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

Abstract In this paper we present an analytical solution for the eigenmodes and corresponding electric fields 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 polar 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 a 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.