Transient excitation of a layered dielectric medium by a pulsed electric dipole: spectral representation

Chapter

Tijhuis, A.G. & Rubio Bretones, A. (2002). Transient excitation of a layered dielectric medium by a pulsed electric dipole: spectral representation. In S.R. Cloude & P.D. Smith (Eds.), Ultra-Wideband, Short-Pulse Electromagnetics 5 (pp. 167-174). Dordrecht: Kluwer Academic/Plenum Publishers. Read more: Medialink/Full text

Abstract

 

Spectral methods are the obvious choice for modeling the transient excitation

of a continuously layered, plane-stratified dielectric halfspace. Such methods typically

involve an inverse spatial Fourier transformation and the evaluation of the constituents.

In this paper, we consider the spectral representation. The idea is to normalize the

spatial wavenumber with respect to frequency. Compared with the Cagniard-De Hoop

method, our approach is different in the sense that we keep the frequency real, and

allow the time variable to become complex. In this respect, our work also resembles

she spectral theory of transients.

We restrict the temporal Fourier inversion to nonnegative frequencies by expressing

the time-domain signal as the real part of a dual analytic signal. Reversing the order

of the temporal and spatial Fourier inversions then leads to the so-called time-domain

Weyl representation for the reflected field. In this representation, accumulated guidedwave

poles give rise to an additional branch cut. The representation thus obtained is

used to derive a suitable combination of Gaussian quadrature rules for the evaluation

of the spectral integral.