  Toroidal dipole, first described by Ia. B. Zeldovich [Sov. Phys. JETP 33,
1184 (1957)], is a distinct electromagnetic excitation that differs both from
the electric and the magnetic dipoles. It has a number of intriguing
properties: static toroidal nuclear dipole is responsible for parity violation
in atomic spectra; interactions between static toroidal dipole and oscillating
magnetic dipole are claimed to violate Newton's Third Law while non-stationary
charge-current configurations involving toroidal multipoles have been predicted
to produce vector potential in the absence of electromagnetic fields. Existence
of the toroidal response in metamaterials was recently demonstrated and is now
a growing field of research. However, no direct analytical link has yet been
established between the transmission and reflection of macroscopic
electromagnetic media and toroidal dipole excitations. To address this
essential gap in electromagnetic theory we have developed an analytical
approach linking microscopic and macroscopic electromagnetic response of a
metamaterial and showed, using a case study, the key role of the toroidal
dipole in shaping the electromagnetic properties of the metamaterial.
