Modal Degeneracy in Equilateral Triangular Waveguides

Abstract

Issues relating to modal degeneracy in an equilateral triangular waveguide are herein treated. Specifically, it is determined precisely which cutoff frequencies can arise, the multiplicity of each such frequency is ascertained, and a procedure is developed which provides a prescription for finding all the modes associated with each of these frequencies. Such modes are degenerate in as much as they share the same propagation constant and are thus susceptible to mode coupling. As an added dividend, we characterize the family of harmonic series into which these frequencies naturally assemble. Just enough of the requisite number theory is appended to make this account reasonably self-contained.