Insights on the Coupling of Plasmonic Nanoparticles from Near-Field Spectra Determined via Discrete Dipole Approximations

Coupling between plasmonic nanoparticles (NPs) in NP assemblies has been investigated extensively via far-field properties, such as absorption and scattering, but very rarely via near-field properties, and a quantitative investigation of near-field properties should provide great insights into the nature of the coupling. We report a numerical procedure to obtain reliable near-field spectra ( Q NF ) around spherical gold NPs (Au NPs) using discrete dipole approximation (DDA). The reliability of the method was tested by comparing Q NF from DDA calculations with exact results from the Mie theory. We then applied the method to examine Au NPs assembled in dimers, trimers, and up to pentamers in a linear arrangement. For the well-studied dimer system, we show that the Q NF enhancement, due to coupling in longitudinal mode, is much greater than the enhancement in Q ext . There is a linear correlation between the Q NF and Q ext peak positions, with the Q NF peak red-shifted from the Q ext peak by an average of approximately 12 nm. In the case of the multimers, Q NF spectra from individual spheres were not always identical and become dependent on the sphere location. In the longitudinal model, the center sphere has the strongest Q NF spectra. For the transverse mode, we differentiate two different scenarios: transverse-Y, where both electric field ( E ) and light propagation vector ( k ) are perpendicular to the chain axis, and transverse-X, where k is parallel to the chain axis. In the transverse-Y mode, coupling leads to reduced Q NF spectra and the center sphere has the lowest Q NF intensity. In the transverse-X mode, there is a retardation effect from the front sphere to the back sphere. The Q NF from the front sphere is stronger than from the back sphere. In addition, due to the phase lag in the k -direction, the Q NF in transverse-X can differ quite significantly from that in transverse-Y for large particles. These results provide new insights into the coupling properties of Au NPs. Collectively, these results can be understood when one considers how the electric field from induced dipoles on neighboring NPs adds with, or subtracts from, the incident E-field. These results provide new insights into the coupling properties of Au NPs.