Toroidal excitations in matter

Data used in Figure 5, Focused Doughnut (FD) pulses, in Papasimakis, N.,
Fedotov, V.A., Savinov, V., Raybould, T.A. and Zheludev, N.I. (2015) Toroidal excitations in matter. Nature Materials.
The toroidal dipole is a localized electromagnetic excitation independent from the familiar magnetic and electric dipoles. While the electric dipole can be understood as separated opposite charges and the magnetic dipole as a current loop, the toroidal dipole corresponds to currents flowing on the surface of a torus. Resonant interactions of induced toroidal dipoles with electromagnetic waves have recently been observed at microwave, terahertz and optical frequencies. They provide distinct and physically significant contributions to the basic characteristics of matter including absorption, dispersion, and optical activity, the origin of which cannot be comprehensively interpreted in the context of standard multipoles alone. Interference of radiating induced toroidal and electric dipoles leads to transparency windows in artificial materials as a manifestation of the dynamic anapole.
Toroidal excitations also exist in free-space as spatially and temporally localized electromagnetic pulses propagating at the speed of light and interacting with matter.