Electromagnetic scattering from complex objects has been an area of in-depth research for many years. A variety of solution methodologies have been developed and utilised for the solution of ever increasingly complex problems. Among these methodologies, the subject of impedance boundary conditions has interested the authors for some time. In short, impedance boundary conditions allow one to replace a complex structure with an appropriate impedance relationship between the electric and magnetic fields on the surface of the object. This simplifies the solution of the problem considerably, allowing one to ignore the complexity of the internal structure beneath the surface. This book examines impedance boundary conditions in electromagnetics. The introductory chapter provides a presentation of the role of the impedance boundary conditions in solving practical electromagnetic problems and some historical background. One of the main objectives of this book is to present a unified and thorough discussion of this important subject. A method based on a spectral domain approach is presented to derive the Higher Order Impedance Boundary Conditions (HOIBC). The method includes all of the existing approximate boundary conditions, such as the Standard Impedence Boundary Condition, the Tensor Impedence Boundary Condition and the Generalised Impedance Boundary Conditions, as special cases. The special domain approach is applicable to complex coatings and surface treatments as well as simple dielectric coatings. The spectral domain approach is employed to determine the appropriate boundary conditions for planar dielectric coatings, chiral coatings and corregated conductors. The accuracy of the proposal boundary conditions is discussed. The approach is then extended to include the effects of curvature and is applied to curved dielectric and chiral coatings. Numerical data is presented to critically assess the accuracy of the results obtained using various forms of the impedence boundary conditions. A number of appendices that provide more detail on some of the topics addressed in the main body of the book and a selective list of references directly related to the topics addressed in this book are also included.
Preface
Nomenclature
Abbreviations
Introduction
Background
Scattering by Conducting Bodies
Scattering by Coated Conducting Bodies
Approximate Boundary Conditions
A Bit of History
Organization of This Book
Spectral Domain Theory of Higher Order Impedance Boundary Conditions
Step 1: Exact Spectral Domain Boundary Conditions
Step 2: Polynomial Approximations
Step 3: Coefficient Determination
Step 4: Construction of the Spatial Domain Equations
Special Cases
TIBC
SIBC
GIBC
Conclusions
Planar Higher Order Impedance Boundary Conditions
Planar Dielectric Coatings
Exact Spectral Domain Boundary Conditions
Higher Order Impedance Boundary Conditions
Examples
Corrugated Conductors
Planar Chiral Coatings
Exact Spectral Domain Boundary Conditions
Higher Order Impedance Boundary Conditions
Examples
Conclusions
Boundary Conditions for Curved Dielectric and Chiral Coatings
Scattering by Dielectric Coated Circular Cylinders using Planar HOIBC
Higher Order Impedance Boundary Conditions for Curved Coatings
Exact Spectral Domain Boundary Conditions
Higher Order Impedance Boundary Conditions
Examples
Conclusions
Scattering by a Dielectric-Filled Grove in a Ground Plane
Higher Order Impedance Boundary Condition Solution
Exterior Region
Interior Region
Edge Conditions
Exact Formulation: A Mode Matching Approach
Examples
Rectangular Grooves
Rectangular Groove: Lossy Dielectric
Asymmetric Groove
Tapered Groove: Two-Layer Dielectric
Conclusions
Scattering by Two-Dimensional Dielectric-Coated Cylinders
HOIBC Solution of the Scattering Problem
Exterior Problem
Interior Problem
Method of Moments Solution
Exact Solution
Superquadric Cylinders
Examples
Impedance Approximation
Circular Cylinder: Bistatic RCS
Superquadric Cylinders: Bistatic RCS
Superquadric Cylinders: Monostatic RCS
Superquadric Cylinder: Magnetic Coating
Conclusions
Scattering by Dielectric-Coated Bodies of Revolution
Problem Geometry
Fourier Series Decomposition
Exact Solution
HOIBC Solution
Exterior Region
Interior Region
Examples
Coated Sphere: Validation
Superquadric Cylinders: Curvature Effects
Spheroid: Monostatic RCS
Superquadric Cylinder: Magnetic Coating
Conclusions
Appendixes
A Properties of Exact Impedance Tensors
A.1 Impedance Matrices for Lossless Boundaries
A.2 Impedance Matrices for Reciprocal Boundaries
B Symmetry Properties for the Polynomials P1-P8
C Surface Waves on Impedance Surfaces
D Plane Wave Scattering at an Impedance Plane
E Plane Wave Scattering at an Impedance Cylinder
F Matrix Elements for the CFIE Portion of the BOR Solution
G Transformation of the HOBIC onto the BOR
H Matrix Elements for the HOBIC Portion of the BOR
Bibliography
Index
Biography
Daniel J. Hoppe