# 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

permittivity and permeability equal to

solution exhibits not only perfectly focused fields for

but also divergent infinite fields in the region

contrast, the solution to the same lossless –1 DNG slab illuminated

by a sinusoidal wave that begins at some initial time

thus has a nonzero bandwidth, unlike the single-frequency excitation

that begins at

focused fields and convergent finite fields everywhere for all finite

time

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

become perfectly focused in the region

in the region

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

single-frequency excitation has been applied.

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 withpermittivity and permeability equal to

*-1*, the single-frequencysolution exhibits not only perfectly focused fields for

*z>2L*but also divergent infinite fields in the region

*2d<z<2L*. Incontrast, the solution to the same lossless –1 DNG slab illuminated

by a sinusoidal wave that begins at some initial time

*t=0*(andthus has a nonzero bandwidth, unlike the single-frequency excitation

that begins at

*t=-infinity*) is proven to have imperfectlyfocused fields and convergent finite fields everywhere for all finite

time

*t*. The proof hinges on the variation of permittivity andpermeability 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 fieldsbecome perfectly focused in the region

*z>2L*and divergentin the region

*2d<z<2L*. These theoretical results, whichare 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 thesingle-frequency excitation has been applied.