A Staggered Upwind Embedded Boundary (SUEB) method to eliminate the FDTD staircasing error

In spite of its flexibility and second-order accuracy in a homogeneous medium, Yee's finite-difference time-domain (FDTD) method suffers from serious degradation when treating material interfaces, greatly reducing its accuracy in the presence of inhomogeneous media and perfect conductors. Indeed, such so-called staircasing approximation may lead to local zeroth-order and global first-order errors. In this work, an embedded FDTD scheme, the staggered upwind embedded boundary (SUEB) method, is developed for the solution of oneand two-dimensional Maxwell's equations. This simple embedded technique uses upwind conditions in the FDTD method to correctly represent the location and physical conditions of material and metallic boundaries, hence eliminating problems caused by the staircasing approximation. Accuracy analysis has been made to show that the SUEB method maintains a second-order accuracy globally. Since the entire problem has been embedded into the simple staggered grid similar to that employed by the Yee's scheme, extra effort is only needed when treating the grid points close to the interfaces. Therefore, little additional computational cost is needed over Yee's scheme. The SUEB method has been validated by analytical solutions for plane wave normally incident to a planar boundary and for the TM wave propagation in the presence of a dielectric cylinder and a perfectly electrically conducting cylinder.     

Electromagnetic imaging of underground targets using constrainedoptimization

Several high-frequency electromagnetic techniques have been used in recent years to detect and identify buried objects. Post-processing of the collected data is performed in many of these techniques to obtain high-quality images of buried targets. Accurate reconstructions of the target's constitutive parameters can be obtained by casting the imaging problem in terms of an inverse electromagnetic scattering problem. A number of techniques have been put forth recently to invert the electromagnetic data to obtain such images. The authors use a frequency-domain Born iterative method to reconstruct images of shallow targets. The Born iterative technique requires successive solutions to a forward scattering problem followed by an inverse scattering problem at each iteration step. They use a finite-difference time-domain (FDTD) algorithm to solve the forward scattering problem and constrained optimization for the inverse problem. Two-dimensional simulated data for several canonical objects buried in the ground are obtained using the FDTD technique. The same FDTD code is also used in calculating the Green's function required for solving the constrained optimization problem. Lossy, inhomogeneous ground models are used in several simulations to illustrate the use of this technique for practical situations. The inversion process can be used to reconstruct images for many realistic dielectric contrasts for which a linear Born approximation fails. Moreover, it is also shown that a small number of measurements results in accurate reconstructions with this technique. Use of multiple frequencies is also investigated     

Full-Waveform Inversion of Crosshole Radar Data Based on 2-D Finite-Difference Time-Domain Solutions of Maxwell's Equations

Crosshole radar techniques are important tools for a wide range of geoscientific and engineering investigations. Unfortunately, the resolution of crosshole radar images may be limited by inadequacies of the ray tomographic methods that are commonly used in inverting the data. Since ray methods are based on high-frequency approximations and only account for a small fraction of the information contained in the radar traces, they are restricted to resolving relatively large-scale features. As a consequence, the true potential of crosshole radar techniques has yet to be realized. To address this issue, we introduce a full-waveform inversion scheme that is based on a finite-difference time-domain solution of Maxwell's equations. We benchmark our new scheme on synthetic crosshole data generated from suites of increasingly complex models. The full-waveform tomographic images accurately reconstruct the following: (1) the locations, sizes, and electrical properties of isolated subwavelength objects embedded in homogeneous media; (2) the locations and sizes of adjacent subwavelength objects embedded in homogeneous media; (3) abrupt media boundaries and average and stochastic electrical property variations of heterogeneous layered models; and (4) the locations, sizes, and electrical conductivities of water-filled tunnels and closely spaced subwavelength pipes embedded in heterogeneous layered models. The new scheme is shown to be remarkably robust to the presence of uncorrelated noise in the radar data. Several limitations of the full-waveform tomographic inversion are also identified. For typical crosshole acquisition geometries and parameters, small resistive bodies and small closely spaced dielectric objects may be difficult to resolve. Furthermore, electrical property contrasts may be underestimated. Nevertheless, the full-waveform inversions usually provide substantially better results than those supplied by traditional ray methods.     

加权总场法在PSTD算法中的应用

伪谱时域(PSTD)方法可以处理电大尺寸目标电磁散射问题。本文介绍了一种能够把入射波有效引入PSTD计算区域的新方法——加权总场法。该方法通过引入类似于FDTD中连接边界的连接层，将计算区域划分为总场区、连接区和散射场区。为了总场区和散射场区的连续，在连接区引入窗函数．通过设置8—10层连接区就可以将入射波有效地引入到PSTD总场区。这样使入射波和目标分离，实现了复杂目标的单独建模，从而使PSTD便于模拟复杂目标的电磁散射。文中以高斯脉冲为入射波，通过二维情况下目标散射宽度的数值结果，验证了加权总场法应用于PSTD算法时的有效性和计算精度。     

平直有耗地面上目标地波散射FDTD近一远场外推

由平直有耗地面上垂直电偶极子产生地波场的解析解和互易原理,本文导出了用FDTD方法处理目标地波散射问题时的近一远场外推公式。在数值结果验证了该公式的正确性之后,对海上一金属半球的地波散射场进行了求解,并以此与李清亮等(1997)提出的工程应用方法相对比,考察了工程应用方法的适用性。     

Multiresolution time-domain analysis of plane-wave scattering fromgeneral three-dimensional surface and subsurface dielectric targets

The multiresolution time domain (MRTD) is used to analyze wide-band plane-wave scattering from general dielectric targets embedded in a lossy half-space, with free-space scattering as a special case. A Haar wavelet expansion is used for simplicity, this constituting a generalization of the widely used finite-difference time-domain (FDTD) method. In addition to developing the mathematical formulation, example results are presented for several targets, with the MRTD results validated through comparison with an independent frequency-domain method-of-moments solution and an FDTD model     

含随机介质的光子晶体波导特性

提出了一种光子晶体波导与随机介质相结合的特殊型波导的设计方法。基于光子晶体波导模型,建立了ZnO随机介质作为线缺陷的光子晶体波导模型,采用时域有限差分(FDTD)法分析了ZnO随机介质的加入对光子晶体波导系统的频率特性、时域特性及增益特性的影响,并且与纯随机介质系统和含有线缺陷的光子晶体波导系统进行对比。分析结果表明,当在光子晶体波导的缺陷层引入ZnO随机介质时,随机介质使得光在缺陷处振荡并得到放大,局域化程度比纯随机介质系统和纯光子晶体波导系统更高;且光与随机介质的相互作用使得光在波导中时间延长,激光阈值降低。这种光子晶体波导可用于制备可嵌入到集成光路领域和低阈值的微型激光器。     

An FDTD near- to far-zone transformation for scatterers buried instratified grounds

The finite-difference time-domain (EDTD) technique is being used with increasing frequency for modeling the scattering characteristics of buried objects. The FDTD has, for some time, been able to model the near-zone scattered fields of buried objects due to near-zone sources. This is adequate for modeling the scattered returns of ground-based ground-penetrating radar, but not for airborne radar. This paper describes an FDTD-compatible technique whereby far-zone scattered fields of objects buried in a stratified ground can be calculated. This technique uses the equivalence principle to model a buried object in terms of equivalent electric and magnetic currents. The fields radiated by these currents in the presence of a stratified ground are then calculated using the reciprocity theorem and the well-known field equations for plane waves in a stratified media. Numerical results are presented that show excellent agreement between this technique and both analytical and numerical results     

Effective permittivities for second-order accurate FDTD equationsat dielectric interfaces

In Yee's finite-difference time-domain (FDTD) scheme, effective permittivities are often used to account for offsets of dielectric interfaces from grid nodes. The specific values of these effective permittivities must be chosen in such a way that the second-order accuracy of the scheme is preserved. It is shown in this work that, contrary to more elaborate techniques proposed recently for the development of these effective permittivities, a rigorous application of the integral forms of Maxwell's curl equations on the Yee's lattice leads to the desired values in a straightforward fashion. Numerical experiments in a two-dimensional (2-D) cavity are used to verify that the calculated effective permittivities preserve the second-order accuracy of the FDTD scheme     

BI-FDTD: a novel finite-difference time-domain formulation for modeling wave propagation in bi-isotropic media

This paper presents a newly developed finite-difference time-domain (FDTD) technique, referred to as BI-FDTD, for modeling electromagnetic wave interactions with bi-isotropic (BI) media. The theoretical foundation for the BI-FDTD method will be developed based on a wavefield decomposition. The main advantage of this approach is that the two sets of wavefields are uncoupled and can be viewed as propagating in an equivalent isotropic medium, which makes it possible to readily apply conventional FDTD analysis techniques. The BI-FDTD scheme will also be extended to include the dispersive nature of chiral media, an important subclass of bi-isotropic media. This extension represents the first of its kind in the FDTD community. Validations of this new model are demonstrated for a chiral half-space and a chiral slab.     

A graphical user interface (GUI) for plane-wave scattering from a conducting, dielectric, or chiral sphere

Various numerical techniques have been developed for modeling electromagnetic field propagation in various novel complex media. The validity of these techniques is usually verified by comparison to the exact solutions of canonical problems. Recently, research has focused on chiral media, a subclass of materials known as bianisotropic materials, and numerical techniques have been developed in order to calculate the interaction of electromagnetic fields with chiral objects. One canonical problem for these techniques is plane-wave scattering from a chiral sphere. This work presents a software package that displays and saves the calculated data for the scattering from a chiral, dielectric, or perfectly conducting sphere using a friendly graphical user interface (GUI).     

二维非球形粒子随机介质中光场的传输特性

研究了散射粒子形状改变对光波在二维随机介质系统中的传输情况的影响。基于整体散射效应模型,建立了非球形粒子作为散射粒子的二维随机介质的模型。构建了模型的Maxwell方程,采用非均匀网格划分的时域有限差分(FDTD)方法解Maxwell方程,得到了TM模在非球形粒子二维随机介质模型中的传输及空间分布。采用快速傅里叶变换(FFT)对仿真获得的数据进行频谱变换,得到光波在频域上的发射谱。与以往的研究相比较,仿真结果表明,在非球形粒子系统中,光波的电场强度与球形粒子系统中电场强度随着散射粒子浓度的增加而增加不同,而是出现振荡的现象;发射谱显示,非球形粒子系统的模式竞争强于球形粒子系统,更易于实现模式选择。     

基于FDTD的运动导体目标电磁散射仿真

提出了一种基于散射模型的等价相对边界条件。将该等价相对边界条件与传统FDTD方法相结合提出了求解运动导体目标电磁散射问题的方法。并将该方法用于计算运动的无限大导体表面的电磁散射问题，计算结果与文献所给方法的计算结果吻合很好，验证了该方法求解运动导体目标电磁散射问题的正确性和有效性。用该方法计算了运动三维导体目标的雷达散射截面。     

有耗媒质中3D目标体散射特性的TSNU-PSTD模拟

结合PML边界条件的傅立叶时域伪谱(PSTD)算法已广泛用于模拟电磁波传播和目标散射,但传统的PSTD方法在每个坐标方向上需要均匀分布的空间坐标网格点,从而不能够很好地模拟曲面目标和与网格空间尺寸不一致的目标,基于变空间的PSTD方法可以很好地克服这些不足。文中将CFS-PML边界条件在PSTD算法中实现并将它与TSNU-PSTD方法结合模拟了大范围有耗媒质中2D\3D曲面介质体目标的电磁散射,部分结果与FDTD计算结果进行了比较。仿真结果表明,基于变空间的PSTD只需平均每波长分成3个网格就可以达到较好的精度,可高效模拟电大尺寸空间曲面形状目标体的电磁散射。     

Hybrid finite-difference time-domain modeling of curved surfacesusing tetrahedral edge elements

A hybrid finite-difference time-domain (FDTD) method is proposed for solving transient electromagnetic problems associated with structures of curved surfaces. The method employs the conventional FDTD method for most of the regular region but introduces the tetrahedral edge-based finite-element scheme to model the region near the curved surfaces. Without any interpolation for the fields on the curved surface, nor any additional stability constraint due to the finer division near the curved surfaces, the novel finite-element scheme is found to have second-order accuracy, unconditional stability, programming ease, and computational efficiency. The hybrid method is applied to solve the electromagnetic scattering of three-dimensional (3-D) arbitrarily shaped dielectric objects to demonstrate its superior performance     

A New Conformal FDTD(2,4) Scheme for Modeling Three-Dimensional Curved Perfectly Conducting Objects

A new high-order conformal FDTD(2,4) scheme is proposed to solve the electromagnetic scattering from 3-D curved perfectly conducting objects. For electric field components, the update equations do not need to be modified. For magnetic field components, the inner loop is treated with the locally conformal technique, and the outer loop is unmodified. Numerical results demonstrate that the high-order conformal scheme can obtain better numerical precision under coarse grid condition compared with the low-order conformal method and the high-order staircasing approach, which in turn saves CPU time and memory.     

Finite difference time domain (FDTD) analysis of optical pulse responses in biological tissues for spectroscopic diffused optical tomography

Finite difference time domain (FDTD) analysis has been successfully formulated for solving diffusion equation in biological tissues. Time-dependent diffusion equations are approximated by FDTD equations by assigning diffuse photon fluence rates and radiant flux defined in the diffusion equations to Yee meshes. At the boundary between scattering and no scattering material, FDTD equation including only fluence rate has been derived, which make it possible to calculate the fluence rate at the boundary. The formulation is useful to solve diffusion equations by iterative algebraic calculations in scattering media with inhomogeneous optical properties. The conditions to give stabilities for numerical solutions have been become clear in terms of scattering coefficients and mean cosine of scattering angles. Using the formulation, the reflectance of three-layered slabs containing a clear layer have been calculated. As a result, it has been found that absorption loss changes of the highly scattering medium beyond the clear layer are estimated from the time profiles of the reflectance.     

双孔散斑照相用于物体通过漫射介质成象

物体通过大雾等漫射介质的成象问题一直吸引众多研究者的注意。光学全息技术、光栅干涉仪技术已经显示出在实验室条件下的有效性。但由于所使用的设备比较复杂，很容易受外界震动的干扰，使其应用场所受到很大制约。本文提出了使用双孔散斑照相技术使物体通过漫射介质成象。用这种技术得到的实验结果显示这项技术在象的对比度方面比直接得到的象有很大提高。同时所使用的设备简单，受外界震动的影响小，因而具有很大的实用价值。     

地下目标的瞬态电磁散射特性分析及成像

地下目标的瞬态电磁散射分析对于探测、检验及识别埋地目标，特别是冲击探地雷达的研究具有重要的理论和应用价值。本文用FDTD三维建模计算在收发天线作用下地下无限长管道的时域散射场，重点探讨适用于吸收土壤中凋落波的GPML吸收边界以及处理有耗色散媒质的(FD)^2TD算法，并利用所得数据进行成像分析。BP方法成像结果证明了整个模拟计算过程的正确性。     

A three-wave FDTD approach to surface scattering with applicationsto remote sensing of geophysical surfaces

A major difficulty in physical interpretation of radio wave scattering from geophysical surfaces is the lack of detailed information on the signatures of geologically plausible discrete objects. Although the aggregate response will never be dominated by any single object, differences in the population of discrete objects on or near the surface (their sizes and shapes, for example) can change the character of a radio echo markedly. When the average surface is modelled as a flat, homogeneous half-space, the field that “drives” the scattering process is a composite consisting of the incident plane wave and the reflected and transmitted plane waves, all of which are known quantities; the total field can then be defined as the sum of the driving field and the scattered field. When a discrete object is near the surface, the total field can be calculated using finite-difference time-domain (FDTD) techniques, and the scattered near field can be calculated accordingly. The Green's functions for electric and magnetic currents above and below the surface, obtained by Sommerfeld theory and employed in conjunction with Huygens' principle, transform the local scattered fields to the far field. The FDTD implementation accommodates discrete lossy dielectric and magnetic scatterers in the vicinity of a dielectric surface; extension to a lossy half-space is straightforward. Two-dimensional results for scattering from perfectly conducting circular cylinders above and below a dielectric surface agree with moment method solutions within a few percent. Results for scattering from a dielectric wedge exhibit expected forward diffraction and internal reflection phenomena