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Nonlinear femtosecond photonics in gas-filled hollow-core photonic crystal fibres [Elektronische Ressource] = Nichtlineare Femtosekunden-Photonik in gas-gefüllten Hohlkernfasern / vorgelegt von Johannes Nold

127 pages
Nonlinear femtosecondphotonics ingas- lledhollow-corephotonic crystal bresNichtlineare Femtosekunden Photonik in gas-gefullten HohlkernfasernDer Naturwissenschaftlichen Fakult atder Friedrich-Alexander-Universit atErlangen-Nurn bergzurErlangung des Doktorgrades Dr. rer. nat.vorgelegt vonJohannes Noldaus StuttgartAls Dissertation genehmigtvon der Naturwissenschaftlichen Fakult atder Friedrich-Alexander Universit at Erlangen-Nurn bergTag der mundlic hen Prufung: 31.03.2011Vorsitzender der Promotionskommission: Prof. Dr. Rainer FinkErstberichterstatter: Prof. Dr. Philip St.J. RussellZweitberichterstatter: Prof. Dr. Eberhard RiedleTo Marleen and ValentinAbstract13 2In the thesis we study the propagation of intense (> 10 W=cm ) 30 fs pulsesin Kagome-lattice hollow-core bers lled with noble-gas. This results in e -cient frequency conversion into the UV spectral region.The rst part of the thesis is devoted to the fabrication of hollow-core photoniccrystal bres (PCFs). This covers their guidance mechanism and propertiessuch as loss and dispersion. As these bres o er di raction-less propagationover extended length, they are attractive candidates for the replacement of thewidely used capillaries in applications like spectral broadening with successivecompression, high harmonic generation or frequency up-conversion.
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Nonlinear femtosecond
photonics in
gas- lled
hollow-core
photonic crystal bres
Nichtlineare Femtosekunden Photonik in gas-gefullten Hohlkernfasern
Der Naturwissenschaftlichen Fakult at
der Friedrich-Alexander-Universit at
Erlangen-Nurn berg
zur
Erlangung des Doktorgrades Dr. rer. nat.
vorgelegt von
Johannes Nold
aus StuttgartAls Dissertation genehmigt
von der Naturwissenschaftlichen Fakult at
der Friedrich-Alexander Universit at Erlangen-Nurn berg
Tag der mundlic hen Prufung: 31.03.2011
Vorsitzender der Promotionskommission: Prof. Dr. Rainer Fink
Erstberichterstatter: Prof. Dr. Philip St.J. Russell
Zweitberichterstatter: Prof. Dr. Eberhard RiedleTo Marleen and ValentinAbstract
13 2In the thesis we study the propagation of intense (> 10 W=cm ) 30 fs pulses
in Kagome-lattice hollow-core bers lled with noble-gas. This results in e -
cient frequency conversion into the UV spectral region.
The rst part of the thesis is devoted to the fabrication of hollow-core photonic
crystal bres (PCFs). This covers their guidance mechanism and properties
such as loss and dispersion. As these bres o er di raction-less propagation
over extended length, they are attractive candidates for the replacement of the
widely used capillaries in applications like spectral broadening with successive
compression, high harmonic generation or frequency up-conversion.
Finite Element modelling of Kagome-lattice hollow-core PCFs indicates that
their dispersion properties can be approximated by the dispersion of capillaries,
although the complete guidance mechanism is still under debate. The resulting
2absolute values of group velocity dispersion are on the order of 10 fs=cm
thus o ering the possibility to tune the overall dispersion and nonlinearity with
a gas lling at various pressures.
In the second part, we performed nonlinear propagation in Ar- lled Kagome
bres. First we used phase-matching between fundamental (HE ) and higher-11
order transverse modes (HE ) guided in the bre in order to convert IR into13
UV via third harmonic process (THG). Phase-matching conditions are ad-
justed through the argon pressure. Generated wavelengths can then be tuned
3over a few nanometres. The process itself is rather ine cient (2 :5 10 % for
1J pump pulse) because of the poor modal overlap and the walk-o between
the pump and the generated pulse. However this allows us to validate our
approximate model for the dispersion of Kagome bre. Another mechanism
for the generation of tunable UV with femtosecond pulse durations is the emis-
sion of dispersive waves from a higher order soliton in the absence of Raman
scattering. In contrast with the THG case, the generated UV is guided in
the fundamental mode of the bre and it can be tuned over nearly 200 nm
(from 170 nm to 350 nm). Moreover the e ciency for this process is on the
level of 7%, thus o ering many applications of this source like pump-probe
spectroscopy, femtochemistry or even seeding of x-ray lasers.
4Zusammenfassung
13 2In der vorliegenden Arbeit wird die Ausbreitung von intensiven (> 10 W=cm
30 fs) Laserpulsen in Argon gefullten Hohlkernglassfasern vom Kagome-Typ
untersucht. Dabei wird die e ziente Erzeugung von Wellenl angen im UV
Bereich beobachtet. Der erste Teil der Arbeit befasst sich mit der Herstel-
lung von mikrostrukturierten Hohlkernglassfasern (PCFs). Dieser beinhaltet
die Leitungsmechanismen und die typischen Eigenschaften wie Verluste und
Dispersion. Da diese Fasern die Beugung des geleiteten Lichts verhindern und
deren Verluste gering sind, haben diese das Potential die oft benutzten Kap-
illaren in Anwendungen wie z. B. spektrale Verbreiterung und anschliessende
Komprimierung von Laserpulsen, Erzeugung hoher Harmonischer zu ersetzen.
Modellierung der Leitungseigenschaften von Kagome-Fasern mit den Meth-
oden der Finiten Elemente deutet an, dass deren Dispersion durch die Dis-
persion von Kapillaren approximiert werden kann. Dabei ist der zugrundele-
gende Leitungsmechanismus dieses Fasertyps noch in der Diskussion. Die ab-
soluten Zahlen der Gruppengeschwindigkeitsdispersion dieses Fasertyps sind
2in der Gr ossenordnung von 10 fs=cm . Damit ero net sich die M oglichkeit
die gesamte Dispersion und die Nichtlinearit at der Fasern durch eine Fullung
mit Gasen bei unterschiedlichen Druc ken zu beein ussen. Im zweiten Teil
wird die Ausbreitung der Laserpulse in Argon geful lten Kagome-Fasern unter-
sucht. Als erstes verwenden wir die phasenangepasste Erzeugung der dritten
Harmonischen in der Faser zwischen der Fundamentalmode (HE ) und einer11
h oheren Mode (HE ) um UV zu erzeugen. Die Phasenanpassung ist dabei13
mit dem Argondruck einstellbar. Dadurch kann die Zentralwellenl ange der
erzeugten dritten Harmonischen ub er einige nm verschoben werden. Dieser
3Prozess trotz Phasenanpassung ine zient (2 :5 10 % fur einen 1J) da der
Modenuberlapp sehr gering ist und der zeitliche Uberlapp zwischen dem Pump-
puls und dem der dritten Harmonischen sehr kurz ist. Jedoch ist dieser Prozess
geeignet die gemachte Approximation der Faserdispersion durch eine Kapillare
experimentell zu best atigen. Einen weiterer Mechanismus zur Erzeugung von
durchstimmbarem UV mit Pulsl angen im fs-Bereich stellt die Propagation von
h oheren Solitonen in den mit Gas gefullten Kagome-Fasern dar. In Kontrast
zu der Erzeugung der dritten Harmonischen wird hierbei der UV-Puls in der
Fundamentalmode der Faser geleitet und kann ub er einen Wellenl angenbereich,
durch Variation des Druckes, von fast 200 nm durchgestimmt werden. Weit-
erhin ist die E zienz dieses Prozesses um Gr ossenordnungen h oher ( 7%).
Dies er o net vielf altige Anwendungen wie z. B. pump-probe Spektroskopie,
Femtochemie.
5Acknowledgement
First of all, I would like to thank my PhD adviser Prof. Dr. Philip Russell
who gave me not only the possibility of carrying out the presented work but
also supported me from all sides whenever needed.
Then I would like to thank all group members who took care of me and sup-
ported me during this time. Especially to Prof. Dr. Nicolas Joly and Dr.
Alexander Podlipensky for the help and advises I received. Also to Haizhen
Ren supporting me from the theory side during his visit in Erlangen.
Besides these I would like to thank:
Amir Abdolvand for all his comments, suggestions and help on almost
all topics. I will never forget the times in at the drawing towers, where
we tried hard to get the bres guiding.
Philipp H olzer for his ideas and experimental support in the lab.
Dr. Wonkeun Chang for providing the numerical codes for used for pulse
propagation and for the support on the theory of the UV generation.
Sebastian Stark for the rst simulations of our performed experiments
and the support with equipment.
Christine Kreuzer for providing also her equipment and the always happy
face.
Dr. Leyun Zang and Dr. Jocelyn Chen for sharing the o ce with me.
Andre Brenn for his help with my Matlab issues.
Hemant Tyagi for the introduction to JCMwave.
Dr. Michael Scharrer and Silke Rammler for showing their tricks on bre
fabrication and for providing bre samples.
Last, but not least, I want to thank my wife, Mariana, and our children,
Valentin and Marleen, for all their support on the non-physics side of life.
6Table of Contents
1 Introduction 9
2 Hollow-core photonic crystal bres 13
2.1 From free space to hollow waveguides . . . . . . . . . . . . . . . 13
2.1.1 The wave equation . . . . . . . . . . . . . . . . . . . . . 14
2.1.2 Capillary . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.3 Periodic one-dimensional structures . . . . . . . . . . . . 20
2.1.4 Photonic crystal bres . . . . . . . . . . . . . . . . . . . 23
2.2 Fabrication of hollow-core bres . . . . . . . . . . . . . . . . . . 34
2.2.1 From tubes to bres . . . . . . . . . . . . . . . . . . . . 36
2.2.2 Hollow-core photonic bandgap bre . . . . . . . . . . . . 41
2.2.3 Kagome bre . . . . . . . . . . . . . . . . . . . . . . . . 45
3 Pulse propagation in hollow waveguides 49
3.1 Generalised nonlinear Schr odinger equation . . . . . . . . . . . . 49
3.2 Numerical strategy . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3 Soliton propagation . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.4 Third harmonic generation . . . . . . . . . . . . . . . . . . . . 62
4 Gas- lled Kagome bre 69
4.1 Pressure distribution in the Kagome bre . . . . . . . . . . . . . 70
4.1.1 Filling from both ends . . . . . . . . . . . . . . . . . . . 70
4.1.2 Pressure gradient . . . . . . . . . . . . . . . . . . . . . . 74
4.2 Properties of argon- lled Kagome bres . . . . . . . . . . . . . . 76
7CONTENTS
4.3 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.4 Third harmonic generation . . . . . . . . . . . . . . . . . . . . . 78
4.4.1 Phase-matching considerations . . . . . . . . . . . . . . . 79
4.4.2hing from HE to HE . . . . . . . . . . . . 8211 13
4.5 Tunable UV in fundamental mode . . . . . . . . . . . . . . . . . 88
4.5.1 Pressure tuning . . . . . . . . . . . . . . . . . . . . . . . 89
4.5.2 Power tuning . . . . . . . . . . . . . . . . . . . . . . . . 90
4.5.3 Temporal self-compression . . . . . . . . . . . . . . . . . 94
4.5.4 Mechanism for DUV generation . . . . . . . . . . . . . . 95
4.6 High harmonic generation in HCPCF . . . . . . . . . . . . . . . 100
4.6.1 Phase mismatch . . . . . . . . . . . . . . . . . . . . . . . 101
4.6.2 Phase-matched generation of x-rays . . . . . . . . . . . . 103
4.6.3 Quasi-phase-matching technique . . . . . . . . . . . . . . 105
5 Conclusion and outlook 109
Bibliography 112
81 Introduction
Since the rst idea to guide light by means of a photonic stop band in 1991
big e ort was made to realise this in a two dimensional structure [1]. Pho-
tonic crystals are periodic arrangements of alternating dielectric materials,
with a period typically on the order of the wavelength of light. With sophis-
ticated techniques they can be fabricated as one-, two- and three-dimensional
structures. Depending on the the speci c structure and direction under in-
vestigation, light of a certain frequency can experience Bragg di raction and
thus cannot propagate in this direction. In analogy to solid-state physics, this
feature of the structure is named photonic stop band. An example of a one-
dimensional with a photonic stop band are dielectric mirrors, which
are nowadays very common in optics. If a photonic crystal has for a certain
frequency photonic stop bands in all directions and for all polarisations, it has
a full photonic bandgap. In this thesis we will consider two-dimensional pho-
tonic crystals which are invariant along the z-direction. They consist typically
of an hexagonal arrangement of air holes in a silica matrix. It is found, that
such structures o er photonic bandgaps for propagation directions in the plane
of the crystal if the refractive index contrast is larger than 2:66. By consider-
ing propagation along the z-direction, which is perpendicular to the plane of
the crystal, this requirement is relaxed [1]. Inserting a defect into the perfect
crystal o ers the possibility of guiding light along the invariant z-direction.
This defect can be either formed by a solid, which will result in a solid core
photonic crystal bre, or by enlarging one hole of the crystal. This will give
raise to a hollow-core photonic bandgap bre (HCPBGF), as the con ned light
will propagate in this hollow channel, running along the length of the bre.
It took until 1996 when the rst bandgap guiding bre was demonstrated [2]
and led to many new applications in optics, for example the supercontinuum
generation in endlessly single mode bres [3, 4]. Some years later, in 1999,
the rst hollow-core photonic crystal bre was fabricated [5] and a big rush
set in to exploit the o ered possibilities of this new bre type. These bres
o er di ractionless propagation of a tight con ned mode and long interaction
9

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