Strong interactions and subradiance in disordered metamaterials

We provide detailed comparisons between experimental findings and numerical simulations of large cooperatively interacting, spatially disordered metamaterial arrays, consisting of asymmetrically split rings. Simulation methods fully incorporate strong field-mediated inter-meta-atom interactions between discrete resonators and statistical properties of disorder, while approximating the resonators' internal structure. Despite the large system size, we find a qualitative agreement between the simulations and experiments and characterize the microscopic origins of the observed disorder response. Our microscopic description of macroscopic electrodynamics reveals how the response of disordered arrays with strong field-mediated interactions is inherently linked to their cooperative response to electromagnetic waves where the multiple scattering induces strong correlations between the excitations of individual resonators. Whereas for a regular array the response can be overwhelmingly dominated by a spatially extended collective eigenmode with subradiant characteristics, a gradual increase of the positional disorder rapidly leads to a spatial localization of both the electric and magnetic dipolar excitation profile of this eigenmode. We show how the effects of disorder and cooperative interactions are mapped onto the transmission resonance in the far field spectrum and measure the ``cooperative Lamb shift'' of the resonance that is shifting toward the red as the disorder increases. The interplay between the disorder and interactions generally is most dramatic in the microwave arrays, but we find that in suitable regimes the strong disorder effects can be achieved also for plasmonic optical systems.