Degenerate modes in the Earth-ionosphere waveguide

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 complex propagation constants of two modes become equal. These modes are then said to be degenerate. Some examples occur in the waveguide formed by the Earth’s surface and the ionosphere. It is shown that, for conditions near degeneracy, there must be an ambiguity in the mode numbering system. For a given source the two modes may be excited with large amplitudes but in antiphase so that they behave like a single composite mode whose excitation is not large. A degenerate mode is selforthogonal, and some consequences of this are discussed. A degenerate mode can often be associated with a complex Brewster angle for the reflexion coefficient of the Earth’s surface or of the ionosphere.

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