Electromagnetic Fields – Restrictions and Approximation

Abstract

1 Introduction. 1.1 Introduction. 1.2 Subject and Method of Investigation. 1.3 Realizability, Approximability, Amplitude Approximability. 1.4 Outline of the Book. 2 Nonapproximability of Patterns. 2.1 Nonapproximability and Zero Lines of the Real Wave Field. 2.2 Examples of Specific Lines. aAA ProhibitedaAA Antenna Shapes. 2.3 Amplitude Nonapproximability. 2.4 Probabilistic Description of Body Shape by the Likeness Principle. 2.5 Body Shape Reconstruction by its Scattered Patterns. 2.6 Properties of Specific Lines. 3 Nonapproximability of Near Fields. 3.1 Approximability Condition for Near Fields. 3.2 Construction of a Field by its Zero Line. Case of the Circle Arc. 3.3 Analytical Extension of the Eigenoscillation Field outside the Boundary of the Domain. 4 The Norm of the Current. 4.1 The Minimal Current Norm at a Given Accuracy of Approximation. 4.2 Generalized Functions of Double Orthogonality. Nonapproximability and Existence of Nonradiating Currents. 4.3 Optimal Current Synthesis. The General Case. 4.4 Domain of Specific Line Influence. 5 Electromagnetic Field. The Maxwell Equations. 5.1 Trivial Generalizations. 5.2 Properties of Specific Surfaces. 6 Long Narrow Beam of Electromagnetic Waves. 6.1 Two--dimensional Fourier Transformation. 6.2 Transmission of Field by Wave Beam: Possibilities and Restrictions. 6.3 Shape of Antenna and Rectenna. Bibliography for Chapters 1aAA6. Appendix: Antenna Synthesis by Amplitude Radiation Pattern and Modified Phase Problem (by N. N. Voitovich). A.1 Synthesis of Antennas by Amplitude Radiation Pattern. A.1.1 Introduction. A.1.2 Problem formulation for the curvilinear antenna. A.1.3 Reducing to the LagrangeaAAEuler equation. A.1.4 Case of linear antenna. Main properties of solutions. A.2 Modified Phase Problem. Continuous Case. A.2.1 Modified phase problem and related mathematical and physical problems. A.2.2 Analytical solutions to the LagrangeaAAEuler equation for linear antenna. Theoretical results. A.2.3 Solution branching. A.2.4 Numerical example. Problem with symmetrical data. A.2.5 Problems with nonsymmetrical data. A.3 Modified Phase Problem. Discrete Case. A.3.1 Problem formulation for linear antenna array. LagrangeaAAEuler equations. A.3.2 Theoretical results. A.3.3 Numerical results. Bibliography for Appendix. Index.