Abstract
A closed loop of magnetic dipoles gives rise to a toroidal dipole, where magnetic dipoles serve as the basic elements. However, magnetic responses are much weaker than electric ones at optical frequencies. Here, we show that toroidal dipole moments can be induced by collective modes in plasmonic nanoparticle clusters instead of using magnetic dipoles. When the geometric parameters of plasmonic clusters are optimized, a dominant radiation from toroidal dipole can be realized guaranteed by the symmetry properties of clusters. Compared to the toroidal model with triple plasmonic nanoparticles, the plane-wave excitation of toroidal dipolar mode can be angular independent for the cluster with particle number N ⩾ 4. These findings of toroidal moments based on collective modes in plasmonic nanoparticle clusters may find potential applications in optical sensing, nano-antennas, and nonlinear optics, etc.
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