Spectral theory of a Neumann-Poincaré-type operator and analysis of cloaking by anomalous localized resonance II

If a body of dielectric material is coated by a plasmonicstructure of negative dielectric constant with nonzero lossparameter, then cloaking by anomalous localized resonance (CALR)may occur as the loss parameter tends to zero. The aim of thispaper is to investigate this phenomenon in two and threedimensions when the coated structure is radial, and the core, shell andmatrix are isotropic materials. In two dimensions,we show that if the real part of the permittivity of the shell is$-1$ (under the assumption that the permittivity of the backgroundis $1$), then CALR takes place. If it is different from $-1$, thenCALR does not occur. In three dimensions, we show that CALR doesnot occur. The analysis of this paper reveals that occurrence ofCALR is determined by the eigenvalue distribution of theNeumann-Poincaré-type operator associated with the structure.