Towards maximum optical efficiency of ensembles of colloidal nanorods

Experimental and theoretical studies of colloidal nanoparticles have primarily focused on accurate characterization and simulation of observable characteristics, such as resonant wavelength. In this paper, we tackle the optimal design of colloidal-nanoparticle ensembles: what is the largest possible per-volume optical cross-section, 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 offer a roadmap to the largest possible optical response of nanoparticle ensembles.