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arXiv · 2504.05619

Mathematical analysis of subwavelength resonant acoustic scattering in multi-layered high-contrast structures

Youjun Deng·Lingzheng Kong·Yongjian Liu·Liyan Zhu
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Abstract

Multi-layered structures are widely used in the construction of metamaterial devices to realize various cutting-edge waveguide applications. This paper makes several contributions to the mathematical analysis of subwavelength resonances in a structure of $N$-layer nested resonators. Firstly, based on the Dirichlet-to-Neumann approach, we reduce the solution of the acoustic scattering problem to an $N$-dimensional linear system, and derive the optimal asymptotic characterization of subwavelength resonant frequencies in terms of the eigenvalues of an $N\times N$ tridiagonal matrix, which we refer to as the generalized capacitance matrix. Moreover, we provide a modal decomposition formula for the scattered field, as well as a monopole approximation for the far-field pattern of the acoustic wave scattered by the $N$-layer nested resonators. Finally, some numerical results are presented to corroborate the theoretical findings.

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Youjun Deng, Lingzheng Kong, Yongjian Liu, Liyan Zhu. 2025-04-08. Mathematical analysis of subwavelength resonant acoustic scattering in multi-layered high-contrast structures. https://arxiv.org/abs/2504.05619

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