Excitation of slots in a conducting screen above a lossy dielectric half space

Abstract

A slot in a conducting screen which separates a lossless from a lossy dielectric half space is excited by a current source which lies in the interface between the two media. This geometry idealizes slot antennas constructed by placing wire mesh on the ground surface or island antennas as proposed by Morgan and Gould. For narrow slots of width <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega&lt;\delta</tex> ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\delta</tex> =skindepth in the lossy medium) the transverse distribution of the electric field in the slot plane is approximated by the static solution. The langitudinal distribution of the potential across the slot is obtained from a Hallén type solution of an integral equation. For slots of negligible width the propagation constant along the slot approaches the propagation constant of a thin wire which lies in the interface between the two dielectrics. For wide slots of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega\gg\delta</tex> the integral equation can be solved for the longitudinal variation of the transverse electric field by Fourier transforms, provided that the variation of the electric field in the transverse direction is negligible. The electric field exhibits approximately the same longitudinal variation in the slot plane as the electric field in a direction transverse to the axis of an infinitely long line current which lies in the interface of the two dielectrics. The radiation efficiency of the wide slot ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega&gt;\delta</tex> ) is larger than the radiation efficiency of narrow slots ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega&lt;\delta</tex> ). Still, the expected efficiency of the wide slots is less than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10^{-3}</tex> for frequencies in the VLF range and below, if the ground conductivity is of the order of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10^{-3}</tex> mho per meter. This indicates an upper limit to the efficiency of an island antenna as proposed by Gould and Morgan.