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When referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given e.g. AUTHOR (year of submission) "Full thesis title", University of Southampton, name of the University School or Department, PhD Thesis, pagination http://eprints.soton.ac.uk UNIVERSITY OF SOUTHAMPTON FACULTY OF ENGINEERING, SCIENCE AND MATHEMATICS Optoelectronics Research Centre Polarization engineering with ultrafast laser writing in transparent media by Martynas Beresna Thesis for the degree of Doctor of Philosophy August 2012 UNIVERSITY OF SOUTHAMPTON ABSTRACT FACULTY OF ENGINEERING, SCIENCE AND MATHEMATICS OPTOELECTRONICS RESEARCH CENTRE Doctor of Philosophy Polarization engineering with ultrafast laser writing in transparent media By Martynas Beresna In this thesis novel developments in the field of femtosecond laser material processing are reported. Thanks to the unique properties of light-matter interaction on ultrashort time scales, this direct writing technique allowed the observation of unique phenomena in transparent media and the engineering of novel polarization devices. Using tightly focused femtosecond laser pulses’, high average power second harmonic light was generated in the air with two orders of magnitude higher normalised efficiency than reported by earlier studies. We also demonstrated optical vortex generation in the air as a result of spin-orbital momentum coupling in the frequency doubling process. The ultrashort laser pulses were also explored as a tool for micro-bubble formation. Due to the high refractive index contrast at the interface of a bubble and the glass substrate we observed edge birefringence, which could be utilised for optical vortex generation or as a radial polarizer. The experimental observation was supported by a theoretical model. Finally, a series of birefringent optical elements were developed based on self- assembled nanostructures induced by ultrashort laser pulses in fused silica. The process was discovered a decade ago and mostly was regarded as a scientific curiosity. However, we demonstrated that these nanostructures can be used as the building blocks for novel optical elements based on spatially varying birefringent properties. Contents UNIVERSITY OF SOUTHAMPTON ___________________________________________________________ 3 ABSTRACT _____________________________________________________________________________________ 3 CONTENTS ______________________________________________________________________________________ I LIST OF FIGURES ______________________________________________________________________________ V LIST OF TABLES _____________________________________________________________________________ XV DECLARATION OF AUTHORSHIP _______________________________________________________ XVII ACKNOWLEDGEMENTS ___________________________________________________________________ XIX DEFINITIONS AND ABBREVIATIONS ____________________________________________________ XXI CHAPTER 1. INTRODUCTION ______________________________________________________________ 1 1.1 Historical background ______________________________________________ 1 1.2 Thesis overview___________________________________________________ 3 CHAPTER 2. LIGHT PROPAGATION IN TRANSPARENT MEDIUM ____________________ 5 2.1 Overview of ultrashort pulse laser systems ____________________________ 5 2.2 Laser beam optics _________________________________________________ 7 2.2.1 Gaussian laser beam ____________________________________________ 7 2.2.2 Optical vortex _________________________________________________ 8 2.3 Material modification with laser pulses _______________________________ 9 2.3.1 Self-focusing of the laser beam __________________________________ 10 2.3.2 Spherical aberration due to refractive index mismatch ________________ 11 2.3.3 Permanent material modification ________________________________ 12 i 2.3.4 Permanent material damage and pulse duration ____________________ 14 2.3.5 Self-assembled nanograting _____________________________________ 17 2.4 Jones calculus for polarization optics ________________________________ 20 CHAPTER 3. EXPERIMENTAL SETUPS __________________________________________________ 23 3.1 Direct-writing setup ______________________________________________ 23 3.1.1 Focusing optics _______________________________________________ 27 3.2 Setup for the birefringence measurements ___________________________ 27 3.3 Digital holographic microscope _____________________________________ 32 CHAPTER 4. HIGH AVERAGE POWER SECOND HARMONIC GENERATION IN AIR 35 4.1 Introduction ____________________________________________________ 35 4.2 Generation of second harmonic in isotropic material ___________________ 36 4.3 Experimental set-up ______________________________________________ 39 4.4 Experimental results _____________________________________________ 40 4.5 Conclusions _____________________________________________________ 45 CHAPTER 5. EFFECT OF EDGE BIREFRINGENCE ______________________________________ 47 5.1 Introduction ____________________________________________________ 47 5.2 Radial edge birefringence _________________________________________ 47 5.3 Bubble formation in fused silica with femtosecond laser pulses ___________ 51 5.4 Experimental results _____________________________________________ 53 5.4.1 Bubble formation _____________________________________________ 53 5.4.2 Polarization conversion ________________________________________ 56 ii 5.5 Conclusion ______________________________________________________ 59 CHAPTER 6. THEORY OF FEMTOSECOND LASER INDUCED NANOGRATINGS ____ 61 6.1 Introduction ____________________________________________________ 61 6.2 Overview of proposed bulk ripple formation theoretical models __________ 63 6.3 Excitonic model of nanograting formation ____________________________ 66 6.4 Discussion ______________________________________________________ 69 6.5 Conclusions _____________________________________________________ 70 CHAPTER 7. PROPERTIES OF FEMTOSECOND LASER PULSE INDUCED NANOGRATINGS _____________________________________________________________________________ 71 7.1 Spectral properties of the nanogratings ______________________________ 71 7.1.1 Modelling spectral properties of nanograting _______________________ 71 7.1.2 Measuring spectral properties of nanograting _______________________ 75 7.1.3 Experimental results ___________________________________________ 77 7.2 Retardance dependence on spherical aberration _______________________ 81 7.3 Retardance dependence on the numerical aperture ____________________ 85 7.4 Conclusions _____________________________________________________ 87 CHAPTER 8. POLARIZATION SENSITIVE ELEMENTS _________________________________ 89 8.1 Introduction ____________________________________________________ 89 8.2 Polarization diffraction grating _____________________________________ 91 8.2.1 Working principle _____________________________________________ 91 8.2.2 Experimental results ___________________________________________ 94 8.2.3 Birefringence measurements with polarization grating _______________ 102 iii 8.3 Polarization converter ___________________________________________ 103 8.3.1 Introduction ________________________________________________ 103 8.3.2 Methods for spatially variant polarization generation _______________ 105 8.3.3 Form birefringence based polarization converters __________________ 108 8.3.4 Fabrication and characterization ________________________________ 111 8.3.5 Application of radial polarization for transparent material processing __ 117 8.4 5 dimensional optical memory ____________________________________ 119 8.4.1 Multi-dimensional optical memory ______________________________ 120 8.4.2 Optical storage based on nanograting ____________________________ 121 8.5 Conclusions ____________________________________________________ 126 CHAPTER 9. CONCLUSIONS AND FUTURE WORK ___________________________________ 129 9.1 Summary and discussion _________________________________________ 129 9.2 Future work ___________________________________________________ 132 LIST OF PUBLICATIONS __________________________________________________________________ 135 BIBLIOGRAPHY ____________________________________________________________________________ 143 iv List of figures Figure 2.1: The intensity distribution of the laser beam focused with a 0.7 NA objective lens into silica glass at a different focusing depth . ‘0’ position on the axis corresponds to the focus position if spherical aberration is neglected. ............. 12 Figure 2.2: Schematic diagram of the photoionization of an electron in an atomic potential for different Keldysh parameter values. Source: C.B. Schaffer et al [33] 13 Figure 2.3: Schematic diagram of avalanche (impact) ionization. The free electron absorbs energy through free carrier absorption acquiring sufficient energy to knock-out another electron from the valance to conduction band. .............................