Advanced Electromagnetic Wave Propagation Methods

Description

This textbook provides a solid foundation into many approaches that are used in the analysis of advanced electromagnetic wave propagation problems. The techniques discussed are essential to obtain closed-form solutions or asymptotic solutions and meet an existing need for instructors and students in electromagnetic theory. The book covers various advanced mathematical methods used in the evaluation of the electromagnetic fields in rectangular, cylindrical and spherical geometries. The mathematics of special functions (i.e., Bessel, Hankel, Airy, Legendre, Error, etc.) are covered in depth, including appropriate Appendices. The author takes particular care to provide detailed explanations of auxiliary potentials, Hertz’s vectors, Debye potentials, as well as the use of Green functions, the Watson transformation and the method of steepest descent in the solution of electromagnetic problems. Overall, this book is a good source for the many skills required in obtaining closed form and asymptotic solution, which in many instances cannot be obtained using computer codes of Maxwell’s equations. Thus, it provides an excellent training for preparing graduate students in their research work. This book is intended for a graduate course in electromagnetic theory for students in electrical engineering. Students in physics and professionals will also find it appropriate and useful. Cover Half Title Title Page Copyright Page Contents Preface Author 1. Maxwell's Equations 1.1 Maxwell's Equations in Vacuum 1.2 Polarization, Magnetization, and Conductivity 1.3 Maxwell's Equations in Terms of the Constitutive Parameters 1.4 Other Forms of Maxwell's Equations 1.5 Vector Potentials 1.6 Gauge Transformations and Lorenz's Conditions 1.7 Hertz's Vectors 1.8 Boundary Conditions 1.9 The Uniqueness Theorem 2. Radiation Fields 2.1 The Hertzian Electric Dipole 2.2 The Line Current Source of Infinite Length 2.3 Far-Field Relations 2.4 Solution to the Inhomogeneous Wave Equation 2.5 The Small-Loop Radiator 2.6 The Hertzian Magnetic Dipole 2.7 Duality 2.8 Images 3. Plane Waves 3.1 Properties of Plane Waves 3.2 Reflection and Transmission of Plane Waves 3.2.1 Perpendicular Polarization 3.2.2 Parallel Polarization 3.3 Reflection and Transmission in Dielectric Regions 3.4 Reflection and Transmission in Lossy Regions 3.4.1 Normal Incidence 3.4.2 Oblique Incidence 3.5 Other Types of Plane Waves 3.5.1 The Zenneck Wave 3.5.2 The Lateral Wave 3.5.3 The Trapped Wave 3.5.4 Other Types of Surface Waves 3.6 Reflection and Transmission from Interfaces 3.7 Waves in Inhomogeneous Regions 3.7.1 Rectangular Coordinates 3.7.2 Cylindrical Coordinates 3.8 The WKBJ Method 3.8.1 Normal Incidence 3.8.2 Oblique Incidence 4. Solutions to the Wave Equation 4.1 Wave Equations 4.2 Wave Equation in Rectangular Coordinates 4.3 Wave Propagation in Rectangular Geometries 4.3.1 Rectangular Waveguide 4.3.2 Rectangular Cavity 4.3.3 Partially Filled Rectangular Waveguide 4.3.4 Rectangular Waveguide Partially Filled with an Inhomogeneous Dielectric 4.3.5 The Rectangular Dielectric Waveguide 4.3.6 Dielectric Waveguide above a Conducting Plane 4.4 Wave Propagation in Cylindrical Geometries 4.4.1 The Cylindrical Waveguide 4.4.2 The Cylindrical Cavity 4.4.3 The Sectoral Waveguide 4.4.4 The Radial Waveguide 4.4.5 The Wedge Waveguide 4.4.6 The Sectoral Horn 4.4.7 The Bend Waveguide 4.4.8 The Cylindrical Dielectric Waveguide 4.4.9 The Dielectric Resonator 4.5 Wave Transformation from Rectangular to Cylindrical Coordinates 4.6 Wave Equation in Spherical Coordinates 4.6.1 The Conical Waveguide 4.6.2 The Spherical Cavity 4.6.3 The Ideal Earth-Ionosphere Cavity 4.7 Wave Transformation from Rectangular to Spherical Coordinates 5. Sturm-Liouville Equation and Green Functions 5.1 The Sturm-Liouville Equation 5.2 The Green Functions 5.3 Electromagnetic Field Sources 5.4 Green Function Using Eigenfunctions Solutions 5.4.1 One-Dimension Green Functions in Rectangular Coordinates 5.4.2 Two-Dimensional Green Functions in Rectangular Coordinates 5.4.3 Two-Dimensional Green Functions in Cylindrical Coordinates 5.4.3.1 An Angular Sector 5.4.3.2 A Cylindrical Region 5.4.4 Green Functions in Spherical Coordinates 5.5 Green Functions with Continuous Eigenvalues 5.5.1 Green Function for an Infinite-Length Angular Configuration 5.6 Direct Method for Green Function Solutions 5.6.1 One Dimension 5.6.2 Rectangular Region 5.6.3 Angular Sector 5.6.4 Infinite-Length Angular Configuration 5.6.5 Cylindrical Region 5.6.5.1 Source Inside the Cylinder 5.6.5.2 Source Outside the Cylinder 5.6.6 Spherical Region 5.6.7 Spherical Conductor 6. Integral Transforms for Green Functions 6.1 Integral Transform for the Wave Equation in Rectangular Coordinates 6.1.1 One-Dimensional Green Function 6.1.2 Two-Dimensional Green Function 6.1.3 Three-Dimensional Green Function 6.2 Integral Transform for the Wave Equation in Cylindrical Coordinates 6.2.1 The Hankel Transform 6.2.2 Two-Dimensional Green Function 6.2.3 Three-Dimensional Green Function 6.3 Integral Transform for the Wave Equation in Spherical Coordinates 6.3.1 The Spherical Hankel Transform 6.3.2 Three-Dimensional Green Function 7. Some Mathematical Methods 7.1 The Watson Transformation 7.2 The Method of Stationary Phase 7.3 The Method of Laplace 7.4 The Method of Steepest Descent 7.5 Pole Near the Saddle Point 8. Further Studies of Electromagnetic Waves in Rectangular Geometries 8.1 The Parallel-Plate Waveguide 8.1.1 TM Modes 8.1.2 TE Modes 8.2 Parallel-Plate Waveguide with a Step Discontinuity 8.3 Electric Line Source above a Perfect Conductor 8.3.1 Electric Line Source above a Lossy Surface 8.4 Radiation from a Narrow Slit 8.5 Vertical Hertzian Dipole above a Lossy Surface 8.5.1 Electric Hertzian Dipole 8.5.2 Magnetic Hertzian Dipole 8.6 Horizontal Electric Hertzian Dipole above a Lossy Surface 8.7 Vertical Electric and Magnetic Dipoles in a Lossy Region 8.7.1 Electric Dipole 8.7.2 Magnetic Dipole 8.8 Radiation from an Aperture in a Plane 8.8.1 Rectangular Aperture 8.8.2 Circular Aperture 8.9 Radiation from Apertures Using the Equivalence Principle 9. Further Studies of Electromagnetic Waves in Cylindricals Geometries 9.1 Diffraction by a Conducting Cylinder 9.2 Diffraction by a Lossy Dielectric Cylinder 9.3 Conducting Cylinder and an Infinite-Length Current Source 9.3.1 Conducting Cylinder and a Dipole Source 9.4 Lossy Dielectric Cylinder and an Infinite-Line Current Source 9.5 A Wedge and an Infinite-Length Current Source 9.5.1 A Wedge and a Dipole Source 9.6 Vertical Electric Hertzian Dipole above a Lossy Surface 9.6.1 Fields in the Air Region 9.6.2 Fields in the Lossy Region 9.7 Vertical Magnetic Hertzian Dipole above a Lossy Surface 9.8 Vertical Electric Dipole in a Three-Layer Region 9.9 Lateral Waves 9.10 An Infinite-Length Slot in a Circular Cylinder 9.11 Radiation from an Aperture in a Circular Cylinder 10. Further Studies of Electromagnetic Waves in Spherical Geometries 10.1 Diffraction by a Conducting Sphere 10.2 Diffraction by a Dielectric Sphere 10.3 A Vertical Electric Dipole above a Conducting Sphere 10.4 A Vertical Electric Dipole above a Spherical Surface 10.5 A Vertical Electric Dipole in a Spherical Waveguide—Zonal Harmonics Solution 10.6 A Vertical Magnetic Dipole in a Spherical Waveguide—Zonal Harmonics Solution 10.7 A Horizontal Electric Dipole in a Spherical Waveguide—Zonal Harmonics Solution 10.8 A Vertical Electric Dipole in the Earth-Ionosphere Waveguide—Modal Solution 10.9 A Vertical Magnetic Dipole in the Earth-Ionosphere Waveguide—Modal Solution 10.10 A Horizontal Electric Dipole in the Earth-Ionosphere Waveguide—Modal Solution Appendix A. Nomenclature and Units Appendix B. Vector and Other Identities Rectangular Coordinates: Cylindrical Coordinates: Spherical Coordinates: Vector Identities: Coordinates Transformations: Vector Transformations: Appendix C. Bessel Functions C.1 Bessel Functions of the First and Second Kind C.2 Hankel Functions C.3 Modified Bessel Functions C.4 Spherical Bessel Functions C.5 Complex Arguments C.6 The Sommerfeld Integrals Appendix D. Airy Functions Appendix E. Legendre Functions E.1 Legendre's Equation E.2 Associated Legendre Equation E.3 Spherical Harmonics E.4 Complex Order Appendix F. The Transformations λ = k sin β and λ = k cos β Appendix G. Error Function Appendix H. Orthogonality of Radial Solutions in Mode Theory Index