Null-Field Method for Waveguides of Arbitrary Cross Section

It is shown how to obtain accurate numerical values for waveguide characteristics using the null-field method, which is derived using Waterman´s extended boundary condition. Computational results are presented for the sector waveguide (for which the field is known in closed form), the cross section of which possesses a sharp re-entrant corner. It is demonstrated that explicitly satisfying the edge conditions at this corner significantly improves the computational accuracy. In agreement with a previous conjecture it is shown, by example using the sector waveguide, that the straightforward point-matching method sometimes gives completely erroneous fields, even when predicting cutoff wavenumbers with moderate accuracy.