Electromagnetic Fields in Stratified Media

229 Pages·2009·3.568 MB·English

by  Prof. Kai Li (auth.)

ADVANCED TOPICS
IN SCIENCE AND TECHNOLOGY IN CHINA
ADVANCED TOPICS
IN SCIENCE AND TECHNOLOGY IN CHINA
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and physics.
Kai Li
Electromagnetic Fields in
Stratified Media
With 100 figures
AUTHOR:
Prof. Kai Li,
TheElectromagneticsAcademy
ZhejiangUniversity
YuquanCampus,Hangzhou
310027,China
E-mail:[email protected]
ISBN 978-7-308-06401-9 Zhejiang University Press, Hangzhou
ISBN 978-3-540-95963-2 Springer Berlin Heidelberg New York
e-ISBN 978-3-540-95964-9 Springer Berlin Heidelberg New York
Series ISSN 1995-6819 Advanced topics in science and technology in China
Series e-ISSN 1995-6827 Advanced topics in science and technology in China
Library of Congress Control Number: 2009920460
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Preface
The properties of the electromagnetic field over the boundary between two
differentmedialikeearthandairaremuchmorecomplicatedwhenthesource
isonorneartheboundarythanwhenitisfarawayandtheincidentwavesare
planewaves.Thissubjecthasbeenintensivelyinvestigatedforoveracentury.
In the pioneering works of Zenneck and Sommerfeld, analytical solutions are
carried out based on a flat-Earth model. With myriad practical applications
in subsurface and close-to-the-surface communications, radar, and geophysi-
cal prospecting and diagnostics, the subject has been investigated widely and
the findings have been summarized in the classic book Dipole radiation in
the presence of a conducting half-space by Ban˜os (Pergamon Press, Oxford,
1966). Lately, investigations are conducted to extend the two-layered case to
three-layered and multi-layered cases, with a long series of papers published.
The details of the research findings are well summarized in the book Elec-
tromagnetic waves in stratified media by Wait (Pergamon Press, New York,
1970) and the book Lateral Electromagnetic Waves by King, Owens, and Wu
(Springer-Verlag, 1992).
In the past decade, the existence or nonexistence of trapped-surface-wave
terms in the solution for a dipole radiating over a dielectric-coated lossy un-
derling medium continued to be a controversial subject. Many investigators
haverevisited the old problem and some new progress has been made. In this
book it is investigated with an emphasis placed on the solution for a dipole
radiating over the planar or spherical boundary of a stratified medium. It is
concerned with an approximate or rigorous analytical solution of the electro-
magneticfieldradiatedbyaverticalorhorizontaldipole.Usually,asimplified
or idealized physical model is founded for a practical problem. Subject to
the boundary conditions, the formulas of the electromagnetic field are always
represented in the exact form of general integrals. These integrals are then
evaluated by using mathematical techniques. The corresponding numerical
results are carried out, and the conclusions are drawn.
Chapter 1 presents the historical and technical overview of the electro-
magnetic fields in stratified media in the past century. In Chapters 2-5, it
VI Preface
is concerned with the approximate solutions for electromagnetic fields radi-
ated by vertical and horizontal electric dipoles in the presence of three- and
four-layered regions. Both the trapped surface wave and the lateral wave are
addressedspecifically.Chapters6and7dealwiththepropagationoftheelec-
tromagnetic waves generated by a dipole on or near the spherical surface of a
layeredEarthwhilethetransientfieldexcitedbydeltafunctionandGaussian
currentsinahorizontalelectricdipoleontheboundarybetweentwodifferent
media is dealt with in Chapters 8 and 9. In the entire book an e−iωt time
dependence is assumed and suppressed.
The author would like to express his gratitude to his advisor, Professor
Wei-YanPanoftheChinaResearchInstituteofRadiowavePropagation,who
introduced him to the fascinating world of electromagnetics. Special thanks
are owed to Professor Hong-Qi Zhang of the China Research Institute of Ra-
dio Propagation. The author also wishes to thank Professor Seong-Ook Park
of the Information and Communications University, Korea and Professor Yi-
Long Lu of the Nanyang Technological University, Singapore for their insight
suggestions and comments. The author is also grateful to his graduate stu-
dents at Zhejiang University, especially to Yin-Lin Wang and Yi-Hui Xu.
Many thanks are also owed to Professor Kang-Sheng Chen, Professor Xian-
Min Zhang, Professor Sai-Ling He, Professor Dong-Xiao Yang, Professor Xi-
DongWu,andProfessorWen-YanYinofZhejiangUniversityfortheirhelpful
supportandencouragement.Finally,theauthorwouldliketoacknowledgethe
support and guidance of the editorial staff of Zhejiang University Press and
Springer.
The author sincerely appreciates the financial support in part of the Na-
tional Science Foundation of China under Grant 60831002 of Shanghai Jiao
Tong University.
The author hopes that the book would help stimulate new ideas and in-
novativeapproachestoelectromagneticfieldsandwavesinstratifiedmediain
the years to come.
Kai Li
Zhejiang University
August 2008
Contents
1 Historical and Technical Overview of Electromagnetic
Fields in Stratified Media.................................. 1
1.1 Electromagnetic Wave Along Air-Earth Boundary ........... 1
1.2 Surface Waves Along Surfaces of Stratified Media............ 3
1.3 Lateral Waves Along the Air-Earth Boundary............... 6
1.4 Trapped SurfaceWavein thePresenceof Three-LayeredRegion 6
1.5 Electromagnetic Field Radiated by a Dipole over Spherical
Earth .................................................. 8
References .................................................. 9
2 Electromagnetic Field of a Vertical Electric Dipole in the
Presence of a Three-Layered Region ....................... 15
2.1 Introduction ............................................ 15
2.2 The Integrated Formulas for Electromagnetic Field in Air .... 16
2.3 Field of Vertical Dipole over Dielectric-Coated Perfect
Conductor.............................................. 20
2.3.1 Integrated Formulas of the Electromagnetic Field in Air 20
2.3.2 Evaluations of Trapped Surface Wave and Lateral Wave 21
2.3.3 Final Formulas for the Electromagnetic Field
Components ...................................... 27
2.3.4 Computations and Discussions ...................... 28
2.4 Field of Vertical Dipole over Dielectric-Coated Imperfect
Conductor.............................................. 32
2.4.1 Statements of the Problem ......................... 32
2.4.2 The Trapped Surface Wave ......................... 33
2.4.3 Lateral Wave ..................................... 35
2.4.4 Final Formulas for the Electromagnetic Field
Components ...................................... 37
2.4.5 Computations and Discussions ...................... 38
2.5 Radiation from Vertical Dipole in Three-Layered Region...... 42
2.5.1 Field of Vertical Dipole in Three-Layered Region ...... 42
VIII Contents
2.5.2 Graphical Representations of the Far Field ........... 46
References .................................................. 53
3 Electromagnetic Field of a Horizontal Electric Dipole in
the Presence of a Three-Layered Region ................... 55
3.1 Introduction ............................................ 55
3.2 Electromagnetic Field of Horizontal Electric Dipole .......... 56
3.2.1 Integrated Formulas for Electromagnetic Field in Air .. 56
3.2.2 Evaluation for the Electric-Type Field ............... 59
3.2.3 Evaluation for the Magnetic-Type Field .............. 62
3.2.4 New Techniques for Determining the Poles λ and λ . 65
E B
3.2.5 Final Formulas for Six Field Components............. 68
3.2.6 Computations and Conclusions...................... 69
3.3 RadiationofHorizontalElectricDipoleandMicrostripAntenna 73
3.3.1 Radiation of a Horizontal Electric Dipole............. 73
3.3.2 Microstrip Antenna................................ 77
3.3.3 Computations and Discussions ...................... 79
3.4 Summary............................................... 84
References .................................................. 84
4 Electromagnetic Field of a Vertical Electric Dipole in the
Presence of a Four-Layered Region ........................ 87
4.1 Introduction ............................................ 87
4.2 Formulation of Problem .................................. 88
4.3 Evaluations of the Trapped Surface Wave and Lateral Wave .. 90
4.4 Computations and Conclusions............................ 96
References .................................................. 99
5 Electromagnetic Field of a Horizontal Electric Dipole in
the Presence of a Four-Layered Region ....................103
5.1 Integrated Formulas for the Electromagnetic Field ...........103
5.2 Evaluation for the Electric-Type Field .....................108
5.3 Evaluation for the Magnetic-Type Field ....................113
5.4 Final Formulas for the Six-Field Components ...............117
5.5 Computations and Conclusions............................118
References ..................................................121
6 Electromagnetic Field Radiated by a Dipole Source over
a Dielectric-Coated Spherical Earth .......................123
6.1 Introduction ............................................123
6.2 Electromagnetic Field due to Vertical Electric Dipole ........124
6.2.1 Formulations of the Problem........................124
6.2.2 Determination of the Coefficient A ..................128
s
6.2.3 Final Formulas of the Electromagnetic Field ..........131
6.2.4 Computations for Parameters t .....................131
s
Contents IX
6.2.5 Analysis and Computations ........................136
6.3 Electromagnetic Field due to Vertical Magnetic Dipole .......137
6.4 Electromagnetic Field due to Horizontal Electric Dipole ......140
6.5 Summary...............................................144
References ..................................................144
7 Electromagnetic Field of a Dipole Source over the
Spherical Surface of Multi-Layered Earth..................147
7.1 Introduction ............................................147
7.2 Electromagnetic Field due to Vertical Electric Dipole ........149
7.3 Electromagnetic Field due to Vertical Magnetic Dipole .......153
7.4 Electromagnetic Field due to Horizontal Electric Dipole ......155
7.5 Computations and Conclusions............................157
References ..................................................162
8 Exact Transient Field of a Horizontal Electric Dipole on
the Boundary Between Two Dielectrics....................165
8.1 Introduction ............................................165
8.2 Exact Transient Field with Delta Function Excitation........166
8.2.1 Formal Representations of Time-independent Field
due to Horizontal Electric Dipole....................166
8.2.2 Time-Dependent Component E ....................169
2ρ
8.2.3 Time-Dependent Component E ...................185
2φ
8.2.4 Time-Dependent Component B ....................190
2z
8.2.5 Discussions and Conclusions ........................193
8.3 Exact Transient Field with Gaussian Excitation .............193
8.3.1 Exact Formulas for the Transient Field of Horizontal
Dipole Excited by a Gaussian Pulse on the Boundary
Between Two Dielectrics ...........................193
8.3.2 Computations and Conclusions......................197
References ..................................................199
9 Approximate Transient Field of Horizontal Electric Dipole
on the Boundary Between a Homogeneous Isotropic
Medium and One-Dimensionally Anisotropic Medium .....203
9.1 Statements of Problem ...................................203
9.2 The Approximate Transient Field with Delta Function
Excitation ..............................................204
9.3 Approximate Formulas for the Transient Field with Gaussian
Excitation ..............................................212
References ..................................................219
Index..........................................................221
1
Historical and Technical Overview of
Electromagnetic Fields in Stratified Media
Theelectromagneticfieldinstratifiedmediahasbeenintensivelyinvestigated
foroveracentury.Inthischapter,weconductaformalreviewontheelectro-
magneticfieldinstratifiedmedia.Attentionshouldbepaidtoearlyanalytical
contributions on the electromagnetic field in two half-spaces by Zenneck and
Sommerfeld.Thesubsequentcontributionsbyotherpioneers,suchasVander
Pol, Ban˜os, Fock, Wait, and King, are outlined. From the new developments
on the electromagnetic field of a dipole in the presence of a three-layered re-
gion, it is seen that a trapped surface wave can be excited efficiently when
both the dipole and the observation point are on or close to the boundary.
1.1 Electromagnetic Wave Along Air-Earth Boundary
The first analytical solution for the propagation of electromagnetic waves
along the planar boundary between the air and the Earth was carried out
by Zenneck (1907). With the existence and significance of the ionosphere
still unknown, a possible explanation was offered that a surface wave could
propagate over great distance with low attenuation. The properties of the
Zenneck surface wave, a radial cylindrical surface wave, are well described by
Barlowand Cullen (1953). Themodelconsidered isaconductingordielectric
half-space, for z (cid:2) 0, with the conductivity σ and permittivity ε . The air,
1 1
forz (cid:3)0,hasauniformpermittivityε .ItisassumedthatbothRegion1and
0
Region 2 are nonmagnetic so that μ =μ =μ . Thus, the wave numbers of
1 2 0
the two regions are
(cid:2) (cid:3) (cid:4)(cid:5)
iσ 1/2
k =β +iα =ω μ ε + 1 , (1.1)
1 1 1 0 1 ω
√
k =k =ω μ ε . (1.2)
2 0 0 0
When the conditions