2011/09/02 by Habib Ammari, Giulio Ciraolo, Ammari, Habib +7 · 4 citations
Mathematics · Engineering · #Numerical methods in inverse problems #Differential Equations and Numerical Methods #Thermoelastic and Magnetoelastic Phenomena
paper · pdf · doi:10.48550/arxiv.1109.0479
The aim of this paper is to give a mathematical justification of cloaking due\nto anomalous localized resonance (CALR). We consider the dielectric problem\nwith a source term in a structure with a layer of plasmonic material. Using\nlayer potentials and symmetrization techniques, we give a necessary and\nsufficient condition on the fixed source term for electromagnetic power\ndissipation to blow up as the loss parameter of the plasmonic material goes to\nzero. This condition is written in terms of the Newtonian potential of the\nsource term. In the case of concentric disks, we make the condition even more\nexplicit. Using the condition, we are able to show that for any source\nsupported outside a critical radius CALR does not take place, and for sources\nlocated inside the critical radius satisfying certain conditions CALR does take\nplace as the loss parameter goes to zero.\n