Unconditionally Stable Complex Envelope Wave Equation PML Algorithm for Band Limited FDTD Simulations

Unconditionally stable complex envelope (CE) perfectly matched layer (PML) absorbing boundary conditions (ABCs) are presented for truncating the scalar wave-equation finite difference time domain (WE-FDTD) grids. The formulations are based on incorporating the alternating direction implicit (ADI) scheme into the CE FDTD implementations of the scalar wave-equation derived in the PML region at the domain boundaries. Numerical example carried out in two dimensional domain shows that the proposed formulations are more accurate than the classical ADI scalar wave equation PML formulations when it is used for modelling band limited electromagnetic applications.     

基于非分裂FDTD的左手介质电磁特性的研究

为验证左手介质的电磁特性,采用非分裂时域有限差分方法对左手介质的Drude模型进行建模.这种方法不需要对电场和磁场进行分裂,也不需要对PML空间进行特殊处理,吸收边界PML和工作空间可以通过参数转换来完成,并且构造的PML层为有耗介质,进入PML层的透射波将迅速衰减.它是一种准确而有效的分析色散和各向异性介质的方法,通过此方法有效地验证了左手介质的负折射效应、汇聚效应、相位补偿效应,充分验证了左手介质及其反常特性的存在性和此方法分析左手介质的有效性. 关键词： 左手介质 非分裂 时域有限差分 Drude     

A Non-Energy-Concentrating Lens Using Left-Handed Material

In a planar lens made of left-handed material (LHM), the rays converge to a focal point in the material and once again in free space. The problems exhibited by the planar lens are its great thickness, the long optical path length, and energy concentration in the LHM. We examine a bowl-shaped LHM lens with an index n = −1. In this lens, the back is a concave hemispherical surface and the rays never converge in the LHM, but in free space only. We also designed a quantized bowl-shaped LHM lens composed of multiple layers of thin LHM plates of uniform thickness. A bowl-shaped LHM lens quantized with more than 4 bits has a lens function similar to that of a smooth curved lens. The bowl-shaped lens is characterized by its thinness, its short optical path length, and the absence of energy concentration in the LHM. Furthermore, the quantized bowl-shaped LHM lens can be fabricated. Wave propagation through these lenses is numerically simulated using the finite difference time domain (FDTD) method.     

Unsplit-Field PML Algorithm for Truncating Nonlinear FDTD Domains

In this paper, unsplit-field Perfectly Matched Layer (PML) formulations are presented for truncating nonlinear dispersive Finite Difference Time Domain (FDTD) grids. The proposed scheme is based on incorporating the nonlinear Z-transform FDTD algorithm into the Auxiliary Differential Equation PML (ADE-PML) formulations. Numerical example carried out in one dimensional domain which includes Lorentz dispersion as well as Kerr and Raman nonlinearities is included to show the validity of the formulations.     

Unconditionally Stable Z-Transform ADI-PML Algorithm for Lorentzian Double Negative Meta-Materials

Unconditionally stable formulations of the anisotropic perfectly matched layer (APML) are presented for truncating double negative (DNG) meta-material finite difference time domain (FDTD) grids. In the proposed formulations, the Z-transform theory is employed in the alternating direction implicit FDTD (ADI-FDTD) scheme to obtain update equations for the field components in the DNG meta-material domains. Numerical examples carried out in one dimensional Lorentzian type DNG meta-material domains are included to show the validity of the proposed formulations.     

非线性左手材料的时域研究

 分析了非线性左手材料模型,推导了非线性左手材料中的时域有限差分法及完美匹配层的计算式。数值模拟了具有Kerr非线性效应的左手材料平板中的电磁波。观察到该材料同样具有电磁聚焦特性。对比线性左手材料,其聚焦点的幅度和位置都会发生偏移。同时改变波源的强度及其到平板边界距离,讨论了不同距离情况下该非线性左手材料平板对电磁波分布的影响。当波源距离材料平板足够远,通过非线性左手材料聚焦的电场强度几乎集中在其外表面。     

可多重聚焦电磁能量的左手材料结构

 功分器在微波工程中广泛应用。基于有损耗的Lorentz模型的时域有限差分(FDTD)方法,分析模拟了左手材料(LHM)的平板结构和环状结构对电磁波源的不同聚焦特性。每个左手材料边界均可以对波源发出的波进行聚焦。同时通过比较,在对称结构中,每个聚焦点的电磁场幅度都相同。说明该左手材料结构可以对电磁波源进行多点聚焦。     

Design and analysis of doped left-handed materials

We devise three sorts of doped left-handed materials （DLHMs） by introducing inductors and capacitors into the traditional left-handed material （LHM） as heterogeneous elements. Some new properties are presented through finitedifference time-domain （FDTD） simulations. On the one hand, the resonance in the traditional LHM is weakened and the original pass band is narrowed by introducing inductors. On the other hand, the original pass band of the LHM can be shifted and a new pass band can be generated by introducing capacitors. When capacitors and inductors are introduced simultaneously, the resonance of traditional LHM is somewhat weakened and the number of original pass bands as well as its bandwidth can be changed.     

基于Z变换的高阶完全匹配层实现

基于拉伸坐标完全匹配层(SC-PML)公式和Z变换方法,提出以非分裂场形式来实现具有多极点的高阶完全匹配层的高效算法,来截断时域有限差分(FDTD)网格.在吸收性能方面,高阶PML同时具有传统PML和复频率偏移完全匹配层(CFS-PML)二者的优点.提供的数值算例是二维TE极化电磁波与无限长且有限宽度的理想电导体(PEC)薄片的相互作用.仿真结果显示,高阶PML公式在衰减低频行波和隐失波及减少后期反射方面效果好,比传统SC-PML和复频率偏移的卷积完全匹配层(CPML)算法有更好的吸收性能.     

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.     

A NEW FREQUENCY SELECTIVE SURFACE COMPOSED OF LEFT-HANDED MATERIALS

The frequency selective characteristics of a new dielectric periodic structure composed of left-handed materials (LHM) are carefully studied by a method which combines the multimode network theory with the rigorous mode matching method. The variations of the frequency selective characteristics with structure parameters and dielectric loss are presented and comparisons for the frequency selective properties between RHM and LHM gratings are also shown with some explanations. Guidelines for accurate design of the LHM dielectric frequency selective surface are given. Supported by the National Natural Science Foundation of China (No. 60171037) (No. 60371010) and (No. 63531020)     

Numerical analysis of propagation characteristics of electromagnetic wave in lossy left-handed material media

The propagation characteristics of electromagnetic wave in lossy left-handed materials (LHM) are studied using finite-difference time-domain (FDTD) method base on auxiliary differential equation (ADE) technology. The LHM medium is realized with lossy Drude models for both the negative electric permittivity and the negative magnetic permeability. The discretized ADE-FDTD equations are derived in detail. The incident wave used in the simulation is a multiple cycle m-n-m pulses source. The term of Poynting's vector E_xH_y was calculated. These numerical results demonstrate conclusively that the phase velocity direction of electromagnetic wave propagation and the direction of the Poynting vectors are anti-parallel in LHM. The amplitude of electric field is reduced with the enhancive distance of LHM slab. It is also demonstrated that the energy of electromagnetic wave in the LHM slab is obviously attenuated, and the attenuation of energy becomes stronger with the angular plasma frequency ω_p increasing. These results indicate that LHM stealth is effective in theory, and reasonable selection of the large negative index of refraction can greatly enhance its effectiveness.     

Simple and Efficient PML Algorithm for Truncating Nonlinear FDTD Domains Based on the Z -Transform Method

Based on the Z-transform method, a simple, efficient and unsplit-field implementation of the Stretched Coordinate Perfectly Matched Layer (SC-PML) is proposed for truncating the nonlinear dispersive Finite Difference Time Domain (FDTD) lattices. In addition, the nonlinear FDTD formulations using the Z-transform method are reformulated with the advantage of a simple derivative process. The proposed algorithm is validated through two numerical examples carried out in one dimensional and two dimensional domains which include Lorentz dispersion as well as Kerr and Raman nonlinearities.     

INVESTIGATION ON EFFECTS OF LEFT-HANDED MATERIALS ON FREQUENCY SELECTIVE CHARACTERISTICS OF DIELECTRIC PERIODIC STRUCTURES

The effects of left-handed materials (LHM) on frequency selective reflection and transmission characteristics of dielectric periodic structures are carefully investigated using a method which combines the multimode network theory with the rigorous mode matching method. In addition, the effects of LHM dielectric loss on the selective properties are also given. It has been shown that the selective behavior of periodic structures can be modified by adding LHM layers above and below the periodic layer. Supported by the National Natural Science Foundation of China (No. 60171037) (No. 60371010) and (No. 63531020)     

PML-FDTD法在分析负折射率材料中的应用

将时域有限差分(FDTD)法引入了对负折射率材料物理现象的仿真研究.给出了二维TM波在负折射率材料中的时域差分方程,并且在吸收边界处使用了理想匹配层(PML).为了避免在迭代过程中出现的不稳定现象,在差分方程的推导中引入了Drude模型, 并对Pendry提出的由负折射率材料构成的平板透镜具有的完美成像现象进行了数值仿真验证.由仿真结果发现,完美成像现象只在平板透镜的折射率n=－1时出现,当n≠－1时则会出现近轴聚焦效应.     

Complete analysis of photonic crystal fibers by full-vectorial 2D-FDTD method

In this paper, an extended finite difference time domain (FDTD) algorithm for the full-vectorial analysis of photonic crystal fibers has been derived. For achieving a good convergence and high accuracy, a kind of modified conformal FDTD method has been applied. An anisotropic perfectly matched layer for truncation of boundary conditions has been introduced. Material and chromatic dispersions are numerically investigated for the photonic crystal fibers with different dimensions and geometrical parameters and different dispersion behaviors are exhibited.     

磁化铁氧体覆盖二维导体目标FDTD分析的移位算子方法

采用移位算子方法把时域有限差分法推广应用于二维磁各向异性色散介质—磁化铁氧体中.证明了电磁波横向入射二维轴向磁化铁氧体目标情形下,电磁波可按目标的轴向分解为横电波(TE波)和横磁波(TM波),且TE波的散射特性与铁氧体介质无关,而TM波的散射特性与介质电磁参量密切相关,同时对其物理原因进行了分析.通过采用移位算子方法处理磁化铁氧体频域本构关系,得到该情形下目标电磁散射的移位算子时域有限差的迭代计算公式,同时解决了电磁波在各向异性和频率色散介质中传播的问题.计算了轴向磁化铁氧体涂敷VonKarman型导体柱的TM波双站雷达散射截面,分析了铁氧体参量对目标双站雷达散射截面的影响.结果表明:恰当地选择铁氧体参量能有效地减少目标的雷达散射截面,本文时谐因子取exp〔jωt〕.     

三层不对称人工电磁材料界面处表面等离子体激元的理论研究

从P和S偏振出发.研究了由常规材料/左手材料/负介电常数材料、及常规材料/左手材料/负磁导率材料这两种三层不对称结构界面上表面等离子体激元(Surface plasmon polaritons,SPPs)的存在区域、色散曲线及其激发.观察到表面等离子体激元的性质强烈地依赖于人工电磁材料的组成参量,例如介质板的厚度和等离子体的频率.最后,使用衰减全反射(Attenuated total reflection,ATR)技术,探究了激发和观察表面等离子体激元的可能性.并针对P和s偏振两种情况计算了衰减全反射光谱.     

Generating mechanism of the energy-stream loops for the evanescent waves in a left-handed material slab

The generating mechanism of the energy-stream loops (ESLs) for the evanescent waves around the interfaces of a left-handed material (LHM) slab has been investigated with a finite-difference time-domain (FDTD) method. The simulations have shown that these ESLs originate from standing waves, attributed to the intervention of counter-propagating evanescent waves. Large numbers of ESLs can appear because of the numerous values of wave vectors k_y. The larger ESLs die out more quickly than the smaller ones in time after the source is switched off, the ESLs shrink continuously with increasing delay, and the oscillated distributions of the evanescent waves between the surfaces can also be validated. It is greatly helpful for the further comprehension on energy fluxes of evanescent waves in the LHM slab.     

二维各向异性磁等离子体的无条件稳定ADE-CNAD-FDTD算法

针对二维各向异性磁等离子体提出一种有效的无条件稳定算法,新算法结合了辅助微分方程(ADE)方法与Crank-Nicolson approximate-decoupling(CNAD)时域有限差分算法仿真各向异性磁等离子体介质。传统的ADE-FDTD方法应用在一维各向异性色散介质具有较高的精度和效率,将提出的新算法ADE-CNAD-FDTD应用到二维各向异性磁等离子体介质中不仅解决了电磁波在具有各向异性和频率色散特性介质中传播的仿真难题,而且去除了CFL稳定性条件。该算法在保留了原有的精度情况下大幅度地提高了计算效率并成为无条件稳定的形式。给出一个算例证明该算法的有效性,通过模拟电磁波在磁等离子体中的传播,仿真结果与传统的ADE-FDTD算法对比,证实了该算法的高效率、无条件稳定性和高精度。