Resonance scattering in a waveguide with identical thick barriers

DOI10.1016/J.AMC.2021.126592arXiv2001.07060MaRDI QIDQ6333162

Publication date: 20 January 2020

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.

Mathematics Subject Classification ID

Wave scattering in solid mechanics (74J20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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