Few-Cycle High-Repetition-Rate
Optical Parametric Ampliers
And Their Synchronisation Schemes
von Diplom-Ingenieur Catherine Yuriko Teisset
aus Osaka, Japan
von der Fakultät V - Verkehrs- und Maschinensysteme
der Technischen Universität Berlin
zur Erlangung des akademischen Grades
Doktor der Ingenieurwissenschaften
- Dr.-Ing. -
genehmigte Dissertation
Berlin 2009
D83
Promotionsausschuss
Vorsitzender: Prof. Dr.-Ing. Henning Meyer (TU Berlin)
1. Gutachter: Prof. Dr. rer. nat. Heinz Lehr (TU Berlin)
2. Gutachter: Dr.-Ing. Alexander Binder (Ingenieurbüro Dr. Binder)
Tag der Erönung des Promotionsverfahrens: 16.10.2009
Tag der wissenschaftlichen Aussprache: 22.12.2009
Susanna:
Sotto i pini... del boschetto...
La Contessa:
Ei già il resto capirà.
Susanna:
Certo, certo il capirà.
Canzonetta sull'aria, Le nozze di Figaro.
Wolfgang Amadeus Mozart
Zusammenfassung
Hochenergetische ultrakurze Lichtpulse mit wenigen optischen Zyklen und vollständig kontrol-
liertem elektromagnetischen Feld sind Voraussetzung für die Erforschung von feldstärkeempnd-
lichen elektronischen Prozessen auf subatomarer Ebene. Insbesondere optische, parametrische
Verstärker für gechirpte Pulse (OPCPA) haben sich als leistungsstarke Alternative zu herkömm-
lichen Titan:Saphir-Lasern erwiesen, um breitbandige Pulse mit wenigen optischen Zyklen und
gleichzeitig hoher mittlerer Leistung zu generieren. Die entscheidenden Vorteile von OPCPAs
sind neben der groÿen Verstärkungsbandbreite die geringe thermische Belastung der nichtlin-
earen Kristalle sowie die im Vergleich zu Lasermedien sehr hohe Verstärkung in einem Durch-
gang durch den Kristall.
Der Prozess der parametrischen Verstärkung in einem nichtlinearen optischen Kristall läuft
ohne Zwischenspeicherung der Pumpenergie ab und benötigt, um Skalierbarkeit und prak-
tische Anwendung einer OPCPA zu gewährleisten, hohe Anforderungen an die Synchronisa-
tion von Pump- und Seedpulsen. Parametrische Verstärker sind zur Zeit die einzige Methode,
mit der hochenergetische, kohärente Lichtpulse weniger optischer Zyklen im vielfachen Milli-
Joulebereich hergestellt werden können. Allerdings werden solche Systeme bisher nur im Bere-
ich von wenigen Hertz Wiederholraten betrieben, da geeignete hochrepetitive Pumplaser bisher
nicht existieren.
Diese Dissertation konzentriert sich auf die Entwicklung von robusten und leistungsstarken
optischen parametrischen Verstärkern mit hohen Wiederholraten für die Erzeugung von Pulsen
mit wenigen optischen Zyklen. Hierfür wurden im Rahmen dieser Arbeit zwei speziell für das
Pumpen von parametrischen Verstärkern zugeschnittene eziente Lasersysteme entwickelt mit
Wiederholraten von 10 kHz und 10 MHz und Pulsenergien von 1.6 mJ beziehungsweise 6
µ
J.
Zusätzlich werden die in dieser Arbeit entwickelten Synchronisationstechniken zwischen der
Femtosekundenseedquelle und den Pumplasern vorgestellt.
1
Abstract
High-energy few-cycle and carrier-envelope phase controlled laser sources are urgently required
in many applications of high-intensity and laser eld-sensitive physics. Optical parametric
chirped pulse amplication (OPCPA) oers a particularly promising route toward compact
ultrashort ultrahigh-peak-power laser systems because of its very broad gain bandwidth, negli-
gible thermal load on the nonlinear crystal, and an extremely high single-pass gain as compared
to ampliers based on laser gain media. Due to the absence of energy storage in the nonlinear
crystal, parametric amplication implies stringent requirements in terms of synchronisation
between the pump and seed pulses which may hinders its scalability and its practical applica-
tion. Synchronisation is thus of crucial importance for the generation of stable intense few-cycle
pulses. Based on this technology terawatt-class multi-millijoule OPCPA systems were already
reported at lower repetition-rates, typically of few Hz, due to power scaling issues of the pump
source.
This thesis focuses on the realisation of robust high-power high-repetition-rate optical para-
metric chirped pulse ampliers for the generation of few-cycle pulses. Within this work, two
ecient picosecond pump sources were developed to amplify the output of a broadband seed
oscillator. These laser sources operate at 10 kHz and approximately 10 MHz with pulse ener-
gies of 1.6 mJ and 6
µ
J, respectively. In addition, two reliable and technologically attractive
solutions for the synchronisation between a femtosecond seed oscillator and an external pump
laser are presented. Broadband amplication of 7-fs pulses is demonstrated up to 700 nJ at
MHz repetition rate. First compression experiments were undertaken with a pulse energy of
240 nJ and resulted in 10 fs pulses.
3
Contents
1 Introduction.................................................................................9
1.1 Motivation for high-peak-power few-cycle pulses ............................................ 9
1.2 Comparison of pulse amplication techniques...............................................11
1.3 Timing jitter .........................................................................................12
1.4 High-repetition-rate................................................................................13
1.5 Thesis outline........................................................................................14
2 Femtosecond optical parametric ampliers...................................... 16
2.1 Phase-matching condition ........................................................................16
2.2 Amplication of ultrashort pulses ..............................................................18
2.3 Stretching and compression of femtosecond pulses.........................................22
2.3.1 Eciency and seed pulse duration .............................................................22
2.3.2 Dispersion management techniques ............................................................23
2.3.3 Pulse characterisation techniques...............................................................24
2.4 Pump sources for parametric ampliers.......................................................27
2.4.1 Regenerative ampliers............................................................................28
2.4.2 Mode-locked oscillators............................................................................30
2.5 Pump-seed synchronisation techniques........................................................34
3 KHz optical parametric chirped pulse amplier............................... 37
3.1 Injection seeding of the pump laser ............................................................37
3.1.1 Frequency-shifted seeding.........................................................................38
3.1.2 Direct seeding .......................................................................................40
3.2 Optically synchronised OPCPA.................................................................40
3.3 Timing jitter .........................................................................................44
3.4 Conclusion............................................................................................46
4 Mode-locked thin-disk oscillator.................................................... 48
4.1 Thin-disk concept...................................................................................48
4.2 A scalable system...................................................................................49
4.3 Design consideration...............................................................................50
4.3.1 Gain material........................................................................................50
4.3.2 Resonator design....................................................................................51
4.3.3 Dispersion ............................................................................................52
5
4.4 1-ps 6
−µ
J thin-disk oscillator ...................................................................54
4.4.1 Amplier head.......................................................................................54
4.4.2 Resonator.............................................................................................55
4.4.3 Experimental realisation ..........................................................................57
4.4.4 Pulse characterisation .............................................................................59
4.5 Second-harmonic generation .....................................................................64
4.6 Further scaling ......................................................................................65
4.6.1 Shorter pulse.........................................................................................66
4.6.2 Higher energy........................................................................................68
5 Pump-seed synchronisation for MHz parametric amplier................. 69
5.1 Introduction..........................................................................................69
5.2 Active synchronisation scheme ..................................................................70
5.2.1 Electronic control loop: phase-locked loop ...................................................70
5.2.2 Optical control loop: sum-frequency generation ............................................70
5.2.3 Combined scheme...................................................................................73
5.3 Experimental realisation ..........................................................................74
5.3.1 Electronic synchronisation set-up...............................................................74
5.3.2 Optical synchronisation set-up ..................................................................74
5.4 Locking results ......................................................................................75
5.4.1 Cross-correlation measurement..................................................................75
5.4.2 Frequency analysis of the timing jitter........................................................77
6 MHz optical parametric chirped pulse amplier .............................. 81
6.1 Preliminary considerations .......................................................................81
6.1.1 Choice of a nonlinear crystal ....................................................................81
6.1.2 Parametric gain and bandwidth ................................................................82
6.2 Experimental realisation ..........................................................................85
6.2.1 Ti:Sapphire seed ....................................................................................85
6.2.2 Amplication results...............................................................................86
6.3 Pulse compression ..................................................................................90
6.3.1 Compressor design..................................................................................90
6.3.2 FROG measurement ...............................................................................94
6.4 Summary of results.................................................................................94
6.5 Applications..........................................................................................96
7 Conclusion and outlook................................................................ 97
A List of acronyms ......................................................................... 99
B List of physical symbols ..............................................................100
C Dispersion and ultrashort pulses ..................................................101
D Bibliography .............................................................................102
7
1 Introduction
Since the advent of the rst ruby laser in 1960 [1], lasers have become a common tool for
scientists and engineers for the study of natural phenomena and the development of new tech-
nologies. Owing to its unique characteristics (spatio-temporal coherence, brightness ...), lasers
are routinely used in our daily life from optical telecommunication, material processing, surgery,
data storage to detection. In particular the technology of ultrafast lasers has opened up new
elds of investigation and application opportunities. Such lasers based on mode-locking tech-
niques produce pulses with durations in the picosecond (1 ps=
10−12
s) to the few-femtosecond
(1 fs=
10−15
s) range and are now commercially available with energies ranging from a few
picojoule and to a few hundreds of nanojoule.
In an industrial context, femtosecond pulses are particularly attractive for their reduced thermal
collateral damage through laser ablation. This permits high-quality machining of microstruc-
tures [2] and high-precision surgery with minimal invasive eects [3]. In fundamental research,
ultrafast lasers can be implemented for the real-time observation of fast-evolving processes. In
these experiments, the laser pulse performs as a camera with an extremely short exposure
time by mapping the temporal evolution of the reaction. Using femtosecond lasers in pump-
probe techniques, the intermediate states of a chemical reaction could be observed for the rst
time in 1987 [4]. The attribution in 1999 of the Nobel price to Prof. A. H. Zewail for his pioneer
work in femtochemistry attests the relevance of this eld of research [5].
Recent advances in the development of highly intense ultrashort laser sources have decreased
the pulse duration close to its natural limit of one optical cycle of the electric eld. For visible
and near-infrared laser sources this corresponds to a minimum of approximately 2 fs, leaving
sub-femtosecond time scale out of reach with conventional laser technology. Acceding to the
attosecond regime (1 as=
10−18
s) requires using much shorter optical cycles and hence shorter
wavelengths. Through extreme nonlinear optical processes based on high harmonic generation,
the optical spectrum of a high-energy ultrashort pulse can be shifted from the visible into the
extreme ultraviolet. The resulting pulses, as short as 80 as [6], can be used as a probe for
investigating ultrafast phenomena with an unprecedented time accuracy. While femtosecond
lasers enabled the measurement of molecule dynamics, attosecond pulses allow for the rst time
direct exploration of electron dynamics.
1.1 Motivation for high-peak-power few-cycle pulses
Present-day ultrashort lasers are essentially based on Ti:Sapphire material for the very large
gain bandwidth of its ions Ti
3+
and the good thermal characteristics of the host [7]. Typically
these lasers deliver output energies in the range of
5
nJ at a repetition rate of 80 MHz with a
pulse duration of 6 fs. At a centre wavelength of 800 nm, this corresponds to approximately
two optical cycles of the electric eld.
9
Through the extreme temporal connement of the light, optical peak power in the range of a
megawatt can be obtained directly from such lasers of modest energy. Unfortunately, these peak
powers are not sucient for many high-eld experiments which require electric eld strengths
comparable to that of the nuclear elds binding the electrons to the ionic core. Amplication
schemes based on chirped pulse amplication (CPA) [8] and optical parametric amplication
(OPA) [9] techniques were thus developed to perform energy-scaling of these ultrashort pulses.
With energetic pulses approaching two oscillations of the electric eld, light-induced nonlinear
eects in matter are temporally located around the peaks of the driving eld. Indeed, in
the presence of a few-cycle pulse, the electric eld amplitude rather than the pulse envelope
becomes the determining factor. Exploiting these circumscribed occurrences, few-cycle pulses
can be employed to trigger more eciently atomic processes in a controlled manner on a sub-
femtosecond scale.
Such experiments need to be undertaken over multiple pulses to record the necessary data and
achieve signicant signal-to-noise ratio. Consequently, reproducible guiding of atomic processes
demands that the electric eld oscillation remains identical from shot to shot. Yet, due do
environmental perturbations acting on the laser oscillator (temperature, air, vibrations ...),
the phase of the electric eld from successive pulses undergoes random uctuations. This phase
is usually referenced with respect to the the pulse envelope and is known as the carrier-envelope
phase (CEP). The electrical elds of two pulses with identical pulse duration but with dierent
carrier-envelope phases are shown in gure 1-1.
Figure 1-1 Pulse envelope and electrical eld of two few-cycle pulses with an phase oset of
π
2
.
Thus controlling the carrier-envelope phase from shot to shot is a prerequisite for light-matter
interactions featuring pulses approaching the single-cycle regime. With the introduction of
phase stabilisation schemes [10, 11, 12], the synthesis of denite electric eld waveform became
possible. In particular the emerging eld of attosecond science benets from the development
of CEP-stabilised pulsed source. Provided suciently short pulses (
∼
5 fs), a single burst of
high-energy photons may be emitted through high-harmonic generation when the peak of the
oscillating electric eld is made to coincide with that of the pulse envelope. This results in
the generation of isolated attosecond pulses in the extreme ultraviolet as opposed to trains of
attosecond pulses observed with longer driving pulses [13]. Based on these single attosecond
signals, time-resolved spectroscopy and steering of electronic motions become possible with a
never-before-achieved precision [14]. In conclusion, using high-peak-power CEP-stabilised few-
10
cycle pulses, attosecond science should allow for better understanding of natural processes in
physics but also in biology and ultimately the development of new technologies. The bridge
between attosecond science and technology could be realised by exploiting coherent X-rays
pumped by intense few-cycle lasers for radiotherapy and diagnostics of cancer competing with
synchrotron sources [15].
1.2 Comparison of pulse amplication techniques
Conventional amplication schemes based on chirped amplication were rst established to
overcome nonlinear eects and avoid the risk of optical damage with increasing pulse energy.
In this approach, a temporally stretched pulse is amplied in a laser medium and subsequently
compressed, as depicted in gure 1-2. Consequently, the peak power in the gain medium is
reduced according to the stretching ratio of the pulse.
Figure 1-2 Principle of chirped pulse amplication.
Using CPA, petawatt (
1015
W) level with
0.5
-ps pulse duration could be reached for the rst
time in 1996 at the Lawrence Livermore National Laboratory [16]. Nonetheless, the nite gain
bandwidth of the laser medium results in a narrowing of the amplied spectrum and ultimately
sets a limit to the scaling of shorter pulses without additional gain narrowing compensating
elements [17]. In order to obtain few-cycle pulses in CPA systems, post-amplication broadening
techniques are commonly used. These techniques make use of self-phase modulation, commonly
in noble gas-lled hollow-bre or in bulk material, to generate new spectral components followed
by pulse compression [18, 19, 20]. Often, these methods suer usually from low throughput
which make them less attractive for high-power systems.
While amplication in CPA systems relies on population inversion of a laser medium under
excitation of a pump, parametric amplication originates from a three-wave mixing process
inside a nonlinear crystal. Combined with the CPA approach, ampliers based on parametric
amplication should provide sucient gain bandwidth for petawatt scale systems with sub-
10-fs pulse duration [21]. This dual approach is known as optical parametric chirped pulse
amplication (OPCPA).
The key to the success of the OPA technique is given by its large amplication bandwidth
combined with extremely high single-pass gain even from few-millimetre-long nonlinear crystals.
In contrast to CPA where the realisation of a population inversion leads to non radiative
processes, there is no energy release in the crystal leading to negligible thermal eects. As a
result, diraction-limited beam quality is compatible with high pumping intensities enabling a
straightforward scaling of the system. Finally, parametric amplication oers many degrees of
11
Figure 1-3 Amplication based on laser material with transition cross section
σ
(left) and opti-
cal parametric amplication in a nonlinear material with second order susceptibility
χ(2)
(right).
freedom to obtain large amplication bandwidths such as the pump wavelength, the nonlinear
crystal and the geometry of the nonlinear interaction. This allows for higher exibility in the
conception and optimisation of the amplier design, as compared to CPA-based systems which
are restricted to the laser amplier medium. On the other hand, the absence of energy storage
imposes temporal overlap of the pulses inside the crystal to ensure interaction between the
pump and the signal pulses. Precise control over the pulse timing is hence required to achieve
reasonable conversion eciency. This issue clearly becomes especially severe with decreased
pump pulse duration. Some of the main advantages and drawbacks of the two amplication
approaches are summarised in table 1-1.
Amp. technique CPA OPA
Pulse duration (mJ level)
∼
26 fs [22]
∼
10 fs
∗
[17]
∼
8 fs [23]
Single-pass gain
∼
10 up to
106
Amp. of pre-pulses Yes In the pump time-window
Background emission Amp. spontaneous emission Amp. superuorescence
Thermal load High Negligible
Pump timing Simple Essential
Design exibility Fixed by the laser Large
Table 1-1 Comparison between CPA and OPA amplication schemes.
∗
with gain shaping op-
tical elements to compensate for the gain narrowing.
It follows that the advantages of parametric amplication are primarily associated to the am-
plier, whereas its drawbacks are related to the pump laser, for which the requirements are
more severe than in the case of laser-medium based ampliers.
1.3 Timing jitter
As mentioned earlier, a crucial point in OPAs is the timing between the pump and the seed
laser pulses since amplication can only occur within the pump time window. In a pulsed
laser, pulses are emitted essentially periodically. However, uctuations of the pulse period are
inevitable due to quantum noise, environmental perturbations and nonlinear processes. These
12
deviations of the pulse temporal localisation from an ideal periodic pulse train are known as
timing jitter.
In the case of a parametric amplier driven by an independent pump, the two interacting
laser sources are subject to dierent vibrations and drifts of their resonator. These eects are
translated into uctuations of the laser repetition rates causing variations of the pulse arrival
time on the OPA. Particularly, thermalisation of the laser optical components leads to a drift
of the resonator length. Figure 1-4 illustrates the oset between two laser pulse trains in the
presence of dierent resonator drifts.
Figure 1-4 Drift of the pulse temporal positions for two lasers.
In order to make the pulses repetitively coincide on the nonlinear crystal, control of the pulse
timing is essential. Synchronisation techniques dene the dierent procedures used to coor-
dinate the emitted pulse trains of dierent sources. The residual timing jitter will notably
determine the performances of a parametric amplier in terms of eciency and stability. In-
deed variations of the pump-seed temporal overlap cause a degradation of the amplied signal
characteristics such as pulse energy and spectrum. For reliable parametric amplication, a tim-
ing jitter below a tenth of the pump pulse width is commonly required. Obviously, diculties
will increase with shorter pulse durations.
In OPCPA systems, active synchronisations are employed in the presence of independent lasers
to discipline the repetition rate of one laser to the another one, or by locking both lasers to
an external reference, usually a microwave source [24, 25]. Passive synchronisations rely on
self-stabilisation mechanisms of the laser repetition rates [26] or an amplier scheme where
the pump and seed lasers are derived from a single source [27]. In this latter case, strict
synchronisation is nevertheless not automatically guaranteed as the two interacting pulses do
not usually follow the same optical path, resulting in the introduction of an additional source
of timing jitter.
1.4 High-repetition-rate
Optical parametric chirped pulse amplication has proven to be a powerful alternative to con-
ventional laser-amplication technologies for energy scaling of few-cycle pulses. Yet, optical
13
parametric ampliers have been essentially demonstrated at low repetition rates or at low out-
put energies as thermal management becomes more critical with increasing pump average power
[28, 29, 30]. This is particularly true for Ti:Sapphire-based pump sources, where higher peak
powers are usually reached at the cost of the pulse repetition rate. Only recently, the availabil-
ity of robust high average power pump sources have opened the way towards multi-kHz and
MHz high-energy parametric ampliers [31, 32, 33, 34].
Because many interesting light-matter interactions are governed by low probabilities or low
eciency, characterisation of these processes requires repeating the measurement over a high
number of laser shots. As a result, extensive recording times are necessary in order to achieve
good signal statistics. Such measurements need to be commonly taken over several hours
involving over millions of shots [13, 35] and conventionally using Ti:Sapphire CPA systems.
Another problem rises from the extreme sensitivity of nonlinear processes to uctuations of the
optical intensity and in some cases even to the electrical eld. External perturbations such as air
turbulence, temperature, mechanical vibrations, electric noise may in return cause uctuations
in pulse energy, carrier-envelope phase, timing jitter, wave front or beam pointing. Hence,
operating at low repetition rates sets accordingly severe criteria on the long-term and shot-to-
shot stability of the laser source for the acquisition of relevant and accurate data. Increasing
the repetition rate would permit to take faster measurements with an improved signal-to-noise
ratio and open new elds of investigation of ultrafast phenomena.
1.5 Thesis outline
In this thesis, two approaches will be addressed for the amplication at 10-kHz and 10-MHz
repetition rate of few-cycle pulses from a broadband seed. Both schemes rely on narrow-band
synchronised pump sources optimised for the generation of high-energy pulses. The kHz-pump
is based on a millijoule amplier, while the MHz-pump consists of a high-energy oscillator
delivering multi-microjoule output pulse energies.
In the second chapter of this thesis, the concept and realisation of optical parametric chirped
pulse ampliers are described. In the rst section, the principles and challenges of broadband
parametric amplication are reviewed. The dispersion management and characterisation of
ultrashort pulses are introduced. Finally dierent approaches for the generation of high-energy
pump pulses and solutions for the synchronisation between a femtosecond seed oscillator and
an external pump laser are presented.
In chapter 3, an optical parametric chirped pulse amplier system operating at kHz repetition
rate is presented based on a Ti:Sapphire seed oscillator and an amplier-type Nd
3+
-pump. The
two lasers are locked to each other using a passive all-optical synchronisation scheme with a
timing jitter estimated to be below 30 fs. These results led to a publication in Optics Express
[36].
The realisation of a 10-MHz optical parametric chirped pulse amplier scheme is described in
14
chapters 4, 5 and 6. This work includes the development of a MHz high-energy pump source
based on a thin-disk mode-locked oscillator (chapter 4), the design of an active synchronisa-
tion with an electronic-optical control loop (chapter 5), and the amplication-compression of
ultrashort pulses (chapter 6). Part of this work was described in references [37, 97]. Using a
high-energy Yb:YAG oscillator, few-nanojoule pulses delivered by a Ti:Sapphire oscillator are
amplied in a single-stage optical parametric amplier. The Yb:YAG laser delivers up to 6-
µ
J
pulses at 11.5 MHz with a duration of 1 ps. After frequency doubling, up to 3.8-
µ
J pulses are
generated at 515 nm for pumping a non-collinear optical parametric amplier. After synchroni-
sation of the two laser sources, a residual timing jitter of approximately 100 fs is measured. In
a single-stage parametric amplier, amplication of the broadband Ti:Sapphire seed is demon-
strated up to 700 nJ. The amplied spectrum still supports pulse durations below 7 fs. First
compression experiments are undertaken with 250-nJ pulses and result in 10-fs pulses.
15
2 Femtosecond optical parametric ampliers
2.1 Phase-matching condition
Parametric amplication is a nonlinear optical phenomenon resulting from a three-wave mixing
process in a nonlinear medium, where an initial high-energy photon splits into two photons of
lower energies. In this instantaneous interaction, the generated photon frequencies are set by
the energy conservation condition. For a pump wave of angular frequency
ωp
, this implies
ωp=ωs+ωi,
(2-1)
where
ωs
and
ωi
are the signal and idler wave angular frequencies, respectively. The sux p
denotes the pump, while s and i refer to the signal and idler. Thus amplication of a low energy
signal can be obtained through an energy transfer from an energetic pump source to the signal
and its resulting idler. Ideally their corresponding wave-vectors
kp
,
ks
and
ki
should full the
phase matching condition:
kp=ks+ki
with
|k|= n(λ)ω
c0
= n(λ)2π
λ,
(2-2)
where
n(λ)
is the refractive index of the nonlinear crystal for the wavelength
λ
and
c0
, the
velocity of light in vacuum. These two conditions are derived from the coupled three-wave
equations [38]. The latter ensures that the generated waves are added constructively across the
nonlinear crystal. Due to chromatic dispersion, this condition is usually not satised. Indeed,
in a normal dispersive crystal, the refractive index of the pump
n(λp)
is always larger than that
of the seed
n(λs)
and idler
n(λi)
.
In a collinear geometry, this results in the following inequation using equations
(2-2)
and
(2-1)
:
n(λp)
λp
>n(λs)
λs
+n(λi)
λi
,
(2-3)
equivalent to
kp>ks+ ki.
(2-4)
Figure 2-1 Wave-vector mismatch in a collinear geometry.
The wave-vectors are represented in gure 2-1 for a collinear geometry. The phase-matching
condition does not need to be satised rigorously but the wave-vector mismatch
∆k
, dened as
∆k=kp−ks−ki,
(2-5)
16
leads to a drop in the conversion eciency of this nonlinear process. In the presence of a non-
zero wave-vector mismatch the interacting waves will progressively run out of phase as they
propagate through the crystal, causing a decrease of the generated signal-idler pair. Destructive
interferences will then gradually annihilate the original build up of the signals.
Collinear phase-matching can be achieved by exploiting the birefringence in nonlinear crystals.
In a negative uniaxial birefringent crystal, the refractive index for the extraordinary wave
ne
is
smaller than for the ordinary wave
no
. For an extraordinary wave propagating along an angle
θ
with respect to the optical axis, the eective refractive index
ne(θ)
experienced by this wave
varies continuously between
no
and
ne
according to the angle
θ
, with
ne(θ) = neno
pn2
osin2θ+ n2
ecos2θ.
(2-6)
Collinear phase-matching in a birefringent crystal consists in determining the angle
θ
that
veries
∆k = 0
, which can be written as
either
npe(θ)
λp
=nso
λs
+nio
λi
,
(2-7)
or
npe(θ)
λp
=nso
λs
+nie(θ)
λi
,
(2-8)
depending on the nature of the interacting waves.
Equations
(2-7)
and
(2-8)
lead to type-I (
e→o+o
) and type-II phase-matching (
e→o+e
),
respectively. As an example, the dispersion of the nonlinear crystal beta barium borate (BBO)
is plotted in gure 2-2.
Figure 2-2 Dispersive curve of BBO for an ordinary wave (red line) and an extraordinary wave
for
θ= 0◦
(blue line). For
λp= 515
nm and
λs= 800
nm, the idler wavelength is
λi= 1445
nm. Type-I phase-matching is obtained in BBO for
θ= 22.7◦
in a collinear
geometry (green line).
17
Other phase-matching techniques include temperature phase-matching, which uses the depen-
dence of the birefringent crystal refractive indices on the temperature, and quasi-phase match-
ing, where the phase mismatch is compensated periodically in a spatially modulated crystal.
In this thesis, only type-I phase-matching in negative uniaxial crystals will be implemented for
the amplication of ultrashort pulses.
2.2 Amplication of ultrashort pulses
Neglecting pump depletion during amplication and assuming no idler wave at the beginning
of the process, the intensity of the amplied signal
Is
can be derived from the coupled-wave
equations within the slowly-varying envelope approximation for at-top spatial and temporal
beam proles [38]. For an initial signal intensity
Is0
, the intensity after amplication inside a
crystal of length L is given by
Is(L) = Is0 "1 + κsinh (gL)
g2#,
(2-9)
with
g = sκ2−∆k
22
,
(2-10)
and
κ= 2d
e
sωsωiZ0Ip
nsninp2c2
0
.
(2-11)
d
e
is the eective second-order nonlinear coecient of the crystal,
Ip
is the pump intensity,
n is the refractive index for the dierent interacting waves and
Z0
is the vacuum impedance,
which is approximately equal to 377
Ω
.
For exact phase-matching (
∆k= 0
),
g = κ
and equation
(2-9)
simplies to
Is(L) = Is0 1 + sinh2(κL)≈Is0
4exp (2κL)
if
κL1.
(2-12)
In this perfect case, the amplied seed grows exponentially. From equation 2-12, higher gains
are possible by either increasing the crystal length or by using higher pump intensities. Unfor-
tunately, using longer crystals is not a solution for ultrashort pulses, as dispersion will make the
pump and signals propagate at dierent speed in the crystal, limiting their actual interaction
length.
According to equation
(2-7)
, perfect angular phase-matching can be achieved for monochro-
matic waves in a collinear geometry through an appropriate orientation of the birefringent
crystal. However, in the presence of ultrashort pulses,
∆k
needs to be minimised over the
whole spectral range of the signal in order to amplify all wavelengths eciently.
18
Figure 2-3 Comparison between collinear (a) and non-collinear geometries (b). In a collinear
geometry, perfect phase-matching is achieved at a given signal wavelength. In a
non-collinear geometry, the direction of the idler wave-vector is wavelength de-
pendent, oering an additional degree of freedom to minimise
∆k
for broadband
phase-matching.
Figure 2-4 Wave-vectors in a non-collinear OPA for type-I phase-matching. The wave-vector
mismatch can be decomposed in a horizontal component
∆kk
along the pump and
a vertical component
∆k⊥
.
Figure 2-5 Phase-matching angle
θ
for dierent non-collinear angles
α
in a BBO type-I OPA
with
λp= 515
nm. In a collinear conguration, phase-matching can only be achieved
in a very narrow spectrum range. For
α≈2.5◦
, the wavelength dependence of
θ
is almost vanished from 700 nm to 1000 nm, allowing amplication of ultrashort
pulses centred around 850 nm.
19
Assuming perfect phase-matching for a signal frequency
ωs
, an increase
∆ω
of the signal
frequency is accompanied by an equal decrease of the idler frequency, since energy conservation
is automatically satised in a parametric process where no energy transfer takes place from the
pump to the crystal. Nonetheless, this does not ensure phase-matching and a non-vanishing
wave-vector mismatch arises at the frequency
ωs+∆ω
. In the case of a monochromatic pump,
the wave-vector mismatch can be approximated to the rst order by
∆k∼
=−∂ks
∂ωs
∆ω +∂ki
∂ωi
∆ω =1
vgi −1
vgs ∆ω,
(2-13)
where
vg=∂ω
∂k
is the group velocity of the pulse.
The full-width at half-maximum (FWHM) of the phase-matching bandwidth can be approxi-
mated from equations
(2-9)
and
(2-13)
to:
∆k
FWHM
∼
=4√ln 2 ·rκ
L
if
κL1
and
κ∆k
FWHM
2
(2-14)
∆ω
FWHM
∼
=4√ln 2 ·rκ
L·1
1
vgi −1
vgs
.
(2-15)
Equation
(2-15)
makes apparent that the dierence of group velocities between the idler and
the seed will restrict the phase-matching bandwidth and thus limit the use of longer crystals. A
solution to this problem consists in employing a non-collinear geometry, as illustrated in gure
2-3. While in the collinear case the group velocities of the seed and idler are set, non-collinear
optical parametric amplication (NOPA) allows to match the group velocities by adjusting the
angle between the seed and the pump [68].
The orientation of the wave-vectors are represented in gure 2-4. The angles
α
and
β
are the
angles of the signal and idler beams in respect to the pump.
α
is xed by the geometry and
is referred as the non-collinear angle, while
β
is wavelength-dependent. As before,
θ
is the
phase-matching angle. For broadband phase-matching, the wave-vector mismatch should be
aected as little as possible by a change of the seed frequency. According to gure 2-4,
∆k
can
be decomposed into a parallel and a perpendicular component:
∆k = (∆kk= kp−kscos α−kicos β
∆k⊥= kssin α−kisin β,
(2-16)
Ideally, both components of
∆k
should equal zero. Assuming a monochromoatic pump and
plane waves, the wave-vector mismatch can be derived to the rst order and written as
20
∆k∼
=
−∂ks
∂ωs
cos α∆ω + kisin β∂β
∂ωi
∆ω −∂ki
∂ωi
cos β∆ω = 0
∂ks
∂ωs
sin α∆ω −kicos β∂β
∂ωi
∆ω −∂ki
∂ωi
sin β∆ω = 0
,
(2-17)
Through multiplication of
∆kk
by
cos(β)
and
∆k⊥
by
sin(β)
with subsequent addition, the
expression simplies to
∂ks
∂ωs
cos Ω+∂ki
∂ωi
= 0
with
Ω=α+β,
(2-18)
which is equivalent to
vgs = vgi cos Ω.
(2-19)
Equation
(2-19)
shows that
∆k
can be cancelled around the seed frequency
ωs
when the
projection of the idler group velocity on the signal direction is equal to that of the seed. To
illustrate this, the phase matching angle
θ
is plotted for dierent values of
α
for a parametric
amplier based on BBO in gure 2-5. One can see that the phase-matching bandwidth strongly
depends on this non-collinear angle. A residual mismatch will nevertheless arise from higher-
order terms of the Taylor expansion of
∆k
.
Assuming perfect phase-matching for the signals
ωs0
and idler
ωi0
, the wave-vector mismatch
can be written as:
∆k≈ni0ωi0 −niωi,
with
ni0ωi0 =qn2
pωp−n2
sωs0 −2ns0ωs0npωpcos α.
(2-20)
The amplied spectra calculated from equations
(2-9)
and
(2-20)
are compared in gure 2-6
for a collinear and non-collinear OPA based on BBO.
In summary, the non-collinear phase-matching technique can provide larger amplication band-
widths by an eective matching of the signal and idler group velocities. High gains over large
spectral range are possible provided the crystal and focusing parameters are chosen adequately.
Thin crystals are essential for amplication of ultrashort pulses, because the accumulated phase-
mismatch
∆kL
lowers the intensity of the amplied signal as shown in equation
(2-9)
. The lower
gain in thinner crystals can be compensated by higher pumping intensities, typically in the or-
der of tens of GW/cm
2
. These intensities can be easily obtained from millijoule-ampliers
operating at lower repetition rates with quasi-collimated beams. Such an OPA is described
in chapter 3. Mode-locked oscillators have been recently scaled to the multi-microjoule level,
making them suited for pumping parametric ampliers at MHz repetition rate with focused
beams. Chapter 6 will present the realisation of a MHz OPA driven by a thin-disk oscillator
and address in more details the design issues for parametric amplication of ultrashort pulses.
21
Figure 2-6 Parametric gain for type-I amplication in a collinear (red line) and in a non-
collinear geometry (black line). The parameters for the calculation are
λp= 515 nm
,
Ip= 18
GW/cm
2
, L
= 4
mm,
θ= 22.9◦
in the collinear case,
θ= 22.02◦
and
α= 2.6◦
in
the non-collinear case.
2.3 Stretching and compression of femtosecond pulses
2.3.1 Eciency and seed pulse duration
Ecient energy extraction requires temporal overlap between the seed and pump pulses. In
high-power OPCPA systems, the pump source is typically narrow-band with pulse durations
ranging from a few tens of nanoseconds to approximately a picosecond depending on the tech-
nology used like a Q-switched laser [39], a master oscillator power amplier [28] or a high-energy
oscillator [34]).
Since the pump pulses are substantially longer than the seed pulses, the seed pulses are tempo-
rally stretched before amplication by a dispersive delay line. Ideally, the pump pulse should
be at-top-shaped and the seed pulse should be of comparable duration to obtain homogeneous
amplication across the seed spectrum. Indeed, as schematically shown in gure 2-7, a Gaussian
pump pulse leads to a non-uniform gain prole across the chirped seed pulse. The edges of the
pulses and hence the edges of the spectrum will experience a lower gain resulting in a reduction
of the amplied pulse bandwidth. In addition, timing jitter will be translated into instabilities
of the amplied spectrum. Pulse shaping techniques based on multi-stage Michelson interfer-
ometers and bre gratings have already been applied to the generation of picosecond at-top
pulses from a superposition of Gaussian pulses [41, 42]. However temporal pulse shaping is not
a trivial issue and will not be addressed in this work.
The amplication bandwidth is thus not only determined by the phase-matching bandwidth of
22
Figure 2-7 Spectral gain narrowing with chirped seed pulses and Gaussian pump pulses. Due
to the limited gain bandwidth the edges of the chirped seed pulse (left) are less
amplied than the central part. The amplied seed (right) has a narrower spectrum,
as shown by the narrower colour gradient on the right.
the nonlinear crystal but also by the pump pulse prole. In OPCPA systems, there is a trade-
o between eciency and bandwidth which is determined by the seed-to-pump pulse duration
ratio. Small ratios permit homogeneous amplication by maintaining the pump intensity almost
constant during amplication. On the other hand, the eciency is lowered because a large
fraction of the pump energy is discarded. From previous works [43], a good compromise can be
obtained for a seed-to-pump ratio of about
50%
.
2.3.2 Dispersion management techniques
There are several ways to create chromatic dispersion in order to lengthen or recompress a
pulse. The pertinence of one approach upon another depends on the amount of group delay
dispersion (GDD) necessary, the damage threshold and dimensions of the optical device, the
pulse bandwidth and the tolerated losses. The mathematical denitions of the parameters
related to the dispersion of ultrashort pulses (group velocity, group delay...) are listed in the
annex C.
Diraction gratings and prisms allow for the generation of large optical delays between the dif-
ferent spectral components of a pulse by exploiting the wavelength dependence of the refraction
and diraction angles, respectively [40]. In these schemes, the input beam is spatially dispersed
through diraction (gratings) or refraction (prisms) and subsequently reshaped, resulting in a
wavelength-dependent optical delay. Depending on the chosen geometry, the optical system
can produce a positive or a negative GDD. The major drawbacks of these systems are their
extreme alignment sensitivity, relatively high losses and large footprints. Further advances in
grating technology have recently permitted the realisation of highly ecient transmission and
reection gratings with diraction eciencies above 97% [44].
Chirped mirrors
The concept of chirped mirrors for introducing group delay goes back to 1994 and was origi-
nally intended for intracavity dispersion compensation in mode-locked oscillators [45]. Their
robustness was a crucial point for the commercialisation of the rst sub-10 fs lasers [46]. Indeed
these dispersive elements create an alignment-insensitive group delay based on their wavelength-
23
dependent penetration depth structure. The principle of operation of such mirrors is presented
in gure 2-8.
Chirped mirrors consist of a dielectric quarter-layer stack exhibiting a monotonic variation
of the multilayer period. This approach enables the realisation of tailored dispersion proles
including higher-order dispersion terms by ajustments of the mirror design. In chirped amplier
systems, their implementation would permit to signicantly reduce the overall-size of the set-
up, where large areas are commonly occupied by the stretcher and the compressor. So far,
they have been essentially used in CPA systems for nal adjustment of the necessary dispersion
because of their originally low average dispersive values.
Figure 2-8 Pulse stretching in a negatively chirped mirror.
The conception of mirrors with extreme parameters in terms of average GDD and bandwidth is
not trivial and requires optimisation of the reection and dispersion properties based on complex
algorithms. In addition, precise fabrication necessitates controlled manufacturing techniques
due to the narrow tolerance on the layer thickness. Only recently, these multilayer structures
have proven to be an alternative to conventional dispersion techniques by an increase in the
accuracy of the layer deposition process and the introduction of novel designs [97]. A low-
loss all-dispersive-mirror compressor was successfully implemented in our laboratory for the
compression from
∼
5 ps to 20 fs after chirped pulse amplication [47]. Despite the high number
of reections on these mirrors (>50), the overall throughput reached approximately 90%. Such
dispersive mirrors open up the way towards robust high-throughput and compact compressor
systems.
2.3.3 Pulse characterisation techniques
Following parametric amplication, the pulse are recompressed by another delay line of opposite
GDD from the stretcher. This is typically done by measuring the recompressed pulse charac-
teristics and correcting the dispersion accordingly. For pulses below a few tens of femtoseconds,
third-order dispersion (TOD) compensation becomes imperative and therefore necessitates ac-
curate pulse diagnostic techniques. Detailed information about these techniques can be found
in reference [48].
The most straightforward way to measure a pulse is to probe it with a much shorter reference
signal. The intensity cross-correlation is based on this principle. In this scheme, the measured
pulse and the reference pulse are spatially overlapped in some nonlinear medium in order
24
to generate a sum-frequency or dierence-frequency signal, which intensity is function of the
relative delay introduced between the two pulses. This signal is then recorded by a photodiode
as shown on gure 2-9. Obviously, this method becomes problematic as the duration of the
pulse of interest decreases. In addition, in order to retrieve the pulse duration from the cross-
correlation measurement, the duration and the shape of the pulse should be known.
The autocorrelation was the rst approach used to determine the duration of an ultrashort
pulse by convoluting the pulse with itself. One of the most widely used autocorrelation tech-
nique is the second-order intensity autocorrelation owing to the simplicity of its set-up. In a
very similar way to the intensity cross-correlation, the pulse is split in two parts and crossed
inside a nonlinear crystal for second-harmonic generation. In an intensity-based measurement,
the information about the temporal phase of the pulse electrical eld is lost. This may not be
an issue for picosecond pulses, however the possibility to identify and measure a chirp is es-
sential for femtosecond pulses. This shortcoming can be partially overcome in a closely related
measurement technique, known as interferometric autocorrelation. In this set-up, the pulses
are superimposed in a collinear geometry in order to produce an interference pattern, which
contains some phase information of the pulse. As opposed to the intensity autocorrelation,
this signal is not background-free since it is superposed to the two additionally emitted second-
harmonic signals, but the peak-to-background ratio is 8:1. This method is usually preferred for
pulses below
∼
100 fs but it still presents some limitations. First, the deconvolution of the auto-
correlation function requires here also a rst assumption on the pulse shape in order to extract
the actual pulse duration. Second, the autocorrelation being by denition symmetric, dierent
pulse shapes can lead to identical autocorrelation traces. Therefore, additional measurements
are required to fully characterise the pulse.
In the last decade, two techniques have emerged as powerful diagnostic tools of ultrashort pulses
by collecting information in the spectral domain. Combined with a programmable acousto-optic
lter, they allow for precise pulse recompression provided the measurement of the pulse and its
retrieval are done accurately [49].
Spectral phase interferometry for direct electric eld reconstruction (SPIDER) uses spectral
interferometry between two spectrally-shifted pulse replica to retrieve the spectral phase [50].
This involves splitting the pulse into three parts: two replica oset by a small delay and one
pulse stretched in a dispersive line. The pulses are crossed inside a nonlinear crystal for sum-
frequency (or dierent-frequency) generation. Due to this small delay, the pulse replicas are
recombined with dierent spectral parts of the chirped pulse, leading to two sum-frequency sig-
nals with shifted central wavelength (spectral shear). By measuring their spectral interferences
for a calibrated delay, the spectral phase can be extracted using an inversion algorithm and
the pulse can be reconstructed accordingly. The main advantage of this approach is its direct
non-iterative measurement of the electric eld, but it suers from calibration issues.
25
Figure 2-9 Examples of pulse measurement techniques. (a): Intensity cross-correlation, (b):
intensity autocorrelation, (c): interferometric autocorrelation, (d): SPIDER and
(e): FROG set-ups. SHG: second-harmonic generation. SFG: sum-frequency gen-
eration.
26
Another technique known as frequency-resolved optical gating (FROG) operates simultaneously
in the time and spectral domain [51]. In its simplest form, FROG consists of an intensity
autocorrelator set-up where a spectrometer is inserted to record the generated second-harmonic
spectra as a function of the timing delay between the two pulses. An iterative phase retrieval
algorithm is then implemented to reconstruct the temporal and spectral features of the pulse.
Some minor ambiguities remain such as the absolute phase, the translation in time (both present
in SPIDER) and the direction of time. As opposed to the intensity autocorrelation, this FROG
measurement leads to a quasi-unique pulse solution. FROG devices have been derived into
various geometries for increasing its accuracy, sensitivity, versatility or practicability. As a
example of these recent developments, grating-eliminated no-nonsense observation of ultrafast
incident laser light E-elds, in short GRENOUILLE, allows for single-shot FROG measurement
in a very compact set-up [52].
Unfortunately, all these phase-sensitive devices are still not on the market for pulse duration
below 10 fs. For the characterisation of shorter pulses, one has to rely on home-made systems
or use commercial interferometric autocorrelators down to to 5 fs.
2.4 Pump sources for parametric ampliers
The realisation of an OPA sets high demands on the pump laser in terms of energy, mode and
pulse proles, as well as stability. First, high-intensity pump pulses are crucial for parametric
amplication of broadband pulses since they enable the use of thinner crystals. Second, the
pulses should exhibit excellent beam quality to ensure homogeneous amplication of the signal
beam prole. Third, the pump temporal prole should be free from any pedestals or wings to
permit ecient pump-to-signal conversion. Fourth, the pulse energy uctuations should be low
to obtain stable parametric amplication. Finally, due to the absence of energy storage in the
nonlinear crystal, strict temporal overlap between the pump and the seed pulses is necessary in
a parametric process. As a consequence, synchronisation of the two laser sources is required.
Provided the synchronisation is not an issue, short pump pulses are favourable for parametric
chirped pulse amplication. Since the pump pulses are substantially longer than the seed
pulses, ecient energy extraction from the pump implies the use of highly chirped seed pulses.
Extensive stretching introduces additional losses for the seed and tends to lead to distorted
pulse proles, which necessitate complex adaptive dispersion management techniques to achieve
optimal recompression. With shorter pump pulses, in the range of a picosecond, the seed pulses
can be easily lengthened through chromatic dispersion in a transparent bulk material. For 6-fs
seed pulses, 3 cm of fused silica are sucient to stretch the pulses to 500 fs. Recompression
would be simultaneously simplied and could consists of multiple bounces on highly ecient
dispersive multilayer mirrors.
As compared to nanosecond pulses, higher pumping intensities are possible due to the increased
optical damage threshold for picosecond pulses [53]. For pulse durations
τp
below 20 ps, the
27
threshold increases even faster than the
1/√τp
scaling law. By driving parametric ampliers
with a picosecond pump pulse, higher peak intensities are achievable and larger amplication
bandwidths can be expected from thinner crystals.
Since the spatial length of a picosecond pump pulse is much shorter than the typical thickness
of the nonlinear crystal (
∼
5 mm), reections of the amplied seed from the crystal surfaces
are not amplied by the pump. Hence, better pulse contrast ratios of the amplied seed are
expected due to the absence of parasitic oscillation and amplication of post-pulses at these
pump pulse durations [54].
High-energy pump sources are conventionally derived from amplication of low-energy oscillator
pulses, typically in the nanojoule level, after reducing the repetition rate (sub-Hz to few kHz)
to decrease the thermal load on the amplier elements. Recent developments on high average
power mode-locked oscillators led to the direct generation of pulse energies beyond
25 µ
J [32],
opening the way toward MHZ OPAs. Following, the principles and constraints of pump lasers
will be introduced for amplier-based systems and high-energy mode-locked oscillators.
2.4.1 Regenerative ampliers
Regenerative ampliers are a powerful scheme for amplifying selected pulses inside an active
resonator by allowing multiple passes through a gain medium. A selected low-energy pulse is
trapped into a resonator by an optical switch. While this pulse experiences amplication at
each round trip, the other pulses are kept out of the resonator. Once the gain is saturated, the
optical switch couples the amplied pulse out and let a new pulse in for amplication. The
general scheme of such ampliers is depicted in gure 2-10.
Figure 2-10 Layout of a regenerative amplier. HR: high reector, PC: Pockel's cell, TFP:
thin-lm polariser, I: isolator, R: rotator,
λ/4
: quarter-wave plate and
λ/2
: half-
wave plate.
The optical switch usually consists of a polariser, a Pockel's cell and a quarter-wave plate. A
Pockel's cell is an electro-optic device, in which an externally applied DC voltage is coupled
into a modication of the refractive index of a nonlinear crystal. Typically the voltage is chosen
so that the phase-shift introduced between the two orthogonal components of the electric eld
28
with respect to the crystal optical axis, originates a rotation of the initial polarisation by 90
◦
in a double-pass.
The principle of coupling in and out is simple. An initial s-polarised seed pulse is reected
from the polariser and directed to the Pockel's cell. At that stage no voltage is applied, so that
the polarisation is rotated by 90
◦
after the double-pass through the quarter-wave plate. As a
result, the p-polarised pulse is transmitted through the polariser and propagates towards the
gain medium. In the mean time, a quarter-wave voltage is applied to the Pockel's cell. Thus, in
combination to the quarter-wave plate, a rotation of the polarisation by 180
◦
is introduced. The
p-polarised pulse is consequently trapped inside the resonator and amplied at each round
trip through the gain medium, as long as the voltage is maintained on the Pockel's cell. Once
the voltage is switched o, the pulse is coupled out by the cavity polariser.
To separate the incoming pulse train from the amplied one, a rotator in combination to a half-
wave plate are usually used. These two optical elements cause a rotation of the incoming pulse
polarisation by 90
◦
(
p→s
), while the outcoupled pulse polarisation stays unchanged (
p→p
).
The outcoupled pulses are consequently reected by the outside polariser. In addition, an
isolator is commonly inserted between the seed oscillator and the amplier to protect the
oscillator from a leakage through the polariser.
Regenerative ampliers present many advantages over multipass ampliers. Increasing the
energy of the pulses is easily done by increasing the duty cycle of the Pockel's cell, thereby
increasing the number of passes through the gain. If the regenerative amplier is designed to
support only the fundamental mode TEM
00
, the output pulse will exhibit diraction-limited
beam quality, regardless of the initial spatial abnormalities. By operating the amplier in a
saturated regime, the stability of the amplied pulse can be below
1%
[31].
These ampliers are very attractive when very high gains are required to scale up the pulse
energy. Yet, with increasing number of round-trips, nonlinear eects become more pronounced.
Eventually the accumulated phase-shift, essentially originated from Kerr-nonlinearity inside
the Pockel's cell, may create pulse and beam distortions setting eventually an upper limit to
the pulse amplication. To overcome this, chirped pulse amplication may be necessary at
the cost of additional complexities in the system. Another issue is the increased timing jitter
usually observed after amplication. Indeed, after a large round-trip number, small changes
of the cavity length due to thermal eects or mechanical perturbations can be translated into
a large timing drift from pulse to pulse. In an OPCPA system, this might result in unstable
amplication both from shot to shot and on a longer time scale. To some extend, improvement
of the timing jitter is possible by reducing the time span between the pulse injection into the
regenerative amplier and its outcoupling. This implies either designing shorter resonators or
using higher pumping intensities for increased single-pass gain. In addition, pulse instabilities
tend to appear at repetition rates close to the gain medium inverse upper state lifetime, which
can even take the extreme form of chaotic pulsing behaviour [55]. In some cases, stable operation
29
can be found inside an intermittent single-energy regime. Using this regime, pulse energies
exceeding 20 mJ were recntly demonstrated in our laboratory [31].
In conclusion, regenerative ampliers are mostly suited for the generation of energetic pump
pulses at repetition rates between 1 to 100 kHz but necessitate a careful design with possibly
CPA to maintain stable operation at increasing pulse energies.
2.4.2 Mode-locked oscillators
In a resonator, a multitude of dierent longitudinal laser modes veries the oscillation con-
dition,
L=qλ
2
, where L the resonator length, q an integer number and
λ
the wavelength of
the longitudinal mode. The number of possible oscillating modes is determined by the gain
bandwidth of the laser medium and ltering eects from the cavity optical elements. When no
phase relationship exists among these modes, the resulting interferences between the existing
longitudinal modes would lead to a noise-like output. However, due to the high number of
modes, this noise actually levels out to a stable continuous signal. On the contrary, if the
modes oscillate in phase (or with a xed phase relationship), the laser will emit a periodically
enhanced signal from the constructive interferences of the longitudinal modes. The laser is then
said to be mode-locked. Through coupling of the dierent longitudinal modes, the laser can
produce pulses which duration is directly related to the number of coupled modes [56]. Besides
the longitudinal modes, the transverse modes can also interfere in the mode-locking process
causing instabilities in the pulse formation mechanism due to the gain competition between
them. Fundamental transverse mode of the laser resonator is hence a prerequisite for stable
mode-locking operation.
Two dierent approaches can be used to mode-lock an oscillator. One relies on the implemen-
tation of a modulator inside the resonator, which introduces time-varying cavity losses, usually
via an acousto-optic or an electro-optic modulator, synchronised to the cavity round-trip. Such
techniques are referred as active mode-locking. The achievable pulse duration lies in the pi-
cosecond domain and is ultimately limited by the external modulation signal [56]. Shorter pulse
duration can be however obtained by passive mode-locking, in which the pulse induces its own
modulation through the nonlinear response of an intracavity element.
Passive mode-locking can be achieved through the insertion of a saturable absorber [57]. The
latter introduces lower absorption losses for higher incident optical intensities, thus favouring
the pulsed regime over the continuous wave operation in a resonator. Another scheme relies on
the direct use of an active medium subject to Kerr-nonlinearity [58]. In the presence of Gaussian
beams, the Kerr-nonlinearity induces self-focusing eects from the space-(and time)-dependent
refractive index n(r,t) given by
n(r,t) = n0+ n2I(r,t),
(2-21)
where
n0
and
n2
are the linear and nonlinear refractive index, respectively, and I(r,t) is the
30
spatio-temporal intensity prole. With an appropriate cavity design, one can use the consecu-
tive focusing of the laser mode in the gain medium to generate a nonlinear eective gain from
the spatial overlap between the pump and the laser mode. Owing to the quasi-instantaneous re-
sponse of Kerr-nonlinearity, the laser behaves as in presence of an ultrafast saturable absorber,
making the generation of
∼
6 fs pulses based on Ti:Sapphire medium possible [59].
For high-power oscillators, mode-locking is preferably done with a saturable absorber because it
eliminates the risk of optical damage in the gain medium through tight focusing and simplies
the resonator design and alignment. Indeed, Kerr-lens mode-locked oscillators need to be
operated close to the stability limit where substantial changes of the laser mode occur. On the
other hand, passive mode-locking with saturable absorbers reduce the damping of relaxation
oscillations and may lead to Q-switching instabilities in the pulse train. Figure 2-11 compares
the CW- and Q-switched mode-locked regimes. CW mode-locked operation is possible provided
that the laser and resonator parameters full the stability criterion [60] given by
E2
p>EL,satEL,sat∆R,
(2-22)
where
EL,sat
and
EA,sat
are the saturation energies of the gain medium and the absorber, respec-
tively.
Ep
is the intracavity pulse energy and
∆R
the absorber modulation depth. Equation
(2-22)
shows that saturable absorbers with low saturation uence and low modulation depth
are preferable because it lowers the pulse engery threshold for stable operation. Yet, with too
low values of
∆R
, pulse perturbations will not be as eciently suppressed by the absorber.
Figure 2-11 CW mode-locking (left) and Q-switched mode-locking (right).
Semiconductor Bragg reectors
Semiconductor Bragg reectors (SBRs) are well established for mode-locking ultrafast lasers
[61]. They consist of a saturable absorber layer integrated into a Bragg mirror. In these devices,
high intensity radiations are mostly reected, while the lower intensities are partially absorbed.
Their saturable absorption originates from the accumulation of electrons in the conduction band
and the depletion of the valence band upon incidence of intense light, preventing further photon
absorption. They are sometimes also referred as semiconductor saturable absorber mirror.
31
Figure 2-12 SBR nonlinear reectivity.
Besides the above-mentioned saturation uence and modulation depth, the most relevant pa-
rameters of a SBR are: its centre wavelength of operation and its recovery time
τA
. For
high-energy oscillators, the damage threshold is an additional critical feature. For a SBR, the
saturation uence denes the necessary uence to increase the nonlinear reectivity by
1/e·∆R
with respect to the linear reectivity, where
∆R
is the maximum nonlinear change of the mir-
ror reectivity. A typical reectivity curve of a SBR is shown in gure 2-12. According to
their recovery times, SBRs are classied between slow absorbers (
τA>τp
) and fast absorbers
(
τA<τp
). Another critical parameter is the non-saturable losses, which are the residual ab-
sorption losses for pulse energy densities far above the saturation uence. These may originate
from the imperfect reectivity of the Bragg reector, scattering losses due to surface defects or
the onset of two-photon absorption at higher uence. Such losses lead to a heat deposition in
the SBR, which can impede high-power lasing operation. Characterisation techniques of SBR
dynamics and nonlinear losses can be found in reference [62].
The main advantage of these devices is the possibility to tune their characteristics over several
orders of magnitude through modications of their designs and growth parameters, allowing
wide ranges of lasing operation and independent optimisation from the cavity design.
Soliton mode-locking
Mode-locking requires that the dierent longitudinal modes retain their phase relationship.
However, due to dispersion, the dierent spectral components will travel at dierent speeds,
thereby lengthening the pulses as they circulate through the cavity. Simultaneously, Kerr-
nonlinearity induces a time-dependent phase-shift according to the time-dependent pulse inten-
sity (equation
(2-21)
in the time domain), leading to a variation of the instantaneous frequency
along the pulse. The leading edge of the pulse is shifted to lower frequencies, while the trailing
edge is shifted to higher frequencies. This eect, known as self-phase modulation (SPM), causes
a positive chirp and spectral broadening. Control over the group velocity dispersion and the
nonlinearity inside the resonator becomes hence essential for ultrashort pulses.
32
Figure 2-13 Mode-locking with a fast absorber (a), a slow absorber and gain saturation (b) and
a slow absorber with soliton formation. In soliton mode-locking, there is a window
of positive net gain behind the pulse, therefore the pulse shaping mechanism cannot
be only explained by the absorber.
Optical solitons are pulses propagating with an invariant shape; they occur when dispersive
eects are compensated by self-phase modulation. In a resonator, soliton-like pulses can be gen-
erated in the presence of anomalous dispersion balancing the Kerr-nonlinearity. Since the two
eects are typically tight to dierent intracavity components (prisms, mirrors, gain medium...),
the pulse prole is not constant inside the cavity but depends on the local predominance of
dispersion or nonlinearity. For this reason, such pulses are in general referred as quasi-solitons.
While the pulse shaping mechanism is essentially achieved in the soliton regime through an in-
terplay between negative dispersion and self-phase modulation [63], mode-locking necessitates
some additional initiating and stabilisation eects, usually from a saturable absorber.
The pulse shaping mechanisms with dierent combinations of saturable absorber and gain
saturation are compared in gure 2-13. Because of the remaining net gain following the pulse,
noise may grow outside the pulse and eventually destabilise the mode-locking process in the
case of a slow absorber. However, the intensity of this noise is not sucient to induce nonlinear
eects. Consequently, the background noise experiences predominantly dispersive eects and
is gradually shifted out of the gain window, as schematically shown in gure 2-14. Thus,
instabilities can be cleaned up through the action of the saturable absorber.
Figure 2-14 Pulse shaping mechanism in the soliton regime. The low-intensity noise behind
the pulse experiences essentially dispersion, while the pulse is lengthened by SPM
and recompressed by the negative GDD. The dispersed noise is pushed out of the
gain window and consequently suppressed.
33
The propagation of soliton pulses through a dispersive nonlinear transparent medium is de-
scribed by the nonlinear Schrödinger equation [38]. In the soliton mode-locking regime, the
pulse duration can be approximated from the fundamental solution of this wave equation, as-
suming a continuous distribution of SPM and GVD in the resonator and neglecting the eects
of the saturable absorber and the nite gain bandwidth in the pulse shaping process. Soliton
mode-locking leads to transformed-limited pulses with hyperbolic secant pulse shape, which
pulse width is determined by the interplay between negative dispersion and nonlinearity. The
condition for stable soliton operation is given by:
τp≈1.76 2|GDD|
|γ
SPM
|Ep
with
γ
SPM
=4n2L
λw,
(2-23)
where
τp
denes the pulse duration, GDD the dispersion and
Ep
the intracavity pulse energy.
γ
SPM
is the nonlinear phase-shift in a material with nonlinear refractive index
n2
accumulated
over a length L for a Gaussian beam of radius w and central wavelength
λ
. According to
equation
(2-23)
, shorter pulse durations can be obtained by decreasing the dispersion. However,
the soliton may break into longer pulses if the dispersion becomes too low. These longer pulses,
hence with narrower bandwidth, will be indeed selectively amplied over a single shorter soliton,
which will suer predominantly from the limited gain bandwidth. This onset of multiple pulsing
ultimately sets a limit for the shortest pulse achievable through soliton mode-locking
In a passively mode-locked oscillator, Q-switching instabilities are of major concerns, since
the peak intensity of the Q-switched pulses may be above the optical damage threshold of
the cavity elements. For soliton mode-locked oscillators, this tendency towards Q-switching is
mostly counterbalanced by soliton eects and gain ltering [60]. Should the energy of the pulse
increase consecutively to relaxation oscillations, self-phase modulation will lead to a broadening
of the pulse spectrum. Yet, this pulse will experience a lower gain because of the limited gain
bandwidth resulting in an additional stabilising eect against pulse perturbations.
The development of a mode-locked oscillators is certainly not a trivial issue as it requires a
careful optimisation of the cavity design, its dispersion and the saturable absorber parameters.
Now reaching the multi-microjoule level, mode-locked oscillators oers an attractive solution
for pumping optical parametric amplication at MHz repetition rates.
2.5 Pump-seed synchronisation techniques
Unlike gain media with inversion storage, the parametric amplier poses a severe challenge of
ensuring strict synchronisation between the pump and seed pulses. Indeed, a timing precision
within a fraction of the pump pulse duration is required for stable and ecient amplication
inside the nonlinear crystal.
Two general approaches to synchronised few-cycle OPCPA schemes can be distinguished. One
relies on a colour-shifted seed, derived from an intense pump source, ensuring automatically op-
34
tical synchronisation between the two laser sources. Such systems are based on superuorescene-
seeded [65] or white-light-continuum-seeded parametric ampliers [27, 66, 67, 68]. Conse-
quently, the duration of the amplied pulse is relatively near to the pump duration, while
the phase of the pulse may experience shot-to-shot variations.
By contrast, ampliers seeded with coherent white light are capable of reducing the duration of
the amplied pulse down to several optical cycles, i.e. by orders of magnitude below the pump
pulse duration [27, 67]. Nevertheless, these devices require short, typically sub-200-fs intense
pulses for reliable white light generation. Therefore, white-light-seeded few-cycle ampliers are
driven exclusively by chirped-pulse ampliers predominantly based on Ti:Sapphire [27, 66, 67,
68] and, more recently, on Yb-doped laser crystals [69]. Superuorescent devices are unsuitable
for carrier-envelope phase-controlled amplication, whereas white-light-seeded ampliers may
exhibit CEP self-stabilisation under special conditions [11, 70].
A straightforward solution to CEP-controlled parametric amplication, similarly to the case of
its laser-amplier counterpart [13], is to use a pre-stabilized seed source [71, 72]. This idea was
recently implemented by Hauri
et al
[18], who demonstrated CEP stability preservation in an
OPCPA seeded from a CEP-locked Ti:Sapphire oscillator and pumped by the second harmonic
of a Ti:Sapphire amplier that was also seeded by the same oscillator. While oering a very
elegant solution to the problems of CEP control and optical synchronisation, this system,
nonetheless, has the power upscale constraints mentioned above. Scaling up the output of
the CPA Ti:Sapphire pump laser becomes particularly unattractive because this laser in turn
requires an upgrade of its own pump source - a green Q-switched ns laser.
The dependence on ultrashort pump lasers is a severe constraint for the development of both
superuorescence- and white-light-seeded ampliers. Indeed the pump necessitates a gain ma-
terial supporting a large amplication bandwidth and allowing energy scaling. Unfortunately,
most laser materials do not perfectly combine these two conditions, thus limiting their imple-
mentation in high-power OPCPA systems.
In the other approach, one laser source is optimised for the generation of narrow-band high-
energy pump pulses, while the seed laser consists of a broadband oscillator delivering low-energy
pulses. The generation of ultrashort pulses is in this case decoupled from that of high-energy
pump pulses by selecting two dierent gain media with optimal characteristics for one or the
other purpose. In this scheme, the scaling of the parametric amplier output is directly related
to the scaling of the narrow-band pump source. Most commonly, the pump is an amplier-based
source, operating in the few Hz to few kHz repetition rate, depending on its energy output.
In the presence of two independent sources, active synchronisation can be achieved by control-
ling the laser cavity length, hence the laser repetition rate, by means of electronic phase-locked
loops (see section 5.2.1). Obviously, the diculties with active synchronisation directly depend
on the pump pulse duration. While active synchronisation of nanosecond Q-switched pulses
does not involve a major eort, sub-picosecond locking necessitates the implementation of faster
35
electronics and complex control loops.
Passive synchronisation, on the other hand, relies on a self-stabilisation of the repetition rate
via a nonlinear coupling of the pulses [26, 64]. Though timing jitters of a few femtosecond
were demonstrated with these methods, the tolerance to cavity length-mismatch in the order
of 10
µ
m limits their practical use. Indeed, locking can only be maintained over a few minutes
as thermalisation cause drifts in the optical path lengths.
In this thesis, high-repetition rate OPCPAs are developed based on a two-colour approach with
a broadband seed oscillator and an external pump laser. This work includes the realisation
of high-power pump sources and the implementation of reliable synchronisation schemes. In
chapter 3, a simple synchronisation technique is demonstrated using a single master oscillator
for all-optical synchronisation between picosecond pump and seed pulses in a few-cycle kHz-
OPCPA system. In chapter 5, an active synchronisation using a combined electronic-optical
control loop is developed for the locking of two mode-locked oscillators. This enables parametric
amplication of ultrashort pulses at MHz repetition rates from high-energy pump oscillators.
36
3 KHz optical parametric chirped pulse amplier
In high-power optical parametric chirped pulse ampliers, due to the heat disposal and pumping
eciency reasons, it is more economical to employ a stand-alone (multi-)kHz picosecond pump
laser that is optimised for production of high-energy narrow-band pulses. This approach was
used in references [24, 25, 77], where a broadband Ti:Sapphire oscillator, employed as OPCPA
seed, was synchronised with the master oscillator of a picosecond pump laser based on Nd: YAG
using a complex electronic servo loop [78]. State-of-the art active synchronisation loops [77],
based on pricey GHz electronics, make it possible to keep the RMS timing jitter between the
seed and pump pulses on a sub-picosecond level. Whereas this locking precision satises well
the demands of OPCPA pumped by Nd-based picosecond lasers (pulse duration range 20-100
ps), it is insucient for use with sub-picosecond Yb-based pump lasers.
As prospective OPCPA pump sources, Ytterbium (Yb) lasers [79] promise to be vastly superior
to their Neodymium (Nd) counterparts because of the shorter pulse duration, reduced parasitic
heat, higher output power, and suitability for CPA operation. Using pump pulses in a 1-ps
range, one can realize ultrabroadband saturated parametric gain in nonlinear crystals as thin as
1 mm [80] without running into problems with the accumulated phase-shift in the parametric
amplier. Shaped pulses with a bandwidth of several nanometres from Yb-based lasers are also
advantageous in terms of maximising OPCPA conversion eciency, reducing superuorescence
background and avoiding gain narrowing. The desired near-rectangular pump pulse prole can
be attained by temporal stretching and pulse wing shaping of the broadband pump pulse. The
use of such chirped multi-ps pump pulses, however, will not lower the demand for femtosecond
timing precision, because the latter is dictated by the steepness of the pump pulse edges.
3.1 Injection seeding of the pump laser
Dierent opportunities for passive optical seed-pump pulse synchronisation in OPCPA are
surveyed in this section to explain our chosen strategy. An interesting OPCPA approach consists
in employing two-colour passively synchronised sources. The motivation behind this concept
is the need to provide strong seed signals that are suciently above the amplied spontaneous
emission (ASE) level in both the OPCPA and the injection-type pump laser. One possibility
of realising a two-colour scheme is to employ self-stabilisation of two mode-locked oscillators
lasing at the seed and pump wavelengths, respectively, via a nonlinear optical (Kerr-lens)
mechanism [26]. In terms of complexity, however, this method is not easier to implement than
active synchronisation of two independent mode-locked oscillators.
Another option to consider is a parametric or Raman-type frequency-converter that creates a
narrowband spectral component at the wavelength of the picosecond amplier. A suitably in-
tense wavelength-shifted pulse can be generated in a synchronously pumped optical parametric
oscillator (OPO) driven by the broadband seed laser oscillator. Unfortunately, the OPO itself
37
Figure 3-1 Injection seeding with and without PCF for all-optically synchronised OPCPA; BS,
50 % beamsplitter; DM, dichroic mirror, SHG, second harmonic generation
requires active cavity stabilisation. In a cavity-less alternative, a very weak frequency-shifted
pulse was produced in a travelling wave superuorescent parametric generator [81]. A separate
two-stage cw-pumped parametric amplier was used to boost this signal to the level suitable
for seeding a laser amplier.
In this work, two straightforward solutions to the synchronisation problems of two-colour
OPCPA schemes are presented for a pump laser based on an amplier. They combine the
simplicity of passively synchronised OPCPA schemes using a single seed oscillator, with the
exibility and scalability of the actively synchronised two-source approach for optimising inde-
pendently pump and seed lasers. Both solutions are illustrated in gure 3-1.
3.1.1 Frequency-shifted seeding
The rst approach relies on a broadband Ti:Sapphire oscillator for seeding an OPCPA stage
and a frequency shifter for seeding a pulsed pump laser. In our set-up, schematically presented
in gure 3-1, the output of a 6-fs 5-nJ 70-MHz chirped-mirror Ti:Sapphire oscillator [59] is
divided into two equal parts. One part is directed into an OPCPA stage and the other is
frequency-converted to obtain the seed for a picosecond Nd:YAG regenerative amplier.
In the case of our unamplied oscillator pulses, parametric frequency-shifters [81] become ex-
tremely inecient because of the low pump eld intensity and group-velocity matching issues.
Under these circumstances, soliton phenomena in optical bres suggest an interesting alter-
native to standard strategies of frequency conversion. Optical solitons propagating in media
with a nonlinear response experience reshaping and continuous frequency down-shifting due
to the Raman eect [82]. This phenomenon, called soliton self-frequency shift (SSFS) [83, 84],
provides a convenient way of generating ultrashort pulses with a tunable carrier frequency. Pho-
tonic crystal bres (PCFs) [85] substantially enhance this nonlinear-optical process [86] due to
a strong eld connement in a small-size bre core and the possibility to tailor dispersion of
guided modes by varying the bre structure [87].
The key advantages of the SSFS-based strategy of frequency shifting originate from the intrinsic
properties of Raman-shifted solitons [88]. In particular, the central frequency of the red-shifted
soliton can be tuned by varying the bre length and the input pulse energy. Radiation energy
carried by this signal is localised in the time domain within a short spike, dominating the
38
Figure 3-2 Layout of soliton-based synchronised OPCPA. PCF: photonic crystal bre, TPF:
thin-lm polarizer, CM, chirped mirrors, BS: 50 % beamsplitter,
λ
/2: half-wave
plate,
λ
/4: quarter-wave plate, Nd:YAG: side-CW-pumped gain modules, FI: Fara-
day isolator, FR: Faraday rotator, DM: dichroic mirror, SHG: second harmonic
generation.
temporal envelope of radiation intensity in the bre. Because of the anomalous group-velocity
dispersion of the PCF, the red-shifted soliton becomes delayed and eventually isolated, both
spectrally and temporally, with respect to the rest of the pump eld. This isolation of the
frequency-shifted soliton suppresses the interference between the solitonic part and the rest of
the spectrum of radiation eld.
For a PCF with a characteristic length of tens of centimetres, the amplitude of the soliton spike
in the temporal envelope of radiation intensity is typically an order of magnitude higher than
the intensity of the remainder of the SPM-broadened pump eld and Cherenkov-type emission,
both of which are spread out in time. As a result, the frequency-shifted solitonic component is
observed in experiments as the most stable part of the output spectrum [88], which is free of
interference fringes, typical of the nonsolitonic part of the radiation eld, including Cherenkov
emission.
In the context of laser amplier seeding, the combined spectro-temporal localisation of the
SSFS pulse makes it ideally suited for suppressing the ASE inside the laser cavity. In addition,
the high amplitude stability of the SSFS pulse is very important for maintaining stability of
the amplier output at repetition rates that are well above the inverse population relaxation
time of the laser gain medium. At such repetition rates, although the average output power can
be saturated, the energy of each amplied pulse cannot be saturated individually. Therefore,
stable and intense seed pulses are required.
39
3.1.2 Direct seeding
The second approach to all-optical synchronisation relies on an octave-spanning Ti:Sapphire [89,
90] oscillator, which is used for both seeding the OPCPA and its pump laser. In a similar way
to our rst solution, the output of the broadband oscillator is split into two equal parts, one to
be parametrically amplied and the other to be injected into a regenerative amplier and serve
as a pump. This solution permits a radical simplication of our previous OPCPA scheme, as it
suppresses the frequency-shifting set-up described above. However these oscillators require the
introduction of highly advanced broadband chirped mirrors, that are still capable of maintaining
a picojoule energy level within the bandwidth of a typical picosecond regenerative amplier.
Such level of the injected seed is required to compete eciently with the ASE in the picosecond
amplier.
To achieve direct optical seeding of the OPCPA pump source, some design modications need
to be introduced in the femtosecond seed oscillator and the pump amplier. First, by inserting
a pair of frequency-shifted set of chirped mirrors and tuning the intracavity dispersion with
a pair of wedges, the near-infrared (NIR) spectral components of the Ti:Sapphire oscillator
can be enhanced without reducing the overall bandwidth nor the output power. Second, the
regenerative amplier is based on Nd:YLF, since it has a slightly blue-shifted gain material
compared to Nd:YAG (Nd:YLF,
λ
=1053 nm, Nd:YAG,
λ
=1064 nm). Through these corrections
of the OPCPA system, the spectral overlap between the pump and the seed lasers can be
increased suciently to provide the necessary picojoule seed for the regenerative amplier.
3.2 Optically synchronised OPCPA
In these experiments, several commercial and research types of PCFs capable of supporting the
SSFS regime were investigated. Finally the commercial bre NL-PM-750 (Crystal Fibre A/S)
was selected since it exhibited a particularly clear solitonic feature in the NIR. The output
spectrum of a 20-cm-long PCF injected with 2-nJ oscillator pulses is presented in gure 3-3.
The oscillator light was injected with a f=7.5 mm aspheric lens. The central wavelength of the
spectral soliton was ne-tuned by adjusting the wave plate in front of the PCF and optimising
the focusing. Figure 3-4 shows the optical coupling for frequency-shifting.
To improve mechanical stability of the PCF and avoid problems with optical damage, a mono-
lithic bre assembly was prepared by Menlo Systems GmbH. Larger-core-diameter end caps
were spliced to the PCF. In addition, the end cap on the incoupling side was wedge polished to
avoid retro-reection into the Ti:Sapphire oscillator, which could destabilise the mode-locking
process. The bre assembly was xed directly on the oscillator breadboard whereas the focusing
and collimating lenses were mounded on xyz-translators. Mounting the bre assembly in this
way permits alignment-free operation for several weeks. A small adjustment of the incoupling
objective is only necessary upon the realignment of the oscillator.
40
Figure 3-3 Wavelength-shift in the photonic crystal bre. The solid curve shows an output
spectrum optimised for injection seeding at 1064 nm. The input spectrum from the
Ti:Sapphire oscillator is shown as dashed curved. BS: Beam splitter
Figure 3-4 Fibre and coupling unit.
41
Figure 3-5 Beam prole at the output of the bre. The beam pattern reveals the waveguide
structure of the PCF.
The output of the PCF, shown in gure 3-1, is directed into a home-made Nd:YAG regenerative
amplier. The coupling eciency into the amplier can be optimised by tuning the position of
the recollimating lens after the PCF, allowing for ne adjustment of the input seed beam diver-
gence. The bre delivers a Gaussian-like beam prole, as shown in gure 3-5 determined by its
fundamental propagation mode. To protect the bre from a back reection or leakage through
the out-coupling polariser of the regenerative amplier, a Faraday isolator was introduced after
the PCF. The estimated seed pulse energy contained within the gain bandwidth of Nd:YAG
is
∼
2 pJ, which proved to be sucient to obtain clean pulse amplication and suppress the
nanosecond Q-switched-pulse background.
This is evidenced by gure 3-6a, which shows the intracavity pulse train corresponding to the
build-up of the amplied pulse in each cavity round-trip. The regenerative amplier operates
in the regime of average power saturation and delivers 240-
µ
J pulses at a 10-kHz repetition
rate (2.4 W average power). If the seed pulse from the PCF is blocked, the output power of
the regenerative amplier drops to 50 mW, which corresponds to the onset of an unsuppressed
nanosecond Q-switched pulse. In order to generate a nanosecond pulse of the same energy as
in the regime of seeded picosecond amplication, the opening time of the Pockel's cell need to
be extended by 5-10 additional cavity round-trips. Therefore, for the given round-trip gain of
the amplier, the seed pulse energy is clearly sucient to overcome ASE issues. An intracavity
etalon was used to control the duration of the amplied picosecond pulse and prevent optical
damage and self-phase modulation inside the regenerative amplier. With a 0.8-mm-thick
etalon, the regenerative amplier delivers clean near-Gaussian 33-ps pulses. The background-
free autocorrelation traces obtained with dierent intracavity etalons are shown in gure 3-6b.
The regenerative amplier is based on a
∅
4 mm Nd:YAG rod in a laser-diode cw-pumping
cavity (model RD40, Northrop Grumman Cutting Edge Optronics). The length of the pumped
42
Figure 3-6 Performance of the regenerative amplier seeded with an optical solitonic pulse
from a PCF: (a) intracavity pulse train of pulses amplied to the energy of 0.2 mJ;
(b) background-free autocorrelation with and without intracavity etalon for a xed
number of intracavity roundtrips
Figure 3-7 Amplied beam prole.
region is about 63 mm. The 5
×
5-mm-aperture RTP Pockel's cell was purchased from Bergmann
Messgeraete Entwicklung KG. After a double-pass home-made cw-pumped 4
×
100-mm Nd:YAG
booster, we obtained 1.6-mJ pulses at 1064 nm in a TEM
00
mode. The amplied beam prole
is depicted in gure 3-7. A Faraday rotator was installed between the passes to compensate
thermally-induced birefringence of the YAG crystal and enable polarisation out-coupling. 0.8-
mJ pulses at 532 nm were obtained in a 10-mm-long critically phase-matched type-I LBO
crystal. The achieved 50% frequency doubling eciency is an additional proof of the clean
seeding and amplication process in our picosecond amplier chain.
In the case of the directly-seeded Nd:YLF amplier, the energy of the oscillator pulses conned
within the gain bandwidth at 1053 nm was limited to approximately 1 pJ. However, this seed
energy was still sucient to overcome the level of spontaneous emission in this lasing medium
that has a lower gain cross-section than Nd:YAG. The regenerative amplier, based on the same
43
amplier head as that of Nd:YAG, delivers up to 4 mJ at 1 kHz from a 3
×
63 mm Nd:YLF
rod without any post-amplication. A KD*P Pockel's Cell with 1-aperture is used to couple
the pulses in and out because of its higher damage threshold. By introducing a 0.8-mm-thick
intracavity etalon, clean Gaussian 27-ps pulses can be obtained after about 40 cavity round-
trips. The measured beam pointing stability is better than
3µ
rad. The SHG conversion
eciency in a 10-mm LBO crystal is up to 57% and the energy stability of the SHG pulse is
better than 1.3%.
To investigate the usability of the frequency-shifted synchronisation technique, a single-stage
parametric amplier was built up based on a 5-mm-long noncollinearly phase-matched BBO.
Due to the noncollinear geometry and tight beam focusing, the real interaction length in BBO
was below 3 mm. The seed pulses were stretched in a dispersive glass block to attain ecient
pump-to-signal energy conversion. The spectrum of the resultant 20-
µ
J signal pulses is depicted
in gure 3-8 and corresponds to a nearly maximum theoretical bandwidth for the given crystal
and pumping conguration.
In addition, the reliability of direct seeding was tested in one- and two-stage parametric am-
pliers pumped by the directly seeded Nd:YLF regenerative amplier as introduced in g-
ure 3-1. The seed pulses were down-chirped to approximately 40 ps in a negative dispersion
stretcher, based on holographic transmission diraction gratings. The stretcher overchirped
the seed pulses to compensate for the positive dispersion in the programmable acousto-optic
lter (DAZZLER, Fastlite) and obtain an adequate temporal overlap between the pump (27 ps)
and seed pulses (25 ps) at the OPA crystal. With the available SHG power of the Nd:YLF
amplier, the broadband pulses are amplied with energies up to
50 µ
J for a single-stage OPA
and
150 µ
J in two stages in 4-5-mm-thick non-collinearly pumped BBO crystals. The two BBO
crystals in the two-stage conguration were rst pumped by 300 mW and then by 1.2 W to
minimise the bandwidth narrowing through amplication. The spectrum and the group delay
of a compressed 11.3-fs pulse, obtained in a saturated single-stage OPA, and the corresponding
pulse parameters are given in reference [135].
Remarkably, the performance of the broadband OPA shown in gure 3-8 is reliably reproduced
each working day without any need to adjust the pump-seed delay, which has been previously
impossible in the actively stabilised OPCPA setup [25].
3.3 Timing jitter
The evaluated residual timing jitter between the seed and the pump pulses lies in the sub-30-
fs domain and could not be measured by optical cross-correlation techniques available to us.
The above-shown results of parametric amplication, a type of cross-correlation measurement,
reveal no traceable jitter. In this following section, the possible sources of residual timing jitter
are discussed.
The most important contribution to the residual jitter in our system results from the cavity
44
Figure 3-8 Results of single-pass parametric amplication with PCF-seeded regenerative am-
plier. Solid curve, amplied seed spectrum that supports sub-6-fs pulse duration
assuming perfect recompression (inset); dashed curve, seed spectrum.
45
length drifts of the Ti:Sapphire oscillator and of the regenerative amplier. The short-term drift
caused by mechanical instability can be disregarded, because the time span between the pulse
injection into the regenerative amplier and the Ti:Sapphire pulse injection into the OPCPA
stage is merely 300-400 ns, well below the period of conceivable vibrations in a laboratory. The
long-term drift is related to the thermal expansion of the cavities of the regenerative amplier
and the seed oscillator and depends on the ratio of the cavity lengths and the number of cavity
round-trips from the moment of seeding of the regenerative amplier. With simple thermal
stabilisation of the laser base plate, it should be possible to control the cavity length to within
a fraction of 1
µ
m. In addition, thermal drift can be compensated by choosing approximately
equal lengths of the oscillator and regenerative amplier cavities, provided the rate of cavity
expansion is similar.
In the case of PCF-based frequency-shifted seeding, another source of timing jitter is related
to the intensity noise at the input of the solitonic bre. Because of the nonlinear nature of
SSFS, intensity uctuations of the Ti:Sapphire oscillator give rise to a variance of the soliton
wavelength-shift, which is translated, through the group delay, into a timing jitter of the soliton
part of the eld at the output of the bre, used as a seed in our experiments. The sensitivity
of the soliton to the variations of the input intensity was evaluated using a numerical model of
SSFS in PCF [88] which uses the generalised nonlinear Schrödinger equation, including high-
order dispersion eects and the Raman response of fused silica. According to these simulations,
a 1% variation in the input pulse energy gives rise to additional spectral,
δλ
, and temporal,
δ
t,
shifts of the soliton estimated as:
δ
t
∆
t
≃δλ
∆λ ≃0.7%,
(3-1)
where
∆
t and
∆λ
are the time and wavelength Raman-induced shifts of the soliton in the
absence of input energy variations. For the PCF length used in these experiments,
∆
t is
∼
5 ps,
which corresponds to
δ
t
≃30
fs. Potentially, this timing jitter can be reduced through the
optimisation of the PCF dispersion prole. In addition, it must be pointed out that this jitter
estimation is rather conservative because the pulse-energy noise of a Ti:Sapphire oscillator can
be below 0.2% RMS [91].
3.4 Conclusion
In conclusion, a signicant improvement in OPCPA synchronisation was demonstrated as well as
a substantial reduction of the complexity and cost of the entire system. Our frequency-shifting
method opens the way to combine ubiquitous Nd-based picosecond ampliers and emerging
1-ps-range Yb-based ampliers with widely available several-nJ broadband Ti:Sapphire seed
oscillators, when no spectral overlap with the pump is achievable. Recently this technique was
successfully implemented to a 640 fs bre-based chirped amplier pump source in a 2 MHz-
OPCPA system producing 500 nJ pulses with 20 fs pulse duration [34]. The pump pulses were
derived from a Ti:Sapphire seed laser after soliton generation in a photonic crystal bre and
46
amplication to 15.5
µ
J in a three-stage bre-amplier.
Direct seeding permits a radical simplication of an OPCPA scheme based on a stand-alone
pump source and a broadband seed, as it suppresses the frequency-shifting set-up. However
these oscillators require the introduction of highly advanced broadband chirped mirrors, that
are still capable of maintaining a picojoule energy level within the bandwidth of a typical
picosecond regenerative amplier. Intermediate bre ampliers can be used to increase the
seed energy level [31] before the regenerative ampliers. In addition, they allow for improved
spectral features and beam prole, leading to improved seed incoupling ratios.
Our simple all-optical seed-pump pulse synchronisations permit hassle-free parametric ampli-
cation of ultrashort light pulses and can be straightforwardly scaled according to the energy
of the amplied pump pulse.
47
4 Mode-locked thin-disk oscillator
4.1 Thin-disk concept
One of the major challenges in the development of high average power solid-state lasers is the
thermal management of the laser cavity components, and in particular of the laser medium.
Since a substantial amount of the pump radiation is converted into heat, thermal eects such
as thermal lensing or thermal birefringence are particularly pronounced in the laser medium.
Ultimately they can lead to a thermal fracture of the material. In addition, nonlinear eects
inside the laser material can lead to severe degradations of the laser characteristics via self-
focusing or self-phase modulation. These phenomena originate respectively from the spatial
and temporal dependence of the intensity, which are coupled into a modication of the material
refractive index by the generation of a nonlinear polarisation.
The thin-disk concept, as shown in gure 4-1, relies on a very thin laser material mounted on
a large heat sink [92]. Through this geometry, a large ratio of the cooled surface to the heated
volume can be realised. Consequently, highly ecient heat removal is obtained, giving rise to
only a small temperature increase as compared to the dissipated power. Since the diameter
of the pump beam is much larger than the laser material thickness, the conguration leads to
a quasi-longitudinal heat ow along the optical axis of the laser. The associated temperature
prole is nearly homogeneous within the pumped region and causes only weak thermal lensing
and depolarisation losses. Thermal aberrations, conned to the border region of the pump
volume, can be neglected by designing the cavity in which the laser mode is slightly smaller
than the pumped area. Thanks to its unique cooling capacity, the thin-disk geometry allows
the generation of laser radiation with high beam quality even at extreme pumping intensities.
Figure 4-1 Thin-disk principle.
In the thin-disk approach the active medium is pumped from the top, typically from bre-
coupled laser diodes, resulting in a very short absorption length. The typical thickness of
a disk lies between 100 and 300
µ
m, while its diameter is usually of a few mm. To ensure
48
ecient absorption of the pump, a multi-pass optical scheme is implemented by means of a
parabolic mirror, which re-collimates the pump in combination with a roof prism to redirect
the unabsorbed light onto the disk as depicted in gure 4-2. Subsequently, the thin-disk requires
distinctive coatings for its front and back surface. The front side necessitates an anti-reection
coating at the pump wavelength and at the lasing wavelength, while a high-reection coating
at both wavelengths is deposited on the back side. The thin-disk can be then used in the cavity
as a folding mirror allowing for a double pass per round-trip through the gain.
Figure 4-2 Set-up of a thin-disk laser head.
The limited thermal lensing attached to the thin-disk makes the technology particularly attrac-
tive for designing high-average-power mode-locked lasers. Indeed, one of the prerequisites for
mode-locking is a diraction-limited beam quality because the pulse formation process would
undergo perturbations from the competition between higher-order transverse modes. Another
major advantage is the limited amount of nonlinear phase-shift introduced by the thin-disk,
relaxing the problem of the dispersion management at higher energy level (see section 2.4.2).
4.2 A scalable system
One of the most interesting features of the thin-disk concept is its direct power scalability arisen
from its quasi-longitudinal heat ow. By using larger disk diameters while keeping the pump
density constant, the temperature prole of the disk is almost unchanged [93] and the ouput
power is increased accordingly. Based on this technology, commercial systems were developed
using multiple thin-disk heads reaching more than 10 kW of CW output power, and 8 kW after
coupling into a high-power bre delivery system [94]. In the ns-pulsed regime, energies in the
hundreds of millijoule level were demonstrated in a cavity dumped system [95].
In section 2.4.2, the basic structure and mode of operation of semiconductor Bragg mirrors
(SBRs) were introduced. In a similar manner to the thin-disk, the SBR geometry leads to a
longitudinal heat dissipation since the absorber layer is much smaller than the beam diameter.
By doubling the mode area on the SBR, a doubling of the pulse energy is possible without
aecting the pulse formation. Thermal and mode-locking issues can be successfully tackled
even at high-power levels, as long as the laser parameters are chosen properly (intracavity
dispersion, mode size in the gain and on the SBR, SBR design and gain medium properties).
49
Combining both technologies oers a power-scalable solution for passively mode-locked lasers.
Providing a suitable gain medium and a SBR design, it allows for the generation of ultrashort
pulses at high-average power directly from an oscillator. Mode-locked powers up to
80
W were
generated from an Yb:YAG thin-disk laser [96]. Recently Neuhaus
et al.
demonstrated energies
up to
25 µ
J directly from an Yb:YAG oscillator by implementing a multi-pass design through
the thin-disk [32]. In the next section, the critical points for designing femtosecond lasers at
high-average power will be reviewed.
4.3 Design consideration
4.3.1 Gain material
The conception of a femtosecond oscillator operating at high-average power calls for a metic-
ulous attention in the choice of a laser material. Besides the spectroscopic properties, the
optical, thermal and mechanical properties of the material are important parameters. While
the dopant essentially denes the spectroscopic behaviour, the thermo-mechanical and thermo-
optical properties are typically given by the host material. The combination of laser ions and
host material determines the relevance of a laser material for the generation of femtosecond
pulses at high-average power.
Over the past decades, Yb:YAG has emerged as a prominent material for systems with high-
CW average power and high-pulse energy [79]. Some of the most interesting properties of the
material are listed below:
1. very low quantum defect (eciency
>91%
at
940
nm)
2. large absorption band (
10
nm @
940
nm [79])
3. high thermal conductivity of YAG (
6.5
W/mK @
5%
Yb doping [98])
4. broad emission band (
∼6
nm;
100
fs with Kerr-lens mode-locking [99])
5. high doping levels possible without quenching (
>20%
)
6. no excited-state absorption or up conversion
7. high tensile strength of the host material
8. long lifetime of upper laser level (
∼1
ms)
9. cubic structure
10. availability of high-quality crystals with large dimension.
Because of the low heat deposition resulting from a low quantum defect, the Yb
3+
ion is par-
ticularly well suited for high-power applications. Despite a high lasing threshold inherent to its
quasi-three-level lasing scheme, Yb:YAG is very attractive for diode-pumped systems. Indeed,
its absorption band is located in the near-infrared, a region for which reliable high-power, high-
50
brightness InGaAs diodes are available. Furthermore, its large absorption band loosens the re-
quirement on the temperature stabilisation, hence the stabilisation of the emission wavelength,
of the laser diodes. Its high thermal conductivity permits high pumping intensities for increased
gain. In addition, its cubic structure leads to isotropic properties resulting in a homogeneous
distribution of thermo-mechanical stress inside the material, which is particular benecial for
achieving a uniform cooling. Finally, its very simple lasing scheme without higher-lying levels
excludes excited-state absorption and up-conversion losses. With high-density pumping capac-
ity and high cooling eciency, the lasing threshold is easily overcome and high optical eciency
achieved. Yb:YAG is available with high doping concentrations without major degradation of
the material spectral properties. Thus, thinner crystals with higher doping concentrations can
be produced, conducting to a shorter pump absorption length, a reduction of material disper-
sion and nonlinear phase-shift. Yb:YAG has been inserted into various laser geometries with
impressive results for slabs [33] or rods [100]. However, the diode-pumped thin-disk approach
showed the most versatile laser developments for both oscillator and amplier systems [94].
During the last decade, the interest for ceramic laser media has dramatically increased with
the availability of improved quality samples. Compared to the melt growth technique, ceramic
materials oer numerous advantages: reduced costs, short production time and large aperture.
In addition, their fabrication allows designs of composite structure (doped/undoped, dierent
doping ions) with complex shapes. Using the proper fabrication technique, Yb:YAG ceramic
material can be produced with similar optical quality to the crystalline form [101]. In the future,
high-power thin-disk lasers and ampliers could benet from the development of ceramic media
with smooth gradient dopant distributions. Such doping prole is associated with a smoother
temperature prole, hence reduced thermal eects are expected at higher pumping intensi-
ties [102]. Despite all these interesting features, the new ceramic technology requires further
developments in the production of high-quality material before large-scale commercialisation.
More recently developed, the Yb
3+
doped sesquioxide materials have become particularly at-
tractive for the development of new high-power femtosecond sources based on thin-disk tech-
nology [103, 104]. They exhibit good thermo-mechanical properties, while supporting a larger
amplication bandwidth than Yb:YAG [105]. Some of these new materials will be reviewed
later in section 4.6.2
4.3.2 Resonator design
The cavity design is at the centre of the conception of any lasers, as it will essentially determine
the laser performances in terms of output power, beam prole and operation stability. The
laser resonator can be precisely modelled through ABCD-matrix calculations [107] when the
characteristic behaviour of each cavity elements is well-dened. Additional conditions on the
laser mode arise for mode-locked oscillators to ensure stable pulse operation (see equation 2-22).
In this section, the most crucial points for the design of a high-energy resonator are discussed.
51
As mentioned earlier, the presence of higher-order modes corrupts the pulse formation process.
Therefore, the cavity should support only the fundamental transverse mode. This condition
can be easily fullled by choosing a laser mode slightly smaller than the pump mode, typically
80%
, while keeping a good power extraction from the pump. Placing an aperture in the cavity
can enforce fundamental-mode lasing but it will result in additional cavity losses.
In the case of a resonator subject to thermal lensing, the laser can operate in the fundamental
transverse mode only within two stability zones, each of them exhibiting distinct stability
characteristics [106]. Magni
et al.
demonstrated that the misalignment sensitivity is larger in
zone II, where the axis displacement rapidly diverges towards one end. This becomes an issue
for systems with relatively small stability range, which is more often the case in high-power
lasers due to their increased thermal lensing. Even though thermal lensing is moderate in a
thin-disk geometry, it is still benecial to design a cavity lasing in zone I, ideally operating in
the centre of the stability range. In this case, the dependence of the laser mode radii is the
weakest on the change of the dioptric power of the thermal lens.
Kerr-nonlinearity may yield to a degradation of the spatio-temporal properties of the soliton
pulses. Therefore a resonator with large beam diameters is preferable to reduce the intracavity
intensity. On the other hand, larger laser modes lead to a higher sensitivity of the cavity to
small perturbations and cause a decrease of the cavity stability range, inversely proportional
to the beam radius squared [106].
In section 2.4.2, the problems of Q-switching instabilities in passively mode-locked oscillators
with saturable absorbers were briey introduced. Stable CW mode-locked operation requires a
threshold intracavity pulse energy. Below this value, the oscillator output consists of a mode-
locked pulse train which amplitude is typically modulated in the kHz range. Some of these
pulses will then have a drastically increased peak intensity, in some cases incompatible with
the operation of some cavity elements (SBR, chirped mirrors). As shown in equation
(2-22)
,
strong saturation of the SBR relaxes the condition on the intracavity pulse energy. A cavity
design with smaller mode on the SBR can therefore reduce the tendency towards Q-switched
mode-locking. On the other hand, this can also lead to SBR damage or pulse break up [108].
In the end, there is a trade-o between minimising the thermal eects by designing a cavity
with larger modes and increasing the mechanical and pulse stability by operating the laser with
smaller mode diameters.
4.3.3 Dispersion
As mentioned earlier in section 2.4.2, soliton mode-locking requires a balance between the
group delay dispersion and the self-phase modulation. Scaling up the pulse energy leads to
an enhancement of the Kerr-nonlinearity inside the cavity, which requires a readjustment of
the cavity dispersion to stabilise the pulse formation process, as shown in equation
(2-23)
.
Dispersion management develops into a problematic at higher energy levels, as it becomes
52
dicult to combine high dispersion values with low losses and large bandwidths.
In high-power soliton mode-locked oscillators, the dispersion is usually introduced by a series
of chirped-mirrors rather than by a prism pair to reduce the nonlinear eects inside the cavity.
Commercially available chirped mirrors typically range between -50 fs
2
and -1000 fs
2
of negative
group delay dispersion (GDD).
In comparison to other laser designs, the nonlinear phase-shift introduced by the thin-disk itself
is very small, owing to the
∼
100
µ
m thickness of the gain medium. The thin-disk approach
is hence particularly well suited for designing mode-locked oscillators with high intracavity
intensity. However, at low repetition rates (
<10
MHz), thus for long cavities, the nonlinearity
of air may become predominant among all source of nonlinearities and dicult to compensate
by commercial dispersive mirrors with typical group delay values below -1000 fs
2
. Table 4-1
shows a comparison of nonlinear contributions between dierent elements in a 10 MHz cavity.
Material n
2
(cm
2
/W) L (mm)
γ
SPM
(rad/W)
Air
4·10−19
30000
4.7·10−9
Yb:YAG
6·10−16
0.8
1.8·10−10
Fused silica
3·10−16
1
1.2·10−10
Table 4-1 Comparison of nonlinear contributions in a 10-MHz thin-disk oscillator assuming an
average 1-mm beam radius.
Three dierent laser approaches have successfully overcome the problems of dispersion com-
pensation with increasing output pulse energies. The rst concept relies on the decrease of
the total self-phase modulation by operating the laser in helium [109]. Indeed, helium exhibits
a nonlinear refractive index about 100 times lower than air [110]. Using this approach, pulse
energies up to
11.3µ
J were obtained from an extended cavity thin-disk oscillator [111]. Though
relatively easy to implement, purging continuously the cavity with helium is a pricey solution
and is therefore not suited for a prolonged operation of the laser system.
An alternative technique makes use of a high out-coupling ratio to reduce the intracavity
intensity and thus the total nonlinearity [32]. Multiple passes through the gain medium allowed
for a out-coupling value of
78%
by an increase of the cavity round-trip gain. While oering
a very elegant solution to the nonlinearity management, a muli-pass arrangement requires a
complex resonator design, which is inevitably bond to a smaller stability range. In such systems,
the thermal behaviour of each optical elements needs to be precisely known for an appropriate
modelling of the resonator. This becomes particularly challenging for lasers with various optical
elements exhibiting dierent thermal properties, as it is the case in reference [32].
The third approach, which is the one followed in this thesis, relies on the design of highly
dispersive mirrors to compensate for the self-phase modulation in air. Here, the main advantage
is the generation of high-energy pulses directly in air from a simple resonator design. Using
this concept, we were able to demonstrate stable single-pulse operation in air up to 5
µ
J using
only three high dispersive multilayer mirrors for a total negative GDD of
−15000
fs
2
[97].
53
Despite their large dispersion level, the mirrors still supported a bandwidth over 20 nm and
had excellent reectivity(
>99.9%
).
4.4 1-ps 6
−µ
J thin-disk oscillator
4.4.1 Amplier head
The laser module used in our Yb:YAG thin-disk oscillator was developed at the Institut für
Strahlwerkzeuge in Stuttgart and is now commercially available from the company Dausinger-
Giesen GmbH. It consists of an amplier head pumped via bre-coupled laser diodes emitting
up to
500
W of average CW power at
940
nm.
At the front, a parabolic mirror images the disk on itself to make use of the unabsorbed light in
each pass. At the back, a turning prism allows for a doubling of the passes. In total, the pump
light is directed 16 times into the thin-disk and almost complete absorption is achieved. To
minimise thermal eects on the parabolic mirror which could aect the pump spot, the front
panel is water-cooled.
By slightly decreasing the distance between the bre output and its re-collimating lens from
its optimal position, the pump image on the disk can be shaped into a more diuse spot. This
conguration allows for a smoother temperature gradient at the edge of the pump spot and
therefore a reduction of thermal aberration in this vicinity, which is essential for maintaining a
fundamental transverse mode. The pump diameter was set to
2.8
mm to allow for a reasonably
large stability range and moderate nonlinear eects.
The thin-disk used throughout this thesis had an Yb
3+
-doping concentration of
7%
and was
polished down to 200
µ
m with a small wedge (0.1
◦
) to eliminate interferences between satellite
pulses in the gain material originating from imperfect anti-reection coatings. A parallel thin-
disk would indeed act as a Fabry-Perot interferometer, hence limiting the pulse bandwidth
through etalon eect and disturbing the pulse formation process. The edges of the front surface
of the disk were additionally smoothened, so that lateral parasitic lasing becomes impossible
despite the high amplication gain.
The crystal features a concave curvature without pumping, which is caused by the soldering
procedure on the heat sink. Interferometric measurements were carried out to check the surface
quality of the disk and determine its initial curvature. The changes in the disk dioptric power
were investigated under pumping condition by analysing the beam parameters of an incident
beam reected from the disk. This measurement was undertaken with another disk with iden-
tical crystal thickness and doping concentration. The lasing behaviour of our laser conrmed
that both disks had similar curvatures.
Figure 4-3 shows that for higher pump power, the thin-disk attens. This behaviour can be
easily explained by the higher heat deposition at the centre of the disk, which creates an
54
Figure 4-3 Thermal-induced lens of an Yb:YAG thin-disk under pumping condition.
additional defocusing eect. The ellipticity of the disk is negligible, which permits a resonator
design without any particular astigmatism compensation scheme.
4.4.2 Resonator
For modelling the laser, thermal eects on the cavity mirrors and in the SBR are neglected.
The target parameters for the cavity are reported below:
•
total cavity length:
∼
15 m for
∼
10-MHz repetition rate,
•
beam diameter on the disk:
∼
2.4 mm for single mode operation (
∼
2.8 mm pump spot),
•
disk curvature under pumping:
∼
ROC
−4500
mm,
•
beam diameter on the SBR: <2 mm to avoid Q-switch instabilities,
•
beam diameter on the output coupler: >2 mm to avoid excess nonlinearity in the material,
•
small angle of incidence on the mirror : to avoid astigmatism.
Simulations through ABCD matrix calculations and experimental optimisations led to a very
simple resonator with a double-pass through the thin-disk as shown in gure 4-4. Three curved
mirrors control the critical mode sizes on the disk, output coupler and SBR. The beam radius
inside the resonator is plotted in gure 4-5. Additional high-reectors are inserted as folding
mirrors to keep the set-up relatively compact. With this arrangement, the footprint of the laser
is less than 1.5 m x 0.5 m. The dierent optical elements are listed in table 4-2.
To check the thermal stability of the laser, the stability range of its equivalent optical system
is rst determined as described in reference [106]. The resonator can be modelled by two plane
mirrors that enclose a lens with variable focal length
f
between two generic optical systems
55
Figure 4-4 Schematic of the laser set-up.
Element ROC (mm) Distance
OC
∞
M1
−5000
OC-M1: 5480 mm
M2
+3000
M1-M2: 3140 mm
TD
−4600
M2-TD: 1030 mm
M3
−4000
TD-M3: 1000 mm
SBR
∞
M3-SA: 2420 mm
Table 4-2 Cavity design. OC: output coupler, M
i
: mirror, TD: thin-disk.
Figure 4-5 Calculated
1/e2
beam radius inside the cavity.
56
with transfer matrix
T1
and
T2
. Using the formalism of [106], the transfer matrix
T
of the
equivalent optical system, from the output-coupler to the SBR is given by:
T=T1·
1 0
−1
f1
·T2
with
T1="1 5480
0 1 #·
1 0
1
−2500 1
·"1 3140
0 1 #·
1 0
1
1500 1
·"1 1030
0 1 #
and
T2="1 2420
0 1 #·
1 0
1
−2000 1
·"1 1000
0 1 #
The simulation shows that the cavity features two stability ranges: one for positive focal lengths
of the disk and one for negative values, which correspond respectively to zone I and zone II .
The laser is stable for
f∈[−3900
mm
,−980
mm
]∩[1700
mm
,+∞[
.
At our pump intensities, the disk does not experience a change from concave to convex cur-
vature. As a result, the laser can only operate in zone I. The focal length
F
of the resonator
equivalent optical system is calculated in order to estimate the misalignment sensitivity due to
thermal lensing. From gure 4-6, it can be seen that the change of the disk focal length causes
only a moderate change of the resonator characteristics.
Figure 4-6 Absolute value of the focal length of the equivalent optical system as a function of
the disk focal thermal lens. The blue vertical line represents the operating point of
the laser.
4.4.3 Experimental realisation
Because of its cubic lattice, the Yb:YAG material does not induce linear polarised laser light.
Mode-locking operation necessitates nevertheless a stable direction of polarisation. In order to
57
restrict the lasing polarisation, a 2-mm glass plate is inserted under Brewster angle to introduce
higher losses for the vertical polarisation. This plate is installed between the output coupler and
the next curved mirror, where the mode-sizes are relatively large to avoid additional nonlinear
eects. The thin-disk leads to four residual reections due to a relatively high value of its
anti-reection coating (
0.5%
). These beams had to be blocked by two water-cooled apertures,
placed in front of the thin-disk.
Mode-locking is achieved by applying an external perturbation to the laser when it operates in
the CW regime. For this purpose, the output coupler is mounted on a translation stage. The
pulse formation process is then initiated, when the user releases the preloaded spring. The max-
imum power can be extracted with a
12%
output coupler. At the other end of the cavity, a SBR
is introduced to passively mode-lock the oscillator. The selected SBR is commercially available
(BATOP SAM-1040-1-500fs) with a saturation uence of
90 µ
J/cm
2
and an modulation depth
of
0.5%
. The non-saturable losses are quite high, with about
1%
. The relaxation time constant
is
500
fs. Experiments were also undertaken with SBRs from the same supplier with
0.4%
and
0.8%
modulation depth but lead to poorer results. In the rst case, the pulse duration was
not as short and in the second case, the laser experienced some instabilities leading to some
damage of the SBR.
Figure 4-7 Dispersion (left) and reectivity of the highly dispersive mirror HD51.
These parameters are surely not ideal for an oscillator delivering pulses in the microjoule level.
Indeed, ideally the SBR should exhibit a low saturation uence to allow for a lower threshold
against Q-swichted mode-locking, see equation
(2-22)
. In addition, the non-saturable losses
should be small to limit the heat deposition. In the oscillator, the intracavity power reaches
approximately
500
W, the SBR absorbs then approximately 5 W of average power. In order to
minimise thermal eects, the SBR is xed to a water-cooled mount.
For this thin-disk oscillator, new dispersive mirrors were produced with a negative group delay
dispersion of
−4500
fs
2
and a reectivity
>99.95%
. The characteristics of these mirrors are
plotted in gure 4-7. Using such mirrors, only few bounces are necessary to compensate for the
58
intracavity nonlinearity.
The cooling of the laser is managed by three independent circuits to isolate the most critical
elements. Fluctuations of the ow rate should be as low as possible on the thin-disk, as they
could generate mode-locking instabilities due to mechanical vibrations. The thin-disk is cooled
down to 17
◦
C by a water-to-air chiller with a temperature precision of
0.1◦
and a ow rate of
0.7
l/min. The parabolic mirror, SBR and beam blockers are also cooled using a water-to-water
chiller. Though this water undergoes some seasonal temperature variations, it did not aect the
laser performances. The laser diodes are temperature-stabilised by an automatic adjustment
of the input water ow passing through the heat exchanger of their cooling unit.
4.4.4 Pulse characterisation
With an incident power of
310
W, the laser delivers
70
W of mode-locked average power resulting
in an optical-to-optical eciency of
22.6%
. Switching from CW to mode-locked operation, an
increase of the average output power in the range of
10−20%
is observed. The slope eciencies
for the two regimes are plotted in gure 4-8. With the selected SBR and the cavity parameters,
self-starting pulsed operation was not possible. Mode-locking was nevertheless easily initiated
through the moving-mirror technique, described in the previous section.
Figure 4-8 Eciency of the thin-disk oscillator in CW (circles) and in ML regimes (squares).
At 11.5-MHz repetition rate, this corresponds to a pulse energy of 6
µ
J. Single-pulse operation
in air was conrmed by the high second-harmonic conversion eciency reported in section 4.5.
In previous works [112], the formation of multiple pulses simultaneously oscillating in the cavity
has been the bottle-neck for scaling up the energy.
Beyond
310
W of pump power, the output power saturates at
70
W. A degradation of the
mode quality is also visible, while pulsed operation becomes unstable. The cavity simulations
did not suggest any dramatic modication of the laser mode at this pumping level. However,
59
these simulations only included a thermally-induced lens inside the gain medium. Additional
thermal eects may arise in other cavity optical components, which eventually restrict the laser
operation to lower pump powers. These eects are most likely to occur inside the saturable
absorber, where there is a substantial heating due to the non-saturable losses.
Increasing the mode size on the SBR would help reducing those thermal eects. Unfortunately,
inspection of these commercial SBR under a microscope reveals some surface defects (scratches,
impurities, voids), which limit the usability of large spot diameters. Furthermore an increase of
the mode size would be accompanied by a shortening of the resonator stability range. Ideally, an
investigation using interferometric measurements under lasing operation should be undertaken
to characterise precisely the thermal behaviour of the SBR. This would help designing resonators
with larger invariance against thermal lensing. To allow further scaling of the pulse energy,
implementation of new SBRs with lower non-saturable losses seems nevertheless unavoidable.
Figure 4-9 SBR damage.
Typically, the laser is operated with 62W of average output power for a total pump power of
260
W. If not mentioned otherwise, the following results were obtained at this power level.
Under this condition, the laser performances were maintained for more than six months, at an
average of
8
hours of continuous operation per day, without any noticeable degradation. Despite
the large intracavity pulse energy, with over 50
µ
J, the dierent components of the laser did not
damage under regular use. Damages only occurred when the laser was submitted to extremely
high mechanical perturbations, typically after accidentally knocking the optical table with heavy
components. The consecutive vibrations cause brief but dramatical Q-switching instabilities.
Figure 4-9 shows such damage spots. For a calculated beam radius of 640
µ
m on the SBR, the
peak intensity reaches almost
9
GW/cm
2
assuming a Gaussian beam prole. The saturation
parameter, dened as the ratio between the pulse uence and the absorber uence, is equal
to 45 and thus relatively high. Under such strong saturation of the absorber, the pulse may
break into closely spaced multiple pulses due to the reduced loss penalty for the following pulses
[108]. However, this eect was never observed at this saturation level. Other works with similar
parameters have also conrmed single pulse operation in this regime [109].
60
The spatial quality of the laser beam is characterised by measuring its M
2
parameter [56]. A
fraction of the beam was focused using a 500-mm lens onto a CCD camera (WincamD) which
recorded the beam waist across the focus. The laser beam prole and the M
2
measurement are
presented in gure 4-10. By a proper optimisation of the pump and laser mode overlap inside
the disk, the oscillator cavity supports only the TEM
00
fundamental laser mode. This results
in a near diraction-limited beam with a measured M
2
below
1.1
.
Figure 4-10 M
2
measurement and beam prole (inset) at 62 W.
Stable single-pulse operation is obtained with approximately
−18000
fs
2
of negative group delay
dispersion per cavity round-trip, using only two dispersive mirrors. In contrast to reference
[109], the laser can simply be operated in air. The pulse duration was estimated from the
measurement of their intensity autocorrelation using the autocorrelator Pulsecheck from APE
GmbH. The pulses are nearly transform-limited with a FWHM pulse duration of
1.1
ps assuming
a Gaussian shape, and a spectral bandwidth of
1.4
nm centred at
1030
nm. The pulse duration
did not depend on the position of the Brewster plate inside the cavity. This conrms that the
most important source of self-phase modulation originates from the ambient air. The thin-disk
causes indeed only moderate nonlinearities, as calculated earlier in table 4-1.
Figure 4-11 (a) Pulse durations at dierent output energies. (b) Optical spectrum at 62 W.
The evolution of the pulse duration at higher energy is depicted in gure 6-6a for a xed
61
amount of intracavity dispersion. From this gure, it is apparent that the pulse duration is
inversely proportional to the pulse energy, which is typical of soliton mode-locked oscillators.
Shorter pulse duration at the highest pulse energy should be possible by decreasing slightly
the intracavity dispersion. In this laser, the pulse energy from the oscillator is not limited by
the onset of double-pulsing but by the degradation of the mode quality at higher pump power.
This suggests that the dispersion is not yet optimised at an output pulse energy of 6
µ
J.
Figure 4-12 Gauss (left) and Sech
2
(right) ts of the oscillator pulses.
The fundamental soliton solution to the nonlinear Schrödinger equation is a pulse with a squared
hyperbolic secant (Sech
2
) temporal shape [38]. Figure 4-12 compares the Sech
2
and Gaussian
ts of the pulse autocorrelation trace. From these pictures, it is dicult to determine the closest
t and thus the actual shape of the pulse. The ambiguity of the pulse denition is translated
into an uncertainty of the pulse duration. This divergence from the theoretical shape is due to
the simplication of the model, which does not take into account higher-order dispersion terms
nor include pulses shaping eects from the SBR.
Multiple pulsing was observed when the introduced negative dispersion was reduced and/or
when the intracavity pulse energy was increased by lowering the outcoupling ratio. A decrease of
the conversion eciency in the second-harmonic generation can reveal the presence of secondary
pulses (gure 4-13), as it indicates a drop of the peak intensity on the doubling crystal. A high
dynamic range autocorrelator can also be used to detect secondary pulses.
The measurement of the power spectrum of the light intensity can be used to characterise pulse
uctuations [113]. Such power spectra are obtained from the processing of a photodiode signal
by a radio-frequency (RF) spectrum analyser. The determination of the actual laser noise from
the power spectrum is a complicated matter, therefore this measurement was only a qualitative
indication of the laser noise levels. The output pulses are recorded using a relatively slow
photodiode (10 ns rise time, Thorlabs DET10C) and a 50-GHz analyser (Agilent E4447A).
This combination is not very fortunate as it is limited by the bandwidth of the photodiode.
62
Figure 4-13 Conversion eciency at dierent dispersion levels in a type-I, with
θ= 22.8◦
and
φ=π
2
. The outcoupling ratio was reduced to
6%
. The focusing parameters
were not optimised for highest conversion eciency.
Figure 4-14 RF spectrum at 6
µ
J (left) and RF-spectra for dierent ow rates (right).
Figure 4-15 (a) Yb:YAG pulse train at 62 W. (b) Frequency-doubled pulse train at 25 W.
63
The RF-spectrum indicates a suppression of the side-bands above
60
dB around the fundamental
harmonic of the laser repetition rate, as shown in gure 4-14. The spectrum was recorded with a
resolution bandwidth of 2.7 kHz and a 300-kHz span. The level of these side-bands are correlated
with the cooling ow rate behind the thin-disk. Because of its small thickness, mechanical
vibrations from the turbulent water are easily transferred to the disk. These vibrations disturb
the mode-locking process leading to an intensication of the noise, as seen from the deterioration
of the laser RF-spectrum at higher ow rates. To increase the thermal stability of the laser
system, the original water-cooled chiller was replaced by a smaller temperature-stabilised air-
cooled chiller. This chiller delivers a maximum ow rate of
0.7
l/min. Despite the lower cooling
capacity, the oscillator delivered exactly the same lasing performances.
The pulse to pulse stability is measured by recording the intensity uctuations of the pulses
with a photodiode. The pulse train, plotted in gure 4-15a, exhibits a RMS intensity uctuation
of
2.2%
. This value is relatively high for a mode-locked oscillator since stability below
0.2%
has been reported with Ti:Sapphire oscillators [114]. Yet, such results were only demonstrated
with inherently stable low-energy Kerr-lens mode-locked oscillators delivering a maximum pulse
energy of a few-nJ.
4.5 Second-harmonic generation
With
6µ
J, the pulse energy of the Yb:YAG thin-disk oscillator is suciently high to pump
a parametric amplier stage. Since the photon energy of the Ti:Sapphire pulses (
∝1
λ
Tisa
) lies
above that of the Yb:YAG infrared pulses, the thin-disk output needs to be rst frequency-
doubled to amplify the near-infrared seed. The experimental set-up of the second-harmonic
generation stage is shown in gure 4-16.
Figure 4-16 Experimental set-up for frequency doubling. OC: output coupler, TFP: thin-lm-
polariser,
λ
/2: half wave plate, HR: high reector, DM: dichroic mirror.
Lithium Triborate LiB
3
O
5
(LBO) is commonly used for high-power nonlinear applications.
Indeed, it combined a very high damage threshold (
>10
GW/cm
2
for ns pulses) with good
opto-mechanical properties. In addition, it can be produced in large dimensions with high
optical quality. Finally, its large nonlinear coecient (d
32 = 1.17
pm/V) leads to a high
eective nonlinear coecient for type-I second-harmonic generation (SHG) driven at 1 micron
in the XY-plane, making it particularly attractive for high-power SHG from Yb-based lasers.
64
Since the conversion eciency scales with the intensity and the length of the nonlinear crystal,
it is in general possible to compensate for the lower peak intensity by using longer crystals.
However, this only holds for signal with limited optical bandwidth, as broader spectra rise
phase-matching issues. Owing to the high beam quality of the infrared oscillator and its nar-
row bandwidth, one can take advantage of longer crystals to increase the conversion eciency
without the risk of optical damage at high intensity. The SHG stage consists of a
4
-mm
critically-phase-matched type-I LBO crystal. The Yb:YAG pulses are gently focused to an
approximately 200-
µ
m spot for limited divergence inside the crystal. With our focusing param-
eters, the Rayleigh range extends over
12
cm and is then much larger than the crystal length
allowing good conversion eciency and little beam distortions.
Due to beam delivery losses from imperfect coatings of steering mirrors, polarisers, half wave-
plate and lenses (not all represented in gure 4-16), only 54 W of power are left in front of the
doubling crystal. Yet, the SHG stage generates up to
43.5
W of
515
-nm radiation with only
10.1
W of remaining fundamental power. These powers were measured after a dichroic mirror,
which reects the green and transmits the infrared light. Since the two radiations have opposite
polarisations (horizontal for the fundamental, and vertical for the second-harmonic), a Glan-
Thompson polariser was placed after the dichroic mirror to select the horizontal polarisation
with an extinction ratio better than
1/106
. The residual 1030-nm radiation is then transmitted
through the polariser. The leakage corresponds to less that
0.2%
of the second harmonic
signal, which conrms that the power measured after the dichroic mirror is essentially free of
the fundamental radiation.
With
81%
, the eciency is remarkably high, while the mode quality of the second-harmonic
signal remains excellent (gure 4-17). To our knowledge, this is the highest conversion eciency
obtained in a LBO crystal. Numerical simulations have shown that conversion eciencies of
84%
were possible with M
2
value below 1.1 [115]. Due to the strong saturation in the frequency
conversion process, the pulse-to-pulse energy uctuations in the green are of
2.2%
RMS (gure
4-15), similarly to that of the fundamental.
4.6 Further scaling
Nonlinear phenomena arise from the interaction of highly intense coherent light with matter.
Since for a Gaussian beam, the peak intensity
Ip
of a pulse is approximately equal to:
Ip≈2Ep
πw2
0·τp
,
(4-1)
increasing the peak intensity is usually realised by using a higher pulse energy, a shorter pulse
duration or a tighter focus. Here, only the possibilities of decreasing the pulse duration and
scaling up the pulse energy for high-average power thin-disk oscillators will be discussed.
65
Figure 4-17 Eciency of the second harmonic generation. Inset: beam prole at the highest
eciency.
4.6.1 Shorter pulse
Despite its large emission bandwidth of Yb:YAG (
∼6
nm), mode-locked operation at higher
pulse energies leads to pulse durations closer to the picosecond than a few hundreds of fem-
toseconds due to the strong gain-ltering eects at higher saturated gain levels [116]. Selecting
a host material with a broader bandwidth would allow for the generation of shorter pulses.
Glasses exhibit a much broader emission spectrum than crystals owing to the broadening of
the ion emission lines in an amorphous material. Nevertheless, they suer from poor thermo-
mechanical and thermo-optical properties, which limit their use in high-power systems.
As prospective material, the sesquioxides promise to be superior to the YAG counterpart be-
cause of the broader emission spectrum and excellent thermal properties. In particular lutetia
(Lu
2
O
3
) stands out by its very high thermal conductivity of
11.0
W/m/K, which is almost
not aected by the ytterbium doping [117]. This originates from the very similar masses and
bonding forces between ytterbium and lutetium. The ytterbium-doping causes only a small
disturbance to the crystal lattice and aects the phonon scattering only slightly. Consequently,
the thermal conductivity of Yb-doped lutetia is nearly twice as high than that of Yb-doped
YAG. One limitation to the development of lutetia-based lasers is its crystal growth, which re-
quires high melting temperatures (>2400
◦
C). Fabrication of Yb:Lu
2
O
3
ceramics could perhaps
elude this problem in the future [120]. Recently, pulse duration of
330
fs at
∼40
W power
were obtained in a passively mode-locked Yb:Lu
2
O
3
thin-disk oscillator [118]. Further scaling
66
should be possible, since the output power was only limited by the available pump power in
this work.
Another approach is to design host materials consisting of mixed crystals. Through the in-
homogeneous line broadening inherent to disordered lattice structure, the gain bandwidth is
enlarged. Such structures are presented as hybrids between amorphous material and crys-
tals. They indeed exhibit intermediate behaviours of the two: better thermal properties and
larger emission spectrum. A recently developed material, Yb:LuScO
3
combines remarkably the
spectral features of two sesquioxides, Yb:Lu
2
O
3
and Yb:Sc
2
O
3
. The bandwidth, centred at
1039 nm, stretches over 20 nm. The thermal conductivity of 3.5 W/m/K remains suciently
high for high-power operation. Used in a passively mode-locked thin-disk oscillator, this laser
material produced pulses as short as 227 fs with 7.2 W of average power [119]. Yet, the dif-
culty to control the growth of these disordered crystals is still a severe limitation to their
commercialisation.
In a similar concept, the generation of shorter pulses can be obtained from multi-gain-media
oscillators rather than disordered crystals. In this case, the gain medium consists of two (or
more) materials with slightly shifted peak emission. As compared to the disordered crystal
approach, these lasers rely on single crystals with better opto-mechanical properties. Toku-
rakawa
et al.
built a mode-locked oscillator based on two ceramic pieces of Yb:Lu
2
O
3
and
Yb:Sc
2
O
3
contacted to each other. The laser delivered 53 fs with 1W of output power without
extra cooling [122]. Energy scaling would in that case require the development of improved
contacting technique to permit higher pumping intensities. Another option consists in using
two separate laser heads with dierent gain media in a cavity. This will however add enormous
costs to the laser system. In addition, the management of two thermal lenses is expected to
become rather challenging at higher pumping levels.
In 2003, Matsubara
et al.
studied the possibility of scaling the output power of a mode-locked
Yb:YAG rod laser and predicted an average output power of 60 W with pulse duration of
approximately 200 fs [123]. Since then, experimental work could only be demonstrated at
much lower power level in the range of few hundreds of mW [99].
A major breakthrough in the development of high-energy oscillators was achieved in the net
positive dispersion regime [124], where the pulse energy can be increased with even broader
spectral bandwidth than in the solitary regime. While soliton mode-locking leads to transform-
limited pulses, oscillators operating in the positive dispersion generate chirped pulses. As a
result, the peak intensity is reduced, and thereby the nonlinearities, allowing for higher pulse
energies. The positively chirped pulses are typically externally recompressed by means of a
prism compressor and dispersive mirrors.
Simulations showed that for our oscillators, the absolute value of dispersion required for high-
energy pulse stabilisation is substantially lower in the positive dispersion regime (
+900
fs
2
)
than that in the negative regime (
−18000
fs
2
) [125]. In this regime, the bandwidth is estimated
67
to be approximately 3.5 nm, which would correspond to a pulse duration of 300 fs. Purging the
cavity with helium or even vacuumisation could be then avoided. Nevertheless, for substantial
energy growth, operation under vacuum of the oscillator would be highly benecial.
4.6.2 Higher energy
The most straight-forward way to obtain higher pulse energy is to increase the average output
power, while keeping the conditions for stable soliton pulse generation fullled (equation
(2-22)
and
(2-23)
). Resonators with multiple passes through the gain medium enable the use of higher
outcoupling ratios, while reducing the intracavity power level. Stability issues may nevertheless
arise from the complexity of the laser system. Without dramatically reducing the stability of
our laser, an additional bounce or two on the disk should permit to reach pulse energies above
10
µ
J with an appropriate cavity design.
An alternative approach to shift up the pulse energy frontier of mode-locked oscillators is based
on a decrease of the repetition rate [126]. Extending the cavity length without aecting the
transverse beam prole on the cavity critical elements can be accomplish by means of a Herriott-
type multi-pass cavity [127, 128]. This design leads to a longer resonator with comparable
average power to the original laser, while the pulse energy is increased by the ratio of the cavity
lengths.
In low repetition rate thin-disk oscillators, the main source of nonlinearities originates from
the air. Helium-ooded cavities can be used to overcome this problem but is accompanied
with higher operation costs [109]. In addition, our experiments showed that the constant ow
of helium in the cavity generates some lasing instabilities due to gas turbulence which were
dicult to suppress. Equally-stable operation of the laser would require an optimised diusion
of the gas. Operation in low-vacuum seems thus more advantageous. Indeed, the oscillator
cavity can be made very compact to t in a simple vacuum chamber which would necessitate
only a small-dimensioned pump.
Finally, better understanding of the thermal eects inside the SBR is essential for designing
of stable resonators at higher intracavity powers. With this actual cavity design, the main
limitation to higher output energy was the beam degradation above 310 W of pump power.
Exploiting the full pump power of 500 W should allow to increase the pulse energy accordingly.
68
5 Pump-seed synchronisation for MHz parametric
amplier
5.1 Introduction
The use of sub-picosecond pulse duration in optical parametric ampliers increases dramatically
the constraints on the synchronisation, as accurate pump-seed timing is essential for ecient
and stable amplication. Like any three-wave mixing process, the exchange of energy between
the pump and the seed can only occur when the two pulses temporally - and spatially - overlap,
since the energy is not stored inside the nonlinear crystal. Large timing jitter will severely
degrade the performances of the amplier by causing uctuations of the amplied pulse energy
and of the amplied spectrum. These instabilities could result in a partial incompressibility
of the amplied pulses. In most systems, a timing jitter of approximately
10%
of the pump
pulse duration is desirable to maintain stable operation of the parametric amplication process.
Besides its locking precision, the requirements for the synchronisation scheme are its long term
stability and simplicity of use.
In chapter 3, an all-optical synchronisation scheme was demonstrated at kHz repetition rate
using frequency-shifted Ti:Sapphire pulses to seed a Nd:YAG regenerative amplier. This laser
served then as a pump source for the amplication of the Ti:Sapphire seed. Recently this
technique was successfully implemented to a 640-fs bre-based amplier pump source in a 2-
MHz parametric amplier producing 500-nJ pulses with 20-fs pulse duration [34]. The pump
pulses were derived from a Ti:Sapphire seed laser after soliton generation in a photonic crystal
bre and amplication to 15.5
µ
J in a three-stage bre-amplier.
This bre approach is quite attractive for high-repetition-rate synchronised pump sources, how-
ever it requires the implementation of a stretcher-compressor in the amplier chain to reduce
the eects of self-phase-modulation accumulated along the bre. Even with a large stretching
ratio and a rigorous recompression, pulse distortions are not fully avoidable. At high-power
level, the pump pulses commonly exhibit a pedestal and/or additional side pulses causing a
degradation of the amplier performances. For our MHz amplier system, one possible syn-
chronisation solution is to employ self-stabilisation of two mode-locked oscillators lasing at the
seed and pump wavelengths via a nonlinear optical (Kerr-lens) mechanism [26]. While solv-
ing the problem of passive synchronisation of two-colour sources, this method necessitates a
particularly complex and critical alignment of the two laser beams inside the Kerr medium.
In addition, cavity-length uctuations originated from environmental disturbances limit such
locking scheme to shorter time scales, typically in the range of a few minutes.
Another option is to employ an active synchronisation scheme via servo-loops. There are two
possibilities to determine the timing error between two pulses. One relies on an electronic
phase measurement by comparing the repetition rates of the two laser sources, while the other
69
method uses the optical nonlinear interaction of the two pulses to measure directly their timing
oset. In this chapter, a locking scheme combining an electronic and an optical control loop
is demonstrated. This synchronisation unies the performances of both locking methods and
results in a timing jitter of
∼100
fs.
5.2 Active synchronisation scheme
5.2.1 Electronic control loop: phase-locked loop
A phase-locked loop (PLL) is a regulator of the phase (thus of the frequency) of a signal
by comparing its value to that of a reference signal. Figure 5-1 shows the function principle
of a conventional PLL, which contains three basics elements: a phase detector, a loop lter
and a voltage controlled oscillator (VCO). A VCO is an electronic oscillator, which oscillation
frequency can be tuned by an applied voltage. The phase detector compares the frequency of
the VCO with a reference source and generates an error signal. A low-pass loop lter is inserted
to damp brusque changes at the input of the oscillator and to stabilise the loop. The VCO
delivers then a signal with a corrected frequency of oscillation.
Figure 5-1 PLL block diagram.
In a similar way, PLL can be used to stabilise the repetition rate of a laser by controlling its
cavity length. This can be easily done by placing a mirror of the laser cavity on a piezoelectric
transducer (PZT). When the phase detector measures a mismatch with the repetition rate of
the reference source, the PZT is activated to readjust the cavity length. The reference can be
a microwave source or another laser pulse train. PLLs are relatively easy to implement and
allow for a wide locking range which only depends on the design of the feedback loop. Although
less than 1-ps timing jitter is achievable with electronic PLL [24], such active synchronisation
employs pricey GHz electronics and presents a long-term phase drift, which originates from
thermal drift and phase noise converted from amplitude noise [78].
5.2.2 Optical control loop: sum-frequency generation
Instead of mixing two electrical signals to produce an error signal, one can mix two optical
signals in a nonlinear crystal. Indeed, the relative timing delay between two pulses can be
70
obtained by measuring the result of their nonlinear interaction as it is conned in time and
space. Just like optical parametric amplication, sum-frequency generation is a three-wave-
mixing process requiring energy conservation and phase-matching condition. The timing delay
between the two pulses is translated into a change in the intensity of the SFG signal, as depicted
in gure 5-2. The resulting SFG signal can then be used as a feedback signal in a control loop
to stabilise the repetition rate of a slave laser to a reference laser via a PZT. This optical timing
detection is often referred as cross-correlation.
Figure 5-2 (a) Reference laser pulse (solid line) and slave pulse with no timing error (blue
shaded area), +600 fs delay (pink shaded area) and -900 fs delay (yellow shaded
area). (b) Correlation signals for the corresponding timing osets.
Based only on the intensity of the SFG signal around its peak value, one cannot identify
whether the slave pulse precedes or follows the reference pulse. Therefore, rather than setting
the reference point for the feedback loop at the maximum of the SFG intensity, one can set it
at half its peak value [129]. In this case, the intensity variations of the cross-correlation signal
have a linear relation to the relative timing error between the two pulses. Another option is to
use a balanced cross-correlator [130]. This optical scheme consists of two sum-frequency stages,
one of which containing an additional optical delay as depicted in gure 5-3. The intensity
of the signals generated in each stage depends on the relative timing delay between the two
pulses on the nonlinear crystal. By subtracting these two SFG signals, one can generate an
error signal for controlling the cavity length of the slave laser. The calculated error signals are
plotted in gure 5-4 for dierent timing osets.
The feedback loop requires a careful alignment of the balanced cross-correlator. The two sum-
frequency stages should indeed deliver identical cross-correlation traces in order to obtain a
symmetric error signal at the zero timing delay. The output of the balanced cross-correlator
is shown on gure 5-5 for dierent optical delays. In addition, the introduced optical delay
between the two stages should be optimised to allow for a compromise between sensitivity and
locking range, as shown in gure 5-5. With a shorter delay, the sensitivity increases, but the
locking range is clearly reduced. On the other hand, a too large delay can create a discontinuity
in the slope of the error signal.
71
Figure 5-3 Balanced cross-correlator.
Figure 5-4 Calculated error signals with (a) -50 fs, (b) 0 fs and (c) +50 fs timing oset. The
pulse durations are 150 fs for the slave and 1 ps for the master laser.
Figure 5-5 Calculated output of the balanced cross-correlator for dierent optical delays. The
pulse durations are 150 fs for the slave and 1 ps for the master laser.
72
In comparison to a synchronisation scheme using only a phase comparator, the main advantage
of an optical control loop is its accuracy with potentially timing jitter below a femtosecond [130].
Unfortunately, its locking range is limited by the laser pulse width making optical schemes only
suitable for laser systems with moderate timing jitter. Miura
et al.
increased the dynamic
range of their cross-correlator approach by stretching one pulse and detecting the bunch of
SFG pulses when the timing error exceeded both pulse durations [129]. The repetition rate
of this bunch was then related to the dierence of repetition rates between the two lasers. In
terms of complexity, this method is not easier to implement than an additional PLL.
5.2.3 Combined scheme
Designing a control loop based on electronic and an optical detection would allow to combine
the large dynamic range of PLLs with the timing precision of the cross-correlation. Ma
et al.
proposed a synchronisation scheme relying on multiple PLLs with dierent timing resolutions
and a SFG signal as an error signal in their last control loop [131]. With this combined approach,
they achieved sub-10 fs timing jitter. However, the system was fairly complex, involving high-
speed electronics, and its stability was only demonstrated over few minutes.
Obviously such timing precision would be superuous for a parametric amplier driven by
1-ps pump pulses. For our MHz system, a synchronisation scheme based on a PLL and a
balanced cross-correlator was developed. The locking is done in two steps. First, the electronic
loop approximately sets the repetition rate of the Ti:Sapphire oscillator. Second, the cross-
correlator generates an optical error signal which adds a small correction to the main electronic
loop. Thanks to the precision of the second feedback signal, this synchronisation scheme does
not require high-speed photodiodes. The synchronisation overview is shown in gure 5-6.
Figure 5-6 Block diagram of the synchronisation.
In this system, the Ti:Sapphire laser is assigned as the slave oscillator and operates at approxi-
mately 69 MHz, while the Yb:YAG laser was designed at 11.5 MHz. Thus only every 6
th
pulse
will be later amplied in the nonlinear crystal. In our rst experiments, the Ti:Sapphire oscilla-
73
tor was set as the reference source and similar timing precision could be obtained. However, the
Yb:YAG oscillator exhibited a stronger tendency towards Q-switching resulting in repetitive
damages of the SBR.
5.3 Experimental realisation
5.3.1 Electronic synchronisation set-up
Two standard 1-ns photodiodes (Thorlabs FDS010) are used to detect the oscillator pulse
trains and generate the signals at the input of the frequency mixer. The cavity length of the
Ti:Sapphire oscillator is rst roughly adjusted by tuning the position of one cavity mirror with
a picomotor so that the beat frequency between the two lasers is minimised. This error signal
is ltered and amplied before being processed by a proportional integrative regulator, which
controls the movement the PZT inside the Ti:Sapphire resonator. The chosen PZT (PiezoJena
P25/10) is able to compensate for drifts up to 50
µ
m with a ms-response time.
The electronic loop is operating at 414 MHz corresponding to the 6
th
harmonic of the Ti:Sapphire
laser repetition rate. The motivation to using higher harmonics of the repetition rate in PLLs
is to obtain an enhanced signal-to-noise ratio. Nevertheless, the possibility of locking onto a
spurious pulse increases as higher harmonics are being used, obliging the user to check for
the pulse temporal overlap at each new locking. The relative phase between the two oscillator
signals, hence the relative timing delay between the pulses on the sum-frequency stages, can
be tuned by adjusting the position of one of two photodiodes which is placed on a translation
stage.
When the gain factor of the proportional integrative regulator is set properly, the Ti:Sapphire
oscillator is locked to the Yb:YAG laser. At that point, optical sum-frequency generation
between the two lasers can already be observed but the timing jitter is too large for stable
operation. Both SFG signals icker in a few-second time scale making the optimisation of
the balanced cross-correlator troublesome. To overcome this problem, a ramp is added to the
electronic error signal which scans periodically the relative phase of the Ti:Sapphire signal. By
doing this, a periodic temporal overlap of the two pulses is created on the nonlinear crystal
leading to a time-averaged sum-frequency signal. These sum-frequency signals are less intense,
however they are more stable and still signicantly higher than the background noise. The
ramp signal is maintained during the whole alignment process of the balanced cross-correlator
and switched o prior to optical locking.
5.3.2 Optical synchronisation set-up
The balanced cross-correlator provides the feedback signal for the second optical loop. As shown
on gure 5-7, a fraction of the two laser beams is directed onto two identical sum-frequency
74
set-ups. Typically, less than 10 nJ pulses from the Yb:YAG laser and 100 fJ pulses from the
Ti:Sapphire oscillator are necessary for locking the two lasers. Each stage is composed of a
2-mm-thick BBO crystal critically phase-matched (
θ= 25.9◦
) for sum-frequency generation
between the 1030-nm and the 800-nm radiations. The sum-frequency signal is generated at
450 nm and thus lies in the blue. In one stage, an optical delay of 2 ps is introduced by 0.6 mm
of glass (Type B260). The beams are focused down on the nonlinear crystal to an 80-
µ
m-
diameter spot by a 150-mm lens. For careful adjustment of the spatial overlap, two cameras
are positioned at the front of the crystal. The optical set-up is depicted in gure 5-7.
Another fraction of the beams is split just before sum-frequency generation in order to control
the pulse arrival time on the crystal and allow for correction of the variable delay of the electronic
loop. When both pulses temporally and spatially overlap in the BBO crystals, two sum-
frequency pulses are generated. These signals are recorded by two slow photodiodes (Thorlabs
FDS100) and subtracted to produce the second feedback signal. An aperture was inserted in
front of each detector to block the unconverted 800-nm and 1030-nm radiations. In addition a
blue lter is used to further improve the signal-to-noise ratio.
By switching on the ramp signal in the electronic loop, the sum-frequency signals can be
observed on an oscilloscope and used to optimise the balanced cross-correlator. The intensities
of the SFG signals are then tuned to the same level by adjusting the optical set-up and varying
the gain level of each photodiode. Once activated, the optical loop adds a small correction to
the basic electronic loop leading to stable and intense sum-frequency generation.
Figure 5-7 Optical control loop. OC: output-coupler, BS: beam-splitter, PD: photodiode, PI
circuit: proportional integrative circuit.
5.4 Locking results
5.4.1 Cross-correlation measurement
The locking performances of this synchronisation scheme were rst investigated by recording
the cross-correlation trace between the Ti:Sapphire and the Yb:YAG pulses, as described in
section 2.3.3. Indeed, the timing jitter between the two lasers can be estimated from the width
75
of the cross-correlation trace and the pulse durations of the two lasers. For this purpose, a third
sum-frequency stage consisting of a 1-mm-thick BBO crystal was additionally set up as shown
in gure 5-6. A motorised translation stage was installed in the optical path of the Ti:Sapphire
beam to scan the relative delay between the two pulses.
Assuming that the temporal shape of both laser pulses and the probability distribution of the
timing jitter have a Gaussian distribution, the cross-correlation function is given by:
Ic(t) = exp −(4 ln 2) t2
τ2
c,
(5-1)
with
τc=qτ2
tisa
+τ2
YAG
+τ2
j,
(5-2)
where
τj
is the full width half maximum (FWHM) of the timing jitter and
τc
is the FWHM
of the cross-correlation function
Ic(t)
.
τ
tisa
and
τ
YAG
are the durations of the Ti:Sapphire and
Yb:YAG pulses, respectively. The RMS timing jitter
σj
is then equal to
σj=1
2√2 ln 2τj,
(5-3)
Figure 5-8 shows the improvement of the locking performance once the optical loop is activated.
With only the electronic loop, no stable sum-frequency generation is possible.
Figure 5-8 Cross-correlation trace with only the electronic loop (left) and after activating the
optical loop (right).
The duration of the Ti:Sapphire pulses on the sum-frequency stage is estimated by calculating
the total dispersion introduced by the dierent optical elements (cf annex A). For a 6-fs pulse
propagating through 5 mm of fused silica, 2 mm of BK7 and 3 m of air, the pulse are lengthened
to 150 fs on the nonlinear crystal. From the autocorrelation trace of the Yb:YAG laser in gure
5-9, the pulse duration is calculated to be 1.08 ps assuming a Gaussian shape. This result shows
good agreement with the cross-correlation measurement with a FWHM of 1.11 ps suggesting
a low timing jitter. From equation
(5-1)
and
(5-3)
, the FWHM timing jitter between the two
mode-locked oscillators can be estimated to be 210 fs, corresponding to a RMS value of 90 fs.
76
Figure 5-9 Cross-correlation (left) and intensity autocorrelation (right) trace of the Yb:YAG
pulse.
5.4.2 Frequency analysis of the timing jitter
For further characterisation, one can analyse the pulse-to-pulse uctuations of the sum-frequency
signal when the two interacting pulses are oset by approximately half the pump pulse width.
In this conguration, the timing jitter
∆t
is directly proportional to the measured intensity
uctuations
∆I
as illustrated in gure 5-10. The RMS timing jitter
σj
can then be simply
retrieved from the RMS intensity uctuations and the calibrated slope of the correlation peak.
In order to improve the locking performance, it can be useful to identify on which time scale
the timing jitter mostly occurs. This can be done by calculating the Allan variance [133] which
is dened by:
σj(τ) = v
u
u
t
1
2(m −1)
m−1
X
i=1
(yk+1 −yk)2,
(5-4)
where
τ
is the sample time,
yk
are the discrete averaged values of a signal over the sample
time
τ
and m the total number of recorded data points of the signal. By estimating the Allan
variance at dierent sample times, one can explore the characteristic time scales of the jitter.
σj(τ)
can be easily determined at dierent time scales from one sample of data by repeating
the following procedure:
1. Calculate
σj(τ)
,
2. Redene the variables:
yk
as
yk+ yk+1
2
and m as
m
2
,
3. Calculate
σj(2τ)
.
To suppress the discrete nature of the pulse train at 11.5MHz, the sum-frequency signal is
measured using a photomultiplier (Hamamatsu H7712-15) with a bandwidth below 500 kHz.
Figure 5-11 shows the recorded signal over 2 s. For a maximum intensity of the sum-frequency
signal at 2 units, and the FWHM of the cross-correlation peak at 1.11 ps, the conversion scale
of the slope can be evaluated at 0.55 ps/unit. From these record of data, the timing jitter is
quantied between 2
µ
s and 1 s; the results are shown in gure 5-12.
77
Figure 5-10 Schematic diagram of the timing jitter. Solid line, Yb:YAG pulse. Red and green
lled area: SFG signal between the Yb:YAG pulse and the Ti:Sapphire pulse.
Figure 5-11 Sum-frequency signals at the cross-correlation peak (a) and half its peak value (b).
Figure 5-12 Allan variance of the timing jitter
78
This measurement shows that the main contribution to the timing jitter lies around 100
µ
s.
As in most passively mode-locked laser systems, the main source of timing jitter has frequency
components around the relaxation oscillation frequency of the laser
f
RO
[134], given by
f
RO
=1
2πsl
τr
P
int
E
sat
−1
41
τg
+P
int
E
sat
,
(5-5)
where l are the total cavity losses,
τr
is the cavity round-trip time,
τg
is the laser material
upper state life time,
P
int
is the intracavity power, and
E
L,sat
is the saturation uence of the
laser material. For solid-state lasers,
τg>> τr
, the expression can be simplied to
f
RO
=1
2πrl
τr
P
int
E
sat
.
(5-6)
Parameters Ti:Sapphire oscillator Yb:YAG oscillator
l 10% 13%
τr
14.5 ns 87 ns
Pint
2.5W 500 W
Esat
0.3 J/cm
2
0.3 J/cm
2
f
RO
140 kHz 6.5 kHz
Table 5-1 Oscillator parameters.
From table 5-1, the relaxation oscillation frequencies of the Ti:Sapphire and Yb:YAG lasers are
estimated to be 140 kHz and 6.5 kHz, respectively. The second value is very close to the highest
component of the timing jitter located around 5 kHz. Most likely, the relaxation oscillations of
the Yb:YAG are the main source of jitter in our system. This coupling of intensity noise into
timing noise has been thoroughly investigated in the case of passively mode-locked lasers [132].
In the presence of a saturable absorber, the damping of the relaxation oscillations tend to be
reduced. This can lead to a timing noise originated from the intensity modulation of the pulse
train produced by the relaxation oscillations.
The synchronisation would certainly benet from an optimisation of the SBR parameters and
the cavity design to improve the stability performances of the oscillator. Another improvement
of the timing precision could be obtained by increasing the feedback bandwidth of our active
control loop to a few kHz. This would require using a faster PZT but also minimising the mass
of the mirror attached to it to obtain a faster response. The feedback loop used in this locking
scheme was originally designed for compensation of large timing drift rather than fast timing
drift. In this perspective, a PZT with a large scanning range (50
µ
m) was implemented in the
Ti:Sapphire oscillator.
With this combined electronic-optical locking scheme, a timing jitter of
∼
120 fs was demon-
strated for the synchronisation between a broadband seed oscillator and a high energy pump
79
oscillator. This residual jitter is still within approximately 10% of the pump pulse width.
Tight phase-locking can be maintained continuously for several hours without readjustment of
the locking parameters. These results allow for rst parametric amplication experiments of
the Ti:Sapphire pulses pumped by the frequency-doubled output of the Yb:YAG laser at MHz
repetition rate.
80
6 MHz optical parametric chirped pulse amplier
Current rapid advancement in the elds of extreme nonlinear optics relies on the availability
of high peak intensity few-cycle lasers. Optical parametric chirped pulse amplication oers
a promising route towards few-cycle high-intensity laser systems. However, optical parametric
ampliers are most commonly operated at sub-Hz to few kHz due to power scaling issues of
the pump sources at increasing repetition rates [28, 29, 135]. Only recently, the availability
of MHz-pump sources with energy beyond the microjoule level has made the development of
ultrafast ampliers possible [34, 136, 137]. Such repetition rates allow for the observation
and characterisation of ultrafast phenomena within a fraction of the previously necessary data
recording time simultaneously with improved signal-to-noise ratios. This would be particularly
benecial for the study of processes with low probability or low conversion eciency, for which
integration times over several hours are often necessary. In this regard, pushing ampliers
towards MHz repetition rate for the generation of carrier-envelope phase stabilised few-cycle
pulses could open novel elds of investigation.
6.1 Preliminary considerations
The realisation of a high-power few-cycle optical noncollinear optical parametric amplier re-
quires a careful optimisation of the nonlinear crystal, the beam geometry and the pump-seed
pulse duration. Especially the design of our amplier has to be adjusted to the large optical
bandwidth (400 nm) of the seed, the relatively low pump energy (
µ
J rather than mJ or J) and
short pump pulse duration (1 ps rather than tens of ps or ns).
6.1.1 Choice of a nonlinear crystal
First, the crystal should exhibit a large eective non-linear optical coecient to permit high
conversion eciencies. Due to the noncollinear geometry the pump and the seed pulse prop-
agate under dierent directions inside the crystal, which for small beam diameters leads to
a shortening of the interaction length. Therefore broadband phase-matching requires a small
noncollinear angle in order to minimise this spatial walk-o. Second, in high-power OPAs even
minor absorption of the pump, seed or idler become particularly problematic as it would cause
a substantial heating inside the crystal. In extreme case, this could lead to a thermal fracture
of the material. Consequently, the crystal should have a large transparency range covering the
spectral region of the interacting pulses. The parametric amplication of our 400-nm band-
width Ti:Sapphire seed is accompanied by the generation of an idler stretching from 1060 nm
to 3.6
µ
m, when pumped at 515 nm. Such broadband amplication necessitates therefore a
transparent medium between 515 nm and 3.6
µ
m. Finally, the crystal should be of high optical
quality with high damage threshold to allow high pumping intensities.
Over the past decades, beta barium borate (BBO), lithium triborate (LBO) and potassium
81
dideuterium phosphat (KD*P) have established themselves as materials of rst choice for the
amplication of ultrashort pulses. KD*P is a good candidate for high-power applications be-
cause of the availability of large-aperture crystals. However, its higher absorption losses towards
the infrared would hinder the amplication of the shorter wavelengths from our seed. Bismuth
triborate (BiBO) is a relatively new nonlinear material with unique optical properties, making
it an potential new competitor to BBO and LBO [138]. The major properties of the above
mentioned crystals are listed in table 6-1. BiBO is very attractive because of its high nonlinear
coecient and non-hygroscopic property in contrast to BBO and to some extent LBO. On the
other hand, the transparency range of BiBO is slighly too short for our Ti:Sapphire seed. LBO
oers a good compromise between LBO and BiBO with its broad phase-matching range and
highest damage threshold [139], which compensates for its lower nonlinear coecient.
Material KD*P BBO LBO BiBO
NLO coecient
0.23 2.02 0.85 2.97
Damage threshold(GW/cm
2
)
0.5 0.5 10 0.3
Peak intensity used (GW/cm
2
)
>60
[140]
>100
[34]
>40
[141]
Transparency range (nm) 180-2000 190-3500 160-3200 290-2500
Hygroscopicity high low very low none
Table 6-1 Comparison of nonlinear crystals. The damage threshold for KD*P, BBO and LBO
are given by the supplier Eksma for 10 ns pulses at 1064 nm. For BiBO, the value
is given by the company Castech for the same pulse parameters.
To select a nonlinear crystal, their phase-matching bandwidths are compared after optimisa-
tion of the phase-matching angle
θ
and
α
using the Sandia National Laboratories Nonlinear
Optics software [142]. We dene the phase-matching deviation as the dierence between the
perfect phase-matching angle at a given wavelength and the optimised angle for broadest phase-
matching around the centre wavelength. Figure 6-1 compares this deviation for LBO, BiBO
and BBO. From these simulations, it can be seen that BBO is better suited than LBO for
amplication of our seed pulses through its atter phase-matching curve in the blue. Because
of the larger spectral overlap between our Ti:Sapphire source and the phase-matching curve of
the BBO, BBO will be exclusively used in this near-infrared OPA system.
6.1.2 Parametric gain and bandwidth
Thin crystals are crucial for broadband parametric amplication because the group velocity
mismatch between the seed and idler waves leads to a narrowing of the amplication bandwidth,
which becomes stronger with increasing crystal lengths. On the other hand, thinner crystals
require higher pumping intensities to compensate for their lower gain, which is ultimately
limited by the damage threshold of the nonlinear material and the onset of incompressible
parametric superuorescence.
Figure 6-2 shows the parametric gain for dierent BBO crystal lengths. The gain is estimated
from equation
(2-9)
using the dispersive properties of BBO given in reference [143]. The pump
82
Figure 6-1 Phase-matching deviation and optical spectrum of the Ti:Sapphire seed source (dot-
ted line). The phase matching are all calculated for type-I frequency mixing, in the
XZ plane for LBO and YZ plane for BiBO.
Figure 6-2 (a) Calculated small signal gain for dierent BBO crystal lengths. The pump wave-
length is 515 nm,
α
and
θ
are set to 2.5
◦
and 22
◦
respectively. (b) Calculated
−10
-dB
bandwidth.
Figure 6-3 (a) Gain acceptance angle at 800 nm with 33-W incident pump power, 100-
µ
m beam
radius and
θ= 22◦
in a 4 mm BBO. (b) Type-I phase matching in NOPA.
83
power is kept constant to 33 W and the beam diameter is adjusted to keep the same maximum
parametric gain. From 5-mm to 1-mm crystals the bandwidth is remarkably extended, mostly
to the infrared, but the necessary intensity is dramatically increased (almost 20 times).
Tight focusing rises additional issues in a OPCPA system. For smaller beam diameters the
interaction length is shortened in a noncollinear geometry, due to the dierent propagation
directions between the pump, seed and idler. Furthermore the parametric gain becomes more
sensitive to the adjustment of the seed-pump beam overlap inside the crystal.
Another yet critical parameter is the beam divergence. Indeed, tighter focusing results in a
stronger angular spread of the wave-vectors, which can decrease the parametric gain and cause a
degradation of the amplied beam through spatial chirp. Thus broadband amplication requires
a careful optimisation of the crystal length and beam radius to maximise the eciency. This
is particularly important for our MHz repetition rate OPA, where the pump pulse energy is
only of a few microjoules. The acceptance angle for the seed can be evaluated by calculating
the parametric gain as a function of
α
. In gure 6-3, the dependence of the gain on
α
is plotted
for a beam waist of 100
µ
m. Based on these beam parameters, the Rayleigh range of the
Ti:Sapphire seed is close to 40 mm. Within a 4-mm crystal, the divergence is then kept very
small around the focus with an almost at wave-front, ensuring negligible eects on the gain
and beam prole. From these rst estimations, longer crystals (3 mm to 5 mm) oer a good
compromise between large gain at moderate intensities and amplication bandwidth.
In a noncollinear parametric amplier, two dierent beam geometries may be used as depicted
in gure 6-3b. The seed beam can either propagate between the direction of the optical axis and
the pump, or it can propagate at a larger angle than the pump with respect to the optical axis.
These geometries are referred as tangential phase-matching and Poynting vector walk-o com-
pensation, respectively. Earlier work showed that the Poynting vector walk-o compensation
conguration leads to a lower gain and a stronger second-harmonic generation [43]. Therefore,
the amplier will be preferably built in a tangential phase-matching geometry.
Figure 6-4 (a) Detuned gain spectrum with
α= 2.63◦
and
θ= 22.14◦
(red line) and optimised
spectrum for broadband gain. (b) Ti:Sapphire seed source used in our experiments
(green line) and an infrared-enhanced spectrum (shaded grey area).
84
From gure 6-2b, it can be seen that amplication of the shortest Ti:Sapphire wavelengths
(
<700
nm) is dicult to achieve from a single BBO crystal pumped at 515 nm. Since the
seed is typically stretched, one could adjust the delay between the pump and the seed in order
to overlap the shortest wavelengths with the central part of the pump. These wavelengths
would experience a larger pump intensity, and hence a larger gain. On the other hand, higher
sensitivity to the timing jitter is expected and some distortions of the amplied seed pulses
may occur. Another option is to use a second stage with dierent angles
α
and
θ
, so that the
amplication gain is enhanced for the blue region in one stage, as illustrated in gure 6-4a.
Rather than extending the parametric bandwidth to shorter wavelength, one can tune the
spectrum of the seed towards the infrared. This can be relatively easily done without modifying
the oscillator layout. Through adjustment of the stability range and the intracavity dispersion,
the longer spectral components of the Ti:Sapphire oscillator can be enhanced. In gure 6-4b,
the seed spectrum is extended almost 100 nm further in the infrared.
6.2 Experimental realisation
6.2.1 Ti:Sapphire seed
The seed laser consists of a Kerr-lens mode-locked Ti:Sapphire oscillator operating in the soliton
regime [59]. The necessary negative dispersion for stable operation is introduced by a set of
ultrabroadband low-loss chirped multilayer dielectric mirrors. Fine tuning of the intracavity
dispersion is achieved through a pair of wedges. The oscillator set-up is represented in gure 6-
5. The laser delivers about 280 mW of mode-locked power resulting in 4-nJ pulses at 69 MHz.
These pulses can be additionally phase-stabilised using the carrier-envelope oset beat signal
generated between self-phase modulation and dierence-frequency generation in a nonlinear
crystal [12].
Figure 6-5 Ti:Sapphire oscillator optical lay-out. TS: Ti:Sapphire crystal, CM: chirped mirror,
HR: high reector for 532 nm, OC: output coupler, CP: compensating plate, L:
focusing lens, PZT: piezoelectric transducer.
Typically, the oscillator is operated with a narrower spectrum (gure 6-6a). The corresponding
transform-limited pulses are calculated to be 5.6 fs. The measurement of the pulse interfer-
ometric autocorrelation indicates a recompression down to
∼7
fs (gure 6-6b). Under these
85
conditions the laser is less sensitive to thermal uctuations in the laboratory. In order to con-
trol the repetition rate of the laser, one of the intracavity mirror is mounted on a piezoelectric
transducer. The synchronisation scheme uses the combined electronic-optical loop described in
chapter 5.
Figure 6-6 Optical spectrum (a) and interferometric autocorrelation of the seed laser (b).
After propagation through the dierent optical elements, the seed pulses are substantially
lengthened before amplication. The total dispersion is estimated to be approximately
∼500
fs
2
from 6 m of air, 6 mm of fused silica (beam splitters and oscillator output coupler) and 3 mm
of BK7 (focusing lens). It follows a pulse duration of
∼220
fs on the OPA crystal.
6.2.2 Amplication results
The experimental set-up of the 11.5MHz is schematically presented in gure 6-7.
Figure 6-7 Schematic set-up of the OPCPA. PLL: Phase-lock-loop, BCC: Balanced cross-
correlator, SHG: Second-harmonic generation, SFG: Sum-frequency generation.
It consists of a single-stage NOPA, optimised according to the previous section. The seed power
at the front of the OPA crystal was measured to be only 100 mW due to beam delivery losses
from 20 reections on silver mirrors and two
10%
beam splitters. The parametric amplier
is driven by the frequency-doubled output of the Yb:YAG thin-disk oscillator. The pump is
86
focused with a 400-mm lens to a beam diameter of
∼200 µ
m, slightly larger than the seed.
The two focused beams are shown in gure 6-8. Pump and seed are crossed at an internal angle
α≈2.5◦
inside a 4-mm BBO crystal cut at
θ= 24◦
for type-I phase-matching. For these beam
diameters and crossing angle, the interaction length is longer than the crystal, ensuring good
conversion eciency and uniform amplication. In this conguration, the o-seed is horizontally
polarised, while the e-pump is vertically polarised and orthogonal to the crystal face. Under
these conditions, the optical plane, dened by the angles
θ
-
α
, is vertical.
The beam spatial overlap can be optimised using a camera, placed above the crystal. A sum-
frequency stage was built in front of the OPA to control the locking stability by monitoring the
intensity uctuations of the generated signal (see gure 6-7).
Figure 6-8 Seed beam (left) and pump beam (right) at focus.
The parametric amplier delivers up to 5.6 W of output power when the crystal is pumped with
34 W of average power. With our focusing parameters, this corresponds to a pump intensity of
about 18 GW/cm
2
. At this pumping level, no superuorescence ring could be observed. The
seed is amplied to approximately 490 nJ at 11.5 MHz, leading to a pump-to-signal conversion
eciency of
17%
. For an initial seed energy of 1.4 nJ, the amplication factor is 340. This is
relatively low, since single-pass gain up to six orders of magnitude are not uncommon in OPCPA
systems. The seeding level is indeed quite high for this OPA driven by a microjoule pump. The
amplied spectra at dierent pump intensities are plotted in gure 6-9. The dierences in the
amplied spectral proles essentially originate from intermediate readjustments of the OPA.
Despite the lower gain of the parametric amplier at shortest wavelength, the transformed-
limited pulses corresponding to these spectra are not signicantly longer than the original seed.
Their pulse widths range from 6 to 6.2 fs, while it is calculated to be 5.8 fs for the unamplied
seed. This originates from an enhancement of the infrared part, which is clearly visible using a
logarithmic scale in gure 6-9.
Using 1-ps pump pulses, the stretcher for the seed can consist of only a few centimetres of
bulk material. Two uncoated fused silica substrates are simply placed at the output of the
Ti:Sapphire oscillator to lengthen the seed pulses. The additional dispersion from 16 mm of
fused silica chirps the pulses to about 500 fs. After reoptimisation of the spatial and temporal
overlap, the seed average power increases to 8 W. This corresponds to a pulse energy of 700 nJ
87
Figure 6-9 Seed spectrum (grey shaded ared) and amplied spectra for 27 W (blue line), 32 W
(red line) and 34 W (green line) of pump power, on linear scale (left) and logarithmic
scale (right).
and a conversion eciency of
24.3%
. In this case, the amplied spectrum becomes narrower, as
shown on gure 6-10. Yet, the bandwidth still supports sub-7fs pulses assuming a at spectral
phase.
The superuorescence background could not be measured with the powermeter available to
us. The superuorescence ring was only visible using a CCD camera and removing the neutral
density lter in front of it. With an optical density of
4.3
, this means a superuorescence-to-
signal ratio in the range of
0.1%
.
Though the mode prole does not substantially degrade at higher pumping intensities, the
seed beam becomes elliptical after amplication. We pictured the beams with and without
amplication but under identical pumping conditions to maintain the same thermal stress on
the crystal. The two beams in the far eld are compared in gure 6-11. From this, it can be
seen that the beam becomes larger in the horizontal plane, while it is almost unchanged in the
other direction. In the presence of a Gaussian pump prole, the amplied pulse may experience
a certain narrowing since the edges of the beam will experience a lower gain. This could result
in a spatial widening of the seed observed in the far eld. However, this should aect both
directions. In the optical (vertical) plane, the spatial walk-o would on the contrary lead to a
spatial widening of the seed. The origins of this ellipticity are still not explained. Operating the
parametric amplier with an eciency of 15%, a pulse-to-pulse stability below
2%
is measured,
which is equivalent to the stabililty of the pump pulses. Figure 6-12 shows the amplied pulse
train.
At this level of amplied seed average power, multiple bulk damages were observed in the
crystal. Typically the crystal heated up and thermal fracture occurred. Despite the absence of
energy storage in the crystal inherent to the instantaneous parametric amplication process,
thermal eects are not completely absent. Even minor absorption losses will create a thermal
load inside the crystal, which can become critical for such a high-power system.
88
Figure 6-10 Amplied spectra for 220-fs (green line) and 500-fs seed (red line) for a pump
intensity of 18 GW/cm
2
.
Figure 6-11 Amplied (left) and non-amplied seed (right).
Figure 6-12 Pulse train with 5 W of amplied seed power.
89
One reason for this heating may be the relative increase of absorption losses above 2
µ
m in
BBO, where still a signicant part of the idler is generated. The transparency range of BBO is
plotted in gure 6-13. It should be additionally mentioned that the only crystals available at
that time were relatively old, with some evidence of previous bulk damages and coating defects.
These could be a further source of power dissipation. In high-power OPA systems, cooling of
the nonlinear crystal would be benecial to reduce thermal eects. Indeed, a temperature
increase of the crystal gives also rise to a modication of the refractive index, thereby altering
the phase-matching relation between the pump, seed and idler waves. Ultimately, this will cause
a decrease of the conversion eciency and a deterioration of the amplied seed characteristics.
Figure 6-13 BBO transparency curve.
6.3 Pulse compression
6.3.1 Compressor design
An all-chirped-mirror compressor was favoured in this system because of its compactness and
simplicity of alignment. Yet, designing and producing chirped mirrors with smooth disper-
sive curve over such large bandwidths is not a trivial issue. In our compressor, double-angle
multilayer mirrors are used to reduce the spectral oscillations [145]. The characteristics of the
complementary pair of mirrors are presented in gure 6-14. These ultra-broadband mirrors
were originally produced for pulse compression after nonlinear broadening in a gas-lled hollow
bre. This system required much less group delay dispersion compensation than in the case of
our OPCPA system. These mirrors support sub-4 fs pulse duration and were optimised for less
than 10 bounces. The average dispersion level is thus relatively low with only approximately
35 fs
2
per bounce at 800 nm.
In our rst experiments, the seed beam was shaped using spherical and cylindrical lenses before
90
Figure 6-14 (a) Dispersive characteristics of the double-angle mirrors PC34 under 5
◦
(red line)
and 20
◦
(green line) incident angle after one bounce. The black line is the combined
dispersion. (b) Residual oscillations for a double-angle mirror pair. For better
readability, the averaged dispersion is also plotted (blue line).
and after amplication as shown in gure 6-15. These transmissive optics introduced additional
chromatic dispersion after the OPA, which needed to be compensated. As a result, pulse
compression required over 30 bounces on the chirped mirrors. Furthermore, a deterioration
of the pulse temporal characteristics was observed with apparent side-wings due to chromatic
aberrations. Figure 6-16 shows the improvement of the autocorrelation traces when reective
optics were used instead of lenses. In these measurements, the amplier was not pumped in
order to discard possible pulse distortions from thermal aberrations inside the crystal. The
nal NOPA set-up using a 3 mm BBO and curved mirrors is represented in gure 6-17.
Due the limited choice of focusing optics, the lower gain of the 3-mm BBO crystal could not
be compensated by reducing the pump diameter for increased pumping intensity. The pump
and seed are focused using a lens and a mirror with both 500 mm of focal length. In this
set-up, the pump intensity is consequently reduced to 12 GW/cm
2
. At this pumping level, the
seed pulses are only amplied to 2.8 W, resulting in a pulse energy of 250 nJ. The compressor
consists of six 1-inch-diameter chirped mirrors with three bounces on each, compensating for
approximately -630 fs
2
of GDD at 800 nm.
Figure 6-15 Schematic set-up of the NOPA with lenses and chirped mirror compressor. SL1
and SL2: spherical lenses, CL1 and CL2: cylindrical lenses, CM: chirped mirror,
AC: autocorrelator.
91
Figure 6-16 Interferometric autocorrelations of the non-amplied seed.
(a) With SL1, SL2, CL1, CL2 and 32 bounces.
(b) With SL1, SL2 and 24 bounces.
(c) With SL1, SL2 replaced by a spherical mirror and 20 bounces.
(d) With SL1 and SL2 replaced by spherical mirrors and 18 bounces
SL1, SL2, CL1, CL2 are the lenses represented in gure 6-15.
92
The calculated residual GDD after 18 bounces is given in gure 6-18a, assuming 6 mm of fused
silica, 3 mm of BBO and a total path in the air of 8 m. From gure 6-18b, it is apparent
that there will be uncompensated third-order dispersion. This will be conrmed by the results
of the pulse characterisation presented in the next section. This higher-order dispersion can
be in principal minimised by playing between dierent combinations of materials of dierent
length and dispersive characteristics, while adjusting the number of bounces on the compressor.
A more elegant but challenging approach consists in measuring this residual dispersion and
producing mirrors of exactly the opposite value.
Despite the high number of reections on the mirrors, the compressor is still relatively ecient
with a throughput of approximately 80%. From 18 bounces on the dispersive mirrors and six
on the silver mirrors (reectivity of 98%), the losses of the dispersive mirrors can be estimated
to be 0.5% per bounce.
Figure 6-17 Schematic set-up of the NOPA with reective optics and chirped mirror compres-
sor. M1, M2: ROC
−1000
mm, Ag: at silver mirror, CM: chirped mirror.
Figure 6-18 (a) Calculated residual GDD (black line) and its averaged value (blue line) after
compression. (b) Calculated residual average GDD (note the change of scale). The
mirrors do not compensate for third-order dispersion.
93
6.3.2 FROG measurement
Due to some remaining laser instabilities, it was not possible to measure a clear interferometric
autocorrelation trace of the amplied pulses. Since this measurement is based on a multi-shot
acquisition, high pulse stability is a prerequisite to resolve the interference fringes. Autocor-
relation techniques can give some qualitative information about the phase, for a quantitative
measurement of the phase other characterisation techniques are usually used such as SPIDER
or FROG (see section 2.3.3). Grenouille is a powerful tool for the single-shot measurement of
low-energy pulses. Indeed, this concept uses a thicker nonlinear crystal which allows for the
generation of an intense second-harmonic signal. Unfortunately, our commercial Grenouille is
not able to handle the average power broadband pulses. The residual fundamental light after
frequency doubling is not attenuated suciently, so that the second-harmonic signal is not
distinguishable from the background noise of the fundamental light.
Pulse characterisation was thus performed with a home-made second-harmonic generation
FROG. The set-up uses a 10-
µ
m-thick BBO crystal cut at
θ= 29◦
for type-I phase-matched
SHG. The second-harmonic signals are recorded for dierent delays by a UV-spectrometer.
Despite an acquisition time of a few minutes, a coherent FROG trace could be measured, as
shown in gure 6-19.
Figure 6-19 Measured (left) and retrieved FROG trace (right).
Figure 6-20a presents the retrieved temporal prole of the amplied pulses. The duration of
the main pulse is
9.8
fs, while the transform-limited pulse is calculated to be
6.8
fs. High-order
dispersion terms from the dierent optical elements could not be compensated over the entire
spectral range in this chirped mirror compressor (gure 6-20b). The uncompensated quadratic
chirp, especially in the blue, is clearly visible in gure 6-19. Such chirp leads to the formation
of satellite pulses, which is conrmed by the pulse retrieval shown in gure 6-20a [146].
6.4 Summary of results
A broadband near-infrared high-power OPCPA system was demonstrated based on two pas-
sively mode-locked pump and seed lasers. The amplier is seeded with 1.5-nJ pulses from a
94
Figure 6-20 (a) FROG retrieval in the time domain and transformed-limited pulse (inset).
(b) FROG retrieval in the spectral domain.
Ti:Sapphire oscillator, while pumped with 2.9-
µ
J pulses from the frequency-doubled output of
an Yb:YAG thin-disk oscillator The two independent lasers are actively synchronised using a
combined electronic and optical control loop. In this preliminary work, up to 700 nJ pulses
are generated from a single-stage parametric amplier. At 11.5 MHz, this corresponds to an
average power of 8 W. The calculated transformed-limited pulses have a duration of 7 fs. De-
spite the relatively low pump pulse energy, a pump-to-signal conversion eciency as high as
24% is obtained when the seed pulses are stretched to about half the pump pulse width. First
compression experiments were undertaken at a lower pulse energy of 250 nJ and resulted in
9.8 fs pulses. The deviation from the transformed-limited pulse duration of approximately 7 fs
originates from essentially uncompensated quadratic chirp.
The recent multiplication of parametric ampliers operating between 100 kHz and few MHz
shows the need for high-peak-power pulses at higher repetition rates. Some of these results
are summarised in table 6-2. Finer compression and increased compressor output should be
possible through new tailored chirped mirrors with higher average GDD values and higher-order
dispersion compensation. Further increase of the amplied seed energy could be easily obtained
by reducing the beam delivery losses of the pump. Overall, 1-
µ
J pulses with 7-fs duration seem
to be in reach resulting in unprecedented peak powers
>100
GW/cm
2
at MHz repetition rates.
Reference
λ
E
p
τ
p
Rep. Rate
[147] 800 nm 16
µ
J 51 fs 80 kHz
[148] 800 nm 37
µ
J 52 fs 97 kHz
[149] 3.5
µ
m 1
µ
J 92 fs 100 kHz
[150] 3.2
µ
m 1.2
µ
J 96 fs 100 kHz
[151] 620 nm 140 nJ 20 fs 500 kHz
[30] 800 nm 30 nJ 16 fs 1 MHz
[34] 800 nm 500 nJ 16 fs 2 MHz
This work 800 nm 200 nJ 10 fs 11.5 MHz
Table 6-2 Comparison bewteen high-repetition-rate OPCPA systems
95
6.5 Applications
Numerous application in physics, chemistry, biology or medicine require high-peak-power ul-
trashort pulses and would benet from MHz repetition rate laser sources by allowing faster
measurements or treatments. This OPCPA system could be used to drive both an electron gun
for the generation of tens of keV electron pulses and excite targets in pump-probe experiments
with few-cycle pump pulses in the microjoule level [152]. Diraction experiments based on this
electron source could be be applied to the characterisation of structural changes in chemical
reactions by resolving molecular reaction dynamics induced by an intense laser pulse.
Another application of this OPCPA could be the study of nanostructures (from material sci-
ence to biology) in operation with a scattering-type scanning near-eld optical microscope
(s-SNOM) [153]. Through dierent frequency generation between the generated idler (1.4
µ
m)
and the residual 1030-nm radiation, it could be possible to obtain a broadband light source
in the mid-infrared. In particular the region between 5 to 10
µ
m is of major interest, as bio-
logical molecules and living tissues exhibit characteristic absorption ngerprints. The s-SNOM
technology combined with this laser source would provide a unique tool capable of topographic
imaging with spectroscopic analysis with 10-nm spatial resolution.
In extreme nonlinear phenomena, the carrier-envelope phase plays a determinant role in the
interaction between the medium an the intense few-cycle light pulse. The CEP-stabilisation of
our laser source could be easily done by implementation of a highly ecient monolithic CEP-
locking scheme to the femtosecond seed oscillator [12]. This would extend the applications
possibilities of the laser system to CEP-sensitive experiments.
Nowadays, femtosecond laser systems are routinely used to generate attosecond pulses by means
of high-harmonic generation in a noble gas. However, this technique requires extremely intense
light sources with energy in the millijoule range [154] typically obtained from Ti:Sapphire-
based ampliers operating at a few kHz repetition rate. Recently, extreme ultraviolet (XUV)
radiations were produced from few hundreds of nanojoule pulses using highly ecient hollow-
core gas-lled photonic crystal bres [155]. Combined with this technology, our OPCPA system
could open the way to attosecond spectroscopy at MHz repetition rates.
A further development for this system is the amplication of infrared pulses around 2
µ
m.
Through frequency mixing of the low and high frequency wings of the Ti:Sapphire pulse spec-
trum, a dierence-frequency signal centred around 2
µ
m can be generated and used as a seed
for a NOPA pumped directly by the Yb:YAG oscillator pulses. Simultaneously, the dierence-
frequency generation scheme ensures self-stabilisation of the pulse carrier-envelope phase, which
is faithfully preserved in the parametric amplication process. Using intense pulses at longer
wavelengths, the cut-o energy of the high-harmonic spectrum can be signicantly extended
allowing for the generation of shorter coherent extreme ultraviolet radiations and novel exper-
iments in high-eld physics [156].
96
7 Conclusion and outlook
Intense few-cycle-pulse laser sources are readily available using chirped pulse amplication and
post-amplication spectral broadening schemes. Based on these technologies sub-femtosecond
time scale could be accessed for the rst time, leading to the emergence of attosecond science.
So far, most of the signicant results in this eld were obtained using a CPA approach. Over
the past decade, great eorts were put into the development of optical parametric chirped pulse
ampliers because of their extreme amplication bandwidths and energy-power scaling possi-
bilities. Unlike gain media with inversion storage, parametric amplication poses nevertheless
a severe challenge of ensuring strict synchronisation between the pump and seed pulses. This
perennial problem of synchronisation has somewhat hindered the establishment of the OPCPA
technology based on two-colour sources for the realisation of high average power systems with
ultrashort pulse durations.
In this thesis, two high-repetition rate parametric ampliers driven by stand-alone pump sources
were presented with their synchronisation schemes. The all-optical synchronisations presented
in chapter 3 oer a substantial reduction of the complexity and cost in the design of an amplier-
based pump source. Soliton-self-frequency-shift in PCFs is a powerful approach for synchro-
nising a laser amplier to a femtosecond seed oscillator in the absence of spectral overlap
between the two lasers. In this scheme, a fraction of the seed is injected in a PCF to obtain a
spectrally-shifted signal inside the gain region of the amplier medium. Provided a suciently
broadband seed oscillator, direct seeding of the amplier yields to a radical simplication of the
entire OPCPA systems. Both approaches were successfully demonstrated in this work. Since
our rst results in 2005, various OPCPA systems were realised using our proposed solutions
[28, 31, 34, 151, 157, 158] conrming their reliability and versatility. The PCF approach is
ideally suited for parametric ampliers pumped by ytterbium-doped bre systems, as it can be
directly spliced to the bre amplier. Further developments could resolve in robust turn-key
all-bre pump lasers for OPCPA.
The ultrafast laser detailed in chapter 4 based on the power-scalable passively mode-locked
thin-disk concept has demonstrated its ability to drive parametric ampliers at MHz repetition
rates with unprecedented average amplied output powers. The elaboration of highly dispersive
dielectric mirrors with reduced losses enabled the operation in ambient air of such a high-energy
oscillator despite the enhanced Kerr-nonlinearity. Stable single-pulse soliton regime could be
obtained with energies up to 6
µ
J. Further increase of the thin-disk pulse energy should be pos-
sible based on the recent advances in the conception of active multipass resonator cavities [32]
and the reduction of the intracavity nonlinearity [109]. Such developments would permit the
direct scaling of the parametric amplier output. Earliest experimental results presented in
chapter 6 showed that amplication of 7 fs pulses to the microjoule level is achievable with
our current pump source. Tight focusing of these pulses can lead to intensities in the range
of
1014
GW/cm
2
, which are suciently high for the generation of soft X-rays by high-order
97
harmonics in gas-jet targets and hollow-core photonic crystal bres [155] or by plasmon eld
enhancement in nanostructures [159]. This would open the way to new extreme ultraviolet
sources in the multi-MHz regime with accordingly increased photon ux.
Both OPCPA schemes developed in the framework of this thesis allow for the amplica-
tion of carrier-envelope phase stabilised few-cycle pulses. With the implementation of CEP-
stabilisation methods, new experiments in high-eld physics are conceivable taking full advan-
tage of these high-repetition-rates. Time-resolved attosecond spectroscopy in the kHz and MHz
regimes would allow faster acquisition times and improved signal-to-noise ratios for accurate
tracing of electron dynamics.
98
A List of acronyms
AC Autocorrelation
ASE Amplied spontaneous emission
BBO Beta barium borate
BiBO Bismuth borate crystal
BK7 Type of borosilicate crown glass
CEP Carrier-envelope phase
CPA Chirped pulse amplication
CW Continuous wave
FROG Frequency-resolved optical gating
FWHM Full-width at half-maximum
GD Group delay
GDD Group dispersion delay
GRENOUILLE
Grating-eliminated no-nonsense observation of ultrafast incident laser light E-elds
GVD Group velocity dispersion
KD*P Potassium dideuterium phosphate
LBO Lithium borate
Lu
2
O
3
Lutetium oxide
Nd Neodymium
NIR Near-infrared
NOPA Noncollinear optical parametric amplication
OPA Optical parametric amplication
OPCPA Optical parametric chirped pulse amplication
OPO Optical parametric oscillator
PCF Photonic crystal bre
PLL Phase-locked loop
PZT Piezo transducer
RF Radio frequency
RMS Root mean square
ROC Radius of curvature
RTP Rubidium titanyle phosphate
SBR Semiconductor Bragg reector
Sc
2
O
3
Scandium oxide
SFG Sum-frequency generation
SHG Second harmonic generation
SNOM Scanning near-eld microscope
SPIDER Spectral phase interferometry for direct electric eld reconstruction
SPM Self-phase modulation
SSFS Soliton self-frequency shift
TEM
00
Transverse electromagnetic mode 00
TOD Third-order dispersion
TL Transform-limited
UV Ultraviolet
VCO Voltage controlled oscillator
XUV Extreme ultraviolet
YAG Yttrium aluminum garnet
Yb Ytterbium
YLF Yttrium lithium uoride
99
B List of physical symbols
α
Noncollinear seed-pump angle
β
Noncollinear idler-pump angle
d
e
Eective second order nonlinear coecient
∆
k Wave vector mismatch
∆k
FWHM
FWHM phase-matching bandwidth
∆
R Modulation depth
∆
ns
Nonsaturable losses
E
p
Pulse energy
f focal length
F
A,sat
Fluence of the saturable absorber
F
L,sat
Fluence of the laser medium
f
RO
Frequency of the relaxation oscillation
γ
SPM
Nonlinear phase-shift
Ip
Pump intensity
Is
Seed intensity
Is0
Initial seed intensity
ki
Idler wave vector
kp
Pump wave vector
ks
Seed wave vector
l Cavity losses
L Length
M
2
Beam quality factor
n Refractive index
ne
Extraordinary refractive index
ni
Idler refractive index
nie
Idler extraordinary refractive index
nio
Idler ordinary refractive index
no
Ordinary refractive index
np
Pump refractive index
npe
Pump extraordinary refractive index
ns
Seed refractive index
nso
Seed ordinary refractive index
n
2
Nonlinear refractive index
ωi
Idler angular frequency
ωp
Pump angular frequency
ωs
Seed angular frequency
P
int
Intracavity power
σj
RMS timing jitter
τa
Recovery time of the absorber
τg
Laser material upper state life time
τi
Timing jitter
τp
Pulse duration
τr
Cavity round-trip time
v
gi
Group velocity of the idler
v
gs
Group velocity of the seed
w 1/e
2
intensity mode radius
Z
0
Vacuum impedance
100
C Dispersion and ultrashort pulses
with
ω= 2πf
,
f = c0
λ
,
k = n2π
λ= nω
c0
,
ϕ=ωt
Phase velocity:
vφ=ω
k=c0
n
Group velocity:
vg=dω
dk = vφ
1
1 + ω
n
dn
dω
= vφ
1
1−λ
n
dn
dλ
Group velocity dispersion (GVD): GVD
=d2k
dω2=d
dω1
vg=λ3
2πc2
0
d2n
dλ2
Third order dispersion (TOD): TOD
=d3k
dω3=−λ4
(2π)2c3
03d2n
dλ2+λd3n
dλ3
Group delay: GD
=dϕ
dω=L
vg
Group delay dispersion (GDD): GDD
=d2ϕ
dω2=
GVD
·L
For an initial transformed limited pulse of duration
τ
TL
, dispersion lengthened to pulse to:
τp(GDD) = τ
TL
·s1 + (4 ln 2 ·GDD
τ2
TL
)2
For the calculation of the GDD, the following expressions of the Sellmeier equation were used.
Material Reference
Air [160]
FS [161]
BK7 [162]
BBO [143]
101
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Acknowledgements
I would rst and foremost like to thank Prof. Ferenc Krausz for giving me the opportunity to
work in his group. This work would not have been possible without his support and encour-
agement. I am deeply grateful to Prof. Heinz Lehr and Dr. Alexander Binder for accepting to
be the reviewers of this thesis and for their assistance in the nal process of this work. Many
thanks to Dr. Alexander Apolonskiy for his supervision but also his direct support in the lab
every time I needed it.
I am also thankful to Xun Gu for his advice and trouble-shooting services on the parametric
amplier. Thanks to my best oce mate and team mate Roswitha Graf for sharing coee,
bruises and my chaotic oce. I am particularly indebted to Thomas Metzger for his invariable
support and letting me know that everything will be all right.
For the pleasant working atmosphere at the LMU, I especially thank Ioachim Pupeza for its
musical lab, Oleg Pronin for his immediate help when needed and Hanieh Fattahi for the
dicult task of overtaking my laser system. Further I gratefully acknowledge the help of
Zsuzsanna Major, Yunpei Deng, László Veisz, Daniel Hermann, Takao Fuji, Sergei Naumov,
László Turi, Atsushi Sugita, Volodymyr Pervak, Nobuhisa Ishii, Andrius Baltuska, Matt Mac
Eckett, Siegfried Herbst, the MPQ-LMU administrative sta, technicians and workshop and
many many others.
The author acknowledges the funding of this work by the German Bundesministerium für
Bildung, Wissenschaft, Forschung und Technologie (BMBF) in the frame of the FEMTONIK
research program FULMINA, project no. (FKZ): 13N8724.
Finally, thanks to my parents for supporting me from the other side of the world ...
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