Review of mode theory of radio propagation in terrestrial waveguides

Abstract

This paper is an expository review of the theory of guided waves that occur in the earth's atmosphere. We introduce the subject by treating the problem of radio propagation around the surface of an airless spherical earth. This leads readily to the classical solutions of van der Pol and Bremmer and the more recent work of Fock in the USSR. The influence of a troposphere with a smooth profile of refractive index is then considered. This analysis, which follows the recent work of Armand, confirms that a monotonically varying or smooth profile will not change the basic structure of the diffraction field. The modifications resulting from the presence of a tropospheric duct are developed by using a parabolic profile of refractive index in the manner suggested by Fock, Weinstein, and Belkina. It is shown that the dominant modes in this system have low attenuation. The second and major part of the paper is devoted to the theory of the mode propagation of VLF radio waves. Here the effective waveguide is the space formed by the earth's surface and the lower edge of the ionosphere. The mode solution is developed as a natural generalization of the classical airless‐earth theory. It is shown, for frequencies less than about 10 kc/s, that the field may be described in terms of flat‐earth modes analogous to those in a straight rectangular microwave guide. At higher frequencies, however, the earth curvature plays a major role and the character and excitation of the modes are changed drastically. Complications resulting from the anisotropy of the ionosphere are also considered. A critical discussion of the recent work on the subject is given.