Wave Scattering Theory: A Series Approach Based on the Fourier Transformation

ISBN-13: 9783642639951 / Angielski / Miękka / 2011 / 244 str.

Hyo J. Eom

Opis

The Fourier transform technique has been widely used in electrical engineer ing, which covers signal processing, communication, system control, electro magnetics, and optics. The Fourier transform-technique is particularly useful in electromagnetics and optics since it provides a convenient mathematical representation for wave scattering, diffraction, and propagation. Thus the Fourier transform technique has been long applied to the wave scattering problems that are often encountered in microwave antenna, radiation, diffrac tion, and electromagnetic interference. In order to u derstand wave scattering in general, it is necessary to solve the wave equation subject to the prescribed boundary conditions. The purpose of this monograph is to present rigorous so lutions to the boundary-value problems by solving the wave equation based on the Fourier transform. In this monograph the technique of separation of vari ables is used to solve the wave equation for canonical scattering geometries such as conducting waveguide structures and rectangular/circular apertures. The Fourier transform, mode-matching, and residue calculus techniques are applied to obtain simple, analytic, and rapidly-convergent series solutions. The residue calculus technique is particularly instrumental in converting the solutions into series representations that are efficient and amenable to nu merical analysis. We next summarize the steps of analysis method for the scattering problems considered in this book. 1. Divide the scattering domain into closed and open regions. 2. Represent the scattered fields in the closed and open regions in terms of the Fourier series and transform, respectively. 3."

Spis treści

1. Rectangular Grooves in a Plane.- 1.1 EM Scattering from a Rectangular Groove in a Conducting Plane.- 1.1.1 TE Scattering [6].- 1.1.2 TM Scattering [7].- 1.1.3 Appendix.- 1.2 EM Scattering from Multiple Grooves in a Conducting Plane.- 1.2.1 TE Scattering [12].- 1.2.2 TM Scattering.- 1.2.3 Appendix.- 1.3 EM Scattering from Grooves in a Dielectric-Covered Ground Plane.- 1.3.1 TE Scattering [14].- 1.3.2 TM Scattering.- 1.3.3 Appendix.- 1.4 EM Scattering from Rectangular Grooves in a Parallel-Plate Waveguide.- 1.4.1 TE Scattering [16].- 1.4.2 TM Scattering [17].- 1.5 EM Scattering from Double Grooves in Parallel Plates [18].- 1.5.1 TE Scattering.- 1.5.2 TM Scattering.- 1.5.3 Appendix.- 1.6 Water Wave Scattering from Rectangular Grooves in a Plane.- References for Chapter 1.- 2. Flanged Parallel-Plate Waveguide Array.- 2.1 EM Radiation from a Flanged Parallel-Plate Waveguide.- 2.1.1 TE Radiation [8,9].- 2.1.2 TM Radiation [10].- 2.2 EM Radiation from a Parallel-Plate Waveguide into a Dielectric Slab.- 2.2.1 TE Radiation.- 2.2.2 TM Radiation [17].- 2.3 TE Scattering from a Parallel-Plate Waveguide Array [18].- 2.4 EM Radiation from Obliquely-Flanged Parallel Plates.- 2.5 EM Radiation from Parallel Plates with a Window [24].- References for Chapter 2.- 3. Slits in a Plane.- 3.1 Electrostatic Potential Distribution Through a Slit in a Plane [1].- 3.2 Electrostatic Potential Distribution due to a Potential Across a Slit [3].- 3.3 EM Scattering from a Slit in a Conducting Plane.- 3.3.1 TE Scattering [10].- 3.3.2 TM Scattering [11].- 3.4 Magnetostatic Potential Distribution Through Slits in a Plane.- 3.5 EM Scattering from Slits in a Conducting Plane [13].- 3.5.1 TE Scattering.- 3.5.2 TM Scattering.- 3.6 EM Scattering from Slits in a Parallel-Plate Waveguide.- 3.6.1 TE Scattering [26].- 3.6.2 TM Scattering [27].- 3.7 EM Scattering from Slits in a Rectangular Cavity.- 3.7.1 TM Scattering [29].- 3.7.2 TE Scattering [30].- 3.8 EM Scattering from Slits in Parallel-Conducting Planes [31].- References for Chapter 3.- 4. Waveguides and Couplers.- 4.1 Inset Dielectric Guide.- 4.2 Groove Guide [4].- 4.2.1 TM Propagation.- 4.2.2 TE Propagation.- 4.3 Multiple Groove Guide [8].- 4.4 Corrugated Coaxial Line [10].- 4.5 Coaxial Line with a Gap [13].- 4.6 Coaxial Line with a Cavity [16].- 4.7 Corrugated Circular Cylinder [18].- 4.8 Parallel-Plate Double Slit Directional Coupler [23].- 4.9 Parallel-Plate Multiple Slit Directional Coupler [29].- References for Chapter 4.- 5. Junctions in Parallel-Plate/Rectangular Waveguide.- 5.1 T-Junction in a Parallel-Plate Waveguide.- 5.1.1 H-Plane T-Junction [4].- 5.1.2 E-Plane T-Junction [5].- 5.2 E-Plane T-Junction in a Rectangular Waveguide [6].- 5.3 H-Plane Double Junction [8].- 5.4 H-Plane Double Bend [9].- 5.5 Acoustic Double Junction in a Rectangular Waveguide [11].- 5.6 Acoustic Hybrid Junction in a Rectangular Waveguide [15].- 5.6.1 Hard-Surface Hybrid Junction.- 5.6.2 Soft-Surface Hybrid Junction.- 5.6.3 Appendix.- References for Chapter 5.- 6. Rectangular Apertures in a Plane.- 6.1 Static Potential Through a Rectangular Aperture in a Plane.- 6.1.1 Electrostatic Distribution [3].- 6.1.2 Magnetostatic Distribution.- 6.2 Acoustic Scattering from a Rectangular Aperture in a Hard Plane [7].- 6.3 Electrostatic Potential Through Rectangular Apertures in a Plane [9].- 6.4 Magnetostatic Potential Through Rectangular Apertures in a Plane [10].- 6.5 EM Scattering from Rectangular Apertures in a Conducting Plane [11].- 6.6 EM Scattering from Rectangular Apertures in a Rectangular Cavity [18].- References for Chapter 6.- 7. Circular Apertures in a Plane.- 7.1 Static Potential Through a Circular Aperture in a Plane.- 7.1.1 Electrostatic Distribution [1].- 7.1.2 Magnetostatic Distribution [4].- 7.2 Acoustic Scattering from a Circular Aperture in a Hard Plane [6].- 7.3 EM Scattering from a Circular Aperture in a Conducting Plane.- 7.4 Acoustic Radiation from a Flanged Circular Cylinder [15].- 7.5 Acoustic Scattering from Circular Apertures in a Hard Plane [17].- 7.6 Acoustic Radiation from Circular Cylinders in a Hard Plane [19].- References for Chapter 7.- 8. Annular Aperture in a Plane.- 8.1 Static Potential Through an Annular Aperture in a Plane.- 8.1.1 Electrostatic Distribution [4,5].- 8.1.2 Magnetostatic Distribution [4].- 8.2 EM Radiation from a Coaxial Line into a Parallel-Plate Waveguide [6].- 8.3 EM Radiation from a Coaxial Line into a Dielectric Slab [10].- 8.4 EM Radiation from a Monopole into a Parallel-Plate Waveguide [17].- References for Chapter 8.- 9. Circumferential Apertures on a Circular Cylinder.- 9.1 EM Radiation from an Aperture on a Shorted Coaxial Line [1].- 9.1.1 Field Analysis.- 9.1.2 Appendix.- 9.2 EM Radiation from Apertures on a Shorted Coaxial Line [3].- 9.3 EM Radiation from Apertures on a Coaxial Line [4].- 9.4 EM Radiation from Apertures on a Coaxial Line with a Cover [6].- 9.5 EM Radiation from Apertures on a Circular Cylinder [10].- 9.5.1 TE Radiation.- 9.5.2 TM Radiation.- References for Chapter 9.- A. Appendix.- A.1 Vector Potentials and Field Representations.

Blurb

The book provides a unified technique of Fourier transform to solve the wave scattering, diffraction, penetration, and radiation problems where the technique of separation of variables is applicable. The book discusses wave scattering from waveguide discontinuities, various apertures, and coupling structures, often encountered in electromagnetic, electrostatic, magnetostatic, and acoustic problems. A system of simultaneous equations for the modal coefficients is formulated and the rapidly-convergent series solutions amenable to numerical computation are presented. The series solutions find practical applications in the design of microwave/acoustic transmission lines, waveguide filters, antennas, and electromagnetic interference/compatibilty-related problems.