Spectral theory of a Neumann-Poincare-type operator and analysis of cloaking due to anomalous localized resonance. (arXiv:1109.0479v1 [math.AP])

Spectral theory of a Neumann-Poincare-type operator and analysis of cloaking due to anomalous localized resonance. (arXiv:1109.0479v1 [math.AP]):
The aim of this paper is to give a mathematical justification of cloaking due
to anomalous localized resonance (CALR). We consider the dielectric problem
with a source term in a structure with a layer of plasmonic material. Using
layer potentials and symmetrization techniques, we give a necessary and
sufficient condition on the fixed source term for electromagnetic power
dissipation to blow up as the loss parameter of the plasmonic material goes to
zero. This condition is written in terms of the Newtonian potential of the
source term. In the case of concentric disks, we make the condition even more
explicit. Using the condition, we are able to show that for any source
supported outside a critical radius CALR does not take place, and for almost
any sources located inside the critical radius CALR does take place as the loss
parameter goes to zero.