Electromagnetic energy within coated spheres containing dispersive metamaterials

• Published in: Journal of optics (2010) 2012-06, Vol.14 (6), p.65101-1-9
• Main Authors: Arruda, Tiago J, Pinheiro, Felipe A, Martinez, Alexandre S
• Format: Article
• Language: English
• Subjects: Aden-Kerker solution; Applied classical electromagnetism; Core loss; Dispersions; dispersive metamaterials; Edge and boundary effects; reflection and refraction; electromagnetic energy; Electromagnetic wave propagation, radiowave propagation; Electromagnetism; electron and ion optics; Energy density; Exact sciences and technology; Exact solutions; Fundamental areas of phenomenology (including applications); Mathematical analysis; Metamaterials; Optical materials; Optics; Photonic bandgap materials; Physics; Shells; Spherical shells; Wave optics
• ISSN: 2040-8978; 2040-8986
• DOI: 10.1088/2040-8978/14/6/065101

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 contributions to the total average energy density. The stored electromagnetic energy is calculated for two situations involving a metamaterial coated sphere: a 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.