An atomistic-electrodynamics theory for the optical response of periodic lattices of metallic nanoparticles in the quantum size regime

We present a new theoretical method for calculating the optical properties of periodic arrays of metallic nanoparticles whose dimensions are in the quantum-size limit and cannot, therefore, be described by macroscopic electrodynamic theory based on Maxwell’s equations. In the first stage, the method calculates the scattering matrix for a single metal nanoparticle described as a polyhedral cluster of atoms, via a discrete-dipole approximation/point-matching technique. The resulting scattering matrix is incorporated into a layer-multiple-scattering technique which allows the modeling of two- and three-dimensional nanostructures containing very small metal nanoparticles. The method is demonstrated for square arrays of silver nanoparticles with radii below 2 nm and the corresponding results are compared against classical local and nonlocal electrodynamic approaches.