Effecti ve optical properties of dilute and dense polymer-gold nanoparticle films: theory and experiments

We study the effective optical properties of composite films made of 14-nm spherical gold nanoparticle in a polymer matrix, both in dilute (5% gold fraction) and dense (20%) regimes. Optical indices and permittivities are extracted from spectroscopic ellipsometry measurements and show effective resonant properties around the plasmon resonance, exhibiting effective negative permittivity for dense samples in a finite frequency range (finite-band metallic behaviour). Measurements are compared to Maxwell-Garnett (MG) predictions: we show that the classical MG formula does not reproduce the experimental results, even in the dilute regime, due to nanoagregation effects in the samples which entails couplings between particles. Since couplings create deformations of the polarizability tensor of the individual particles, we propose to take them into account in an empirical way using a modified MG formula based on a distribution of ellipsoids. We show that this modified Maxwell Garnett model works sucessfully, allowing for good fits of the experimental data in the dilute regime (using a distribution of ellispoidal polarizabilities centered on a mean isotropic polarizability) as well as in the dense regime up to 20% (using polarizability distribution centered on a mean ellipsoidal polarizability).