Coupled-mode theory of field enhancement in complex metal nanostructures

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 multipole 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 nanogaps 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 efficient antennas, while the modes in the gaps or near the smaller particles act as the compact subwavelength cavities. The present analytical approach can be conveniently extended to incorporate large numbers of particles in various intricate arrangements.