Eigenmode Decomposition of the Near-Field Enhancement in Localized Surface Plasmon Resonances of Metallic Nanoparticles

I present a direct and intuitive eigenmode method that evaluates the near-field enhancement around the surface of metallic nanoparticles of arbitrary shape. The method is based on the boundary integral equation (BIE) in the electrostatic limit. Besides the nanoparticle polarizability and the far-field response, the near-field enhancement around nanoparticles can be also conveniently expressed as an eigenmode sum of resonant terms. Moreover, the spatial configuration of the near-field enhancement depends explicitly on the eigenfunctions of both the BIE integral operator and of its adjoint. It has also established a direct physical meaning of the two types of eigenfunctions. While it is well known that the eigenfunctions of the BIE operator are electric charge modes, it is less known and used that the eigenfunctions of the adjoint represent the electric potential generated by the charge modes. For the enhanced spectroscopies, the present method allows an easy identification of hot spots which are located in the regions with maximum charge densities and/or regions with fast variations of the electric potential generated by the charge modes on the surface. This study also clarifies the similarities and the differences between the far-field and the near-field behavior of plasmonic systems. Finally, the analysis of concrete examples like the nearly touching dimer, the prolate spheroid, and the nanorod illustrate some modalities to improve the near-field enhancement.