Almost Complete Transmission of Waves Through Perforated Cross-Walls in a Waveguide with Dirichlet Boundary Condition

S. A. Nazarov, L. Chesnel

Research output: Contribution to journalArticlepeer-review

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 heightand the criterion involves an equationrelating some geometrical characteristics of the waveguideto the wave numbers in the trunks,while any mirror symmetry turns the criterion trivial.

Original languageEnglish
Pages (from-to)272-291
JournalSiberian Mathematical Journal
Volume62
Issue number2
DOIs
StatePublished - Mar 2021

Scopus subject areas

  • Mathematics(all)

Keywords

  • almost complete transmission of waves
  • asymptotics of scattering coefficients
  • Dirichlet boundary condition
  • perforated cross-walls
  • waveguide

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