Macroscopic electromagnetic response of metamaterials with toroidal resonances

TL;DR

This paper develops an analytical framework linking microscopic toroidal dipole excitations to the macroscopic electromagnetic response of metamaterials, highlighting the toroidal dipole's significant influence on their properties.

Contribution

It introduces a novel analytical approach that connects microscopic toroidal dipoles with the macroscopic electromagnetic response of metamaterials, filling a key theoretical gap.

Findings

Established a direct analytical link between toroidal dipoles and metamaterial response.

Demonstrated the key role of toroidal dipoles in shaping electromagnetic properties.

Provided a case study illustrating the impact of toroidal excitations.

Abstract

Toroidal dipole, first described by Ia. B. Zeldovich [Sov. Phys. JETP 33, 1184 (1957)], is a distinct electromagnetic excitation that differs both from the electric and the magnetic dipoles. It has a number of intriguing properties: static toroidal nuclear dipole is responsible for parity violation in atomic spectra; interactions between static toroidal dipole and oscillating magnetic dipole are claimed to violate Newton's Third Law while non-stationary charge-current configurations involving toroidal multipoles have been predicted to produce vector potential in the absence of electromagnetic fields. Existence of the toroidal response in metamaterials was recently demonstrated and is now a growing field of research. However, no direct analytical link has yet been established between the transmission and reflection of macroscopic electromagnetic media and toroidal dipole excitations. To address this essential gap in electromagnetic theory we have developed an analytical approach linking microscopic and macroscopic electromagnetic response of a metamaterial and showed, using a case study, the key role of the toroidal dipole in shaping the electromagnetic properties of the metamaterial.