全反角进行判定;测量具有吸收效应的介质折射率时,采用布儒斯特角进行判定.     

光子晶体光纤气体传感灵敏度的有限差分法分析

提出了一种适合于高灵敏度气体传感器的新型光子晶体光纤结构.采用全矢量频域有限差分方法，研究了基于不同结构光子晶体光纤的气体传感器的相对灵敏度.由全矢量频域有限差分法，通过直接求解由麦克斯韦方程组导出的标准特征值方程，可以得到光纤中可能存在的不同模式的传播常量、电场分布和磁场分布.分别给出了三种不同结构光子晶体光纤在波长为1.3312 μm处，与结构参量变化对应的相对灵敏度变化以及在不同波长情况下的相对灵敏度变化.结果证明,该新结构具有较其它代表性的折射率引导型光子晶体光纤结构更高的灵敏度，特别适合作气体传感器.     

一种简化的分析光纤布拉格光栅的时域有限差分束传输法

提出了一种便于分析光纤布拉格光栅(FBG)、基于强制边界条件的简化TD-FD-BPM模型.采用交替隐式法(ADIM)和综合道格拉斯(GD)法,离散化时域束传输方程,获得比普通差分格式低二阶的误差。提出并采用强制边界条件,简化了光波导分析中边界处理问题.重点讨论和确定了在此条件下激励源位置、脉冲形状和径向分布函数、连续波激励条件等.在修正的正弦脉冲激励情况下,通过离散傅利叶变换,直接得到较为理想的短FBG反射谱.此法可减少数值计算时间,直观反映光脉冲传输.     

光纤纤芯及包层模有效折射率计算及仿真

光纤结构设计、模间色散求解、光纤光栅模式耦合等问题的研究, 都需要对光纤纤芯及包层模的有效折射率进行精确计算. 本文以光纤三层结构模型为基础, 结合该模型下的模式本征方程, 使用截弦法求解了纤芯模有效折射率, 并将计算结果与COMSOL软件模拟的对应纤芯模的传输光场进行对比, 验证了计算结果正确.使用区间遍历算法对包层模有效折射率进行了求解, 与已有的传统方法相比, 该方法可以有效防止求解过程中根的遗漏、避免特征方程产生的奇点, 并能保证模式的正规性.本文采用Mathematica软件对求解过程进行仿真, 获得了纤芯模和包层模有效折射率与波长关系曲线. 关键词： 光纤传输模式 有效折射率 截弦法 区间遍历算法     

Numerical treatment of acoustic problems with the smoothed finite element method

We incorporated a cell-wise acoustic pressure gradient smoothing operation into the standard compatible finite element method and extended the smoothed finite element method (SFEM) for 2D acoustic problems. This enhancement was especially useful for dealing with the problem of an arbitrary shape with violent distortion elements. In this method, the domain integrals that involve shape function gradients can be converted into boundary integrals that involve only shape functions. Restrictions on the shape elements can be removed, and the problem domain can be discretized in more flexible ways. Numerical results showed that the proposed method achieved more accurate results and higher convergence rates than the corresponding finite element methods, even for violently distorted meshes. The most promising feature of SFEM is its insensitivity to mesh distortion. The superiority of the method is remarkable, especially when solving problems that have high wave numbers. Hence, SFEM can be beneficially applied in solving two-dimensional acoustic problems with severely distorted elements, which, in practice, have more foreground than regularity mesh.     

Design of shaped piezoelectric modal sensor for beam with arbitrary boundary conditions by using Adomian decomposition method

The theory for designing distributed piezoelectric modal sensors is well established for beam structures. However, the current modal sensor theory is limited in scope in that it can only be applied in the case of classical boundary conditions (i.e., either clamped, free, simply supported or sliding). In this paper a solution to the problem of finding the shape of piezoelectric modal sensors for a beam with arbitrary boundary conditions is proposed, using the Adomian decomposition method (ADM). A general expression for designing the shape of a piezoelectric modal sensor is presented, in which the output signal of the designed sensor is proportional to the response of the target mode. Other modes are filtered out. The modal sensor shape is expressed as a function of the second spatial derivative of the structural mode shape function. Based on the ADM and employing some simple mathematical operations, the closed-form series solution of the second spatial derivative of the mode shapes can be determined. Then the shapes of the designed modal sensors are obtained. Finally, some numerical examples are given to demonstrate the feasibility of the proposed modal sensors. It is shown that, for classical boundary conditions, the shapes of the modal sensors based on the ADM agree well with analytical and numerical results given in the literature. For general boundary conditions it is found that the shape of the modal sensors is influenced by the number of modes of interest because the second spatial derivatives of the mode shapes are not orthogonal to one another. The modal sensors for general boundary conditions can be considered as modal filters within a limited frequency band.     

有限元法求解任意折射率分布光纤模场分布

 应用有限元方法求解了任意径向非均匀折射率分布园柱对称介质波导中纵向场耦合波动方程定解问题所对应的变分问题,该方法不受弱导或高斯模场分布等限制,可方便地求解光纤中介质波导的模场分布。用此方法研究了带阶跃环的三角型分段折射率分布光纤中归一化模场半径与芯层传输功率比值随光纤不同结构参数的变化规律。     

全矢量有限差分法分析任意截面波导模式

针对不规则端口模式加载的需求, 改进了全矢量有限差分法, 推导了边界条件, 建立了模式求解器, 解决了不规则端口任意模式加载的难题. 该求解器对计算资源要求较低, 可以求解任意形状的波导模式. 计算了不同形状波导的模式特性, 得到了与解析解和商用软件结果相一致的计算结果. 关键词： 全矢量有限差分法 波导 模式     

The R-function method for the free vibration analysis of thin orthotropic plates of arbitrary shape

Free flexural vibrations of homogeneous, thin, orthotropic plates of an arbitrary shape with mixed boundary conditions are studied using the R-function method. The proposed method is based on the use of the R-function theory and variational methods. In contrast to the widely used methods of the network type (finite differences, finite element, and boundary element methods), in the R-function method all the geometric information given in the boundary value problem statement is represented in an analytical form. This allows one to seek a solution in a form of some formulas called a solution structure. These solution structures contain some indefinite functional components that can be determined by using any variational method. A method of constructing the solution structures satisfying the required mixed boundary conditions for eigenvalue plate bending problems is described. Numerical examples for the vibration analysis of orthotropic plates of complex geometry with mixed boundary conditions for illustrating the aforementioned R-function method and comparison against the other methods are made to demonstrate its merits.     

小尺度阻尼边界封闭空间声传递函数的有限元素法计算

如何求解阻尼边界封闭空间中声源点到接收点的低频声传递函数已成为目前小尺度封闭空间可听化技术研究的关键技术，能处理任意形状及复杂边界条件的有限元素法可作为求解该问题的适合方法，以室内声声有源Helmholtz方程及其相应边界方程为基础，本文推导出了用于小尺度阻尼边界封闭空间声传递函数的有限元素求解方法，并编制了相应的计算机程序，在算例中，首先通过与模态叠加法计算结果进行比较，验证了该方法的正确性。最后计算了某型车体内腔中任意两点间声传递函数。     

有限元/边界积分方法在海面及其上方弹体目标电磁散射中的应用

本文将有限元/边界积分方法(FE/BIM)结合区域分解方法引入到粗糙海面及其上方目标 的电磁散射问题的研究中. 由于积分边界可以以任意形状设置在距模型表面任意远的距离处, 故本文采用共形人工边界结合区域分解建模方法截断模型的开放计算区域以减少求解未知量, 在截断区域内部采用有限元方法求解, 而计算区域的边界条件通过边界积分方程方法得到. 通过与矩量法获得的数值计算结果进行比较, 证明了该混合算法及模型处理方法的正确性, 进而研究了海面上方弹体目标的电磁散射特性, 并讨论了其双站散射系数随电磁波入射角度、目标高度、海面风速以及弹体尺寸的电磁散射特性变化情况. 本文结果可用于反演复杂背景下的目标信息及目标探测等领域. 关键词： 电磁散射 粗糙海面 目标 有限元/边界积分方法     

First passage time distributions for finite one-dimensional random walks

We present closed expressions for the characteristic function of the first passage time distribution for biased and unbiased random walks on finite chains and continuous segments with reflecting boundary conditions. Earlier results on mean first passage times for one-dimensional random walks emerge as special cases. The divergences that result as the boundary is moved out to infinity are exhibited explicitly. For a symmetric random walk on a line, the distribution is an elliptic theta function that goes over into the known Lévy distribution with exponent 1/2 as the boundary tends to ∞.     

Transparent boundary conditions for the Helmholtz equation in some ramified domains with a fractal boundary

The paper addresses a class of boundary value problems in some self-similar ramified domains, with the Laplace or Helmholtz equations. Much stress is placed on transparent boundary conditions which allow the solutions to be computed in subdomains. A self similar finite element method is proposed and tested. It can be used for numerically computing the spectrum of the Laplace operator with Neumann boundary conditions, as well as the eigenmodes. The eigenmodes are normalized by means of a perturbation method and the spectral decomposition of a compactly supported function is carried out. Finally, a numerical method for the wave equation is addressed.     

Source implementation to eliminate low-frequency artifacts in finite difference time domain room acoustic simulation

The finite difference time domain (FDTD) method is a numerical technique that is straight forward to implement for the simulation of acoustic propagation. For room acoustics applications, the implementation of efficient source excitation and frequency dependent boundary conditions on arbitrary geometry can be seen as two of the most significant problems. This paper deals with the source implementation problem. Among existing source implementation methods, the hard source implementation is the simplest and computationally most efficient. Unfortunately, it generates a large low-frequency modulation in the measured time response. This paper presents a detailed investigation into these side effects. Surprisingly, some of these side effects are found to exist even if a transparent source implementation is used. By combing a time limited approach with a class of more natural source pulse function, this paper develops a source implementation method in FDTD that is as simple and computationally as efficient as a hard source implementation and yet capable of producing results that are virtually the same as a true transparent source. It is believed that the source implementation method developed in this paper will provide an improvement to the practical usability of the FDTD method for room acoustic simulation.