An FDTD absorbing boundary condition for anisotropic media based on NPML

Based on the nearly perfectly matched layer (NPML) theory, a finite-difference time-domain (FDTD) absorbing boundary condition (ABC) is presented for truncating three-dimensional (3-D) anisotropic medium. In the proposed technique, the complex coordinate stretching in the NPML scheme and the spatial interpolation method are employed. The associated ABC formulations have the advantage of simplicity in the FDTD implementations. The radiation fields of an electric dipole in anisotropic media are calculated using the presented ABC. The results are numerically verified by the comparison with the reference solutions. Furthermore, in order to clearly show the effective absorbing performance of the proposed method, the reflection coefficient and time-dependent relative error for different layers NPML absorbing boundary are also simulated.     

一种适用于任意阶空间差分时域有限差分方法的色散介质通用吸收边界条件算法

基于伸展坐标完全匹配层方程和辅助微分方程 方法, 给出了一种在时域有限差分(FDTD) 计算中适用于常见色散介质的通用边界条件算法. 该算法适用于任意阶的FDTD空间差分, 并且由于所采用的D-H方程独立于计算区域, 所以可以被用于截断任意电介质. 数值试验结果表明, 与卷积完全匹配层 算法相比较, 所提出的吸收边界条件算法不仅通用性强、 计算复杂度低、 计算时间短, 并且吸收效果有明显的提高.     

一种色散介质FDTD通用吸收边界

由单轴各向异性介质所满足的场方程出发,并根据相位匹配原理以得到介质中的色散关系和无反射条件.结合频域到时域的转换关系（即用/t代替jω）和移位算子时域有限差分（SO-FDTD）方法提出了一种适用于各向同性常见色散介质模型,包括德拜模型、洛伦兹模型、德鲁德模型等的通用UPML吸收边界.数值结果表明了该算法的通用性和高效性. 关键词： 时域有限差分 吸收边界 移位算子 色散介质     

A FDTD formulation for high order dispersive media of muscle-equivalent

In this paper, shift operator finite-difference time-domain (SO-FDTD) method is applied for the calculation of the dispersive medium. The high efficiency and accuracy of this method is verified by calculating the reflection of the plane electromagnetic wave impinging on a muscle slab. For human tissues where multiterm Debye relaxation equations must generally be used. We describe a new differential equation approach, which can be used for general dispersive media. In this method D(t) is expressed in terms of E(t) by means of a differential equation involving D, E, and their time derivatives. The method is illustrated by means of example of media for which relative permittivity is given by a multiterm Debye equation, and for an approximate two-thirds muscle-equivalent model of the human body.     

截断各向异性等离子体的修正各向异性完全匹配层吸收边界

基于磁化等离子体本构方程,提出了一种截断各向异性色散介质的修正的各向异性完全匹配层(M-UPML)吸收边界算法。通过等效相对介电常数,将UPML推广到截断各向异性等离子体介质的情形,并推导了其时域有限差分方法(FDTD)迭代式。用该方法计算了半空间磁化与非磁化等离子体的反射系数,计算结果与解析解相一致,表明该吸收边界具有良好的吸收效果。     

截断各向异性等离子体的修正各向异性完全匹配层吸收边界

 基于磁化等离子体本构方程,提出了一种截断各向异性色散介质的修正的各向异性完全匹配层(M-UPML)吸收边界算法。通过等效相对介电常数,将UPML推广到截断各向异性等离子体介质的情形,并推导了其时域有限差分方法(FDTD)迭代式。用该方法计算了半空间磁化与非磁化等离子体的反射系数,计算结果与解析解相一致,表明该吸收边界具有良好的吸收效果。     

高阶色散介质的改进移位算子时域有限差分方法

提出一种适用于高阶Debye,Drude,Lorentz及其混合模型的改进移位算子的时域有限差分(SO-FDTD)方法。从介质极化率函数出发,将其写成一阶或二阶有理分式求和的形式,并在随时间步推进计算的过程中,通过引入中间变量和设置临时变量,克服了常规SO-FDTD将高阶模型直接转化为有理分式所导致的计算复杂性和内存占用量大的问题。同时,改进SO-FDTD方法的时域推进计算步骤具有通用性,克服了常规递归卷积(RC-FDTD)方法对各种高阶模型具有不同计算公式,因而不能形成通用计算程序的问题。最后,通过空气-高阶色散介质界面的反射系数计算验证了算法的有效性和通用性。     

高阶色散介质的改进移位算子时域有限差分方法

提出一种适用于高阶Debye,Drude,Lorentz及其混合模型的改进移位算子的时域有限差分(SO-FDTD)方法。从介质极化率函数出发,将其写成一阶或二阶有理分式求和的形式,并在随时间步推进计算的过程中,通过引入中间变量和设置临时变量,克服了常规SO-FDTD将高阶模型直接转化为有理分式所导致的计算复杂性和内存占用量大的问题。同时,改进SO-FDTD方法的时域推进计算步骤具有通用性,克服了常规递归卷积(RC-FDTD)方法对各种高阶模型具有不同计算公式,因而不能形成通用计算程序的问题。最后,通过空气-高阶色散介质界面的反射系数计算验证了算法的有效性和通用性。     

High-order FDTD methods for transverse electromagnetic systems in dispersive inhomogeneous media

This Letter introduces a novel finite-difference time-domain (FDTD) formulation for solving transverse electromagnetic systems in dispersive media. Based on the auxiliary differential equation approach, the Debye dispersion model is coupled with Maxwell's equations to derive a supplementary ordinary differential equation for describing the regularity changes in electromagnetic fields at the dispersive interface. The resulting time-dependent jump conditions are rigorously enforced in the FDTD discretization by means of the matched interface and boundary scheme. High-order convergences are numerically achieved for the first time in the literature in the FDTD simulations of dispersive inhomogeneous media.     

有耗介质空间完全匹配层吸收边界条件及其应用

针对Gedney提出的完全匹配层(PML)无法用于有耗各向同性计算域的截断及其对倏逝波的衰减不理想等问题,提出了一种扩展方法。扩展的PML的主要思想是在各向异性的PML中引入与有耗介质空间相一致的复介电常数和复磁导率,使之可以与有耗介质计算域相匹配。通过给PML的张量介电常数、张量磁导率增加衰减因子以加速倏逝波的衰减。构造了PML吸收效果验证模型,数值结果证明了扩展的PML在处理有耗介质计算域截断问题中的有效性。利用该吸收边界条件,采用时域有限差分法计算了电磁脉冲作用下地面铺设电缆的电磁脉冲响应,计算结果和试验结果取得了较好的一致。     

High-order harmonic generation in absorbing, dispersive, and ionizing media

Experimental and theoretical investigations of high-order harmonic generation in absorbing, dispersive, and ionizing media are reported. All factors limiting the high-order harmonic generation efficiency are taken into account. Good agreement between calculations and experimental results is obtained.     

Propagation of partially polarized Gaussian Schell-model beams in dispersive and absorbing media

Analytical transform formulae for partially polarized Gaussian Schell-model (GSM) beams propagating in dispersive and absorbing media are derived by use of a new tensor method. Using the derived formulae, we studied the polarization and irradiance distribution properties of partially polarized GSM beams in dispersive and absorbing media. The results show that the dispersive and absorbing media has strong influence on the polarization and irradiance distribution of partially polarized GSM beams. The polarization and irradiance distribution of partially polarized GSM beams in dispersive and absorbing media are also closely related to the initial coherence and the source spectral width of partially polarized GSM beams. The propagation properties of an nonpolarized GSM beam and partially polarized GSM beams are compared and discussed. Our method provides a convenient way to treat the propagation of partially polarized GSM beams in different linear medium.     

二维单步交替方向隐式时域有限差分法吸收边界性能分析

给出了两种适用于二维单步交替方向隐式时域有限差分(2-D Leapfrog ADI-FDTD)方法的吸收边界：Mur边界和卷积完全匹配层(CPML)边界。单步交替方向隐式时域有限差分(Leapfrog ADI-FDTD)方法是一种无条件稳定的全隐式差分算法,由于二维空间Leapfrog ADI-FDTD的迭代同时存在显式和隐式方程,故而不同电磁分量的边界条件也存在差异。从原理出发,推导了适用于2-D Leapfrog ADI-FDTD方法的CPML边界条件,并与一阶Mur边界进行比较,利用自由空间的反射误差来表征两种边界的吸收性能,简要总结了两种吸收边界的优缺点。     

基于半解析递归卷积的通用色散介质FDTD方法

基于数字信号处理中的半解析递归卷积（SARC）算法,提出了一种用于色散介质电磁特性分析的半解析递归卷积时域有限差分方法（SARC FDTD）. 该方法既保持了FDTD方法处理复杂目标的灵活性,又吸取了线性系统SARC算法的绝对稳定性和高精度、低内存、高效率等优点,只需给出色散介质模型的极点和对应系数,即可运用SARC FDTD递推公式和通用程序进行计算,具有较好的通用性. 通过Debye,Drude和Lorentz三种常用色散介质模型对算法进行了验证. 关键词： 时域有限差分 色散介质 半解析递归卷积     

Electrodynamics of bounded spatially dispersive media: The additional boundary conditions

The eigenfunction for the center of mass motion of a Mott-Wannier exciton in a bounded medium has been determined by solving asymptotically an effective mass equation, assuming electron and hole reflect perfectly from the surface: the surface potential is taken as an infinite barrier. Using this eigenfunction, the non-local susceptibility was determined. From it the relevant additional boundary condition for this model follows: the total flux associated with the sum of the polarization waves vanishes at the surface.     

双色散模型的辛时域有限差分算法

结合有耗的Drude-Lorentz色散模型,提出了处理双色散模型的辛时域有限差分算法.基于矩阵分裂,辛传播算子和辅助差分方程技术,结合严格而巧妙的公式推导,构建了算法框架,并给出了详细的公式推导过程.为了验证本文算法的有效性和精确性,首先计算了一维空间双色散平板的透射系数,并与解析解对比,结果较好地符合,证明了该算法是有效而精确的.然后计算了三维空间中有实际意义的银分裂环,金属银的介电参数由Drude模型拟合.计算了该结构的透射系数,反射系数和吸收系数,得到了银分裂环的谐振频率和吸收频率,为实际实验结果提供了可供参考的计算结果.     

An FDTD method for the simulation of dispersive metallic structures

In this paper, we present a formulation of the finite-difference time-domain method for the simulation of metallic structures. The frequency dependent dielectric function of metals is approximated by a combined Drude–Lorentzian multi-pole expansion and fitting errors of only a few percent are obtained. An auxiliary differential equation technique is used to extend the standard FDTD algorithm with the dispersive material equations. The algorithm is validated by calculating reflection and transmission coefficients for thin metal layers, elliptical nano-particles and by simulating a surface plasmon resonance device. Excellent agreement between the FDTD simulations and exact theoretical results are obtained.     

Accurate absorbing boundary conditions for anisotropic elastic media. Part 2: Untilted non-elliptic anisotropy

With the ultimate goal of devising effective absorbing boundary conditions (ABCs) for general elastic media, we investigate the accuracy aspects of local ABCs designed for untilted non-elliptic anisotropy in the frequency domain (time-harmonic analysis). While simple space–time transformations are available to treat the wavemodes with opposing phase and group velocities present in elliptic anisotropic media, no such transformations are known to exist for the case of non-elliptic anisotropy. In this paper, we use the concept of layer groupings along with an unconventional stretching of the finite element mesh to guarantee the accuracy of local ABCs designed to treat all propagating wavemodes, even those with opposing phase and group velocities. The local ABC used here is the perfectly matched discrete layer (PMDL) which is a simple variant of perfectly matched layers (PMLs) that is also equivalent to rational approximation-based local ABCs (rational ABCs); it inherits the straightforward approximation properties of rational ABCs along with the versatility of PML. The approximation properties of PMDL quantified through its reflection matrix allow us to (a) show that it is impossible to design an accurate PMDL with wavenumber-independent parameters, (b) theoretically demonstrate the ability of wavenumber-dependent parameters to ensure accuracy, and finally (c) design a practical though unconventional stretching of the finite element PMDL mesh that facilitates the implementation of wavenumber-dependent parameters. The validity of this work is demonstrated through a series of numerical experiments.