# Cooperative field localization and excitation eigenmodes in disordered metamaterials

## TL;DR

This paper explores how disorder affects the collective electromagnetic responses of disordered metamaterials with split ring resonators, revealing enhanced Purcell factors and the potential for engineered device functionalities.

## Contribution

It introduces a numerical and experimental framework to analyze cooperative responses and eigenmodes in disordered metamaterials, highlighting the impact of disorder on Purcell enhancement.

## Key findings

- Disorder increases the variability of Purcell enhancement.
- High Purcell factors are associated with collective eigenmodes, especially magnetic ones.
- Disorder significantly alters cooperative responses even with high dissipation.

## Abstract

We investigate numerically and experimentally the near-field response of disordered arrays comprising asymmetrically split ring resonators that exhibit strong cooperative response. Our simulations treat the unit cell split ring resonators as discrete pointlike oscillators with associated electric and magnetic point dipole radiation, while the strong cooperative radiative coupling between the different split rings is fully included at all orders. The methods allow to calculate local field and Purcell factor enhancement arising from the collective electric and magnetic excitations. We find substantially increased standard deviation of the Purcell-enhancement with disorder, making it increasingly likely to find collective excitation eigenmodes with very high Purcell factors that are also stronger for magnetic than electric excitations. We show that disorder can dramatically modify the cooperative response of the metamaterial even in the presence of strong dissipation losses as is the case for plasmonic systems. Our analysis in terms of collective eigenmodes paves a way for controlled engineering of electromagnetic device functionalities based on strongly interacting metamaterial arrays.