Degenerate modes in the earth-ionosphere waveguide

The present work analyzes mode degeneracy in unbounded guiding systems containing lossy media such as the earth-ionosphere waveguide. Two modes are said to be degenerate in such a system if the complex propagation constants of the two modes are equal and if all characteristics are similar, including configuration of the electromagnetic field. Examples of degenerate modes in the earth-ionosphere waveguide are shown, particularly for radio waves in the VLF or ELF range. One consequence of degeneracy is that there is no unique way of numbering the modes. Calculations of the frequency dependence of mode characteristics are made for a guide where degeneracy is approached for some frequency in the range covered. Degenerate modes also have the property of self-orthogonality. It is shown that there is often a connection between mode degeneracy and the occurrence of a complex Brewster angle. Some curves are presented showing the frequency dependence of the signal received at a great distance from the transmitter when conditions approach degeneracy for some frequency in the range covered.