Plane-Wave Theory of Time-Domain Fields: Near-Field Scanning Applications (IEEE Press Series on Electromagnetic Wave Theory) PDF
Preview Plane-Wave Theory of Time-Domain Fields: Near-Field Scanning Applications (IEEE Press Series on Electromagnetic Wave Theory)
PLANE-WAVE THEORY OF TIME-DOMAIN FIELDS IEEEPRESSSERIESONELECTROMAGNETICWAVETHEORY The IEEE Press Series onElectromagneticWaveTheoryconsistsofnewtitles aswell as reprintingsandrevisionsofrecognizedclassicsthat maintainlong-termarchival significance inelectromagneticwavesand applications. SeriesEditor AssociateEditors DonaldG.Dudley ElectromagneticTheory,Scattering, and Diffraction UniversityofArizona EhudHeyman Tel-AvivUniversity DifferentialEquationMethods AdvisoryBoard AndreasC.Cangellaris Robert E.Collin UniversityofIllinois,Urbana-Champaign CaseWestern ReserveUniversity Integral EquationMethods DonaldR.Wilton Akira Ishimaru UniversityofHouston UniversityofWashington Antennas, Propagation, andMicrowaves D.S.Jones David R.Jackson UniversityofDundee UniversityofHouston BOOKSINTHEIEEEPRESSSERIESONELECTROMAGNETICWAVETHEORY Chew,W.C., Wavesand FieldsinInhomogeneousMedia Christopoulos,C., TheTransmission-LineModelingMethods: TLM Clemmow, P.C., ThePlane WaveSpectrum RepresentationofElectromagneticFields Collin, R.E., FieldTheory ofGuidedWaves,SecondEdition Dudley, D.G.,MathematicalFoundationsforElectromagneticTheory Elliott, R.S.,Electromagnetics: History, Theory,andApplications Felsen, L.B., and Marcuvitz,N., Radiationand ScatteringofWaves Harrington, R.F.,Field ComputationbyMomentMethods Hansen, T.B., andYaghjian,A.D., Plane-WaveTheory ofTime-Domain Fields:Near-Field ScanningApplications Jones, D.S.,Methods inElectromagneticWavePropagation, SecondEdition Lindell, I.V.,MethodsforElectromagneticFieldAnalysis PetersonetaI.,ComputationalMethodsfor Electromagnetics Tai,c.T.,GeneralizedVectorand DyadicAnalysis:AppliedMathematics inFieldTheory Tai,C.T.,Dyadic GreenFunctions inElectromagneticTheory, SecondEdition VanBladel, J.,SingularElectromagneticFields and Sources VolakisetaI.,FiniteElementMethodforElectromagnetics:Antennas, Microwave Circuits, and ScatteringApplications Wait,J.,ElectromagneticWavesinStratifiedMedia PLANE-WAVE THEORY OF TIME-DOMAIN FIELDS Near-Field Scanning Applications IEEE Press Series on Electromagnetic Wave Theory Thorkild B. Hansen Schlumberger-Doll Research Ridgefield, Connecticut Arthur D. Yaghjian Visiting Scientist AirForceResearch Laboratory Hanscom AFB, Massachusetts IEEE Antennas & Propagation Society, Sponsor • IEEE PRESS The InstituteofElectricalandElectronicsEngineers,Inc., NewYork This bookand otherbooks may bepurchasedatadiscount from thepublisherwhen orderedinbulk quantities. Contact: IEEE Press Marketing Attn: SpecialSales Piscataway,NJ 08855-1331 Fax: (732) 981-9334 For more informationaboutIEEEPRESS products, visit theIEEEPress HomePage: http://www.ieee.org/organizations/pubs/press © 1999bythe InstituteofElectricaland ElectronicsEngineers,Inc. 3ParkAvenue, 17thFloor, NewYork,NY 10016-5997 Allrights reserved. Nopartofthisbookmay be reproducedinanyform, normay itbestoredina retrieval systemor transmittedinanyform, withoutwritten permissionfrom thepublisher. Printedinthe UnitedStatesofAmerica 10 9 8 7 6 5 4 3 2 ISBN0-7803-3428-0 IEEEOrderNumber: PC5702 LibraryofCongressCataloging-in-PublicationData Hansen,Thorkild, 1965- Plane-wavetheoryoftime-domainfields: near-fieldscanning applications / ThorkildB.Hansen,ArthurD.Yaghjian. p. em. -- (IEEEPress series onelectromagneticwavetheory) "IEEEAntennas& PropagationSociety, sponsor." Includesbibliographicalreferencesand index. ISBN 0-7803-3428-0 1. Antennas (Electronics)--Mathematicalmodels. 2. Electromagneticfields--Mathematicalmodels. 3. Time-domain analysis. 4. Green'sfunctions. 5. Electro-acoustictransducers- -Mathematicalmodels. I. Yaghjian,ArthurD. II. IEEEAntennas and PropagationSociety. III. Title. IV. Series. TK7871.6.H352 1999 621.382'4--dc21 99-17759 CIP A. D.Yaghjian dedicates this book to the memory ofhis father, NubarYaghjian IEEE Press 445 Hoes Lane, ~O. Box 1331 Piscataway,NJ 08855-1331 IEEE Press EditorialBoard RobertJ.Herrick,EditorinChief J.B.Anderson S.Furui P.Laplante P.M.Anderson A.H. Haddad M.Padgett M. Eden S.Kartalopoulos W.D. Reeve M.E.El-Hawary D. Kirk G.Zobrist Kenneth Moore,DirectorofIEEEPress Karen Hawkins,ExecutiveEditor LindaMatarazzo,AssistantEditor SurendraBhimani,ProductionEditor IEEEAntennas& PropagationSociety, Sponsor AP-S LiaisontoIEEE Press, RobertMailloux Cover design: WilliamT.Donnelly, WTDesign TechnicalReviewers Ehud Heyman, Tel-AvivUniversity, Israel Ali Sadigh, IBM, HopewellJunction, NewYork Contents Preface xiii Acknowledgments xv Chapter1 Introduction 1 Chapter2 ElectromagneticandAcousticField Equations 7 2.1 Time-DomainElectromagneticField Equations 8 2.1.1 First-OrderDifferentialEquations 9 2.1.2 Second-OrderDifferentialEquations 12 2.1.3 Causality 12 2.1.4 EquivalenceofFirst-andSecond-OrderDifferentialEquations 13 2.1.5 UniquenessofSolution 16 2.1.6 ExistenceofSolution 19 2.1.7 VolumeIntegral ExpressionsfortheElectricandMagnetic Fields 25 2.1.8 Electric andMagnetic Fields ofaMoving PointCharge 27 2.1.9 Surface Integral ExpressionsfortheElectric andMagnetic Fields (Huygens' Sources) 30 2.1.10 Force-PowerandMomentum-EnergyRelations 36 Force andPower with PolarizationDensities Included 37 Force andPowerforAmperian Dipoles 41 Force andPowerforMagnetic-ChargeModel ofMagneticDipole 44 Force and PoweronPolarizationDensities Derived from Point-Dipole Force andPower 45 Electromagnetic Momentumand Energy 48 2.2 Time-DomainAcoustic Field Equations 52 2.2.1 First-OrderLinear DifferentialEquations 52 2.2.2 Second-OrderDifferentialEquations 54 2.2.3 Equivalence ofFirst- andSecond-OrderDifferentialEquations 55 2.2.4 UniquenessofSolution 56 2.2.5 ExistenceofSolution 58 2.2.6 VolumeIntegral Expressionsforthe PressureandVelocityFields 62 2.2.7 Surface Integral Expressions forthePressure andVelocityFields (Huygens' Sources) 65 2.2.8 Wave-Force,Wave-Momentum,Power,andEnergy Relations 68 2.3 Frequency-DomainElectromagneticField Equations 70 2.3.1 FourierTransforms 70 2.3.2 First-OrderDifferential Equations 72 vii viii Contents 2.3.3 Second-OrderDifferentialEquations 74 2.3.4 Equivalence ofFirst- andSecond-OrderDifferentialEquations 74 2.3.5 UniquenessofSolution 75 2.3.6 ExistenceofSolution 79 2.3.7 VolumeIntegral ExpressionsfortheElectricandMagneticFields 80 2.3.8 Surface Integral Expressionsfor theElectric andMagneticFields (Huygens' Sources) 81 2.3.9 Time-Average Force andPower 83 2.4 Frequency-DomainAcoustic Field Equations 87 2.4.1 First-OrderLinearDifferentialEquations 87 2.4.2 Second-OrderDifferentialEquations 87 2.4.3 Equivalence ofFirst- andSecond-OrderDifferentialEquations 88 2.4.4 UniquenessofSolution 88 2.4.5 ExistenceofSolution 89 2.4.6 VolumeIntegral ExpressionsforthePressureandVelocityFields 90 2.4.7 Surface Integral ExpressionsforthePressure andVelocityFields (Huygens' Sources) 91 2.4.8 Time-AverageWaveForce andPower 92 2.5 Equationsfor Lossy Media 93 2.5.1 ElectromagneticFields 94 Frequency Domain 94 TimeDomain 96 Dispersion Relations 97 2.5.2 Acoustic Fields 99 Frequency Domain 99 TimeDomain....................................................................................................... 101 Chapter3 Frequency-DomainRepresentations 103 3.1 Green'sFunctionRepresentations 105 3.1.1 Far-FieldExpressions 108 3.1.2 Low-FrequencyBehavioroftheFar-FieldPatterns 112 3.2 Plane-WaveSpectrumRepresentations 112 3.2.1 PropagatingandEvanescentFields ofaPoint Source- 117 e ObservationPointswith = 0 117 e ObservationPointswith0< <nl2 118 e Observation Pointswith =nl2 120 3.2.2 SpectrumGiveninTermsoftheSources 122 3.2.3 SingularitiesandAsymptoticBehavioroftheSpectrum 124 3.2.4 AnalyticityofSpectrum,Far-FieldPattern, andFields 126 Analyticity oftheSpectrum andtheFar-FieldFunction 126 Analyticity oftheFar-FieldPattern 127 Analyticity oftheFields 128 3.2.5 Far-FieldExpressions 128 e FarFieldsfor =0 129 FarFieldsfor0<()<nl2 130 e FarFieldsfor =nl2 132 PowerRadiated intotheHemisphere 133 3.2.6 NearFields inTermsoftheFarFields inSphericalCoordinates 135 3.2.7 HomogeneousFields 138 InverseSource Formulas 141 Contents ix 3.2.8 MinimumSource Region for aGiven Far-FieldPattern 143 Circular-DiskAcousticRadiator 145 3.2.9 Power andMomentum-Flux(Radiation-Force)Relations 146 3.3 Lossy Media 150 Chapter4 StaticElectricandMagneticFields 155 4.1 Green'sFunctionRepresentationsfor the Static ElectricField 156 4.1.1 ExpressionsInvolvingthe Static ElectricFieldonaClosedSurface 157 4.1.2 ExpressionsInvolvingthe Static ElectricFieldinaPlane 160 4.2 Green'sFunctionRepresentationsforthe Static MagneticField 165 4.2.1 ExpressionsInvolvingthe Static MagneticField onaClosedSurface ..166 4.2.2 ExpressionsInvolvingthe Static MagneticFieldinaPlane 166 4.3 Plane-Wave SpectrumRepresentations 167 4.3.1 Static ElectricField 167 4.3.2 Static MagneticField 171 Chapter5 Time-DomainRepresentations 173 5.1 Green'sFunctionRepresentations 174 5.1.1 Derivationfrom theFourierTransform 174 5.1.2 Derivationfrom Time-DomainGreen'sFunctions 176 5.1.3 Velocity and MagneticField inTerms ofPressureandElectricField 179 5.1.4 Far-FieldExpressions 182 5.1.5 Far Fields IntegratedoverTime 188 5.2 Time-DomainAnalogs ofthePlane-Wave SpectrumRepresentations 190 5.2.1 PropagatingandEvanescentFields of aPoint Source 197 e ObservationPoints with = 0 198 e ObservationPoints with0< <nl2 198 e ObservationPoints with = nl2 199 The Rectangular-Pulse Point Source 199 5.2.2 SpectrumGiven inTermsofthe Sources 201 5.2.3 Singularitiesofthe Spectrum 205 5.2.4 Analyticityofthe Far-FieldPattern and ItsRelation totheFar-FieldFunction 208 Propertiesofthe Far-FieldPattern 208 Relationsbetweenthe Far-FieldPattern andthe Far-FieldFunction 210 Example 211 Electromagnetic Fields 211 5.2.5 Far-FieldExpressions 212 e Far Fields for0 ::; <rr/2 212 FarFields for e=rr/2 212 5.2.6 Near Fields inTerms oftheFarFields inSphericalCoordinates 213 5.2.7 Energy and MomentumRelations 218 Time-Domain AntennaParameters 221 5.3 Analytic-SignalAnalogs ofthePlane-Wave SpectrumRepresentations 222 5.3.1 SpectrumGiven inTermsofthe Sources 226 5.3.2 Singularitiesofthe Spectrum 228 5.3.3 Analyticity ofthe Far-FieldPattern andtheFar-FieldFunction 229 Propertiesofthe Far-Field Pattern 230 x Contents Properties oftheFar-Field Function 231 Relations between theFar-Field Pattern andtheFar-Field Function 231 Example 232 Electromagnetic Fields 232 5.3.4 Far-Field Expressions 233 e FarFieldsfor0~ <rc/2 233 FarFieldsfor e=rc/2 234 5.3.5 NearFields inTermsofFarFields inSpherical Coordinates 234 5.4 ElectromagneticMissiles 236 5.4.1 EMMissiles forAcceleratingPoint Charges 237 5.4.2 EM Missiles for aContinuumofCurrentandfor Huygens' Sources 239 5.4.3 Fields from aCircularDisk ofUniform Surface Current 241 Current withDelta-FunctionTimeDependence(Impulse Response) 245 Current withUnit-Step Time Dependence 247 5.4.4 ConcludingRemarks onElectromagneticMissiles 250 Chapter6 ProbeCorrectioninthe FrequencyDomain 253 6.1 AcousticFields 256 6.1.1 Derivation from theHelmholtzEquation 258 6.1.2 FormulasforReciprocalProbes 261 6.2 ElectromagneticFields 262 6.2.1 Derivation from theHelmholtzEquation 264 6.2.2 FormulasforReciprocalProbes 266 6.2.3 TheReciprocalElementaryElectricDipole Probe 268 Chapter7 ProbeCorrectionin theTimeDomain 271 7.1 AcousticFields 273 7.1.1 FormulasObtainedfrom theFourierTransform 275 7.1.2 FormulasObtainedDirectlyintheTimeDomain 276 7.1.3 Derivationfrom theWaveEquation 278 7.1.4 FormulasforTime-Derivative Probes 280 7.1.5 FormulasforReciprocalProbes 282 Reciprocal Time-Derivative Probes 283 7.2 ElectromagneticFields 284 7.2.1 FormulasObtainedfrom theFourierTransform 284 7.2.2 FormulasObtainedDirectlyintheTimeDomain 287 7.2.3 Derivationfrom the WaveEquation 287 7.2.4 FormulasforD-Dot Probes 289 7.2.5 FormulasforReciprocalProbes 291 Reciprocal D-Dot Probes 292 7.2.6 The ReciprocalElementaryElectric Dipole Probe 293 7.2.7 AReciprocalProbe with aFrequency-IndependentFarField 296 Chapter8 SamplingTheoremsand ComputationSchemes 297 8.1 Frequency-DomainSamplingTheoremsandComputationSchemes 298 8.1.1 Acoustic Fields Computedfrom thePressureintheScan Plane 299 Number ofOperations 302
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