Optical Properties of a Particle above a Dielectric Interface: Cross Sections, Benchmark Calculations, and Analysis of the Intrinsic Substrate Effects

We show that the optical properties of a particle above a plane dielectric interface differ dramatically from those of the same particle embedded in a homogeneous matrix. Calculations for gold and silver spheres have been carried out in using the exact multipole expansion method, providing thus benchmark results for testing the accuracy of the available numerical methods. For silver spheres, the dependence of the extinction cross-section has been studied in detail as a function of the parameters characterizing the particle/interface system, namely, the radius of the sphere, the particle-surface distance, and the dielectric index of the substrate, as well as those characterizing the light excitation, that is, the angle of incidence and the polarization. Throughout this study we have separated the effects arising from the inhomogeneity of the applied field (interference between the incoming and reflected plane waves) from the intrinsic substrate effects resulting from the interaction with the induced surface charges on the surface. These last effects are, in the present formalism, encoded in the reflected scattered field impinging on the particle. For particles close to the interface, a rich multipolar plasmonic structure is observed, which can be described in the frame of a hybridization scheme similar to that developed for dealing with layered particles or dimers. Comparison with approximate models is also provided