# Anapole

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In [physics](/source/Physics), an **anapole** () is a system of [currents](/source/Electric_current) that does not radiate into the [far field](/source/Near_and_far_field). The term "anapole" first appeared in the work of [Zel'dovich](/source/Yakov_Zeldovich), in which he thanks [A. S. Kompaneets](/source/Alexander_Kompaneyets), who first proposed the name.[1]

An anapole is a system of currents that transforms under all transformations of the symmetry group [O(3)](/source/Orthogonal_group) as a certain [multipole](/source/Multipole) (or the corresponding [vector spherical harmonic](/source/Vector_spherical_harmonics)), but does not radiate to the [far field](/source/Near_and_far_field).

## Photonics

In photonics, anapoles first appeared in 2015[2] as zeros in the [Mie-coefficient](/source/Mie_theory) of a particular [multipole](/source/Vector_spherical_harmonic) in the scattering spectrum. They can also be explained as destructive interference of a "cartesian multipole" and a "[toroidal](/source/Toroidal_moment) multipole". The anapole state is not an [eigenmode](/source/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](/source/Toroidal_moment) were once used synonymously,[5][6] but this is no longer common.

## See also

- [Toroidal moment](/source/Toroidal_moment)

## References

1. Zel’Dovich, I. B. (1958). Electromagnetic interaction with parity violation. Sov. Phys. JETP, 6(6), 1184-1186.

1. 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.

1. 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.

1. 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.

1. Lewis, Robert R. "Anapole moment of a diatomic polar molecule." Physical Review A 49.5 (1994): 3376.

1. 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.

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