Karl S. Kunz

A frequency-dependent finite-difference time-domain formulation for dispersive materials

The traditional finite-difference time-domain (FDTD) formulation is extended to include a discrete time-domain convolution, which is efficiently evaluated using recursion. The accuracy of the extension is demonstrated by computing the reflection coefficient at an air-water interface over a wide frequency band including the effects of the frequency-dependent permittivity of water. Extension to frequency-dependent permeability and to three dimensions is straightforward. The frequency dependent FDTD formulation allows computation of electromagnetic interaction with virtually any material and geometry (subject only to computer resource limitations) with pulse excitation. Materials that are highly dispersive, such as snow, ice, plasma, and radar-absorbing material, can be considered efficiently by using this formulation. >

A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma

Previous FDTD (finite-difference time-domain) formulations were not capable of analyzing plasmas for two reasons. First, FDTD requires that at each time step the permittivity and conductivity be specified as constants that do not depend on frequency, while even for the simplest plasmas these parameters vary with frequency. Second, the permittivity of a plasma can be negative, which can cause terms in FDTD expressions to become singular. A novel FDTD formulation for frequency-dependent materials (FD)/sup 2/TD has been developed. It is shown that (FD)/sup 2/TD can be applied to compute transient propagation in plasma when the plasma can be characterized by a complex frequency-dependent permittivity. While the computational example presented is for a pulse normally incident on an isotropic plasma slab, the (FD)/sup 2/TD formulation is fully three-dimensional. It can accommodate arbitrary transient excitation, with the limitation that the excitation pulse must have no zero frequency energy component. Time-varying electron densities and/or collision frequencies could also be included. The formulation presented is for an isotropic plasma, but extension to anisotropic plasma should be fairly straightforward. >

A finite-difference time-domain near zone to far zone transformation (electromagnetic scattering)

An efficient time-domain near-zone-to-far-zone transformation for FDTD (finite-difference-time-domain) computations is presented. The approach is to keep a running accumulation of the far-zone time-domain vector potentials due to the tangential electric and magnetic fields on a closed surface surrounding the scatterer at each time step. At the end of the computation, these vector potentials are converted to time-domain far-zone fields. Many far-zone bistatic directions can be included efficiently during one FDTD computational run. Frequency domain results can be obtained via fast Fourier transform. Wideband results for scattering from a perfectly conducting plate were obtained from a single FDTD computation transformed to the frequency domain, and compared with moment method results. This approach is significantly more efficient than computing many FDTD results using sinusoidally varying excitation if a wide frequency band is of interest. Coupled with recent advances in computing FDTD results for frequency-dependent materials, wideband results for far-zone scattering from targets including frequency-dependent materials can be obtained efficiently. >

Finite-difference time-domain implementation of surface impedance boundary 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. >

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. >

FDTD calculation of scattering from frequency-dependent materials

An efficient method to include frequency-dependent materials in finite difference time domain calculations based on the recursive evaluation of the convolution of the electric field and the susceptibility function has previously been presented. The method has been applied to various materials, including those with the Debye, Drude, and Lorentz forms of complex permittivity, and to anisotropic magnetized plasmas. Previous demonstrations of this approach have been confined to total field calculations in one dimension. In this paper the recursive convolution method is extended to three-dimensional scattered field calculations. The accuracy of the method is demonstrated by calculating scattering from spheres of various sizes composed of three different types of frequency-dependent materials. >

A Technique for Increasing the Resolution of Finite-Difference Solutions of the Maxwell Equation

A two-step expansion technique has been developed for finite-difference codes that can increase the spectral resolution of such codes over selected subvolumes of the original problem space. The utility of this technique is demonstrated by predicting the responses arising from the coupling of an incident exterior field across an aperture in a hollow cylinder to an interior wire. Expansions on the order of fourfold or more are possible. The cost of such increased resolution is a second computer run, doubling the cost as opposed to a cost increase of a factor of 64 if the resolution equivalent to a fourfold expansion were sought from a single run. Possible applications extend to many diverse areas, but most importantly, interior coupling problems may be treated using this technique. For example, this technique may provide a useful method for estimating the responses of cables interior to an aircraft.

FDTD modeling of thin impedance sheets (radar cross section calculation)

Thin sheets of resistive or dielectric material are commonly encountered in radar cross section calculations. Analysis of such sheets is simplified by using sheet impedances. It is shown that sheet impedances can be modeled easily and accurately using finite-difference time-domain methods. >

An interactive demonstration of electromagnetic wave propagation using time-domain finite differences

The finite difference time-domain (FDTD) method is one of the most widely used computational methods in electromagnetics. Using FDTF, Maxwells equations are solved directly in the time domain via finite differences and time stepping. the basic approach is relatively easy to understand and is an alternative to the more usual frequency-domain approaches. In order to take advantage of this, an interactive personal computer program based on FDTD has been developed. The program directly solves Maxwells equation via finite differences. The solution is for one dimension, corresponding to normal incidence propagation through a planar stratified medium. The program displays an electromagnetic pulse as it propagates through the medium. Since Maxwells equations are solved directly, the reflected and transmitted pulse amplitudes demonstrate how the reflection and transmission coefficients determine reflected and transmitted wave amplitudes. Since lossy material layers can be included, frequency dispersion can be demonstrated. >

Finite difference time domain calculations of antenna mutual coupling

The finite-difference-time-domain (FD-TD) technique is applied to calculations of self and mutual admittances between wire antennas. The results are compared with results obtained using the method of moments. The agreement is quite good, indicating the possibilities for FDTD application to antenna impedance and coupling. >