On Quasi-Static Cloaking Due to Anomalous Localized Resonance in $\mathbb{R}^3$

Abstract

This work concerns the cloaking due to anomalous localized resonance (CALR) in the quasi-static regime. We extend the related two-dimensional studies in [H. Ammari et al., Arch. Ration. Mech. Anal., 208 (2013), pp. 667--692; R. V. Kohn et al., Comm. Math. Phys., 328 (2014), pp. 1--27] to the three-dimensional setting. CALR is shown not to take place for the plasmonic configuration considered in these two papers in the three-dimensional case. We give two different constructions which ensure the occurrence of CALR. There may be no core or an arbitrarily shaped core for the cloaking device. If there is a core, then the dielectric distribution inside it could be arbitrary.