Nonradiating anapole modes in dielectric nanoparticles

Abstract

Nonradiating current configurations attract attention of physicists for many years as possible models of stable atoms. One intriguing example of such a nonradiating source is known as ‘anapole'. An anapole mode can be viewed as a composition of electric and toroidal dipole moments, resulting in destructive interference of the radiation fields due to similarity of their far-field scattering patterns. Here we demonstrate experimentally that dielectric nanoparticles can exhibit a radiationless anapole mode in visible. We achieve the spectral overlap of the toroidal and electric dipole modes through a geometry tuning, and observe a highly pronounced dip in the far-field scattering accompanied by the specific near-field distribution associated with the anapole mode. The anapole physics provides a unique playground for the study of electromagnetic properties of nontrivial excitations of complex fields, reciprocity violation and Aharonov–Bohm like phenomena at optical frequencies.

Electromagnetic toroidal excitations in matter and free space

“…3h), where it was shown that the destructive interference between coherently oscillating electric and toroidal dipoles provides a new mechanism of electromagnetic transparency that yields narrow and symmetric Lorentzian transparency lines. Similar resonances were recently detected in the scattering spectra of dielectric nanoparticles 49 (Fig. 3i) and were also predicted for core-shell wires 74 and hybrid nanoparticles 66 .…”

“…While strong toroidal contribution is expected only from large toroidal "molecules" (comparable with the wavelength of light), this contribution can be profound. Toroidal resonances can destructively interfere with other modes of excitations in the materials providing a new mechanism of induced transparency (slow light) and scattering suppression 49,73 that can be used in narrow-band filters and for controlling emission. Toroidal metamaterials provide useful platform for tailoring electromagnetic environment of complex symmetry and topology for light confinement, trapping and sensor applications (highly gradient electric filed is strong in the centre of the torus).…”

“…Dynamic toroidal dipoles, in contrast to their static counterparts, interact with oscillating electromagnetic fields, and thus contribute to the optical properties of materials across the entire electromagnetic spectrum 3 . However, the inclusion or omission of the dynamic toroidal multipoles from the multipole expansion has been the subject of an on going discussion [46][47][48] , in particular with respect to equivalent descriptions, such as Mie theory 49,50 . We address this in detail in a dedicated section (see tutorial inset II), where we demonstrate that although both the vector spherical harmonic Mie expansion and the (full, including toroidal contributions) charge-current multipole expansion are complete, the toroidal multipoles appear as distinct entities only in the latter.…”

Suppression of scattering for small dielectric particles: anapole mode and invisibility

“…Similar toroidal fields 32 recently attract a lot of attention. Dominant contributions of electric and toroidal dipole moments can be clearly seen in Cartesian coordinates 31 . Thus, one can conclude that this Fano resonance is related to constructive and destructive interference of electrical dipole and toroidal dipole moments.…”

“…Previously it was shown that such type of interference, the socalled anapole mode 31,32 , could be observed in Si nanodisks. For nanodisks, this anapole mode can be achieved at a specific wavelength and for some fixed ratio of the disk height to its diameter.…”