Phase Optimization Problems

1 Introduction
2 Formulation of physical problems
2.1 Forming fields of given structure
2.2 Antenna synthesis problems
2.3 Phase optimization problems in waveguides and open resonators
3 Mathematical formulation of the problems
3.1 Variational problems with no amplitude-phase restrictions on sought functions
3.2 Variational problems with amplitude-phase restrictions on sought functions
3.3 Homogeneous optimization problems
4 Analytical solutions
4.1 A general class of Hammerstein nonlinear integral equations with free phase
4.2 Particular case: one-dimensional Fourier transform
4.3 Particular case: discrete Fourier transform
4.4 Particular case: Hankel transform
4.5 Generalized nonlinear integral equation concerned regularized problems
5 Numerical methods, algorithms, and results
5.1 Theoretical results
5.2 Methods of Newton type
5.3 Method of opposite directions
5.4 Method of generalized separation of variables
5.5 Homogeneous problems
6 Nonstandard inverse problems of diffraction theory
6.1 Introduction
6.2 Diffraction on impedance surfaces. "Invisible" bodies and screens
6.3 Metallic short-periodical arrays
6.4 Creation of fields with circular polarization
Afterword: Ethical aspects of scientific work