Plane-wave solutions to frequency-domain and time-domain scattering from negative permittivity and permeability slabs

Tuesday, October 3, 2006 - 1:30pm - 2:20pm
EE/CS 3-180
Arthur Yaghjian (US Air Force Research Laboratory)
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.