Pulsed Vertical Electric Dipole Over a Lossy Halfspace: On the Time-Domain Zenneck Wave
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918467952705536 |
|---|---|
| author | Lovat, Giampiero |
| author_facet | Lovat, Giampiero |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23254 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pulsed Vertical Electric Dipole Over a Lossy Halfspace: On the Time-Domain Zenneck Wave Lovat, Giampiero Optics Mesoscale and Nanoscale Physics Mathematical Physics Applied Physics 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. |
| title | Pulsed Vertical Electric Dipole Over a Lossy Halfspace: On the Time-Domain Zenneck Wave |
| topic | Optics Mesoscale and Nanoscale Physics Mathematical Physics Applied Physics |
| url | https://arxiv.org/abs/2604.23254 |