Two time-derivative Lorentz material (2TDLM) formulation of aMaxwellian absorbing layer matched to a lossy medium

A two time-derivative Lorentz material (2TDLM) is introduced to define polarization and magnetization fields that lead to an absorbing layer that can be matched to a lossy dielectric medium. The 2TDLM is a generalization of the successful uniaxial polarization and magnetization time-derivative Lorentz material (TDLM) which has been introduced as an absorbing boundary condition for simulation regions dealing with lossless materials. Expressions are derived to describe the propagation of an arbitrary plane wave in this 2TDLM Maxwellian absorbing material. They are used to study the scattering from a semi-infinite 2TDLM half-space of an arbitrary plane wave incident upon it from a lossy isotropic dielectric medium. Matching conditions are derived which produce reflectionless transmission through such an interface for any angle of incidence and frequency. Numerical tests are given which demonstrate the effectiveness of the resulting 2TDLM absorbing layer     

The effect of dielectric loss in FDTD simulations of microstripstructures

The importance of dielectric losses in planar microstrip structures is evaluated with the finite-difference time-domain (FDTD) method. This analysis was previously not possible in many FDTD simulators due to a lack of absorbing boundary conditions (ABCs), which appropriately terminate air/dielectric interfaces for which the dielectric is lossy. The newly proposed lossy two-time derivative Lorentzian material (L2TDLM) model ABC allows for these terminations and is presented and implemented here for three-dimensional FDTD simulations. The effect of dielectric losses on several well-known planar microstrip structures is evaluated. It is shown that the inclusion of these losses in FDTD simulations, which is facilitated by the L2TDLM ABC, is, in fact, important to predict the performance of resonant structure on lossy dielectric substrates     

The design of Maxwellian absorbers for numerical boundaryconditions and for practical applications using engineered artificialmaterials

A Maxwellian material interpretation of the Berenger (see J. Computat. Phys., vol.114, p.185-200, 1994) perfectly matched layer (PML) is developed using polarization and magnetization fields. The PML material is found to be a passive lossy electric and magnetic medium with particular conductivity and Debye dispersion characteristics. Although it is recognized that the PML medium is physically unrealizable, this polarization and magnetization field interpretation reveals the necessary characteristics of a perfect electromagnetic absorber. A Maxwellian material that has perfect absorption properties and may be physically realizable is derived with these concepts. This Maxwellian absorber is based upon a time-derivative Lorentz material (TD-LM) model for the dispersive and absorptive electric and magnetic properties of a material. This TD-LM model represents a straightforward generalization of the standard Lorentz material model to include the time derivatives of the fields as driving mechanisms for the polarization and magnetization fields. The numerical implementation of the perfect absorber is given and the resulting reflection coefficients from a perfect electric conductor-backed slab of this material are characterized. It is shown for broad bandwidth pulsed fields that this Maxwellian TD-LM slab, like the non-Maxwellian PML, has absorption characteristics in the 70-110-dB range for large angles of incidence. Strategies are discussed for engineering this dispersive electric and magnetic TD-LM absorber artificially with a substrate that has an array of pairs of appropriately designed small coil-loaded dipole radiating elements embedded in it     

Time-derivative Lorentz material model-based absorbing boundarycondition

A physically realizable electromagnetic absorber that is constructed from a time-derivative Lorentz material (TD-LM) model for the polarization and magnetization fields is used to define an absorbing boundary condition (ABC) for the finite-difference time-domain method. This Maxwellian ABC is shown to have performance characteristics that are comparable to the non-Maxwellian-Berenger (see J. Comput. Phys., vol.114, p.185-200, Oct. 1994) perfectly matched layer (PML) ABC     

截断各向异性介质的修正NPML吸收边界条件

基于各向异性介质中的时域有限差分（Finite-Difference Time-Domain,FDTD）方法及近似完全匹配层（Nearly Perfect Match Layer,NPML）原理,提出一种截断各向异性介质的修正的NPML吸收边界条件.通过对Maxwell旋度方程中的空间偏导数进行坐标拉伸并结合空间插值方法,推导出易于在FDTD方法中实现的吸收边界公式.计算了电偶极子辐射场的反射误差,验证了这种吸收边界截断二维各向异性介质的有效性.三维算例中数值模拟了时谐场的相位分布,以及不同网格NPML吸收层随时间变化的反射误差.数值结果表明NPML吸收边界能有效吸收各向异性介质中的电磁波.     

An absorber tip diffraction coefficient

The UTD corner diffraction solution for a perfectly conducting corner is empirically modified for the case of a dielectric corner. The dielectric may be lossless or lossy, but is assumed to be homogeneous. This modified solution is used to calculate the bistatic scattering from the tip of a dielectric pyramid. Sample calculations display some features of the scattering from a single lossy dielectric pyramid. To verify the solution, calculations are compared with backscatter measurements of a single pyramid that is cut from a homogeneous lossless dielectric (polyethylene). Calculations are then compared with measurements for the more pertinent case of bistatic scattering from a wall of pyramidal radar absorbing material     

基于帕德近似法模拟一般色散媒质电波传播的ADE-FDTD-CPML统一实现方案

为方便一站式处理常见几类各向同性、线性、无磁耗电色散媒质的电波传播问题,提出了一种ADE-FDTD-CPML统一实现方案:一是问题空间和吸收边界的统一处理;二是色散特性的统一建模:适用的媒质类型可以是单一的Havriliak-Negami(H-N)媒质、Davidson-Cole(D-C)媒质、Cole-Cole(C-C)媒质、Debye媒质、常规媒质或其任意组合;媒质属性可以是单极或多极的、有电耗的或无电耗的.该方案利用帕德(Padé)近似法,导出了一组整数阶辅助微分方程(ADEs),既克服了时域描述时遇到的分数阶导数困难,又展现了通用性好、复杂度低等优势.几个一维、三维算例解析、数值结果之间的对比,初步证实了统一实现方案的可行性和有效性.     

Full-vectorial finite element beam propagation method withperfectly matched layers for anisotropic optical waveguides

Perfectly matched layer (PML) boundary conditions are incorporated into the full-vectorial beam propagation method (BPM) based on a finite element scheme for the three-dimensional (3-D) anisotropic optical waveguide analysis. In the present approach, edge elements based on linear-tangential and quadratic-normal vector basis functions are used for the transverse field components. To show the validity and usefulness of this approach, numerical examples are shown for Gaussian beam propagation in proton-exchanged LiNbO₃ optical waveguides. Numerical accuracy of the present PML boundary condition is investigated in detail by comparing the results with those of the conventional absorbing boundary condition (ABC)     

Optimization of nonlinear dispersive APML ABC for the FDTD analysis of optical solitons

We have investigated the parameter optimization for the nonlinear dispersive anisotropic perfectly matched layer (A-PML) absorbing boundary conditions (ABCs) for the two- and the three-dimensional (2D and 3D) finite-difference time-domain (FDTD) analyses of optical soliton propagation. The proposed PML is applied to the FDTD method of the standard and the high-spatial-order schemes. We first searched for the optimum values of the loss factor, permittivity, and the order of polynomial grading for particular numbers of APML layers in a two-dimensional (2-D) setting with Kerr and the Raman nonlinearity and Lorentz dispersion, and then we applied the optimized APML to a full three-dimensional (3-D) analysis of nonlinear optical pulse propagation in a glass substrate. An optical pulse of spatial and temporal soliton profile has been launched with sufficient intensity of electric field to yield a soliton pulse, and a reflection of -60dB has been typically obtained both for the 2-D and the 3-D cases.     

Lossy-to-lossless compression of medical volumetric data using three-dimensional integer wavelet transforms

We study lossy-to-lossless compression of medical volumetric data using three-dimensional (3-D) integer wavelet transforms. To achieve good lossy coding performance, it is important to have transforms that are unitary. In addition to the lifting approach, we first introduce a general 3-D integer wavelet packet transform structure that allows implicit bit shifting of wavelet coefficients to approximate a 3-D unitary transformation. We then focus on context modeling for efficient arithmetic coding of wavelet coefficients. Two state-of-the-art 3-D wavelet video coding techniques, namely, 3-D set partitioning in hierarchical trees (Kim et al., 2000) and 3-D embedded subband coding with optimal truncation (Xu et al., 2001), are modified and applied to compression of medical volumetric data, achieving the best performance published so far in the literature-both in terms of lossy and lossless compression.     

An anisotropic perfectly matched layer-absorbing medium for thetruncation of FDTD lattices

A perfectly matched layer (PML) absorbing material composed of a uniaxial anisotropic material is presented for the truncation of finite-difference time-domain (FDTD) lattices. It is shown that the uniaxial PML material formulation is mathematically equivalent to the perfectly matched layer method published by Berenger (see J. Computat. Phys., Oct. 1994). However, unlike Berenger's technique, the uniaxial PML absorbing medium presented in this paper is based on a Maxwellian formulation. Numerical examples demonstrate that the FDTD implementation of the uniaxial PML medium is stable, equal in effectiveness as compared to Berenger's PML medium, while being more computationally efficient     

An FDTD algorithm with perfectly matched layers for generaldispersive media

A three-dimensional (3-D) finite difference time domain (FDTD) algorithm with perfectly matched layer (PML) absorbing boundary condition (ABC) is presented for general inhomogeneous, dispersive, conductive media. The modified time-domain Maxwell's equations for dispersive media are expressed in terms of coordinate-stretching variables. We extend the recursive convolution (RC) and piecewise linear recursive convolution (PLRC) approaches to arbitrary dispersive media in a more general form. The algorithm is tested for homogeneous and inhomogeneous media with three typical kinds of dispersive media, i.e., Lorentz medium, unmagnetized plasma, and Debye medium. Excellent agreement between the FDTD results and analytical solutions is obtained for all testing cases with both RC and PLRC approaches. We demonstrate the applications of the algorithm with several examples in subsurface radar detection of mine-like objects, cylinders, and spheres buried in a dispersive half-space and the mapping of a curved interface. Because of their generality, the algorithm and computer program can be used to model biological materials, artificial dielectrics, optical materials, and other dispersive media     

Full vectorial finite-element-based imaginary distance beampropagation solution of complex modes in optical waveguides

In this paper, we address accurate computation of complex propagation constants and field distributions of different modes, in general, lossless and lossy optical dielectric waveguides. Using the vector finite-element formulation of the beam propagation method combined with the imaginary distance propagation technique, sequence of both the guided and leaky modes can be accurately calculated. To show the versatility and numerical precision of the proposed technique, we compute the modes of three different three-dimensional (3-D) waveguide structures and compare the results against those of other, different, vector formulations. Further, we present the design of a higher order mode filtering device, based on a 3-D leaky mode optical waveguide     

An equivalent transmission-line model containing dispersion forhigh-speed digital lines-with an FDTD implementation

The increase in processor speeds in the last few years has created a growing need for the accurate characterization of waveform propagation on lossy printed-circuit-board (PCB) transmission lines. Due to the dispersive nature of pulse propagation on lossy transmission lines, approximations of the classic transmission-line model can fail in this application (i.e., lossless or DC losses approximations). This paper shows how an equivalent transmission-line model can be used to analyze dispersive transmission lines for high-speed digital applications. The equivalent-circuit elements of this transmission-line model incorporate the frequency dependence of the per unit length impedance and admittance caused by the finite conductivity of the conductors as well as the dielectric losses. We show that these equivalent circuit elements can be readily implemented into finite-difference time-domain (FDTD) transmission-line codes, and we present such a FDTD implementation. S-parameters and pulsed waveforms for a circular wire, coplanar waveguides (CPW) and microstrip lines are shown. Finally, we present approximate expressions for analytically obtaining the resistance and inductance per length of a microstrip line     

Analysis of microstrip structures with an inhomogeneous dielectric layer in an unbounded region

The method of lines (MoL) is used to compute the frequency dependent propagation characteristics of planar waveguides with an inhomogeneous dielectric layer. To simulate unbounded regions, absorbing boundary conditions (ABC) are used. It is shown that in this case excellent results are achieved even if the boundaries are placed very close to the dielectric edge of the structure.<>     

A Total-Field/Scattered-Field Plane-Wave Source for the FDTD Analysis of Layered Media

A total-field/scattered-field (TF/SF) plane-wave source is developed for the finite-difference time-domain analysis of general (possibly lossy) planar layered media. A 1-D auxiliary grid is created to generate the incident field in the presence of the layered medium. Inhomogeneous plane waves are also allowed for lossless layers and narrowband excitation.     

Analysis of the numerical One-Step method for the study applied on bio electromagnetics

The development of wireless technologies arises important questions about the effects of the wave propagation in the human body. To study accurately these effects, we have to use rigorous numerical methods. In this paper, we present and analyze the One-Step time domain method. This method, which was proposed by De Raedt [Phys Rev E 67(056706):1–12, 2003] for lossless media, is known to be unconditionally stable and so it can be used for applications for which the Courant–Friedrich–Levy (CFL) stability condition can be a limiting factor, e.g., for bioelectromagnetic applications. The numerical dispersion and the insertion of lossy media in the One-Step method are evaluated. The perfectly matched layer (PML) absorbing conditions are also introduced in our study.     

A wavelet-based two-stage near-lossless coder.

In this paper, we present a two-stage near-lossless compression scheme. It belongs to the class of "lossy plus residual coding" and consists of a wavelet-based lossy layer followed by arithmetic coding of the quantized residual to guarantee a given L(infinity) error bound in the pixel domain. We focus on the selection of the optimum bit rate for the lossy layer to achieve the minimum total bit rate. Unlike other similar lossy plus lossless approaches using a wavelet-based lossy layer, the proposed method does not require iteration of decoding and inverse discrete wavelet transform in succession to locate the optimum bit rate. We propose a simple method to estimate the optimal bit rate, with a theoretical justification based on the critical rate argument from the rate-distortion theory and the independence of the residual error.     

Mur Absorbing Boundary Condition for Efficient Fundamental 3-D LOD-FDTD

This letter presents the implementations of Mur first-order absorbing boundary condition (ABC) for efficient fundamental scheme of 3-D locally one-dimensional finite-difference time-domain (LOD-FDTD) method. The Mur ABC is incorporated into the efficient fundamental scheme using consistent implementation and a novel implementation with lower reflection coefficient. Both implementations in the efficient fundamental scheme are compared and validated with the conventional LOD-FDTD scheme. By comparing the CPU time of both conventional and efficient fundamental schemes, it is ascertained that substantial gain in the overall efficiency may be achieved for the latter even with Mur ABC incorporated.