Designing Commensurate and Incommensurate Resonances for Enhanced Dipole Emission in Coupled Plasmonic Nanorods

Plasmonic nanorods and their clusters are the fundamental units in plasmonic nanoantenna engineering. A theory that can predict the resonance of single nanorod already exists but is in lack for a heterodimer. Here, we propose a model combining the effective circuit theory for the response of spherical nanoparticles together with standard transmission line theory for hemispherically capped nanorod antennas. The resonances of multiple orders are predictable by defining the reflection phase at the terminals of such antennas, in both symmetric and asymmetric coupled nanorods. The theoretical results compare favorably with full-wave finite element numerical calculations. By the analytical formula, it is easy to control the length of the antennas for regulating the cooperative resonant properties and consequently the radiation characteristics of a nearby electric dipole. Consequently, we obtain both commensurate and incommensurate resonance features in such nanorod-based heterodimer antennas, showing respectively cumulative and selective responses from the individual nanorods.