# Poloidal and toroidal plasmons and fields of multilayer nanorings

## TL;DR

This paper analyzes the surface plasmon modes of multilayer toroidal nanorings, deriving dispersion relations, resonance frequencies, and Green's functions, with applications to controlling electromagnetic fields and quantum emitters.

## Contribution

It introduces a comprehensive theoretical framework for poloidal and toroidal plasmons in multilayer nanorings, including new Janus nanoring configurations and generalized Green's functions.

## Key findings

- Derived canonical dispersion relations for layered nanorings.
- Identified distinct forward and backward mode coupling in tori.
- Calculated resonance frequencies for gold, silver, aluminum, and silicon nanorings.

## Abstract

Composite and janus type metallo-dielectric nanoparticles are increasingly considered as a means to control the spatial and temporal behavior of electromagnetic fields in diverse applications such as coupling to quantum emitters, achieve invisibility cloaks, and obtain quantum correlations between qubits. We investigate the surface modes of a toroidal nano-structure and obtain the canonical plasmon dispersion relations and resonance modes for arbitrarily layered nanorings. Unlike particle plasmon eigenmodes in other geometries, the amplitudes of the eigenmodes of tori exhibit a distinct forward and backward coupling. We present the plasmon dispersion relations for several relevant toroidal configurations in the quasistatic limit and obtain the dominant retarded dispersion relations of a single ring for comparison, discuss mode complementarity and hybridization, and introduce two new types of toroidal particles in the form of janus nanorings. The resonance frequencies for the first few dominant modes of a ring composed of plasmon supporting materials such as gold, silver, and aluminum are provided and compared to those for a silicon ring. A generalized Green's function is obtained for multilayer tori allowing for calculation of the scattering response to interacting fields. Employing the Green's function, the scalar electric potential distribution corresponding to individual poloidal and toroidal modes in response to an arbitrarily polarized external field and the field of electrons is obtained. The results are applied to obtain the local density of states and decay rate of a dipole near the center of the torus.