  When arranged in a periodic geometry, arrays of metallic nanostructures are
capable of supporting collective modes known as lattice resonances. These
modes, which originate from the coherent multiple scattering between the
elements of the array, give rise to very strong and spectrally narrow optical
responses. Here, we show that, thanks to their collective nature, the lattice
resonances of a periodic array of metallic nanoparticles can mediate an
efficient long-range coupling between dipole emitters placed near the array.
Specifically, using a coupled dipole approach, we calculate the Green tensor of
the array connecting two points and analyze its spectral and spatial
characteristics. This quantity represents the electromagnetic field produced by
the array at a given position when excited by a unit dipole emitter located at
another one. We find that, when a lattice resonance is excited, the Green
tensor is significantly larger and decays more slowly with distance than the
Green tensor of vacuum. Therefore, in addition to advancing the fundamental
understanding of lattice resonances, our results show that periodic arrays of
nanostructures are capable of enhancing the long-range coupling between
collections of dipole emitters, which makes them a promising platform for
applications such as nanoscale energy transfer and quantum information
processing.
