Radio wave propagation in critical coupling media: Comparison of the generalized WKB and Katsenelenbaum's methods

Abstract

Adopting two basic concepts from the generalized WKB method, Katsenelenbaum claims to have obtained, in a simple manner, equations which would be more convenient and clear than the unwieldy and obscure results of the generalized WKB method and to have developed further these results. The purpose of this paper is to familiarize the reader with the versatility of the generalized WKB method and to examine in detail the claims by Katsenelenbaum. It is shown that all the coefficients in the generalized WKB equations (which are derived through a single transformation) have precise physical interpretations which can be verified independently. The generalized WKB method can be applied to dissipative or nondissipative media, with different types of turning points, for both vertically and horizontally polarized waves. This method has been used to obtain solutions to propagation problems for which no solutions are known in terms of listed mathematical functions, and it has also been applied to propagation in dielectric wave guides. Katsenelenbaum's analysis, which is restricted in scope, involves a series of transformations for the complex magnitude and (real) phase of the wave amplitudes. It is shown that there are errors in the coupling coefficients that appear in his equations and that they are not suitable at turning points, where most of the coupling between the upward and downward propagating waves occur. As a result his main result for the incremental reflection coefficient due to a small inflection in the permittivity profile is incorrect, even though he restricts his analysis to positive real (nondissipative) permittivity profiles.