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Main Authors: Deng, Youjun, Liu, Hongyu, Tang, Wanjing, Zheng, Guang-Hui
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2512.17513
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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