Field expansions for systems of strongly coupled plasmonic nanoparticles

TL;DR

This paper develops and compares three expansion schemes for efficiently approximating the scattering problem in strongly coupled plasmonic nanoparticle systems, highlighting the resonant expansion's efficiency near the particles.

Contribution

It introduces three novel expansion methods for modeling strongly coupled plasmonic particles, analyzing their relations and advantages both analytically and numerically.

Findings

Resonant expansion efficiently approximates near fields.

Hybridized resonant expansion improves basis representation.

Multipole expansion offers an alternative approximation method.

Abstract

This paper is concerned with efficient representations and approximations of the solution to the scattering problem by a system of strongly coupled plasmonic particles. Three schemes are developed: the first is the resonant expansion which uses the resonant modes of the system of particles computed by a conformal transformation, the second is the hybridized resonant expansion which uses linear combinations of the resonant modes for each of the particles in the system as a basis to represent the solution, and the last one is the multipole expansion with respect to the origin. By considering a system formed by two plasmonic particles of circular shape, we demonstrate the relations between these expansion schemes and their advantages and disadvantages both analytically and numerically. In particular, we emphasize the efficiency of the resonant expansion scheme in approximating the near field of the system of particles. The difference between these plasmonic particle systems and the nonresonant dielectric particle system is also highlighted. The paper provides a guidance on the challenges for numerical simulations of strongly coupled plasmonic systems.