Toroidal dipole resonances by a sub-wavelength all-dielectric torus

Electromagnetic toroidal excitations open up a new avenue for strong light-matter interactions. Although toroidal dipole resonances (TDRs) based on artificial meta-molecules were reported intensely, the TDRs supported in a single dielectric particle remain largely unknown. In this work, we show that an all-dielectric sub-wavelength torus can support a dominant TDR. The magnetic field can be enhanced greatly, and it shows a "vortex-like" configuration in the torus, confirming the toroidal excitation. The evolutions of the TDRs due to the geometrical parameters, dielectric permittivity, and polarization are discussed. It is found that the toroidal excitation is achieved mainly for TM polarization, while the anapole state is uncovered for TE polarization. This work suggests a new strategy for toroidal excitations based on a simple dielectric resonator.