Hyper-Frequency Wave Guides---Mathematical Theory

T HE object of this paper is to derive and discuss the characteristics of two novel guided wave transmission systems. Structurally one consists simply of a straight hollow 1 conducting cylinder of circular cross-section. The electromagnetic wave is confined inside the cylindrical sheath and is propagated along the axis of the cylinder. The other consists simply of a dielectric wire, within which the major part of the electric field is confined. The mathematical theory developed below does not deal with the question as to how such waves are established nor with the reflection phenomena which must occur at the terminals and other points of discontinuity. The analysis is limited to finding the types of waves which are possible in such systems, and to investigating and describing their characteristics. The historical background of the problem is interesting. In 1897 Rayleigh published a paper entitled "On the Passage of Electric Waves through Tubes, or the Vibrations of Dielectric Cylinders." 2 Dealing solely with ideal cylinders of perfect conductivity he showed that for all types of waves that can exist inside the cylinders there are critical frequencies below which the waves are attenuated and above which they are freely transmitted. The first paper on transmission along dielectric wires was that published in 1910 by Hondros and Debye entitled " Elektromagnetische Wellen an dielektrischen Drahten." 3 This deals theoretically with transmission along cylinders of ideally nonconducting material, somewhat along the lines followed in Section IV