Toroidal eigenmodes in all-dielectric metamolecules

Abstract

We present a thorough investigation of the electromagnetic resonant modes supported by systems of polaritonic rods placed at the vertices of canonical polygons. The study is conducted with rigorous finite-element eigenvalue simulations. To provide physical insight, the simulations are complemented with coupled mode theory (the analog of LCAO in molecular and solid state physics) and a lumped wire model capturing the coupling-caused reorganizations of the currents in each rod. The systems of rods, which form all-dielectric cyclic metamolecules, are found to support the unconventional toroidal dipole mode, consisting of the magnetic dipole mode in each rod. Besides the toroidal modes, the spectrally adjacent collective modes are identified. The evolution of all resonant frequencies with rod separation is examined. They are found to oscillate about the single-rod magnetic dipole resonance, a feature attributed to the leaky nature of the constituent modes. Importantly, we observe that ensembles of an odd number of rods produce larger frequency separation between the toroidal mode and its neighbor than the ones with even number of rods. This increased spectral isolation, along with the low quality factor exhibited by the toroidal mode, favors the coupling of the commonly silent toroidal dipole to the outside world, rendering the proposed structure a prime candidate for controlling the observation of toroidal excitations and their interaction with the usually present electric dipole.

Nonradiating sources, dynamic anapole, and Aharonov-Bohm effect

“…Indeed, a number of recent works have already confirmed the key role of anapole excitations in controlling scattering properties of very simple electromagnetic systems, such as nanodisks and nanowires [15][16][17][18][19][20][21][22][23]. Correspondingly, one may want to revisit the analysis of the electromagnetic response of structurally more complex metamaterials, where the dynamic anapoles could underpin, for example, the microscopic mechanisms of electromagnetic transparency [14] and high-Q effects.…”

“…In general, relation (22) cannot be satisfied exactly (unless D = 0), because T , being a higher order multipole moment, depends on the origin of the multipole expansion, and so the high-order correction O(a 2 k 2 ) in (22) arises as the result of this uncertainty.…”

Toroidal Dipole Resonances in All‐Dielectric Oligomer Metasurfaces

“…[25][26][27] Nevertheless, after accounting for the feasibility of fabrication and optical measurements in realistic scenarios, we suggest that the frontal excitation utilized here might be more compatible with experimental designs and potential applications. Metamolecules (unit cells) are arranged periodically in xand ydirection with equal periodicity P, forming infinitely large metasurfaces in the xy-plane.…”

Theory and applications of toroidal moments in electrodynamics: their emergence, characteristics, and technological relevance

“…The anapole configuration is described in detail in Section 5.1. In parallel, the dielectric metamaterial [121] was proposed to overcome dissipation loss of metals as encountered in metal-based toroidal metamaterial [112]. It has been pointed out that dissipation losses in metals originating from the ohmic resistance can hinder the excitation …”