Resonance scattering in a waveguide with identical thick barriers

TL;DR

This paper demonstrates how waves can pass through small barriers in a waveguide at specific resonance frequencies, using elementary methods to explicitly determine these frequencies, contrasting with more abstract traditional approaches.

Contribution

It introduces a constructive, elementary approach to identify resonance frequencies in waveguides with thick barriers, making the analysis accessible and explicit.

Findings

Resonance frequencies enable near-complete wave transmission through small barriers.

Explicit equations for resonance frequencies are derived.

Elementary methods are used instead of complex spectral analysis.

Abstract

We consider wave propagation across an infinite waveguide of an arbitrary bounded cross-section, whose interior is blocked by two identical thick barriers with holes. When the holes are small, the waves over a broad range of frequencies are almost fully reflected. However, we show the existence of a resonance frequency at which the wave is almost fully transmitted, even for very small holes. This resonance scattering, which is known as tunneling effect in quantum mechanics, is demonstrated in a constructive way by rather elementary tools, in contrast to commonly used abstract methods such as searching for complex-valued poles of the scattering matrix or non-stationary scattering theory. In particular, we derived an explicit equation that determines the resonance frequency. The employed elementary tools make the paper accessible to non-experts and educationally appealing.