Eigenmode decomposition of the near-field enhancement in localized surface plasmon resonances of metallic nanoparticles

摘要

I present a direct and intuitive eigenmode method that evaluates thenear-field enhancement around the surface of metallic nanoparticles ofarbitrary shape. The method is based on the boundary integral equation in theelectrostatic limit. Besides the nanoparticle polarizability and the far-fieldresponse, the near-field enhancement around nanoparticles can be alsoconveniently expressed as an eigenmode sum of resonant terms. Moreover, thespatial configuration of the near-field enhancement depends explicitly on theeigenfunctions of both the BIE integral operator and of its adjoint. It is alsoestablished a direct physical meaning of the two types of eigenfunctions. Whileit is well known that the eigenfunctions of the BIE operator are electriccharge modes, it is less known and used that the eigenfunctions of the adjointrepresent the electric potential generated by the charge modes. For theenhanced spectroscopies the present method allows an easy identification of hotspots which are located in the regions with maximum charge densities and/orregions with fast variations of the electric potential generated by the chargemodes on the surface. This study also clarifies the similarities and thedifferences between the far-field and the near-field behavior of plasmonicsystems. Finally, the analysis of concrete examples like the nearly touchingdimer, the prolate spheroid, and the nanorod illustrate some modalities toimprove the near-field enhancement.