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We study the electromagnetic behaviour of dense, spherical clusters made ofhundreds of plasmonic nanoparticules under illumination by a plane wave. Usinghigh-precision T-matrix numerical calculations, we compute the multipolarresponse of clusters up to 80 nm in radius and up to 44\% in particle volumefraction. We then investigate whether it is possible to obtain an effectivemedium description for the clusters, taking into account weak spatialdispersion in a fully consistent way. We find that the average scattered fieldas well as the average inner field of the spherical cluster can be accuratelyreproduced by applying an extended Mie theory to an equivalent homogeneoussphere characterized by three effective parameters: an electric permittivity$\varepsilon_{\mathrm{eff}}$ and a magnetic permeability $\mu_{\mathrm{eff}}$,associated to transverse modes, and a wavevector $k_\mathrm{L}$, associated toa longitudinal mode in the sphere. Our results show that artificial magnetismarises from interparticle couplings in the dense cluster, despite inclusionsnot displaying any individual magnetic dipole. We also find that, althoughlargely overlooked in the literature on metamaterials, the presence of thelongitudinal mode is essential to accurately reproduce the fields of thecluster, on par with the role of artificial magnetism. Our study thereforeproves that, even for high concentration in inclusions, it is possibleempirically to treat a cluster of plasmonic particles as a sphere made of aspatially-dispersive homogeneous medium. This offers a practical solutionfacilitating the computation of electromagnetic responses of such dense randommedia in diverse configurations of interest for the design of metamaterials andmetasurfaces.

Effective medium description of dense clusters of plasmonic nanoparticles with spatial dispersion