  Arrays of nanostructures have emerged as exceptional tools for the
manipulation and control of light. Oftentimes, despite the fact that real
implementations of nanostructure arrays must be finite, these systems are
modeled as perfectly periodic, and therefore infinite. Here, we investigate the
legitimacy of this approximation by studying the evolution of the optical
response of finite arrays of nanostructures as their number of elements is
increased. We find that the number of elements necessary to reach the infinite
array limit is determined by the strength of the coupling between them, and
that, even when that limit is reached, the individual responses of the elements
may still display significant variations. In addition, we show that, when
retardation is negligible, the resonance frequency for the infinite array is
always redshifted compared to the single particle. However, in the opposite
situation, there could be either a blue- or a redshift. We also study the
effects of inhomogeneity in size and position of the elements on the optical
response of the array. This work advances the understanding of the behavior of
finite and infinite arrays of nanostructures, and therefore provides guidance
to design applications that utilize these systems.
