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The critical coupling of modes in a tapered earth-ionosphere wave guide

Published online by Cambridge University Press:  24 October 2008

K. G. Budden
K. G. Budden
Affiliation:
Cavendish Laboratory, University of Cambridge
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Abstract

In a stratified wave guiding system, it is often possible to adjust parameters, such as the wave frequency or some dimension of the guide, so that the propagation constants of two modes become equal. These modes are then said to be degenerate. In a tapered guide some of the parameters are slowly varying functions of distance x measured along the guide, and the conditions of degeneracy can be satisfied for some value x0 of x, possibly complex. Here the two modes are said to be critically coupled, and x0 is called a ‘coupling point’ in the complex x-plane. Cases are known where two modes in the earth-ionosphere wave guide could approach critical coupling in the twilight region of the earth, where the guide is tapered. The x dependence of the composite field for the two modes can then be expressed in terms of an Airy Integral function. The theory is closely analogous to that used for studying critical coupling of Ordinary and Extraordinary radio waves within a horizontally stratified ionosphere.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 77 , Issue 3 , May 1975 , pp. 567 - 580
Copyright
Copyright © Cambridge Philosophical Society 1975

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