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