The Essence of Dielectric Waveguides

529 Pages·2008·7.982 MB·English

by  C. Yeh, F. Shimabukuro

The Essence of Dielectric Waveguides
C. Yeh F. I. Shimabukuro
•
The Essence of Dielectric
Waveguides
123
C.Yeh F.I.Shimabukuro
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(cid:176)c 2008SpringerScience+BusinessMedia,LLC
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To
OurFamilies
Vivian,John,andEvelyn;Siblings-Dorothy,Richard,andVicky
Karen,SusanandLee
PREFACE
“Itisourresponsibilityasscientists,knowingthegreatprogresswhichcomes
from a satisfactory philosophy of ignorance, the great progress which is the fruit
offreedomofthought,toproclaimthevalueofthisfreedom,toteachhowdoubtis
not to be feared but welcomed and discussed; and to demand this freedom as our
dutytoallcominggenerations”——RichardFeynman,1955——
First, as students from Cal Tech and MIT and then as researchers and teachers
from other universities and industry, we are benefited greatly from the philoso-
phy of learning practiced by these and other distinguished universities in the US,
namely,learnandteachthefundamentalsandnotthefashions.Underthisguiding
light, this comprehensive book was formed, covering the most important modern
topics on guided waves. As such, it may be used as a research reference book or
asatextbookforseniorundergraduatestudentsorfirst-yeargraduatestudents.The
lectures for an one-semester or one-quarter course on guided waves along surface
wave structures can begin with a review of EM fundamentals (Chap.2), and then
move on to a discussion on the general important and relevant characteristics of
theseguidedsurfacewaves(Chap.3).Thenfollowstherigorousanalytictreatment
for canonical structures (planar, circular, and elliptical) (Chaps.4–8). By the end
of these lectures, the students would have gained a very solid theoretical foun-
dation on this subject. Then the fun part starts. The students can now learn how
theymaymakeuseoftheirfundamentalknowledgetotreatthemanymodernup-
to-date applications: linear and nonlinear wave propagation in fibers, solitons in
fibers and WDM beams propagation in fibers (Chaps.9 and 10), plasmon (sub-
wavelength) waves (Chap.12), waves in periodic structures (photonic structures)
(Chap.13), surface waves on metamaterial (artificial material) and other exotic
(moving medium) structures (Chap.14). Finally, the students can now be intro-
duced to the many numerical approaches (Chap.15) that can be used on the vari-
ous guided wave structures, with the comforting knowledge that they possess the
necessarytheoreticalfoundationtocorrectlyinterpretthenumericaldata.
Substantialamountofthematerialofthetextappearsinbookformforthefirst
time. References are given to the original sources. However, unintentional over-
sightbyusisunavoidable.Forthistheauthorsoffertheirapologies.Itiscuriousto
note that many popular references (with many citations in the literature) may not
representthepaperspublishedbytheoriginatorsoftheconcepts.Specialcarehas
beentakenbyusnottofollowthiserroneouspath.Referencesarelistedattheend
ofeachchapterforclarityandeaseofusage.
Asfarasnomenclaturesandsymbolsareconcerned,wehavenotbeenableto
haveagivensymboltorepresentasingleuniqueentitythroughoutthewholebook.
viiiPreface
Instead, we only make sure that a given symbol clearly and uniquely represents a
single entity in that chapter. Whenever possible, universally accepted nomencla-
turesareusedtorepresentvectorandscalarquantities.
It is with deep gratitude and great pleasure for us to acknowledge the sig-
nificant guidance and encouragement given to us by Professors C. H. Papas,
J.R.Whinnery, and R. W. Gould. We also wish to acknowledge with special
thanks to Dr. Peter Siegel who introduced us to the field of terahertz research and
who planted the seed for us to pursue the writing of this book. Throughout our
professional careers, we benefited greatly from the many positive advice and en-
couragementfromourcolleagues.Weexpressourdeepestthanksandgratitudeto
them.Finally,weexpressoursincerestthankstoMarshallKwongforhisdedicated
professional graphic arts work for this book, without which this book would be
incomplete.
We greatly appreciate the careful reading and constructive comments by the
reviewers.
C.Yeh
F.I.Shimabukuro
LosAngeles
CONTENTS
1. Introduction..........................................................1
1.1 BriefHistoricalBackground ........................................ 1
1.2 ScopeofthisBook.................................................7
References........................................................8
2. FundamentalElectromagneticFieldEquations........................11
2.1 MaxwellEquations ............................................... 11
2.2 TheConstitutiveRelations.........................................13
2.2.1 SimpleMedium(LinearandIsotropic)........................14
2.2.2 AnisotropicMedium ........................................ 15
2.2.3 Left-HandedMedium(Metamaterial) ......................... 16
2.2.4 ConductingMedium.........................................16
2.2.5 DielectricMediumwithLoss.................................17
2.2.6 NonlinearMedium..........................................18
2.3 BoundaryConditions,RadiationCondition,andEdgeCondition.......20
2.3.1 BoundaryConditions........................................20
2.3.2 RadiationCondition.........................................28
2.3.3 EdgeCondition.............................................28
2.3.4 UniquenessTheorem........................................29
2.4 EnergyRelations:Poynting’sVectorTheorem.......................29
2.5 ClassificationofFields............................................32
2.5.1 TheDebyePotentials........................................33
2.5.2 BasicWaveTypes...........................................34
2.5.3 SeparationofVariables......................................39
2.5.3.1 RectangularCoordinates(x,y,z)......................39
2.5.3.2 CircularCylinderCoordinates(r,θ,z).................40
2.5.3.3 EllipticalCylinderCoordinates(ξ,η,z)................41
2.5.3.4 ParabolicCylinderCoordinates(ξ,η,z)................42
2.6 PolarizationofWaves.............................................44
2.6.1 LinearlyPolarizedWaves....................................44
2.6.2 CircularlyPolarizedWaves...................................44
2.6.3 EllipticallyPolarizedWaves..................................44
2.7 PhaseVelocityandGroupVelocity .................................44
2.8 TheImpedanceConcept...........................................46
2.9 ValidityoftheScalarWaveApproach...............................47
References.......................................................52
xContents
3. PropagationCharacteristicsofGuidedWavesAlongaDielectric
Guide...............................................................55
3.1 TypicalSurfaceWaveguideStructures .............................55
3.2 FormalApproachtotheSurfaceWaveguideProblems...............57
3.3 Theω-β Diagram:DispersionRelations............................59
3.4 GeometricalOpticsApproach.....................................62
3.5 AttenuationConstant.............................................65
3.5.1 SingleModeCase..........................................66
3.5.2 MultimodeCase...........................................68
3.6 SignalDispersionandDistortion..................................70
3.7 αandQ ........................................................ 76
3.8 ExcitationofModesonaDielectricWaveguide.....................79
3.8.1 ExcitationThroughDirectIncidence.........................79
3.8.1.1 IncidentPlaneWave................................81
3.8.1.2 IncidentGaussianBeam.............................82
3.8.2 ExcitationThroughEfficientTransitions......................85
3.9 CoupledModeTheory...........................................87
3.10 BendsandCornersforDielectricWaveguides ...................... 89
3.11 SystemsandNoise...............................................92
References......................................................96
4. PlanarDielectricWaveguides.........................................99
4.1 FundamentalEquations............................................99
4.2 DielectricSlabWaveguide........................................100
4.2.1 TheTMSurfaceWaveModes...............................101
4.2.1.1 CutoffConditionsforTMModes.....................103
4.2.1.2 DistributionofGuidedPower........................105
4.2.1.3 Attenuation........................................106
4.2.2 TheTESurfaceWaveMode ................................ 107
4.2.3 SpecialCasesandNumericalExamples......................109
4.3 LeakyWaveinaHeteroepitaxialFilmSlabWaveguide..............112
4.3.1 LeakyModesalonganAsymmetricDielectric
Waveguide................................................114
4.3.2 ApproximateSolutionsoftheCharacteristicEquations.........115
4.4 MultilayeredDielectricSlabWaveguides...........................118
4.5 CouplingBetweenTwoParallelDielectricSlabWaveguides ......... 122
4.6 TheSommerfeld–ZenneckSurfaceImpedanceWaveguide...........131
References......................................................135
Contentsxi
5. CircularDielectricWaveguides......................................137
5.1 FundamentalEquations .......................................... 138
5.2 ModesonUniformSolidCoreCircularDielectricCylinder..........139
5.2.1 DispersionRelations.......................................141
5.2.2 CutoffConditions..........................................144
5.2.3 Attenuation................................................147
5.2.3.1 TheExactApproach................................147
5.2.3.2 ThePerturbationApproach..........................148
5.2.4 FieldConfigurations........................................150
5.3 TheSommerfeld–GoubauWire...................................152
5.4 ModesonRadiallyInhomogeneousCoreCircularDielectric
Cylinder........................................................155
5.4.1 FormulationoftheProblem.................................155
5.4.2 SelectedExamples.........................................160
5.4.3 HollowCylindricalDielectricWaveguide.....................165
5.5 ExperimentalDeterminationofPropagationCharacteristics
ofCircularDielectricWaveguides.................................167
5.5.1 UltrahighQDielectricRodResonantCavity..................167
5.5.2 MeasuredResults..........................................172
5.6 SummaryandConclusions ....................................... 176
References......................................................177
6. EllipticalDielectricWaveguides.....................................179
6.1 FormulationoftheProblem.......................................180
6.2 BoundaryConditions ............................................ 184
6.3 ModeClassifications.............................................188
6.4 TheDispersionRelations.........................................189
6.4.1 CutoffFrequenciesofModes................................197
6.4.2 TransitiontoCircularCross-Section ......................... 199
6.4.3 ApproximateCharacteristicEquations ....................... 201
6.4.4 PropagationCharacteristics.................................203
6.4.4.1 TheEvenDominant HE Mode .................... 204
e 11
6.4.4.2 TheOddDominant HE Mode.....................205
o 11
6.4.4.3 HigherOrdere,oHEn(cid:1)m(cid:1) Modes ...................... 206
6.4.5 FieldConfigurationsoftheDominantModes ................. 207
6.4.6 AttenuationCalculation.....................................209
6.5 WeaklyGuidingEllipticalDielectricWaveguides...................210
6.6 ExperimentalResults ............................................ 214
6.7 Comments......................................................218
References......................................................218