Taylor, Alasdair (2014) Aspects of optical meterology systems for space- borne gravitational wave detectors. PhD thesis. http://theses.gla.ac.uk/5741/ Copyright and moral rights for this thesis are retained by the author A copy can be downloaded for personal non-commercial research or study, without prior permission or charge This thesis cannot be reproduced or quoted extensively from without first obtaining permission in writing from the Author The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the Author When referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given Glasgow Theses Service http://theses.gla.ac.uk/ [email protected] Aspects of Optical Metrology Systems for Space-Borne Gravitational Wave Detectors Alasdair Taylor School of Physics and Astronomy, University of Glasgow Presented as a thesis for the degree of Ph.D. in the University of Glasgow, University Avenue, Glasgow G12 8QQ (cid:13)c Alasdair Taylor, 2013 November 2, 2014 Contents Acknowledgements xxiv Acronyms xxvi Preface xxix Summary 1 1 Introduction to Gravitational Waves Research 1 1.1 Theory of gravity . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Gravitational waves . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 Prediction of gravitational waves . . . . . . . . . . . . . 2 1.2.2 Polarisation states . . . . . . . . . . . . . . . . . . . . . 4 1.2.3 Production of gravitational waves . . . . . . . . . . . . . 4 1.2.4 Indirect evidence of gravitational waves . . . . . . . . . . 5 2 Gravitational Wave Astronomy 7 2.1 A new window . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Gravitational wave detection . . . . . . . . . . . . . . . . . . . . 8 2.2.1 Principles . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.2 Ground based detectors . . . . . . . . . . . . . . . . . . 8 2.2.3 Space based detection . . . . . . . . . . . . . . . . . . . 9 2.3 Sources of gravitational waves . . . . . . . . . . . . . . . . . . . 11 2.4 Testing G.R. in the strong field regime . . . . . . . . . . . . . . 14 2.4.1 Supermassive blackhole binaries . . . . . . . . . . . . . . 14 2.4.2 Extreme mass ratio inspiral . . . . . . . . . . . . . . . . 15 3 Reflectivity of a Hydroxide-Catalysed Silicate Bond 16 i 3.1 Introduction to bonding . . . . . . . . . . . . . . . . . . . . . . 16 3.1.1 Summary of bonding theory . . . . . . . . . . . . . . . . 18 3.1.2 Goal of this experiment . . . . . . . . . . . . . . . . . . 19 3.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2.1 Optical layout . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2.2 Sample alignment . . . . . . . . . . . . . . . . . . . . . . 27 3.2.3 Probe beam wavelengths . . . . . . . . . . . . . . . . . . 28 3.3 Initial experimental results . . . . . . . . . . . . . . . . . . . . . 29 3.3.1 Single disk testing . . . . . . . . . . . . . . . . . . . . . 29 3.3.2 Angular tilt caused by rail . . . . . . . . . . . . . . . . . 30 3.3.3 Measured bond reflectivity . . . . . . . . . . . . . . . . . 31 3.4 Optical modeling of the bond layer . . . . . . . . . . . . . . . . 33 3.4.1 Model concept . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4.2 Mathematical description . . . . . . . . . . . . . . . . . 34 3.4.3 Model variables and outputs . . . . . . . . . . . . . . . . 36 3.4.4 Model results . . . . . . . . . . . . . . . . . . . . . . . . 38 3.5 Final results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4 Optical Modeling of Second Generation Fibre Injectors 45 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.2 Design concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.2.1 eLISA FIOS requirements . . . . . . . . . . . . . . . . . 48 4.2.2 Design options . . . . . . . . . . . . . . . . . . . . . . . 48 4.3 FIOS components . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.3.1 FMA and fibre guard . . . . . . . . . . . . . . . . . . . . 53 4.3.2 Silica spacer . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.3.3 Spacer to lens interface . . . . . . . . . . . . . . . . . . . 54 4.3.4 Lens options . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.3.5 FIOS focal length . . . . . . . . . . . . . . . . . . . . . . 57 4.4 Optical performance . . . . . . . . . . . . . . . . . . . . . . . . 58 4.4.1 Modelled beam parameters . . . . . . . . . . . . . . . . . 58 4.4.2 Experimental results . . . . . . . . . . . . . . . . . . . . 60 4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 ii 5 Optical Testing of Short Focal Length Components 64 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 5.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5.2.1 Measurement principles . . . . . . . . . . . . . . . . . . . 66 5.2.2 Methods of absolute measurement considered . . . . . . 67 5.2.3 Relative measurements . . . . . . . . . . . . . . . . . . . 71 5.3 Experimental method and setup . . . . . . . . . . . . . . . . . . 72 5.3.1 Optical setup . . . . . . . . . . . . . . . . . . . . . . . . 72 5.3.2 Lens placement and orientation . . . . . . . . . . . . . . 73 5.3.3 Wavefront sensor alignment . . . . . . . . . . . . . . . . 74 5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.4.1 Measured focal positions . . . . . . . . . . . . . . . . . . 75 5.4.2 Expected uncertainty . . . . . . . . . . . . . . . . . . . . 76 5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6 Performance testing of photodiodes 78 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.1.1 OSI InGaAs photodiodes . . . . . . . . . . . . . . . . . . 80 6.1.2 Lewicki/Silicon Sensor photodiodes . . . . . . . . . . . . 81 6.2 Photon detection by InGaAs and Silicon . . . . . . . . . . . . . 83 6.2.1 Silicon photodiodes in the visible spectrum . . . . . . . . 83 6.2.2 InGaAs photodiodes in near infrared spectrum . . . . . . 83 6.2.3 Silicon photodiodes in near infrared spectrum . . . . . . 85 6.2.4 Enhancing Silicon responsivity to near infrared light . . . 85 6.3 Photodiode characterisations . . . . . . . . . . . . . . . . . . . . 87 6.3.1 Spatial uniformity testing . . . . . . . . . . . . . . . . . 87 6.3.2 Frequency response testing . . . . . . . . . . . . . . . . . 88 6.4 Spatial intensity response . . . . . . . . . . . . . . . . . . . . . 89 6.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 89 6.4.2 Birmingham University scans . . . . . . . . . . . . . . . 92 6.4.3 Glasgow University scans . . . . . . . . . . . . . . . . . . 94 6.4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 6.4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.5 Frequency response . . . . . . . . . . . . . . . . . . . . . . . . . 104 iii 6.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 104 6.5.2 Low frequency transfer functions . . . . . . . . . . . . . 105 6.5.3 High frequency transfer functions . . . . . . . . . . . . . 108 6.5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 113 6.6 Pulse response times of photodiodes . . . . . . . . . . . . . . . . 114 6.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 114 6.6.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 6.6.3 Experimental setup . . . . . . . . . . . . . . . . . . . . . 115 6.6.4 Prompt response . . . . . . . . . . . . . . . . . . . . . . 117 6.6.5 Slow response . . . . . . . . . . . . . . . . . . . . . . . . 119 6.6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 120 6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 7 Induced Longitudinal Path Length Noise 122 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 7.2 Model of QP22-E characteristics . . . . . . . . . . . . . . . . . . 124 7.2.1 Intensity response of QP22-E . . . . . . . . . . . . . . . 124 7.2.2 Phase lag of QP22-E . . . . . . . . . . . . . . . . . . . . 125 7.2.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . 126 7.3 Experimental investigation . . . . . . . . . . . . . . . . . . . . . 129 7.4 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . 130 7.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 8 Beam Dump Optical Design and Testing 133 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 8.1.1 Stray light from unwanted beams . . . . . . . . . . . . . 134 8.2 Light suppression goal . . . . . . . . . . . . . . . . . . . . . . . 136 8.2.1 Interferometer requirement . . . . . . . . . . . . . . . . . 136 8.2.2 Stray light in a LISA-type optical bench . . . . . . . . . 139 8.3 Possible beam dump designs . . . . . . . . . . . . . . . . . . . . 141 8.3.1 Commercial beam dump design . . . . . . . . . . . . . . 141 8.3.2 Conic cutout design . . . . . . . . . . . . . . . . . . . . . 142 8.3.3 Light pipe . . . . . . . . . . . . . . . . . . . . . . . . . . 144 8.3.4 Spirals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 iv 8.4 Geometric analysis of spiral designs . . . . . . . . . . . . . . . . 146 8.4.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 8.4.2 Initial designs . . . . . . . . . . . . . . . . . . . . . . . . 146 8.5 Theoretical performance . . . . . . . . . . . . . . . . . . . . . . 151 8.5.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 8.5.2 Model results . . . . . . . . . . . . . . . . . . . . . . . . 154 8.5.3 Simulation summary . . . . . . . . . . . . . . . . . . . . 156 8.6 Experimental testing of a prototype beam dump . . . . . . . . . 159 8.6.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 8.6.2 Optical setup . . . . . . . . . . . . . . . . . . . . . . . . 159 8.6.3 RF cross-talk . . . . . . . . . . . . . . . . . . . . . . . . 161 8.6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 8.7 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 8.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 9 Outlook 166 Bibliography 167 v List of Figures 1.1 Illustration of the effect of a passing gravitational wave on a ring of test particles. The direction of propagation is through the page along the ‘z’ axis. The upper series of rings show the effect of ‘+’ polarisation, while the lower rings show ‘×’ polarisation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1 Illustration of the range in frequency of gravitational wave sources. Credit: NASA [26] . . . . . . . . . . . . . . . . . . . . 11 3.1 Illustration of the measurement concept. Incident beam with amplitudeΨ producesthreemainbeamsfromthefront,middle, i and back of the sample. These beams have amplitudes Ψ , Ψ , a b and Ψ . Note that beam Ψ is the combination of multiple c b beams from the bond layer. . . . . . . . . . . . . . . . . . . . . 21 vi 3.2 Diagram of the optical layout showing the key optics. The quadrantphotodiode(QPD)monitorsthealignmentoftheover- lapped beams, local oscillator and selected probe beam. The measurement PD is a single element photodiode. Both Lasers are shown, as are the acoustic-optic modulators (AOM), which modulatedthefrequencyofboththereferenceandprobebeams, to produce the desired heterodyne frequency. Also shown is the motorised mounting of the sample and a number of aperture stops which were needed to block unwanted beams from both the AOMs and the sample. The alignment mirrors where used to optimise the overlap from both lasers after they had been through the AOMs. The interference contrast was optimised at the final beam splitter (BS-2). The three beams from the sample, in both green and red, can be seen. . . . . . . . . . . . 24 3.3 This graphic shows how the probe beams, in red, are slected through the motion of the sample. The reference beam, in blue, interferes with a selected probe beam reflection to form the pur- ple beam. The purple beams are detected by the photodiodes. Due to the size of the photodiode and the prospect of stray beams there is a need for apertures. The aperture before the beam combiner, blocks all but a selected probe beam reflection from the sample. By moving the sample the reflected beam passingthroughtheapertureischanged. Eventhoughthebeam combiner had an anit-reflection coating, a reflected local beam combining with a stray beam from the sample could be stronger than the bond layer signal. . . . . . . . . . . . . . . . . . . . . . 26 vii 3.4 This graphic shows the readout signal chain. The photodiodes were Thorlabs PDA36A-EC, single element photodiodes with a built in amplifier where the gain was adjustable. These were connected to a second ac coupled amplifier and finally the out- putofthisamplifierwasfedintotheNationalInstruments(N.I.) cDAQ-9178, containing a NI 9215 module, which is a 16-bit adc system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.5 Diagram of the single fused silica disk and the beams produced through reflections at the air (n ) to silica (n ) boundaries. The 1 2 input light Ψ was 633nm of S-polarisation. . . . . . . . . . . . 29 i 3.6 This collection of figures illustrates the ideas that the model is based on. The top left figure shows the way in which beams can be produced from multiple internal reflections inside the bond layer. The right figure shows the layout of main beams of the model: beams A, B, and C; being the front, middle and back beams. The boundaries are also labeled in terms of the reflection and transmission, e.g. R is the reflected beam am- 34 plitude between the boundaries of refractive index n and n . 3 4 The small circular image is the place where the phase of the beams is combined to calculate the interference. . . . . . . . . 34 3.7 This graph illustrates the different modeled amplitude ratios of the reflected beams for a fixed refractive index change of 0.005 from silica to bond at each wavelength. The natural look of this graph on a linear y-axis scale is a sin wave; however it is more convenient to have the y-axis in dB when drawing comparisons between the different parameters. . . . . . . . . . . . . . . . . . 38 viii