Asymptotic analysis and numerical evaluation of short pulse radiation from a point dipole in a grounded dielectric layer

In a companion paper (see ibid., p.747-54, Jun 1993) spectral options for the synthesis of the electromagnetic fields radiated into the exterior by a pulsed electric current element inside a grounded dielectric layer are presented. The exact spectral integrals, which implement these spectral alternatives, are reduced here by asymptotic methods that extract explicit approximate forms for wavefront contributions, time-domain (TD) leaky mode contributions with space-time dependent wavenumbers and frequencies, and self-consistent hybrid combinations of both. The resulting hybrid wavefront-TD-leaky-mode algorithm is explained in physical terms and tested numerically. For both TE and TM contributions, it is found that in their domain of validity, the TD leaky modes excited within the frequency spectrum of the source pulse synthesize with remarkable accuracy the highly resolved pulse train obtained by direct tracking of multiple reflected wavefronts. Of special interest is the anomalous behavior of the TM-TD leaky modes when their angular spectra are near the Brewster angle for the air-dielectric interface. The correspondingly anomalous asymptotics is explained in detail