Issue |
ESAIM: M2AN
Volume 58, Number 4, July-August 2024
|
|
---|---|---|
Page(s) | 1413 - 1440 | |
DOI | https://doi.org/10.1051/m2an/2024041 | |
Published online | 31 July 2024 |
Elastostatics within multi-layer metamaterial structures and an algebraic framework for polariton resonances
1
School of Mathematics and Statistics, Central South University, Changsha 410083, P.R. China
2
Department of Mathematics, City University of Hong Kong, Hong Kong SAR, P.R. China
* Corresponding author: youjundeng@csu.edu.cn
Received:
20
June
2023
Accepted:
21
May
2024
Multi-layer structures are ubiquitous in constructing metamaterial devices to realise various frontier applications including super-resolution imaging and invisibility cloaking. In this paper, we develop a general mathematical framework for studying elastostatics within multi-layer material structures in Rd, d = 2, 3. The multi-layer structure is formed by concentric balls and each layer is filled by either a regular elastic material or an elastic metamaterial. The number of layers can be arbitrary and the material parameters in each layer may be different from one another. In practice, the multi-layer structure can serve as the building block for various material devices. Considering the impingement of an incident field on the multi-layer structure, we first derive the exact perturbed field in terms of an elastic momentum matrix, whose dimension is the same as the number of layers. By highly intricate and delicate analysis, we derive a comprehensive study of the spectral properties of the elastic momentum matrix. This enables us to establish a handy algebraic framework for studying polariton resonances associated with multi-layer metamaterial structures, which forms the fundamental basis for many metamaterial applications.
Mathematics Subject Classification: 35B34 / 35L05 / 35P15 / 74B05 / 74J20
Key words: Multi-layer solid structure / negative elastic materials / polariton resonance / elastic momentum matrix / spectral analysis / characteristic polynomial
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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