Strong near-field couplings of anapole modes and formation of higher-order electromagnetic modes in stacked all-dielectric nanodisks

We theoretically study the near-field couplings of two stacked all-dielectric nanodisks, where each disk has an electric anapole mode consisting of an electric dipole mode and an electric toroidal dipole (ETD) mode. Strong bonding and anti-bonding hybridizations of the ETD modes of the two disks occur. The bonding hybridized ETD can interfere with the dimer's electric dipole mode and induce a new electric anapole mode. The anti-bonding hybridization of the ETD modes can induce a magnetic toroidal dipole (MTD) response in the disk dimer. The MTD and magnetic dipole resonances of the dimer form a magnetic anapole mode. Thus, two dips associated with the hybridized modes appear on the scattering spectrum of the dimer. Furthermore, the MTD mode is also accompanied by an electric toroidal quadrupole mode. The hybridizations of the ETD and the induced higher-order modes can be adjusted by varying the geometries of the disks. The strong anapole mode couplings and the corresponding rich higher-order mode responses in simple all-dielectric nanostructures can provide new opportunities for nanoscale optical manipulations.