Plasmonic interaction between nanospheres

When metallic (or plasmonic) nanospheres are nearly touching, strong concentration of light can occur in the narrow gap regions. This phenomenon has potential applications in nanophotonics, biosensing, and spectroscopy. Understanding the strong interaction between the plasmonic spheres turns out to be quite challenging; indeed, an extremely high computational cost is required to compute the electromagnetic field. Also, the classical method of image charges, which is effective for the dielectric spheres system, is not valid for plasmonic spheres because of their negative permittivities. Here we develop new analytical and numerical methods for the plasmonic spheres system by clarifying the connection between transformation optics and the method of image charges. We derive fully analytic solutions valid for two plasmonic spheres. We then develop a hybrid numerical scheme for computing the field distribution produced by an arbitrary number of spheres. Our method is highly efficient and accurate even in the nearly touching case and is valid for plasmonic spheres.