Laser interferometry with gratings [Elektronische Ressource] / von Alexander Bunkowski

Alexander Bunkowski

Sujets

• Physik

Informations

• Publié par: gottfried_wilhelm_leibniz_universitat_hannover
• Publié le: 01 janvier 2006
• Nombre de lectures: 38
• Langue: Deutsch
• Poids de l'ouvrage: 1 Mo

Extrait

Laser interferometry
with gratings
Von der Fakultat¨ fur¨ Mathematik und Physik
der Gottfried Willhelm Leibniz Universit¨ at Hannover
zur Erlangung des Grades
Doktor der Naturwissenschaften
– Dr. rer. nat. –
genehmigte Dissertation von
Dipl.-Phys. Alexander Bunkowski,
geboren am 22. Februar 1976 in Kassel.
Dezember 2006Referent: JProf. R. Schnabel
Korreferent: JProf. J. Arlt
Tag der Promotion: 20. Dezember 2006Zusammenfassung
Der Einsatz von Interferometerkonzepten auf der Basis von verlustarmen Beugungsgit-
tern soll die Empfindlichkeit zukunftiger¨ Laserinterferometer zur Messung von Gravi-
tationswellen steigern.
Im Rahmen dieser Arbeit wurde ein rein-reflektierender optischer Resonator mit
einer Finesse von 1580 durch die Benutzung eines Reflexionsgitters in Littrow Anord-
nung erster Ordnung experimentell realisiert. Dadurch konnten bisher unerreichte
Werte in Bezug auf hohe Beugungseffizienz (99,635%) und niedrige optische Verluste
(0,185%) fur¨ ein dielektrisches Gitter nachgewiesen werden.
Erstmalig wurde die experimentelle Realisierung eines rein-reflektierenden Res-
onators durch die Benutzung eines Gitters in Littrow Anordnung zweiter Ordnung
gezeigt. Im Gegensatz zu dem vorhergenannten Konzept, wurde dabei große Leis-
tungsub¨ erh¨ ohung im Resonator durch den Einsatz eines Gitters mit niedriger (0,58 %)
Beugungseffizienz erzielt.
Aufgrund der Geometrie des Resonatorkonzeptes interferieren drei, statt ublic¨ her-
weise zwei Laserstrahlen gleichzeitig am Gitter, was zu neuen Resonatoreigenschaften
f¨uhrt. Eine theoretische Analyse von Phasenbeziehungen eines generischen Drei-Port
Kopplers fuhrte¨ zur Erkl¨ arung dieser Eigenschaften und damit zu einer Verallge-
meinerung der bisher bekannter Resonatortheorie. Die fur¨ die Resonatoreigenschaften
verantwortlichen Phasen konnten als alleinige Funktion der Beugungseffizienzen dar-
gestellt werden. Damit wurden Vorhersagen von Resonatoreigenschaften aufgrund von
leicht zug¨ anglichen Ergebnissen von Effizienzmessungen, bei volliger¨ Unkenntnis des
physikalischen Aufbaus des Gitters, moglic¨ h. Diese konnten im Experiment erfolgreich
best¨atigt werden.
Um dem Problem des thermischen Beschichtungsrauschens von hochreflektierenden
Spiegeln entgegenzuwirken, wurde eine dunne,¨ einlagige Beschichtung auf der Basis
eines resonanten Gitterwellenleiters vorgeschlagen. Funktionsweise und Beispielrech-
nungen zum Design solcher Beschichtungen wurden vorgestellt.
Stichworte: Gravitationswellendetektor, Laserinterferometrie, BeugungsgitterAbstract
The application of interferometric concepts on the basis of low-loss diffraction grat-
ings should boost the sensitivity of future laser interferometers for the detection of
gravitational waves.
In the context of this thesis an all-reflective optical resonator with a finesse of 1580
was experimentally demonstrated by using a reflection grating in a first order Lit-
trow mount. Thereby, unprecedented values with respect to high diffraction efficiency
(99.635%) and low optical loss (0.185%) for a dielectric grating could be verified.
For the first time the experimental realization of an all-reflective resonator employ-
ing a diffraction grating in a second order Littrow mount was shown. In contrast to
the aforesaid concept, high power gain inside the resonator was achieved by employing
a diffraction grating with low (0.58 %) diffraction efficiency.
Due to the geometry of the resonator concept, three – instead of the usual two –
laser beams interfere at the grating simultaneously, leading to new resonator properties.
A theoretical analysis of phase relations of a generic three-port coupler led to an
explanation of these properties and thus, to a generalization of the previously known
theory of resonators. The phases governing the properties of the resonator could be
represented as functions which solely depend on diffraction efficiencies. Therefore,
predictions about resonator properties could be made due to the easily accessible results
of efficiency measurements; no knowledge about the physical properties of the grating
was required. An experiment successfully validated these predictions.
To counteract the problem of coating thermal noise due to highly reflective mirrors,
a thin, single layer coating on the basis of a resonant grating waveguide was proposed.
Mode of operation and sample calculations considering the design of such gratings were
presented.
Key words: Gravitational wave detector, laser interferometry, diffraction gratingAcknowledgements
Special thanks go to Oliver Burmeister and Daniel Friedrich. I hope they had as much
fun working with me as I had working with them.
As a member of Roman’s Advanced interferometry and squeezing light group I
could not only enjoy our weekly group discussions and seminars, but I could also rely
on many helping hands and minds. I am deeply grateful for the support I got from
each member of the group.
A substantial part of my work resulted from a collaboration with the Institut fur¨
Angewandte Physik in Jena. I would like to thank Tina Clausnitzer, Stephan Fahr,
Ernst-Bernhard Kley, and Andreas Tunnermann¨ for working together with us and
providing us with gratings.
I also want to thank Andreas Freise for the upgrade of his simulation software
Finesse in which I could participate. Some of our discussions were quite enlightening
for me. For further interesting exchanges I want to thank Peter Beyersdorf from
Stanford and San Jose State University who worked with us in the lab for one month
and Roland Schilling with whom I had interesting conversations about phase relations.
Benno Willke, Gerhard Heinzel, and their respective GEO- and LISA-teams were a
great resource of in-depth knowledge of interferometry, electronics, computers as well
as many other things. Thank you for sharing!
I would also like to thank Jan Arlt from the Institut fur¨ Quantenoptik for being
the second referee of my thesis and Paul Cochrane for proofreading.
With Roman Schnabel I was lucky to have a dedicated thesis advisor. He always
took time to discuss our project. His scientific input as well as his humor and optimism
showed me that it is possible to do science successfully and have fun at the same time.
At the Institut fur¨ Gravitationsphysik I found ideal conditions of work: A friendly
atmosphere, motivated and skilled scientists, superb technical support, and enough
funds to buy stuff and travel. I was guided when needed, but more importantly, I was
given freedom to develop ideas. I would like to thank Karsten Danzmann for creating
and leading such a place.Contents
Zusammenfassung ................................ iii
Abstract ...................................... v
Acknowledgements ...............................vi
Table of contents ix
1 Introduction 1
1.1 Historicalnotesongravitationalwavedetectorsandgratings ...... 1
1.1.1 Bardetectors............................. 2
1.1.2 Laserinterferometers......................... 3
1.1.3 Diffractiongratings.......................... 5
1.2 Currentandfutureinterferometers..................... 7
1.2.1 Opticalconfigurationsofinterferometricdetectors ........ 7
1.2.2 Keyopticalcomponents....................... 9
1.2.3 Thermalnoise ............................10
1.2.4 Advantagesofgratinginterferometers...............13
1.3 Interferometryconceptsbasedongratings.................13
1.3.1 Al-reflectiveinterferometers.....................14
1.3.2 Gratingwaveguidecoatings16
1.4 Structureofthethesis.17
References......................................18
2 Optical characterization of ultrahigh diffraction efficiency gratings 27
2.1 Introduction..................................28
2.2 ExperimentalProcedure...........................29
ixContents
2.3 Conclusion ..................................33
References......................................35
3 Low-loss grating for coupling to a high-finesse cavity 37
References43
4 Input-output relations for a three-port grating coupled Fabry-Perot
cavity 45
References52
5 Demonstration of three-port grating phase relations 53
References......................................60
6 Three-port beam splitters-combiners for interferometer applications 61
References68
7 High reflectivity grating waveguide coatings for 1064 nm 69
7.1 Introduction..................................69
7.2 Resonantgratingwaveguidestructures...................70
7.3 Spectralresponseofwaveguidecoatings72
7.4 Thicknessofthecoating...........................74
7.5 Parametertolerances.............................76
7.6 Conclusion77
References......................................77
8 Summary 81
8.1 Conclusion ..................................81
8.2 Outlook....................................82
References86
A Diffraction efficiency calculations 89
References......................................90
B An extension of Finesse to include gratings 91
References94
x