Toroidal multipoles are the terms missing in the standard multipole expansion; they are usually overlooked due to their relatively weak coupling to the electromagnetic fields. Here, we propose and theoretically study all-dielectric metamaterials of a special class that represent a simple electromagnetic system supporting toroidal dipolar excitations in the THz part of the spectrum. We show that resonant transmission and reflection of such metamaterials is dominated by toroidal dipole scattering, the neglect of which would result in a misunderstanding interpretation of the metamaterials' macroscopic response. Because of the unique field configuration of the toroidal mode, the proposed metamaterials could serve as a platform for sensing or enhancement of light absorption and optical nonlinearities.

We demonstrate that ideal anapole metamaterials have infinite Q-factor. We have designed and fabricated a metamaterial consisting of planar metamolecules which exhibit anapole behavior in the sense that the electric dipole radiation is almost cancelled by the toroidal dipole one, producing thus an extremely high Q-factor at the resonance frequency. The size of the system, at the mm range, and the parasitic magnetic quadrupole radiation are the factors limiting the size of the Q-factor. In spite of the very low radiation losses the local fields at the metamolecules are extremely high, of the order of 4 10 higher than the external incoming field.

We show that for a particular choice of gauge the vector potential of any non-radiating source is spatially localized along with its electric and magnetic fields. Important on its own, this special property of non-radiating sources dramatically simplifies the analysis of their quantitative aspects, and enables the interpretation of non-radiating sources as distributions of the elementary dynamic anapoles. Using the developed approach we identify and discuss a possible scenario for observing the time-dependent version of the Aharonov-Bohm effect in such systems.

In this paper, we demonstrate the relation between cloaking effect and its nonradiating state by considering the destructive multipolar interaction between near-field scattering by bare object and surrounding coating located in its proximity. This cloaking effect is underpinned by anapole mode excitation and it occurs as destructive interference between the electric dipole moment, generated by a bare object (here a central metallic scatterer) and the toroidal moment, formed inside the cloak (a surrounding cluster of dielectric cylinders). Numerical results show how a cloaking effect based on the formation of the anapole mode can lead to an overall nonradiating metamolecule with all-dielectric materials in the coating region.

The complete dynamic multipole expansion of electromagnetic sources contains more types of multipole terms than it is conventionally perceived. The toroidal multipoles are one of the examples of such contributions that have been widely studied in recent years. Here we inspect more closely the other type of commonly overlooked terms known as the mean-square radii. In particular, we discuss both quantitative and qualitative aspects of the mean-square radii and provide a general geometrical framework for their visualization. We also consider the role of the mean-square radii in expanding the family of non-trivial non-radiating electromagnetic sources.

Dynamic anapole is a promising element for future nonradiating devices, such as cloaked sources and sensors, quantum emitters, and especially the sources for observing dynamic Aharonov-Bohm effect. However, the anapole response can be damped by the Joule losses. In this paper we theoretically propose and experimentally demonstrate a novel type of active all-dielectric source, which is in some sense, realizes the elementary anapole of Afanasiev, and study its radiative/nonradiative regimes in the microwave range.

We experimentally demonstrate for the first time the toroidal dipolar response in metamaterials based on clusters of cylindrical dielectric particles in microwave frequency range. Instead of expensive ceramic elements we used distilled water with permittivity at room temperature is about 75, while the dielectric loss tangent is not large at frequencies up to 4 GHz. Moreover, we show all-dielectric metamaterial consisting of water box with hollow tubes which is more practical for future applications. Our findings also demonstrate that the proposed ideas can be applicable in optics with low-index dielectrics.

We present and analyze unique phenomena of enhanced transmission through systems of subwavelength dielectric cylinders embedded in an epsilon near zero host. Our analysis shows that these phenomena are due to Mie-resonance modes arisen in the dielectric cylinders. Subwavelength waveguides and lenses are proposed based on coupling of these modes between neighboring cylinders. Finally, the proposed phenomena and their possible applications are numerically demonstrated in the THz regime in a realistic polaritonic material of LiF rods in KCl.