Analytical Study of the Propagation Modes into a Perturbed Border Waveguide

This article analytically approaches the problem of a propagating wave in a waveguide with a border characterized by an arbitrary angular dependence. We find a relationship between the Fourier coefficients of the function describing the border of the waveguide and the propagation constant beta of the propagating wave. The proposed solution to the problem provides an analytical tool to obtain information about the shape of a waveguide. The analysis of the propagating wave reveals that, from a theoretical point of view, it is possible to partially, or even completely, reconstruct the border of the waveguide.