Raymond J. Luebbers

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. >

Piecewise linear recursive convolution for dispersive media using FDTD

Electromagnetic propagation through linear dispersive media can be analyzed using the finite-difference time-domain (FDTD) method by employing the recursive convolution (RC) approach to evaluate the discrete time convolution of the electric field and the dielectric susceptibility function. The RC approach results in a fast and computationally efficient algorithm; however, the accuracy achieved is not generally as good as that obtained with other methods. A new piecewise linear recursive convolution (PLRC) method is described here that has greatly improved accuracy over the original RC approach but retains its speed and efficiency advantages.

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. >

FDTD local grid with material traverse

Often, a finite-difference time-domain (FDTD) calculation requires a relatively higher mesh resolution in only small subvolumes of the total mesh space. By locally applying finer grids (local grids) to these volumes, the necessary resolution can be obtained. Computation time and memory requirements may be far less than for an FDTD space with the smaller mesh resolution throughout. In many situations, it is important that these local-grids function when materials traverse the main-grid-local-grid (MG-LG) boundary surfaces, since the volumes that require local grids may not be isolated in a homogeneous medium. A local-grid method, which allows dielectric and/or conducting materials to traverse the boundaries, is developed. Three different FDTD problems that utilize the local-grid method are used as validation tests. Results are compared with uniform mesh FDTD solutions.

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. >

A heuristic UTD slope diffraction coefficient for rough lossy wedges

Heuristic wedge diffraction coefficients for computing propagation path loss over finitely conducting earth are extended to include slope diffraction, with the assumption that propagation of energy through the wedge is negligible. The slope diffraction terms for the lossy wedge are obtained in an analogous manner as for the perfectly conducting case, except that special care must be taken with the factor multiplying the incident field for grazing incidence. Results given show that the slope diffraction term produces continuous results that behave reasonably when compared with results for perfectly conducting wedges. >

FDTD calculation of radiation patterns, impedance, and gain for a monopole antenna on a conducting box

The ability of the finite-difference-time-domain (FDTD) method to calculate radiation patterns, input impedance, and gain for a monopole antenna on a conducting box is demonstrated. Results are given for the bare box and with the box coated with a dielectric layer. Radiation patterns are compared with measurements and with the method of moments for the bare box. Radiation patterns for the dielectric-covered box and all impedance and gain results are compared with measurements only. Good agreement is obtained in all cases. The FDTD approach includes a dielectric covering quite easily, while this would be quite difficult for a method of moments approach. The FDTD method requires similar computer time as the method of moments for a single-frequency result, but produces wide-bandwidth impedance and gain results with much less computer time. >

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. >