Cooperative field localization and excitation eigenmodes in disordered metamaterials

Abstract

We investigate numerically and experimentally the near-field response of disordered arrays comprising asymmetrically split ring resonators that exhibit a 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 us 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 the way for controlled engineering of electromagnetic device functionalities based on strongly interacting metamaterial arrays.