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Characterization of the laser induced damage threshold of mirrors in ...

Characterization of the laser induced damage threshold of mirrors in ...

Contents 1 Introduction

Contents 1 Introduction 1 1.1 About the necessity of high damage threshold optics . . . . . . . . . . . . . 1 1.2 Goal of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Femtosecond Damage Threshold 4 2.1 Definition of optical damage, and damage threshold . . . . . . . . . . . . . 4 2.2 Femtosecond laser interaction with dielectrics . . . . . . . . . . . . . . . . 6 2.2.1 Theoretical understanding of fs damage . . . . . . . . . . . . . . . . 6 2.2.2 Mathematical modeling of the fs damage threshold . . . . . . . . . 9 2.3 Dependence of the damage threshold on different parameters . . . . . . . . 13 2.3.1 Dependence on the pulse duration . . . . . . . . . . . . . . . . . . . 13 2.3.2 Pulse frequency dependence . . . . . . . . . . . . . . . . . . . . . . 14 2.3.3 Influence of the center wavelength . . . . . . . . . . . . . . . . . . . 15 2.3.4 Incubation effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3.5 Impact of the beam diameter on the damage threshold . . . . . . . 16 2.3.6 Dependence on the band gap . . . . . . . . . . . . . . . . . . . . . 17 2.4 About literature values of damage threshold . . . . . . . . . . . . . . . . . 17 3 Materials and Methods 19 3.1 The laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.1.1 Laser design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.1.2 Laser output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.2 The damage threshold setup . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2.1 Damage detection principle . . . . . . . . . . . . . . . . . . . . . . 22 3.2.2 Setup design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2.3 Focus characterization . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2.4 Measurement procedure . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2.5 Calibration and measurement . . . . . . . . . . . . . . . . . . . . . 26 3.2.6 Error evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 ii

4 Presentation of Results 31 4.1 Comparative measurement of different mirror types . . . . . . . . . . . . . 31 4.2 Measured damage threshold of fused silica substrate and a gold mirror vs. literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.3 Problems with the measurement . . . . . . . . . . . . . . . . . . . . . . . . 34 5 Conclusion and Outlook 36 5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5.2.1 Improvement of the setup . . . . . . . . . . . . . . . . . . . . . . . 37 5.2.2 Introducing a model for the better evaluation of the measurement data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5.2.3 Crosscheck with an established setup and verification of the results 37 5.2.4 Investigations on damage mechanisms and improvement of damage threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 6 Appendix 39 6.1 Appendix A: Derivation of the critical electron density . . . . . . . . . . . 39 6.1.1 The movement of an electron in a solid under the influence of an external electric field . . . . . . . . . . . . . . . . . . . . . . . . . . 39 6.1.2 The dielectric function of a solid including a contribution of free carriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 6.1.3 The plasma frequency and plasma charge density . . . . . . . . . . 40 6.2 Appendix B: Derivation of the evaluation expression . . . . . . . . . . . . . 41 6.2.1 The power measured via the power meter . . . . . . . . . . . . . . . 41 6.2.2 The peak fluence as a function of the time averaged power . . . . . 41 List of References 43 iii

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