Universal dispersion of surface plasmons in flat nanostructures

Abstract

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.

Quantum description of the optical response of charged monolayer–thick metallic patch nanoantennas

“…This mode is axially symmetric and it is characterized by an antisymmetric charge density distribution induced at the top and bottom surfaces of the nanodisk. Different from the propagating edge plasmons discussed classically 20,[23][24][25]73,95 , the edge mode of the nanodisk found here stems from lateral coordinate dependence of the confining potential and it is similar to the transverse edge mode reported in quantum calculations of the monoatomic wires [91][92][93] For nanodisks negatively charged by electron doping several quantum effects are important:…”

“…This later property of the present EM with no nodal structure in angular dependence with ϕ makes it quite different from the classically attainable plasmons propagating along the edges of the nanostructures 20,23-25 , or multipolar plasmons in metallic nanodisks 73 . Interestingly, both have been also shown to obey the same dispersion relation 95 . As we mentioned above the physics underlying the formation of the EM in the present case is similar to the one discussed for the monoatomic nanowires [91][92][93] , and it can not be retrieved in the classical calculations.…”

“…Nowadays, plasmonic devices exploit propagating plasmons confined to (nanostructured) metal surfaces, or localised plasmons in single nanoparticles and nanoparticle assemblies. Along with these three-dimensional structures, plasmonics in lower dimensional structures such as nanowires [14][15][16][17][18] or edges [19][20][21][22][23][24][25] or two-dimensional materials [23][24][25][26][27][28][29] offers further perspectives in miniaturization of optoelectronic devices, light confinement, active control of response, and directional plasmon propagation. Albeit the ongoing discussion on the applicability of the term "plasmonic" to describe optical resonances in molecular structures, these structures represent the smallest devices where the optical response reflects the quantum nature of collective electronic excitations and thus requires quantum description [30][31][32] .…”

Real-space mapping of tailored sheet and edge plasmons in graphene nanoresonators

“…A comprehensive experimental characterization of graphene plasmonic nanoresonators and their sheet and edge modes has thus been elusive so far. On the other hand, plasmonic edge modes have been shown to propagate along sharp edges of gold films, graphene and 2D electron gases 11,[23][24][25][26][27][28] and provide stronger confinement of the electromagnetic fields compared to the sheet plasmons.Here we image and analyze the near-field structure of both plasmonic sheet and edge modes in graphene disks and rectangular nanoresonators. We employ scattering-type scanning near-field optical microscopy (s-SNOM) 29 , which to date is the only available tool for real-space imaging of the propagation and confinement characteristics of graphene plasmons 8,9,11 .…”

“…A comprehensive experimental characterization of graphene plasmonic nanoresonators and their sheet and edge modes has thus been elusive so far. On the other hand, plasmonic edge modes have been shown to propagate along sharp edges of gold films, graphene and 2D electron gases 11,[23][24][25][26][27][28] and provide stronger confinement of the electromagnetic fields compared to the sheet plasmons.…”