anapole
{{Short description|System of currents that do not radiate into the far field}}
{{Technical|date=December 2023}}
In physics, an anapole ({{ety|el|ἀνά (ana)|above||πόλος (polos)|pole}}) is a system of currents that does not radiate into the far field. The term "anapole" first appeared in the work of Zel'dovich, in which he thanks A. S. Kompaneets, who first proposed the name.Zel’Dovich, I. B. (1958). Electromagnetic interaction with parity violation. Sov. Phys. JETP, 6(6), 1184-1186.
An anapole is a system of currents that transforms under all transformations of the symmetry group O(3) as a certain multipole (or the corresponding vector spherical harmonic), but does not radiate to the far field.
Photonics
File:Anapoles.png by a dielectric nanoparticle with refractive index n=4.5. Normalized scattering cross-section spectrum in linear and log scale. Zeros, which refer to anapole states, are marked.]]
In photonics, anapoles first appeared in 2015Miroshnichenko, Andrey E., et al. "Nonradiating anapole modes in dielectric nanoparticles." Nat. Commun., vol. 6, no. 8069, 27 Aug. 2015, pp. 1-8, doi:10.1038/ncomms9069. as zeros in the Mie-coefficient of a particular multipole in the scattering spectrum. They can also be explained as destructive interference of a "cartesian multipole" and a "toroidal multipole". The anapole state is not an eigenmode. Total scattering cross-section is not zero in the anapole state, due to the contribution of other multipoles.Zenin, Vladimir A., et al. "Direct Amplitude-Phase Near-Field Observation of Higher-Order Anapole States." Nano Lett., vol. 17, no. 11, 8 Nov. 2017, pp. 7152-9, doi:10.1021/acs.nanolett.7b04200.Baryshnikova, Kseniia V., et al. "Optical Anapoles: Concepts and Applications." Adv. Opt. Mater., vol. 7, no. 14, 1 July 2019, p. 1801350, doi:10.1002/adom.201801350.
The terms "anapole" and toroidal moment were once used synonymously,Lewis, Robert R. "Anapole moment of a diatomic polar molecule." Physical Review A 49.5 (1994): 3376.Popov, A. I., D. I. Plokhov, and A. K. Zvezdin. "Anapole moment and spin-electric interactions in rare-earth nanoclusters." Europhysics Letters 87.6 (2009): 67004. but this is no longer common.