Table Of ContentNew Foundations for
Applied Electromagnetics
The Spatial Structure of Fields
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New Foundations for
Applied Electromagnetics
The Spatial Structure of Fields
Said Mikki
Yahia Antar
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Cover design by John Gomes
ISBN 13: 978-1-60807-919-3
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Contents
Chapter1 GeneralOutlineandScopeoftheBook 1
1.1 Motivation 1
1.2 ThePresentStageofElectromagneticScience 4
1.3 FromStructuresinSpacetoSpaceStructures 7
1.4 TheRelevanceofSpatialStructurestothePresent
TechnologicalWorld 9
1.5 TheStructureoftheBook 12
1.5.1 PartI:TheTheoryofNearFields 12
1.5.2 PartII:TheAntennaCurrentGreen’sFunction 15
1.5.3 PartIII:NonlocalMetamaterials 17
1.5.4 PartIV:VariousApplications 18
I TheTheoryofElectromagneticNearFields 19
Chapter2 ReactiveEnergyandtheNearField 21
2.1 Introduction 21
2.2 ElectromagneticEnergyinAntennaTheory 23
2.3 OnReactiveEnergy 27
2.3.1 Introduction 27
2.3.2 BackgroundtotheConceptofReactiveEnergy 28
2.3.3 AGeneralizedApproachtoReactiveEnergy 31
2.3.4 TheLimitsoftheReactiveEnergyConceptandthe
NeedtoMoveBeyond 37
2.4 RemarksonStoredEnergy 38
v
vi Contents
2.5 BeyondReactiveEnergy 40
2.6 RelevanceofaFundamentalUnderstandingof
ElectromagneticEnergytoOtherMainstreamResearch
Directions 44
2.7 Conclusion 46
Chapter3 TheSpatialTheoryofElectromagneticFields 49
3.1 Introduction 49
3.1.1 MotivationsfortheSearchforaTheoryofAntenna
NearFields 49
3.1.2 PhilosophyoftheNewTheoreticalProgram 51
3.1.3 OverviewoftheChapter 53
3.2 General Consideration for Energetics and Power Flow in
AntennaSystems 54
3.3 TheStructureoftheAntennaNearFieldintheSpatial
Domain 57
3.4 DirectConstructionoftheAntennaNear-FieldStartingfrom
aGivenFar-fieldRadiationPattern 62
3.4.1 Introduction 62
3.4.2 MathematicalDescriptionoftheFar-FieldRadiation
PatternandtheConcomitantNear-Field 63
3.4.3 DerivationoftheExteriorDomainNear-Fieldfrom
theFar-FieldRadiationPattern 65
3.4.4 GeneralRemarks 68
3.5 APhenomenologicalExaminationoftheSpatialDistribution
ofElectromagneticEnergyintheAntennaExteriorRegion 70
3.5.1 Introduction 70
3.5.2 Self-InteractionoftheOutermostRegion(FarZone,
RadiationDensity) 70
3.5.3 Self-InteractionsoftheInnerRegions 71
3.5.4 Mutual Interaction Between the Outermost Region
andTheInnerRegions 71
3.5.5 MutualInteractionBetweenDifferentInnerRegions 73
3.5.6 SummaryandConclusion 74
3.6 TheConceptofReactiveEnergy:TheCircuitPointofView
ofAntennaSystems 74
3.6.1 Introduction 74
3.6.2 ConstructionoftheReactiveEnergyDensities 76
Contents vii
3.6.3 RemarksandGeneralDiscussion 79
3.6.4 AdditionalRemarks 80
3.6.5 AmbiguityoftheConceptofReactiveFieldEnergy 81
3.6.6 CriticalReexaminationoftheNear-FieldShell 83
3.7 Conclusion 85
3.8 AppendicesandSupplementaryMaterials 87
3.8.1 On the Uniform Convergence of the Energy Series
usingWilcoxExpansion 87
3.8.2 ComputationoftheFunctionsg4 (l,m),g5 (l,m),
n,n(cid:1) n,n(cid:1)
andg6 (l,m) 87
n,n(cid:1)
3.8.3 OnRearrangementoftheY /rnTermsinthe
lm
MultipoleExpansion 88
3.8.4 OnRearrangementofthe1/rnTermsinthe
MultipoleExpansion 96
Chapter4 TheSpectralTheoryofElectromagneticFields 99
4.1 Introduction 99
4.2 SpectralAnalysis ofAntenna Near Fields: The Concept of
Radialstreamlines 101
4.2.1 SpectralDecompositionUsingtheWeylExpansion 101
4.2.2 Concept of Propagation in theAntenna Near-Field
Zone 106
4.2.3 TheConceptofAntennaNear-FieldRadial
Streamlines 109
4.2.4 IndependenceoftheSpectralExpansionto
ArbitraryRotationAroundtheMainAxisof
Propagation/Nonpropagation 111
4.2.5 ThePropagatingandNonpropagatingPartsare
Maxwellian 113
4.2.6 SummaryandInterpretation 116
4.3 TheConceptofLocalizedandStoredEnergiesintheAntenna
ElectromagneticField 120
4.3.1 Introduction 120
4.3.2 GeneralizationoftheComplexPoyntingTheorem 120
4.3.3 TheMultifariousAspectsoftheEnergyFluxinthe
NearField 124
4.3.4 TheConceptofLocalizedEnergyinthe
ElectromagneticField 125
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4.3.5 TheRadialEvanescentFieldEnergyinthe
Near-FieldShell 126
4.3.6 Electromagnetic Interactions Between Propagating
andNonpropagatingFields 127
4.3.7 TheConceptofStoredEnergy 129
4.3.8 DependenceoftheRadialLocalizedEnergyonthe
ChoiceoftheOrigin 133
4.4 TheNear-FieldRadialStreamlinesfromtheFarFieldPoint
ofView 134
4.4.1 Introduction 134
4.4.2 GeneralizationoftheWeylExpansion 136
4.4.3 TheHybridWilcox-WeylExpansion 137
4.4.4 GeneralRemarks 140
4.5 TheMechanismofFarFieldFormation 141
4.6 Conclusion 143
4.7 AppendicesandSupplementaryMaterials 146
4.7.1 AbsoluteandUniformConvergenceoftheWeyl
Expansion 146
4.7.2 Interchange of Integration and Differentiation in
WeylExpansion 146
4.7.3 Exchange of Order of Integrations in the Radiated
FieldFormulaViatheSpectralRepresentationofthe
DyadicGreen’sFunction 147
4.7.4 DerivationoftheRotationMatrix 147
4.7.5 TheTime-DependentInteractionPoyntingTheorem 148
4.7.6 On the Divergence of the Total Evanescent Field
EnergywithFixedAxisofDecomposition 149
Chapter5 TheScalarAntennaNearField 155
5.1 Introduction 155
5.2 MotivationfortheStudyofStudyofScalarnear-fieldtheory 156
5.3 DevelopmentoftheRadialLocalizedNear-Field
Green’sFunction 158
5.4 DerivationoftheRadialLocalizedNear-Field
Green’sFunctionfortheScalarProblem 162
5.5 DiscussionoftheResultsandtheirPhysicalConsequences 163
5.6 TheCaseofMultipleScalarSources 170
5.7 Conclusion 172
Contents ix
Chapter6 MorphogenesisofElectromagneticRadiationinthe
Near-FieldZone 175
6.1 Introduction 175
6.1.1 PhilosophicalResume 175
6.1.2 GeneralScopeofthischapter 177
6.2 TheFundamentalProblemofMorphogenesisin
AntennaTheory 178
6.2.1 PropagationModelfortheAntennaFields 180
6.2.2 TheIdeaoftheAntennaPropagationPotential 186
6.2.3 TheFundamentalEvolutionEquationsofthe
AntennaNearFields 189
6.3 ComparisonwithThePoyntingFlow 191
6.4 TheRoleofSingularities 193
6.5 FromTheoreticalBiologytoAntennaEngineering 195
6.5.1 Epigenesis 197
6.5.2 Waddington’sCanalization 199
6.5.3 TheVirtualandtheActual 201
6.5.4 TheConceptoftheMorphogeneticField 205
6.6 Conclusion 206
II TheAntennaCurrentGreen’sFunction(ACGF)
Formalism 209
Chapter7 TheAntennaCurrentGreen’sFunctionFormalismasaParadigm 211
7.1 General Introduction: The Program of Electromagnetic
Systems 211
7.1.1 ExplanatoryAdequacyinScientificResearch 211
7.1.2 ContextandMotivations 213
7.1.3 OverviewofthePresentWork 217
7.1.4 FundamentalAssumptionaboutGeneral
ElectromagneticSystems 219
7.1.5 TheCirculationofInformationinGeneral
ElectromagneticSystems 220
7.1.6 TheInterrelationBetweenSynthesisandAnalysis 221
7.2 OutlineoftheGeneralProblemsofAntennaTheory 222
Chapter8 FoundationsoftheAntennaCurrentGreen’sFunctionFormalism 229
8.1 DefinitionofTheAntennaCurrentGreen’sFunction 229
