Long-Range Coupling of Toroidal Moments for the Visible

Dynamic toroidal multipoles are the third independent family of elementary electromagnetic sources in addition to electric and magnetic multipoles. Whereas the dipole–dipole coupling in electric and magnetic multipole families has been well studied, such fundamental coupling effects in the toroidal multipole family have not yet been experimentally investigated. Here we propose a plasmonic decamer nanocavity structure to realize transverse coupling between magnetic toroidal dipoles. The coupling effect was investigated both experimentally and theoretically, by means of electron energy-loss spectroscopy and energy-filtered transmission electron microscopy, together with finite-difference time-domain calculations. We observe that the coupling causes a reorientation of the magnetic moment loops surrounding the initial toroidal moments. This coupling results in three eigenstates of this toroidal system. The underlying coupling mechanism is qualitatively demonstrated. Our investigations pave the way toward a better understanding of coupling phenomena of toroidal moments and will bias applications in the long-range ordering of moments in metamaterials, e.g., for transfer of electromagnetic energy using toroidal moments (by analogy with chain metallic waveguides).