The Grounded Dielectric Slab as a Planar Leaky-Wave Applicator.
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THE GROUNDED DIELECTRIC SLAB AS A PLANAR LEAKY-WAVE APPLICATOR. G. d'AMBROSIO, G. FERRARA", R.MASSA* d'Ambrosio, Massa:Univ. di Napoli, Dip. Ing. Elettronica, via Claudio I - 80125 Napoli,Italy. ** Ferrara:Ist. di Informatica e Telec., v.le A. Doria, I - 95125 Catania, Italy. INTRODUCTION It is well known that a leaky wave in free space may show a decay rate even less than zero, or, in other words, its amplitude may grow instead of decay (1,2,3,41. The above behaviour is very attractive from the point of view of deep processing of materials (5,6]; thus we extended the leaky-wave antenna theory to the lossy (half) space case and analyzed in detail the channel guide applicator [7,8,9]. In this work a simple planar applicator was considered. The transverse resonance condition was used extensively: from the pole location in the complex angle plane, the kind of the pole plane-wave contribution (proper or improper) was found, and the complex wavenumbers in both the dielectric slab and in the lossy half space were calculated. The most significant parameters were found to be the decay rate along the dielectric slab, the transverse decay rate in the lossy material, and the angular amplitude of the region where the leaky wave is expected to be effective. Indutrial as well as therapeutical applications were considered, and criteria were found for the best choice of dielectric slab permittivity and thickness, for deep processing of materials. ANALYTICAL MODEL A grounded dielectrical layer, having real permittivity Cleo, and thickness a, is faced with a lossy half-space having complex permittivity 6 2 9 0 (fig. 1). The magnetic constant is supposed to be equal to that of the free space for both the dielectric slab and the lossy half-space (Al = AL2 = P0). An x axis normal to the plane interfaces p:ints toward the lossy half-space and a z axis lies on the interface between the dielectric and the lossy medium. No y variations are assumed to take place.
xl Oo
LEAKY
P D \ •FEE•3
WAVE
I a
Fig.1: Grounded dielectric slab and lossy half space, parallel plate feed, and leaky-wave region. Mat. Res. Soc. Symp. Proc. Vol. 189. @1991Materials Research Society
130
w2 copo = ki = ki, + k1X 1
Let:
W C 2 Copo-=k
2
-=k2 .+ k~z
From the condition
(= k.) S=/k 2 dependence: e-iwt): (time equations resonance transverse and from the W k2.
-o
iW#o tan(kIa) = 0 ki.
k 2 =, 2 ik 1 = -
UJC2
tan(ki,a) =0
WeSl
(TE)
(TM)
at a given frequency the following parameters were calculated according to a numrical technique outlined in [101: i) ki. = /1. + iaj, ii) k, ==/3 + iaz iii) k 2. = #2. + ia 2.
(transverse wavenumber in the lossless dielectric layer); (longitudinal wavenumber); (transverse wavenumber in the lossy half-space).
Given the relationships: k_
=k
2
sint9
kC2, = k2 cos 0,
the complex angle t9 = 0' + i0", was also found. Given the steepest descent path, whose equation is [9]: 02
cos(0' - t9') cosh t9" + a 2 sin(t9' - 0') sinh 0" =/32
(being /2 + iC12 = k2 ) the angular region p00 = 7r/2 - t'9 (fig. 1) where the leaky
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