The High-Order Toroidal Moments and Anapole States in All-Dielectric Photonics

All-dielectric nanophotonics attracts ever increasing attention nowadays due to the possibility of controlling and configuring light scattering on high-index semiconductor nanoparticles. It opens a room of opportunities for designing novel types of nanoscale elements and devices, and paves the way for advanced technologies of light energy manipulation. One of the exciting and promising prospects is associated with utilizing the so-called toroidal moment, being the result of poloidal currents excitation, and anapole states, corresponding to the interference of dipole and toroidal electric moments. Here, higher-order toroidal moments of both types (up to the electric octupole toroidal moment) are presented and investigated in detail via the direct Cartesian multipole decomposition allowing new near- and far-field configurations to be obtained. Poloidal currents can be associated with vortex-like distributions of the displacement currents inside nanoparticles, revealing the physical meaning of the high-order toroidal moments and the convenience of the Cartesian multipoles as an auxiliary tool for analysis. High-order nonradiating anapole states accompanied by the excitation of intense near-fields are demonstrated. It is believed that the results are of high importance for both the fundamental understanding of light scattering by high-index particles and a variety of nanophotonics applications and light governing on nanoscale.