6533b856fe1ef96bd12b2944

RESEARCH PRODUCT

Spectral theory of a Neumann-Poincare-type operator and analysis of cloaking due to anomalous localized resonance

Hyundae LeeGraeme W. MiltonHabib AmmariGiulio CiraoloHyeonbae Kang

subject

PermittivitySpectral theoryShell (structure)Physics::OpticsFOS: Physical sciencesCloakingDielectricBlow up01 natural sciencesResonance (particle physics)Mathematics (miscellaneous)Mathematics - Analysis of PDEsSettore MAT/05 - Analisi MatematicaQuantum mechanicsFOS: Mathematics0101 mathematicsPhysicsCondensed Matter - Materials ScienceMechanical EngineeringOperator (physics)010102 general mathematicsIsotropyMaterials Science (cond-mat.mtrl-sci)Partial Differential EquationsNeumann–Poincaré operator010101 applied mathematicsAnalysisAnalysis of PDEs (math.AP)Optics (physics.optics)Physics - Optics

description

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 sources located inside the critical radius satisfying certain conditions CALR does take place as the loss parameter goes to zero.

yearjournalcountryeditionlanguage
2011-09-02
http://arxiv.org/abs/1109.0479