Resonant signal reversal in a waveguide connected to a resonator

It has been proven that when connecting two infinite semi-cylinders or waveguides with a finite cylinder or resonator at a certain frequency, it is possible to transmit a signal almost completely from one semi-cylinder to another. In this case, the reflected field is arbitrarily small. A very simple technique based on the expansion of the solution in a Fourier series in cylinders and matching the series for the signal and its derivatives in the conjugation boundaries of cylinders of different radii is used for the proof. The main feature of this method is its elementary nature, which allows for a certain class of boundaries to establish resonant scattering effects.