Contents
Foreword
Preface
Acknowledgments
List of Figures
List of Tables
1. Introduction
1.1 Plasmonics: Generalities
1.2 Plasmonics: Recent Developments
2. Electromagnetic Properties of Solids in a Nutshell
2.1 Classical Electrodynamics Basics
2.1.1 Maxwell’s equations
2.1.2 Boundary conditions
2.2 Drude Model
2.3 Preliminaries to Graphene Plasmonics
2.3.1 Elementary electronic properties
2.3.2 The optical conductivity of graphene
2.3.3 Lindhard function: Beyond the local approximation
2.3.4 Lindhard polarization function in relaxation-time approximation: The case of graphene
2.4 The Transfer-Matrix Method and the First Appearance of Plasmons in Graphene
2.4.1 Transfer-matrix for a graphene monolayer
2.4.2 Transmittance, reflectance and absorbance of electromagnetic radiation by a graphene monolayer
2.4.3 Transfer-matrix for a graphene double-layer
2.4.4 Transfer-matrix for multi-layer graphene structures
2.4.5 Plasmons: A transfer-matrix approach
3. Surface Plasmon-Polaritons at Dielectric-Metal Interfaces
3.1 Single Dielectric-Metal Interface
3.1.1 Dispersion relation
3.1.1.1 Zero damping (γ = 0)
3.1.1.2 Finite damping (γ ≠ 0)
3.1.2 Propagation length and field confinement
3.2 Multilayer Structures
3.2.1 Double Interface
3.2.2 Dispersion relation
3.3 A Short Note on Perfect Conductors
4. Graphene Surface Plasmons
4.1 Monolayer Graphene
4.1.1 Spectrum of GSPs
4.1.2 Field profile of GSPs in single-layer graphene
4.1.3 Plasmon dispersion revisited
4.1.4 Loss function
4.1.5 A word on TE surface waves
4.2 Double-Layer Graphene
4.2.1 Dispersion relation
4.2.2 Field profile of GSPs in double-layer graphene
4.2.3 Plasmon dispersion beyond the Drude model approximation
4.3 Surface Plasmon-Phonon-Polaritons in Graphene
4.3.1 Graphene on SiC
4.3.2 Graphene on SiO2
4.4 Magneto-Plasmons in Monolayer Graphene
4.4.1 Derivation of the spectrum’s condition
4.4.2 Solution of the semi-classical spectrum’s condition in a special limit
4.4.3 Spectrum of magneto-plasmons in the quantum regime: Landau quantization
4.5 A Detour: Surface Phonon-Polaritons in hBN
4.5.1 Solution of the electromagnetic problem
4.5.2 Guided phonon-polariton modes
5. Excitation of Graphene Surface Plasmons
5.1 Grating Coupling
5.1.1 Graphene on Gallium-Arsenide: The role of SO phonons
5.2 Prism Coupling
5.2.1 Otto configuration: Single-layer graphene
5.3 Near-field Excitation and Imaging of GSPs
5.4 Others
5.5 Excitation of SPP’s by a Moving Line of Charge
6. Launching Plasmons Using a Metallic Antenna
6.1 Theoretical Model and Integral Equation
6.2 Approximate Solution via Fourier Expansion
6.3 Results and Discussion
7. Plasmonics in Periodic Arrays of Graphene Ribbons
7.1 A Seminal Paper
7.2 Theoretical Model
7.2.1 Setting up the model
7.2.2 The scattering problem
7.3 Applications and Results
7.3.1 Periodic array of graphene ribbon
7.3.2 Theory versus experiment
7.4 A THz Polarizer
7.5 Scattering From a Periodic Grid in the Regime kw < 1
8. Plasmons in Graphene Nanostructures and in One-dimensional Channels
8.1 Edge Plasmons in a Graphene Nanoribbon
8.1.1 Prelude: Green’s functions for a 2-layered medium
8.1.1.1 Homogeneous medium
8.1.1.2 2-layered medium
8.1.2 Plasmonic spectrum of a graphene nanoribbon
8.1.2.1 Plasmonic spectrum of a graphene nanoribbon: results
8.1.3 An extension: magneto-plasmons in a graphene ribbon
8.1.4 Scattering of THz radiation by a graphene micro-ribbon
8.2 Localized Surface Plasmons in a Graphene Ring
8.2.1 Spectrum of graphene plasmons in a graphene ring
8.2.1.1 Plasmonic spectrum of a graphene ring: results
8.3 Plasmonic Excitations in a Graphene Nanodisk
8.4 Scattering of Graphene Plasmons by a Conductivity Step
8.4.1 The mathematical problem
8.4.2 Solution of the Riemann-Hilbert problem
8.4.3 Further details
8.4.4 Calculation of the reflection amplitude
8.4.5 An alternative derivation of Eq. (8.137)
8.5 Localized Surface Plasmons in a Graphene Sheet with a Gaussian Groove
8.5.1 Few useful definitions
8.5.2 Formulation of the problem
8.5.3 Green’s theorem, Green’s functions, and the eigenvalue problem
8.5.4 Spectrum of surface plasmon-polaritons in the presence of a Gaussian groove
9. Excitation of Surface Plasmon-Polaritons Using Dielectric Gratings
9.1 Some Basic Definitions and Results
9.2 Tangent and Normal Vectors, and Boundary Conditions
9.3 A Trivial Example: Recovering Previous Results
9.4 The Fields in D+ and D−
9.4.1 Reflectance and transmittance efficiencies
9.4.2 Particular limits for the transmittance and the reflectance
9.5 A Non-Trivial Example: A Grating with a Sine-Profile
10. Excitation of Plasmons by an Emitting Dipole
10.1 Statement of the Problem and a Bit of Electrostatics
10.2 Calculation of the Non-Radiative Transition Rate: Particle-Hole Excitations Pathway
10.3 Calculation of the Total Transition Rate: Full Electromagnetic Calculation
10.4 Purcell Effect in Hyperbolic Materials
11. Concluding Remarks
Appendix A Derivation of the Susceptibility of Graphene
A.1 Undoped Susceptibility
A.1.1 The imaginary part of the undoped susceptibility
A.1.2 The real part of the undoped susceptibility
A.2 Doped Part: Fermi Sea Contributions
A.2.1 Intraband term
A.2.2 Interband term
A.2.3 Imaginary part of
A.2.4 Imaginary part of
A.2.5 Real Part of and
A.3 Summary for the Real and Imaginary Parts of Graphene Susceptibility
A.3.1 Real part of the susceptibility
A.3.2 Imaginary part of the susceptibility
A.4 Some Useful Integrals
Appendix B Derivation of the Intra- and Inter-band Conductivity of Graphene
Appendix C Inhomogeneous Drude Conductivity
C.1 Longitudinal Conductivity
C.2 Transverse Conductivity
Appendix D Derivation of the Expression Relating the Longitudinal Conductivity with the Polarizability
Appendix E Derivation of the Polarization of Graphene in the Relaxation-Time Approximation
E.1 Hamiltonian and Particle and Current Densities
E.2 Local Equilibrium Density Matrix
E.3 A Useful Identity
E.4 Equation of Motion for the Density Matrix
E.5 Polarization in the Relaxation-Time Approximation
Appendix F RPA for Double-Layer Graphene
F.1 Equation of Motion Method
F.2 Diagrammatic Approach
Appendix G Effective Dielectric Constants for Coulomb-Coupled Double-Layer Graphene
Appendix H Magneto-Optical Conductivity of Graphene
Appendix I Supplementary Material for Chapter 7
I.1 Derivation of the Expressions for the Transmittance and Reflectance
I.2 Modes Contributing to Each Resonance
Appendix J The Method of Toigo
Appendix K Boundary Condition in the Dipole Problem
Appendix L Fourier Transform of the Dipole Potential
Appendix M Non-Radiative Decaying Rate: Electrostatic Calculation
M.1 Doped Graphene
M.2 A Detour: Neutral Graphene
Appendix N Reflection Amplitude of an Electromagnetic Wave due to a Graphene Interface
N.1 The Simple Case of Free Standing Graphene
N.2 Reflection and Transmission Amplitudes: Fresnel Coefficients
N.2.1 TE (transverse electric) / s−components
N.2.2 TM (transverse magnetic) / p−components
Appendix O Green’s Functions in the Rope Problem
O.1 The Homogeneous Rope
O.1.1 Response to a localized force
O.2 The Inhomogeneous Rope
O.2.1 Reflection and transmition coefficients
O.2.2 Response to an external force in the inhomogeneous regime
Appendix P Derivation of the Transition Rate of a Quantum Emitter Near an Interface
P.1 Polarization Vectors and Green’s Functions
P.1.1 Definition of s− and p−polarization vectors and angular spectrum representation
P.1.2 The free space Green’s function
P.1.3 Green’s functions for problems with flat interfaces I
P.2 Dipole Decaying Rate
P.3 Explicit Form of the Tensor Product of the Polarization Vectors
P.4 The Free Green’s Function in Real Space
P.5 Green’s Function for Problems With Flat Interfaces II
P.5.1 Free-space Green’s function revisited
P.5.2 Electric field from a dipole in terms of Green’s functions
P.5.3 Green’s functions: s−component
P.5.4 Green’s functions: p−component
P.5.5 Derivation of the matrix structure of the Green’s functions
Bibliography
Index
