Leaky-wave analysis of transient fields due to sources in planarly layered media

The transient field due to canonical sources in planarly layered media is obtained using a leaky-wave analysis. By proper choice of integration paths in both the complex frequency and complex wavenumber planes, transient fields are obtained exactly as a temporal inversion integral over a discrete sum of residues. The residues include both proper and improper surface-wave modes, analytically continued into the complex frequency plane. The method is applicable for all times of interest, although for certain source-receiver locations an "early-time" period is identified which encompasses the specular reflection from the nearest interface, and during which time the residue series requires special treatment. The presented analysis leads to a computationally simple and efficient method for obtaining transient fields due to sources in layered media. Results are shown for the transient potential due to line and point sources over a grounded dielectric slab, although the technique is applicable to multiple planar layers.