Resonant signal reversal in a waveguide connected to a resonator

TL;DR

This paper demonstrates a resonant signal reversal phenomenon in a waveguide-resonator system, showing near-complete signal transmission with minimal reflection at specific frequencies using a Fourier series matching technique.

Contribution

It introduces a simple, elementary method based on Fourier series expansion to prove resonant scattering effects in waveguide-resonator systems.

Findings

Near-complete signal transmission at resonance

Minimal reflection at specific frequencies

Effective Fourier series matching technique

Abstract

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.