On the role of longitudinal currents in radiating systems of charges.

The time derivative of a charge density is linked to a current density by the continuity equation. However, it features only the longitudinal part of a current density, which is known to produce no radiation. This fact usually remains unnoticed and may appear puzzling at first, suggesting that the temporal variation of a charge density should be also irrelevant to radiation. We alleviate the apparent contradiction by showing that the effective longitudinal currents are not spatially confined, even when the time-dependent radiating charge density that generates them is. This enforces the co-existence of the complementary, i.e. transverse, part of the current, which, in turn, gives rise to radiation. We illustrate the necessarily delocalized nature and relevance of longitudinal currents to the emission of electromagnetic waves by a dynamic electric dipole, discussing the practical implications of that for radation in partially conducting condensed matter. More generally, we show how the connection between the longitudinal and transverse currents shapes the structure of the conventional multipole expansion and fuels the ongoing confusion surrounding the charge and toroidal multipoles.

Nonradiating anapole condition derived from Devaney-Wolf theorem and excited in a broken-symmetry dielectric particle.

In this work, we first derive the nonradiating anapole condition with a straightforward theoretical demonstration exploiting one of the Devaney-Wolf theorems for nonradiating currents. Based on the equivalent volumetric and surface electromagnetic sources, it is possible to establish a unique compact conditions directly from Maxwell's Equations in order to ensure nonradiating anapole state. In addition, we support our theoretical findings with a numerical investigation on a broken-symmetry dielectric particle, building block of a metamaterial structure, demonstrating through a detailed multiple expansion the nonradiating anapole condition behind these peculiar destructive interactions.

Nontrivial nonradiating all-dielectric anapole.

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.