John wiley sons electrodynamics of solids microwave superconductivity zhou

Electrodynamics of Solids and Microwave Superconductivity Shu-Ang Zhou Copyright  1999 John Wiley & Sons, Inc ISBNs: 0-471-35440-6 (Hardback); 0-471-20646-6 (Electronic) Electrodynamics of Solids and Microwave Superconductivity Electrodynamics of Solids and Microwave Superconductivity SHU-ANG ZHOU EricssonComponentsAB New York l A Wiley-IntersciencePublication JOHN WILEY & SONS,INC Chichester Weinheim Brisbane Singapore l l l l Toronto This text is printed on acid-free paper @ Copyright 1999by John Wiley & Sons,Inc All rights reserved Publishedsimultaneouslyin Canada No part of this publication may be reproduced,storedin a retrieval systemor transmittedin any form or by any means,electronic, mechanical,photocopying,recording,scanningor otherwise, except as permittedunder Section 107 or 108of the 1976United StatesCopyright Act, without either the prior written permissionof the Publisher,or authorizationthrough payment of the appropriateper-copyfee to the Copyright ClearanceCenter.222 RosewoodDrive, Danvers,MA 01923, (978) 750-8400,fax (978) 7504744 Requeststo the Publisherfor permission should be addressedto the PermissionsDepartment,John Wiley & Sons,Inc., 605 Third Avenue, New York, NY 10158-0012,(2 12) 850-6011,fax (2 12) 850-6008,E-Mail: PERMREQ @ WILEY.COM For ordering and customerservice,call 1-800-CALL-WILEY Library of Congress Cataloging in Publication Data: Zhou, Shu-Ang Electrodynamicsof solids and microwave superconductivity/ Shu -Ang Zhou p cm - (Wiley seriesin microwave and optical engineering) “A Wiley-Intersciencepublication.” Includesbibliographical referencesand index ISBN O-47l-35440-6 (alk paper) Electrodynamics Superconductivity 1.Title II Series QC631.Z565 1999 537.6-dc2 99-25308 Printed in the United Statesof America 10987654321 Contents Foreword Preface Introduction to Classical Electrodynamics x111 xv 1.l Charges and Current 1 1.l l Charges and Charge Density 1.1.2 Current Density 1.1.3 Conservation Law of Charge 1.1.4 Coulomb’s Law 1.2 Electric and Magnetic Fields 1.2.1 Electric Field 1.2.2 Electric Potential 1.2.3 Gauss’ Theorem for Electric Field 10 1.2.4 Electric Multipoles in Free Space 11 14 1.2.5 Interaction of Electric Multipoles with External Field 15 1.2.6 Magnetic Field and the Lorentz Force 1.3 Laws of Electrodynamics and Maxwell’s Equations in Free Space 17 17 1.3.1 Ampere’s Circuital Law in Free Space 1.3.2 Gauss’ Law for Magnetic Field 18 1.3.3 The Biot-Savart Law 19 1.3.4 Magnetic Force on Current Circuit 20 1.3.5 Magnetic Multipoles in Free Space 20 1.3.6 Interaction of Magnetic Multipoles with External Field 23 1.3.7 Faraday’s Law of Induction 24 1.3.8 Maxwell’s Equations in Free Space 25 27 1.4 Maxwell’s Equations for Materials at Rest 1.4.1 Dipole Model of Electromagnetic Solids 28 1.4.2 Gauss’ Theorem in Material Medium 30 31 1.4.3 Ampere’s Circuital Law in Material Medium 34 1.4.4 Maxwell’s Equations for Materials at Rest V vi CONTENTS 1.45 Electromagnetic Potentials and Gauge Transformation 1.4.6 Time-Harmonic Fields and the Kramers-Kronig Relations 1.4.7 Dispersion in Materials 1.48 Inter-facial Polarization 1.4.9 Velocities of Wave Propagation 1.5 Electromagnetic Energy, Momentum, and Variational Principles 15.1 Electric Field Energy for Charges 1.5.2 Electrostatic Energy for Material Media 15.3 Variational Principle for Electrostatic System 1.5.4 Thomson’s Theorem and Earnshaw’s Theorem 15.5 Magnetic Field Energy for Currents and Material Media 1.5.6 Variational Principle for Magnetostatic System 1.5.7 Poynting’s Theorem for Electrodynamic Systems 1.5.8 Poynting’s Theorem for Quasistatic Systems 1.5.9 Poynting’s Theorem for Time-Harmonic Systems 1.5.10 Variational Principle for Electrodynamic System 1.5.11 Uniqueness Theorem 1.5.12 Momentum of Electromagnetic Fields 1.6 Maxwell’s Equations for Moving Media 1.6.1 Principles of Relativity and the Lorentz Transformation 1.6.2 Covariance of Maxwell’s Equations 1.6.3 Covariance of Potential Equations 1.6.4 Plane Wave and the Doppler Effect 1.6.5 Minkowski’s Electrodynamic Theory for Moving Media 1.7 Electromagneto-Quasistatic Approximations 1.7.1 Galillean Approximation 1.7.2 Maxwell’s Equations at Magneto-Quasistatic Approximation 1.7.3 Maxwell’s Equations at Electra-Quasistatic Approximation 1.8 Electromagnetics of Magnetic Solids 1.8.1 Saturation Magnetization and Magnetic Hysteresis 1.8.2 Gyromagetic Media 1.8.3 The Faraday Rotation 1.8.4 Bianisotropic Media and Chiral Media 1.9 Electromagnetics of Circuits 1.9.1 Lumped Circuit Elements and Source Functions 1.9.2 Kirchhoff’s Voltage and Current Laws 1.9.3 Electromagnetic Energy and Power in a Circuit 1.10 Some Examples in Classical Electrodynamics 1.10.1 CapacitanceCalculations of Some Capacitors 1.10.2 Inductance Calculations of Some Inductors 1.10.3 Reflection and Refraction of Electromagnetic Wave at Dielectric Interface 1.10.4 Radiation Pressureon a Good Conductor 1.10.5 Charged Particle in Electromagnetic Fields 38 40 44 48 50 53 53 55 57 59 60 62 63 65 65 69 70 72 75 76 78 79 80 82 85 85 86 88 90 90 93 95 98 101 101 107 108 110 110 113 118 123 125 CONTENTS Continuum Electrodynamics of Deformable Solids 2.1 Mass and Motion of Continuous Media 2.1.1 Mass and Mass Density 2.1.2 Motion of Continuum Media 2.1.3 Conservation Law of Mass 2.2 Continuum Deformation and Strain Analysis 2.2.1 Deformation and Strain Tensors 2.2.2 Rate of Deformation and Rigid Body Rotation 2.2.3 Compatibility Conditions 2.3 The Laws of Motion and Stress Hypothesis 2.3.1 Objective Tensors 2.3.2 The Laws of Motion 2.3.3 StressTensor 2.4 The Laws of Continuum Thermodynamics 2.5 On Formulation of Electrodynamics for Deformable Media 2.6 Continuum Theory of Thermoelastic Conductors 2.6.1 Constitutive Equations for Non-Magnetizable Conductors 2.6.2 Constitutive Equations for Magnetizable Conductors 2.6.3 Linearized Model for Thermoelastic Conductors 2.6.4 Field Equations and Boundary Conditions 2.7 Continuum Theory of Thermoelastic Dielectrics 2.7.1 Constitutive Equations for Thermoelastic Dielectrics 2.7.2 Linearized Model for Thermopiezoelectric Solids 2.7.3 Field Equations and Boundary Conditions 2.8 Photothermoelasticity 2.8.1 Principal Stressesand Principal Refractive Indices 2.8.2 Optical Birefringence 2.8.3 Photothermoelastic Law 2.9 On Continuum Models and Their Limitations 2.10 Continuum Theory of Material Composites 2.10.1 Solution of an Ellipsoidal Inhomogeneity in an Elastic Dielectric 2.10.2 Statistical Continuum Material Multipoles 2.10.3 Statistical Continuum Multipole Modeling of Composites 2.10.4 Effective Properties of Composite with Random Microstructure 2.10.5 Overall Behavior of Elastic Dielectric Composites 2.11 Some Examples of Boundary-Value Problems 2.11.1 Circular Cylindrical Tube Subjected to Pressure 2.11.2 The Rayleigh Surface Wave 2.11.3 Thermal Stress-InducedIndex Profile Distortion in an Optical Fiber vii 129 129 129 130 132 133 133 135 136 138 138 138 140 142 145 149 149 152 156 161 163 163 166 169 170 171 173 I75 178 185 186 191 195 201 209 212 213 216 218 VIII CONTENTS Electrodynamics of Superconductors in Weak Fields 3.1 Basic Phenomenaof Superconductivity 3.1.l Zero Resistanceand Transition Temperature 3.1.2 Critical Magnetic Field 3.1.3 The Meissner Effect The London Theory of Superconductors 3.2 3.2.1 Free Electron Model 3.2.2 Macroscopic Quatum Wave Model 3.2.3 Classical Two-Fluid Model 3.2.4 The London Theory for Superconductorsin AC Fileds 3.2.5 Energy Theorem and Uniqueness Theorem 3.2.6 Electromagnetic Pressure 3.3 Some Boundary Value Problems in London’s Theory 3.3.1 Superconducting Half-Space in a Static Magnetic Field 3.3.2 Superconducting Cylinder Carrying DC Current 3.3.3 Superconducting Coaxial Line 3.3.4 Superconducting Cylinder in a Static Magnetic Field 3.3.5 Magnetic Field Shielding by Superconductor 3.3.6 Superconducting Half-Space in a Time-Harmonic Magnetic Field 3.3.7 Reflection and Transmission of Normally Incident Plane Wave 3.4 Electrodynamic Behaviors of Superconductors at High Frequencies 3.4.1 Full-Wave Solution of a Superconducting Planar Waveguide 3.4.2 Modified Two-Fluid Model 3.4.3 Surface Resistanceof a Superconductor at High Frequency 3.4.4 Dispersion and Attenuation Distortion 3.4.5 Pippard’s CoherenceLength and Nonlocal Relation 3.4.6 The Mattis-Bardeen Theory 3.5 The London Electrodynamic Model for Anisotropic Superconductors 3.5.1 The London Equations for Anisotropic Superconductors 3.5.2 Field Solution of an Anisotropic Superconducting Planar Waveguide 3.5.3 Effect of Material Anisotropy on Kinetic Inductance 3.5.4 Effect of Material Anisotropy on Wave Dispersion and Attenuation 3.6 Microscopic Mechanism of Superconductivity 3.6.1 Isotope Effect 3.6.2 The Cooper Pair of Electrons 3.6.3 The BCS Theory of Superconductivity 227 227 227 231 233 235 235 238 242 245 249 253 254 254 255 256 259 260 263 265 268 268 274 278 282 286 289 292 292 294 298 300 303 303 303 306 CONTENTS Electrodynamics of Superconductors in Strong Fields 4.1 Thermodynamics of PhaseTransitions in Superconductors 4.1.1 Thermodynamic Functions for Superconductors 4.1.2 First and Second-Order PhaseTransitions in Superconductors 4.1.3 Discontinuity of Specific Heat at Transition Temperature 4.2 The Ginzburg-Landau Theory of Superconductors 4.2.1 Complex Order Parameter 4.2.2 The Ginzburg-Landau Equations 4.2.3 Critical Fluctuation and Validity of the Ginzburg-Landau Theory 4.2.4 The Ginzburg-Landau ParameterK 4.25 Upper Critical Magnetic Field Bc2 4.2.6 Classification of SuperconductorsAccording to the G-L Theory 4.2.7 The Abrikosov Mixed State in Type II Superconductors 4.2.8 A Solution of the Ginzburg-Landau Equations for Thin Film 4.2.9 Critical Field for Thin Film 4.2.10 Critical Current in Thin Film 4.3 Vortex Dynamics and the London-Bean Model 4.3.1 The London Model of Vortex Line and Lower Critical Field B,l 4.3.2 Interaction Between Two Vortex Lines 4.3.3 Flux Flow, Pinning, and Critical State 4.3.4 Flux Creep and the Anderson-Kim Model 4.3.5 The London-Bean Model for Hard Superconductors 4.3.6 Magnetization of High-Field Superconductor 4.3.7 AC Loss in a Thin Superconducting Plate 4.38 Magnetothermal Instability of Hard Superconductors 4.4 Electrodynamic Model for Type II Superconductors at High Frequencies 4.4.1 Vortex Electric Field in Type II Superconductors in AC Fields 4.4.2 Possible Effect of Inertia of Flux Lines 4.4.3 E-J Relation for Anisotropic Type II Superconductors in the Mixed State 4.4.4 Nonlinear Field Equations and Linearization 4.5 Microwave Properties of Planar Superconducting Waveguide in DC Magnetic Field 4.5.1 Field Equation and Wave Solution 4.5.2 Surface Impedance of Type II Superconductor in the Mixed State ix 315 315 315 318 320 321 321 324 325 328 330 332 335 341 343 345 347 347 350 352 355 360 362 366 370 375 375 378 383 385 388 388 390 X CONTENTS 4.5.3 DC Magnetic Field Effect on Wave Attenuation and Dispersion 4.5.4 Magnetic Field Dependenceof Quality Factor Q and Resonant Frequency 4.6 Thermomagnetoelectric Effects in Type II Superconductors in the Mixed State 4.6.1 Formulation of Thermomagnetoelectric Effects in Type II Superconductors 4.6.2 Linearized Model for Thermomagnetoelectric Effects 4.6.3 Flux-Flow Hall Effect and Flux-Flow Righi-Leduc Effect 4.6.4 Flux-Flow SeebeckEffect and Flux-Flow Nernst Effect 4.6.5 Plane Thermomagnetic Wave in Superconductors in the Mixed State Electrodynamics of Josephson Junctions and Circuits 5.1 Macroscopic Quantum State and JosephsonEffects 5.1.1 Macroscopic Quantum State and DC JosephsonEffect 5.1.2 Electrodynamic Equations for the JosephsonJunctions 5.1.3 AC JosephsonEffect 5.2 Superconducting Quantum Interference Devices 5.2.1 Single JosephsonJunction in Magnetic Fields 5.2.2 Double JosephsonJunctions in Magnetic Fields 5.2.3 SQUIDS and Their Applications 5.3 The JosephsonLogic Circuits and Quantum Electronic Devices 5.3.1 Circuit Model of the JosephsonJunction 5.3.2 Voltage-State Logic Circuits 5.3.3 Single Flux Quantum Logic Circuit 5.3.4 Superconducting Transistor 5.3.5 The Coulomb Blockade and Single-Electron Tunneling 5.3.6 Quantum-Effect Devices 5.4 Some Physical Limits in Switching Technologies 5.4.1 Basic Physical Limits 5.4.2 Logic-Level Voltage Limit 5.4.3 Physical Limits on Interconnect and Packaging Electromagnetic Analysis of Transmission Line and Waveguide 6.1 Transmission Line Theory 6.1.1 Formulation of Transmission Lines 6.1.2 Incident and Reflected Wave Along a Transmission Line 6.1.3 Pulse Propagation in a Transmission Line 393 396 398 398 404 407 409 410 413 413 413 417 420 424 424 426 429 432 432 434 435 437 439 440 441 441 445 446 453 453 453 457 461 CONTENTS 6.1.4 6.2 6.3 6.4 6.5 Scattering Matrix Representationof Transmission Line Parameters Electromagnetic Field Analysis of Transmission Line Parameters 6.2.1 TEM Wave at Quasistatic Approximation 6.2.2 Formulation of Skin Effect at Quasi-TEM Approximation 6.2.3 Finite Element Formulation of Multi-Conductor Systems 6.2.4 Finite Element Analysis of Coaxial Line at High Frequencies 6.2.5 Analysis of Composite Superconducting Striplines 6.2.6 Analysis of Nonlinear Superconducting Microstrip Lines 6.2.7 Harmonic Generation and Two-Tone Intermodulation 6.2.8 Method of Equivalence Between Distributed-Circuit and Full-Wave Analyses 6.2.9 Full-Wave Analysis of Anisotropic Superconducting Planar Waveguide Analysis of Coupled Transmission Lines and Directional Couplers 6.3.1 Formulation of Coupled Transmission Lines 6.3.2 Characterization of Directional Couplers 6.3.3 Finite Element Analysis of 3dB Directional Couplers Full-Wave Analysis of Waveguide with Conducting Boundary 6.4.1 Rectangular Waveguide 6.4.2 Energy Transmission in a Waveguide 6.4.3 Wave Attenuation in Lossy Waveguide Microwave Resonators 6.5.1 Lumped Element Resonant Circuits 6.5.2 Transmission Line Resonators 6.5.3 Cavity Resonators xi Electrodynamics of Deformable Superconductors 7.1 Modeling of Moving Deformable Superconductors 7.1.1 On Limitation of Minkowski’s Theory 7.1.2 London’s Formulation for Rotating Superconductors 7.1.3 Formulation of Moving Deformable Superconductors 7.2 Some Wave Phenomenain Elastic Superconductors 7.2.1 Magnetic Wave Induced by Elastic Wave in Superconductors 7.2.2 Magnetic Surface Wave Induced by the Rayleigh Elastic Surface Wave 7.2.3 Electromagnetoelastic Surface Wave 7.3 Macroscopic Quantum Effects in Moving Deformable Superconductors 462 467 467 470 476 478 481 489 493 496 499 508 508 510 513 516 516 520 522 525 525 529 531 537 537 537 540 542 547 547 549 554 556 VECTOR FORMULAS A4 VECTOR FORMULAS A (B x C) = B.(CxA) Ax(BxC) = C.(AxB) = (A.C)B-(A.B)C wb+v) = w+w V.(A+B) = V.A+V.B Vx(A+B) = VxA+VxB ww) V.&A) = WV + vvo = A+++q%A V.(A xB) = B.(VxA)-A.(VxB) Vx(AxB) = A(V.B)-B(V.A)+(B.V)A-(A.V)B v-(VI/J) = v2qJ (A.10) V*(VxA) (A.ll) Vx(VqJ) Vx(VxA) V(A.B) (A4 (A-2) W) (A4 (A.51 (A-6) vo (A.8) (A-9) = = = V(V*A)-V2A = (A.V)B+(B.V)A+Ax(VxB)+Bx(VxA) (A.12) (A.13) (A.14) APPENDIX A5 THEOREMS FROM VECTOR CALCULUS Divergence theorem: (A.15) $ V*AdV=SA*ndS V S J VqdV V J VxAdV V (A.16) = J VndS S = s nxAdS (A.17) S Green ‘s first identity: s (+V2~ + V$ VqQdV = s @z V+L!3 V (A.18) S Green’s theorem: J ($V2v -vV2Q)dV V = J (@VW-qV$) * ndS (A.19) S where 4, I& andA are well-behaved functions V is the volume andSis a closed surface bounding V, with the unit outward normal vector n Stokes ‘s theorem: J (VxA).ndS = j A-d1 S (A.20) L S nxVqdS S = s vdl (A.21) L where S is an open surface and L is the contour bounding it, with line element dl The normal n to S is defined by the right-hand side rule in relation to the senseof the line integral around L FORMS OF VECTOR OPERATORS A6 FORMS OF VECTOR OPERATORS COORDINATE SYSTEMS 599 IN CURVILINEAR In cylindrical coordinate system (r, 8, z) with e,, ee, and e, being the corresponding unit directional vectors: a.4)+;zee 1w +zez WJ a,er VI) = V.A VxA = (A.22) (A.23) (A.24) = Ia V2q-&‘~ aq ( 1 a2q a2q rae az +72+Yy (A.29 In spherical coordinate system (r, 8, cp) with e,, ee, and eq being the corresponding unit directional vectors: Vtj V.A VxA = t$er+ 1av zeo + w rsin8 aqev (A.26) (A.27) = = (A.28) + r2(ske)2$ (A.29) 600 A7 APPENDIX TENSOR NOTATION AND SUMMATION CONVENTION In tensor analysis, one makes extensive use of indices A set of n variables, x1, x2, “‘, X, is usually denoted asxi, i = 1,2, n A set of n x n variables, tll, t12, 121 , tnn is usually denoted as tip i,j = 1, 2, It Summation convention: The repetition of an index (whether superscript or subscript) in a term will denote a summation with respect to that index over its range The range of an index i is generally the set of n integer values to n An index that is summed over is called a dummy index; one that is not summed out is called a free index Examples are n aiXi s LZiXi (A.30) sib’ (A.31) tii (A.32) i=l n sib’ E Ic i=l n t s 11 i=l n df(X,, X2, ) Xn) = ~dxi ~ ~ ~dxi i i=l (A.33) i n aitij E Ix t ij 0’ = 192, n) (A.34) i=l where i is the dummy index, and j is the free index with its range from to n Here, we emphasize that b’, b2, b” are n independent variables and not the first n powers of the variable b Since a dummy index just indicates summation, it is immaterial which symbol is used Thus a$i may be replaced by a& For instance, n tijaiCj E tklakcl E n tklakcl (A.39 k=ll=l if the range of the dummy index i (or k) is from to n, and the range of the dummy index j (or I) is also from to n TENSOR NOTATION AND SUMMATION CONVENTION 601 Kronecker delta 6ij is defined by the equations: a,, = 6,, = (A.36) 62, = 61, = $1 = 6,, = 6,, = (A.37) 11 12 = = with the understanding that the range of the indices i andj is to here Permutation symbol ehn is defined by the equations: elll = e222 = e333 = e112 = e113 = e221 = e223 = e331 = e332 = o (A.38) e123 = e231 = e312 = ’ (A.39) e213 = e321 = e132 = -1 (A.40) In other words, ekmnvanishes whenever the values of any two indices coincide; ehn = when the subscripts permute like 1,2,3; and ehn = -1 otherwise There is a relation between the Kronecker delta 6ij and the permutation symbol ehn, which is given by e qk e.1st = ‘js’kt - ‘jt’ks (A.4 1) Electrodynamics of Solids and Microwave Superconductivity Shu-Ang Zhou Copyright  1999 John Wiley & Sons, Inc ISBNs: 0-471-35440-6 (Hardback); 0-471-20646-6 (Electronic) WILEY SERIES IN MICROWAVE AND OPTICAL ENGINEERING KAI CHANG, Editor Texas A&M University FIBER-OPTIC COMMUNICATION SYSTEMS, Second Edition COHERENT OPTICAL COMMUNICATIONS Eugenio lannone l Covind P Agrawal SYSTEMS l Silvello Betti, Ciancarlo De Marchis and HIGH-FREQUENCY ELECTROMAGNETIC TECHNIQUES: RECENT ADVANCES AND APPLICATIONS l Asoke K Bhattachatyya COMPUTATIONAL METHODS FOR ELECTROMAGNETICS AND MICROWAVES Richard C Booton, jr MICROWAVE RING CIRCUITS AND ANTENNAS l Kai Chang MICROWAVE SOLID-STATE CIRCUITS AND APPLICATIONS l Kai Chang DIODE LASERSAND PHOTONIC INTEGRATED CIRCUITS l Larry Coldren and Scott Corzine MULTICONDUCTOR Faria TRANSMISSION-LINE STRUCTURES: MODAL ANALYSIS TECHNIQUES l A Brand20 PHASED ARRAY-BASED SYSTEMS AND APPLICATIONS l Nick Fourikis FUNDAMENTALS OF MICROWAVE TRANSMISSION LINES l jon C freeman OPTICAL SEMICONDUCTOR DEVICES l Mitsuo Fukuda MICROSTRIP CIRCUITS l Fred Cardiol HIGH-SPEED VLSI INTERCONNECTIONS: MODELING, ANALYSIS, AND SIMULATION l A K Coel FUNDAMENTALS OF WAVELETS: THEORY, ALGORITHMS, AND APPLICATIONS l laideva C Goswami and Andrew K Chan ANALYSIS AND DESIGN OF INTEGRATED CIRCUIT ANTENNA MODULES l K C Cupta and Peter S Hall PHASED ARRAY ANTENNAS l R C Hansen HIGH-FREQUENCY ANALOG INTEGRATED CIRCUIT DESIGN Ravender Coyal (ed.) MICROWAVE APPROACH TO HIGHLY IRREGULAR FIBER OPTICS l Huang Hung-Chia NONLINEAR OPTICAL COMMUNICATION Antonio Mecozzi, NETWORKS l Eugenio lannone, Francesco Matera, and Marina Settembre FINITE ELEMENT SOFTWARE FOR MICROWAVE ENGINEERING l Tatsuo Itoh, Ciuseppe Pelosi and Peter P Silvester teds.) SUPERCONDUCTOR TECHNOLOGY: APPLICATIONS TO MICROWAVE, ELECTRO-OPTICS, ELECTRICAL MACHINES, AND PROPULSION SYSTEMS l A R Iha OPTICAL COMPUTING: AN INTRODUCTION l M A Karim and A S S Awwa/ INTRODUCTION TO ELECTROMAGNETIC AND MICROWAVE ENGINEERING Paul R Karmel, Gabriel D Co/et and Raymond L Camisa MILLIMETER WAVE OPTICAL DIELECTRIC INTEGRATED GUIDES AND CIRCUITS l Shiban K Koul MICROWAVE DEVICES, CIRCUITS AND THEIR INTERACTION l Charles A Lee and C Conrad Da/man ADVANCES IN MICROSTRIP AND PRINTED ANTENNAS l Kai-Fong Lee and Wei Chen feds.) OPTICAL FILTER DESIGN AND ANALYSIS: A SIGNAL PROCESSING APPROACH l Christi K Madsen and jian H Zhao OPTOELECTRONIC PACKAGING A R Mickelson, N R Basavanhally, and Y C Lee (eds.) OPTICAL CHARACTER RECOGNITION l Shunji Mori, Hirobumi Nishida, and Hiromitsu Yamada ANTENNAS FOR RADAR AND COMMUNICATIONS: A POLARIMETRIC APPROACH Harold Mott INTEGRATED ACTIVE ANTENNAS AND SPATIAL POWER COMBINING l lulio A Navarro and Kai Chang FREQUENCY CONTROL OF SEMICONDUCTOR LASERS l Motoichi Oh&u (ed.) SOLAR CELLS AND THEIR APPLICATIONS l Larry D Partain (ed.) ANALYSIS OF MULTICONDUCTOR TRANSMISSION LINES l Clayton R Paul INTRODUCTION TO ELECTROMAGNETIC COMPATIBILITY l Clayton R Paul INTRODUCTION TO HIGH-SPEED ELECTRONICS AND OPTOELECTRONICS Leonard M Riaziat NEW FRONTIERS IN MEDICAL DFVICE TECHNOLOGY Arye Rosen and Hare/ Rosen (eds.) ELECTROMAGNETIC PROPAGATION IN MULTI-MODE RANDOM MEDIA l Harrison E Rowe ELECTROMAGNETIC SYSTEM DESIGN USING EVOLUTIONARY OPTIMIZATION l Yahya Rahmat-Samii and Eric Michielssen NONLINEAR OPTICS l E C Sauter InP-BASED MATERIALS AND DEVICES: PHYSICS AND TECHNOLOGY and Hideki Hasegawa (eds.) l Osamu Wada DESIGN OF NONPLANAR MICROSTRIP ANTENNAS AND TRANSMISSION LINES l Kin-Lu Wong FREQUENCY SELECTIVESURFACE AND GRID ARRAY l T K Wu (ed.) ACTIVE AND QUASI-OPTICAL ARRAYS FOR SOLID-STATE POWER COMBINING Robert A York and Zoya Popovid (eds.) OPTICAL SIGNAL PROCESSING, COMPUTING AND NEURAL NETWORKS l Francis T Yu and Suganda lutamulia SiGe, GaAs, AND InP HETEROJUNCTION BIPOLAR TRANSISTORS l liann Yuan ELECTRODYNAMICS OF SOLIDS AND MICROWAVE SUPERCONDUCTIVITY l Shu-Ang Zhou Electrodynamics of Solids and Microwave Superconductivity Shu-Ang Zhou Copyright  1999 John Wiley & Sons, Inc ISBNs: 0-471-35440-6 (Hardback); 0-471-20646-6 (Electronic) Index Absolute space, 544 Acceleration, 85, 131,539 Anisotropy, statistical, 201 Approximation(s), 85 electro-quasistatic, 88 Galilean, 85 magneto-quasistatic, 86 quasi-TEM, 471 Attenuation coefficient, 269 Attenuation distortion, 282 Axiom, 147 of admissibility, 148 of determinism, 147 of equipresence, 147 of material invariance, 148 of memory, 147 of neighborhood, 147 of objectivity, 147 Balance law, 139 of angular momentum, 139 of linear momentum, 139 Birefringence, 173 optical, 173 Boundary condition(s), 31,34,161,169 Body couple, 139 electric, 164 electromagnetic, 153 Brewster angle, 123 Capacitance, 105, 110 line, 455 Capacitor(s), 49,105, 110 Cartesian coordinate system, 130 Cauchy stress ellipsoid, 172 Charge(s), conservation law of, volume density of, Clausius-Duhem inequality, 144 Coaxial line, 256,478 superconducting, 256 Coefficient(s), 57,61 capacity, 57 current transmission, 458 of mutual inductance, 61 of self-inductance, 61 principal dielectric, 172 voltage transmission, 458 Coherence length, 244,326 Ginzburg-Landau, 327 intrinsic, 288, 327 Pippard, 286 phase, 440 Compatibility conditions, 136 Composite(s), 181, 185, 195 dielectric, 206 elastic dielectric, 209 superconducting stripline( 481 superconductor(s), 372 Conductance, 102 boundary, 162 line, 455 Conductivity, 37,572 complex, 244,482,572 Complex flux-flow, 387,391 Constitutive equation(s), 36,41,83,163 for non-magnetizable conductors, 149 for soft-ferromagnetic conductors, 152 for thermoelastic dielectrics, 163 of moving media, 83 Continuity, equation of, 4, 133 vortex, 385 Continuum electrodynamics, 129 Coulomb blockade, 439 Critical current, 232,345,427 density, 232,354,384,415 Critical magnetic field, 231,317,343 lower, 349 upper, 331 Critical state, 354 equation, 354 Cryotron, 318 Current density, 2, 619 620 INDEX conduction, 34 convection, 34 displacement, 17 surface, 32 Current-phase relation, Josephson, 415 Deformation, 133 gradient, 134 rate of, 135 Degenerate mode(s), 519 Delay line(s), 273 Demagnetizing factor, 316 Depinning frequency, 380,391 Diamagnetism, 32 Diamagnetic moment, 32 Dipole(s), 12 electric, 12, 13 magnetic, 22 Directional coupler(s), 508-516 Directivity, 512 Dispersion, 44,282,300 anomalous, 47 in materials, 44 normal, 47 space, 99 Displacement vector, 134 electric, 31 Doppler effect, 82 Dynamic mobility, 377 Electromagnetic pressure, 253 Electromigration, 448 Electron(s), Cooper pair of, 303 Energy, 23 barrier, 356 electric field, 53 electrostatic, 55 gap, 312 magnetic field, 60 magnetic interaction, 23 potential, 15, 24 relativistic, 127 rest, 127 surface, 333 time-average electric, 68 time-average reactive, 68 transmission, 520 Ensemble, 192 average, 194 Gibbs, 192 Entropy, 143,319 balance equation of, 143,152 flux, 144 production of, 144 specific, 144 Faraday rotation, 95 Fermi-Dirac distribution, 11 Ferromagnet(s), 90 Field(s), electric, electromagnetic, 25 magnetic, 15 magnetic intensity, 33 neuromagnetic, 431 phasor, 40 theory, time-harmonic, 40 vortex electric, 352 vortex magnetic, 352 Finite element, 475 analysis, 478 method, 477 Fluctuation, 326,357 Flux, 19 bundle(s), 356 creep, 356,392 entropy, 144 heat, 144 line(s), 350 magnetic, 19,240 power, 64 quantum, 241 time-average power, 66 Flux-ffow, 352 Hall coefficient, 407 Hall effect, 402,407 Nemst coefficient, 410 Nemst effect, 409 resistivity, 353,377,384 Righi-Leduc coefficient, 408 Righi-Leduc effect, 408 Seebeck coefficient, 409 Seebeck effect, 409 viscosity, 380,567 viscosity tensor, 400 Fluxoid, 242 INDEX Fluxon, 241 Force(s), 5,6, 14 coercive, 91 electric body, 163 electric dipole, 14 electromagnetic body, 149, 153 electromotive, 24 electrostatic, fictitious, 543 gravitational, Lore&, 15 magnetic, 15, 20 Magnus, 401 Minkowski, 126 pinning, 354 thermal, 400 Frame, 83,538 inertial, 83,538 instantaneous rest, 85,538 generalized instantaneous rest, 543 laboratory, 83,538 pointwise instantaneous rest, 543 rest, 83,538 Free energy, 322 Gibbs, 316 Free space, Frequency, cutoff, 18 Fresnel’s equations, 122 Fresnell ellipsoid, 173 Function(s), 10 Bessel, 421 Dirac delta, 10 Hankel, 348 indicative, 195 thermodynamic, 315 Gap frequency, 275,281 Gap voltage, 416 Gauge, 19,557 Coulomb, 19,40 invariance, 557 Lorentz, 39 transformation(s), 39, 239 Gauss’law for magnetic field, 18 Gauss’ theorem, lo,30 for electric field, 10 in material medium, 30 Gaussian pulse(s), 461 Ginzburg-Landau equation, 324 Ginzburg-Landau parameter, 328 Gravitational constant, Green’s function, 12 elastic, 186 electric, 12 magnetic, 21 Gyromagnetic media, 93 Gyromagnetic ratio, 93 Harmonic generation, 493 Heat, 144 conduction, 152,403 flux, 144 latent, 319 specific, 320 Homogenization method, 184 Impedance, 27,455 characteristic, 456,503 complex surface, 264 input, 460 intrinsic, 27 load, 457 source, 457 surface, 271,390 Index of refraction, 46 Inductance, 113,258 external, 258 internal, 259 kinetic, 298,478 line, 258,455 partial, 114 Inductor(s), 113 Inertia, 76 of flux line, 378 system of, 76 Insertion loss, 512 Interaction, long-range, short-range, Interconnect, 446 Interface condition(s), 35,88,89 Interference device(s), 424 superconducting quantum, 424-432 Interferometer, 561 rotating superconducting, 561 Intermediate state, 334 Intermodulation, two-tone, 493 Irreversibility line, 359 621 622 INDEX Isolation, 512 Isotope effect, 303 Josephson effect, 413 dc, 416 ac, 420 Josephson frequency, 421 Joule heating, 149 Junction(s), 414,559 deformable Josephson, 559 Josephson, 414 Kinetic energy, 249 density, 249 of superelectrons, 249 time-averaged, 252 Kramers-Kronig relations, 44 Kronecker delta, 134,601 Lame stress ellipsoid, 172 Lame’s constants, 158 Laplace equation, 468,473 Law(s), 16 Ampere circuital, 17,31 Biot-Savart, 19 Coulomb’s, energy conservation, 143 Faraday’s, 24 Fourier, 167 Fourier-Ohm’s, 151 Hooke’s, 182 Kirchhoff current, 5, 108 Kirchhoff voltage, 107 Lenz, 25 Lorentz force, 16 Newton’s, 138 Ohm‘s, 36 of continuum thermodynamics, 142 of motion, 138 photothermoelastic, 175 Snell’s, 120 Limit(s), 441 electron-number fluctuation, 443 light speed, 450 minimum thermal energy, 441 nonlinear, 443 photon-number fluctuation, 441 physical, 441 power dissipation, 448 quantum, 441 resistance, 447 thermal transfer, 443 voltage, 445 Logic circuit(s), 432-436 single flux quantum, 435 voltage-state, 434 London-Bean model, 361 London equation(s), 236,237 generalized, 577 London moment, 540 Loss, 41 ac, 366 dielectric, 41 eddy current, 93 hysteresis, 92 ohmic, 64 tangent, 42 Lumped circuit elements, 101 Magnetic hysteresis, 90 loop, 91 Magnetic field shielding, 260 Magnetization, 28 macroscopic, 36 orbital current, 32 orientational, 32 remnant, 91 saturation, 90 spin, 32 Magnetocardiogram, 430 Magnetothermal instability, 370 Magnetothermoelastic effect(s), 579 Mass, 126, 129 center of mass, 130 conservation law of, 132 point mass, 130 relativistic, 126 rest, 126 Mass density, 74,130 electromagnetic, 74 Matching condition, 464 Material time derivative, 132 Matrix, ABCD, 465 Maxwell’s equations, 25 at electro-quasistatic, 88 at magneto-quasistatic, 86 Covariance of, 78 for materials at rest, 34 INDEX for moving media, 75 in free space, 25 Maxwell stress tensor, 73 Media, 37 bianisotropic, 98 chiral, 98 continuous, 129 gyromagnetic, 93 Meissner effect, 234 Microstrip line(s), 486 nonlinear superconducting, 489 Microstructure(s), 180, 185 Minkowski’s theory, 83 Mixed state, 334, 565 Abrikosov, 335 Model(s), 28,230 dipole, 28,32 free-electron, 235 macroscopic quantum wave, 238, 557 modified two-fluid, 274 resistively shunted junction, 433 two-fluid, 230,242,490 Modulus, 158 elastic bulk, 158 elastic shear, 158 Young’s, 158 Momentum, 72 angular, 139 conservation of, 73 density of, 74 of electromagnetic fields, 72 flux-density of, 73 mechanical, 73 relaxation time, 243 time average density of, 74 Monopole moment, 12 electric, 12 Motion, 130 Eulerian description of, 130 Lagrangian description of, 130 rigid-body, 134 vortex, 352 Multipole( 11, 191,195 continuum material, 191 elastic, 193 electric, 11 magnetic, 20 statistical continuum, 195 Nonlocal relation, 287 Nonlocal theory, 185 Nuclear gyroscope, 431 Optical fiber(s), 219 step-index, 224 Order parameter, 321 complex, 322 Packaging, 446,448 Parity, 35 Penetration depth, 237,288,327,570 complex, 570 Josephson, 420 London, 237 rf, 277 Permeability, 17,36 complex, 67 gyromagnetic, 94 magnetic, 36 of free space, 17 relative, 36 Permittivity, 6, 36 complex, 42 dielectric, 36 of free space, relative, 36 Phase constant, 50 Phase shift, 456,576 Phase transition(s), 315, 323 of the second-order, 320 of the first-order, 320 Photoelastic coefficient, 175 Photon(s), 75,127 Photothermal coeffrceint, 176 Photothermoelasticity, 170-178 Physical limit(s), 441-451 Piezoelectric coefficients, 167 Poisson’s equation, 19 Poisson’s ratio, 158 Polarization, 28 density, 29,31 electronic, 28 interfacial, 48 ionic, 29 macroscopic, 36 orientational, 29 Potential(s), electric, 623 624 INDEX electromagnetic, 38 node,.477 scalar, 14 vector magnetic, 19 Power, 64 active, 109 electromagnetic, 149, 154, 164 flux density, 64 in a circuit, 108 reactive, 109 time-average, 67 vector, 109 Principal coordinate system, 171 Principal refractive indices, 176 Principle(s), covariance, 82 linear superposition, of equivalence, 544 of relativity, 76 variational, 53,57,62,69 Propagation constant, 269 complex, 455,503 Proton, Proximity effect, 325 Pyroelectric coefficients, 167, 175 Quality factor, 42,396,528, 534 Quantum dot(s), 440,445 Quantum effect device(s), 440 Quantum wire(s), 440,445 Radiation condition, 41 Radiation pressure, 75, 123 Reactance, 264,394 surface, 394 surface inductive, 264 Reflection, 118 laws of, 119 Reflection coefficient, 267, 458 complex, 267 current, 458 power wave, 464 voltage, 457 Refraction, 118 Refractive index, 174 Relativistic mass, 126 Relativity, 75 Einstein’s special theory of, 75 Galilean, 76 Generalized Galilean, 542 postulate of, 76, Relaxation time, 246,392 momentum, 243,279 vortex, 379 Resistance, line, 455 Resistivity, flow, 353 ac flux-flow, 380 dc flux-flow, 380 effective ac, 384 Resistor(s), 49 Resonance frequency, 331,397,532 cyclotron, 331 Resonator(s), 525 cavity, 531 dielectric, 535 microwave, 525 transmission line, 529 Rutgers’ formula, 320 Scattering matrix, 462,512 parameters, 462 Schrodinger equation, 304,330 Selectivity, 528 Self-consistent scheme, 183 Shapiro step(s), 422 Shifter, 134 Skin depth, normal, 263,571 Skin effect, 185,470 anomalous, 185,279,287 Space reflection, 35 Speed, 19 of light, 19 Strain, 133 infinitesimal, 135 principal, 177 Strain-optical coefficients, 177 Stress(es), 141 electric, 164 electromagnetic, 153,253 normal, 141 principal, 171 shearing, 141 thermal, 219,226 Stress-optical coefficients, 176 Superconductivity, 228 Superconductor(s), 229 anisotropic, 292 deformable, 542 INDEX elastic, 546 hard, 353,360 moving, 540 rotating, 540 soft, 361 Supercurrent, 235 density, 235 Surface charge density, Surface free charge density, 31 Surface impedance, 271,390 Surface resistance, 264,278,394,469 Surface wave, 216 electromagnetoelastic, 554 magnetic, 549 Rayleigh, 216,549 Susceptibility, 36 electric, 36 magnetic, 36 Synchronous system, 450 Temperature, 144 absolute, 144, critical, 91, 229 Curie, 91 reduced, 275 transition, 229 Tensor(s), 133 Cauchy deformation, 134 Cauchy stress, 142 deformation gradient, 134 electromagnetic stress, 148 Euclidean metric, 134 infinitesimal strain, 135 Lagrangian strain, 134 objective, 138 rate of strain, 135 rotation, 136 spin, 135 stress, 140 Theorem Cauchy’s, 141 Eamshaw’s, 60 Gauss’, lo,30 Poynting’s, 63,65 Thomson’s, 59 Uniqueness, 70,249 Theory, 1, 149, 185,235,306,321,565 BCS, 306 electromagnetic, London, 235,245 magnetoelastic, 565 Mattis-Bardeen, 289 Minkowski, 84,537 of relativity, 75 Thermal conductivity, 151,581 Thermally activated flux-flow, 358 Thermodynamics, 142 the first law of, 143 the second law of, 143 Thermoelastic conductors, 149-163 Thermoelastic dielectrics, 163-170 Thermoelectric coefficient, 152 Thermopiezoelectric solid(s), 166 Thin film, 341,343 Time reversal, 35 Torque, 15 electric, 164 magnetic, 153 Transformation(s), 36,42,75 Euclidean, 138 Fourier, 42 Galilean, 85 gauge, 39,557 Lorentz, 75,77 of coordinate(s), 77 Transistor, superconducting, 437 Transmission coefficient, 267,458 complex, 267 voltage, 458 Transmission line(s), 453 coupled, 508 equations, 455 equivalent, 498 superconducting, 469 Tunneling, 414 Josephson pair, 559 phonon-assisted, 559 single electron, 439 Vector(s), 31 axial, 36 complex Poynting, 66 displacement, 134 electric displacement, 31 four-, 79 four-current, 78 four-momentum, 126 four-potential, 80 625 four-velocity, 125 polar, 36 Poynting, 64 propagation,42 pseudo-,36 roation, 136 stress,141 vorticity, 136 Velocity, 50, 131 flux-flow, 355 gradient, 135 group, 51,521 phasevelocity, 42,50 Voltage-phaserelation, Josephson,416 Voltage standing-waveratio, 459 Vortex dynamics,347,379 Vortex electric field, 352, 376 Vortex line(s), 347,351 Vortex magneticfield, 376,385 Wave(s),26,583 attenuation,522 circularly polarized, 95 elastic,547,576 electromagnetic,26 equation,26 linearly polarized, 97 magnetic,547,576 magnetoelastic,546 magnetoelasticplane,569 packet,51 plane,26,80 power, 462 reflected, 118,265,457 surface,216 TEM, 467 thermomagnetic,410 transmitted,118,266 voltage, 457 Waveguide( 388 rectangular,516 superconductingplanar,268,388 anisotropic,295,499 Wavelength,cutoff, 518 Weak link(s), 414 Zero dc-resistance,230 .. .Electrodynamics of Solids and Microwave Superconductivity SHU-ANG ZHOU EricssonComponentsAB New York l A Wiley- IntersciencePublication JOHN WILEY & SONS, INC Chichester Weinheim... 1-800-CALL -WILEY Library of Congress Cataloging in Publication Data: Zhou, Shu-Ang Electrodynamicsof solids and microwave superconductivity/ Shu -Ang Zhou p cm - (Wiley seriesin microwave and optical... field of electrodynamics of continua was reopened by a group of scientists in the field of mechanics who had seldom engagedin researchin the field of electrodynamics of continua since the time of