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

Supervisors’ Foreword
Abstract
Publications Related to this ThesisThe list of papers that have been published by the author in international peer-reviewed journals during the course of the author’s Ph.D. studies is presented below (in inverse chronological order). Publications A, F, J, K, and N are discussed in this thesis.Papers published in peer-reviewed journals during the author’s Ph.D. studies:P. A. D. Gonçalves, T. Christensen, N. Rivera, A.-P. Jauho, N. A. Mortensen, M. Soljačić, Plasmon–Emitter Interactions at the Nanoscale, Nat. Commun. 11, 366 (2020)M. Geisler, X. Cui, J. Wang, T. Rindzevicius, L. Gammelgaard, B. S. Jessen, P. A. D. Gonçalves, F. Todisco, P. Bøggild, A. Boisen, M. Wubs, N. A. Mortensen, S. Xiao, N. Stenger, Single-Crystalline Gold Nanodisks on WS2 Mono- and Multilayers for Strong Coupling at Room Temperature, ACS Photonics 6 (4), 994–1001 (2019).Y. You, P. A. D. Gonçalves, L. Shen, M. Wubs, X. Deng, S. Xiao, Magnetoplasmons in monolayer black phosphorus structures, Opt. Lett. 44, 554–557 (2019).C. Tserkezis, P. A. D. Gonçalves, C. Wolff, F. Todisco, K. Busch, N. A. Mortensen, Mie excitons: Understanding strong coupling in dielectric nanoparticles, Phys. Rev. B 98, 155439 (2018).N. A. Mortensen, P. A. D. Gonçalves, M. Khajavikhan, D. N. Christodoulides, C. Tserkezis, C. Wolff, Fluctuations and noise-limited sensing near the exceptional point of parity-time-symmetric resonator systems, Optica 5, 1342–1346 (2018).E. J. C. Dias, D. A. Iranzo, P. A. D. Gonçalves, Y. Hajati, Y. V. Bludov, A.-P. Jauho, N. A. Mortensen, F. H. L. Koppens, N. M. R. Peres, Probing nonlocal effects in metals with graphene plasmons, Phys. Rev. B 97, 245405 (2018).A. J. Chaves, B. Amorim, Y. V. Bludov, P. A. D. Gonçalves, N. M. R. Peres, Scattering of graphene plasmons at abrupt interfaces: An analytic and numeric study, Phys. Rev. B 97, 035434 (2018).P. A. D. Gonçalves, L. P. Bertelsen, S. Xiao, N. A. Mortensen, Plasmon-exciton polaritons in two-dimensional semiconductor/metal interfaces, Phys. Rev. B 97, 041402(R) (2018).B. Amorim, P. A. D. Gonçalves, M. I. Vasilevskiy, N. M. R. Peres, Impact of Graphene on the Polarizability of a Neighbour Nanoparticle: A Dyadic Green’s Function Study, Appl. Sci. 7 (11), 1158 (2017).P. A. D. Gonçalves, S. Xiao, N. M. R. Peres, N. A. Mortensen, Hybridized Plasmons in 2D Nanoslits: From Graphene to Anisotropic 2D Materials, ACS Photonics 4 (12), 3045–3054 (2017).P. A. D. Gonçalves, S. I. Bozhevolnyi, N. A. Mortensen, N. M. R. Peres, Universal description of channel plasmons in two-dimensional materials, Optica 4, 595–600 (2017).U. Levy, M. Grajower, P. A. D. Gonçalves, N. A. Mortensen, J. B. Khurgin, Plasmonic silicon Schottky photodetectors: The physics behind graphene enhanced internal photoemission, APL Photonics 2, 026103 (2017).P. A. D. Gonçalves, E. J. C. Dias, Y. V. Bludov, N. M. R. Peres, Modeling the excitation of graphene plasmons in periodic grids of graphene ribbons: An analytical approach, Phys. Rev. B 94, 195421 (2016).P. A. D. Gonçalves, E. J. C. Dias, S. Xiao, M. I. Vasilevskiy, N. A. Mortensen, N. M. R. Peres, Graphene Plasmons in Triangular Wedges and Grooves, ACS Photonics 3 (11), 2176–2183 (2016).
Acknowledgements
Contents
Acronyms
Part I Classical Plasmonics
1 Introduction
	1.1 Structure and Scope of This Thesis
		1.1.1 Outline
	References
2 Classical Electrodynamics of Solids
	2.1 Foundations of Classical Electrodynamics
		2.1.1 Maxwell\'s Equations and Constitutive Relations
		2.1.2 Boundary Conditions at Interfaces
		2.1.3 Local-Response Approximation
		2.1.4 The Drude Model of the Free-Electron Gas
	2.2 Fundamentals of Plasmonics
		2.2.1 Surface Plasmon Polaritons at Planar Interfaces
		2.2.2 Localized Surface Plasmons in Metal Spheres
		2.2.3 Other Geometries
	2.3 Dipole Emission: Spontaneous Decay Rate and Optical Local Density of States
		2.3.1 Electric Dipole in a Homogeneous Medium
		2.3.2 Electric Dipole in an Inhomogeneous Medium: LDOS and Purcell Enhancement
		2.3.3 Electric Dipole Above a Planar Interface
	References
3 Electronic and Optical Properties of Graphene
	3.1 Electronic Structure of Graphene
		3.1.1 Crystal Structure of Monolayer Graphene
		3.1.2 Tight-Binding Description
		3.1.3 The Continuum Limit: Massless Dirac Hamiltonian
	3.2 Optical Properties of Graphene
		3.2.1 Dynamical Conductivity of Graphene
		3.2.2 Nonlocal Conductivity of Graphene and the Nonlocal RPA Dielectric Function
	References
4 Fundamentals of Graphene Plasmonics
	4.1 Plasmons in Extended Graphene
		4.1.1 Plasmons in Monolayer Graphene
		4.1.2 Plasmons in Double-Layer Graphene
	4.2 Plasmons in Nanostructured Graphene
		4.2.1 Nonretarded Framework for Graphene Plasmons in Generic Nanostructures
		4.2.2 Hybridized Plasmons in Two-Dimensional Nanoslits
	References
5 Two-Dimensional Channel Plasmons  in Nonplanar Geometries
	5.1 Graphene Plasmons in Triangular Channels: Wedge and Groove Configurations
	5.2 Effective-Index Description of Channel Plasmons in Two-Dimensional Materials
	References
Part II Quantum Plasmonics
6 Electrodynamics of Metals Beyond  the Local-Response Approximation: Nonlocal Effects
	6.1 Hydrodynamic Theory of an Electron Gas
	6.2 Nonlocal Optical Response of Metals
		6.2.1 Nonlocal Effects in the SPP Dispersion at a Planar Dielectric–Metal Interface
		6.2.2 Nonlocal Plasmonic Response of Metallic Nanospheres
	6.3 Nonlocality at a Planar Interface between a Dielectric and Lindhard Metal
	References
7 Quantum Nonlocal Effects Probed by Ultraconfined Graphene Plasmons
	7.1 Acoustic-Like Graphene Plasmons in a Nutshell
	7.2 Nonlocal and Quantum Graphene Plasmonics
	7.3 Probing the Nonlocal Response of Metals with Graphene Plasmons
	References
8 Quantum Corrections in Plasmonics and Plasmon–Emitter Interactions
	8.1 Quantum Plasmonics at Planar Interfaces: Feibelman d-Parameters
		8.1.1 Nonretarded Reflection and Transmission Coefficients and Surface Plasmon Dispersion
		8.1.2 Surface Plasmon Polaritons: Quantum Surface Corrections Incorporated via d-Parameters
	8.2 Quantum Nonlocal Response of Plasmonic Spheres
		8.2.1 Multipolar Polarizability of a Nanosphere Including Feibelman d-Parameters
		8.2.2 Generalized Mie Theory with Feibelman d-Parameters
	8.3 Plasmon–Emitter Interactions at the Nanoscale
		8.3.1 Nonclassical LDOS: Purcell Enhancement
		8.3.2 Dipole-Forbidden Electric Multipolar Transitions
		8.3.3 Energy Transfer Between Two Emitters Near a Metal Surface
		8.3.4 Plasmon-Enhanced Two-Photon Emission
	8.4 Graphene–Dielectric–Metal Structures: Application  of the d-Parameters\' Formalism
	References
9 Conclusions and Outlook
	References
Appendix A Lindhard Dielectric Function  of a Homogeneous 3DEG
Appendix B Derivation of the Specular Reflection Model  for Nonlocal Plasmonics
B.1  Reflection Coefficient for TM Waves in Terms  of Surface Impedance
B.2  Surface Impedance in a Nonlocal Medium: Specular Reflection Model
B.3  Reflection Coefficient and Nonlocal Plasmons Within   the Specular Reflection Model
Appendix C Mie Theory with d-Parameters
Appendix D Macroscopic Quantum Electrodynamics  and Multipolar Decay Rates