Electromagnetic energy within coated spheres containing dispersive metamaterials

TL;DR

This paper derives exact formulas for electromagnetic energy stored inside coated spheres with dispersive metamaterials, revealing how energy relates to absorption efficiency and Fano interference effects, with potential applications in negative refraction metamaterials.

Contribution

It provides analytical expressions for electromagnetic energy within dispersive coated spheres, linking stored energy to optical absorption and interference effects, which is novel for such complex structures.

Findings

Stored energy is sensitive to field interferences and Fano effects.

Explicit relation between stored energy and absorption efficiency.

Metamaterials with negative refraction enhance Fano effects.

Abstract

An exact expression is derived for the time-averaged electromagnetic energy within a magneto-dielectric coated sphere, which is irradiated by a plane and time-harmonic electromagnetic wave. Both the spherical shell and core are considered to be dispersive and lossy, with a realistic dispersion relation of an isotropic split-ring resonator metamaterial. We obtain analytical expressions for the stored electromagnetic energies inside the core and the shell separately and calculate their contribution to the total average energy density. The stored electromagnetic energy is calculated for two situations involving a metamaterial coated sphere: the dielectric shell and dispersive metamaterial core, and vice-versa. An explicit relation between the stored energy and the optical absorption efficiency is also obtained. We show that the stored electromagnetic energy is an observable sensitive to field interferences responsible for the Fano effect. This result, together with the fact that the Fano effect is more likely to occur in metamaterials with negative refraction, suggest that our findings may be explored in applications.