Error Bounds on Perturbation Analysis for the Dominant Mode of Rectangular Corrugated Waveguide

An error bound on the expansion of multiple scales method is deduced. The filtering properties of a periodically corrugated rectangular metallic waveguide are considered as an example to clarify this. The paper asses the spectral response of the filter using two independent software packages. Their results will be compared with the perturbation method of multiple scales expanded up to the second order.