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.

Piecewise linear recursive convolution for dispersive media using FDTD

The frequency-dependent finite-difference time-domain method (FD)/sup 2/TD method has been shown to be capable of correctly calculating electromagnetic propagation through media whose dielectric properties are frequency dependent. However, as researchers search for more elaborate applications, the formulation of the (FD)/sup 2/TD methods becomes more complex. In this work, the mathematics of the (FD)/sup 2/TD method is developed using Z transform theory. This has the advantages of presenting a clearer formulation, and allowing researchers to draw on the literature of systems analysis and signal processing disciplines. >

Frequency-dependent FDTD methods using Z transforms

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. >

FDTD for Nth-order dispersive media

A weakness of the finite-difference-time-domain (FDTD) method is that dispersion of the dielectric properties of the scattering/absorbing body is often ignored and frequency-independent properties are generally taken. While this is not a disadvantage for CW or narrowband irradiation, the results thus obtained may be highly erroneous for short pulses where ultrawide bandwidths are involved. In some recent publications, procedures based on a convolution integral describing D(t) in terms of E(t) are given for media for which the complex permittivity in *( omega ) may be described by a single-order Debye relaxation equation or a modified version thereof. Procedures are, however, needed for general dispersive media for which in *( omega ) and mu *( omega ) may be expressible in terms of rational functions, or for human tissues for which multiterm Debye relaxation equations must generally be used. The authors describe a new differential equation approach, which can be used for general dispersive media. In this method D(t) in terms of E(t) by means of a differential equation involving E, and their time derivatives. The method is illustrated for several examples. >

A frequency-dependent finite-difference time-domain formulation for general dispersive media

The finite-difference time-domain (FDTD) method is arguably the most popular numerical method for the solution of problems in electromagnetics. Although the FDTD method has existed for nearly 30 years, its popularity continues to grow as computing costs continue to decline. Furthermore, extensions and enhancements to the method are continually being published, which further broaden its appeal. Because of the tremendous amount of FDTD-related research activity, tracking the FDTD literature can be a daunting task. We present a selective survey of FDTD publications. This survey presents some of the significant works that made the FDTD method so popular, and tracks its development up to the present-day state-of-the-art in several areas. An "on-line" BibT/sub E/X database, which contains bibliographic information about many FDTD publications, is also presented. >

A selective survey of the finite-difference time-domain literature

The propagation of transient electromagnetic fields in dispersive dielectric media is studied. The dielectric medium is assumed to be linear, isotropic, and homogeneous, and is described by the Debye model. Incident fields are assumed to be transverse electromagnetic plane wave pulses. The dielectric body can assume the form of infinite half space or an infinite circular cylinder, either of which may be homogeneous or stratified. The electric fields induced in the dielectric are calculated from time-domain Maxwell's equations using the finite-difference time-domain method. >

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S.S. Stuchly

Papers

Propagation of transients in dispersive dielectric media