Adventures in Contemporary Electromagnetic Theory

Contents
1 Introduction
	Reference
2 Our Werner Always Brought Us Joy
3 Scalar Potentials and Applications
	3.1 Introduction
	3.2 Potential-Based Methods
		3.2.1 Simple Medium
		3.2.2 Biisotropic Medium
		3.2.3 General Bianisotropic Medium
		3.2.4 Gyrotropic Bianisotropic Media
	3.3 Salient Features of the Scalar Potential Formulation
		3.3.1 Boundary Conditions
		3.3.2 Depolarization Tensors
		3.3.3 Current Densities
	3.4 Application
	3.5 Conclusion
	Epilog
	References
4 A Novel Approach to Electromagnetic Constitutive Relations
	4.1 Introduction
	4.2 Two Models of a Permanent Magnet
		4.2.1 Bulk Model
		4.2.2 Surface-Current Model
		4.2.3 Comparison
	4.3 A New Approach to Electromagnetic Constitutive Relations
		4.3.1 Traditional Axionic Electromagnetic Response
		4.3.2 Axionic Response Within the CMCRs
		4.3.3 Emulating an Axionic Response
		4.3.4 A Metamechanical Implementation of the Axionic Response
	4.4 The Electromagnetic Response of Vacuum
		4.4.1 Charge Conservation and Stokes\' Theorem
		4.4.2 Breaking the Link Between Local and Global Charge Conservation
		4.4.3 Reality
	4.5 Conclusion
	Appendix: Maxwell\'s Equations in Differential Form Notation
	References
5 On the Anatomy of Voigt Plane Waves
	5.1 Introduction
	5.2 Propagation in an Unbounded Biaxial Dielectric Medium
		5.2.1 Theory
			5.2.1.1 Nondegenerate Case
			5.2.1.2 Degenerate Cases
			5.2.1.3 Boundary Values for Voigt Plane Waves
		5.2.2 Numerical Investigations
	5.3 Propagation Through a Slab of a Biaxial Dielectric Material
		5.3.1 Theory
		5.3.2 Numerical Investigations
	5.4 Discussion
	Epilog on Werner S. Weiglhofer
	References
6 Electromagnetic Radiation by Finite-Sized Electric and Magnetic Dipoles Embedded in Homogeneous Uniaxial Dielectric Materials
	6.1 Introduction
	6.2 Dyadic Green Functions
	6.3 Point Dipoles
		6.3.1 Point Electric Dipole
		6.3.2 Point Magnetic Dipole
	6.4 Finite-Sized Electric Dipole
		6.4.1 Dipole and Optic Axis Parallel to x Axis
			6.4.1.1 Near Zone
			6.4.1.2 Far Zone
		6.4.2 Dipole Parallel to z Axis and Optic Axis Parallel to x Axis
			6.4.2.1 Near Zone
			6.4.2.2 Far-Zone Field Except on the Optic Axis
			6.4.2.3 Far-Zone Field on the Optic Axis
		6.4.3 Dipole and Optic Axis Parallel to z Axis
		6.4.4 Radiation Patterns
	6.5 Finite-Sized Current Loop
		6.5.1 Loop Axis and Optic Axis Parallel to z Axis
		6.5.2 Loop Axis Parallel to z Axis and Optic Axis Parallel to x Axis
		6.5.3  Electrically Small Current Loop (Point Magnetic Dipole)
		6.5.4 Radiation Patterns
	6.6 Concluding Remarks
	References
7 Near-Field Microwave Imaging Employing Measured Point-Spread Functions
	7.1 Introduction
	7.2 Direct Reconstruction Algorithms Employing Point-Spread Functions
	7.3 Calibration Measurements
	7.4 Forward Model of Scattering
		7.4.1 Born\'s Approximation
		7.4.2 Rytov\'s Approximation
	7.5 Quantitative Real-Time Inversion Methods
		7.5.1 Quantitative Microwave Holography
		7.5.2 Combining the Born and Rytov Data Extractions in QMH
		7.5.3 Scattered-Power Mapping
	7.6 Simulation Example
	7.7 Experimental Example
	7.8 Conclusion
	Epilogue
	Appendix: QMH Matrix Composition for Combined Use of the Born and Rytov Data-Extraction Strategies
	References
8 Electromagnetic Wave Propagation Inside Rectangular Chirowaveguides Using the Coupled Mode Method
	8.1 Introduction
	8.2 Characterization of Chiral Mediums
		8.2.1 Chirality and Optical Activity
		8.2.2 Electromagnetic Activity
		8.2.3 Constitutive Relations of the Isotropic Chiral Medium
		8.2.4 Manufacturing Chiral Mediums
		8.2.5 Experimental Characterization of Chiral Mediums
	8.3 Numerical Analysis of Chirowaveguides
		8.3.1 The Coupled Mode Method
		8.3.2 The Different Formulations of the Coupled Mode Method
			8.3.2.1 EH-Formulation of the Coupled Mode Method
			8.3.2.2 EB-Formulation
		8.3.3 Results
			8.3.3.1 Convergence Analysis
			8.3.3.2 Electromagnetic Field Analysis
	8.4 Summary
	8.5 Further Reading
	References
9 On a Steklov Spectrum in Electromagnetics
	9.1 Introduction
		9.1.1 Time-Harmonic Maxwell\'s Equations in a Linear Homogeneous Isotropic Dielectric Medium
		9.1.2 The Classical Steklov Eigenvalue Problem
		9.1.3 The Electromagnetic Steklov Eigenvalue Problem
	9.2 On the Classical Steklov Eigenvalue Problem
		9.2.1 Some Indicative Applications
			9.2.1.1 Details on the Formulation and Its Connections to Trace Theory
	9.3 On the Electromagnetic Steklov Eigenproblem
		9.3.1 Remarks on Trace Problems and Steklov Expansions
	9.4 The Case Where Ω Is the Unit Ball
	9.5 Summary
	Epilog
	References
10 Using Boundary Conditions with the Ewald–Oseen Extinction Theorem
	Prolog
	10.1 Introduction
	10.2 Before Boundary Conditions
		10.2.1 Constitutive Relations
		10.2.2 Dyadic Green Functions
		10.2.3 Source Fields
		10.2.4 Ewald–Oseen Extinction Theorem
	10.3 Incorporation of Boundary Conditions
		10.3.1 Scattering Problem
		10.3.2 Boundary Conditions
		10.3.3 Impedance Boundary Condition
	10.4 Closing Remarks
	Epilog
	References
11 Spatial Sampling and Interpolation Techniques in Computational Electromagnetics and Beyond
	11.1 Introduction
		11.1.1 Integral Equation Treatment of Static and Quasi-Static Problems
		11.1.2 Numerically Rigorous Analysis in the Frequency Domain
		11.1.3 High-Frequency Radiation and Scattering
		11.1.4 Time-Domain Radiation and Scattering
		11.1.5 Imaging
	11.2 Spatial Sampling and Interpolation
		11.2.1 Optimal Sampling of Static and Quasi-Static Fields
		11.2.2 Sampling Radiated Fields in the Spatial-Baseband
		11.2.3 Optimal Sampling Fields of More Complicated Structures
	11.3 Fast Far-Field Computation: Multilevel Interpolation and Aggregation
		11.3.1 Fast Far-Field Pattern Computation
		11.3.2 Fast Field Integration for Finite Observer Distance
		11.3.3 Fast Field Integration for Finite Observer Distance
	11.4 Fast Field Evaluation: The Multilevel Non-Uniform Grid Algorithm for Integral Equation Solvers
		11.4.1 MLNG Fast Field Evaluation
		11.4.2 Flavors and Variants of the MLNG Algorithms
	11.5 Fast Impedance Matrix Block Compression: Spectral Analysis of Grid Interaction Matrices
		11.5.1 Fast Low-Rank Approximation of Off-Diagonal Blocks
		11.5.2 Low-Rank Approximation for Nested-Bases Compression
	11.6 Conclusion
	References
12 Light-Matter Interaction at the Sub-Wavelength Scale: Pathways to Design Nanophotonic Devices
	12.1 Introduction
	12.2 Hyperbolic Metamaterials
		12.2.1 Types of HMMs
		12.2.2 Response of HMMs
		12.2.3 Negative Refraction in HMMs
	12.3 Designing HMMs
	12.4 Phase-Change Mediums in Metamaterials
	12.5 HMM as Programmable Reflection Modulator in Visible Light
		12.5.1 Structural Details of the HMM
		12.5.2 Constitutive Properties and Spectral Features
		12.5.3 Effect of Unit Cells and Defect Layer on the Reflection Response
		12.5.4 Effect of Oblique Incidence
		12.5.5 Application of the HMM as Modulator
	12.6 HMM as Broadband THz Brewster Modulator
		12.6.1 HMM Structure, Constitutive Properties, and Spectral Response
		12.6.2 Effect of Geometrical Properties
		12.6.3 Thermal Effect on the Spectral Response
		12.6.4 Application of HMM as Brewster Modulator
	12.7 Conclusion
	References
13 Integrated Photonics with Near-Zero Index Materials
	13.1 Electromagnetism with Near-Zero Index Materials
	13.2 The Supercoupling Effect
	13.3 Coherence in Low-index Materials
	13.4 Dirac\'s Triple Point and Near-Zero-Index Materials
	13.5 Conclusion
	References
14 Correlated Disorder in Broadband Dielectric Multilayered Reflectors
	14.1 Introduction
	14.2 Disordered One-Dimensional Photonic Structures
		14.2.1 Reflectance Spectra
		14.2.2 First-Order Statistical Analysis: Distribution Properties
		14.2.3 Second-Order Statistical Analysis: Autocorrelation Properties
	14.3 Searching for High-Performance Disordered Mirrors by Genetic Algorithm: Methods and Results
		14.3.1 Genetic Algorithms: Short Description
		14.3.2 First-Order Statistical Analysis: Distribution Properties
		14.3.3 Second-Order Statistical Analysis: Autocorrelation Properties
	14.4 Statistical Tools
		14.4.1 Statistical Tests and p-Values
		14.4.2 Kolmogorov–Smirnov Test
		14.4.3 Ljung–Box Test
		14.4.4 Correlation Coefficient: A Simple Rule-of-Thumb
	14.5 Conclusions
	References
15 Scattering from Reconfigurable Metasurfaces and Their Applications
	15.1 Modelling of Metasurfaces
	15.2 Self-Reconfigurable Metasurfaces for Power- and Wave-Form-Dependent Effects
		15.2.1 Non-Linear Metasurfaces for Power-Dependent Radiating Structures
		15.2.2 Non-Linear Metasurfaces for Waveform-Dependent Radiating Structures
	15.3 Reconfigurable Metasurfaces for Frequency Tunability of Antennas
		15.3.1 Antenna Impedance Tuning Through Metasurface Coatings
		15.3.2 Design of Varactor-Loaded Reconfigurable Metasurface
	15.4 Dynamic Metasurfaces for Frequency Harmonic Generation and Control
		15.4.1 Analog Dynamic Metasurfaces for Harmonic Generation
		15.4.2 Digital Dynamic Metasurfaces for Harmonic Generation
	15.5 Closing Remarks
	References
16 Specular Reflection and Transmission of Electromagnetic Waves by Disordered Metasurfaces
	16.1 Introduction
	16.2 Basics of Electromagnetic Scattering by Particles
		16.2.1 Wave Equations
		16.2.2 Lippmann–Schwinger Equation
		16.2.3 Transition Operator
		16.2.4 Dyadic Green Function in a Homogeneous Medium
		16.2.5 Scattering of a Planewave by a Particle
	16.3 Specular Reflection and Transmission by Particle Monolayers
		16.3.1 Multiple Scattering by Discrete Media
		16.3.2 Coherent and Incoherent Intensity
		16.3.3 Average Scattered Field
		16.3.4 Independent Scattering Approximation (ISA)
		16.3.5 Effective Field Approximation (EFA)
		16.3.6 Generalization to Particle Monolayers on Layered Substrates
	16.4 Numerical Validation of Theoretical Predictions
	16.5 Concluding Remarks
	References
17 Continuity of Field Patterns for Exceptional Surface Waves and Exceptional Compound Waves
	17.1 Introduction
	17.2  Unexceptional and Exceptional Surface Waves
		17.2.1 Theory: Canonical Boundary-Value Problem
			17.2.1.1 Preliminaries
			17.2.1.2 Half-Space z>0
			17.2.1.3  Half-Space z<0
			17.2.1.4 Boundary Conditions
		17.2.2 Numerical Studies
			17.2.2.1 Dyakonov Surface Waves
			17.2.2.2  Surface-Plasmon-Polariton Waves
	17.3 Unexceptional and Exceptional Compound Waves
		17.3.1 Theory: Canonical Boundary-Value Problem
			17.3.1.1 Preliminaries
			17.3.1.2 Half-Spaces z>D and z<0
			17.3.1.3 Bounded Region 0< z