# Toroidal eigenmodes in all-dielectric metamolecules

## TL;DR

This paper investigates electromagnetic toroidal eigenmodes in all-dielectric polygonal metamolecules using simulations and models, revealing their spectral properties and potential for controlling toroidal excitations.

## Contribution

It introduces a comprehensive analysis of toroidal modes in dielectric metamolecules, combining simulations with coupled mode theory and a lumped wire model, highlighting their spectral behavior and coupling potential.

## Key findings

- Toroidal dipole modes are supported in dielectric polygonal systems.
- Odd-numbered rod ensembles exhibit larger frequency separation.
- Toroidal modes have low quality factors, enabling external coupling.

## 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