Optical Response of Gold-Nanoparticle-Amplified Surface Plasmon Resonance Spectroscopy

A simple formalism that predicts optical constants of a two-dimensionally distributed nanoparticle (NP) thin film is presented for analysis of the NP-amplified surface plasmon resonance. The dielectric constant of the NP thin film can be evaluated with simple expressions at low coverages (σ < 0.08), whereas the local fields induced by surrounding polarizations of NPs should be taken into account at coverages of σ > 0.08. Analytical and numerical calculations are carried out for evaluating the local fields at different conditions. The Clausius−Mossoti relation, which is usually used for evaluation of dielectric constants of a binary medium, does not hold in the NP thin films, because of the large interparticle distance and/or the retardation effect. We carried out SPR measurements for NP films with different NP coverages, and the results support the proposed analytical formalism. Finally we propose a procedure to evaluate the NP coverage from the NP-SPR profile experimentally obtained.