Optimization Methods in Electromagnetic Radiation

Contents
Preface
1 Arrays of Point and Line Sources, and Optimization
1.1 The Problem of Antenna Optimization
1.2 Arrays of Point Sources
1.2.1 The Linear Array
1.2.2 Circular Arrays
1.3 Maximization of Directivity and Super-gain
1.3.1 Directivity and Other Measures of Performance
1.3.2 Maximization of Directivity
1.4 Dolph-Tschebyshe. Arrays
1.4.1 Tschebyshe. Polynomials
1.4.2 The Dolph Problem
1.5 Line Sources
1.5.1 The Linear Line Source
1.5.2 The Circular Line Source
1.5.3 Numerical Quadrature
1.6 Conclusion 2 Discussion of Maxwell s Equations
2.1 Introduction
2.2 Geometry of the Radiating Structure
2.3 Maxwell s Equations in Integral Form
2.4 The Constitutive Relations
2.5 Maxwell s Equations in Differential Form
2.6 Energy Flow and the Poynting Vector
2.7 Time Harmonic Fields
2.8 Vector Potentials
2.9 Radiation Condition, Far Field Pattern
2.10 Radiating Dipoles and Line Sources
2.11 Boundary Conditions on Interfaces
2.12 Hertz Potentials and Classes of Solutions
2.13 Radiation Problems in Two Dimensions 3 Optimization Theory for Antennas
3.1 Introductory Remarks
3.2 The General Optimization Problem
3.2.1 Existence and Uniqueness
3.2.2 The Modeling of Constraints
3.2.3 Extreme Points and Optimal Solutions
3.2.4 The Lagrange Multiplier Rule
3.2.5 Methods of Finite Dimensional Approximation
3.3 Far Field Patterns and Far Field Operators
3.4 Measures of Antenna Performance 4 The Synthesis Problem
4.1 Introductory Remarks
4.2 Remarks on Ill-Posed Problems
4.3 Regularization by Constraints
4.4 The Tikhonov Regularization
4.5 The Synthesis Problem for the Finite Linear Line Source
4.5.1 Basic Equations
4.5.2 The Nystr om Method
4.5.3 Numerical Solution of the Normal Equations
4.5.4 Applications of the Regularization Techniques 5Boundary Value Problems for the Two-Dimensional Helmholtz Equation
5.1 Introduction and Formulation of the Problems
5.2 Rellich s Lemma and