Effective medium description of plasmonic couplings in disordered polymer and gold nanoparticle composites

Abstract

Disordered gold nanocomposite films were obtained by introducing spherical gold nanoparticles into a polymer matrix. These films were structurally characterized using microscopy techniques, and then analyzed for their effective optical indices using spectroscopic ellipsometry. It is found that even for a low volume fraction of gold nanoparticles (f~1−5%), the observed plasmonic resonance is affected by electromagnetic coupling between particles, related to the disorder of the particles. We show that the classical Maxwell Garnett Effective Medium Approximation (EMA) fails to predict the measured indices. Since couplings create deformations of the polarizability tensor of individual particles, we propose to take them into account phenomenologically using a modified Maxwell Garnett EMA based on a distribution of ellipsoidal polarizabilities. This modified model, albeit simple, appears appropriate: in simple cases, a unimodal distribution of ellipsoidal polarizabilities is used, allowing for good fits of the experimental data with only two free parameters. Bimodal distributions make it possible to handle more complex cases where the resonance presents a shoulder, suggesting that particles can then be categorized into weakly vs. strongly coupled resonators. Such modified Maxwell Garnett EMAs present the advantage of relying on physically meaningful parameters and could be a general tool for the phenomenological description of plasmonic couplings in different disordered nanocomposites.