Comparison of electric field enhancements: Linear and triangular oligomers versus hexagonal arrays of plasmonic nanospheres

We investigate local electromagnetic field enhancements in oligomers of plasmonic nanospheres. We first evaluate via full-wave simulations the field between spheres in several oligomer systems: linear dimers, linear trimers, trimers 60°, trimers 90° and linear quadrumers. To gain a better understanding of the field enhancement values, we compare the results with local fields in a hexagonal close-packed (HCP) configuration with same structural dimensions. We then inter-relate the field enhancement values found via full-wave simulations to SERS enhancements of actual fabricated self-assembled oligomers. We find that linear oligomers provide the largest field enhancement values. Finally, we provide closed-form formulas for the prediction of the resonance frequency responsible for field enhancement in linear oligomers, namely dimers, trimers and quadrumers, modeling each nanosphere as a single electric dipole. These formulas provide with resonance values less than 7% shifted when compared to full-wave results even when the gap between spheres is only about one fifth of the radius, showing the powerfulness of dipolar approximations. The results shown in this paper demonstrate that ad hoc clusters of nanospheres can be designed and fabricated to obtain larger field enhancements than with the HCP structure and this may pave the way for the development of improved sensors for molecular spectroscopy.