The transmission characteristics of a corrugated guide

Abstract

The transmission characteristics of a corrugated guide are analyzed under the assumption that the guide wavelength is always much greater than the "corrugation constant" ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D_{1}+D_{2}</tex> ). The corrugated guide is, therefore, replaced by a quasi-homogeneous but anisotropic medium whose dielectric constant and permeability are represented by tensors. It turns out that the corrugated guide behaves much like the Goubau guide if the corrugation depth is small with respect to the wavelength. Corresponding to the influence of the dielectric on the Gouban guide, increasing depth of the corrugations increases also, on this guide, the attenuation of the waves, decreases the phase velocity, and increases the field concentration around the guide accordingly. As a rule, however, the corrugated guide acts as a low pass whose pass bands are about at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k\dot0.5 &lt; d/\lambda_{0}&lt;(0.25+k\dot0.5)</tex> and whose stop bands are about at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(0.25+k\dot0.5) &lt; d/\lambda_{0} &lt; 0.5(1 + k)</tex> ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k=0, 1, 2, . . . , d</tex> =corrugation depth, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\lambda_{0}</tex> =wavelength of a plane wave in space). Since, in the case of long radio waves, parallel building fronts and mountain ranges may be thought of as corrugated guides, one of the results of the paper is the fact that the propagation of waves around the earth cannot only be considerably curbed by building fronts and mountain ranges, but can even be suppressed altogether.