Ismo V. Lindell

Multiforms, Dyadics, and Electromagnetic Media (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book applies the four-dimensional formalism with an extended toolbox of operation rules, allowing readers to define more general classes of electromagnetic media and to analyze EM waves that can exist in them * End-of-chapter exercises * Formalism allows readers to find novel classes of media * Covers various properties of electromagnetic media in terms of which they can be set in different classes

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 416
• Erscheinungstermin: 18. Februar 2015
• Englisch
• ISBN-13: 9781119052401
• Artikelnr.: 42366876

Autorenporträt

Ismo V. Lindell is a Professor Emeritus in the Department of Radio Science and Engineering, in the School of Electrical Engineering at the Aalto University, Finland. Dr. Lindell has received many honors in the course of his career, including his recognition as an IEEE Fellow in 1990 for his contributions to electromagnetic theory and for the development of education in electromagnetics in Finland. Dr. Lindell has authored or co-authored 3 books in English, authored or co-authored 10 books in Finnish, and published several hundred articles in professional journals, conference proceedings, and contributed chapters to other books.

Inhaltsangabe

Preface xi 1 Multivectors and Multiforms 1 1.1 Vectors and One-Forms, 1
1.1.1 Bar Product 1 1.1.2 Basis Expansions 2 1.2 Bivectors and Two-Forms,
3 1.2.1 Wedge Product ^ 3 1.2.2 Basis Expansions 4 1.2.3 Bar Product 5
1.2.4 Contraction Products rfloor and lfloor 6 1.2.5 Decomposition of
Vectors and One-Forms 8 1.3 Multivectors and Multiforms, 8 1.3.1 Basis of
Multivectors 9 1.3.2 Bar Product of Multivectors and Multiforms 10 1.3.3
Contraction of Trivectors and Three-Forms 11 1.3.4 Contraction of
Quadrivectors and Four-Forms 12 1.3.5 Construction of Reciprocal Basis 13
1.3.6 Contraction of Quintivector 14 1.3.7 Generalized Bac-Cab Rules 14 1.4
Some Properties of Bivectors and Two-Forms, 16 1.4.1 Bivector Invariant 16
1.4.2 Natural Dot Product 17 1.4.3 Bivector as Mapping 17 Problems, 18 2
Dyadics 21 2.1 Mapping Vectors and One-Forms, 21 2.1.1 Dyadics 21 2.1.2
Double-Bar Product 23 2.1.3 Metric Dyadics 24 2.2 Mapping Multivectors
and Multiforms, 25 2.2.1 Bidyadics 25 2.2.2 Double-Wedge Product ^^ 2.2.3
Double-Wedge Powers 28 2.2.4 Double Contractions lfloor lfloor and rfloor
rfloor 30 2.2.5 Natural Dot Product for Bidyadics 31 2.3 Dyadic Identities,
32 2.3.1 Contraction Identities 32 2.3.2 Special Cases 33 2.3.3 More
General Rules 35 2.3.4 Cayley-Hamilton Equation 36 2.3.5 Inverse Dyadics 36
2.4 Rank of Dyadics, 39 2.5 Eigenproblems, 41 2.5.1 Eigenvectors and Eigen
One-Forms 41 2.5.2 Reduced Cayley-Hamilton Equations 42 2.5.3 Construction
of Eigenvectors 43 2.6 Metric Dyadics, 45 2.6.1 Symmetric Dyadics 46 2.6.2
Antisymmetric Dyadics 47 2.6.3 Inverse Rules for Metric Dyadics 48
Problems, 49 3 Bidyadics 53 3.1 Cayley-Hamilton Equation, 54 3.1.1
Coefficient Functions 55 3.1.2 Determinant of a Bidyadic 57 3.1.3
Antisymmetric Bidyadic 57 3.2 Bidyadic Eigenproblem, 58 3.2.1 Eigenbidyadic
C. 60 3.2.2 Eigenbidyadic C+ 60 3.3 Hehl-Obukhov Decomposition, 61 3.4
Example: Simple Antisymmetric Bidyadic, 64 3.5 Inverse Rules for Bidyadics,
66 3.5.1 Skewon Bidyadic 67 3.5.2 Extended Bidyadics 70 3.5.3 3D Expansions
73 Problems, 74 4 Special Dyadics and Bidyadics 79 4.1 Orthogonality
Conditions, 79 4.1.1 Orthogonality of Dyadics 79 4.1.2 Orthogonality of
Bidyadics 81 4.2 Nilpotent Dyadics and Bidyadics, 81 4.3 Projection Dyadics
and Bidyadics, 83 4.4 Unipotent Dyadics and Bidyadics, 85 4.5
Almost-Complex Dyadics, 87 4.5.1 Two-Dimensional AC Dyadics 89 4.5.2
Four-Dimensional AC Dyadics 89 4.6 Almost-Complex Bidyadics, 91 4.7
Modified Closure Relation, 93 4.7.1 Equivalent Conditions 94 4.7.2
Solutions 94 4.7.3 Testing the Two Solutions 96 Problems, 98 5
Electromagnetic Fields 101 5.1 Field Equations, 101 5.1.1 Differentiation
Operator 101 5.1.2 Maxwell Equations 103 5.1.3 Potential One-Form 105 5.2
Medium Equations, 106 5.2.1 Medium Bidyadics 106 5.2.2 Potential Equation
107 5.2.3 Expansions of Medium Bidyadics 107 5.2.4 Gibbsian Representation
109 5.3 Basic Classes of Media, 110 5.3.1 Hehl-Obukhov Decomposition 110
5.3.2 3D Expansions 112 5.3.3 Simple Principal Medium 114 5.4 Interfaces
and Boundaries, 117 5.4.1 Interface Conditions 117 5.4.2 Boundary
Conditions 119 5.5 Power and Energy, 123 5.5.1 Bilinear Invariants 123
5.5.2 The Stress-Energy Dyadic 125 5.5.3 Differentiation Rule 127 5.6 Plane
Waves, 128 5.6.1 Basic Equations 128 5.6.2 Dispersion Equation 130 5.6.3
Special Cases 132 5.6.4 Plane-Wave Fields 132 5.6.5 Simple Principal Medium
134 5.6.6 Handedness of Plane Wave 135 Problems, 136 6 Transformation of
Fields and Media 141 6.1 Affine Transformation, 141 6.1.1 Transformation of
Fields 141 6.1.2 Transformation of Media 142 6.1.3 Dispersion Equation 144
6.1.4 Simple Principal Medium 145 6.2 Duality Transformation, 145 6.2.1
Transformation of Fields 146 6.2.2 Involutionary Duality Transformation 147
6.2.3 Transformation of Media 149 6.3 Transformation of Boundary
Conditions, 150 6.3.1 Simple Principal Medium 152 6.3.2 Plane Wave 152 6.4
Reciprocity Transformation, 153 6.4.1 Medium Transformation 153 6.4.2
Reciprocity Conditions 155 6.4.3 Field Relations 157 6.4.4 Time-Harmonic
Fields 158 6.5 Conformal Transformation, 159 6.5.1 Properties of the
Conformal Transformation 160 6.5.2 Field Transformation 164 6.5.3 Medium
Transformation 165 Problems, 166 7 Basic Classes of Electromagnetic Media
169 7.1 Gibbsian Isotropy, 169 7.1.1 Gibbsian Isotropic Medium 169 7.1.2
Gibbsian Bi-isotropic Medium 170 7.1.3 Decomposition of GBI Medium 171
7.1.4 Affine Transformation 173 7.1.5 Eigenfields in GBI Medium 174 7.1.6
Plane Wave in GBI Medium 176 7.2 The Axion Medium, 178 7.2.1 Perfect
Electromagnetic Conductor 179 7.2.2 PEMC as Limiting Case of GBI Medium 180
7.2.3 PEMC Boundary Problems 181 7.3 Skewon-Axion Media, 182 7.3.1 Plane
Wave in Skewon-Axion Medium 184 7.3.2 Gibbsian Representation 185 7.3.3
Boundary Conditions 187 7.4 Extended Skewon-Axion Media, 192 Problems, 194
8 Quadratic Media 197 8.1 P Media and Q Media, 197 8.2 Transformations, 200
8.3 Spatial Expansions, 201 8.3.1 Spatial Expansion of Q Media 201 8.3.2
Spatial Expansion of P Media 203 8.3.3 Relation Between P Media and Q Media
204 8.4 Plane Waves, 205 8.4.1 Plane Waves in Q Media 205 8.4.2 Plane Waves
in P Media 207 8.4.3 P Medium as Boundary Material 208 8.5 P-Axion and
Q-Axion Media, 209 8.6 Extended Q Media, 211 8.6.1 Gibbsian Representation
211 8.6.2 Field Decomposition 214 8.6.3 Transformations 215 8.6.4 Plane
Waves in Extended Q Media 215 8.7 Extended P Media, 218 8.7.1 Medium
Conditions 218 8.7.2 Plane Waves in Extended P Media 219 8.7.3 Field
Conditions 220 Problems, 221 9 Media Defined by Bidyadic Equations 225 9.1
Quadratic Equation, 226 9.1.1 SD Media 227 9.1.2 Eigenexpansions 228 9.1.3
Duality Transformation 229 9.1.4 3D Representations 231 9.1.5 SDN Media 234
9.2 Cubic Equation, 235 9.2.1 CU Media 235 9.2.2 Eigenexpansions 236 9.2.3
Examples of CU Media 238 9.3 Bi-Quadratic Equation, 240 9.3.1 BQ Media 241
9.3.2 Eigenexpansions 242 9.3.3 3D Representation 244 9.3.4 Special Case
245 Problems, 246 10 Media Defined by Plane-Wave Properties 249 10.1 Media
with No Dispersion Equation (NDE Media), 249 10.1.1 Two Cases of Solutions
250 10.1.2 Plane-Wave Fields in NDE Media 255 10.1.3 Other Possible NDE
Media 257 10.2 Decomposable Media, 259 10.2.1 Special Cases 259 10.2.2
DC-Medium Subclasses 263 10.2.3 Plane-Wave Properties 267 Problems, 269
Appendix A Solutions to Problems 273 Appendix B Transformation to Gibbsian
Formalism 369 Appendix C Multivector and Dyadic Identities 375 References
389 Index 395