Optimization of resonances for multilayer x-ray resonators

Preface of the series editor
......Page 7
Contents
......Page 9
1.2 Overview and Outline
......Page 11
1.3 Related work
......Page 14
2.1 Scattering problem
......Page 17
2.2 Optimization problem
......Page 19
2.3 Reformulation of the differential equation
......Page 22
2.4 Resonances
......Page 25
2.5 Optimization problem using resonances
......Page 29
3.1 Introduction to the kinematic approximation
......Page 33
3.2 General formalism......Page 34
3.3 Application to step profiles/Kinematic approximation
......Page 44
3.4 Conclusion
......Page 50
4.1 Derivatives of eigenvalues
......Page 51
4.2 Derivatives of eigenvalues and eigenvectors for a generalized eigenvalue problem
......Page 61
4.3 Objective function and discretization
......Page 65
4.4 Derivative of the discrete objective function
......Page 72
4.5 Derivative with respect to layer changes
......Page 77
5.1 Introductory examples
......Page 81
5.2 Matrix derivatives
......Page 85
5.3 Optimization results
......Page 89
6 Summary and Outlook
......Page 117
Appendix
......Page 119
Bibliography
......Page 121
Nomenclature
......Page 127
Acknowledgements
......Page 131
Buchrücken
......Page 134