Advances in Non-Archimedean Analysis and Applications: The p-adic Methodology in STEAM-H (STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health)

Preface
Acknowledgements
Contents
Contributors
1 Analytical Methods for (Near-Field) Optics and Plasmonics
	1.1 Maxwell\'s Equations
	1.2 Fresnel Relations
	1.3 Transfer Matrix
		1.3.1 Example: Surface Plasmon Polariton
		1.3.2 Example: Short-Range and Long-Range Surface Plasmons
		1.3.3 Example: Surface Plasmon Resonance Sensing
	1.4 Effective Index Method
		1.4.1 Example: Rectangular Plasmonic Waveguide
	1.5 Single Mode Matching
		1.5.1 Orthogonality
		1.5.2 Example: Light in a Slit
			1.5.2.1 Single Channel Limit
			1.5.2.2 Resonance Condition
			1.5.2.3 Field Enhancement
	1.6 Quasistatic Methods
		1.6.1 Rayleigh Particle
			1.6.1.1 Maximum Local Field at Plasmonic Resonance
		1.6.2 Dipole Polarization and Circuit Theory
		1.6.3 Retardation and Single Channel Limit
	1.7 Formal Perturbation Theory
	1.8 Coupled Mode Theory
		1.8.1 Complex Coupled Mode Equations
		1.8.2 Example: Counter and Codirectional Coupling
		1.8.3 Example: Uniform Dielectric Discontinuity
		1.8.4 Example: Numerical Method
	1.9 Summary and Outlook
	References
2 Fundamental Limits to Near-Field Optical Response
	2.1 Introduction
	2.2 Near-Field Optical Response Functions
		2.2.1 LDOS
		2.2.2 Free-Electron Radiation
		2.2.3 CDOS
		2.2.4 Surface-Enhanced Raman Scattering (SERS)
		2.2.5 Near-Field Radiative Heat Transfer
		2.2.6 Mode Volume
	2.3 Analytical and Computational Bound Approaches
		2.3.1 Global Conservation Laws
		2.3.2 Channel Bounds
		2.3.3 Local Conservation Laws
		2.3.4 Sum Rules
	2.4 Fundamental Limits in the Near Field
		2.4.1 Single-Frequency Bounds
			2.4.1.1 Spontaneous Emission
			2.4.1.2 CDOS
			2.4.1.3 Smith–Purcell Radiation
			2.4.1.4 Spectral NFRHT
		2.4.2 All-Frequency Sum Rules
		2.4.3 Finite, Nonzero Bandwidth
			2.4.3.1 Complex-Frequency Bounds
			2.4.3.2 Oscillator-Representation Bounds
		2.4.4 Mode Volume
	2.5 Summary and Looking Forward
	2.6 Appendix: Complex Analysis for Sum Rules
	References
3 Quasinormal Mode Theories and Applications in Classical and Quantum Nanophotonics
	3.1 Introduction
	3.2 Theory
		3.2.1 Maxwell\'s Equations, Helmholtz Equation, and Green Functions
		3.2.2 Dyson Equation for the Self-Consistent Green Function
		3.2.3 Normal Modes, Completeness, and Green Function Expansions
		3.2.4 Quasinormal Modes, Completeness, and Green Function Expansions
		3.2.5 Total Electromagnetic Fields and Regularized Quasinormal Modes
		3.2.6 Analytical Example: One-Dimensional Quasinormal Modes for Dielectric Barriers
		3.2.7 Purcell\'s Formula for Enhanced Spontaneous Emission and a Generalized Effective Mode Volume
		3.2.8 Nonradiative and Radiative Decay Rates and Beta Factors
			3.2.8.1 Nonradiative Decay Rates
			3.2.8.2 Radiative Decay Rates
			3.2.8.3 Classical Radiative and Nonradiative Beta Factors
		3.2.9 Quantized Quasinormal Modes
		3.2.10 Bad Cavity Limit Solution from the Quantized Quasinormal Mode Master Equation
		3.2.11 Coupled-Mode Theories Using Quasinormal Modes
			3.2.11.1 Classical Purcell Factors Using Quasinormal Modes and Coupled-Mode Theory
			3.2.11.2 Classical Purcell Factors Using Mode Expansions from Coupled-Mode Theory
			3.2.11.3 Quantum Purcell Factors in the Bad Cavity Limit, Using Quasinormal Modes and Normal Modes Obtained from Coupled-Mode Theory
	3.3 Applications
		3.3.1 One-Dimensional Quasinormal Modes and Green Functions for Dielectric Barriers
		3.3.2 Gold Dimer Quasinormal Modes for Localized Plasmons
		3.3.3 Hybrid Metal-Dielectric Quasinormal Modes for Metal Dimers on Photonic Crystal Cavity beams
		3.3.4 Coupled-Cavity Quasinormal Modes
	3.4 Conclusions and Future Prospects
	References
4 Probing the Optical Near-Field
	4.1 Introduction
	4.2 Principles
		4.2.1 Huygens Fresnel Formalism
		4.2.2 Scalar Fourier Theory of Diffraction
	4.3 Probing the Near-Field with a Physical Optical Nanoantenna
	4.4 Probing the Near-Field with Electrons
		4.4.1 Electron Energy Loss Imaging Microscopy (Electron In, Electron Out)
		4.4.2 Cathodoluminescence (CL) Imaging Microscopy – (Electron In, Photon Out)
		4.4.3 Photon-Induced Near-Field Electron Imaging Microscopy (Photon In, Electron In, Electron Out)
		4.4.4 Photoemission Electron Imaging Microscopy PEEM (Photon In, Electron Out)
	4.5 Probing the Near-Field Through Nanochemistry
		4.5.1 Use of Azoic Molecular Nanomotors Undergoing Photo-isomerization
		4.5.2 Nanoscale Photopolymerization
		4.5.3 Other Chemical Reactions
	4.6 Conclusion and Last Remarks
	References
5 On-Chip Nanoscale Light Sources
	5.1 Introduction
	5.2 NanoLEDs
	5.3 Plasmonic Lasers
	5.4 Photonic Crystal Lasers
	5.5 Metamaterials
	References
Index