Finite-size effects on periodic arrays of nanostructures

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.