Table Of ContentBoris Z. Katsenelenbaum
High-frequency Electrodynamics
High-frequencyElectrodynamics.BorisZ.Katsenelenbaum
Copyright(cid:1)c 2006WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
ISBN:3-527-40529-1
Boris Z. Katsenelenbaum
High-frequency Electrodynamics
WILEY-VCH Verlag GmbH & Co. KGaA
The Author All books published by Wiley-VCH are carefully
Prof. Dr. Boris Z. Katsenelenbaum produced. Nevertheless, authors, editors, and
Nahariya, Israel publisher do not warrant the information
contained in these books, including this book, to
be free of errors. Readers are advised to keep in
The Editor/Translator mind that statements, data, illustrations,
Prof. Dr. N. N. Voitovich procedural details or other items may
Institute of Applied Problems of Mechanics and inadvertently be inaccurate.
Mathematics NASU, Lviv, Ukraine
Library of Congress Card No.:
Cover applied for
MaX-1 simulation by Christian Hafner
http://www.wiley.co.uk/max-1/
British Library Cataloguing-in-Publication
Data
A catalogue record for this book is available from
the British Library.
Bibliographic information published by
Die Deutsche Bibliothek
Die Deutsche Bibliothek lists this publication in
the Deutsche Nationalbibliografie; detailed
bibliographic data is available in the Internet at
<http://dnb.ddb.de>.
(cid:164) 2006 WILEY-VCH Verlag GmbH & Co. KGaA,
Weinheim
Printing betz-druck GmbH, Darmstadt
Binding Schäffer GmbH, Grünstadt
All rights reserved (including those of translation
into other languages). No part of this book may be
reproduced in any form – by photoprinting,
microfilm, or any other means –nor transmitted or
translated into a machine language without
written permission from the publishers.
Registered names, trademarks, etc. used in this
book, even when not specifically marked as such,
are not to be considered unprotected by law.
Printed in the Federal Republic of Germany
Printed on acid-free paper
ISBN-13: 978-3-527-40529-9
ISBN-10: 3-527-40529-1
V
Contents
Preface XI
1 TheMaxwellEquations 1
1.1 Complexamplitudes 1
1.1.1 Harmonic(monochromatic)oscillations 1
1.1.2 Complexamplitudes 2
1.1.3 Theperiod-averageproductoftwoharmonicfunctions 3
1.2 TheMaxwellequations 4
1.2.1 Theconductioncurrentandtheextrinsiccurrent 4
1.2.2 TheMaxwellequations 5
1.2.3 Dielectricpermittivityandmagneticpermeabilityofamedium 6
1.2.4 Thepolarizationcurrent 7
1.2.5 Thefrequencydispersionandthespatialdispersion(chirality) 10
1.2.6 Complexpermittivity 11
1.2.7 Theradiationcondition 12
1.2.8 Thewaveequations 14
1.2.9 Thereciprocityconditions 16
1.2.10 Averageenergylosses 18
1.2.11 Thedispersionrelations 19
1.3 Idealizedobjects 22
1.3.1 Interfaceoftwomedia 22
1.3.2 Theimpedance(one-side)boundaryconditions 24
1.3.3 Skinlayer 24
1.3.4 Idealconductor 27
1.3.5 Singularitiesoffieldsneartheedgeorvertex 28
1.3.6 Thelinecurrentandthepointcurrent 32
1.4 Uniquenessandexistenceofsolution 35
1.4.1 Uniquenessofsolution 35
1.4.2 Violationoftheuniquenesstheorem: eigenoscillations 38
High-frequencyElectrodynamics.BorisZ.Katsenelenbaum
Copyright(cid:1)c 2006WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
ISBN:3-527-40529-1
VI Contents
2 PlaneWaves 41
2.1 Planewavesinaninfinitehomogeneousmedium 41
2.1.1 Thephasevelocity 41
2.1.2 Theellipticpolarization 43
2.1.3 Eigenwavesinchiralmedia 45
2.1.4 Turningofthepolarizationplaneinthechiralmedia 47
2.1.5 Thegroupvelocity 48
2.1.6 Therelativityrestrictionsonthepropagationfactor 50
2.2 Planewavesinaplano-layeredmedium 52
2.2.1 Mediumwithconstantwaveresistance 52
2.2.2 Theslowlyvaryingwaveresistance 55
2.2.3 Theperiodicallayer 57
2.2.4 Nonreflectingcoating 59
2.2.5 Theobliqueincidence 61
2.2.6 Plano-parallelchiralmedium 64
2.2.7 Mediawithε <0,µ <0 66
3 ClosedWaveguides 71
3.1 Eigenmodesinnonfilledwaveguides 71
3.1.1 Eigenmodes 71
3.1.2 TheTM-,TE-,andTEM-modes 74
3.1.3 Thefunctionalorthogonalityofthefieldsofeigenmodes 75
3.1.4 TheelectricandmagneticHertzvectors 77
3.1.5 Rectangularwaveguides 78
3.1.6 Circularwaveguides 81
3.1.7 Multiple-connectedcross-sections 83
3.2 Wavesinwaveguideswithnonhomogeneouscross-section
filling 86
3.2.1 Nonhomogeneousfillingandimpedancewalls 86
3.2.2 Wavenumberinimpedancewaveguide 87
3.2.3 Lossesinimpedancewaveguide 91
3.2.4 Orthogonalitycondition 93
3.2.5 Complexandassociatedmodes 95
3.3 Excitationofclosedwaveguides 97
3.3.1 Excitationbyextrinsiccurrent 97
3.3.2 Theslotexcitationandend-planeexcitation 100
3.3.3 Integrationintheplaneofacomplexvariable 102
3.4 Nonregularclosedwaveguides 108
3.4.1 Thecross-sectionmethod 108
3.4.2 Slowlyvaryingparameters 113
3.4.3 Thediaphragm: equationforfieldintheslot 116
3.4.4 Thediaphragm: equationforcurrentonstrips 119
Contents VII
3.4.5 Diffractiononthescreenwithahole 120
3.4.6 Openendofwaveguide 125
4 ClosedResonators 129
4.1 Resonatorswithideal-conductingwalls 129
4.1.1 Waveguideresonatorswithoutfilling 129
4.1.2 Resonatorsofarbitraryshape 132
4.1.3 Calculationofeigenfrequencies 134
4.1.4 Variationaltechnique 136
4.1.5 Excitationofresonators 139
4.2 Resonatorswithimpedancewalls 143
4.2.1 Complexeigenfrequencies 143
4.2.2 Displacementofeigenfrequencies 146
4.2.3 Impedanceasaspectralparameter 147
5 OpenLines 151
5.1 Dielectricwaveguides 151
5.1.1 Circulardielectricwaveguides 151
5.1.2 Eigenmodesofdielectricwaveguideswitharbitrary
cross-section 154
5.1.3 Excitationofdielectricwaveguides 157
5.1.4 Nonregulardielectricwaveguides 163
5.1.5 Theopticalfiber 166
5.2 Thelineswithsurfacewave 170
5.2.1 Nonidealmetalliccylinder 170
5.2.2 Theidealmetalliccylindercoveredbyathindielectriclayer 173
5.2.3 Theshort-periodicalsurface 175
5.2.4 Thecorrugatedsurface 178
5.2.5 Slowwavesinclosedwaveguides 181
5.2.6 Thehelixline;thearray 184
5.2.7 Themicrostripline 187
5.3 Thewavebeam 189
5.3.1 Thewavebeam 189
5.3.2 Parabolicequation 193
5.3.3 Theenergytransmissioncoefficient 195
5.3.4 Optimalantennaandrectennashapes 198
5.3.5 Fieldsintherectennaplane 201
5.3.6 Freephaseofdesiredfieldonrectenna 203
5.3.7 Thelensline 206
6 BackgroundsofAntennaTheory 211
6.1 Radiationofcurrentset 211
VIII Contents
6.1.1 Theelementaryelectricdipoleandmultipole 211
6.1.2 Fieldofarbitrarycurrents 215
6.1.3 Theelementarymagneticdipoleandmultipole 218
6.1.4 Thehalf-wavevibrator 219
6.1.5 Themultivibratorantenna 224
6.2 Apertureantennas 225
6.2.1 Radiationfromaperture 225
6.2.2 TheGreenfunctionmethod 228
6.2.3 Theradiationpattern 230
6.2.4 Inverseproblem 232
6.2.5 Thenearfieldzone,Fresnelzone,andfarfieldzone 234
6.2.6 Geometricoptics 236
6.3 Volumeantennas 239
6.3.1 Radiationfromholes 239
6.3.2 Fieldinnarrowlongslot 243
6.3.3 Resonantantennas 245
6.3.4 Transparencyofshort-periodicalarray 247
6.3.5 Dielectricantennas 249
6.3.6 Theinverseproblemforvolumeantennas 253
6.3.7 Analyticalcontinuationofthefield 257
7 DiffractiononMetallicandDielectricObjects 261
7.1 Diffractionoftheplanewaveoncircularwaveguide 261
7.1.1 Scalarpotentials 261
7.1.2 Thevariableseparationmethod: theRayleighseries 262
7.1.3 TheWatsonseries 264
7.1.4 Dielectriccylinder 269
7.2 Diffractiononmetallichalf-plane 271
7.2.1 Usageofthevariableseparationmethod 271
7.2.2 Currentsonmetallicsurface 273
7.2.3 Thefarfield 274
7.3 TheDebyepotentials: diffractiononametallicsphere 277
7.3.1 TheDebyepotentials 277
7.3.2 TheDebyepotentialsforfieldsofelementarysources 278
7.3.3 Fieldsofelementarysourceslocatedatpointwithcomplex
coordinates 279
7.3.4 Diffractionoftheplanewaveonmetallicsphere:theRayleigh
series 281
7.3.5 Smallsphere:dipolemomenta 284
7.3.6 Largesphere: theWatsonseries 285
7.4 Smallbodies;largebodies 288
7.4.1 Diffractiononthebodywithnoncoordinatesurface 288
Contents IX
7.4.2 Smallmetallicbodies 291
7.4.3 Thedualityprinciplefortheholeinplainscreen 294
7.4.4 Thinmetalliccylinderofarbitrarycross-section: the
H-polarization 298
7.4.5 Thinmetalliccylinderofarbitrarycross-section: the
E-polarization 300
7.4.6 Thecurrentonametallicsurfaceofsmallcurvature 304
7.4.7 Raystructureofthefieldinshadow: geometro-opticaltheoryof
diffraction 306
7.4.8 Themethodofauxiliarysources 308
7.4.9 Theopticaltheorem 312
7.4.10 Spectralmethodforthediffractionproblems 316
GeneralReferences 321
ComplementaryReferences 322
Index 325
XI
Preface
The subject of this book is the lawsof formation and propagationof electro-
magnetic waves. It is an advanced textbook for college and university stu-
dents,PhDstudents,andscientists.
Two main objectives were set by the author when writing this book. The
first one consists in relatively complete description of the modern state of
high-frequencyelectrodynamics. Studyingthe book should give areaderan
abilitytounderstandthemonographsandjournalarticlesofthisfieldaswell
as to take an active part in conferences and seminars. In particular, certain
brevity of the derivation is caused by this objective. Almost throughout the
book all intermediate derivations are omitted and replaced by their descrip-
tions. Carryingoutoftheomittedderivationbyareaderisprobablythebest
waytohave anin-depthstudyof the subject. Inthe bookthe qualitative so-
lutiontoaproblemanditsanalysisareoftengivenrightafterformulatingthe
problemandonlythenderivationofthesolutioniscarriedout. Anewideais
understoodeasierifitisformulatedandanalyzedatthesametime,whereas
thelogicofderivationismoreeasilygraspedifthereaderknowstowhatheor
sheisled. Besides,havingfamiliarizedhimselfor herselfonly withproblem
formulationandresult,thereadermayomitderivations.
Thesecondobjectivechallengingtheauthoristogiveareaderwhohasal-
readystudiedelectrodynamicswithinageneraluniversitycourseofphysics,
the foundation sufficient for enabling him or her to work on some practical
problemsofthis type. The structureof thebook isdeterminedbythisobjec-
tive.
High-frequency electrodynamics is a common area of physics and mathe-
matics(being,ontheauthor’sopinion,abranchofphysics). Thephysicalap-
proachconsistsinmaximally“nondestructive”simplificationpermittingusto
replacetherealproblembyacertainidealizedonewhichpreservesall“essen-
tial” peculiarities of the realproblem, but can be exactly solved. The notion
“essential”cannotbedeterminedformally.Formulationoftheidealizedprob-
lemcannotbe algorithmized. Itshould relyonexperience,imagination, and
intuition. The mathematicalapproachconsists in quantitative description of
High-frequencyElectrodynamics.BorisZ.Katsenelenbaum
Copyright(cid:1)c 2006WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
ISBN:3-527-40529-1
XII Preface
the idealizedmodel with exactlyformulated properties. The question about
thedegreeofconsistencybetweenthemodelandtherealobjectisnotasubject
ofmathematics.
Study of the high-frequency electrodynamics can be carried out in two
ways: byfollowingthe investigationobjectsor thesolutionmethodsforcor-
respondingproblems. Thefirstway, usualinphysics textbooks, ischosen in
thebook.
Methods of diffraction theory are described, as a rule, in connection with
solving certain electrodynamic problems arisen when developing different
practical devices. Exposition of these methods is always very brief; it only
delivers the main idea to a reader and indicates the branch of mathemati-
calphysics, and the notions used in the methods. Detailed derivation of the
diffractiontheorybasiswouldonlyincreasethesizeofthebookalmosttwice.
Thebookcanbeusedforgettingfamiliarizedwithaconcreteproblemwith-
out studying the whole discipline. For instance, it is not obligatory to know
the theory of open resonators when developing antireflection coatings. The
background material, necessary for reading, is given in severalfirst sections
ofeachchapter.
Ofcourse,theauthordoesnotpretendtothecompletecoveringofthesub-
jectannouncedinthebooktitle. Expositionofthewholehigh-frequencyelec-
trodynamicsincludingthenumericalmethodseveninabriefstylesimilarto
thatinthisbookwouldtakethreetofourvolumeslikethisone. Detailedanal-
ysisofanumberofparticularproblemsrequirescreationofthewholelibrary
suchas,forinstance,theIEEEseries. Selectionofproblemsincludedintothe
bookisdeterminednotonlybytheirsignificancebutalsobythescientificin-
terestsoftheauthor.
Asanautonomousscience,high-frequencyelectrodynamicswasformedin
thefortiesofthelastcentury. Appearanceofradiolocationasawayofthetar-
getdeterminationinair,onground,andseawasthemainstimulusofworks
in this field. In these years novel theories were developed such as antenna
theory, including multivibrator and parabolic (mirror) antennas, the theory
ofwaveguideelements,theoryofradiowavepropagation,accountingnonho-
mogeneityandcurvatureofthegroundsurfaceaswellasatmospherenonho-
mogeneity,etc. Ofcourse,classicaldiffractionproblems(oncylinder,sphere,
half-plane)andthoseconnectedwithsignaltransmissionbymeansofmega-
hertzwaveshavebeensolvedearlier,butthisdirectionhasnotbeendevelop-
ingintensively.
In these years, as well as nowadays, development of science was stimu-
latedbymilitaryinvestmentswhereasthescientificinterestsweresecondary
consequencesofworksonthe“defence”objectives. Thissituationisnotonly
immoralandeconomicallyinexpedientbutalsoillogical. However,probably,
it has always existed. Even Archimedes was a military engineer in a mod-
