Abstract
Dynamic toroidal dipoles, a distinguished class of fundamental electromagnetic sources, receive increasing interest and participate in fascinating electrodynamic phenomena and sensing applications. As described in the literature, the radiative nature of dynamic toroidal dipoles is sometimes confounded, intermixing with static toroidal dipoles and plasmonic dark modes. Here, we elucidate this issue and provide proof-of-principle experiments exclusively on the radiation behavior of dynamic toroidal moments. Optical toroidal modes in plasmonic heptamer nanocavities are analyzed by electron energy loss spectroscopy and energy-filtered transmission electron microscopy supported by finite-difference time-domain numerical calculations. Additionally, their corresponding radiation behaviors are experimentally investigated by means of cathodoluminescence. The observed contrasting behaviors of a single dynamic toroidal dipole mode and an antiparallel toroidal dipole pair mode are discussed and elucidated. Our findings further clarify the electromagnetic properties of dynamic toroidal dipoles and serve as important guidance for the use of toroidal dipole moments in future applications.
Highlights
Elementary electromagnetic (EM) sources with welldefined near- and far-field properties form the fundamentals to systematically describe and understand observed electromagnetic phenomena of objects and their interactions
Toroidal multipoles are considered as the third family of elementary EM sources due to their distinct charge−current configuration and unique parity properties as compared to their electric and magnetic counterparts.[1,2]
We first employed near-field measurements with EELS to probe the resonances of the supported toroidal modes in the heptamer structure with a selective excitation scheme along its symmetry axis (Figure 1a)
Summary
Elementary electromagnetic (EM) sources with welldefined near- and far-field properties form the fundamentals to systematically describe and understand observed electromagnetic phenomena of objects and their interactions. As an electric dipole can be formed by two charges with opposite sign and a magnetic dipole by a current loop, a toroidal dipole is yielded by poloidal currents on the surface of a torus.[1] More generally, toroidal multipoles are considered as the third family of elementary EM sources due to their distinct charge−current configuration and unique parity properties as compared to their electric and magnetic counterparts.[1,2] Fascinating phenomena have been shown to have a close association with toroidal excitations, such as optical activity[3] and electromagnetic-induced transparency.[4] toroidal excitations show a feasible potential in applications as nanophotonic devices.[5−7]. Its scattering field can be as strong as that of an electric dipole.[33,34] In the literature, there exists confusion about the properties of dynamic toroidal dipoles, partially from the conception interchange with the static toroidal dipoles and merging with a plasmonic dark mode. It is urgent to clarify this issue, as the research interest in dynamic toroidal moments is apparently increasing, even in the aspect of practical applications.[5,7,35] It is worth noting that the radiation properties of dynamic toroidal dipoles have been considered in a number of experiments.[34,36] there are no exclusive experiments in demonstrating the radiation of a single dynamic toroidal moment
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