On spectral properties of neuman-poincaré operator and plasmonic resonances in 3D elastostatics

Youjun Deng, Hongjie Li, Hongyu LIU

Research output: Contribution to journalJournal articlepeer-review

25 Citations (Scopus)


We consider plasmon resonances and cloaking for the elastostatic system in R3 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 systemin 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.

Original languageEnglish
Pages (from-to)767-789
Number of pages23
JournalJournal of Spectral Theory
Issue number3
Early online date25 Oct 2018
Publication statusPublished - Jul 2019

Scopus Subject Areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Geometry and Topology

User-Defined Keywords

  • Anomalous localized resonance
  • Cloaking
  • Elastostatics
  • Negative elastic materials
  • Plasmonicmaterial


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