Journal of Spectral Theory


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Published online first: 2018-10-25
DOI: 10.4171/JST/262

On spectral properties of Neuman–Poincaré operator and plasmonic resonances in 3D elastostatics

Youjun Deng[1], Hongjie Li[2] and Hongyu Liu[3]

(1) Central South University, Changsha Hunan, China
(2) Hong Kong Baptist University, Hong Kong, China
(3) Hong Kong Baptist University, Hong Kong

We consider plasmon resonances and cloaking for the elastostatic system in $\mathbb{R}^3$ via the spectral theory of the Neumann–Poincaré operator. We first derive the full spectral properties of the Neumann–Poincaré operator for the 3D elastostatic system in the spherical geometry. The spectral result is of significant interest for its own sake, and serves as a highly nontrivial extension of the corresponding 2D study in [4]. The derivation of the spectral result in 3D involves much more complicated and subtle calculations and arguments than that for the 2D case. Then we consider a 3D plasmonic structure in elastostatics which takes a general core-shell-matrix form with the metamaterial located in the shell. Using the obtained spectral result, we provide an accurate characterisation of the anomalous localised resonance and cloaking associated to such a plasmonic structure.

Keywords: Anomalous localized resonance, cloaking, plasmonic material, negative elastic materials, elastostatics

Deng Youjun, Li Hongjie, Liu Hongyu: On spectral properties of Neuman–Poincaré operator and plasmonic resonances in 3D elastostatics. J. Spectr. Theory Electronically published on October 25, 2018. doi: 10.4171/JST/262 (to appear in print)