# Plasmonic edge states: an electrostatic eigenmode description

## TL;DR

This paper presents an electrostatic eigenmode approach to analyze plasmonic edge states in periodic metal nanostructure arrangements, revealing how collective resonances can be understood as superpositions of individual nanostructure modes.

## Contribution

It introduces a formalism that describes collective plasmonic resonances as superpositions of individual eigenmodes, enabling the design of plasmonic edge states in periodic structures.

## Key findings

- Collective surface plasmon resonances are superpositions of eigenmodes of individual nanostructures.
- The formalism accounts for and predicts plasmonic edge states in periodic arrangements.
- The approach simplifies the analysis of complex plasmonic systems.

## Abstract

We consider periodic arrangements of metal nanostructures and study the effect of periodicity on the localised surface plasmon resonance of the structures within an electrostatic eigenmode approximation. We show that within this limit, the collective surface plasmon resonances of the periodic structures can be expressed in terms of superpositions of the eigenmodes of uncoupled nanostructures that exhibit a standing--wave character delocalised across the entire periodic structure. The formalism derived successfully enables the design and accounts for the observation of plasmonic edge-states in periodic structures.