Eigenvalues of pyramidal waveguides

Various attempts to determine the eigenvalues of a pyramidal waveguide and the assumptions made in each case are described. Numerical comparison between the eigenvalues for the lowest-order mode is also presented. Examination of our numerical results indicates that the eigenvalues for the four flat wall model is sufficiently simple and accurate compared with Narasimhan´s results (1973), particularly since it also corresponds to the actual geometry of pyramidal waveguides which are truncated to produce pyramidal horn antennas. As expected, the agreement of Narasimhan with the two simplified models improves as the flare angle increases since the curved walls in such cases approach the flat walls geometry.