Coupling of plasmonic nanoparticles on a semiconductor substrate a modified discrete dipole approximation method.

Understanding the plasmonic coupling between a set of metallic nanoparticles (NPs) in a 2D array, and how a substrate affects such coupling, is fundamental for the development of optimized optoelectronic structures. Here, a simple semi-analytical procedure based on discrete dipole approximation (DDA) is reported to simulate the far-field and near-field properties of arrays of NPs, considering the coupling between particles, and the effect of the presence of a semiconductor substrate based on the image dipole approach. The method is validated for Ag NP dimers and single Ag NPs on a gallium nitride (GaN) substrate, a semiconductor widely used in optical devices, by comparison with the results obtained by the finite element method (FEM), indicating a good agreement in the weak coupling regime. Next, the method is applied to square and random arrays of Ag NPs on a GaN substrate. The increase in the surface density of NPs on a GaN substrate mainly results in a redshift of the dipolar resonance frequency and an increase in the near-field enhancement. This model, based on a single dipole approach, grants very low computational times, representing an advantage to predict the optical properties of large NP arrays on a semiconductor substrate for different applications.