Calculation of TM0n mode dispersion relations in rippled-wall waveguides

A novel technique for calculating the dispersion relation for TM _0n modes in a rippled-wall waveguide is reported. A standard eigenvalue solver for the two-dimensional Helmholtz equation is used to calculate the frequencies for several special values of the wavenumber. For other wavenumbers, the frequencies of the lowest order mode are calculated by interpolation using a function based on an equivalent circuit model, whose parameters are determined from the numerically calculable cases. The advantages of this approach are ease of use and the ability to handle a variable dielectric constant inside of the waveguide