Plane-Wave Solutions to Frequency-Domain and Time-Domain Scattering from Magnetodielectric Slabs
| dc.creator | Yaghjian, Arthur D. | |
| dc.creator | Hansen, Thorkild B. | |
| dc.date | 2005-12-21 | |
| dc.date | 2006-04-19 | |
| dc.date.accessioned | 2026-07-07T12:34:58Z | |
| dc.date.available | 2026-07-07T12:34:58Z | |
| dc.description | Plane-wave representations are used to formulate the exact solutions to frequency-domain and time-domain sources illuminating a magnetodielectric slab with complex permittivity and permeability. In the special case of a line source at z=0 a distance d<L in front of an L wide lossless double negative (DNG) slab with permittivity and permeability equal to -1, the single-frequency solution exhibits not only "perfectly focused" fields for z>2L but also divergent infinite fields in the region 2d<z<2L. In contrast, the solution to the same lossless -1 DNG slab illuminated by a sinusoidal wave that begins at some initial time t =0 (and thus has a nonzero bandwidth, unlike the single-frequency excitation that begins at t=-infinity) is proven to have imperfectly focused fields and convergent finite fields everywhere for all finite time t. The proof hinges on the variation of permittivity and permeability having a lower bound imposed by causality and energy conservation. The minimum time found to produce a given resolution is proportional to the estimate obtained by [Gomez-Santos, Phys. Rev. Lett., 90, 077401 (2003)]. Only as t approaches infinity do the fields become perfectly focused in the region z>2L and divergent in the region 2d<z<2L. These theoretical results, which are confirmed by numerical examples, imply that divergent fields of the single-frequency solution are not caused by an inherent inconsistency in assuming an ideal lossless -1 DNG material, but are the result of the continuous single-frequency wave (which contains infinite energy) building up infinite reactive fields during the infinite duration of time from t=-infinity to the present time t that the single-frequency excitation has been applied. | |
| dc.description | 25 pages, 4 figures, changes for publication in Physical Review E | |
| dc.identifier | https://arxiv.org/abs/math-ph/0512067 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0512067 | |
| dc.identifier | Physical Review E, 73, 046608, 17 April 2006 | |
| dc.identifier | doi:10.1103/PhysRevE.73.046608 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217628 | |
| dc.subject | Mathematical Physics | |
| dc.title | Plane-Wave Solutions to Frequency-Domain and Time-Domain Scattering from Magnetodielectric Slabs | |
| dc.type | text |