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Almost complete transmission of waves through perforated cross-walls in a waveguide with Dirichlet boundary condition
S. A. Nazarova, L. Chesnelb a St. Petersburg State University, St. Petersburg, Russia
b INRIA/Centre de mathématiques appliquées, École Polytechnique, Palaiseau, France
Abstract:
We consider a waveguide composed of two not necessity equal semi-infinite strips (trunks) and a rectangle (resonator) connected by narrow openings in the shared walls. As their diameter vanishes, we construct asymptotics for the scattering coefficients, justifying them by the technique of weighted spaces with detached asymptotics. We establish a criterion for the possibility of observing, at a given frequency, almost complete transmission of waves through both perforated cross-walls. This effect is revealed due to a fine-tuning of the resonator height and the criterion involves an equation relating some geometrical characteristics of the waveguide to the wave numbers in the trunks, while any mirror symmetry turns the criterion trivial.
Keywords:
waveguide, Dirichlet boundary condition, perforated cross-walls, asymptotics of scattering coefficients, almost complete transmission of waves.
Received: 10.09.2020 Revised: 16.11.2020 Accepted: 18.11.2020
Citation:
S. A. Nazarov, L. Chesnel, “Almost complete transmission of waves through perforated cross-walls in a waveguide with Dirichlet boundary condition”, Sibirsk. Mat. Zh., 62:2 (2021), 339–361; Siberian Math. J., 62:2 (2021), 272–291
Linking options:
https://www.mathnet.ru/eng/smj7560 https://www.mathnet.ru/eng/smj/v62/i2/p339
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