Dynamic toroidal dipole

In classical electrodynamics, the dynamic toroidal dipole arises from time-dependent currents flowing along the poloidal direction on the surface of a torus.

[1] In relativistic quantum mechanics, spin contributions to the toroidal dipole needs to be taken into account.

[1] Hence combining a dynamic toroidal dipole with an electric dipole can result in a non-radiating charge-current configuration (termed dynamic anapole), in which the electromagnetic fields vanish outside the source, whereas the vector potential persists.

[9] Non-radiating anapoles were observed experimentally for the first time in 2013 as peak of transmission of structured matter at microwave frequencies[10] and in 2015 at optical wavelengths in nanoparticles.

[11] Electrodynamics of dynamic toroidal dipole and anapoles is now massively influencing research in metamaterials, nanoparticles, plasmonics, sensors, lasers and spectroscopy[1][12] Note: The terminology of dynamic "electric" and "magnetic" toroidal multipoles has also been introduced.

Schematic illustrations of static electric, magnetic, and toroidal dipoles in classical electrodynamics. In relativistic quantum physics, apart from magnetic and toroidal moments induced by charge currents, spin must be considered because it can also contribute to the toroidal dipole moment. [ 2 ] Image created by Diego P. Araujo (Biosteam)