Magnetic toroidal dipole response in individual all-dielectric nanodisk clusters

Multipole electromagnetic resonances and their couplings are of crucial importance for both the fundamental understanding of light scattering by high-index all-dielectric nanostructures and lots of nanophotonic applications based on those nanostructures. Here, we show that magnetic dipole modes in a dielectric nanodisk cluster can easily form a magnetic toroidal dipole (MTD) mode. The cluster consists of five silicon nanodisks, where each nanodisk holds a magnetic dipole mode. These magnetic dipole modes can collectively couple with each other and form a MTD mode under suitable excitation. The MTD mode is confirmed by multipole expansion calculations and near field distributions, where two closed loops of magnetic field with opposite directions are seen. The response of the MTD is strong and comparable to that of a common electric dipole or magnetic dipole mode. It is also found that the MTD resonance is accompanied by an electric toroidal quadrupole mode in the cluster. The MTD mode is tunable by varying the geometries. We also fabricated silicon nanoparticle clusters and verified the MTD mode in the experiment. Our results illustrate the controllable excitation of strong high-order electromagnetic modes and these modes may open new opportunities for light manipulation at the nanoscale.