A Generic Minimal Discrete Model for Toroidal Moments and Its Experimental Realization

TL;DR

This paper introduces a simple, symmetry-based discrete electric dipole model that supports toroidal moments across a wide frequency range, demonstrated through experiments with microwave and optical structures.

Contribution

A minimal, symmetry-driven model using three aligned electric dipoles to generate and analyze toroidal moments from microwave to optical frequencies.

Findings

The model guarantees resonant toroidal modes through symmetry.

Experimental microwave results confirm theoretical predictions.

Supports non-radiating anapoles in both microwave and optical regimes.

Abstract

It is well known that a closed loop of magnetic dipoles can give rise to the rather elusive toroidal moment. However, artificial structures required to generate the necessary magnetic moments are typically optically large, complex to make and easily compromised by the kinetic inductance at high frequencies. Instead of using magnetic dipoles, we propose a minimal model based on just three aligned discrete electric dipoles in which the occurrence of resonant toroidal modes is guaranteed by symmetry. The advantage of this model is its simplicity and the same model supports toroidal moments from the microwave regime up to optical frequencies as exemplified by a three-antenna array and a system consisting of three nano-sized plasmonic particles. Both the microwave and high-frequency configurations exhibit non-radiating "anapoles". Experiments in the microwave regime confirm the theoretical predictions.