Giulio Ciraolo

Spectral Theory of a Neumann–Poincaré-Type Operator and Analysis of Cloaking Due to Anomalous Localized Resonance

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.

Anomalous localized resonance using a folded geometry in three dimensions

If a body of dielectric material is coated by a plasmonic structure of negative dielectric material with non-zero loss parameter, then cloaking by anomalous localized resonance (CALR) may occur as the loss parameter tends to zero. If the coated structure is circular (two dimensions) and the dielectric constant of the shell is a negative constant (with loss parameter), then CALR occurs, and if the coated structure is spherical (three dimensions), then CALR does not occur. The aim of this paper is to show that CALR takes place if the spherical coated structure has a specially designed anisotropic dielectric tensor. The anisotropic dielectric tensor is designed by unfolding a folded geometry.

Symmetry of minimizers with a level surface parallel to the boundary

We consider the functional

Wave propagation in a 3-D optical waveguide

I_\Omega(v) = \int_\Omega [f(|Dv|) - v] dx,

A method of variation of boundaries for waveguide grating couplers

where

A rigidity problem on the round sphere

\Omega

A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional

is a bounded domain and

A Radiation Condition for the 2-D Helmholtz Equation in Stratified Media

f