An efficient method for analysing confocal coaxial elliptical waveguides is
presented. Using elliptical coordinates, the differential Helmholtz equati
on is transformed into a linear matrix eigenvalue problem by means of the m
ethod of moments. The expressions of the vector mode functions for the full
spectrum of these guides are constructed, including the TEM, TM and TE mod
es. The convergence of the method is very good, giving an efficient and acc
urate code. Comparisons with numerical results found in the technical liter
ature validate the presented theory.