Taylor, Alasdair (2014) Aspects of optical meterology systems for

206 Pages·2014·19.47 MB·English

Taylor, Alasdair (2014) Aspects of optical meterology systems for space-
borne gravitational wave detectors. PhD thesis.

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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