二维共形匹配层的衰减参数研究

给出了各向异性媒质的张量本构参数,由含各向异性媒质的三维波动方程出发推导了包含此类介质的散射问题的有限元变分公式,研究了共形匹配层衰减参数随目标尺寸和形状的变化规律,分析了参数选择对匹配层吸收效果的影响,数值结果表明衰减参数的最佳值将随散射体尺寸的变大而增加。得出的变化规律对共形匹配层和有限元的应用极有参考价值。     

带ABC底面的共形完全匹配层按层积分算法

本文构造了一种共形完全匹配层(Conformal Perfectly latched Layer,CPML)矢量单元按层积分算法,将多层单元积分运算叠加到一层单元中进行,即保留了多层单元的几何和材料信息,又减少了计算规模;为了进一步增强吸收,减少底面反射,应用矢量ABE(Absorbing Boundary Condition,ABC)吸收边界作为CPML底面.数值算例表明,这种按层积分CPML结合矢量ABC吸收边界的方法,吸收效果好,计算量小,效率高;具有良好的应用前景.     

半矢量模式求解在光波导弯曲损耗计算中的应用

以柱坐标下的半矢量波动方程为基础,采用基于完美匹配层(PML)边界条件的有限差分方法,对弯曲波导进行模式求解,进而得到波导弯曲引起的辐射损耗.基于计算得到的直弯波导的模场分布,采用二维重叠积分法计算了两者连接时的过渡损耗.计算结果与已有实验结果符合较好.采用该方法,研究了SOI脊型波导的弯曲损耗与波导结构参数之间的关系,并对直弯波导的连接进行了优化.     

Perfectly matched layer media with CFS for an unconditionallystable ADI-FDTD method

A perfectly matched layer (PML) medium with complex frequency shifted (CFS) constitutive parameters is introduced for the three-dimensional alternating direction implicit (ADI) formulation of the finite-difference time-domain (FDTD) method. The absorbing boundary is implemented using the convolutional PML (CPML) approach. It is demonstrated that the resulting ADI-CPML scheme is unconditionally stable. The effectiveness of the absorbing medium as a function of the time step is also demonstrated. The proposed method has the advantage that it allows the application of the ADI method to low-frequency analysis     

Convolutional Perfectly Matched Layer for an Unconditionally Stable LOD-FDTD Method

This letter presents the development and implementation of the convolutional perfectly matched layer (CPML) for the recently proposed locally 1-D finite difference time domain method LOD-FDTD. Two different examples are simulated. Their results are compared with the FDTD-PML method and it is found that the proposed method has 16 dB less reflection error at a Courant Friedrich Levy number of one.     

Diffraction of a coaxial resonator’s hybrid modes by a transverse slot and a cylindrical dielectric layer

The partial-domain method is applied to theoretically solve the problem of diffraction of a hybrid resonance mode by an inner ring slot and a cylindrical dielectric layer in a coaxial cavity with perfectly conducting walls of a finite thickness. The boundary equations for field amplitudes are solved with the use of Tikhonov’s regularization method, and a stable algorithm of calculation of the complex wave number (i.e., the resonance frequency and Q factor of free field oscillations) is developed. Conditions for the energy balance on the slot in the presence of a resonance are considered. Being independent of the field equations, these conditions complement them.     

Application of a perfectly matched layer in problems of simulation of electromagnetic ultralong wave propagation in the spherical earth-ionosphere waveguide channel

A method based on the use of a perfectly matched layer is proposed for creating a nonreflecting boundary involved in the simulation of ultralong electromagnetic wave propagation in the spherical Earthionosphere waveguide channel. It is shown that this channel provides for the attenuation of electromagnetic waves propagating in a perfectly matched layer along a radio path. A system of differential equations describing the propagation of electromagnetic waves in this region is presented.     

Side-Polished Microstructured Optical Fiber for Temperature Sensor Application

We propose new microstructured optical fiber (MOF) designs for temperature sensing applications. Such fiber designs consist of a side-polished MOF with the flat side coated with a large thermooptic coefficient external medium. Numerical analysis based on a full-vector finite-element method with a perfectly matched layer was applied to evaluate the power loss caused by the evanescent field going through the external medium. Our calculations demonstrate that it is possible to change the sensor sensitivity by selecting an adequate microstructured fiber geometry. Also, different external media can be used to shift the operational range of temperature sensing.     

三维柱坐标ADI-FDTD算法及其CPML实现

提出一种三维柱坐标交互隐式方向(ADI)时域有限差分算法(FDTD)及其卷积完全匹配层(CPML)的实现方案。首先,为了简化公式的冗繁和编程的需要,将传统三维柱坐标时域有限差分算法转换成矩阵表达式的形式。其次,以矩阵变换的方式提出三维柱坐标系下ADI-FDTD 算法的矩阵表达式。最后,将匹配层的影响参数以辅助变量的方式添加至该算法中,从而完成本文算法的CPML实现。算例证明本文算法在时域和频域均有较好的效率和精度,并且具有良好的CPML 吸收效果,其反射系数可达-63 ~ -70 dB。     

A novel efficient algorithm for scattering from a complex BOR usingmixed finite elements and cylindrical PML

An efficient finite-element method (FEM) is developed to compute scattering from a complex body of revolution (BOR). The BOR is composed of a perfect conductor and impedance surfaces and arbitrary inhomogeneous materials. The method uses edge-based vector basis functions to expand the transverse field components and node-based scalar basis functions to expand the angular component. The use of vector basis functions eliminates the problem of spurious solutions suffered by other three component FEM formulations. The FEM mesh is truncated with a perfectly matched layer (PML) in cylindrical coordinates. The use of PML in cylindrical coordinates avoids the wasted computation which results from a spherical mesh boundary with an elongated scatterer. The FEM equations are solved by ordering the unknowns with a reverse Cuthill-McKee algorithm and applying a banded-matrix solution algorithm. The method is capable of handling large, realistic radar targets, and good agreement with measured results is achieved for benchmark targets     

三维柱坐标下ADI-WLP FDTD算法的CPML实现

提出一种三维柱坐标系下交变方向隐式(ADI)的加权拉盖尔时域有限差分(WLP-FDTD)算法,并利用卷积完全匹配层(CPML)实现。通过引入微扰项可将大型稀疏矩阵的CPML 形式分解为6个三对角矩阵,之后结合高斯-赛德尔思想,将6 个三对角矩阵划分为两部分迭代计算,可进一步提升计算效率和收敛速度。在柱坐标模型的应用算例中,数值计算结果显示该算法的CPML 吸收边界对比Mur 吸收边界有较好的吸收效果。     

Efficient analytical and numerical methods for the computation of bent loss in planar waveguides

In this paper, we present new analytical and numerical modal analyses of bent planar waveguides allowing precise computation of the bending loss. The analytical method is based on an accurate algorithm for evaluating Bessel and Hankel functions. The numerical one relies on a finite-element model derived from the cylindrical coordinates version of the Maxwell system. To eliminate spurious reflections from the artificial boundary of the computational domain, an efficient perfectly matched layer technique is adapted to the formulation. A thorough comparison shows that our analytical approach is both simple and highly accurate whereas the numerical method is cheap and easily extendible to higher dimensions and other geometries.     

表面等离子体共振类熊猫型光子晶体光纤传感器

分析了基于表面等离子体共振类熊猫型的光子晶体光纤传感器,采用基于全矢量有限元法（FEM）对光纤模式进行了数值计算,在各向异性完美匹配层（PML）边界条件下,求解模场的有效折射率。讨论了各个参量的尺寸对传感的影响。计算表明,激发的等离子体对环境介质折射率的变化非常敏感,所设计传感器最大光谱灵敏度达到2 μm/RIU,若光谱仪的分辨率为10 pm,则传感器的分辨率可以达到5×10-6 RIU。     

A scalar finite-difference time-domain method with cylindrical perfectly matched layers: application to guided and leaky modes of optical waveguides

A new scheme for the scalar finite-difference time-domain (FDTD) method with perfectly matched layer boundary conditions in cylindrical coordinate system is developed and presented. The FDTD method is applied successfully for the calculation of both guided and leaky modes of optical waveguides with circular symmetry.     

A new 2-D FDTD method applied to scattering by infinite objects with oblique incidence

A new two-dimensional (2-D) finite-difference time domain (FDTD) method applied to scattering by infinite objects with oblique incidence is proposed. 2-D Maxwell's equations, differential equations, and perfectly matched layer (PML) absorbing boundary conditions (ABC) are derived. The incident wave, computed by the 1-D FDTD method, is set on the connecting boundary. The accuracy and the efficiency of the proposed method have been verified by comparing the results of the split-field periodic FDTD method, the sine-cosine method, and the transmission line theory method with the proposed method.     

Analysis of Perfectly Matched Double Negative Layers Via Complex Coordinate Transformations

Complex coordinate transformations are introduced for the analysis of time-harmonic electromagnetic wave propagation in perfectly matched double negative layers. The layer is perfectly matched to free space in the sense that any incident plane wave is transmitted through the free space-material interface without reflection, irrespective of the frequency and angle of incidence of the plane wave. The material constitutive parameters are obtained by mapping spatial coordinates into a manifold in complex space. The layer turns out to be anisotropic in general, and the special case where the medium is isotropic can be deduced from the coordinate transformations. The left-handedness, as well as the reversal in phase velocity appear naturally as a result of the mapping of the spatial coordinates into complex space. The consequences of this analysis are demonstrated by some examples     

PSTD算法及其吸收边界分析

在解时域电大尺寸电磁场问题时,由于受到有限差分格式二阶精度的限制,传统FDTD算法的效率很低,对内存的要求高.采用以伪谱方法离散Maxwell微分方程为核心的Pseudospectral time-domain(PSTD)算法计算电大尺寸电磁场时域问题,将大大提高计算效率,降低内存需求.本文重点探讨了在PSTD技术中,电大尺寸问题的高效实现,并和传统FDTD算法进行了比较.此外还分析了其吸收边界－完全匹配层(PML)所发挥的作用,PML的设置以及各参数对场吸收的影响.     

Single-polarization single-mode photonic crystal fibers

A new structure of single-polarization single-mode (SPSM) photonic crystal fiber (PCF) is proposed and analyzed by using a full-vector finite element method with anisotropic perfectly matched layers. From the numerical results it is confirmed that the proposed fiber is low-loss SPSM-PCF within the wavelengths ranging from 1.48 to 1.6 /spl mu/m, where only the slow-axis mode exists and the confinement loss is less than 0.1 dB/km.     

A simple, nearly perfectly matched layer for general electromagnetic media

A new implementation of the perfectly matched layer (PML) absorbing boundary condition is presented. This formulation is designed such that the partial differential equations in the PML are identical to those in the regular medium for any linear electromagnetic material. This makes this method particularly simple to implement, especially in dispersive and anisotropic materials. We call this method the nearly perfectly matched layer (NPML) because it employs variable changes that are not strictly exact when the PML conductivity is spatially variant. Comparisons with the convolutional PML in a Lorentz dielectric show that the NPML is as effective an absorber as exact PML formulations.     

FDTD-PLRC Technique for Modeling of Anisotropic-Dispersive Media and Metamaterial Devices

The goal of this paper is to develop a versatile computational engine based on the finite-difference time-domain (FDTD) technique to comprehensively demonstrate the broadband behaviors of devices designed utilizing anisotropic-dispersive metamaterials. In this regard, the frequency-dependent behavior of dispersive materials is incorporated into the FDTD equations with the use of a piecewise linear recursive convolution (PLRC) approach. The FDTD domain is effectively terminated utilizing convolutional perfectly matched layered (CPML) absorbing walls, which are derived from the complex frequency-shifted (CFS) formulation. The CPML has the advantage that it operates only on the filed intensities and has nothing to do with the and constitutive relationships. The CPML is also highly absorptive to both propagating and evanescent waves. Therefore, it would be of great interest for terminating metamaterials having complex constitutive parameters. The developed method is also capable of characterizing periodic configurations illuminated by normal incident plane waves. The FDTD engine is successfully validated through the analyses of several complex metamaterials. The design and characterization of novel devices such as a patch antenna printed on metasubstrate with anisotropic epsiv (omega) - mu (omega)parameters, an electrically small antenna embedded in negative permittivity resonator, and an anisotropic-dispersive self-biased hexagonal ferrite-coupled line (FCL) circulator are highlighted.