Finite-difference time-domain solution of Maxwell's equations forthe dispersive ionosphere

The application of the finite-difference time-domain (FDTD) technique to problems in ionospheric radio wave propagation is complicated by the dispersive nature of the ionospheric plasma. In the time domain, the electric displacement is the convolution of the dielectric tensor with the electric field, and thus requires information from the entire signal history. It is shown that this difficulty can be avoided by returning to the dynamical equations from which the dielectric tensor is derived. By integrating these differential equations simultaneously with the Maxwell equations, temporal dispersion is fully incorporated. An FDTD approach utilizing the vector wave equation is also presented. The accuracy of the method is shown by comparison for a special case for which an analytic solution is available. The method is demonstrated with examples of pulse propagation in one and two dimensions. The computational limitations of present-generation computers are discussed. The application of this approach to the study of wave propagation in randomly structured ionization is addressed     

Finite-difference time-domain method for antenna radiation

The finite-difference time-domain (FDTD) method is used to model and predict the radiation patterns of wire and aperture antennas of three basic configurations. A critical step in each is the modeling of the feed. Alternate suggestions are made and some are implemented. The first antenna is a quarter-wavelength monopole and the second is a waveguide aperture antenna. In both bases the antenna is mounted on ground planes, either perfectly conducting or of composite material. The results obtained using the FDTD technique are compared with results obtained using the geometrical theory of diffraction (GTD) and measurements. The third configuration of interest is a pyramidal horn antenna. To model the flared parts of the horn, a staircase approximation was applied to the antenna surface. The computed radiation patterns compared well with measurements     

Wavelet packets for fast solution of electromagnetic integralequations

This paper considers the problem of wavelet sparsification of matrices arising in the numerical solution of electromagnetic integral equations by the method of moments. Scattering of plane waves from two-dimensional (2-D) cylinders is computed numerically using a constant number of test functions per wavelength. Discrete wavelet packet (DWP) similarity transformations and thresholding are applied to system matrices to obtain sparsity. If thresholds are selected to keep the relative residual error constant the matrix sparsity is of order O(N^P) with p<2. This stands in contrast with O(N² ) sparsities obtained with standard wavelet transformations. Numerical tests also show that the DWP method yields faster matrix-vector multiplication than some fast multipole algorithms     

Finite-difference and pseudospectral time-domain methods applied to backward-wave metamaterials

Backward-wave (BW) materials that have simultaneously negative real parts of their electric permittivity and magnetic permeability can support waves where phase and power propagation occur in opposite directions. These materials were predicted to have many unusual electromagnetic properties, among them amplification of the near-field of a point source, which could lead to the perfect reconstruction of the source field in an image [J. Pendry, Phys. Rev. Lett. vol. 85, pp. 3966, 2000]. Often systems containing BW materials are simulated using the finite-difference time-domain technique. We show that this technique suffers from a numerical artifact due to its staggered grid that makes its use in simulations involving BW materials problematic. The pseudospectral time-domain technique, on the other hand, uses a collocated grid and is free of this artifact. It is also shown that when modeling the dispersive BW material, the linear frequency approximation method introduces error that affects the frequency of vanishing reflection, while the auxiliary differential equation, the Z-transform, and the bilinear frequency approximation method produce vanishing reflection at the correct frequency. The case of vanishing reflection is of particular interest for field reconstruction in imaging applications.     

A study of wavelets for the solution of electromagnetic integralequations

The use of wavelet basis functions for the efficient solution of electromagnetic integral equations is studied. It has previously been demonstrated that the use of wavelets for expansion and testing functions produces a sparse moment-method matrix. Here, this effect is examined and analyzed in terms of the radiation/receiving characteristics of the wavelet basis functions. The limitations of wavelets as an efficient solution technique are discussed, and a comparison is made to other fast algorithms     

Finite-difference time-domain analysis of the Celestron-8 telescope

Electromagnetic interference analyses of large complex systems demand large computational resources and give limited information on general types of systems. A finite-difference time-domain (FDTD) code was used to determine the response of a “generic” optical system to microwave radiation. A plane wave with a Gaussian pulse excitation was used along with “point sensors” within the system model to determine time and frequency response. In the low-frequency region, ramped sinusoidal excitation from a point within the sensor was used to determine angles of high sensitivity and field distributions within the sensor. From these field distributions, resonance modes were identified that are similar to those found in a simple cylindrical cavity     

Finite-difference time-domain implementation of surface impedanceboundary conditions

Surface impedance boundary conditions can be utilized to avoid using small cells, made necessary by shorter wavelengths in conducting media throughout the solution volume. The standard approach is to approximate the surface impedance over a very small bandwidth by its value at the center frequency, and then use that result in the boundary condition. In this paper, two implementations of the surface impedance boundary condition are presented. One implementation is a constant surface impedance boundary condition and the other is a dispersive surface impedance boundary condition that is applicable over a very large frequency bandwidth and over a large range of conductivities. Frequency domain results are presented in one dimension for two conductivity values and are compared with exact results. Scattering width results from an infinite square cylinder are presented as a two dimensional demonstration     

Fast spectral domain algorithm for rapid solution of integralequations

A fast spectral domain algorithm is presented for rapid solution of planar surface integral equations. The method of moments coupling integral matrix is formulated in the spectral domain but not explicitly calculated. Thus, in conjunction with an iterative equation solver, the pertinent matrix/vector products are evaluated with complexity O(n) where n is the number of unknowns. Validation and timing results are presented for an array analysis approach using a hybrid finite element (FE)-boundary integral implementation     

Finite-difference time-domain analysis of HF antennas on helicopterairframes

In this paper, the finite-difference time-domain (FDTD) method with the Berenger perfectly matched layer (PML) absorbing boundary condition (ABC) is used to model the radiation characteristics of high frequency (HF) antennas operating in the 2-30 MHz range on a full-scale helicopter. The computed input impedance of both antennas is compared with actual measurements from an operational full-scale helicopter and also with measurements on a scale model NASA generic advanced attack helicopter (GAAH). To study the coupling effects of the helicopter fuselage on the antenna systems, the S-parameters are computed and compared with measurements on the NASA GAAH scale model. Finally, computed gain patterns are compared with actual in-flight measurements of the antenna systems on an operational full-scale helicopter     

Finite-difference time-domain analysis of flip-chip interconnectswith staggered bumps

This paper presents finite-difference time-domain (FDTD) analysis of flip-chip interconnects. Transitions between coplanar waveguides on the chip and the mother board are investigated over a broad band of frequency by means of Fourier transform of the time-domain results. Objectives of the analysis include the evaluation of bump reflection and insertion loss as well as the reconfiguration of the transition to improve package performance. Novel designs have been developed and presented to reduce the effects of package discontinuities and asymmetry. Staggering the bumps has been found to reduce reflection and insertion loss over a broad band of frequency. A reduction In bump reflection of up to 8 dB per transition can be achieved by staggering the ground and signal connects. The degradation in package performance due to structure asymmetry is also studied. The present designs have also been found to reduce the effects of flip-chip asymmetry on insertion and reflection losses     

Finite-difference time-domain algorithm for solving Maxwell'sequations in rotationally symmetric geometries

In this paper, an efficient finite-difference time-domain algorithm (FDTD) is presented for solving Maxwell's equations with rotationally symmetric geometries. The azimuthal symmetry enables us to employ a two-dimensional (2-D) difference lattice by projecting the three-dimensional (3-D) Yee-cell in cylindrical coordinates (r, φ, z) onto the r-z plane. Extensive numerical results have been derived for various cavity structures and these results have been compared with those available in the literature. Excellent agreement has been observed for all of the cases investigated     

Finite-difference, time-domain analysis of lossy transmission lines

An active and efficient method of including frequency-dependent conductor losses into the time-domain solution of the multiconductor transmission line equations is presented. It is shown that the usual A+B√s representation of these frequency-dependent losses is not valid for some practical geometries. The reason for this the representation of the internal inductance the at lower frequencies. A computationally efficient method for improving this representation in the finite-difference time-domain (FDTD) solution method is given and is verified using the conventional time-domain to frequency-domain (TDFD) solution technique     

Finite-difference time-domain (FDTD) analysis of magnetic diffusion

Problems with very slow waveforms or very long diffusion times may be difficult to treat using finite-difference time-domain techniques because of the Courant stability condition. Problems of this class, however, often prove to have a response which does not depend on the speed of light. The examples presented here show cases where internal fields do not change if c is reduced by as much as five orders of magnitude. This permits Δt to be proportionally increased. For simplicity much of this paper is restricted to one dimension, although generalization to three dimensions is also presented. The author considers an aluminum enclosure. Initially, the transient field will induce eddy currents on the enclosure which exactly cancel the external field and exclude it from the enclosure interior. This scheme has been, in fact, proposed to shield large systems which contain magnetic memories     

Finite-difference time-domain modeling of curved surfaces [EMscattering]

The finite-difference-time-domain (FDTD) method is generalized to include the accurate modeling of curved surfaces. This generalization, the contour path CP), method, accurately models the illumination of bodies with curved surfaces, yet retains the ability to model corners and edges. CP modeling of two-dimensional electromagnetic wave scattering from objects of various shapes and compositions is presented     

Finite-difference time-domain analysis of laser diodes integratedwith tapered beam-expanders

Waveguide properties of laser diodes integrated with horizontally tapered beam-expanders are analyzed by the finite-difference time-domain method. The taper length dependence of the radiation loss and fiber-coupling efficiency are clarified. Lower loss and higher fiber-coupling efficiency are achieved in the exponentially tapered beam-expander compared with a linearly tapered one having an equivalent length     

Finite-difference time-domain calculation of the spontaneousemission coupling factor in optical microcavities

We present a general method for the β factor calculation in optical microcavities. The analysis is based on the classical model for atomic transitions in a semiconductor active medium. The finite-difference time-domain method is used to evolve the electromagnetic fields of the system and calculate the total radiated energy, as well as the energy radiated into the mode of interest. We analyze the microdisk laser and compare our result with the previous theoretical and experimental analyses. We also calculate the β factor of the microcavity based on a two-dimensional (2-D) photonic crystal in an optically thin dielectric slab. From the β calculations, we are able to estimate the coupling to radiation modes in both the microdisk and the 2-D photonic crystal cavity, thereby showing the effectiveness of the photonic crystal in suppressing in-plane radiation modes     

Finite-difference time-domain simulation of scattering from objectsin continuous random media

A three-dimensional (3D) finite-difference time-domain (FDTD) scheme is introduced to model the scattering from objects in continuous random media. FDTD techniques have been previously applied to scattering from random rough surfaces and randomly placed objects in a homogeneous background, but little has been done to simulate continuous random media with embedded objects where volumetric scattering effects are important. In this work, Monte Carlo analysis is used in conjunction with FDTD to study the scattering from perfectly electrically conducting (PEC) objects embedded in continuous random media. The random medium models under consideration are chosen to be inhomogeneous soils with a spatially fluctuating random permittivities and prescribed correlation functions. The ability of frequency averaging techniques to discriminate objects in this scenarion is also briefly investigated. The simulation scheme described in this work can be adapted and used to help in interpreting the scattered field data from targets in random environments such as geophysical media, biological media, or atmospheric turbulence     

基于FDTD的罗兰-C信号地波传播特性的时域分析

罗兰-C信号为载波调制的高斯脉冲,而传统方法对其传播特性预测均是基于100 kHz单频信号结果。文章采用FDTD方法计算了实际罗兰信号的时域特性,并和100 kHz连续单频信号结果进行了比较。结果显示:对于地形起伏不大的传播路径,两种信号结果吻合得很好,而对于地形起伏较大路径,脉冲信号结果与单频信号结果存在较大差异。该结果对地波传播特性工程测量与分析具有一定指导意义。     

Finite-difference time-domain analysis of gyrotropic media. I.Magnetized plasma

When subjected to a constant magnetic field, both plasmas and ferrites exhibit anisotropic constitutive parameters. For electronic plasmas this anisotropy must be described by using a permittivity tensor in place of the usual scalar permittivity. Each member of this tensor is also very frequency dependent. A finite-difference time-domain formulation which incorporates both anisotropy and frequency dispersion, enabling the wideband transient analysis of magnetoactive plasma, is described. Results are shown for the reflection and transmission through a magnetized plasma layer, with the direction of propagation parallel to the direction of the biasing field. A comparison to frequency-domain analytic results is included     

Finite-difference time-domain modeling of frequency selective surfaces using impedance sheet conditions

Novel finite-difference time-domain (FDTD) models of frequency-selective surfaces (FSS) based on impedance sheet conditions are developed. The analytical basis of the models lies in impedance sheet conditions with general reactive grid impedances applying to a great variety of grid realizations. New models for periodic arrays of metal particles and for the complementary structures of slots in metal screen are formulated for FDTD in the case of normal incidence. The properties of the FSS are included in the grid impedance, which is implemented into FDTD, considerably simplifying the otherwise extremely cumbersome modeling task. The convergence and the accuracy of the models are assessed with numerical simulations by comparing with analytical and measured reference results.