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 β 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.