Dimensionality has a significant impact on the optical properties of solid-state nanostructures. For example, dimensionality-dependent carrier confinement in semiconductors leads to the formation of quantum wells, quantum wires and quantum dots. While semiconductor properties are governed by excitonic effects, the optical response of metal nanostructures is dominated by surface plasmons. Here we find that, in contrast to excitonic systems, the mode dispersions in plasmonic structures of different dimensionality are related by simple scaling rules. Employing electron energy loss spectroscopy, we show that the modes of silver nanodisks can be scaled to the surface and edge modes of extended silver thin films. We thereby introduce a general and intuitive ordering scheme for plasmonic excitations with edge and surface modes as the elementary building blocks.
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