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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.17513 |
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| _version_ | 1866915686447579136 |
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| author | Deng, Youjun Liu, Hongyu Tang, Wanjing Zheng, Guang-Hui |
| author_facet | Deng, Youjun Liu, Hongyu Tang, Wanjing Zheng, Guang-Hui |
| contents | This paper investigates surface polariton resonance (SPR) in three-dimensional elastic metamaterials with nanorod geometry. The primary motivation is to surpass the physical limitations imposed by the quasi-static approximation for SPRs through anisotropic geometric design. The analysis boils down to analyzing the spectral properties of the matrix-valued elastic Neumann-Poincaré (NP) operator defined on the nanorod boundary. We develop novel analytical techniques and conduct a rigorous asymptotic analysis of elastic layer potential operators, specifically adapted for highly anisotropic structures. Within this framework, we derive precise asymptotic formulas for the scattered field in the quasi-static regime. A thorough examination of these expressions yields explicit resonance conditions that intricately link three fundamental parameters: elastic material parameters, wave frequency, and nanorod geometry. Furthermore, we characterize the intrinsic relationship between these parameters and the associated energy blow-up rate of the resonant field. This analysis explicitly establishes a sharp curvature concentration effect at the nanorod extremities, where field enhancement is locally maximized. Our work provides a rigorous theoretical foundation for harnessing elastic SPRs through anisotropic geometric engineering, with implications for sensing, wave focusing, and metamaterial applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17513 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On surface polariton resonance and its curvature concentration effects from 3D elastic nanorods Deng, Youjun Liu, Hongyu Tang, Wanjing Zheng, Guang-Hui Mathematical Physics This paper investigates surface polariton resonance (SPR) in three-dimensional elastic metamaterials with nanorod geometry. The primary motivation is to surpass the physical limitations imposed by the quasi-static approximation for SPRs through anisotropic geometric design. The analysis boils down to analyzing the spectral properties of the matrix-valued elastic Neumann-Poincaré (NP) operator defined on the nanorod boundary. We develop novel analytical techniques and conduct a rigorous asymptotic analysis of elastic layer potential operators, specifically adapted for highly anisotropic structures. Within this framework, we derive precise asymptotic formulas for the scattered field in the quasi-static regime. A thorough examination of these expressions yields explicit resonance conditions that intricately link three fundamental parameters: elastic material parameters, wave frequency, and nanorod geometry. Furthermore, we characterize the intrinsic relationship between these parameters and the associated energy blow-up rate of the resonant field. This analysis explicitly establishes a sharp curvature concentration effect at the nanorod extremities, where field enhancement is locally maximized. Our work provides a rigorous theoretical foundation for harnessing elastic SPRs through anisotropic geometric engineering, with implications for sensing, wave focusing, and metamaterial applications. |
| title | On surface polariton resonance and its curvature concentration effects from 3D elastic nanorods |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2512.17513 |