Plasmonics and Light–Matter Interactions in Two-dimensional Materials and in Metal Nanostructures: Classical and Quantum Considerations

Paulo André Dias Gonçalves

Research output: Book/ReportPh.D. thesis


This thesis presents a comprehensive theoretical description of classical and quantum plasmonics in three and two dimensions and in hybrid systems containing elements with different dimensionalities. It focuses on the theoretical understanding of the salient features of plasmons in nanosystems as well as on the multifaceted aspects of plasmon-enhanced light–matter interactions at the nanometer scale, with special emphasis on the modeling of nonclassical behavior across the transition between classical and quantum domains.

In the first part of the thesis, following an introduction to the foundational concepts behind the theory of classical electrodynamics and to the core elements of classical plasmonics in three and two dimensions, we develop a general theoretical formalism for calculating plasmons in various two-dimensional (2D) geometries. We have then applied that framework to study plasmon coupling and hybridization in 2D nanoslits. Our method is valid for any 2D plasmon-supporting material (including ultrathin metallic films). Next, after having dealt with strictly planar 2D configurations, we expand our investigations to nonplanar structures based on 2D materials. Concretely, we consider one-dimensional channels formed by engineering the 2D material into either a V- or a Λ-shape (i.e., resulting in a groove or in a wedge, respectively). Our results show that these modes exhibit levels of light localization that are deeply subwavelength, even larger than what could possibly be obtained by exploiting plasmons in the planar, continuous host 2D medium.

Title of the PhD Thesis
Plasmonics and Light–Matter Interactions in Two-dimensional Materials and in Metal Nanostructures: Classical and Quantum Considerations Name of Author Paulo André Dias Gonçalves Rights I hereby allow DTU Fotonik to publish my thesis on and I have retained the Copyright on the material to do so.

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In the second part of the thesis, we identify the main shortcoming associated with classical treatments of plasmonics, and then propose a number of different theoretical approaches for overcoming those shortcomings. We start by reviewing the hydrodynamic model for the homogeneous electron gas in three-dimensions (which includes nonlocality to lowest-order), and then briefly discuss the so-called specular reflection model which includes the full nonlocal dielectric. Next, we investigate how quantum nonlocal effects influence the dispersion of acoustic-like graphene plasmons, which are ultraconfined graphene plasmons that can be excited when a graphene sheet lies in close proximity to a metal substrate. We find significant deviations from classicality pertaining to the plasmonic response of graphene, and then exploit the remarkable confinement attained by this kind of graphene plasmons to probe nonlocal effects in the metal's optical response.

Lastly, we present a unified theoretical treatment of mesoscopic electrodynamics— rooted on the d-parameter formalism—whose applicability encompasses both the classical and quantum regimes, and, crucially, spans the challenging transition region where classical and quantum effects can coexist. In particular, our approach allows a simultaneous account of nonlocality, electronic spill-out, and surface-enabled Landau damping, while also including retardation. We derive analytical expressions for the nonclassical scattering coefficients in selected geometries, from which we determine the systems’ plasmonic excitations. Our results show that, for a broad range of experimentally-relevant parameters, the latter incur in substantial nonclassical resonant shifts (broadenings) parameterized by a geometry-dependent factor times the real (imaginary) part of the d⊥-parameter. Furthermore, we extend and apply our mesoscopic formalism to a plethora of plasmon–emitter interactions. Specifically, we investigate the role of quantum surface corrections to the plasmonic Purcell enhancement along with their influence in enhancing dipole-forbidden transitions, plasmon-mediated energy transfer between two emitters, as well as two-photon emission. Our findings underscore the importance of incorporating nonclassical corrections in quantum nanoplasmonics; this becomes increasingly important as current state-ofthe-art nanoplasmonic studies continue to probe ever-smaller nanostructures and/or emitter–metal separations.
Original languageEnglish
PublisherTechnical University of Denmark
Publication statusPublished - 2019

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