Coupled-Mode Theory of Field Enhancement in Complex Metal Nanostructures

TL;DR

This paper introduces a coupled-mode theoretical model for estimating plasmonic field enhancement in complex metal nanostructures, enabling optimization of 'hot spots' for applications in nanophotonics.

Contribution

The paper presents a simple, rigorous analytical model treating complex structures as coupled multi-pole modes, allowing for optimization of field enhancements in nanostructures.

Findings

Field enhancement can reach Q^2 for two spherical particles.

Hot spots occur in nano-gaps or near smaller particles.

Extended dipole modes act as antennas, enhancing local fields.

Abstract

We describe a simple yet rigorous theoretical model capable of analytical estimation of plasmonic field enhancement in complex metal structures. We show that one can treat the complex structures as coupled multi-pole modes with highest enhancements obtained due to superposition of high order modes in small particles. The model allows one to optimize the structures for the largest possible field enhancements, which depends on the quality factor Q of the metal and can be as high as Q^2 for two spherical particles. The "hot spot" can occur either in the nano-gaps between the particles or near the smaller particles. We trace the optimum field enhancement mechanism to the fact that the extended dipole modes of larger particles act as the efficient antennas while the modes in the gaps or near the smaller particles act as the compact sub-wavelength cavities. We also show how easily our approach can be extended to incorporate large numbers of particles in intricate arrangements.