Plasmonics response of a nanorod in the vicinity of a metallic surface: local approach with analytical solution

TL;DR

This paper provides an analytical solution for the plasmonic response of a nanorod near a metallic surface, enabling precise modeling and benchmarking of such nanostructured systems.

Contribution

It introduces a boundary integral method-based analytical approach for eigenmodes and electric fields in nanorod-metal systems, addressing different symmetries and simplifying for large distances.

Findings

Analytical eigenmodes and electric fields derived for nanorod-metal systems.

Solution simplifies for large rod-surface distances.

Results serve as benchmarks for numerical methods.

Abstract

In this paper we present an analytical solution for the eigenmodes and corresponding electric field of a composite system made of a nanorod in the vicinity of a plasmonic semi-infinite metallic system. To be specific, we choose Silver as the material for both the nanorod and the semi-infinite metal. The system is composed of two sub-systems with different symmetries: the rod has symmetry, while the interface has a rectangular one. Using a boundary integral method, proposed by Eyges, we are able to compute analytically the integrals that sew together the two systems. In the end, the problem is reduced to one of linear algebra, where all the terms in the system are known analytically. For large distances between the rod and the planar surface, only a few of those integrals are needed and a full analytical solution can be obtained. Our results are important to benchmark other numerical approaches and represent a starting point in the discussion of systems composed of nanorods and two-dimensional materials.