  Experimental and theoretical studies of colloidal nanoparticles have
primarily focused on accurate characterization and simulation of observable
characteristics, such as resonant wavelength. In this Letter, we tackle the
optimal design of colloidal-nanoparticle ensembles: what is the largest
possible optical response, which designs might achieve them, and can such
response be experimentally demonstrated? We combine theory and experiment to
answer each of these questions. We derive general bounds on the maximum
cross-sections per volume, and we apply an analytical antenna model to show
that resonant nanorods should nearly achieve such bounds. We use a modified
seed-mediated synthesis approach to synthesize ensembles of gold nanorods with
small polydispersity, i.e., small variations in size and aspect ratio.
Polydispersity is the key determinant of how closely such ensembles can
approach their respective bounds yet is difficult to characterize
experimentally without near-field measurements. We show that a certain
"extinction metric," connecting extinction cross-section per volume with the
radiative efficiencies of the nanoparticles, offers a quantitative prediction
of polydispersity via quantities that can be rapidly measured with far-field
characterization tools. Our predictions apply generally across all plasmonic
materials and offers a roadmap to the largest possible optical response of
nanoparticle ensembles.
