Pulsed Vertical Electric Dipole Over a Lossy Halfspace: On the Time-Domain Zenneck Wave
We investigate the transient electromagnetic field radiated by a pulsed vertical electric dipole above a lossy half-space and identify its time-domain signatures associated with the Zenneck wave. Starting from the classical Sommerfeld representation, we derive a causal time-domain formulation based on the double-deformation technique, with successive contour deformations in the transverse-wavenumber and frequency planes. This yields an explicit decomposition of the field into source-pole, loss-pole, modal-pole, and residual steepest-descent contributions. The resulting expressions exactly satisfy causality and are validated against a reference solution obtained through a standard double inverse transform. The analysis shows that one modal contribution, generated by the frequency-plane deformation and related to the frequency-domain Zenneck pole, exhibits reduced-time invariance and a spatial attenuation consistent with a surface-wave component. Under suitable source and observation conditions, this term can dominate the field over a broad and physically relevant finite late-time interval. At the same time, for the considered damped-sinusoidal excitation, the strict asymptotic tail at fixed distance remains algebraic of order $t^{-5/2}$, with contributions from both the residual continuous spectrum and the modal-pole family. These results provide a rigorous and physically interpretable time-domain manifestation of the frequency-domain Zenneck wave in the pulsed half-space problem.