  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.
