Far-field optical response of plasmonic nanoparticle dispersions. To assess how changing the concentration of plasmonic particles influences far-field optical properties, we first examine the extinction spectra of dispersions of Drude nanoparticles with hard-sphere (U 0 = 0) interactions simulated at different volume fraction η, as computed by MPM (see Fig. ). Two qualitative trends are observed. First, increasing packing fraction results in a systematic redshift of the resonant frequency ω res , a prediction that is also captured by the mean-field Maxwell Garnett approximation (see Fig. ). Second, MPM predicts a pronounced nonmonotonic variation in the spectral linewidth W with η, with the broadest linewidths occuring around an intermediate packing fraction of η = 0.20. The mean-field approximation incorrectly predicts a constant linewidth independent of η (see Fig. ). This indicates that local structural variations-ignored by the mean-field approximation-play an important role in determining broadening for disordered structures. We will show below that the linewidth variations of MPM reflect heterogeneous contributions by individual particles to the ensemble spectra. The maximal heterogeneity in single particle resonances produces the greatest ensemble broadening. Furthermore, many-body interactions are important to understanding how the MPM-computed spectral lineshapes evolve with packing fraction. The pairwise coupling approximation, which omits mutual polarization effects due to such many-body interactions, becomes nonphysical as η increases above the smallest non-zero packing fraction investigated, predicting negative extinction at high frequencies (see Fig. ). The pairwise coupling approximation is clearly inadequate for the packing fractions considered here and won't be considered further. On the contrary, we will find Maxwell Garnett mean-field approximations provide a helpful contrast to the predictions of MPM to highlight the role that structure plays in determining the optical properties of fluid and gel-like disordered states.