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Laser characterization and stabilization for precision interferometry [Elektronische Ressource] / Patrick Kwee

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Laser Characterization and Stabilizationfor Precision InterferometryVon der Fakult at fur Mathematik und Physikder Gottfried Wilhelm Leibniz Universit at Hannoverzur Erlangung des GradesDoktor der Naturwissenschaften{ Dr.rer.nat. {genehmigte DissertationvonDipl.-Phys. Patrick Kweegeboren am 10. Juni 1979 in Hannover2010Prof. Dr. Karsten DanzmannReferent:Priv. Doz. Dr. Benno WillkeKorreferent:Tag der Promotion: 8. Januar 2010PrefaceThe last four years, during my doctoral studies at the Albert-Einstein-Institute inHannover, have been a great and fascinating time, which I enjoyed a lot, but whichat the same time also went by much too fast. The institute, the people, and the eldof research contributed each in their own way to this period of my life. During mystudies it was especially a pleasure to design, plan and perform experiments and tocarry out my own ideas. Interferometric gravitational wave detectors are an excitingand in particular a wide-ranging eld of research. Thus I learned many di erentaspects from the experts at the institute, ranging from optics over electronics todata analysis. Of course many persons contributed to this enjoyable time and Iwould like to express my gratitude at this point.I would like to thank Karsten Danzmann for the exceptional infrastructure ofthe Albert-Einstein-Institute, which allowed me to concentrate on the really im-portant aspects of research.

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Published 01 January 2010
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Laser Characterization and Stabilization
for Precision Interferometry
Von der Fakult at fur Mathematik und Physik
der Gottfried Wilhelm Leibniz Universit at Hannover
zur Erlangung des Grades
Doktor der Naturwissenschaften
{ Dr.rer.nat. {
genehmigte Dissertation
von
Dipl.-Phys. Patrick Kwee
geboren am 10. Juni 1979 in Hannover
2010Prof. Dr. Karsten DanzmannReferent:
Priv. Doz. Dr. Benno WillkeKorreferent:
Tag der Promotion: 8. Januar 2010Preface
The last four years, during my doctoral studies at the Albert-Einstein-Institute in
Hannover, have been a great and fascinating time, which I enjoyed a lot, but which
at the same time also went by much too fast. The institute, the people, and the eld
of research contributed each in their own way to this period of my life. During my
studies it was especially a pleasure to design, plan and perform experiments and to
carry out my own ideas. Interferometric gravitational wave detectors are an exciting
and in particular a wide-ranging eld of research. Thus I learned many di erent
aspects from the experts at the institute, ranging from optics over electronics to
data analysis. Of course many persons contributed to this enjoyable time and I
would like to express my gratitude at this point.
I would like to thank Karsten Danzmann for the exceptional infrastructure of
the Albert-Einstein-Institute, which allowed me to concentrate on the really im-
portant aspects of research. I want to thank Benno Willke for the very personal
and dedicated mentoring, for his guidance, and for the countless scienti c discus-
sions. For the friendly working atmosphere, the interesting group meetings and
the joint laboratory work I am grateful to my colleagues of the laser group, Tobias
Meier, Henning Ryll, Jessica Duc k, Marc Tesch, Anatoli Fedynitch, Hyunjoo Kim,
Christina Kr amer, Marina Dehne, and Robin B ahre. In particular I would like to
thank Frank Seifert for the many years of close collaboration, Michaela Pickenpack
for taking over the fabrication of the diagnostic breadboards, and Jan P old for the
dedicated support in working with the Advanced LIGO laser { not to forget all
the other colleagues of the institute, with whom it was a pleasure to share ideas
and experiences, and the electrical and mechanical workshop, which built so many
components for my experiments. I would like to thank the colleagues of the Laser
Zentrum Hannover, Lutz Winkelmann, Oliver Puncken, Christian Veltkamp, Bas-
tian Schulz, Sascha Wagner, Matthias Hildebrandt, Maik Frede, and Peter We els,
for such a good collaboration concerning various laser systems. I thank Albrecht
Rudiger for many helpful comments and proofreading of not only this thesis but
also of several articles in the last few years.
Finally a special thanks goes to my family, in particular to my wife, for their
support of my doctoral studies and everything beyond.
Patrick Kwee, November 2009
iiiAbstract
Lasers for high-precision optical measurements, in particular for ground-based in-
terferometric gravitational wave detectors, were characterized and stabilized. A
compact, automated laser beam diagnostic instrument, based on an optical ring
resonator, was developed and used to characterize the output beam of di erent
continuos-wave, single-frequency lasers at wavelengths of 1064 nm and 1550 nm.
The laser beam uctuations in power, frequency and pointing as well as the spatial
beam quality were investigated. The results were used, amongst others, for laser
stabilization design.
Di erent laser stabilization methods are reviewed and the laser stabilization con-
cept for the second-generation gravitational wave detector Advanced LIGO is de-
scribed. Important components of this stabilization were developed, such as the
so-called pre-mode-cleaner resonator for ltering various laser beam parameters.
Furthermore, several laser power stabilization experiments were performed. A
high-sensitivity, quantum-noise-limited detector for power uctuations consisting
of an array of photodiodes was developed and was used to stabilize the output
power of a laser in the audio frequency band, achieving an independently measured
9 1=2relative power noise of 2:4 10 Hz at 10 Hz. In addition, a novel power-
uctuation detection technique, called optical ac coupling, which is based on photo-
detection in re ection of an optical resonator, was investigated theoretically and
experimentally. This technique allows new power stabilization schemes, especially
important for next generation gravitational wave detectors, and it can beat the
theoretical quantum limit of traditional schemes by up to 6 dB, among other bene ts.
10 1=2A sensitivity of 7 10 Hz for relative power uctuations was experimentally
demonstrated at radio frequencies using an optical ac coupled photodetector.
Keywords: laser characterization, laser power stabilization, gravitational wave de-
tector.
ivKurzfassung
Laser fur optische Prazisionsmessungen, insbesondere fur interferometrische Gra-
vitationswellendetektoren, wurden charakterisiert und stabilisiert. Ein kompaktes,
automatisiertes Diagnoseinstrument fur Laserstrahlen, basierend auf einem opti-
schen Ringresonator, wurde entwickelt und verwendet, um die Strahlen verschiede-
ner einfrequenter Dauerstrichlaser bei Wellenlangen von 1064 nm und 1550 nm zu
charakterisieren. Dabei wurde das Rauschen der Ausgangsleistung, der Frequenz
und der Strahllage als auch die Strahlqualitat untersucht. Die Ergebnisse wurden
unter anderem fur das Design von Laserstabilisierungen verwendet.
Verschiedene Laserstabilisierungsverfahren und das Stabilisierungskonzept fur
den Gravitationswellendetektor zweiter Generation Advanced LIGO sind beschrie-
ben. Bedeutende Komponenten dieser Stabilisierung wurden entwickelt, wie z.B. der
so genannte pre-mode-cleaner Resonator, der mehrere Laserstrahlparameter ltert.
Darub er hinaus wurden mehrere Experimente zur Leistungsstabilisierung von La-
sern durchgefuhrt. Ein hochemp ndlicher, quantenrauschbegrenzter Detektor f ur
Leistungs uktuationen, der aus mehreren Photodioden bestand, wurde entwickelt
und benutzt, um die Ausgangsleistung eines Lasers im Audiofrequenzbereich zu sta-
bilisieren. Dabei wurde ein unabhangig gemessenes relatives Leistungsrauschen von
9 1=22:4 10 Hz bei 10 Hz erreicht. Weiterhin wurde eine neuartige Detektions-
technik fur Leistungs uktuationen, das so genannte optical ac coupling, basierend
auf der Leistungsdetektion in Re exion eines optischen Resonators, theoretisch und
experimentell untersucht. Diese Technik ermoglicht neue Leistungsstabilisierungs-
schemata, die insbesondere fur die nac hste Generation von Gravitationswellende-
tektoren bedeutend sein werden und die neben anderen Vorteilen die theoretische
Quantengrenze traditioneller Schemata um bis zu 6 dB unterbieten konnen. Eine
10 1=2Emp ndlichkeit von 7 10 Hz fur relatives Leistungsrauschen bei Radio-
frequenzen konnte mithilfe eines optical ac coupled Photodetektors experimentell
demonstriert werden.
Schlagworte: Lasercharakterisierung, Laserleistungsstabilisierung, Gravitationswel-
lendetektor.
vContents
1 Introduction 1
2 Laser Characterization 3
2.1 Laser Beam Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Diagnostic Breadboard . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 Experiment and Methods . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Exptal Challenges . . . . . . . . . . . . . . . . . . . . . 16
2.2.3 Control and Automation . . . . . . . . . . . . . . . . . . . . . 21
2.3 Characterizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.1 Nonplanar Ring Oscillator . . . . . . . . . . . . . . . . . . . . 26
2.3.2 Advanced LIGO Laser . . . . . . . . . . . . . . . . . . . . . . 31
2.3.3 Photonic Crystal Fiber Laser . . . . . . . . . . . . . . . . . . 34
2.3.4 Fiber Laser at 1550 nm . . . . . . . . . . . . . . . . . . . . . 36
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3 Laser Stabilization 39
3.1 Review of Stabilization Methods . . . . . . . . . . . . . . . . . . . . 40
3.1.1 Passive Filtering vs. Active Feedback . . . . . . . . . . . . . 40
3.1.2 Power Stabilization . . . . . . . . . . . . . . . . . . . . . . . . 42
3.1.3 Frequency . . . . . . . . . . . . . . . . . . . . . 45
3.1.4 Pointing . . . . . . . . . . . . . . . . . . . . . . 47
3.1.5 Beam Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2 Stabilization Concept of Advanced LIGO . . . . . . . . . . . . . . . 50
3.2.1 Advanced LIGO . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2.2 Power Stabilization Concept . . . . . . . . . . . . . . . . . . . 54
3.2.3 Frequency Concept . . . . . . . . . . . . . . . . 57
3.2.4 Pointing . . . . . . . . . . . . . . . . . 58
3.2.5 Beam Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.2.6 Pre-mode-cleaner . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
viiContents
4 Traditional Power Stabilization 63
4.1 Quantum Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2 High Power Photodiode Array . . . . . . . . . . . . . . . . . . . . . . 70
4.2.1 Optical and Mechanical Design . . . . . . . . . . . . . . . . . 70
4.2.2 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.3 Power Stabilization Experiment . . . . . . . . . . . . . . . . . . . . . 75
4.3.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . 75
4.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5 Optical AC Coupling 83
5.1 Optical AC Coupling Technique . . . . . . . . . . . . . . . . . . . . . 84
5.2 Quantum Limit of Power Stabilization Schemes . . . . . . . . . . . . 87
5.2.1 Limit of Di erent Stabilizations . . . . . . . . . . . . . . . . . 88
5.2.2 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.3.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.3.2 Experimental Challenges . . . . . . . . . . . . . . . . . . . . . 102
5.4 Noise Couplings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.4.1 Residual Frequency Noise . . . . . . . . . . . . . . . . . . . . 107
5.4.2 Mode Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . 108
5.4.3 Resonator-internal Scattering . . . . . . . . . . . . . . . . . . 110
5.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6 Conclusion 129
viiiSymbols
Abbreviations
ACC ac coupling cavity
A/D analog to digital
AOM acousto-optical modulator
CDS control and data systems
D/A digital to analog
DAQ data acquisition
DBB diagnostic breadboard
DWS di erential wave front sensing
EOAM electro-optic amplitude modulator
EOM modulator
FSR free spectral range
GWD gravitational wave detector
HEPA High E ciency Particulate Air
IMC input mode-cleaner
InGaAs indium gallium arsenide
IO input optics
LIGO Laser Interferometer Gravitational-Wave Observatory
Nd:YAG neodymium-doped yttrium aluminum garnet
NPRO nonplanar ring oscillator
PDH Pound-Drever-Hall
PMC pre-mode-cleaner
PRC power recycling cavity
PRM power recycling mirror
PSL pre-stabilized laser
PZT piezoelectric transducer
RF radio frequency
RPN relative power noise
TEM transversal electromagnetic wave
ULE ultra low expansion glass
Symbols
carrier amplitude, see Eq. 4.6
2 2 ; average laser beam photon ow
las
; ; beam pointing, see Eq. 2.6x y
Gouy phase
Gaussian beam half divergence angleD
wavelength
optical frequency
ix