Analysis of the Limits of the Near-Field Produced by Nanoparticle Arrays

Periodic arrays are an exceptionally interesting arrangement for metallic nanostructures because of their ability to support collective lattice resonances. These modes, which arise from the coherent multiple scattering enabled by the lattice periodicity, give rise to very strong and spectrally narrow optical responses. Here, we investigate the enhancement of the near-field produced by the lattice resonances of arrays of metallic nanoparticles when illuminated with a plane wave. We find that, for infinite arrays, this enhancement can be made arbitrarily large by appropriately designing the geometrical characteristics of the array. On the other hand, in the case of finite arrays, the near-field enhancement is limited by the number of elements of the array that interact coherently. Furthermore, we show that, as the near-field enhancement increases, the length scale over which it extends above and below the array becomes larger and its spectral linewidth narrows. We also analyze the impact that material losses have on these behaviors. As a direct application of our results, we investigate the interaction between a nanoparticle array and a dielectric slab placed a certain distance above it and show that the extraordinary near-field enhancement produced by the lattice resonance can lead to very strong interactions, even at significantly large separations. This work provides a detailed characterization of the limits of the near-field produced by lattice resonances and, therefore, advances our knowledge of the optical response of periodic arrays of nanostructures, which can be used to design and develop applications exploiting the extraordinary properties of these systems.