Propagation of electromagnetic waves inside a cylindrical metal tube and along other types of guides

Abstract

The prime purpose of this paper is to base the discussion of the properties of propagation of electromagnetic waves inside a metal tube upon the theory of complex functions. The general expressions for the field components for different types of excitation systems are obtained in a rigorous manner starting from that of an electric and a magnetic dipole. The formal mathematical generalization is achieved by means of the transformation formulae of cylindrical functions and the results of the theory of integral equations. The integral equations thus obtained are expanded into series by aid of residual calculus for actual numerical calculation. The residues at the poles of singularities give rise to different distinct modes of propagation and thereby a comprehensive discussion of all the important physical properties is made. At the same time, problems arising in practical applications, say for long distance transmission for television purposes, are analyzed and some interesting conclusions obtained. The unique and rigorous analysis is only made possible by the free use of the results of the theory of complex functions. A comparison of the properties of propagation with regard especially to the attenuations and the velocities of propagation inside a hollow cylindrical metal tube guide and that of a concentric system is made. It is hoped that the conclusions obtained therefrom will throw some light on the merits of both systems and will point out those things which require careful consideration in practical design.