From Classical to Quantum Plasmonics in Three and Two Dimensions

Thomas Christensen

Research output: Book/ReportPh.D. thesisResearch

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This thesis presents theoretical results for the description and understanding of plasmonsin three- and two-dimensional platforms, with a special emphasis on the evolution from classical to nonclassical behavior as the optical and structural length scales are reduced towards the intrinsic scales of the electronic plasma. The content is divided into two parts and split by dimensionality. First, following a general introduction to the topic of plasmonics in three dimensions, we review the fundamental shortcomings of the conventional classical approach, finding its limitations to fall in four categories. We center our efforts on the deficiencies originating in the disregard of nonlocality, and explore its inclusion by means of a hydrodynamic model, which accounts to lowest order for the momentum-dispersion of the dielectric response. Concretely, we apply the hydrodynamic framework to the half-space, thin film, and spherical geometries. In the latter case, we extend the understanding of hydrodynamics beyond the dipolar regime, by contrasting optical probes of far- and near-field character. For short probe-to-surface separations, we establish that near- and far-field measurements provide significantly dissimilar weighting of spectral features, with particular importance to the excitation of multipole plasmons. Moreover, for these multipole plasmons, we find a hydrodynamic shift which increases with multipole order. This shift removes the singular classical pile-up of multipoles near the planar surface plasmon frequency. Complementing these considerations, we present results arising from an experimental collaboration, in which, using electron energyloss spectroscopy, the impact of higher-order multipoles are identified in embedded silver nanoparticles with radii down to 4 nm. Finally, in recognizing the limitations of the hydrodynamic model, we propose the outline of an extension of the Feibelmand-parameter approach to arbitrary geometries. Formally, this extension achieves a simultaneous first-order account of spill-out, nonlocality, and Landau damping, by instating a natural division between electronic and optical aspects. Our treatment of two-dimensional plasmonics centers on the platform of graphene. After a short review of graphene’s intrinsic electronic and optical properties, we introduce and explicate the main characteristic features of graphene plasmonics. We tabulate and discuss the resonance conditions and properties for the extended sheet, half-sheet, ribbon, disk, and regular polygons. In addition, we consider the existence of graphene plasmons in the non-planar geometry of a coated nanosphere. Proceeding to a consideration of effects beyond the conventional approach, we present first an adaptation of the hydrodynamic model to graphene. Next, we review the recently introduced tight-binding approach to the quantum plasmonic response of graphene nanostructures. We demonstrate how this frequency-domain method finds an equivalent implementation in the time-domain. Using this method and a related Dirac equation approach, we investigate the role of edge states in graphene, finding significant differences between the plasmonic properties of armchair- and non-armchair-terminated nanostructures. Lastly, we discuss the influence of a nonlinear Kerr interaction on the plasmons supported by a graphene nanoribbon, finding redshifting behavior relative to the linear case. We offer a straightforward and general perturbative understanding of this prediction, which depends only on the plasmon’s spatial inhomogeneity and geometry-averaged field intensity.
Original languageEnglish
PublisherTechnical University of Denmark
Number of pages235
Publication statusPublished - 2015


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