Breakdown of the Dipole-Dipole Approximation at Short Distances and Hot Spot Formation between a Pair of Silver Nanocubes

ABSTRACTAg or Au nanocubes are known to be plasmonic nanoparticles with strong plasmonic fields concentrated around their corners1. When these nanoparticles aggregate the individual plasmonic oscillations of each particle begin to couple. The coupling between the two plasmonic nanoparticles is assumed to be dipolar in nature which results in an exponential red shift dependence of their localized surface plasmon resonance (LSPR) on the dimer separation2. Unfortunately, this exponential behavior is shown to fail as the separation distance between the two 42 nm nanocube dimer becomes 6nm or smaller3. Hooshmand et al4 have noted that these separation distances are marked by the formation of hot spots between the facets of the dimer.This dipolar exponential behavior results from a treatment of the coupling between the two excited nanocubes as a coupling between two oscillating dipole moments2. As a result, the vectorial addition of all the oscillating electronic dipoles is assumed to interact with the nearest nanoparticle as a single oscillating electronic dipole. Herein we suggest that as the separation distance becomes increasingly small, the coupling between the individual oscillating dipoles on the different nanocubes becomes significant. Thus, the dipolar exponential behavior fails to accurately predict the near field coupling between two nanoparticles with small separation distances.This leads to the realization that the interaction between the individual oscillating dipoles on the two nanocubes changes in a complicated manner as a function of separation distance. At 2nm, a good fraction of the oscillating dipoles are between the adjacent facets of the nanocubes as well as between the the corners. While at 3 nm less are in between the two facets of the nanocubes and a larger portion are localized at the corners. Thus, the coupling is not only dependent on the separation distance but also on what the separation does to the net interaction between the oscillating dipoles on each facet of the two coupled nanocubes. This results in the failure of the exponential behavior as the dipole moment on each nanocube is changing with distance in a complicated manner.