physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

, an anapole () is a system of

currents Currents, Current or The Current may refer to: Science and technology * Current (fluid), the flow of a liquid or a gas ** Air current, a flow of air ** Ocean current, a current in the ocean *** Rip current, a kind of water current ** Current (hy ...

that does not radiate into the

far field The near field and far field are regions of the electromagnetic (EM) field around an object, such as a transmitting antenna, or the result of radiation scattering off an object. Non-radiative ''near-field'' behaviors dominate close to the an ...

. The term "anapole" first appeared in the work of Zel'dovich, in which he thanks A. S. Kompaneets, who first proposed the name. An anapole is a system of currents that transforms under all transformations of the symmetry group

O(3) In mathematics, the orthogonal group in dimension , denoted , is the group of distance-preserving transformations of a Euclidean space of dimension that preserve a fixed point, where the group operation is given by composing transformations. T ...

as a certain

multipole A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles used in the spherical coordinate system (the polar and azimuthal angles) for three-dimensional Euclidean space, \R^3. Multipol ...

(or the corresponding vector spherical harmonic), but does not radiate to the

Photonics

In photonics, anapoles first appeared in 2015 as zeros in the Mie-coefficient of a particular

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 The mode of electromagnetic systems describes the field pattern of the propagating waves. Some of the classifications of electromagnetic modes include; * Modes in waveguides and transmission lines. These modes are analogous to the normal modes of ...

. Total scattering cross-section is not zero in the anapole state, due to the contribution of other multipoles. The terms "anapole" and

toroidal moment In electromagnetism, a toroidal moment is an independent term in the multipole expansion of the electromagnetic field which is distinct from magnetic and electric multipoles. In the electrostatic multipole expansion, all charge and current distr ...

were once used synonymously,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.

References

{{Reflist Electric current Electromagnetic radiation Photonics

Photonics

See also

References