Remark on resonance scattering by two barriers in a waveguide

For resonance scattering by two infinitely thin barriers in a waveguide, an elementary proof is given for the existence of a frequency at which the reflection coefficient is arbitrarily low. The proof is obtained using only the method of mode matching. It turns out that the existence of resonances, which are the complex poles of the Green’s function of the scattering problem, do not need to be considered in the method.