Anapole

System of currents that do not radiate into the far field

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In physics, an anapole (from Greek ἀνά (ana) 'above' and 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.[1]

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

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Mie scattering 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 2015[2] 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.[3][4]

The terms "anapole" and toroidal moment were once used synonymously,[5][6] but this is no longer common.

## See also

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* Toroidal moment

## References

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1. ^ Zel’Dovich, I. B. (1958). Electromagnetic interaction with parity violation. Sov. Phys. JETP, 6(6), 1184-1186.
2. ^ Miroshnichenko, 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.
3. ^ 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.
4. ^ 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.
5. ^ Lewis, Robert R. "Anapole moment of a diatomic polar molecule." Physical Review A 49.5 (1994): 3376.
6. ^ 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.