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Subwavelength resonances in 1D high-contrast acoustic media

by F. Feppon and Z. Cheng and H. Ammari

(Report number 2022-29)

Abstract
We propose a mathematical theory of acoustic wave scattering in one-dimensional finite high-contrast media. The system considered is constituted of a finite alternance of high-contrast segments of arbitrary lengths and interdistances, called the ``resonators'', and a background medium. We prove the existence of subwavelength resonances, which are the counterparts of the well-known Minnaert resonances in 3D systems. Our main contribution is to show that the resonant frequencies, as well as the transmission and reflection properties of the system can be accurately predicted by a ``capacitance'' eigenvalue problem, analogously to the 3D setting. Numerical results considering different situations with \(N=1\) to \(N=6\) resonators are provided to support our mathematical analysis, and to illustrate the various possibilities offered by high-contrast resonators to manipulate waves at subwavelength scales.

Keywords: Acoustic waves, subwavelength resonances, high-contrast, one-dimensional media, transmission coefficient.

@Techreport{FCA22_1017,
  author = {F. Feppon and Z. Cheng and H. Ammari},
  title = { Subwavelength resonances in 1D high-contrast acoustic media},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2022-29},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2022/2022-29.pdf },
  year = {2022}
}

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