Universal Scaling and Fano Resonance in the Plasmon Coupling between Gold Nanorods

The plasmon coupling between metal nanocrystals can lead to large plasmon shifts, enormous electric field enhancements, and new plasmon modes. Metal nanorods, unlike spherical ones, possess a transverse and a longitudinal plasmon mode owing to their geometrical anisotropy. Consequently, the plasmon coupling between metal nanorods is much more complicated than that between nanospheres. For the latter, experimental approaches, simple scaling relationships, and exact analytic solutions have been developed for describing the plasmon coupling. In this study, we have carried out extensive finite-difference time-domain simulations to understand the plasmon coupling in the dimers of Au nanorods that are aligned along their length axes. The effects of the gap distance, longitudinal plasmon energy, and end shape of the nanorod monomers on the plasmon coupling have been scrutinized. The coupling energy diagrams show a general anticrossing behavior. All of them can be rescaled into one simple and universal hyperbolic formula. A theoretical model based on two interacting mechanical oscillators has been developed to understand the plasmon coupling between two arbitrarily varying Au nanorods. This model, together with the universal equation, allows for the determination of the coupled plasmon energies of Au nanorod dimers with high accuracies. Furthermore, the Fano interference has been observed in the nanorod heterodimers, with its behavior being dependent on the gap distance and plasmon energies of the nanorod monomers. Our results will be useful for predicting the coupled plasmon energies of metal nanorod dimers in a variety of plasmonic applications and understanding the Fano resonance in plasmonic nanostructures.