Efficient simulation methods for taking nonlocal effects in nanostructures into account have been developed, but they are usually computationally expensive or provide little insight into underlying physics. A multipolar expansion approach, among others, holds promise to properly describe electromagnetic interactions in complex nanosystems. Conventionally, the electric dipole dominates in plasmonic nanostructures, while higher order multipoles, especially the magnetic dipole, electric quadrupole, magnetic quadrupole, and electric octopole, can be responsible for many optical phenomena. The higher order multipoles not only result in specific optical resonances, but they are also involved in the cross-multipole coupling, thus giving rise to new effects. In this work, we introduce a simple yet accurate simulation modeling technique, based on the transfer-matrix method, to compute higher-order nonlocal corrections to the effective permittivity of 1d plasmonic periodic nanostructures. In particular, we show how to specify the material parameters and the arrangement of the nanolayers in order to maximize or minimize various nonlocal corrections. The obtained results provide a framework for guiding and interpreting experiments, as well as for designing metamaterials with desired dielectric and optical properties.
Keywords: metamaterials; multipoles; nonlocality; plasmonic nanostructures; transfer-matrix method.