F. Hunsberger

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. >

FDTD for Nth-order dispersive media

Previously, a method for applying the finite-difference time domain (FDTD) method to dispersive media with complex permittivity described by a function with a single first-order pole was presented. This method involved the recursive evaluation of a discrete convolution, and was therefore relatively efficient. In this work, the recursive convolution approach is extended to media with dispersions described by multiple second-order poles. The significant change from the first-order implementation is that the single backstore variable for each second-order pole is complex. The approach is demonstrated for a pulsed plane wave incident on a medium with a complex permittivity described by two second-order poles, and excellent agreement is obtained with the exact solution. >

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 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. >

Calculation and measurement of the effective chirality parameter of a composite chiral material over a wide frequency band

Materials that are effectively chiral at microwave frequencies can be fabricated by embedding identical, randomly oriented chiral inclusions, often metal helices, in a continuous matrix. We show that the chirality parameter can be calculated in the dilute limit using single scattering theory. The required tumble-averaged forward scattering by an individual inclusion is determined by the method of moments. Values of the effective chirality parameter are determined directly from the constitutive parameters of the matrix and the geometry and concentration of the inclusions. Comparisons are made with measurements previously reported in the literature. In addition, a chiral composite material was fabricated specifically to validate the calculations over frequencies including resonance. The measurements agree well with the calculations, providing quantitative values of the chirality parameter over a wide frequency band. It appears that the chirality parameter is appreciable only near the resonant frequencies of the inclusion. Finally, it is clear that an oscillator model can be used to describe the frequency dependence of the complex chirality parameter, and that therefore our results are consistent with the Kramers-Kronig relation. >

Microwave-absorbing chiral composites: Is chirality essential or accidental?

Suspensions of wire helices are absorbing at microwave frequencies. Although such suspensions are chiral, this may be accidental rather than essential for absorption in coatings. Nonchiral suspensions of connected loop arrays behave similarly to suspensions of helices.

Application of the finite-difference time-domain method to electromagnetic scattering from 3-D chiral objects

It is shown how the finite-difference time-domain (FDTD) method has been adapted to handle electromagnetic wave propagation through chiral media. Two solutions to this problem are presented, enabling the FDTD method to handle propagation through chiral, as well as achiral, media. One solution is exact, involving the recursive (but still parallel) solution of the field update equations. This method produces results comparable to those obtained by theoretical means, as well as by other computational methods (the method of moments). The second solution has been implemented via a scattered-field formulation and has been successfully applied to problems of scattering from three-dimensional chiral objects.<<ETX>>

Finite difference time domain recursive convolution for second order dispersive materials

The finite-difference-time-domain method has been applied to frequency-dependent dispersive materials through an efficient recursive discrete convolution with results given for first-order dispersive materials including polar liquids (Debye) and cold plasmas. The recursive convolution utilizes the exponential behavior of the first-order time-domain susceptibilities. Alternatively a differential approach, valid for both first- and second-order dispersion relations, has been demonstrated. In the present work, the extension of the recursive convolution approach to second-order dispersion relations is discussed. The extension is very straightforward, with the only added computational burden being a complex recursive accumulation variable. The method has been applied to second-order dispersion relations for magnetized plasmas and ferrites with good accuracy, and appears simpler and more efficient than the differential methods.<<ETX>>

FDTD formulation for frequency dependent permittivity

Current finite-difference time-domain (FDTD) formulations require the permittivity, permeability, and conductivity to be constant. However, for many real materials of interest these parameters vary significantly with frequency. The effects of constitutive parameters which vary with frequency are included in a frequency dependent FDTD formulation, (FD)/sup 2/TD, by extending the traditional Yee formulation to include discrete time-domain convolution. To apply (FD)/sup 2/TD all of the frequency domain information (in the complex permittivity function) is Fourier-transformed to a time-domain susceptibility function. To demonstrate (FD)/sup 2/TD computation of wideband reflections at an air-water interface the authors consider a one-dimensional problem space consisting of 1000 cells: 499 cells were used to model free space (air) and 501 cells were used for water. They compare (FD)/sup 2/TD results after 1200 time steps and FDTD results (with 20-GHz permittivity and conductivity values constant) after 8000 time steps with the exact analytical frequency domain result. The (FD)/sup 2/TD formulation is clearly much more accurate than traditional FDTD.<<ETX>>