Cutoff frequencies of uniform waveguides of regular polygonal cross section

This letter deals with the problem of calculating the cutoff frequencies of hollow piped waveguides of regular polygonal cross section. By conformally transforming the given cross section onto a unit circle, the boundary conditions can be identically satisfied; however, the transformed partial differential equation must be solved by approximate procedures. The results are considered excellent, demonstrating remarkable agreement with the exact values in the case of square and circular cross sections. Only TM modes are considered in the present study; TE modes can be treated in a similar manner.