Cloaking due to anomalous localized resonance in plasmonic structures of confocal ellipses

If a core of dielectric material is coated by a plasmonic structure of negative dielectric material with non-zero loss parameter, then anomalous localized resonance may occur as the loss parameter tends to zero and the source outside the structure can be cloaked. It has been proved that the cloaking due to anomalous localized resonance (CALR) takes place for structures of concentric disks and the critical radius inside which the sources are cloaked has been computed. In this paper, it is proved that CALR takes place for structures of confocal ellipses and the critical elliptic radii are computed. The method of this paper uses the spectral analysis of the Neumann-Poincar\'e type operator associated with two interfaces (the boundaries of the core and the shell)

Analytical results regarding electrostatic resonances of surface phonon/plasmon polaritons: separation of variables with a twist

The boundary integral equation method ascertains explicit relations between localized surface phonon and plasmon polariton resonances and the eigenvalues of its associated electrostatic operator. We show that group-theoretical analysis of Laplace equation can be used to calculate the full set of eigenvalues and eigenfunctions of the electrostatic operator for shapes and shells described by separable coordinate systems. These results not only unify and generalize many existing studies but also offer the opportunity to expand the study of phenomena like cloaking by anomalous localized resonance. For that reason we calculate the eigenvalues and eigenfunctions of elliptic and circular cylinders. We illustrate the benefits of using the boundary integral equation method to interpret recent experiments involving localized surface phonon polariton resonances and the size scaling of plasmon resonances in graphene nano-disks. Finally, symmetry-based operator analysis can be extended from electrostatic to full-wave regime. Thus, bound states of light in the continuum can be studied for shapes beyond spherical configurations.Comment: 25 pages, 3 figures, to be published Proc. Royal Soc.

On Absence and Existence of the Anomalous Localized Resonance without the Quasi-static Approximation

The paper considers the transmission problems for Helmholtz equation with bodies that have negative material parameters. Such material parameters are used to model metals on optical frequencies and so-called metamaterials. As the absorption of the materials in the model tends to zero the fields may blow up. When the speed of the blow up is suitable, this is called the Anomalous Localized Reconance (ALR). In this paper we study this phenomenon and formulate a new condition, the weak Anomalous Localized Reconance (w-ALR), where the speed of the blow up of fields may be slower. Using this concept, we can study the blow up of fields in the presence of negative material parameters without the commonly used quasi-static approximation. We give simple geometric conditions under which w-ALR or ALR may, or may not appear. In particular, we show that in a case of a curved layer of negative material with a strictly convex boundary neither ALR nor w-ALR appears with non-zero frequencies (i.e. in the dynamic range) in dimensions $d\ge 3$. In the case when the boundary of the negative material contains a flat subset we show that the w-ALR always happens with some point sources in dimensions $d\ge 2$. These results, together with the earlier results of Milton et al. ( [22, 23]) and Ammari et al. ([2]) show that for strictly convex bodies ALR may appear only for bodies so small that the quasi-static approximation is realistic. This gives limits for size of the objects for which invisibility cloaking methods based on ALR may be used.Comment: 30 pages, 7 figure