Abdelkhalak El Hami - Applications and Metrology at Nanometer-Scale 2

1 Cover

2 Title Page Reliability of Multiphysical Systems Set coordinated by Abdelkhalak El Hami Volume 10

3 Copyright First published 2021 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 27-37 St George’s Road London SW19 4EU UK www.iste.co.uk John Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USA www.wiley.com © ISTE Ltd 2021 The rights of Pierre-Richard Dahoo, Philippe Pougnet and Abdelkhalak El Hami to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Control Number: 2020950471 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-78630-687-6

4 Preface

5 Introduction

6 1 Measurement Systems Using Polarized Light 1.1. Introduction 1.2. Matrix optics 1.3. Photon emission and detection 1.4. Application exercises on interferometry 1.5. Appendices 1.6. Conclusion

7 2 Quantum-scale Interaction 2.1. Introduction 2.2. The spin through the Dirac equation 2.3. The density matrix for a two-level laser system 2.4. Ising’s phenomenological model for cooperative effects

8 3 Quantum Optics and Quantum Computers 3.1. Introduction 3.2. Polarized light in quantum mechanics 3.3. Introduction to quantum computers 3.4. Preparing a qubit 3.5. Application: interaction of a qubit with a classical field 3.6. Applying Ramsey fringes to evaluate the duration of phase coherence

9 4 Reliability-based Design Optimization of Structures 4.1. Introduction 4.2. Deterministic optimization 4.3. Reliability analysis 4.4. Reliability-based design optimization 4.5. Applications 4.6. Reliability-based design optimization in nanotechnology 4.7. Conclusion

10 Appendix: Short Overview of Quantum Mechanics

11 References

12 Index

13 End User License Agreement

1 Chapter 1 Figure 1.1. Crossing of a plane diopter for n1n2. For a colo... Figure 1.2. Light radiation or vector radius of parameters r and θ. For a color ... Figure 1.3. Transfer matrix in an isotropic and homogeneous medium Figure 1.4. Transfer matrix at the crossing of a diopter Figure 1.5. Optical transfer matrices of different centered systems Figure 1.6. Optical assembly for a telescope in a lidar Figure 1.7. Transmission of a Gaussian beam by a thin lens Figure 1.8. Optical mounting of mirrors and retro-reflectors Figure 1.9. Light polarization states. For a color version of this figure, seew... Figure 1.10. Electric field vibrations in the polarization plane as a function o... Figure 1.11. Electric field vibration after a linear polarizer. For a color vers... Figure 1.12. Vibration of the electric field after a linear polarizer and differ... Figure 1.13. Electric field vibration after a rotator. For a color version of th... Figure 1.14. Combination of three devices. For a color version of this figure, s... Figure 1.15. Cross polarizers. For a color version of this figure, seewww.iste.... Figure 1.16. Probability distribution for a thermal source. For a color version ... Figure 1.17. Probability distribution for a coherent source. For a color version... Figure 1.18. Light detection Figure 1.19. Beam splitter devices Figure 1.20. Diagram of an interferometer. For a color version of this figure, s...Figure 1.21. Diagram of a Fabry–Pérot cavity. For a color version of this figure...Figure 1.22. Schematic diagram of the device of a lambda meter. For a color vers... Reminder: Figure 1.22. Schematic diagram of the device of a lambda meter Reminder: Figure 1.22. Schematic diagram of the device of a lambda meter Figure 1.23. Diagram of the light path and reference axes Figure 1.24. Coordinate axes for p wave and s wave. For a color version of this ...Figure 1.25. Diagram of a homodyne interferometer and of the paths s and p. For ...Figure 1.26. Diagram of the interferometric measurement device. For a color vers...Figure 1.27. Laser interferometer: a) homodyne and b) heterodyne. For a color ve...Figure 1.28. Dimensional metrology. For a color version of this figure, see www....Figure 1.29. Heterodyne laser interferometer with cube corners. For a color vers... Reminder: Figure 1.29. Heterodyne laser interferometer with cube corners Figure 1.30. Electrical signals measured in the detection bandwidth. For a color...Figure 1.31. Elliptical polarization state and ellipsometric parameters [DAH 16] Figure 1.32. Diagram of a phase modulation ellipsometer. For a color version of ...Figure 1.33. Diagram of an ellipsometer in PCSA mode and reflected light. For a ...Figure 1.34. Reference mark and sign convention to be adopted. For a color versi...

2 Chapter 2Figure 2.1. Parallel spins. For a color version of this figure, see www.iste.co....Figure 2.2. Antiparallel spins. For a color version of this figure, see www.iste...

3 Chapter 3Figure 3.1. Energy diagram of a two-level quantum system: a ground state ∣...Figure 3.2. Bloch sphere of unit radius defined by a polar angle θ and an azimut...Figure 3.3. Graphical representation of the CNOT gate acting on a two-qubit regi...Figure 3.4. Schematic diagram of a quantum computation. The time goes from left ...Figure 3.5. Realization of the Deutsch algorithm in a quantum computer with a tw...Figure 3.6. Variation of the probability of the excited state population as a fu...

4 Chapter 4Figure 4.1. Deterministic optimization based on reaching a safety factor level. ...Figure 4.2. Normal physical space. For a color version of this figure, see www.i...Figure 4.3. Reliability index assessment process Figure 4.4. Comparison between the solutions of the RBDO and DDO methods. For a ...Figure 4.5. Total cost (CT), cost of failure (Cf) and initial cost of the struct...Figure 4.6. Cantilever beam in free bending mode. For a color version of this fi...Figure 4.7. 3D circular plate. For a color version of this figure, see www.iste....Figure 4.8. Amplitude of the displacement versus frequency; the area correspondi...Figure 4.9. Model of the circular plate. For a color version of this figure, see ...Figure 4.10. Dimensions of the section of the hook under study. For a color vers...Figure 4.11. Finite element model of the hook. For a color Figure 4.12. Sensitivity analysis of the parameters D1, D2, D3, D5, D6, Rc, R0 w...Figure 4.13. Sensitivity analysis of the parameters D1, D2, D3, D5, D6, Rc, R0 w...Figure 4.14. Various shapes of the optimal volume solution for the safety factor...Figure 4.15. Optimal solution shape of volume and von Mises stress. For a color ...Figure 4.16. The von Mises stress and the first mode along the X axis of the opt...Figure 4.17. Schematic cross-section of a six-layer printed circuit r Figure 4.18. Architecture of the fiber-reinforced PCB: a) overview, b) detail of.