On three-dimensional plasmon resonances in elastostatics

We consider plasmon resonances for the elastostatic system in ℝ³ associated with a very broad class of sources. The plasmonic device takes a general core–shell–matrix form with the metamaterial located in the shell. It is shown that the plasmonic device in the literature which induces resonance in ℝ² does not induce resonance in ℝ³. We then construct two novel plasmonic devices with suitable plasmon constants, varying according to the source term or the loss parameter, that can induce resonances. If there is no core, we show that resonance always occurs. If there is a core of an arbitrary shape, we show that the resonance strongly depends on the location of the source. In fact, there exists a critical radius such that resonance occurs for sources lying within the critical radius, whereas resonance does not occur for sources lying outside the critical radius. Our argument is based on the variational technique by making use of the primal and dual variational principles for the elastostatic system, along with a highly technical construction of the associated perfect plasmon elastic waves. © 2016, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg.