Interfacial Susceptibilities in Nanoplasmonics via Inversion of Fresnel Coefficients

Abstract

The reflection coefficients of a nanoparticle film are driven to a large extent by perpendicular and parallel interfacial susceptibilities that have the meaning of “dielectric thicknesses” which combine the actual geometry of the film and its dielectric properties. The direct determination of these parameters faces the long-standing issue of the derivation of complex optical constants from Fresnel coefficients via a unique spectroscopic measurement. The present work sets up an iterative algorithm based on inversion of the reflection coefficients recorded in the UV–visible range for two polarization states s and p and Kramers–Kronig (KK) analysis. To calculate the KK integrals over a limited energy window, the strategy was to complement measurements by spectra calculated in the framework of the spheroidal dipole approximation. The algorithm has been successfully tested on synthetic data of differential reflectivity for supported truncated spheres. These were chosen to span different dielectric behaviors, involving (a) for the particles, metals whose optical response is dominated by plasmonic excitations with a noticeable Drude behavior (Ag and Au) and (b) for the substrate, either nonabsorbing wide bandgap (alumina) or semiconducting (zincite and titania) oxides. Unlike the thin plate model, the approach was proven to apply to “dielectric thicknesses” of several tens of nanometres in cases in which, even for geometric sizes of the order of the nanometer, the classical long-wavelength dielectric approximation fails because of strong plasmon resonances. Therefore, the disentanglement of dielectric behaviors along the parallel and perpendicular directions simplifies the understanding on the interface polarization process by removing substrate contribution. The present work that deals with plasmonics in nanoparticles can be easily generalized to different morphologies as well as to other combinations of Fresnel coefficients.