Metamaterials and Nanophotonics: Principles, Techniques and Applications

Contents
Introduction
1. Vectorial Field Theory and Modelling of 3D Dielectric Waveguides
1.1 Introduction
1.2 Maxwell's Equations of Electromagnetism
1.3 The Wave Equations
1.3.1 Vectorial Wave Equation for the Electric Field E
1.3.2 Vectorial Wave Equation for the Magnetic Field H
1.4 Boundary Conditions for the Electromagnetic Fields
1.5 Exact Analysis of a Three-Layer Slab Dielectric Waveguide
1.6 Effective Index Method
1.7 Marcatili's Method
1.8 Finite-Difference Frequency-Domain Mode-Solvers
1.8.1 Vectorial Wave Equations for the E-Field Components
1.8.2 Vectorial Wave Equations for the H-Field Components
1.8.3 Semi-Vectorial Wave Equations
1.8.4 Finite-Difference Discretization
1.8.5 Numerical Examples of the FV-FDFD Mode-Solver
2. Conventional and Nonstandard Finite-Difference Time-Domain Method
2.1 Introduction
2.2 The Yee Algorithm
2.3 Stability of the Yee Algorithm
2.4 "Exact" and "Nonstandard" Finite-Differences
2.5 Generalization to Three Dimensions
2.5.1 Standard Wave-Equation Finite-Difference Algorithm
2.5.2 Non-Standard Finite-Difference Time-Domain Algorithm
2.6 Application of the NS-FDTD Method in the Simulation of a 3D Dielectric Waveguide
3. Light Propagation in Negative-Refractive-Index Metamaterials and Waveguides
3.1 Introduction
3.2 A Brief History of Metamaterials
3.3 Sign of the Refractive Index and Energy Density Expression in Passive "Double Negative" Metamaterials
3.4 Refraction and E-H-k Vector Triad Inside a "Double Negative" Metamaterial
3.5 Fresnel's Formulas for Plane Wave Incidence at a Planar RH/LH Media Interface
3.6 Metamaterial-Enabled "Perfect" Lens
3.7 Surface Plasmon Polaritons in Asymmetric DNGM Slab Heterostructures
3.7.1 Surface Plasmon Polaritons at a Planar LH/RH Interface
3.7.2 Surface Plasmon Polaritons in Asymmetric LH Slab Waveguides
3.7.3 Summary of the Identified SPP Solutions
3.8 Oscillatory Guided Modes Supported by Asymmetric DNGM Slab Heterostructures
4. Plasmonic and Metamaterial Waveguides
4.1 Introduction
4.2 Maxwell's Equations
4.3 Planar Waveguide Structures
4.3.1 The Transfer Matrix Method
4.3.2 Radiation Modes
4.3.3 Bound Modes and the Dispersion Equation
4.3.4 Leaky Modes
4.4 Metals and the Surface Plasmon Polariton
4.4.1 The Negative Permittivity of Metals
4.4.2 Surface Plasmon at a Single Interface
4.4.3 Coupled SPPs in Gaps and on Thin Films
4.4.4 Ohmic Loss and Alternative Plasmonic Materials
4.5 Modelling Effective Media: The Metamaterial Limit
4.5.1 Negative Refractive Index
4.5.2 Electrical Response
4.5.3 Magnetic Response
4.5.4 Optical NRI Metamaterials
4.5.5 NRI Waveguides
4.6 Summary
5. Design Methods for Constructing Metamaterials
5.1 Introduction
5.2 Metamaterials with Negative Effective Permittivity in the Microwave Regime
5.3 Metamaterials with Negative Effective Permeability in the Microwave Regime
5.4 Intrinsically Lossless Magnetic Metamaterials
5.4.1 Case of "Isolated" Unit Cells
5.4.2 Calculations of Active Powers in the Equivalent Electrical Circuits
5.4.3 Case of "Tightly Coupled" Unit Cells
5.4.4 Remarks on the Working Principle of the Magnetically Lossless 2-DEG Configuration
5.4.5 Issues with the Homogenisation Method for the Case of "Tightly Coupled" Unit Cells
5.4.6 Systems with M Degrees of Freedom
6. "Trapped Rainbow": Stopping of Light in Metamaterials
6.1 Introduction
6.2 Broadband Stopping of Light in Metamaterial Waveguides
6.3 Derivation of Spatiotemporal Field-Component Equations Used in the Adiabatic Variation
6.4 Derivation of the Expressions for Light-Ray Goos–Hänchen Spatial Displacements
6.5 Derivation of the Relation between the Total Time-Averaged Power Flow and the Effective Thickness of the Waveguide
6.6 Characteristic Impedance of Left- and Right-Handed Waveguides
7. Passive Stopped-Light Waveguides
7.1 Introduction
7.2 Modal Characteristics of the Plasmonic and Metamaterial Waveguides
7.3 Dissipative Loss and Band Splitting
7.3.1 Complex-k
7.3.2 Complex-ω
7.4 Incoupling at the Stopped-Light Point
7.5 Temporal Mode Dynamics
7.5.1 The FDTD Method
7.5.2 Excitation SchemeThe simulation setup, designed to
7.5.3 Extracting the Complex-ω Band
7.6 Velocity, Dispersion and Loss in the Time Domain
7.6.1 Centre of Energy Velocity
7.6.2 Extraction of Effective Loss Rates
7.6.3 Extremely Low Group Velocity and Pulse Broadening in the Lossy MIM Waveguide
7.6.4 Loss Induced Spectral Shift
7.7 Controlling the Radiative Loss
7.8 Conclusion
8. Impact of Surface Roughness on Stopped-Light
8.1 Introduction
8.2 Scattering Theory
8.3 Implementing Roughness in FDTD
8.4 Effect on Velocity
8.5 Modal Loss
8.6 Conclusion
9. Maxwell–Bloch Theory and Gain
9.1 Preliminaries. Two-Level System
9.1.1 Bloch Equations
9.1.2 Interaction of TLS with Electromagnetic Field
9.1.3 Rotating Wave Approximation (RWA)
9.1.4 The Density Operator
9.2 Optical Bloch Equations for a Two-Level System
9.3 Loss Compensation in Metamaterials
9.4 Four-Level System as Model of Gain Mediu
9.4.1 Results
10. Summary of Surface Plasmons and Active Plasmonics
10.1 Mathematical Formulation
10.1.1 Dielectric Constant
10.1.2 Classical Models for Plasmons
10.1.2.1 Drude model
10.1.2.2 AC dielectric constant
10.1.2.3 Lorentz model
10.2 Plasmons Across a Single Interface
10.2.1 TM Polarised Modes
10.3 Plasmons Across Infinite Double Interface
10.3.1 General
10.3.2 Symmetric Plasmon Modes
10.3.3 Antisymmetric Plasmon Modes
10.4 Stripe Waveguides
10.5 Summary of Properties
10.6 Localized Surface Plasmons
10.7 Origin of Losses
10.7.1 Scattering
10.7.2 Ohmic Loss
10.8 Methods for Compensating Losses
10.9 Practical Approaches to Compensate Losses in SPP
10.10 Some Applications of LRSPP
10.11 Plasmons in a DC Electric Field
11. Quantum Plasmonics
11.1 Early Evidence of Quantum Effects in Plasmonics
11.1.1 Comparison of Classical and Quantum Plasmonics
11.2 Young's Double-Slit Experiments
11.2.1 Basics — Optics
11.2.2 Young-Type Experiments with Plasmons
11.2.2.1 Schouten (2005) experiment
11.2.2.2 Zia 2007 paper
11.2.2.3 Alam (2013)
11.3 Quantum Information at the Nanoscale. HOM Interference
11.3.1 Optical Hong–Ou–Mandel Effect
11.3.2 HOM Effect with Plasmons
11.3.2.1 Experiment by Reinier W. Heeres et al. (2013)
11.3.2.2 G. Di Martino et al. (2014)
11.4 Tunneling of Plasmonics
11.5 Quantum Models of Plasmonics
11.5.1 Cordaro (2017). Quantum Drude Model (Au Nanowires)
11.5.2 Dasgupta (1977)
11.5.3 Nakamura (1983)
11.5.4 Nga (2015) — Second Quantization
11.5.5 Fundamental Hydrodynamic Approach
11.5.6 Field-Theoretical Approaches
11.6 Time-Dependent DFT
11.6.1 Density Functional Theory. General
11.6.1.1 The Kohn{Sham approach
11.6.1.2 LDA
11.6.2 TDDFT
11.6.3 Results
12. Nanolasers
12.1 Denition of Nanolaser
12.1.1 Types of Nanolasers
12.2 Progress in Nanolasers
12.2.1 Microdisk Lasers
12.2.2 Photonic Crystal Laser
12.3 Summary of Analysis of Nanowire Nanolasers
12.3.1 General Theory
12.3.2 Dispersion Relation of the Lowest Order
12.3.3 General Properties
12.4 Some Examples
12.4.1 First Demonstrations of Plasmonic Nanolasers
12.4.2 More Demonstrations
12.5 Basic Principles of Spaser
12.5.1 General
12.5.2 Quantum Theory of Spaser
12.5.2.1 SP eigenmodes and their quantisation
12.5.2.2 Quantum density matrix equations for spasers
12.5.3 Possible Applications of Nanolasers
Bibliography
Index