Scaling Infrared Femtosecond Optical Parametric
Oscillators to High Average Powers
by
Travis S. Petersen
Submitted in Partial Fulfillment of the
Requirements for the Degree
Doctor of Philosophy
Supervised by
Dr. Jake Bromage
The Institute of Optics
Arts, Sciences and Engineering
Edmund A. Hajim School of Engineering and Applied Sciences
University of Rochester
Rochester, New York
2017
ii
Dedicated to my Mom and Dad for all the help they gave
to make me the man I am today.
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Table of Contents
Biographical Sketch .............................................................................................. vii
Acknowledgments.................................................................................................. ix
Abstract ................................................................................................................ xiii
Contributors and Funding Sources.........................................................................xv
List of Figures ..................................................................................................... xvii
1 Introduction .......................................................................................................1
1.1 Brief History of Optical Parametric Oscillators ........................................ 1
1.2 Recent Advancements in Scalable Ultrafast OPO’s ................................. 3
1.3 Applications for Infrared Ultrafast Optical Pulses .................................... 6
1.4 Outline ....................................................................................................... 7
2 Optical Parametric Oscillator Fundamentals .....................................................8
2.1 Fundamental Principles of Nonlinear Optics ............................................ 8
2.1.1 The Nonlinear Optical Susceptibility .................................................. 8
2.1.2 Description of Nonlinear Optical Processes...................................... 10
2.1.3 Coupled-Wave Equations .................................................................. 11
2.1.4 Critical Phase Matching .................................................................... 13
2.2 Characteristics of Optical Parametric Oscillators ................................... 17
2.2.1 Parametric Gain ................................................................................. 17
iv
2.2.2 Synchronous Pumping and Cavity Length Stabilization................... 19
2.3 Properties of Ultrafast Pulses .................................................................. 20
2.3.1 Definition of Spectral Phase and Dispersion..................................... 20
2.3.2 Sources of Dispersion........................................................................ 22
2.3.3 Self-phase Modulation ...................................................................... 24
2.4 Pulse Characterization Techniques ......................................................... 24
3 Thin-Disk Mode-Locked Pump Laser .............................................................26
3.1 A Review of Thin-Disk Lasers................................................................ 26
3.2 Principles of Thin-Disk Operation .......................................................... 27
3.2.1 Thin-Disk Laser................................................................................. 27
3.2.2 Yb:YAG as a Laser Material ............................................................. 28
3.2.3 Thermal Lensing ............................................................................... 30
3.3 Cavity Design .......................................................................................... 31
3.3.1 Thin-Disk Head ................................................................................. 31
3.3.2 Active Multipass Cavity .................................................................... 34
3.3.3 Cavity Design .................................................................................... 35
3.4 Mode-Locking ......................................................................................... 37
3.4.1 Soliton Formation .............................................................................. 37
3.4.2 Initiation of Mode-Locking ............................................................... 40
3.4.3 Mode-Locking Instabilities ............................................................... 41
3.5 TDML as a Pump Source ........................................................................ 45
3.5.1 Output Power and Stability Regimes ................................................ 45
3.5.2 3.5.1 Pulse Duration .......................................................................... 46
3.5.3 Beam Quality..................................................................................... 48
v
3.5.4 Temporal Stability ............................................................................. 49
4 Design of the Optical Parametric Oscillator ....................................................51
4.1 Nonlinear crystal ..................................................................................... 51
4.1.1 Availability of Crystals ..................................................................... 51
4.1.2 BiBO Transparency ........................................................................... 55
4.1.3 Noncollinear Geometry ..................................................................... 57
4.1.4 Crystal Coatings ................................................................................ 58
4.2 Cavity Design .......................................................................................... 59
4.2.1 Multipass Cavity Design ................................................................... 59
4.2.2 Folded Cavity Design ........................................................................ 64
4.2.3 ABCD Analysis ................................................................................. 67
5 Characterization of the Ultrafast Optical Parametric Oscillator ......................69
5.1 Pulse Duration ......................................................................................... 69
5.2 Spectral Measurements ........................................................................... 71
5.3 Temporal Stability ................................................................................... 75
5.4 Output Power and Scaling Limitations ................................................... 77
5.5 Beam Quality........................................................................................... 78
6 Thermal Analysis and Limitations of High-Power Operation .........................82
6.1 Motivation of Thermal Analysis ............................................................. 82
6.1.1 2-µm Absorption in BiBO and Total Absorbed Power ..................... 82
6.1.2 Active Cooling of the OPO ............................................................... 83
6.2 Measurement of Thermal Properties ....................................................... 86
6.2.1 Thermal Camera Selection and Image Acquisition........................... 86
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6.2.2 Preparation of Thermal Images for Data Analysis ............................ 87
6.2.3 Final Thermal Images........................................................................ 88
6.3 Impact of Internal Power on the Thermal Gradient ................................ 89
6.4 Thermally Induced Phase-Matching Errors ............................................ 90
6.5 Power Limitations from Thermal Lensing .............................................. 93
7 Outlook and Conclusions.................................................................................97
7.1 Summary ................................................................................................. 97
7.2 Outlook .................................................................................................... 98
7.2.1 OPO Pulse Duration .......................................................................... 99
7.2.2 Pump Laser Power and Energy ......................................................... 99
7.2.3 Timing Jitter Stabilization ............................................................... 100
7.2.4 Thermal Management of Nonlinear Crystals .................................. 102
7.2.5 Cavity Design .................................................................................. 103
7.3 Conclusions ........................................................................................... 105
References ............................................................................................................107
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Biographical Sketch
Travis S. Petersen was born in Sacramento, CA in 1986 and grew up in time split
between Reno, NV, and Puyallup, WA. In 2009, he graduated cum laude from Central
Washington University (CWU) with a Bachelor of Science degree in Physics, a Bachelor
of Arts degree in Philosophy and a minor in Mathematics. While the study of philosophy
was his first passion, a critical understanding of physical science seemed imperative to
comprehend modern philosophical arguments. Physics became the primary focus of his
education and he pursued a variety of research interests.
The first major research Travis performed was with the assistance of the cwU
Science Honors Program under Dr. Andy Piacsek. The propagation of sound from wind
turbines was modeled from acoustical measurements of nearby wind farms to assess the
impact of a proposed wind farm in Ellensburg, WA. Involvement with the local chapter of
the Society of Physics Students (SPS) led to an interesting research opportunity with the
help of Dr. Mike Braunstein to construct a circuit to model chaotic differential equations
and model key parameters for characterizing chaotic behavior. After this research was
completed, a new opportunity with Dr. Mike Jackson became available, which sparked
Travis’s interest in optics. A laser laboratory was constructed from the ground up, which
characterized isotopic methanol using heterodyned CO2 lasers. This research was funded
in part by the cwU Science Honors Program, which led to his passion for laser science.
In 2009, Travis entered the doctoral program at The Institute of Optics at the
University of Rochester. One year later, he joined the Laser Development Group at the
Laboratory for Laser Energetics (LLE) under the supervision of Dr. Jake Bromage to study
high-average-power ultrafast parametric systems with the support of a Horton Fellowship.
He received a Master of Science degree in Optics in 2015.
viii
Publications
1. T. Petersen, J. Zuegel, and J. Bromage, “Thermal Effects in an Ultrafast BiB3O6
Optical Parametric Oscillator at High Average Powers,” Applied Optics, 2017,
56(24): pp. 6923-6929.
2. T. Petersen, J. Zuegel, and J. Bromage, “High-average-power, 2-μm femtosecond
optical parametric oscillator synchronously pumped by a thin-disk, mode-locked
laser,” Optics Express, 2017, 25(8): pp. 8840–8844.
3. M. Jackson, T. Petersen, and L. R. Zink. “Frequencies and Wavelengths From a
New Far-Infrared Lasing Gas: 13CHD2OH,” IEEE Journal of Quantum Electronics,
2009, 45(7): pp. 830–832.
Conference Proceedings
1. T. Petersen, J. Zuegel, and J. Bromage, “High-Energy Infrared Femtosecond
Optical Parametric Oscillator Synchronously Pumped by a Thin-Disk Laser,” in
Lasers Congress (ASSL, LCL, LAC), pATu1A.6 (2016).
2. T. Petersen and J. Bromage, “Thin-Disk Pumped, High-Average-Power, 2.06-μm
BiB3O6 Femtosecond Optical Parametric Oscillator”, Frontiers in Optics,
pLTh4I.6 (2015).
3. T. Petersen and J. Bromage, “Intracavity Chirped-Pulse Amplification for High-
Energy Ultrafast Optical Parametric Oscillators,” Frontiers in Optics, pFM4G.3
(2012).
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Acknowledgments
This work would have not been possible without the support of many talented
people and the patience of many friends. Therefore, I will use this small space to give a
small dedication of my gratitude to the following.
Many thanks are due to Dr. Jake Bromage, my advisor. Being Jake’s first graduate
student has been an amazing adventure. It is quite an honor to be able to have taken this
journey with such a talented laser physicist. His deep understanding of ultrafast phenomena
and practical laser engineering has taught me so much in the past years that I would not
have been able to learn in many other places. Jake is an extremely driven individual who
is active in the lab, supports the Laser Development Group (not only a group member but
also through his recent promotion as the group leader), and serves as a volunteer firefighter,
all on top of being an academic advisor. The success of this research would not have been
possible without the countless hours of planning and review during our weekly hour-long
meetings. It has truly been a pleasure to work and learn under Jake’s guidance, and I will
always be grateful for this experience.
Humble cheers are due to the members of the Laser Development Group. Rick
Roides, who gave unique insight into laser development techniques with his many years of
experience. Dr. Ildar Begishev, who stayed late on a few occasions so I could work longer
in the lab, provided engineering insight for parametric devices, and babysat my laser from
time to time. Dr. Christophe Dorrer, who shared years of insight on ultrafast pulse
dynamics during group meetings. Bob Cuffney, who helped me find a great deal of
equipment around the lab that I could borrow for my experiments. Dr. Andrey Okishev,
who helped with foreign correspondences and provided key infrared diagnostics. Dr.
Seung-Whan Bahk, who provided a great deal of information and code for the imaging
needs of this study. Finally, Dr. Jon Zuegel, whose tireless work over the years as group
x
leader, and more recently as Laser Development and Engineering Division Director,
ensured that finances were never a concern and that working with his group was always a
joy.
From a student’s point of view, LLE has many different disciplines under the same
roof, providing great services from various departments that allow one to spend more time
on one’s research. The Purchasing Department, headed by Bill Byrne, has been absolutely
phenomenal in handling my many requisitions and complicated orders. The Publications
Department, led by Jen Taylor, has never missed a deadline and has always gone the extra
mile to make any last-minute changes when I asked. It is amazing what they accomplish in
this building with such a small crew. Cindy Dorfner and the members of the Computer
Support Group helped me solve problems in a fraction of the time of what I could have
done on my own, if at all. The Machine Shop has been a wonderful resource, with both
requisitions for specialty equipment and the availability to make modifications on my own.
Alexei Kozlov gave me a lot of advice on his personal time about laser damage and thermal
mitigation. The Optical Manufacturing Group has been an invaluable resource to have in
the same building. Gary Mitchell taught me how to get optical surfaces cleaner than I
thought possible, cleaned specialty optics and optomechanics for me on his own time, and
showed me that not all isopropyl alcohols are created equal. Alex Maltsev created custom
optical cuts to mirrors at a fraction of the cost of a commercial vendor in half the time.
There are so many more to thank that I could probably fill half the thesis with an adequate
description. LLE truly has been an amazing place to spend my time as a graduate student.
The staff in The Institute of Optics, which includes Kari Brick, Maria Schnitzler,
Gina Kern, Lori Russell, Gayle Thompson, Noelene Votens, kept all the paperwork in order
and sheltered me from the bureaucracy of higher education. Kari deserves special thanks
because she has helped me navigate many complicated issues arising from performing my
research off-campus and questions about the graduate process. Kari and the entire staff
have always been cheerful and willing to help at a moment’s notice.
xi
The Central Washington University Physics Department should receive more
attention for the service they provide to their undergraduate students. I was not sure I
wanted to pursue physics when I started college, and looking back I know that many
students would not have selected cwU to study physics. However, the opportunities
available to undergraduate students in that department, as well as cwU , are quite
astounding. Being able to perform four years of research alongside my curriculum gave me
skills that I am unsure if I could have obtained elsewhere. The wonderful professors in our
small department maximized the potential of having such small classes with personal
attention and feedback that I felt honored to be a part of the process. I would also like to
thank the Science Honors program, which provided research funds and stipends that
introduced students from every discipline to the work expected from you at a graduate level
while also diversifying a student’s scientific knowledge.
I could not thank Professor Mike Jackson enough, who served as my advisor during
my last year of undergraduate research. I am sure that without the research opportunities
he brought with him, I would not have been accepted into the doctoral program at The
Institute of Optics. It was Professor Jackson who first sparked my interest in optics. The
experimental work with lasers led me to find my true passion in research, which might not
have ever happened if he had not come to cwU. He was truly a gift to the students at cwU
and I will be forever grateful for the impact he had on my life.
Although it has been many years since, Mrs. Julie Brownlee, my high school debate
coach continues to be a source of inspiration to me. Although I did quite well in high
school, I was never particularly fond of it. If it were not for my involvement in debate, it is
questionable if I would have attended college at all. Debate nurtured an interest in arguing
into a passion for philosophical thought and critical reasoning. This likely would not have
appealed to me if it were not for Mrs. Brownlee’s effort, which went well beyond the
expectations as an instructor.
It goes without saying that I could not have made it this far without my wonderful
family. I will always cherish the love and support my mother gave me as a child to help
xii
me excel at school and nurtured my inquisitive mind. Always a source of love, you have
fueled my life with excitement and optimism that has kept my sanity during these past
crazy years. My father has been a solid foundation of support and encouragement my entire
life. A man of his word and one of the most respectable people I know, I am honored to
have had you guide me through this journey. Karen, your love and support have enriched
my life. It seems crazy that 20 years have gone by but I just cannot imagine how life would
have been without you in it. Ken, you have done so much to make California feel like home
and it is hard to express my appreciation for what you have brought to my life.
Even though we have lived on opposite sides of the country for many years, my
longtime friend Jeston Loux and I have maintained a friendship that has been a vital to my
sanity throughout the college experience. Our paths in life have been about as different as
they get, yet a bond that I will never fully understand has always kept us on the same page.
You have kept me grounded, realizing that there are other things in life besides graduate
school, which at times can be all-consuming. Thanks for always being there, man.
I was lucky to have met my colleague and dear friend Justin Schultz and to have
your friendship throughout graduate school. Although our work was in very different
regions of optics, the ability to discuss research difficulties or blow off steam about
graduate school with you is something for which I am very grateful. Our occasional dinners
and late-night scotches made some of the most difficult parts of the graduate process
bearable, and I am glad to have known someone with such a brilliant mind and kind heart.
Words cannot express how thankful I am to have had my love, Amelia McMullen,
in my life during the most challenging time of my research. Your patience, motivation, and
willingness to listen put me in a debt that I can never fully repay. When staying the course
seemed so difficult, you were there to help carry the weight. I will always treasure what
you brought to my life. Thank you, from the bottom of my heart.
xiii
Abstract
A demand for ultrafast, highly energetic laser sources in the infrared exists for
various applications such as high-harmonic generation, waveguide inscription, and remote
sensing. These applications require high repetition rates for faster processing speed and
better signal-to-noise ratios. Until recently, laser pulses used in these systems were usually
provided by optical parametric oscillators and amplifiers pumped by Ti:sapphire laser
systems. The output power and spectral bandwidth of this pump source are fundamentally
restricted due to unavoidable limitations caused by the quantum-defect heating and
restricted emission spectrum of the gain medium. Advancements to Yb-based sources have
provided a significant increase in average power and pulse energy available from ultrafast
pumps, thereby increasing the capabilities of parametric devices.
In this thesis, an ultrafast optical parametric oscillator was constructed as a test bed
for investigating the scaling potential of these devices. The main goals of this study were
to utilize recent technological advancements to ultrafast pump sources and test the limits
for obtaining high-energy pulses with high average powers from an optical parametric
oscillator. Various nonlinear crystals and parametric pumping geometries were
investigated to determine how best to use the available power of a home-built pump laser
and the general potential for scalability. To utilize recent developments of similar pump
sources, a long cavity was designed to take advantage of the high-average-powers with
scalable pulse energies. While the designing the cavity, it became apparent that the cavity
length could be done easily without notable change to critical cavity parameters by using
telescopic imaging relays.
It was discovered that limitations to the power scalability of this system were
directly linked to problems with the thermal management of the nonlinear crystal. While
minor changes could have been implemented to reduce the impact of these boundaries,
xiv
understanding thermal effects in parametric devices will be critical to fully utilizing the
state-of-the-art pump sources. Simple and cost-effective methods were developed for
characterizing the impact of the thermal gradient on the available gain. This analysis could
easily be extended to other systems for predicting and mitigating thermally induced power
scaling limitations.
xv
Contributors and Funding Sources
This dissertation was supervised by Jake Bromage, Senior Scientist and Group
Leader at the Laboratory for Laser Energetics. The dissertation committee, chaired by
Professor Todd Krauss (Chemistry) consisted of Dr. Jake Bromage (LLE), Professors
Wayne Knox (Optics), Robert Boyd (Optics), and Nicholas Bigelow (Physics).
This research was supported by the Department of Energy National Nuclear
Security Administration under Award Number DE-NA0001944, the University of
Rochester, and the New York State Energy Research and Development Authority. This
report was prepared as an account of work sponsored by an agency of the U.S. Government.
Neither the U.S. Government nor any agency thereof, nor any of their employees, makes
any warranty, express or implied, or assumes any legal liability or responsibility for the
accuracy, completeness, or usefulness of any information, apparatus, product, or process
disclosed, or represents that its use would not infringe privately owned rights. Reference
herein to any specific commercial product, process, or service by trade name, trademark,
manufacturer, or otherwise does not necessarily constitute or imply its endorsement,
recommendation, or favoring by the U.S. Government or any agency thereof. The views
and opinions of authors expressed herein do not necessarily state or reflect those of the
U.S. Government or any agency thereof.
The author’s graduate study was funded by a Horton Fellowship, which has been
an invaluable resource for countless students working at LLE.
This work would have not been possible if not for the numerous contributions from
the Electronics Department at LLE. Numerous home-built electronic devices including
laser locks, noise characterization circuits, and thermoelectric cooling controllers were
constructed that were vital to the operation of the systems used in this study. Wade Bittle
xvi
was a great resource for general knowledge of general electronics and characterization
equipment.
The work shown here could not have been accomplished without the generous
contributions from TRUMPF GmbH. The pump laser used in this investigation was built
using a TRUMPF thin-disk head obtained through a collaborative agreement. Prior to
receiving this equipment, commercial thin-disk devices for scientific investigations were
not available, and the ability to test the potential of Yb-based pump sources would not have
been possible if it were not for support from TRUMPF, headed by Dr. Dirk Sutter. The
author would like to personally thank Dr. Dominik Bauer. During his graduate studies, he
provided invaluable guidance for optimizing the thin-disk pump laser during long
conference calls and email correspondences. This assistance was provided on his own time
with no direct personal benefit. He went above and beyond to ensure the success of this
laser at the LLE.
xvii
List of Figures
Figure 1.1: Historical sampling of ultrafast OPO’s ............................................................ 5
Figure 2.1: Noncollinear interaction geometry . ............................................................... 15
Figure 3.1: Schematic of the thin-disk laser head ............................................................ 28
Figure 3.2: Yb:YAG material information ....................................................................... 29
Figure 3.3: Diagram of thin-disk head baseplate .............................................................. 33
Figure 3.4: Alignment of cw-pump spot ........................................................................... 34
Figure 3.5: Diagram of the TDML cavity ......................................................................... 36
Figure 3.6: Example of cw background ............................................................................ 44
Figure 3.7: Efficiency of the TDML. ................................................................................ 45
Figure 3.8: Autocorrelation and spectrum of the TDML .................................................. 47
Figure 3.9 Near-field beam profile of the TDML ............................................................. 49
Figure 4.1: OPO crystal parameters ................................................................................. 54
Figure 4.2: Unpolarized transmission spectrum of BiBO ................................................. 55
Figure 4.3: Measured BiBO crystal transmission ............................................................. 56
Figure 4.4: Noncollinear phase-matching curves ............................................................. 57
Figure 4.5: Multipass OPO cavity schematic ................................................................... 60
Figure 4.6: Mirror reflectivity and GDD for various cavities ........................................... 62
Figure 4.7: Folded OPO cavity schematic ........................................................................ 64
Figure 4.8: Total linear dispersion of the folded OPO cavity ........................................... 66
Figure 4.9: Images of the crystal mount and beam orientation ......................................... 67
xviii
Figure 5.1: Autocorrelation trace of the OPO ................................................................... 71
Figure 5.2: Diagram of the home-built spectrometer........................................................ 72
Figure 5.3: OPO spectrum ................................................................................................ 74
Figure 5.4: Radio-frequency spectrum of the signal and pump ....................................... 76
Figure 5.5: Output power of the signal and idler .............................................................. 77
Figure 5.6: Beam profiles at different output powers ....................................................... 79
Figure 5.7: Beam-quality measurements and M2 fit ........................................................ 80
Figure 6.1: Schematic of the thermoelectric cooler and heat sink .................................... 84
Figure 6.2: TEC temperature setting and the signal power .............................................. 85
Figure 6.3: Schematic and sample thermal image of crystal face ..................................... 89
Figure 6.4: Change in thermal gradient as a function of SWIR power ............................. 90
Figure 6.5: Thermal images various powers and wavelengths ......................................... 91
Figure 6.6: Changes to cavity dynamics predicted by thermal analysis ........................... 95
Figure 6.7: Signal power and calculated beam spot size versus pump power .................. 96
1
1 Introduction
1.1 Brief History of Optical Parametric Oscillators
An optical parametric oscillator (OPO) is an optical frequency conversion system
using the frequency-mixing characteristics of a nonlinear crystal, where one or two waves
are resonated inside a cavity during the process of nonlinear frequency conversion. An
OPO is a wavelength-tunable light source with a unique set of advantages including a broad
tuning range, high stability, and a simple structure. Traditionally, OPOs have been of
interest for their ability to generate coherent light at frequencies not available to
conventional lasers.
The development of OPOs has grown with advancements in both nonlinear crystals
and available pump sources. In the early 1960’s, multiple groups predicted the possibility
of parametric gain during a three-wave interaction [1-3]. The first OPO was demonstrated
quickly after the development of the first laser with pulsed operation. In 1965, Giodmaine
and Miller obtained a signal-beam tuning range of 0.97 to 1.15 µm using a lithium niobate
crystal pumped by a Q-switched multimode laser [4]. Soon, Boyd et al. proposed the
possibility of a continuous-wave (cw) OPO to overcome inherent instabilities and produce
narrow linewidths [5]. In 1968 cw OPO’s were successfully obtained, and numerous
studies investigated improving the tuning range, uniform tuning power and narrow
linewidth of OPO’s for numerous applications, most notably spectroscopy [5-7]. For
pulsed OPO’s, numerous improvements to Q-switched pump sources provided
breakthroughs in obtaining pump thresholds with higher peak powers for nanosecond (ns)
pulses without the need for high average powers.
2
The next large development for OPO’s was extending pulsed operation to the
picosecond (ps) and femtosecond (fs) regimes using ultrafast mode-locked sources. These
devices had significantly higher peak powers than nanosecond (ns) OPO’s but lower pulse
energies. Unlike Q-switched laser–pumped OPO’s, where the ns pulses usually span
several cavity lengths, mode-locked OPO’s can generate pulse durations much shorter than
a cavity length. This allows the resonated pulse to be amplified by an undepleted pump
pulse for each round-trip inside the cavity. The output of the OPO follows the pulse
dynamics of the mode-locked pump laser, so characteristics of the output can be controlled
and designed for a specific application.
First demonstrated in 1972, synchronous pumping of an OPO occurs when the
signal pulse arrives at the nonlinear crystal at the same rate as the pulse laser such that the
𝑐/2𝐿 frequencies of the pump laser and the OPO are identical [8]. After this achievement,
analytic expressions for an OPO pumped by a mode-locked laser were presented for
transient and steady states [9]. The timing synchronization requires identical repetition
rates between the pump laser and the synchronously pumped OPO. After a characteristic
buildup time, the signal reaches steady-state operation and oscillates in the cavity. Initial
synchronously pumped systems were restricted to pump sources using Q-switched mode
locking, which had room for improvement due to unwanted damage caused by the high
intensities from nonuniform pulse trains.
As interest in synchronously pumped systems grew, improvements to numerical
simulations of the parametric process were derived from the master mode-locking equation
and using the split-step Fourier method [10-14]. The first fs OPO was demonstrated by
D.C. Edelstein et al. in 1989 using a KTP crystal synchronously pumped by a colliding-
pulse passively mode-locked dye laser [15]. This analysis was done alongside experimental
demonstrations of synchronously pumped fs OPO’s pumped by the growing popularity of
Kerr-lens mode-locked Ti:sapphire lasers using a variety of phase-matching techniques
[16-20]. Additionally, soliton formation in fs OPO’s has been achieved with appropriate
conditions for dispersion and self-phase modulation [21, 22]. Broad tunability around
3
degeneracy using diffraction gratings or birefringent filters as frequency-selective devices
to induce singly resonant operation in synchronously pumped OPO’s has also been
demonstrated [23, 24].
Many advancements have been made with free-space fs OPO’s synchronously
pumped by Ti:sapphire lasers in the last 25 years. Ultrafast systems have been developed
from wavelengths between 0.25 and 8.0 µm with a wide variety of goals for individual
investigations. The focus of some investigations has been wide tunability in a single
system. Examples of this are a periodically poled lithium niobate OPO that has near-
continuous tunability from 0.98 to 4.55 µm with pulse durations of 150 fs and a AgGaSe2-
based OPO with tunability from 2 to 8 µm with pulse widths ranging from 400 to 500 fs
across the available wavelengths [20, 25]. When tunability was not a concern, pulse
durations below 100 fs have been achieved at energies between 1 and 10 nJ from the visible
to the mid-infrared [26-34].
Ti:sapphire–pumped ultrafast OPO’s are typically limited to producing sub-watt
average powers due to restrictions on the available power from Ti:sapphire lasers. Using
state-of-the-art 18-W, solid-state green lasers to pump fs Ti:sapphire oscillators, it is now
possible for commercial ultrafast singly resonant (and thus tunable) OPO’s to reach near-
10-nJ energy levels [35]. This pulse energy is likely to represent an upper limit for this
technology because of the increasingly difficult thermal management required in strongly
pumped Ti:sapphire oscillators.
1.2 Recent Advancements in Scalable Ultrafast OPO’s
In the past decade, to surpass the capabilities of the Ti:sapphire laser, development
of ultrafast, high-average-power laser sources has been dominated by three technologies:
Innoslab amplifiers, fiber amplifiers, and thin-disk lasers. Innoslab-based amplifiers have
recently achieved kilowatt (kW) average powers with pulse durations of 615 fs [36].
Similarly, fiber amplifier systems have achieved average powers of 830 W with pulse
durations of 640 fs [37]. Both types of systems are based on a master-oscillator/power-
4
amplifier scheme, which must employ complex amplifier stages to achieve these powers.
To reduce these complexities, high-average-power femtosecond pulses have been achieved
in a single oscillator using a thin disk as the gain medium.
These ytterbium-based systems have shown great promise in scaling high-average-
power, ultrafast pulses near 1-μm wavelengths. Recently 145-W, 1.1-ps pulses containing
more than 41 J of energy pulses with peak powers of 37 MW have been produced when
operated in an ambient atmosphere [38]. Additionally, 250-W, 210-fs pulses with peak
powers of 38 MW have been achieved in air with use of Kerr lens mode-locking instead of
the conventional semiconductor saturable absorbing mirror techniques [39]. This
technology shows promise of reaching 100-MW peak powers within a few years in addition
to different approaches to scaling techniques [40].
While each of these systems produces high-average-power fs pulses, there still exist
inherent limitations to tunability and wavelength selection due to the relatively narrow
emission spectra of their respective gain medium. The use of these systems as pump
sources for ultrafast OPO’s makes it possible to achieve high-average-powers at
wavelengths across the visible and infrared.
A few groups have already employed these pump sources in ultrafast OPO’s with
significant return in the output power and energy. Using a noncollinear pump geometry in
tandem with a Yb:KLu(WO4)2 thin-disk oscillator, an ultrafast OPO was able to produce
visible light with average powers exceeding 3 W with a repetition rate of 34 MHz and pulse
durations of ~70 fs from a β-barium borate (BBO) crystal [26]. Another system employed
a Yb:fiber laser pump source, capable of producing watt-level 1530-nm pulses from a
MgO:PPLN crystal with energies greater than 70 nJ with pulse durations of 1.5 ps [41].
Modifications to this system by lowering the repetition rate through cavity dumping
produced 650 nJ at 1.52 μm with pulse durations of 228 fs, at sub-watt levels, which are
the most energetic pulses from a synchronously pumped fs OPO to date [42].
5
To understand the significance of these improvements, it is useful to compare the
performance of Yb-pumped ultrafast OPO’s to ones using a Ti:sapphire pump. A sampling
of synchronously pumped free-space ultrafast OPO’s created in the last 25 years is shown
in Fig. 1.1.
Figure 1.1: Sampling of free-space ultrafast OPO’s created in the last 25 years operated at
different wavelength regions. Wavelength regions represent areas where the OPO primarily
operated; however, in some cases resonated signal and idler waves spanned multiple
regions (e.g., from 650 to 900 nm). The OPO’s represented in the top half of the figure
were pumped by Yb-based pump sources, while those on the bottom were Ti:sapphire
pumped.
The majority of ultrafast OPO’s with pulse durations below 500 fs were pumped with a
Ti:sapphire laser. Since OPO’s were only sampled in this figure, the prevalence of this
pump source is vastly understated, which is understandable considering the Ti:sapphire
laser has truly been the workhorse of the ultrafast field. Despite the presence of nanojoule
(nJ) level pulses across the optical spectrum, the increase in available energy from the new
class of Yb-based pump sources becomes obvious. These systems did change how OPO’s
were fundamentally operated, but were simply able to take advantage of the dramatic
6
increase in pump pulse energy available from recent technological advancements. The key
question becomes; What are the limitations to this new available power and for what
applications would they be best suited?
1.3 Applications for Infrared Ultrafast Optical Pulses
Recent improvements to OPO’s and the potential for scalability, both in power and
energy, from a tunable ultrafast source open applications previously not addressable with
OPO’s. Illustrated by the examples below, an increasing number of applications require
high-intensity pulses with high average powers in the infrared (IR). In general, ultrafast
OPO’s have the capability to meet the needs of these applications because of their wide
tunability and strong potential for scalable ultrafast laser pulses with superb beam quality.
In high-harmonic generation (HHG) [43], the electron energies for production of
extreme ultraviolet (UV) light scale with pump intensity and 𝜆2, making high-intensity
pulses in the IR an attractive source for HHG. Furthermore, high repetition rates are
beneficial for improved performance in HHG applications including spectroscopy,
microscopy, and frequency metrology [44-46].
Ultrafast sources with high repetition rates reduce the modification threshold and
improve waveguide quality in ultrafast waveguide inscription [47]. However, no suitable
sources exist beyond 1040 nm, despite a real demand. Advancements in the energy
available from ultrafast OPO’s offer an alternative method for achieving high-energy, high-
repetition-rate pulses with the broad spectral selection that is traditionally available from
an OPO.
For remote sensing applications, there is a particular need for high-intensity pulses
with high repetition rates for monitoring atmospheric CO2 and H2O at eye-safe
wavelengths near 2 µm [48-50]. The large bandwidth and spatial coherence available from
these types of OPO’s enable remote sensing over long distances.
7
1.4 Outline
In this thesis, the author investigates the power-scaling potential of ultrafast OPO’s.
So far, a brief introduction to OPO’s has been given and the capabilities of state-of-the-art
systems has been outlined. The need for increasing the pulse energy of fs oscillators in
high-average-power systems has been described. This thesis will focus on the design and
characterization of one such system. The limitations related to power scaling this OPO will
be discussed and potential improvements for obtaining even higher powers will be
explored.
A description of the components of this thesis are as follows. In Chap. 2 the
fundamental physics behind the relevant processes is presented to the reader. In Chap. 3,
the design and characterization of the scalable thin-disk laser used to pump the OPO are
described. Chapter 4 outlines the design principles used to build the OPO used in this
investigation. Alternative cavity designs and considerations for scaling the cavity to longer
lengths for higher-energy pulses are explored. Chapter 5 shows the results of the OPO
characterization, and explains in detail how these measurements were accomplished.
During the characterization of the OPO it became obvious that full use of the available
pump power was not possible due to difficulties in thermal management of the nonlinear
crystal at high average powers. In Chapt. 6, the methods used to analyze the thermal effects
in the crystal are explored. Using information about the thermal gradient of the crystal
caused by the high-average-power beams, the power limitations of the OPO could be
understood. Finally, Chap. 7 summarizes the findings of this investigation and briefly
discusses possible improvements and future work.
8
2 Optical Parametric Oscillator
Fundamentals
Starting with the basic principles of nonlinear optics, fundamental concepts that are
critical to the operation and characterization of an ultrafast OPO are explained. The reader
is provided with a brief introduction to nonlinear optics, focusing on χ(2)-related processes.
Phase-matching conditions for these processes are covered with special attention to
critically phase-matched systems. Parametric gain from such devices and the conditions
necessary to achieve synchronous pumping are discussed. Special considerations necessary
for the characterization of subnanosecond pulses such as spectral phase, dispersion, and
self-phase modulation are covered. The chapter concludes with a description of
interferometric autocorrelation as a method for characterizing the temporal shape of
ultrafast pulses experimentally.
2.1 Fundamental Principles of Nonlinear Optics
2.1.1 The Nonlinear Optical Susceptibility
Nonlinear optics is the field of study for phenomena that occur when light of
sufficient intensity can modify the optical properties of a material. To understand how this
occurs, it is useful to consider how the dipole moment per unit volume, or polarization
𝑃(𝑡), of a material depends on the strength of an applied electric field 𝐸(𝑡). For
9
conventional optical systems, the induced polarization depends linearly on the electric field
strength and is commonly expressed as
𝑃(𝑡) = 𝜖0𝜒(1)𝐸(𝑡), (2.1)
where χ(1) is known as the linear susceptibility and 𝜖0 is the permittivity of free space. In
the presence of intense electrical fields, which is commonly the case in ultrafast systems,
the optical response can often be described by expanding Eq. (2.1) into a power series [51]
as
𝑃(𝑡) = 𝜖0[𝜒(1)𝐸(𝑡) + 𝜒(2)𝐸2(𝑡) + 𝜒(3)𝐸3(𝑡) + ⋯ ], (2.2)
which assumes a lossless and dispersionless medium. The quantities χ(2) and χ(3) are
referred to as the second- and third-order nonlinear optical susceptibilities, respectively. In
general, the nonlinear susceptibilities are complex variables that typically depend on the
frequencies of the applied fields. The real and imaginary parts can generally be represented
by the equation
𝜒(𝑛) = 𝜒(𝑛)′ − 𝑖𝜒(𝑛)′′. (2.3)
The real part of the linear susceptibility is associated with the frequency-dependent linear
refractive index by
𝑛0(𝜔) = √1 + Re{𝜒(1)}, (2.4)
which is also related to linear dispersion and birefringence. The imaginary part of the linear
susceptibility describes the dissipative effect of linear absorption of photon energy by the
medium and the re-emission at longer wavelengths, the latter of which is related to
parametric gain.
The real part of the second-order nonlinear susceptibility is related to parametric
frequency interactions such as three-wave mixing [sum–frequency generation (SFG),
difference–frequency generation (DFG), second-harmonic generation (SHG), and
10
parametric amplification] and the electro-optic effect. The imaginary part 𝑖𝜒(2)′′ is zero,
which means that 𝜒(2) processes do not store photon energy in the interacting medium.
The real part of the third-order nonlinear susceptibility is connected to four-wave
mixing [e.g., third-harmonic generation (THG)] and the Kerr effect (self-focusing, self-
phase modulation). The imaginary part of the third-order nonlinearity is associated energy
exchange between the photon and the medium, which is responsible for Raman scattering,
Brillouin scattering, and multiphoton absorption.
Since all 𝜒(2) processes involve only phase-related interactions between the optical
fields, with no energy stored in the medium, the nonlinear process becomes particularly
appealing due to the high potential efficiency and relaxed cooling requirements that are
essential for traditional laser gain materials operated at high peak powers. As a result, 𝜒(2)
nonlinear interactions are power scalable, limited only by the damage-threshold (both from
linear and multiphoton absorption) and photorefractive effects [52-54]. The impact of these
factors is dependent on the material properties of the nonlinear crystal used in the
interaction, so the relevance of these limitations is very application specific.
2.1.2 Description of Nonlinear Optical Processes
In the previous section the various nonlinear optical phenomena that can occur from
the second-order nonlinear susceptibility were described. These can be described in terms
of the nonlinear contributions to the polarization described by Eq. (2.2). First, consider a
case in which the optical field incident on a second-order nonlinear optical medium consists
of two frequency components, which can be represented as
𝐸(𝑡) = 𝐸1𝑒−𝑖𝜔1𝑡 + 𝐸2𝑒−𝑖𝜔2𝑡 + 𝑐. 𝑐. . (2.5)
It follows from Eq. (2.2) that the second-order contribution to the nonlinear polarization
can be written as
𝑃(2)(𝑡) = 𝜖0𝜒(2)𝐸(𝑡)2. (2.6)
11
The nonlinear polarization is then given by
𝑃(2)(𝑡) = 𝜖0𝜒(2)[𝐸12𝑒−2𝑖𝜔1𝑡 + 𝐸2
2𝑒−2𝑖𝜔2𝑡 + 2𝐸1𝐸2𝑒−𝑖(𝜔1+𝜔2)𝑡 + 2𝐸1𝐸2∗𝑒−𝑖(𝜔1−𝜔2)𝑡 +
𝑐. 𝑐. ] + 2𝜖0𝜒(2)[𝐸1𝐸1∗ + 𝐸2𝐸2
∗].
(2.7)
This result can be expressed more conveniently as
𝑃(2)(𝑡) = ∑ 𝑃(𝜔𝑛)𝑒−𝑖𝜔𝑛𝑡𝑛 , (2.8)
where the summation extends over positive and negative frequencies 𝜔𝑛. The complex
amplitudes of the different frequency components of the nonlinear polarization are then
[51]
𝑃(2𝜔1) = 𝜖0𝜒(2)𝐸12 (SHG),
𝑃(2𝜔2) = 𝜖0𝜒(2)𝐸22 (SHG),
𝑃(𝜔1 + 𝜔2) = 2𝜖0𝜒(2)𝐸1𝐸2 (SFG), (2.9)
𝑃(𝜔1 − 𝜔2) = 2𝜖0𝜒(2)𝐸1𝐸2∗ (DFG),
𝑃(0) = 2𝜖0𝜒(2)(𝐸1𝐸1∗ + 𝐸2𝐸2
∗) (OR).
Here, each expression has been labeled by the physical process it represents. The
dependence of SHG, SFG, and DFG on the second-order nonlinear susceptibility 𝜒(2) was
described above. The final expression describes the optical rectification (OR), which is the
inverse process of the electro-optic effect [51].
2.1.3 Coupled-Wave Equations
Having described how the nonlinear polarization can be characterized when a
medium is subject to an intense electric field, we can now apply Maxwell’s equations to
describe the generation of these components to the electromagnetic field. This will show
12
how the interacting fields become coupled by the nonlinear interaction and what conditions
must be met to make the process efficient. An extension of the standard wave equation is
necessary to address the additional second–order nonlinear polarization and can be stated
as [51]
𝛻2𝑬 −1
𝑐2
𝜕2
𝜕𝑡2𝑬 =
1
𝜖0𝑐2
𝜕2
𝜕𝑡2𝑷. (2.10)
The derivation of the wave equations is cumbersome, even with the limitation of
restricting the analysis to three frequencies, 𝜔𝑝, 𝜔𝑠, 𝜔𝑖, and propagation along a single
direction (collinear), commonly denoted as 𝑧. If the three interacting waves are defined
such that 𝜔𝑖 < 𝜔𝑠 < 𝜔𝑝, they can be referred to as the pump, signal, and idler waves,
respectively, as is common in parametric systems. It is convenient to express the electric
field as a linearly polarized, monochromatic plane wave at frequency 𝜔, progagating in the
𝑧 direction:
𝐸(𝑧, 𝑡) = Re{𝐴(𝑡)exp [𝑖(𝜔𝑡 − 𝑘𝑧)]}, (2.11)
where 𝑘 is given by
𝑘 =2𝜋
𝜆. (2.12)
Within the slowly varying amplitude approximation the following propagation equation
can be derived:
𝑑𝐴
𝑑𝑧= −𝑖
𝜇0𝑐0𝜔
2𝑛𝑃𝑒−𝑖𝑘𝑧, (2.13)
where 𝜇0 is the permeability of free space and 𝑛 is the index of the material. The resulting
coupled-wave equations are expressed as [7, 51]
𝑑𝐴𝑖
𝑑𝑧= −𝑖
𝜔𝑖𝑑eff
𝑛𝑖𝑐0𝐴𝑠
∗𝐴𝑝𝑒−𝑖∆𝑘𝑧, (2.14)
𝑑𝐴𝑠
𝑑𝑧= −𝑖
𝜔𝑠𝑑eff
𝑛𝑠𝑐0𝐴𝑖
∗𝐴𝑝𝑒−𝑖∆𝑘𝑧, (2.15)
13
𝑑𝐴𝑝
𝑑𝑧= −𝑖
𝜔𝑝𝑑eff
𝑛𝑝𝑐0𝐴𝑖𝐴𝑠𝑒𝑖∆𝑘𝑧, (2.16)
where 𝑑eff is the so-called effective nonlinear optical coefficient, which is dependent on
the propagation duration and the polarization of the three beams, and
∆𝑘 = 𝑘𝑝 − 𝑘𝑠 − 𝑘𝑖, (2.17)
defined as the wave-vector mismatch.
2.1.4 Critical Phase Matching
Efficiency in the nonlinear interaction is maximized when ∆𝑘 = 0. This condition
can be achieved the by careful choice of propagation directions inside a dispersive and
birefringent medium. The phase-matching condition can be recast in the form
𝑛𝑝 =𝑛𝑖𝜔𝑖+𝑛𝑠𝜔𝑠
𝜔𝑝. (2.18)
It is straightforward to show that this condition cannot be fulfilled in bulk isotropic
materials in the usual dispersion region (𝑛𝑖 < 𝑛𝑠 < 𝑛𝑝). In certain birefringent crystals,
phase matching can be accomplished by choosing the polarization direction for the higher-
frequency pump (𝜔𝑝) that gives a lower refractive index. In this case, which is common
for ultrafast parametric devices, negative uniaxial crystals (𝑛𝑒 < 𝑛𝑜) can be used. When
the pump beam is polarized along the extraordinary axis of the crystal, phase matching can
be achieved for a certain combination of the signal and idler wavelengths. If both the signal
and idler beams are polarized perpendicular to the ordinary axis of the crystal, it is referred
to as type I (or 𝑜𝑠 + 𝑜𝑖 → 𝑒𝑝) phase matching. If one of the two is polarized in the same
direction as the pump, it is referred to as type II phase matching. This can be the case when
either the signal (𝑒𝑠 + 𝑜𝑖 → 𝑒𝑝) or the idler (𝑜𝑠 + 𝑒𝑖 → 𝑒𝑝) has the polarization along the
extraordinary axis [55]. This condition can of course be reversed for certain situations using
positive uniaxial crystals (𝑛𝑜 < 𝑛𝑒), where the pump is oriented along the ordinary axis.
Additionally, this procedure can be extended to biaxial crystals, which are typically
14
operated on one of the three optical planes, which can then be treated as a negative or
positive uniaxial crystal. Operation outside of these planes is possible, although many
biaxial nonlinear crystals are difficult to characterize and the nonlinear interactions are hard
to predict [56].
Usually, the phase-matching condition is achieved by adjusting the angle 𝜃𝑚
between the wave vector of the propagating beam and the extraordinary (optical) axis of
the nonlinear crystal (angular phase matching). Alternatively, the refractive indices can be
changed by adjusting the temperature of the crystal (temperature or noncritically phase
matching). Another method, quasi phase matching, utilizes periodic polling of the material
to achieve phase matching over long interaction lengths with pump, signal, and idler beams
having the same polarization. Critical phase matching was employed in this investigation,
and the methods used to optimize this process for broadband beams require further
explanation.
As an example, we consider a negative uniaxial crystal where type I phase matching
is achieved when [57]
1
𝑛𝑒,𝑝2 (𝜃𝑚)
=sin2(𝜃𝑚)
𝑛𝑒,𝑝2 +
cos2(𝜃𝑚)
𝑛𝑜,𝑝2 , (2.19)
where 𝑛𝑒,𝑝 and 𝑛𝑜,𝑝 are the principle extraordinary and ordinary refractive indices at the
pump wavelength. The phase-matching angle can then be obtained using
𝜃𝑚 = asin [𝑛𝑒,𝑝
𝑛𝑒,𝑝(𝜃𝑚)√
𝑛𝑜,𝑝2 −𝑛𝑜,𝑝
2 (𝜃𝑚)
𝑛𝑜,𝑝2 −𝑛𝑒,𝑝
2 ]. (2.20)
It is worth noting that, in general, the phase-matching angle shows a less-pronounced
wavelength dependence for type I with respect to type II phase matching. The above
analysis assumes a collinear interaction geometry between the monochromatic pump,
signal, and idler beams. The propagation direction is typically selected to satisfy the phase-
matching condition for a given signal wavelength.
15
This analysis can also be extended for broadband pulses, which is particularly
useful for ultrafast pulses. The coupled wave equations can be extended to include waves
propagating in the nonlinear crystal with different group velocities 𝜐𝑔 = 𝜕𝜔/𝜕𝑘 [58, 59].
The resulting wave equations show how the amplification of ultrafast pulses is significantly
related to the group-velocity mismatch (GVM) between the interacting pulses. The GVM
between the pump and amplified pulses limits the interaction length, where energy can be
efficiency transferred from the pump due to temporal walk-off. Additionally, the GVM
between the signal and idler pulses limits the phase matching bandwidth available and
therefore is the main limitation for creating shorter pulses. It can be shown that if the signal
frequency increases to 𝜔𝑠 + ∆𝜔 (and by energy conservation, the idler frequency decreases
to 𝜔𝑖 − ∆𝜔), then the wave-vector mismatch can be approximated to first order, as [60]
∆𝑘 ≅ −𝜕𝑘𝑠
𝜕𝜔𝑠∆𝜔 +
𝜕𝑘𝑖
𝜕𝜔𝑖∆𝜔 = (
1
𝜐𝑔𝑖−
1
𝜐𝑔𝑠)∆𝜔. (2.21)
For a parametric process using a collinear interaction geometry, the propagation
direction is selected to satisfy the phase-matching condition for a certain signal wavelength.
In this condition, the signal and idler group velocities are fixed and, as a result, the-phase
matching bandwidth. An additional degree of freedom can be introduced by using a
noncollinear geometry, which is illustrated in Fig. 2.1.
Figure 2.1: A schematic of the noncollinear interaction geometry where angles have been
exaggerated for clarity. Not shown here is the angle Ω between the signal and idler beams,
which varies with signal wavelength.
16
The angle 𝛼 between the pump and signal wave vectors is constant for a broadband
signal beam. The idler is emitted at an angle Ω with respect to the signal and is dependent
on the signal wavelength. This results in an angularly dispersed but broadband idler pulse.
The phase-matching condition can be described as a vector equation, which can be
separated into two parts (parallel and perpendicular to the signal wave vector), and
becomes
𝛥𝑘par = 𝑘𝑝 cos 𝛼 − 𝑘𝑠 − 𝑘𝑖 cos 𝛺 = 0, (2.22)
𝛥𝑘perp = 𝑘𝑝 sin 𝛼 − 𝑘𝑖 sin 𝛺 = 0. (2.23)
Like the collinear analysis, if the signal frequency increases by Δ𝜔, the wave-vector
mismatch along the two directions can be approximated (to first order) as
∆𝑘par ≅ −𝜕𝑘𝑠
𝜕𝜔𝑠∆𝜔 + cos Ω
𝜕𝑘𝑖
𝜕𝜔𝑖∆𝜔 − 𝑘𝑖 sin Ω
𝜕𝛺
𝜕𝜔𝑖𝛥𝜔, (2.24)
∆𝑘perp ≅ − sin Ω𝜕𝑘𝑖
𝜕𝜔𝑖∆𝜔 + 𝑘𝑖 cos Ω
𝜕Ω
𝜕𝜔𝑖𝛥𝜔. (2.25)
To obtain broadband phase matching, both Δ𝑘par and Δ𝑘perp must be zero. With some
simple arithmetic, this condition be shown to be equivalent to
𝜕𝑘𝑖
𝜕𝜔𝑖− cos Ω
𝜕𝑘𝑠
𝜕𝜔𝑠= 0, (2.26)
which can be expressed more simply as
𝜐𝑔𝑠 = 𝜐𝑔𝑖 cos Ω. (2.27)
Equation (2.27) shows that broadband phase matching can be achieved for an angle
Ω so that the group velocity of the signal equals the projection of the group velocity of the
idler along the signal direction. In the collinear case, the signal and idler moving with
different group velocities will get separated over a small interaction length, causing a
reduction in bandwidth. For a noncollinear geometry the two pulses can stay overlapped,
17
allowing for significantly more broadband amplification. The signal–idler angle Ω is
important for understanding the improvement in performance between collinear and
noncollinear geometries; however, it is much more helpful to know the pump–signal angle
𝛼 for the design and operation of an ultrafast device. Without losing conditions required
for broadband phase matching, the pump–signal angle is given by [60]
𝛼 = arcsin (1−𝜐𝑔𝑠
2 /𝜐𝑔𝑖2
1+2𝜐𝑔𝑠𝑛𝑠𝜆𝑖𝜐𝑔𝑖𝑛𝑖𝜆𝑠
+𝑛𝑠2𝜆𝑖
2/𝑛𝑖2𝜆𝑠
2)
1/2
. (2.28)
2.2 Characteristics of Optical Parametric Oscillators
2.2.1 Parametric Gain
The gain and amplification of the signal and idler fields in the parametric process
can be derived from the coupled-wave equations presented above. As is characteristic of
the system in this study, if pump depletion is neglected (𝐴𝑝 ≅ const.) and assuming the
signal intensity 𝐴𝑠0 and no initial idler beam, Eqs. (2.14)–(2.16) can be solved for the signal
and idler intensities after passing through a nonlinear crystal of length 𝐿 [60]:
𝐼𝑠(𝐿) = 𝐼𝑠0 [1 +𝛤2
𝑔2 sinh2(𝑔𝐿)], (2.29)
𝐼𝑖(𝐿) = 𝐼𝑠0𝜔𝑖
𝜔𝑠
𝛤2
𝑔2 sinh2(𝑔𝐿), (2.30)
where
𝑔 = √Γ2 − (𝛥𝑘
2)
2
, (2.31)
Γ2 =2𝜔𝑖𝜔𝑠𝑑eff
2 𝐼𝑝
𝑛𝑖𝑛𝑠𝑛𝑝𝜖0𝑐03 . (2.32)
18
In the case of perfect phase matching (Δ𝑘 = 0, 𝑔 = Γ) and in the large gain approximation
(Γ𝐿 ≫ 1), the intensities of the signal and idler simplify to
𝐼𝑠(𝐿) ≅1
4𝐼𝑠0exp (2Γ𝐿), (2.33)
𝐼𝑖(𝐿) ≅𝜔𝑖
4𝜔𝑠𝐼𝑠0exp (2Γ𝐿). (2.34)
It is also important to note that the ratio of signal and idler intensities must be such that an
equal number of signal and idler photons are created. Equations (2.33) and (2.34) allow the
parametric gain to be defined as
𝐺 =𝐼𝑠(𝐿)
𝐼𝑠0=
1
4exp(2Γ𝐿), (2.35)
where the gain grows exponentially with the crystal length and the nonlinear coefficient Γ.
It is worth mentioning that most of the gain control is done through careful consideration
of the parameters in Γ, which is dependent on the pump intensity, signal and idler
wavelengths, the effective nonlinearity of the material, and the refractive indices at the
interacting wavelengths.
This exponential growth of the signal and idler beams is qualitatively different from
the gain seen for other second-order nonlinear processes, such as SFG and SHG. In a strong
pump field, the presence of an existing signal photon stimulates the generation of an
additional signal photon as well as a photon at the idler wavelength. Additionally, due to
the symmetry of the signal and the idler, the amplification of the idler stimulates the
generation of a signal photon. The amplification of the signal field promotes the generation
of the idler field and vice versa, giving rise to exponential growth of both waves.
In the presence of imperfect phase matching, it is useful to create a metric that
expresses the gain as a function of the phase matching and crystal length. In the large gain
approximation, the parametric gain can be shown to be proportional to the phase-matching
condition and the crystal length as [61, 62]
19
𝐺 ∝ sinc2(∆𝑘∙𝐿
2). (2.36)
As has been shown for critically phase-matched systems, ∆𝑘 is dependent on the angle
between the extraordinary beam and the crystal axis, which allows this expression to
become useful in determining the gain available in a parametric device when the angular
acceptance or crystal length is a concern for efficient operation.
2.2.2 Synchronous Pumping and Cavity Length Stabilization
The development of ultrafast pump sources has greatly increased the use of
synchronous pumping in OPO’s. To achieve optimal synchronous pumping, the optical
path length inside the OPO cavity must equal that of the pump source. For ultrafast systems,
this tolerance can be quite tight (of the order of tens of µm), creating restrictions on the
cavity length not typically present in conventional lasers.
The stability of the pulse duration, operating wavelength, repetition frequency, and
output power is extremely important for utilizing the potential of synchronously pumped
OPO’s. The stabilization of the OPO cavity is an important parameter to control when it is
synchronously pumped. In traditional synchronously pumped lasers, the intrinsic gain
storage allows for a small repetition rate mismatch at the expense of an increase in the pulse
duration [63]. However, a synchronously pumped OPO responds to the mismatch by
utilizing the group-delay dispersion (GDD) in the cavity. The wavelength-dependent gain
of an OPO usually results in a change in the central wavelength by modifying the cavity
length, which subsequently modifies the power of the OPO [64]. As a result, changes in
the pump laser’s repetition rate, or environmental fluctuations (e.g., heating or air flow)
that modify the optical path length for either the pump or the OPO, will result in a myriad
of instabilities in the OPO itself.
A straightforward way to stabilize the power level of any source could be to monitor
the output power and adjust the cavity length to maintain a constant power. In
synchronously pumped lasers, the sensitivity of the pulse repetition rate to the cavity length
20
can be exploited to provide an error signal by comparing the rate to either an electronic
oscillator or a reference cavity [65-67].
2.3 Properties of Ultrafast Pulses
Ultrafast pulses are continuously reshaped by their temporal and spectral profile by
both linear and nonlinear mechanisms. These can be from the material in which the pulse
propagates as well as dispersion from the surfaces on which the beam is incident inside the
resonator. In some cases, this can be used to optimize the pulse dynamics and counteract
undesirable effects inside the cavity. To understand these effects, a brief description of the
involved process is given in this section.
2.3.1 Definition of Spectral Phase and Dispersion
It is convenient to consider a wave traveling through a medium where the refractive
index does not change as the pulse propagates. Similar to the procedure employed in Sec.
2.1 but neglecting spatial variation, consider that a pulse with a center frequency at 𝜔0 can
be represented by a time-dependent complex envelope function with the real electric field
as
𝐸(𝑡) ∝ Re{𝐴(𝑡)𝑒𝑖𝜔0𝑡}, (2.37)
where 𝐴(𝑡) is the normalized time-dependent electric field amplitude with the
instantaneous optical power |𝐴(𝑡)|2, which is monitored by a conventional detector. A
Fourier transform of the complex field gives the spectral domain analytically as
𝐴(𝜔) =1
2𝜋∫ 𝐴(𝑡)𝑒−𝑖𝜔0𝑡𝑑𝑡
∞
−∞. (2.38)
Since the electric field amplitude has been defined here as a normalized quantity, we can
equivalently obtain the real power spectrum of the pulse with |𝐴(𝜔)|2.
The relationship between the temporal width of a pulse ∆𝜏𝑝 and its spectral
bandwidth ∆𝜈𝑝 is commonly referred to as the time–bandwidth product (TBP). In this
21
study, both the spectral and temporal widths of a pulse are measured at the full width at
half maximum (FWHM), although other definitions (such as 1/𝑒2) are used. Two
important temporal shapes for ultrafast pulses are the Gaussian pulse (𝑒−2𝑙𝑛2 𝑡2/𝛥𝜏𝑝2) and
the hyperbolic secant pulse [sech2(1.763𝑡/∆𝜏𝑝)]. The minimum TPB of a Gaussian pulse
and hyperbolic secant pulse is 0.441 and 0.315, respectively. Any chirping (either positive
or negative) on the pulse or higher-order dispersion effects will increase the time-
bandwidth product and is typically useful for determining the minimum pulse duration
possible from the amplified spectrum in the parametric process.
Except for a vacuum, any medium introduces dispersion, which arises from the fact
that the refractive index is frequency dependent, implying that the spectral phase
components of a pulse travel at different velocities through the medium, introducing a
phase delay. This can be characterized by first introducing a frequency-dependent phase
term with
𝐴(𝜔)′ = 𝐴(𝜔)𝑒−𝑖𝜑(𝜔). (2.39)
The spectral phase variations corresponding to the first-, second-, and higher-order
dispersions is usually defined via the Taylor expansion of the wave vector 𝑘, giving the
spectral phase change per unit length as a function of the angular frequency 𝜔 relative to
the center frequency of the pulse 𝜔0:
𝜑(𝜔) = 𝜑(𝜔0) + (𝜔 − 𝜔0) (𝜕𝜑
𝜕𝜔) |𝜔0
+1
2(𝜔 − 𝜔0)2 (
𝜕2𝜑
𝜕𝜔2) |𝜔0
+ ⋯ . (2.40)
The zero-order term represents a common phase shift of the carrier wave that has no effect
on the pulse shape and phase distortions. The first-order term introduces the linear change
of the phase in the frequency domain, where the corresponding time domain component is
commonly referred to as “group delay.”
Qualitatively, the higher-order terms of the expansion are a measure of the change
of the group delay with respect to wavelength and have a significant impact pulse dynamics
22
during propagation. The GDD describes how the delay changes during propagation inside
a dispersive medium and is given by
GDD = (𝜕2𝜑
𝜕𝜔2) |𝜔0 (2.41)
and is typically given in units of fs2.
The third-order term of the expansion is associated with the cubic spectral phase
variations and is known as third-order dispersion (TOD), where
TOD = (𝜕3𝜑
𝜕𝜔3) |𝜔0 (2.42)
and has units of fs3. This process leads to a steepening of one edge of the pulse and a
stretching of the other, which can eventually lead to a separation of the pulse, commonly
referred to as “pulse breakup” [68]. TOD can be the cause of unforeseen pulse defects due
to the difficulty involved in controlling material properties in manufacturing. Optical
coatings that are widely available can reduce GDD or be able to achieve discrete levels of
GDD. However, balancing the needs for an ultrafast system’s high-power or ultra-
broadband reflectivity usually comes at the cost of significant TOD, leading to unwanted
pulse distortions. Controlling the net intracavity dispersion is critical for achieving ultrafast
pulses (especially those in the few-cycle regime). This is normally achieved once the
quadradic and higher-order spectral phase terms in a single round-trip are negligible across
the spectral bandwidth of the pulse. The accumulated dispersion may result from several
sources, some of which will be discussed in the next section.
2.3.2 Sources of Dispersion
Material dispersion is associated with the frequency-dependent refractive index of
a dielectric medium, which, in an OPO, is introduced by the nonlinear crystal. For
propagation in bulk dielectric materials, the dispersion can be determined in terms of the
rate of change of the index with respect to the wavelength. The wavelength-dependent
refractive index is available for many materials through the use of a Sellmeier equation
23
[69, 70]. Therefore, in practice it is much more useful to define the GDD and TOD in terms
of the refractive index and wavelength, which are given by
GDD =𝜆3𝑧
2𝜋𝑐2
𝑑2𝑛
𝑑𝜆2 (2.43)
and
TOD = −𝜆3𝑧
2𝜋𝑐2 (3𝑑2𝑛
𝑑𝜆2 + 𝜆𝑑3𝑛
𝑑𝜆3). (2.44)
Contrary to material dispersion, geometrical dispersion arises from the wavelength-
dependent path lengths that can be overserved in optical systems that have angular
dispersion, such as prisms or diffraction gratings. The GDD and TOD of these dispersive
elements may be controllable by a careful combination of both the materials and layout
used for dispersion compensation.
The use of a prism to control dispersion (both inside or outside the cavity) requires
careful calculation of the material dispersion introduced by traveling through additional
glass and the relative angles of incidence for the cut of the prism. This can be calculated
using [71, 72]
GDD =𝜕2𝜑
𝜕𝜔2 =𝜆3
𝜋𝑐2𝑟2
𝑑2𝐼
𝑑𝜆2. (2.45)
Another common method to achieve geometrical dispersion is the use of diffraction
gratings, although none were used in this investigation. The GDD available from a pair of
gratings and the relevant properties of such devices is given in [73, 74].
Another alternative that has been widely used in fs lasers is chirped mirrors with
multilayer coatings [75, 76]. The use of chirped mirrors allows one to add discrete amounts
of GDD to the laser with low loss; these mirrors can be specifically designed to compensate
for higher orders of dispersion [77]. While chirped mirrors usually limit the available GDD
to a few fs2, Gires-Tournois interferometer (GTI) mirrors have been used to generate larger
amounts of negative GDD inside a laser resonator [78, 79].
24
2.3.3 Self-phase Modulation
Self-phase modulation (SPM) occurs when an optical pulse with sufficiently high
intensity changes the refractive index of the material in such a way that the phase of the
pulse is affected. The origin of this effect is directly related to the optical Kerr effect and
can be characterized by a refractive index according to [51, 80]
𝑛 = 𝑛0 + 𝑛2𝐼(𝑡), (2.46)
where 𝐼(𝑡) = 2𝑛0𝜖0𝑐|𝐴(𝑡)|2. It is assumed that the medium is able to respond
instantaneously to the pulse and the length of the medium is sufficiently small that the
optical pulse will not be shaped by the medium. The resulting frequency shift of the pulse
after traveling through a medium with length 𝐿 can be expressed as
𝜑𝑁𝐿(𝑡) = −𝑛2𝐼(𝑡)𝜔0𝐿/𝑐. (2.47)
The result of the time-varying phase component of the wave is that the spectrum will be
modified and, in most cases, broader than the initial pulse. In such cases the center of the
pulse undergoes a nearly linear positive chirp, which can be compensated for with an equal
amount of negative GDD, as is commonly done with systems employing temporal solitons.
2.4 Pulse Characterization Techniques
Temporal properties of ultrafast pulses are not accessible with any direct electrical
measurement technique. With the growing popularity of ultrafast systems in the last few
decades, many techniques have been created to either estimate or precisely acquire the
temporal shape. Ultrafast pulses must be sampled with the use of a second ultrafast pulse
and measured indirectly. One commonly employed estimation is temporal autocorrelation.
The interferometric autocorrelation function is the correlation of the electric field with
itself [81]:
𝑔2(𝜏) =∫ |{𝐸(𝑡)+𝐸(𝑡−𝜏)}2|
2𝑑𝑡
∞−∞
∫ |𝐸2(𝑡)|2𝑑𝑡∞
−∞
, (2.48)
25
requiring two identical pulses with a variable delay 𝜏 between them. The most common
experimental setup is a classical Michelson interferometer with a beam splitter providing
equal power to the pulse in each arm. The length of one arm of the interferometer is
repetitively changed to induce a delay from −𝜏 to 𝜏. The two pulses are sent to a nonlinear
crystal, where the SHG signal of the interfering pulses is measured, normally using a
photodiode or a photomultiplier tube. If the detector has insufficient bandwidth, the
autocorrelation fringes become smeared into averaged traces known as an intensity
autocorrelation, analytically described as
𝑠(𝜏) = 2∫ 𝐼(𝑡)𝐼(𝑡−𝜏)𝑑𝑡
∞−∞
∫ 𝐼2(𝑡)𝑑𝑡∞
−∞
. (2.49)
The measured autocorrelation signal is always symmetric and requires an assumption of
the pulse shape to calculate the pulse duration. For pulses longer than a few cycles, this
assumption can be normally justified by mode-locking, such as the case with soliton pulses
having a sech2 pulse shape.
Often, the spectrum of the pulse used in the autocorrelation is measured
simultaneously (or separately given the same operating conditions) to determine qualitative
effects of the pulse’s phase. The width of the spectrum can easily be compared the to
calculated width of the pulse. If the TBP has not been minimized for the given pulse shape,
uncompensated GDD and higher-order dispersion can be attributed to the increase in pulse
duration.
Because the spectral phase cannot be determined with this approach, it is impossible
to retrieve the exact pulse shape. For pulses containing complicated spectra and complex
phase profiles, frequency-resolved optical gating (FROG) or spectral phase interferometry
for direct electric-field reconstruction (SPIDER) offer a much more systematic way to
obtain temporal shape of the pulse [82-84]. These techniques can provide the information
necessary for a true characterization of the pulse profile and are particularly useful for few-
cycle ultrafast pulses.
26
3 Thin-Disk Mode-Locked Pump
Laser
A critical component to a synchronously pumped OPO is the pump laser. This
section provides a description of the home-built thin-disk laser used to pump the ultrafast
OPO. First, a brief history of thin-disk systems is presented. The fundamental properties
of Yb:YAG and physics for operating thin-disk lasers at high powers are discussed.
Modifications to the design of this laser relative to previous system are described, with
special attention to the active multipass cavity used to extend the cavity length and achieve
high-energy pulses at high average powers. Finally, the performance of the laser as a pump
source is characterized.
3.1 A Review of Thin-Disk Lasers
The creation of the thin-disk laser in 1994 gave rise to a reliable source of scalable
ultrafast pulses that has been in strict competition with fiber- and slab- based oscillators
[85]. The common point between these technologies is the cooling geometry of the gain
medium, which is suitable for high-average-power operation and power scaling. Among
these, thin-disk technology is ideally suited for short pulses from the minimization of both
nonlinearities and thermal distortions [86].
Thin-disk mode-locked oscillators and amplifiers have both gained significant
ground in the past few years toward the power scaling of ultrafast pulses [87-90].
Unprecedented high-energy and average-power levels can be reached directly from a
passively mode-locked oscillator without any external amplification. The advantages of
this oscillator over amplifier systems with similar performance are in terms of noise level,
27
pulse quality, reliably, long-term stability, and complexity, if adequate engineering effort
is applied.
Most of the energy and power scaling of mode-locked thin-disk oscillators has used
Yb:YAG as the gain medium [91]. Many alternative Yb-doped materials are currently
being investigated to improve thin-disk systems by increasing the available gain
bandwidth, which has already been shown to produce pulses with durations less than 200
fs [92-96].
The thin-disk mode-locked laser (TDML) used in this study was based on earlier
work that has since been surpassed due to advances in both systems engineering and
material properties [97, 98]. The TDML was a home-built laser that helped to improve the
expertise needed to build a complicated free-space oscillator as well as serve as a test bed
for the capabilities in power-scaling pump sources. With the recent advancements to thin-
disk technology, it is obvious that these systems can be used as extraordinary pump
sources, well surpassing traditional pump lasers.
3.2 Principles of Thin-Disk Operation
3.2.1 Thin-Disk Laser
Thin-disk lasers can achieve stable operation at extremely high average powers by
using a material thickness significantly smaller than the spot diameter of the pump and
laser mode [85]. The thin-disk is mounted on a heat sink to allow for nearly one-
dimensional heat flow, which reduces the transverse refractive-index gradient. The thin
disk is chemically bonded to the heat sink, which is water cooled with a ceramic–diamond
composite [99]. Compared to other solid-state lasers, the ratio of the cooling surface to the
pumped volume is increased, which is a basic advantage to extracting high average powers
from a small volume [100].
An antireflection (AR) coating is placed on the front of the disk to minimize the cw
pump and laser reflectivity and a high-reflection (HR) coating on the back surface. This
28
allows the thin disk to act as an end mirror for the pumping geometry and the laser cavity
while being actively cooled.
Since the thickness of the disk is ~100 µm, the absorption efficiency of the pump
light is very low. To get a reasonable efficiency, the unabsorbed cw-pump beam is re-
imaged onto the disk several times, as shown in Fig 3.1. The thin-disk laser head used in
this work was provided by TRUMPF Laser GmbH, which was based on the concept of
pump geometry allowing up to 20 passes of pump light through the thin disk [85].
Figure 3.1: Schematic of the thin-disk laser head. The parabolic mirror allows for 20 passes
of pump light through the thin disk by using several roof prisms (not shown here). Ten
passes are completed before the pump beam is reflected [101]. The front of the disk is AR
coated for 940 nm and 1030 nm and HR coated on the back at the same wavelengths.
3.2.2 Yb:YAG as a Laser Material
The spectroscopic properties of Yb3+-doped laser materials are based on a simple
[Xe]4f116s2 electronic structure, as shown in Fig 3.2(a). Two manifolds, 2F7/2 and its
excited-state counterpart 2F5/2, and their subordinate Stark levels participate in the lasing
process. The two manifolds and the spectral distribution of the cross section are shown in
Fig 3.2(a). Since YAG has a relatively high Debye temperature (~ 550 K) and Stark levels
29
with a distance ≈1000 cm-1 in between one another, a Boltzmann population distribution
between them will be established at the lattice temperature in less thn 10 ps [102].
Figure 3.2: (a) Energy levels for Yb:YAG [103]; (b) absorption and emission cross section
of a 5%-doped Yb:YAG crystal at room temperature [103].
The pump ground level, which is the lowest Stark level of the lower manifold, is
populated at room temperature with a probability of 88%, while the ground level is given
by the upper three Stark levels of the lower manifold, each being only 200 cm–1 apart [103].
The specific arrangement of the energy levels results in a thermal population of the lasing
ground levels at room temperatures. This results in Yb3+-doped laser materials behaving as
a quasi-three-level system and show ground-state absorption at the laser wavelength. As a
result, the lasing threshold pump power is significantly increased ( > 1.5 kW/cm2 at 300 K
[85]) in comparison to operation at lower temperatures as a result of cooling, which can
reduce the lower laser-level population and improve efficiency.
Quantum defect is one of the greatest sources of heat generation for solid-state laser
sources. A small quantum defect of 9% when pumped at 941 nm is a major advantage of
Yb3+ compared with other four-level systems. The resulting low heat deposition makes
Yb3+ an attractive material for high-power lasers. The ratio of generated heat to absorbed
energy is < 11% for Yb:YAG [85], while Nd:YAG is ~35% when pumped at 808 nm [104].
30
Small pump-absorption bandwidths require sophisticated pumping concepts, while
large bandwidths allow for conventional high-power pump sources (e.g., semiconductor
diode arrays) without strict requirements on their operating temperature to keep the
emission wavelength constant. Yb3+-doped laser materials can be pumped by many
conventional sources, such as strained layer InGaAs diode lasers in relatively large
wavelength ranges between 0.9 and 1.05 µm as shown by the absorption and emission cross
sections in Fig. 3.2(b).
While pumping at 972 nm [105] would result in a lower quantum defect than
pumping at 941 nm, the absorption bandwidth is significantly lower, requiring more
sophisticated and expensive wavelength-stabilized pump diodes. The absorption peak at
941 nm has a bandwidth roughly 5x larger than 972 nm while maintaining a low quantum
defect. The wide absorption peak at 941 nm allows one to use less-expensive cw-pump
sources that do not require fine control of the pump’s linewidth.
3.2.3 Thermal Lensing
Intense pumping of solid-state media inevitably leads to optical-phase distortions.
For this type of media, the thermally induced stress can result in a different expansion of
the front and back sides of the thin disk and bending of the disk, leading to a thermal lens.
Although the thin disk allows for improved one-dimensional heat flow over conventional
solid-state gain media, the presence of high average powers still results in some phase
distortions that can have a significant impact on laser performance.
For Yb:YAG the bending of the disk dominates for large-mode sizes on the disk
[106], resulting in defocusing. Additionally, the refractive index of the material might
change by the excitation of the Yb3+ ions. The linear polarizability of the excited ion differs
from that of the unexcited ion [107] and for intensively pumped Yb:YAG thin disks, the
index change caused by electronic mechanisms can become even larger than those caused
by thermal heating [108].
31
The thermal-lens dioptric power caused by the change in index is different when
operating under lasing or non-lasing conditions. When lasing, the dioptric power shows
an approximate linear relationship with the absorbed pump power, but under non-lasing
conditions there is a noticeable roll-off in the observable dioptric power [109]. The index
change and thermal bending lead to a spherical optical phase distortion with opposite signs,
suggesting that there must be a combination of the thickness of the thin disk and pump-
spot diameter for a specific lasing condition, such that thermal lensing vanishes.
One can compensate for spherical optical phase distortions by adjusting the stability
zone of the resonator. However, nonspherical distortions result in surface scattering losses
and higher mode operation. For this investigation, these should be negligible since it has
been shown that nonspherical phase distortions for Yb:YAG thin-disk lasers occur only for
pump powers exceeding 300 W (with optical phase distortions < 100 nm [100]).
Nonspherical phase distortions occur mostly at the edges of the pump spot suggesting that
the mode diameter of the laser is optimized when the mode overlap is 80% of the pump for
fundamental mode operation [101].
3.3 Cavity Design
To utilize the potential of thin-disk systems, a home-built Yb:YAG thin-disk mode-
locked laser (TDML) was constructed. In the following section the design of the TDML
pump is discussed.
3.3.1 Thin-Disk Head
The pump laser was a high-power diode laser module from Jenoptik, model JOLD-
250-CPXF-2P2-938-0.4. This laser can provide up to 250 W at wavelengths near 940 nm.
The power supply was a Xantrex XFR12-220 DC Supply. Operation of the laser was
operated by keeping the voltage at a near constant value of 6.05 V and varying the current
to modify the output power and wavelength.
32
The diode laser was water cooled with a Thermo Scientific NESLAB RTE-220
stand-alone chiller, capable of providing 4 liters per minute at a temperature range of 8 to
40°C. An interlock was used to protect the laser from overheating and to ensure a constant
wavelength of the pump laser. The output of the laser module was connected to a fiber
coupler, injecting the light into a fiber with a 600-µm core diameter with no alignment or
fine tuning needed.
Power measurements were made for a specific temperature setting, which was used
to tune the wavelength output at optimal power. In all cases the spectrum changed as the
current supplied to the diode was increased. Before an optimal pump power was identified,
spectral measurements were made across the operating powers for different temperatures
to ensure that the correct spectrum would be used after the pump power had been
optimized.
Alignment of the pump laser onto the thin disk required optimization of six separate
degrees of freedom. The first was the proper collimation of the fiber output, which was
tested with low powers (in LED mode) over a 9-ft distance. The next were the x and y
positions of the collimation optics. Both the x and y axes are controlled using a custom
collimation package from TRUMPF. The y axis is controlled with a spring-loaded screw.
An optimum y position was chosen such that the collimation optics were in the same plane
as the thin disk. The x axis was controlled using two set screws on the left and right sides
of the collimation optics. The optimal position was chosen such that the first reflected beam
was located near the center of the thin disk.
It was crucial to ensure the flatness between the parabolic mirror and the
collimation optics. Both the collimation optics and the thin-disk head were fastened to a
custom metal block that was screwed into the optical table, as shown in Fig. 3.3. The
collimation optics allowed for rough pointing and x-axis centering, while fine tuning could
be done with optomechanical controls. The pointing of the thin-disk head was more
restricted. Slight tuning of the pointing of the parabolic mirror and roof mirrors (enclosed
in a single mount shown in red) with respect to the thin-disk mount (shown in purple) could
33
be done by rotating of the mount. The thin-disk mount was the focal point of the alignment
after making the mount flush with the height change in the plate, shown as the black line.
The 22.5-mm change in height was due to the adaptation of TRUMPF components to fit
on the optical table.
Figure 3.3: Diagram of baseplate created for the thin-disk head and collimation optics. The
collimator is shown in blue. The thin-disk mount and heat sink are shown in purple. The
parabolic mirror and roof prisms are enclosed in a metal housing, shown in red.
This mount had minor degrees of freedom to adjust the flatness between the
parabolic mirror and the collimation mount. The x and y positions of the parabolic mirror
and roof prisms could be used to fine tune the position of the mirror with respect to the
disk. The thin disk could be moved in and out of the focal plane of the parabolic mirror to
achieve the uniform pump spot needed to create a super-Gaussian mode profile.
The entire alignment procedure was necessary to create a super-Gaussian mode
profile for the pump. Figure 3.4 shows the effect of alignment on the cw-pump beam.
Individual passes of the cw-pump beams can easily be seen in Fig. 3.4(a) as bright
ellipsoidal spots. The ellipsoidal shape is due to the projection of the Gaussian beam profile
on a flat surface at an angle. The outer ring is the edge of the thin disk heat sink. The faint
ring shows the thin-disk, which is 1 cm in diameter. The steps above were used iteratively
to optimize the pump spot, which is shown in Fig 3.4(c). When all ten passes of the pump
light were properly aligned, the individual ellipsoidal spots could be combined into a single
super-Gaussian mode profile.
34
Figure 3.4: (a) Severe misalignment of the pump spot. All ten reflections of the pump spot
can be seen with poor overlap. (b) Improved alignment as the ten spots become closer to
each other. (c) A properly aligned pump spot with a super-Gaussian mode profile.
Fine adjustments to the collimation optics and the parabolic mirror were made at
high powers for optimal alignment. When the laser was operational, the thin disk was
imaged using a short-pass filter to image the green pump fluorescence. This was done to
avoid imaging of the 1030-nm laser output as well as the 940-nm pump light. Lineouts in
the x and y axis were taken from these images and used to optimize the mode profile.
3.3.2 Active Multipass Cavity
The weak small-signal gain (SSG) of a thin-disk laser appears to call for a low-loss
cavity. In many thin-disk oscillators, the intracavity energies exceed the external energies
by a factor of ten or more. This can have a significant effect on the intracavity SPM and
pulse shaping in mode-locked operation.
Normally, to increase the SSG, the doping level or the thickness of the disk must
be increased. However, without losing the advantage of the thin disk in terms of its good
thermal management (and therefore power scaling potential), a cavity configuration using
multiple passes of the laser mode through the gain medium was used. Multiple passes
through the gain media have been used in solid-state laser amplifiers with low gain rods
[110], as well as thin-disk amplifiers [111]. The use of an active multipass cavity (AMC)
compensates the low SSG by achieving many amplifications in a single round-trip and,
consequently, greater output coupling (OC) and lower nonlinearities.
35
In addition to the large OC rates available through multiple passes, the energy of
the pulse also increases. Multiple passes increase the cavity length while maintaing a
relatively constant average power, leading to an increase in the pulse energy. This is
important to consider for dispersion management and soliton formation, which is discussed
further in Sec. 3.4.1.
The number of passes in the AMC was determined by maximizing the number of
passes without sacrificing cavity stability. A maximum of 12 passes was achieved using
the cavity configuration shown in Fig. 3.5. Power instabilities and mode-locking
difficulties were minimized however when using only six passes through the AMC,
resulting in a repetition rate of 7.08 MHz.
3.3.3 Cavity Design
A schematic of the TDML based on previous thin-disk designs [98], is shown in
Fig. 3.5. All mirrors were provided by Layertec, GmbH, except for the semiconductor
saturable absorber mirror (SESAM), which was provided by BATOP, GmbH. All mirrors
denoted with M were HR with reflectivity > 99.9% from 1020 to 1040 nm with near-zero
dispersion. The GTI mirrors used for this cavity were provided by Layertec, with a
reflectivity >99.5% from 1020 to 1040 nm. GTI2 and GTI7 had a focal length of 1.5 m.
This dispersion of these mirrors is discussed further in section 3.4.1.
All mirrors were 1-in. optics with the exception of M2–M9, which were 2-in
mirrors that allowed for an increased number of passes in the AMC. The pick-off mirror
(M10) was a D-cut mirror with a shaved edge for increased clearance along the beam path
between M8 and GTI7. This also prevented beam clipping when the space between cavity
modes of successive passes in the AMC were very close together.
The focal power of M11, GTI2, and GTI7 was chosen to create a cavity mode size
of 0.95 mm on the thin disk for optimal mode matching with the cw-pump spot size. The
GTI2 and GTI7 mirrors were set at distances 2f from each other to achieve a telescopic
36
relay. This allowed for an arbitrary number of passes in the AMC without disturbing the
vital cavity parameters, mainly the spot sizes on the thin disk and the SESAM.
Figure 3.5: Diagram of the TDML cavity. The number of passes depicted has been reduced
for simplicity. SESAM: semiconductor saturable absorbing mirror; M: HR mirror; GTI:
Gires-Tournois Interferometer mirror [112].
To achieve a telescopic relay in the AMC the dioptric power of the thin-disk had to
be compensated for by adjusting the distance between M7 and M8. An ABCD matrix
calculation was performed to establish a constraint on the distance dtele between the GTI7,
M8, M9, and GIT2 in the AMC [113]. The relationship between this distance and the focal
power of the thin disk is given by
𝑑tele = 2𝑓tele −𝑓tele
2
𝑓TD, (3.1)
where ftd is the focal length of the thin disk and ftele is the focal length of GTI2/GTI7. The
design of the AMC provides a simple way to increase the number of passes through the
AMC by tilting the pick-off mirror M10 (as shown in Fig. 3.5) toward the outer edge of
GTI7, decreasing the separation between adjacent passes in the cavity. Once a suitable
distance between modes was established, M9 could be moved perpendicular to the M1
beamline to easily change the number of passes.
A thin-film polarizer was used in conjunction with a double pass through a quarter-
wave plate (QWP) as a variable output coupler. The light was s polarized inside the AMC.
37
The polarizer was Brewster cut to minimize the losses of the incoming light. After a double
pass through a QWP, a portion of the light was transferred to p polarization, which passed
through the polarizer. The output coupler had a transmission of 73%, which was optimized
for maximum power when the optical-to-optical efficiency peaked at 34%. Alignment
sensitivity of this optic was quite critical due to the lack of sufficient humidity control in
the room, which changed the Brewster angle of the s polarized beams and, consequently,
the efficient output coupling of light.
Unless gross realignment was necessary, alignment was always changed by
adjusting the tip and tilt of the M1 and the SESAM mount. Alignment of the cavity had to
be fine tuned at full power for reliable long-term operation.
3.4 Mode-Locking
To generate laser pulses, a number of lasing modes must be coupled together. When
no attempt is made to control the laser spectrum, a laser always runs on a multitude of
different modes with a spacing of 𝛿𝜈 = 𝑐/2𝐿, given by the geometry of the laser resonator.
Only on a very short timescale, given by the inverse of the optical bandwidth ∆𝜈, some or
all the modes can radiate in phase, producing a sharp feature in the laser output described
as a coherence spike. If all the modes of the laser can be made to oscillate in phase, e.g., if
they can be locked together, the laser output becomes temporally well defined, with a
period corresponding to the cavity round-trip time, giving rise to ultrafast laser pulses. A
good general review of mode-locking is given by [114].
3.4.1 Soliton Formation
For the TDML, pulsed operation was possible through temporal soliton formation.
A thorough review of soliton formation and control is given by [51], although a short
summary of the fundamental principles will be given here with their relation to pulse
duration control in the TDML.
38
Soliton formation is possible by balancing the self-phase modulation (SPM, 𝛾SPM)
of the pulse, the group-delay dispersion (GDD, 𝛽2), the pulse duration (𝜏FWHM), and the
peak power (𝜈peak2 ) of the pulse. This relationship is given by [115-117]
𝜏FWHM = √|𝛽2|
𝛾SPM|𝜈peak|
−1≈ √
1.76∙2∙0.88|𝛽2|
𝐵≈ 1.76 ∙
2∙|𝛽2|
|𝛾SPM|𝐸𝑃. (3.2)
Here, B is the B-integral and the approximation is only valid for a sech2 pulse shape. The
SPM coefficient and total amount of GDD used when applying this formula on the solitons
inside a laser resonator are specified for one complete round-trip, and both quantities must
have the opposite sign.
For an AMC-based laser with large OC, a modified version of the soliton area
theorem must be used to describe the relationship between pulse duration, external pulse
energy, total GDD, and the SPM coefficient. Assuming an exponential increase in the pulse
energy inside the cavity, the soliton area theorem can be approximated by
𝜏FWHM =≈ 1.76 ∙2∙|𝛽2|𝑙𝑛 (1−𝑂𝐶)
|𝛾𝑆𝑃𝑀|𝐸𝑃,ext. (3.3)
Due to the complexity of the mode size in the cavity, the B-integral can be quite difficult
to calculate. However, it must be precisely known to control the intracavity GDD for
control of the pulse duration. To calculate the B-integral, we first look at the change in the
refractive index when the intensity of the beam is very large. This can be expressed
mathematically as
𝑛(𝐼) = 𝑛0 + 𝑛2𝐼, (3.4)
where 𝑛0 is the linear refractive index, 𝑛2 is the nonlinear refractive index, and 𝐼 is the
pulse intensity along the beam axis, which for a Gaussian beam is given by 𝐼 = 2𝑃/𝐴. The
phase change due to the nonlinear refractive index is given by [118]
𝑑𝜑(𝑧) = −2𝜋
𝜆[𝑛0 + 𝑛2𝐼(𝑧)]𝑑𝑧. (3.5)
39
The round-trip B-integral can be calculated by [101]
𝐵 = ∫ 𝑑𝜑(𝑧) 𝑑𝑧 =2𝜋
𝜆∫ 𝑛2𝐼peak(𝑧)𝑑𝑧 = ∑ 𝛾𝑆𝑃𝑀(𝑧𝑖)𝑃peak(𝑧𝑖)𝑖
2𝐿
0, (3.6)
where L is the length of the cavity. For resonators with low output coupling, 𝐼(𝑧) can be
calculated for one complete round-trip. In the case of a laser using an AMC, the peak power
strongly depends on the position of the pulse with respect to the output coupler and any
other gain or loss element. The calculation of 𝛾SPM can be simplified for telescopic image
relays of Gaussian beams. For a Gaussian beam with radius 𝑤, 𝛾SPM is given by
𝛾𝑆𝑃𝑀 = ∫4𝑛2
𝜆𝑤2(𝑧)𝑑𝑧
∆𝐿
0. (3.7)
For a Gaussian beam over a propagation distance through a telescopic arrangement, we see
that [101]
∫1
𝑤2(𝑧)𝑑𝑧
′4𝑓′
0=
𝜋2
𝜆. (3.8)
Equation (3.7) becomes
𝛾SPM =4𝑛2
𝜆∙ 2 ∙ 𝑁img ∙
𝜋2
𝜆𝑚−1 ≈ 2 ∙ 𝑁img1.4885 ∙ 10−3𝑀𝑊−1. (3.9)
𝑁𝑖𝑚𝑔 is given by the number of passes through the AMC, corresponding to one pass
through a 4f imaging system, plus the number of telescopic arrangements in the remaining
cavity arm and some fraction giving the SPM coefficient for the rest of the cavity. The
factor of 2 accounts for the fact that the SPM coefficient is calculated for one complete
round-trip. Therefore, the SPM coefficient scales linearly with the number of optical
images inside the laser cavity. For our cavity configuration, 𝑁𝑖𝑚𝑔 = 6. Using Eq. (3.9), we
can accurately calculate the B-integral, allowing for adequate control of the pulse duration
with appropriate control of the GDD.
40
The GDD per mirror was specified at –1300 fs2 at 1030 nm, although the dispersion
varied by ±150 fs2 over the clear aperture of the mirror. Measurements of the spatially
dependent GDD, provided by Layertec, were used to calculate the total GDD of the cavity,
which for the optimal output power of the TDML was –0.125 ps2. Fine control of the GDD
was not possible and the total GDD could be modified only by swapping GTI mirrors for
HR mirrors or by changing the number of passes in the AMC. Since the number of passes,
was optimized to provide the greatest stability with the largest number of passes only
swapping HR mirrors with GTI mirrors could be used to control the GDD, resulting in
limited control of the pulse duration.
3.4.2 Initiation of Mode-Locking
For passive mode-locking of the TDML, an intracavity SESAM was used [119-
121]. Upon the incidence of laser radiation, due to the strong absorption bleaching, caused
mostly by band-filling through Pauli’s exclusion principle, semiconductors show a
nonlinear transmission characteristic, which makes them suitable to be used as saturable
absorbers. Epitaxial growth techniques, such as molecular beam epitaxy and metal-organic
chemical vapor deposition, can be used with different growth parameters to tailor linear
and nonlinear optical properties of semiconductor layer structures. The advanced growth
and processing technology offers the possibility of precise control of the optical
nonlinearity of these devices.
The key design parameters of a SESAM are its saturation behavior, the dynamic
response and the wavelength of operation. The saturation properties of a SESAM can be
characterized after determining the reflectivity R for various incident pulse energy fluences
F. Nonlinear optical absorption and refraction in general are investigated by using z-scan
experiments [122-126], while time-resolved experiments are performed with “pump–
probe” setups [127]. SESAM specific measurement techniques are also reviewed in Haiml
et al. [128].
41
The key component for efficient initiation of mode-locking is making sure that the
losses for pulsed operation are less than the losses of cw radiation. This is achieved by
having a high modulation depth ΔR. The reflectivity losses for cw operation can be seen
when the reflectivity of the SESAM is considered as a function of pulse fluence. The
reflectivity of a SESAM is given by
𝑅 = 1 − 𝐴𝑛𝑠 −𝛥𝑅∙𝐹sat
𝐹∙𝑙𝑛(1+𝐹
𝐹𝑠𝑎𝑡)
−𝛽∙𝐹∙𝑑
𝜏𝑃, (3.10)
where Ans is the nonsaturable absorption loss, Fsat is the saturation fluence, F is the pulse
fluence, τP is the pulse duration, 𝑑 is the thickness of the absorption layer, and β is the two-
photon absorption coefficient. The modulation depth, which is calculated by taking the
difference between reflectivity of the pulse and cw radiation, must be carefully considered
for the initiation of mode-locking and control of mode-locking instabilities.
When the TDML was constructed, the options for choice parameters of
commercially available SESAM’s were quite limited. In general, modulation depth and
saturation fluence of the SESAM were tied in such a way that mode-locking instabilities
(discussed in the next section) were difficult to eliminate. Furthermore, choices in
relaxation times, which are a critical parameter for the behavior of the SESAM as a slow-
saturable absorber, were limited.
For this experiment, a BATOP SAM-1040-4-5ps-4.0-12.7s-c SESAM was chosen.
The absorbance was 4% with a modulation depth of 2.6% and a relaxation time of 5 ps.
The chip was 4.0 mm square on a 12.7-mm-diameter copper heat sink. This heat sink was
attached to a custom water-cooled kinematic mount to prevent damage and to limit thermal
lensing effects from use at high average powers. The saturation fluence of 40 µJ/cm2 was
chosen to create stable pulsing at maximum output power.
3.4.3 Mode-Locking Instabilities
Passive continuous-wave mode-locking (CWML) is ideally characterized by one
single pulse oscillating inside the laser cavity with the same pulse energy, amplitude and
42
pulse duration for each round-trip. Although stable operation could be achieved for >8 h
over the course of a few years, it was necessary to overcome instabilities that interfere with
stable pulsing by carefully designing the cavity. These instabilities included Q-switching,
cw background and multiple pulsing, which were affected by the gain material, cavity
design, and choice of SESAM. These instabilities had to be understood and controlled for
the TDML to function adequately as a pump source for the OPO.
When pulse energies are below a certain marginal value, determined by both the
gain medium and the saturable absorber, Q-switched mode-locking (QML) instabilities
will occur as a result of undamped relaxation oscillations [129]. Historically, the saturation
energies of most solid-state lasers were large enough to ensure that saturable absorbers
would always produce QML behavior.
In 1992 the invention of semiconductor saturable absorbers led to saturation
fluences that were able to suppress the QML output of solid-state lasers [130, 131]. The
pulse energy required to overcome QML for a saturable absorber with a relaxation time
much shorter than the laser’s repetition rate and small enough pulse fluences to prevent
effects like two-photon absorption is given by [131]
𝐸𝑃2 > 𝐸𝑠𝑎𝑡,𝑔𝐸𝑠𝑎𝑡,𝑙∆𝑅. (3.11)
Esat,g and Esat,l are the saturation energies for the gain and saturable absorber, respectively.
EP is the intracavity pulse energy and ΔR is the modulation depth of the SESAM. When
QML instabilities occur, the amplitudes of the mode-locked pulses are controlled by an
oscillating envelope function with a frequency lower than the repetition rate of the laser.
The maximum pulse energy can be significantly increased, which can lead to damaged
optical components.
The choice of the SESAM, mode size and intracavity power are the only points of
control to eliminate the QML instability. Due to limitations from the collimator and
wanting to avoid paying for additional collimation optics, 𝐸𝑠𝑎𝑡,𝑔 = 79.2 µW. The spot size
on the SESAM could be decreased to ensure that QML could be overcome at lower
43
energies. The focal length of M11 in Fig. 3.5 was chosen to be 750 mm to create a 600 µm
spot size on the SESAM, resulting in 𝐸sat,𝑙 = 2.74 mW with a modulation depth of 2.4%.
The resulting pulse energy to overcome QML required an average power of 30.7 W with a
cavity repetition rate of 7.08 MHz, which was well within the capabilities of TDML.
Various contributing factors can give rise to a gain advantage of a cw background.
At the center of the spectral gain distribution, the continuum might have a gain advantage
when compared to the spectrum of the pulse due to the limited gain bandwidth. Caused by
an additional loss provided by the saturable absorber for the cw background and any
additional pulses, these instabilities are suppressed in the case of stable CWML. For soliton
mode-locking, the relaxation time of the saturable absorber might be larger than the pulse
itself. Therefore, the gain window is relatively large, giving rise for a possible amplification
of the continuum.
The cw background did not affect the total average power of the TDML. As shown
in Fig. 3.6, a sharp peak located at 1030.8 nm was clearly visible in the spectrum in the
presence of cw-background. The total power of the cw background could be calculated by
fitting the spectrum to a sech2 pulse shape, subtracting that from the measured spectrum
and comparing the area between the two to give a percentage of their contribution to the
total average power.
Regardless of the cw background’s contribution to the total power, the average
output power of the TDML was unaffected. This was confirmed by simultaneous
measurements of the spectrum and output power, which showed that if the cavity was
CWML, the total power stayed stable within 200 mW.
44
Figure 3.6: Example of cw background by changing the alignment of the cavity. Output
power remained constant but the spectrum of the TDML changes significantly. As power
shifts into the pulse, the spectrum become wider (allowing for shorter pulses) and
experiences a slight red shift. The green curve represents the best cw background reduction
through alignment only, even though it was completely removed with proper wavelength
calibration of the pump laser, as shown in Fig. 3.10(b).
When strong cw background was present, the pulse duration increased, as would
be expected when pulse energy is being shifted into cw radiation. Since the total average
power of the TDML remained unchanged despite the amount of cw background, the pulse
energy was reduced as the amount of cw light grew. Due to soliton mode-locking, the result
of this energy transfer was an increase in the pulse duration to balance the soliton theorem
as shown in Eq. (3.2). This was tested and verified with autocorrelation measurements at
varying amounts of cw background.
While the impact of each of the factors that contribute to the cw background is not
clearly understood in the TDML, both the alignment of the cavity and the wavelength of
the cw pump beam had a significant impact on the presence of the cw background. The cw
light could be completely suppressed by carefully aligning the cavity and maintaining
proper calibration of the pump wavelength.
Another instability that had to be considered was multiple pulsing. Multiple pulsing
can occur when, due to gain filtering, double pulses (or higher combinations) with a
respectively smaller spectrum experience a gain advantage large enough to overcome
45
additional losses required for saturating the SESAM [132]. There is a great deal of
information about multiple pulsing in thin-disk oscillators and SESAM-based devices since
it is critical to the initial design of the system [117, 133]. In the TDML, double pulsing was
observed but only when the laser was pushed well beyond maximum efficiency. This
source of instability was not nearly as much of a concern for this study as the two
mentioned above.
3.5 The TDML as a Pump Source
3.5.1 Output Power and Stability Regimes
To maintain safe operation of the TDML, efficient power extraction of the absorbed
pump light on the thin disk was necessary. The efficiency falloff at high powers is well
known in thin-disk oscillators, and maintaining an optical to optical efficiency greater than
30% was required to prevent damage [98]. The efficiency of the TDML is plotted in Fig.
3.7.
Figure 3.7: Efficiency of the TDML as a function of pump power. Pump power was
increased until falloff was noticeable and efficiency was near minimum safety levels. The
different regimes of operation are color coded. CW: continuous-wave operation; QML: Q-
switched mode-locked; CWML: continuous-wave mode-locked (stable); DP: double
pulsing.
46
The SESAM could not initiate mode-locking until the pulse fluence rose high
enough to create a substantial difference between cw losses and pulsed losses. Continuous-
wave operation is present until the pump power reaches roughly 55-W. As the power
increases, the TDML begins to operate in QML. Because of the risk of damage, the pump
power is rapidly increased during this time to minimize operation in QML. CWML is
achieved for a relatively small region. For stability reasons, the TDML was operated near
the top of the efficiency curve. This removed long-term behavior from sporadically
switching to either QML or double pulsing.
The TDML operated at maximum stable power to ensure a constant pulse duration
as a pump source. The maximum average power used to pump the OPO was 44.8 W, which
was measured after the losses introduced by relay optics and a variable throttle outside the
cavity. A throttle was introduced outside the cavity to change the available power to the
OPO without changing the cavity dynamics of the TDML. The throttle was a half-wave
plate used in combination with a thin-film polarizer that allowed for partial convergence
of the p-polarized output light to be converted into s-polarized light and reflected off the
polarizer. The s-polarized light was sent to a high-power beam dump, while the other beam
was sent to either the diagnostics or the OPO cavity. With careful alignment, the output
power of the TDML could be varied between 99.5% and 0.5% of the available power with
negligible impact on the beam quality and pulse duration. The throttle made it possible to
use a pulse with variable power without impacting the pulse duration, which was of critical
importance for the TDML to operate as an adequate pump source for the OPO.
3.5.2 Pulse Duration
An autocorrelation was performed to measure the pulse duration with a commercial
FR-103MN/LiIO3 autocorrelator from Femtochrome. A typical autocorrelation trace,
averaged over ten acquisitions, is shown in Fig. 3.8(a). The FWHM of the autocorrelation
was 1.5 ps, corresponding to a pulse with of 1.0 ps, assuming a sech2 pulse shape.
47
Figure 3.8: (a) Autocorrelation trace of the TDML; (b) corresponding spectrum of the
TDML pulse [112].
Pulse widths as high as 2.1 ps were recorded, which depended both on operation at
lower powers and with more GTI mirrors than were shown in Fig. 3.5. Since GTI mirrors
were the dominant form of negative dispersion in the cavity, decreasing the number of GTI
mirrors should also decrease the pulse duration, which is evident from Eq. (3.2). Pulse
duration tests were performed with fewer GTI mirrors; however, mode-locking instabilities
dominated over the full range of available power. Although shorter pulse durations were
desirable as a pump source, 1.0 ps was adequate for this study.
The spectrum corresponding to the autocorrelation measurement is shown in Fig.
3.8(b) with a FWHM of 1.1-nm. The spectrum revealed that the time-bandwidth product
[51] of the pulse 0.316, showing near transform limited operation for a sech2 pulse, which
is to be expected from soliton mode-locking.
The spectrum was typically measured with an Ocean Optics 4000 spectrometer.
The spectrometer used an H6 composite grating with optimal performance for 500 to 1100
nm. The slit width was 5 µm to maximize resolution with the ample power available from
the TDML. For ease of use, a multimode fiber was used to couple light into the
spectrometer; however, this produced heavy fringes during normal use. These fringes could
be eliminated by quickly shaking the fiber during spectral measurements that were
averaged 20x with 50-ms acquisition windows.
48
The spectrometer was the primary tool to determine if stable mode-locking had
been achieved, as well as optimization of alignment through the removal of cw background.
A higher-resolution optical spectrum analyzer was also used to verify resolution of the
spectral width. Due to the low scanning speeds and the bulk of the instrument, it was
deemed unnecessary for daily use.
Both cw and QML operations showed narrow peaks in the spectrum while cwML
had a broad sech2 shape. This metric was most helpful when determining if the TDML had
stable mode-locking or if adjustments to the alignment were necessary. There was a
negligible difference in the output power in each of these regimes and the spectrum
provided a quick method by which to determine not only if the TDML was CWML but if
cw background had been suppressed.
3.5.3 Beam Quality
High beam quality was necessary for the TDML to perform as an adequate pump
source for the OPO. Multiple beam-quality measurements were performed to ensure that
the beam could be focused inside a crystal and could accurately represent the beam
parameters used to calculate the gain of the OPO. Images of the output beam were used to
qualitatively characterize the beam shape and 𝑀2 measurements were taken to verify the
beam’s Gaussian behavior.
The near-field beam profile had few irregularities and was quite Gaussian, as shown
in Fig. 3.9. The beam profile looks fairly uniform and Gaussian, which is to be expected
from the output of an oscillator. However, the beam is slightly tilted off-axis and elongated
slightly in the x direction. Slight astigmatism of the pump beam was unavoidable due to
off-axis angles of incidence on spherical mirrors inside the AMC. In order to obtain a
more-quantitative analysis of beam quality, an 𝑀2 measurement was performed on the
TDML output [134].
49
Figure 3.9 Image of the near-field beam profile of the TDML. The image was taken with
an Imaging Source DMK 41BU02 camera with a 1030-nm bandpass filter.
Despite the astigmatism, the measured beam quality was fairly high with a 𝑀2 <
1.4, which is consistent with previous cavities of similar design [98]. The locations of the
focal point on the x and y axes were separated by 30 mm. 𝑀2 measurements were
performed using a knife-edge technique that allowed for beam characterization at high
powers without throttling the pump beam below 5% [134, 135]. The beam size was
measured using an 84/16 method to directly measure the 1/e2 spot size [136]. A 400-mm-
focal-length lens was used to focus the beam, ensuring that the focal spot was large enough
to be measured and the beam could be adequately sampled though focus.
3.5.4 Temporal Stability
The TDML was not locked to an external source, as is typically done for many
mode-locked oscillators to maximize temporal stability [137]. Without external locking,
variations in pulse amplitude and long-term drift were a significant concern. These
characteristics were investigated to determine their impact on the TDML as a pump source.
The variation in pulse amplitude was measured using oscilloscope traces from a
DET10A Thorlabs photodetector. The pulse amplitude measured from the photodetector
has a linear relationship to the peak power of the pulse. Traces were taken with maximum
resolution on a 300-MHz oscilloscope for accuracy in the peak voltages. These traces were
50
analyzed in MATLAB by gating the temporal window of an individual pulse and
characterizing the entire acquisition, which had over one million pulses. The maximum
value of the pulse amplitude was stored; then a mean and standard deviation was calculated
from these values. The standard deviation was calculated to be less than 0.5% of the peak
amplitude and was consistent for multiple traces taken.
Long-term drift was evident when the pulse train was monitored with a radio-
frequency (rf) spectrum analyzer. Drift was characterized by measuring the repetition rate
over multiple hours of use, showing a typical change of 120 Hz in 4 h of operation,
corresponding to a change in cavity length of ~350 µm. This neglects the rapid change that
occurred in the first 30 min of operation during the warm-up period of the TDML. The
change in cavity length was likely due to heating inside the TDML enclosure, which saw
a typical rise of 2.5°C. The temperature’s effect on optomechanics inside the enclosure
would always cause the cavity to decrease in length and then reset to almost the exact same
length after given sufficient time to cool.
51
4 Design of the Optical Parametric
Oscillator
The construction of a cavity that could be synchronously pumped by the TDML
just presented required careful design. In this chapter, the most important aspects of the
OPO design are described. Section 4.1 is dedicated to the nonlinear crystal. The reasoning
behind crystal choice is given. Material properties of the chosen crystal are discussed with
particular focus on the linear absorption. The section concludes with the phase-matching
geometry and choice of optical coatings for the crystal. Section 4.2 describes cavities that
were explored during this investigation. Finally, in Sec. 4.2.3, an ABCD model was used
to hypothesize how the cavity design principles could be used to achieve longer cavity
lengths and obtain higher pulse energies.
4.1 Nonlinear crystal
4.1.1 Availability of Crystals
The choice of the nonlinear crystal was a critical design consideration of the OPO.
The key factors for determining a proper crystal were the transparency range, phase-
matching capabilities, effective nonlinearity, and commercial availability.
To get the maximum output power from the OPO, it was desirable to use direct
1030-nm output of the TDML without any frequency conversion. The nonlinear crystal
must be transparent not only for the pump but also for the signal and idler wavelengths.
With a pump wavelength near 1 µm, the signal and idler wavelengths could span between
1250 and 6000 nm [138-140]. Appropriate choice of the signal wavelength was critical
when considering possible absorption of most conventional crystals in this wavelength
range [141]. With high average powers, even if the idler is not being resonated (therefore
52
having significantly less power than the signal), high absorption at longer wavelengths can
create unwanted heating inside the crystal [142].
If the OPO is operated near degeneracy, the signal and idler wavelengths will be
nearly the same, which limits the transparency range requirements of the crystal.
Additionally, this allows the crystal length to be much longer than normal while
maintaining enough bandwidth to create ultrashort pulses [143]. Operating at exact
degeneracy is beneficial because both the signal and idler will be in phase, creating
additional output power from the combination of both beams. However, it removes the
inherent benefit of tunability from the OPO, restricting the output to a single central
wavelength as well as increased requirements on oscillator stability [5, 144].
Phase matching was a critical design consideration of the OPO. Multiple methods
could be employed to achieve the phase-matching condition required to make the
parametric process efficient, namely critically phase matching, quasi-phase matching, and
noncritical phase matching (sometimes called temperature phase matching). Choosing of
the type of method to employ for this study relied on the ability to power scale these
methods.
Noncritically phase-matched systems are typically not used in high-power ultrafast
systems since these devices are typically employed for their ease of use and tunability in a
single device [55, 145, 146]. Difficulties in power scaling these devices stem from the
limited phase-matching bandwidth and temperature dependence, which is difficult to
control at high average powers. Also, the damage threshold of ovens used to control the
temperature typically have a damage threshold lower than the crystals themselves, making
this option the least attractive of the three.
Recent advances to femtosecond quasi-phase-matched systems have shown
potential for their power scaling capabilities [3, 147]. However, to achieve broadband
phase-matching at high average powers, exotic crystal designs are required, greatly
increasing the cost and complexity of these systems. One notable crystal using this type of
53
phase matching is periodically polled lithium niobate (PPNL) and doped variations, which
have shown great promise for high-power ultrafast OPO’s [32, 41, 148, 149]. There are
concerns, however, that quasi-phase-matched systems can be applied only to crystals with
limited thickness, which excludes large-aperture devices for high average powers.
Critically phase-matched systems have shown great potential for power scaling,
limited only by the size of the crystal growth [44, 150, 151]. Additionally, techniques used
in different experiments can easily be applied to other systems as long as phase matching
can be achieved in regions with relatively high effective nonlinearities. As such, the search
for crystals for this investigation was limited to ones using critical phase matching. Figure
4.1 summarizes the properties of various crystals that were considered.
Of the crystals considered, bismuth triborate (BiB3O6, BiBO) was the most
promising nonlinear crystal due to the combination of transparency, effective nonlinearity,
damage threshold and maturity of the crystal development. Although KTA and KTP have
been used extensively in parametric devices, the effective nonlinearity was not useful for
near degenerate operation with a 1-µm pump. CSP and AGS were also attractive due to
their high effective nonlinearity and transparency, however, the low damage threshold
made them problematic for power scaling. Commonly used crystals like BBO and LBO
were also considered; however, the transparency of these crystals limited the power scaling
potential due to high absorption.
Although the transparency range of these crystals (noted in Fig. 4.1) seemed useful
for operation near 2 µm, transmission values greater than 95% were desirable for scalability
into higher powers. Typically, when transparency is reported, all wavelengths providing
transparency values greater than 50% are reported. However, these levels of absorption
would result in significant thermal problems at the anticipated high average powers of the
OPO. Exotic crystals, such as BGS, were highly attractive but were not obtainable since
the growth and characterization of these crystals are in their infancy.
54
Crystal Transparency
Range
(nm)
Usable*
Effective
Nonlinearity
(pm/V)
Damage
Threshold
(J/cm2)
Maturity
AgGaS2
(AGS) 470 to 13,000 12.5 2.3 √√√
BaB2O4
(BBO) 190 to 2250 1.9 13 √√√
BiB3O6
(BiBO) 286 to 2500 2.1 10 √√
BaGa4S7
(BGS) 350 to 10,500 5.4 25 √
CdSiP2
(CSP) 500 to 9000 85 3.0 √√
LiB3O5
(LBO) 160 to 2600 0.6 34 √√√
KTiOAsO4
(KTA) 350 to 4000 0.0 15 √√√
KTiOPO4
(KTP) 350 to 4500 0.0 5.0 √√√
ZnGeP2
(ZGP) 720 to12,000 75 3.0 √√
Figure 4.1: Table of some of the relevant parameters for various critically phase-matched
crystals investigated as a gain medium for the OPO [152-162]. The transparency range
corresponds to transparencies greater than 50% for typical crystal lengths. The maturity
level is ranked from one to three check marks, with three being the highest level of
maturity. *Usable refers to the effective nonlinearity in the region that can be phase
matched for a 1-µm pump and a near-2-µm signal.
55
BiBO was the best option for a power-scalable ultrafast OPO. It has been used in
numerous OPO’s and has had most of its relevant material properties characterized [156,
163, 164]. The parameters of the crystal relevant to the operation of a scalable ultrafast
OPO are discussed in depth in the following subsections.
4.1.2 BiBO Transparency
The transparency reported from earlier investigations was made using a BiBO
crystal attractive for operation near 2 µm [156]. Figure 4.2 shows the unpolarized
transmission of a 1-mm BiBO crystal measured by Hellwig et al. with reflection losses
from an uncoated crystal. Anticipated absorption from 1950 to 2150 nm was less than 5%.
The sharp drop in transmission near 2250 nm was well outside the anticipated wavelengths
of the OPO.
Figure 4.2: Unpolarized transmission spectrum of BiBO [156].
Preliminary tests on the BiBO crystals used in this study showed unanticipated
signs of heating. To investigate the source of this heating, it was necessary to measure the
transmission of the BiBO crystals that were used. Measurements were attempted at LLE
with a Lambda 900 spectrophotometer from PerkinElmer. However, lack of sensitivity in
the detector along with alignment difficulties made it impossible to obtain a meaningful
56
transmission spectrum. Transmission data were available for wavelengths up to 3 µm but
this required a switch in the photodetector, resulting in significant noise for wavelengths
exceeding 1300 nm. This resulted in an error of 6% over the wavelengths of interest,
making it difficult to measure fine details in transmission spectrum. The size of the crystal
also made it difficult to make precise measurements. The spectrophotometer was designed
for 12- to 48-mm-diam optics, while the crystal face was a 5 5-mm clear aperture.
Modifications were made to accommodate the crystal size but at an additional sacrifice to
the precision of the results.
The crystal manufacturer (Conex System Technology) was able to provide
transmission measurements from the crystal batch used in this investigation after a special
request was made and their equipment was upgraded. Using the absorption data provided,
the transmission through an 8.4-mm BiBO crystal was calculated, neglecting reflection
losses (shown in Fig. 4.3).
Figure 4.3: Transmission through an 8.4-mm BiBO crystal, neglecting reflection losses for
the pump wavelength (dashed blue line) and the OPO tunability range (dashed red lines)
[165].
At 1030 nm (pump wavelength), negligible absorption was observed, which was
expected from earlier measurements of the transmission. Absorption exceeded
expectations for wavelengths greater than 1600 nm and narrowband absorption peaks are
evident. The sharp drops in transmission suggest that there were likely contaminants
57
present in the crystal growth process [166, 167]. These contaminants were likely caused
by impurities in the bismuth oxide or water deposition during the vapor deposition process,
which could be prevented at additional manufacturing cost along with care during the
crystal growth process. For this study, both time and cost prohibited investigating
improvements to the crystal. Evidence of thermal effects did arise from this absorption,
which is discussed in more detail in Chap. 6.
4.1.3 Noncollinear Geometry
A small noncollinear angle could be introduced between the pump and signal
beams. The noncollinear geometry increases the available bandwidth in the parametric gain
and prevents the idler beam from resonating, which reduces the complication for a doubly
resonant cavity [60, 168]. The calculated phase-matching curve is shown in Fig. 4.4.
Figure 4.4: Phase-matching calculation for an 8.4-mm BiBO crystal with an internal
noncollinear angle of 0.2° [165].
Despite the 8.4-mm crystal length (which is relatively long compared to typical
crystal lengths of less than 2 mm in OPO’s), the phase-matching bandwidth available in
this system is quite impressive. This is due to near-degenerate operation as well as the
exceptional phase-matching capabilities of BiBO. As shown in Fig. 4.4, the phase-
matching curve is flattest near degeneracy at 2060 nm. The optimal phase-matching angle
was chosen as 8.65°, which gives near-uniform phase matching from 1.95 to 2.17 µm.
58
Increasing the noncollinear angle also increases the bandwidth to a limit, but there
are multiple reasons why a small noncollinear angle is sufficient. The bandwidth in this
setup is already large enough to produce sub-100-fs pulses. Increasing the noncollinear
angle would have placed additional constraints on the beam dumps needed to collect
reflected beams from the crystal face. Additionally, the idler beam produced would have
greater angular dispersion. The available space for collecting stray beams and appropriate
locations for beam dumps was already limited with a small collinear angle, so the increased
angular dispersion of the idler beam made safe engineering practices increasingly difficult.
Finally, because of the large crystal length, the spatial walk-off between the pump and the
signal was important. As the noncollinear angle was increased, the impact of the spatial
walk-off between the pump and the signal had a negative impact on the gain as the spatial
overlap between the beams decreased [169, 170].
4.1.4 Crystal Coatings
Antireflection (AR) coatings on the crystal were necessary to mitigate unwanted
watt-level stray beams inside the cavity and to prevent unnecessary losses in the cavity. If
left uncoated, the high index (n =1.78) of the material caused Fresnel reflections of roughly
7.5% for pump, signal, and idler beams [171]. Multiple AR coating strategies were
reviewed to minimize the impact of these reflections on the cavity performance.
A multilayer dielectric coating was optimal for minimizing the reflectivity at the
pump, signal, and idler wavelengths. Calculations showed that reflectivity of less than
0.1% could be achieved at 1030 nm and from 2000 to 2200 nm. Coating difficulties were
encountered, however, due to the high-index of the material and the wavelength range of
the OPO. The thickness of the coating had a considerable risk of cracking due to poor
adhesion to the substrate, regardless of the power incident on the crystal [172]. These
cracks give rise to high-order aberrations, affecting the mode quality of the OPO and
reducing the available gain from poor mode overlap between the pump and signal beams.
Furthermore, cracks would also reduce the damage threshold of the coating below the bulk-
damage threshold of the crystal. Due to the anticipated powers of the OPO and the high
59
repetition rates, it was very likely that a multilayer dielectric–coated BiBO crystal would
quickly cause the OPO to cease lasing.
An acceptable alternative was found by using a single-layer coating. Using a single-
layer SiO2 AR coating could minimize the reflectivity for 2060 nm at a sacrifice of
increased reflectivity at the pump wavelength. By using a single-layer coating, the damage
threshold could be higher than the bulk damage of the crystal. Also, since single-layer
coating deposition does not change significantly for different materials or wavelengths, the
coating could be reliably engineered such that optical defects would depend less on the
coating than the surface quality of the crystal itself [173]. By optimizing the thickness, the
reflectivity was minimized for degenerate operation. This yielded a reflectivity of 8.7% at
1030 nm and less than 2% reflectivity from 1950 to 2200 nm. The decrease in available
pump power was negligible when compared to the uncoated crystal, while the reflectivity
at the signal and idler wavelengths was dramatically improved.
4.2 Cavity Design
4.2.1 Multipass Cavity Design
Multiple cavity designs were considered before the final decision was made. The
first cavity constructed had a cavity length 6× shorter than the pump cavity and consisted
of only four mirrors. This cavity was built to perform initial tests on the crystal quality and
diagnostic performance; however, irregularities in the amplitude of pulses and stability
problems made this design suboptimal compared to a synchronously pumped cavity.
The first synchronously pumped cavity used a multipass design similar to the
TDML, in order to scale the cavity length in unison with the pump. Although the pump
cavity was operated at a repetition rate of 7.08 MHz, the cavity length could be extended
to achieve pulse energies by more than a factor of 2 at the same average power. The
increase in cavity length was achieved by increasing the number of passes in the multipass
section of the cavity, as described in Sec. 3.3.2. The multipass OPO is shown in Fig. 4.5.
60
Figure 4.5: Multipass OPO. Unlabeled mirrors are high-reflectivity mirrors (either 0° or
45° angles of incidence); DC: dichroic mirrors; OC: output coupler, 5% transmission. All
curved mirrors had a focal length of 1.5-m [174].
The compact cavity design accommodated the pump laser, OPO and diagnostics
for both lasers on the same 4-ft 10-ft optical table. The OPO was designed for collinear
pumping, although it would be straightforward to adjust the cavity alignment slightly to
accommodate a noncollinear pump/signal geometry. The cavity can be separated into two
main parts, the pump section and the multipass cavity, which are shown in the Fig. 4.5 on
the left and right sides, respectively.
In the pump section, dichroic mirrors were used to achieve collinear pumping. The
back of the mirrors were AR coated for 1030 nm to prevent unnecessary losses as well as
heating and ghost reflections from light reflected off the front surface of the mirrors. The
front surfaces of the mirrors were AR coated for 1030-nm light and HR coated for
wavelengths between 1950-2150 nm. Folding mirrors were used to ensure the BiBO crystal
was placed at the focus of the pump section. Folding mirrors were also used to minimize
the angles of incidence (AOI’s) on the curved mirrors to reduce astigmatism. The focal
length and position of these mirrors were chosen to recreate the non-AMC length segment
of the pump laser.
The multipass section worked similarly to the AMC in the pump laser. The largest
difference is the length segment of the dtele section. In the pump laser, this segment served
two purposes: the first was to accommodate the focal power of the thin disk at high-power
operation; the second was for ease of alignment of the angularly multiplexed cavity
extension. The latter worked the same in the OPO cavity; however, the focal spot no longer
61
occurred on an optic that changed with internal power. A flat mirror was used in the OPO
cavity, which increased the length of dtele. In the final arm of the OPO, space was left for a
prism set to manage the internal dispersion of the cavity. The length of this segment could
be adjusted without changing the critical cavity parameters, making it ideal for fine tuning
the cavity length to achieve synchronous operation. The prism set was not implemented
and the inclusion of dispersion control will be discussed in Chap. 7.
Despite a great deal of effort, this cavity was never able to achieve lasing, which
was primarily due to alignment difficulties in the laser. To achieve lasing, the cavity length
of the OPO must match that of the pump laser within 40 µm as well plus the pump and
cavity mode in the crystal must precisely overlap. Although practice in aligning the
multipass section of the cavity had been thoroughly explored with the pump laser, finding
an appropriate alignment source made alignment through the multipass section exceedingly
difficult. Due to the complicated cavity layout, four separate types of mirror coatings had
to be employed: an output coupler, a 0° broadband HR, a 45° s-polarized broadband HR,
and the dichroic mirrors. Finding an adequate alignment laser that provided enough usable
light for a single round-trip in the cavity proved more difficult than expected. The
reflectivity and GDD of the mirrors used in this investigation are shown in Fig. . The
reflectivity was measured by the Optical Manufacturing Group at LLE using a Lambda
900 spectrophotometer from PerkinElmer, and the GDD was measured using an
experimental Chromatis upgrade from KMLabs.
Although each mirror had its reflectivity optimized at 2060 nm, the performance at
other wavelengths varied significantly. The reflectivity of each mirror is shown in Fig. (a).
It is immediately obvious that the reflectivity of the dichroic mirrors falls off at higher
wavelengths significantly more than the other mirrors. Additionally, there is no obvious
wavelength that would be good to use for an alignment source due to high-reflectivity
bands for different mirrors having poor overlap for wavelengths between 400-1100 nm. In
Fig. (c) the total reflectivity for each cavities designed for this investigation is shown. The
multipass cavity, shown in blue, has no useful source for alignment, with the best
62
wavelength being 690 nm at a reflectivity of less than 1%. As mentioned above, this made
it extremely difficult to align this complicated cavity design. When one compares the total
reflectivity between the two cavities, the benefits of the alternative design are obvious.
Figure 4.6: (a) Measured reflectivity for all mirrors used in both OPO cavities excluding
the output coupler. (b) The measured GDD of each type of mirror. (c) Total reflectivity
from the mirrors in each OPO cavity. Losses from the output coupler and crystal face are
not considered in this calculation. (d) Total GDD in each OPO cavity, not accounting for
dispersion obtained from the crystal or SPM. In both (a) and (c) the tunability of the OPO
has been highlighted with dashed black lines.
The total reflectivity of the cavity was calculated by taking the reflectivity of each
individual mirror into account for a single round-trip. The impact of the large number of
mirror bounces becomes obvious when comparing the contribution of a single mirror to
the losses seen in one oscillation. In the multipass cavity, there are 76 bounces off various
mirror coatings, whereas in the final design (folded cavity), there are only 24 bounces from
63
a single coating. In these calculations neither the output coupler, the crystal absorption, nor
the losses from the crystal faces is taken into consideration.
Due to the insensitivity of the spectrophotometer at wavelengths exceeding 1300
nm the reflectivity measurements become quite noisy. This noise is amplified in the total
reflectivity calculation, which is not very precise for wavelength regions near the tunability
range of the OPO. For instance, the folded cavity has less than a total 5% loss from the
mirrors in the cavity during one round-trip, which is nearly uniform from 1950 to 2200 nm.
This value was calculated from manufacture-provide high-precision measurements that
were difficult to use for broadband analysis.
There are multiple benefits to a cavity using only 0° HR mirrors, which is discussed
thoroughly in the next section. Multiple wavelengths are available to align the cavity since
losses at discrete bands are minimal for an individual coating type. Additionally, the
reflectivity around the wavelengths of interest for the OPO are considerably higher. Near
2060 nm the total losses are ~5% less than with the multipass cavity. For wavelengths
greater than 2070 nm the reflectivity is significantly higher, suggesting that the multipass
cavity would have significantly less tunability and potential bandwidth than a cavity using
only 0° HR mirrors.
The presence of significant GDD also varies between the two cavity designs. In
Fig. (b) the GDD from each mirror can be seen. Although the GDD from both the 45° HR
and the 0° HR was fairly uniform, the GDD from the dichroic mirrors was significantly
higher than expected with a fairly large defect at 2140 nm. The mirrors were initially
designed to have near-zero GDD from 2010 to 2110 nm, which was almost achieved with
the exception of the dichroic mirrors. During the design phase of the mirrors, the GDD was
an extremely difficult constraint to control due to the tight requirements on broadband high
reflectivity and damage threshold.
A new cavity was designed to alleviate the alignment problems caused by the
previous cavity using only 0° HR mirrors except for the output coupler. This allowed for
64
the use of an inexpensive 695-nm cw diode laser as an alignment source that could maintain
high brightness despite the considerable number of mirror bounces. The folded cavity
design also improved the uniformity of the GDD and total reflectivity over operational
wavelengths of the OPO.
4.2.2 Folded Cavity Design
The schematic of the cavity, drawn to scale, is shown in Fig. 4.7. The focusing
mirrors inside the cavity—12.8-mm-diam optics; 25-mm optic adapters—were used in
tandem with clear edge mounts to increase the beam clearance inside the cavity and to
accommodate the compact design shown here. In some cases, the adapters were cut to
achieve very close clearance between the beam and the edge of the mirror. The cavity
length is 21.2-m, but the cavity is folded into a 1.0 0.2-m enclosure. The AOI on the
curved mirrors was limited to less than 2° to reduce astigmatism.
Figure 4.7: Schematic of the 21.2-m synchronously pumped OPO. HR: 1950 to 2250-nm
high reflector; OC: 20% output coupler, 3.0-m radius of curvature (ROC); BiBO: nonlinear
crystal; MP: 1.5-m ROC pump mirror; M1.5: 1.5-m ROC; M2: 2.0-m ROC; M3: 3.0-m ROC.
The pump (blue) and idler (dashed red) are not resonated in the cavity with the signal beam
(solid red) [165].
Two focusing optics down-collimated the pump beam with a slightly diverging
wavefront before arriving at a 1.5-m focusing mirror. The pump beam was focused to a
570-µm radius inside the nonlinear crystal and exited without coming into contact with any
mirrors. The unused pump light was sent to a beam dump, not shown in the schematic. The
angularly dispersed idler beam was sent out near the pump beam and monitored with a
Coherent PM30V1Q thermopile sensor or collected in a beam dump.
65
The position of the M3 end mirror was adjusted using a micrometer to achieve
synchronous pumping. The cavity length was manually tuned while carefully monitoring
the repetition rate of the pump to maintain long-term use, although automated stabilization
could be used [175]. The size of the cavity mode at the crystal and the stability of the
cavity were controlled by the curvature and position of the end mirrors and the mirrors
closest to the crystal. Although these four mirrors were the critical pieces for obtaining
good stability and the correct mode size, it was difficult to find mirrors that could be used
to create the long cavity length required to achieve synchronous pumping. The cavity
length was extended to 21.2 m using image relays by setting all other mirrors at a distance
of 2f from each other [176]. This technique is explained further in the following section.
As discussed in the previous section, there was no additional dispersion control in
the folded cavity. The linear dispersion was dominated by the coatings on the mirror, but
there was a small contribution from the material dispersion of the BiBO crystal. The total
linear dispersion in the cavity over the tunability of the OPO is shown in Fig. 4.8. The
dispersion is slightly positive near 2 µm, but most of the dispersion is slightly negative.
Near the edge of the OPO tunability the material dispersion is significantly increased,
which is due to the multitude of reflections off the mirrors in the folded cavity. The balance
of the negative linear dispersion with the positive GDD obtained through SPM is not well
understood, due to the long cavity length in air and the significant change in mode size
throughout the cavity. Ideally, uniform dispersion over the tunability of the OPO was
desired so that the linear dispersion could easily offset the SPM, which would create
transform limited pulse durations. As shown in Chap. 5, transform-limited pulses were not
achieved, suggesting that the intracavity dispersion could be improved to optimize the
pulse duration.
66
Figure 4.8: Total linear dispersion of the folded OPO cavity. GDD values were calculated
from the total combination of all mirrors in the cavity and the material dispersion of BiBO
for an 8.4-mm-long crystal.
The crystal was held in a custom mount designed for high precision control of the
crystal orientation and mitigation of thermal effects. The crystal was actively cooled using
a Peltier module (CP0.8-127-06L, Laird Technologies) to enable stable steady-state
operation at higher powers resulting from absorption of the signal and idler beams. The
unpolished crystal face was placed on a chemically etched indium foil for good thermal
contact with a 6 12 12-mm aluminum block that was temperature controlled by the
thermoelectric cooler, as shown in Fig. 4.9.
The thermoelectric cooler (TEC) was bolted to a modified kinematic mount for
initial coarse alignment and to ensure that the crystal was oriented correctly. The aluminum
blocks were attached to a post for variable height control on the crystal. At the base was a
Newport UTR80S precision steel rotation stage for fine tuning control of the angle between
the pump and crystal axis.
67
Figure 4.9: Images of the crystal mount and beam orientation. (a) Top-down view of the
crystal with the pump (green), signal (red), and idler (red outline). Angles are exaggerated
for clarity. (b) Side view of the crystal mount, with all beams in plane with the middle of
the crystal. (c) Clear image of the crystal, mount thermistor, and thermoelectric cooler
(TEC).
4.2.3 ABCD Analysis
An ABCD analysis [177] was used to design the cavity. This ensured that (1) the
correct cavity mode size for optimal pump/signal beam overlap could be achieved, (2) the
cavity was stable, and (3) the cavity length could be easily adjusted.
Using an ABCD model, the mode size at the crystal was modified by adjusting the
radius of curvature (ROC) and distances between the cavity mirrors. The beam size at the
crystal was determined by the bulk damage threshold of the BiBO crystal, which had to be
greater than 550 µm. This limitation was due to maximum intensity anticipated in the cavity
and the damage threshold of the crystal, which was reported by the manufacturer to be 1
GW/cm2. Higher intensities may be possible without causing damage to the crystal, but the
damage threshold of BiBO has not been thoroughly investigated for ultrafast pulses. The
beam waist was designed to have a 570-µm radius for both the pump and signal beams,
which ensured adequate gain and a minimal risk of damage to the crystal.
The stability of the cavity was important to increasing the reliability of the laser.
Instabilities could result in pointing fluctuations in the beam, which could cause significant
68
problems due to the sensitive alignment requirements of a critically phase-matched
oscillator. The cavity stability, determined from the mean of the main diagonal of the
ABCD matrix for the cavity, was calculated to be 0.07 on a scale of –1 to 1, suggesting the
cavity was very stable [113, 177].
The core components that determined the spot size and stability of the OPO were
the separation between the two mirrors closest to the crystal and the curvatures of these
two mirrors and the end mirrors of the cavity. If all other mirrors were set at a distance of
2f from the neighboring mirror, the fundamental cavity parameters did not change. Either
end mirror could be moved over 300 mm, resulting in a 0.1% effect in both the cavity
stability and the beam size. However, movement of over 5 mm of the position between the
inner mirrors and/or the crystal caused a notable change to both the beam size and the
stability. Invariance to the cavity length was an important feature to be able to achieve
synchronous pumping since the pump laser experienced significant drift over the course of
the day, as mentioned above.
The ABCD model showed that additional telescopic relays between these mirrors
had no noticeable effect on the cavity. This shows that additional mirrors can be added to
arbitrarily extend the cavity length as long as they are placed at distances of twice their
focal length from the neighboring mirror. This can be a useful tool for extending the cavity
and taking advantage of the high-energy pulses available from longer pump cavities.
69
5 Characterization of the Ultrafast
Optical Parametric Oscillator
After the ultrafast OPO was constructed and stable operation was achieved, the
cavity was characterized. The spectrum and pulse duration were measured as well as the
beam quality and output power. The characterization methods and the results of the
measurements will be discussed in depth in this chapter.
5.1 Pulse Duration
One of the most critical measurements of an ultrafast system is the pulse duration.
The most practical method for measuring an ultrafast pulse near 2-µm was to use a
commercial autocorrelator that could make an intensity autocorrelation of the OPO output
[81]. The system used to measure the autocorrelation signal was a modified FR-
103MN/LiIO3 autocorrelator from Femtochrome. The sensor was swapped from the
traditional photomultiplier tube (PMT) to a high sensitivity photodiode. The PMT was
insensitive to wavelengths of less than 800 nm so it could not be used to detect the second-
harmonic output of the LiIO3 crystal for the range of available signal wavelengths. The
photodiode required a separate alignment of the autocorrelator due to the placement of the
detector. Additional internal electronics were also required to switch between operation for
the pump and OPO output. The LiIO3 crystal could be used in both cases to obtain a second-
harmonic beam for the pump and OPO, even though different tuning angles were required.
Although these modifications allowed for autocorrelation measurements of both systems,
significantly more power was required from the OPO. The low conversion efficiency of
LiIO3 for creating SHG from 2 µm meant that more power was required from the OPO to
obtain a usable autocorrelation signal. This problem was exacerbated by the poor
70
sensitivity of the photodetector compared to the PMT. A minimum of 0.4 W of 2-µm power
was required to obtain a useable autocorrelation trace.
A typical autocorrelation trace is shown in Fig. 5.1. The 455-fs pulse duration of
was obtained assuming a sech2 pulse shape, which was chosen due to the characteristics of
the pump pulse as well as the measured spectrum of the OPO output, discussed in the
following section. The autocorrelation trace is heavily averaged due to the acquisition time
of the autocorrelator and averaging done in the oscilloscope. The autocorrelator used
rotating mirrors to sweep over the length of the two arms of the interferometer. The mirrors
rotated at a rate of 45 Hz, which means that individual traces consisted of over 150,000
pulses. To improve the signal-to-noise, the averaging function of the oscilloscope was used
to calculate the mean of 16 traces. The pulse duration was obtained by performing this
method ten times, which resulted in an average pulse duration of 455 fs with a standard
deviation of 47 fs.
The autocorrelation measurement shown in Fig. 5.1 was taken with an output power
of 0.7 W. No measurable change in the pulse duration was observed between output powers
of 0.5 and 1.0 W. Additionally, autocorrelation measurements with center wavelengths
between 2040 and 2080 nm showed no measurable effect on the pulse duration.
Autocorrelation measurements were not possible at wavelengths outside this range due to
small fluctuations in the peak power that interfered with the shape of the autocorrelation
trace.
71
Figure 5.1: Autocorrelation trace of the OPO giving a 455-fs pulse duration assuming a
sech2 pulse shape [165].
5.2 Spectral Measurements
Measurements of the pulse spectrum are another fundamental characterization of
ultrafast pulses. Since more-advanced techniques like FROG and SPIDER were not used
for pulse characterization, the shape and width of the pulse were necessary to infer
information about the spectral phase [82, 83].
The spectrum of the OPO was measured using a home-built spectrometer, a
schematic of which is shown in Fig. 5.2. Light from the output of the OPO passed first
through a variable slit. A lens, placed a focal length away from the slit, then collimated the
light before it continued on to two separate uncoated SF10 prisms. In this configuration,
two prisms were necessary to obtain adequate spectral resolution. After the prisms, a 92-
mm-focal-length lens was used to focus the angularly dispersed light onto a Pyrocam III
beam analyzer with a Si window, AR coated for 1.05 to 2.5 µm.
Various components of the spectrometer had to be optimized to ensure that the
resolution of the spectrometer did not interfere with the width of the measured pulse
spectrum [178]. The variable slit was optimized to give the maximum amount of light
without affecting the width of the spectral measurements. The optimal slit size was found
to be 35 µm. The dispersion obtained from two prisms allowed the spectrum to be sampled
by the detector array over the entire tuning range of the OPO. The pixels on the detector
72
were 70 70 µm with an array size of 12 mm, corresponding to 171 pixels. Tests were
performed with a single prism, but the resulting spectral resolution was too broad for an
accurate measurement of the pulse spectrum. Since the spectrometer was built in-house, a
combination of calibration methods were used to ensure accurate measurements. In
general, this required that the pixels of the detector were mapped to the correct wavelengths
and that the nm/pixel was well understood. Typically, narrowband sources at multiple
wavelengths are used to calibrate spectrometers. However, due to the expense of these
sources and the intensity required for a strong signal on the detector that was used,
alternative methods of calibration were necessary.
Figure 5.2: Diagram of the home-built spectrometer, not drawn to scale. L1: 210-mm
focusing lens; L2: 92-mm focusing lens; prisms: uncoated SF10 prisms with a 60.9° apex
angle.
The first calibration technique focused on characterizing the wavelength range of
the spectrometer. The SHG of the OPO output was first focused through a 1-mm crystal.
The unused 2-µm light was reflected off a dichroic mirror (described in Chap. 4). The
second-harmonic light was injected into a multimode fiber and sent to an Ocean Optics
HR4000+ spectrometer. The center wavelength of the SHG spectrum was used to
characterize the tunability of the OPO. The spectrum collected from the home-built
spectrometer was then calibrated such that the edges were known; then a distribution of the
73
how many nm/pixel could be calculated. The dispersion of the prisms and the focusing lens
were arranged such that the full tuning range of the OPO could be viewed over the pixel
array of the detector.
An alternative method was used to determine the wavelength range by changing
the cavity length to map the wavelength between the SHG output and the home-built
spectrometer. The SHG and OPO spectrum were measured by the same method just
described. Instead of measuring the edges of the spectrum, however, a map of the spectrum
as a function of cavity length was investigated. The cavity length was changed at a constant
speed in the same direction for both spectra. For the SHG, the central wavelength could be
plotted as a function of the cavity length. When this process was repeated for the home-
built spectrometer, the wavelength as a function of the cavity length was used to calibrate
the discrete wavelength bands for the individual pixels. The result of this calibration
confirmed the previous method, in which the nm/pixel distribution was inferred strictly
from the edges of the OPO tunability. In this case, a nm/pixel map was created as a function
of the change in cavity length and showed good agreement between the two methods. Even
though narrow linewidth sources were not used in calibration, the agreement between these
two measurements gave strong confidence in the accuracy of the spectrometer.
The final calibration ensured that the resolution of the spectrometer did not interfere
with the spectral width of the measured pulses. The resolution was controlled by several
different spectrometer parameters: the slit width, the pixel size on the detector, the focal
power of the optical element before the detector, and the dispersion placed on the beam
from the prism pair [178]. Except for the pixel size (which was fixed due to the detector),
the spectrometer elements were optimized in a trial by error due to interconnectedness of
their performance. The slit width was initially optimized by minimizing the slit so that the
weakest parts of the spectrum had just enough power to be measured by the detector. The
first prism of the prism pair almost introduced enough dispersion on its own, so the second
prism could be used to fine tune the angular dispersion of the spectrum. The second prism
was optimized such that a full tuning range of the spectrum could be viewed on the detector.
74
To ensure that the resolution in this arrangement did not affect the pulse duration, the
second prism was tuned such that the spectrum from 2140 to 2200 nm could be viewed.
The spectral width between the two configurations was compared and found to be identical,
suggesting that the resolution of the spectrometer could accurately measure the spectrum
of a pulse over the entire tunability of the OPO.
The spectrum of the OPO is shown in Fig. . The spectrum of an individual pulse is
shown in blue. The sech2 pulse shape is evident, supporting the use of the sech2
deconvolution factor in the autocorrelation. The FWHM of the spectrum is nearly constant
over the full tunability of the OPO, which is shown in black. The tunability spectrum of
the OPO is slightly more complex than the figure would suggest.
Figure 5.3: The spectrum of on individual pulse with a bandwidth of ~30 nm is shown in
blue; the spectrum over the tunability of the OPO is shown in black [165].
It would be easiest to understand this curve as the relative spectral power of pulses
across the full tunability of the OPO. The shape of the tunability curve was determined by
compiling the pulse spectrum while tuning the OPO over the entire bandwidth (which was
done by slowly changing the cavity length). The cavity was tuned over 100 µm at a rate of
0.1 µm/s over the full range of cavity lengths that allowed the cavity to lase. The rate was
chosen to be slow enough to avoid power fluctuations that arise during rapid tuning of the
cavity length. The spectrum was sampled at 24 Hz and stored for analysis.
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Using this data, a program was able to analyze a few thousand spectrum samples to
compile the relative spectral power over the tunability of the OPO. An empty array was
created for wavelengths between 1950 and 2250 nm. A pulse spectrum was then loaded
and compared to the array. If the amplitude of the spectrum was larger than the array, those
values were replaced. This procedure was iterated for each measured spectrum over the
full tunability of the OPO. As the cavity was tuned, the maximum value was stored,
replacing previous spectral amplitudes when applicable. The amplitudes of the spectrum
over the tunability of the OPO were compared with power measurements and shown to be
in good agreement, as was expected, to the uniform spectral response of the detector in the
area of interest. The result is the dashed black curve shown in Fig. 5.3, which represents
the relative spectral power for a device that is continuously tunable over 200 nm.
Features in the tunability spectrum present a few interesting facts about the
behavior of the OPO. The tunability curve is extremely similar to the transmission
measurements shown in Fig. 4.3. This is not too surprising considering that losses from
linear absorption in the crystal dominated the wavelength-dependent losses in the cavity.
The spectrum at 2150 nm is roughly 40% as powerful as the spectrum at 2060 nm. This
amplitude difference is directly related to the power of the OPO, where the maximum
power can be obtained only in the spectral range between 2040 and 2100 nm. In addition
to power, this area of operation also gave the most spectral and temporal stability. Near
2060 nm (degenerate operation) the center wavelength was very stable and would stay
constant within 5 nm. However, the spectrum near the edges would drift back and forth
over 20 nm, making it difficult to maintain at a constant wavelength.
5.3 Temporal Stability
The 7.08-MHz pulse repetition rate and temporal stability were investigated using
a rf spectrum analyzer connected to a Thorlabs DET100A Si photodetector and DET10D
InGaAs photodetector for the pump and signal, respectively. The free-running pump
showed significant temporal jitter that could be reduced with active stabilization, which is
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discussed in Chap. 7. This noise appeared in the rf spectrum of the OPO as well, as was
expected because of the lack of active control (shown in Fig. 5.4).
Figure 5.4: Radio-frequency (rf) spectrum of the signal (blue) and pump (red) [165].
The presence of noise in the rf spectrum for frequencies < 50 kHz can easily be
seen in Fig. 5.4. Most of the features in the noise seen in the pump’s rf spectrum can also
be seen in OPO’s the rf spectrum. The difference in amplitude between the two suggests
that the temporal jitter of the pump was amplified in the OPO, which could be eliminated
by active stabilization of the TDML. Additionally, low-frequency noise is present in the
OPO near 10 kHz, which is not present in the pump. The exact cause of this noise unknown,
but it is not too surprising due to the lack of independent stabilization of the OPO and the
operation of the OPO in air without a full enclosure to protect against air flow. Despite the
presence of this noise, the OPO output had less than 2% rms peak-to-peak power
fluctuations over the course of 4 h, and control of the center wavelength of the OPO to
within 5 nm for operation between 2040 and 2100 nm was possible. Active stabilization of
the pump is discussed in section 7.2.3. Active stabilization of the OPO based on wavelength
stabilization with position-sensitive photodiodes is a commonly employed technology that
could have been used in this system but was outside the scope of this investigation [18,
169, 175].
77
5.4 Output Power and Scaling Limitations
Signal and idler powers measured simultaneously in this system are shown in Fig.
5.5. The pump power threshold of the OPO was 14.5 W. Reliable performance was
obtained for signal (and idler) powers of 2.5 W (5.2 W) corresponding to 350-nJ (730-nJ)
pulses with a slope efficiency of 14%. At maximum pump power, the OPO was unstable
and the beam became deformed from local heating of the BiBO crystal, which is discussed
thoroughly in Chap. 6. The maximum output powers obtained under these conditions were
3.0 W with 430 nJ pulses and 7.6 W with 1.1-J pulses from the signal and idler,
respectively. The conversion efficiency, calculated by comparing the amplified signal
beam and the measured power of the idler with the total pump power, was estimated to be
25%, decreasing near maximum power to 22%.
Figure 5.5: Output power of the signal (blue) and nonresonated idler (red) [165].
Power measurements were taken with a Coherent PM10V1 thermopile sensor
connected to a LabMax-TOP power meter. Using the built-in features of the power meter,
the output power was measured using data collected at 10 Hz over the course of 120 s. For
measurements with less than 30 W of pump power the standard deviation of the output
power was less than 10% of the mean. At higher powers, however, instabilities began to
cause a significant reduction in performance, with standard deviations to the powers shown
up to 22%.
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Thermal stabilization of the laser was of critical importance to obtain the powers
shown in Fig. 5.5. Initially the TEC was set to a temperature of 29.8°C, which ensured the
crystal was properly phase matched at low temperatures. As the laser power was increased,
the TEC was unable to sufficiently cool the crystal, so the temperature setting had to be
reduced to achieve maximum output power. At maximum power the optimal TEC
temperature was 24.3°C. The combination of the decreased temperature setting of the TEC
and the falloff in efficiency suggested that the TEC could not sufficiently cool the crystal
at higher powers. This was the motivation for an investigation of the thermal properties of
the OPO, which is the focus of Chap. 6.
5.5 Beam Quality
Beam-quality measurements of the OPO were important for evaluating the
usefulness of the OPO for various applications and understanding problems in the system.
For pump powers less than 30 W, the output beam had very high quality. At higher powers
the beam showed significant deformation in addition to the instabilities mentioned earlier.
The far-field signal beam profiles of each case are shown in Fig. 5.6. Images of the idler
output could not be obtained due to the high average powers and limited table space.
Qualitatively it was possible to see that the idler beam had high angular dispersion, which
was expected from the noncollinear interaction geometry between the pump and signal
beams [60]. Although the high output powers of the idler would make it of interest for other
applications, the poor beam quality would make the beam much less useful than the signal.
The beam quality shown in Fig. 5.6(a) is representative of the output beam for pump
powers of less than 30 W where the slope efficiency is 14%. The beam is nearly a perfect
Gaussian profile in both the x and y axes, while being slightly larger along the x axis. This
is likely due to a slight astigmatism in the cavity from the off-axis AOI of eight separate
spherical mirrors. At pump powers exceeding 30 W the beam became deformed due to
local heating effects inside the crystal. Local deformations on the bottom-right quadrant of
the beam can easily be seen and the beam becomes slightly elongated in the y axis. The
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exact cause of these deformations is not well understood, even though it must be related to
operation near maximum power.
Figure 5.6: Beam profiles at output powers of (a) 0.4 W and (b) 3.0 W. Local heating
effects become noticeable and cannot be mitigated by actively cooling the crystal. As can
be seen in (b), the local heating begins to deform the beam [179].
Beam quality was measured to ensure that the beam shown in Fig. 5.6(a) was indeed
Gaussian. Unlike the TDML, this measurement was not performed with the knife-edge
technique. Initial attempts were made to use this technique but the 10% power fluctuations
made this exceedingly difficult. Furthermore, the time required to perform the knife-edge
measurements is usually of the order of a few hours for a single set of measurements. The
power fluctuations made the knife-edge technique impractical since precise power
measurements within 1% of the maximum power were required to get accurate
measurements of the beam size using the 84/16 method [136]. An additional difficulty was
controlling the long-term drift of the pump laser. Since compensating for drift was done
manually, it proved very difficult to ensure that the OPO’s center wavelength was
unchanged for multiple hours.
To obtain an accurate 𝑀2 measurement, images of the output beam at various
distances from a focusing element were used. Beam quality could be measured by this
technique much quicker than by using the knife-edge technique. A Pyrocam III beam
profiler was used to measure the size of the output beam. The OPO output was passed
80
through an uncoated 500-mm-focal-length lens, and images of the beam were measured
through focus to obtain adequate sampling of the beam at discreate distances from the lens
[134, 135, 170]. The result of this measurement is shown in Fig. 5.7.
Figure 5.7: Beam-quality measurements along both the x (red) and y (blue) axes with
corresponding M 2 fit [165].
The refresh rate of the beam profiler was 24 Hz, which provided nearly 300,000
pulses per measurement. Electronic triggering for images of individual pulses was not
possible with this repetition rate without significant cost to the detector. On top of the
averaging as a result of the sampling rage, individual images were averaged over 20
acquisitions to account for the power fluctuations over time. The centroid of the beam was
then identified, and lineouts along the x and y axes were taken. Due to the pixel size, these
lineouts were quite rough. To smooth the curves these pixel arrays were averaged for ±1
pixel in both directions. A built-in interpolation function in MATLAB was used to
calculate the 1/e2 full width, half of which was used to calculate the beam radius. This
process was repeated 3×, and the resulting average of the calculated beam radius was used
in a fitting algorithm to calculated the value of 𝑀2 [134]. The fitting routine created a curve
from the measured data to fit the equation
𝑓 = 𝑏√1 + [𝑎(𝑧−𝑐)𝜆
𝜋 𝑏2 ]2
. (5.1)
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Here, z is the distance from the lens, c is the location of the beam waist, b is the size
of the beam at focus, and a is the value of the beam quality 𝑀2. The fitting parameters
were confined such that the values must be physical, e.g., a > 1.0. The fitting algorithm
was run to calculate the mean value of the three trials, as well as the minimum and
maximum values to account for error. The minimum and maximum values of the beam size
were used to calculate the standard deviation of the three trials. The resulting 𝑀2 value is
shown in Fig. 5.7, which suggests a maximum 𝑀2 value of 1.10 and 1.12 for the x axis and
y axis, respectively. As expected, the beam quality from the output of the OPO is quite
good when the cavity is well behaved.
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6 Thermal Analysis and Limitations
of High-Power Operation
In this chapter, the impact of the high intracavity powers on the nonlinear crystal is
explored. Although strategies were employed to mitigate thermal effects, limitations in the
output power were still present. First, the motivation of the thermal analysis is explored.
The methods that were used to measure the thermal properties of the crystal are then
explained. Next, the impact of the total absorbed power from the signal and idler power on
the thermal gradient in the crystal is discussed. The chapter concludes by investigating the
impact of the thermal effects on the OPO, the most significant of which are the thermally
induced phase matching errors and thermal lensing.
6.1 Motivation of Thermal Analysis
6.1.1 2-µm Absorption in BiBO and Total Absorbed Power
The most important reason why an investigation into the thermal properties of the
nonlinear crystal was necessary was the unexpected absorption near 2 µm, which can be
seen in Fig. 4.3. Sharp drops in transmission due to absorption near the signal and idler
wavelengths make operating with high average powers a difficult endeavor in a critically
phase-matched parametric device.
Since the OPO is operated near degeneracy (which occurs at 2060 nm), both the
signal and idler usually have some component of their spectrum in the sharp absorption
peaks near 2150 nm. Due to the relatively broad spectrum of the signal and idler pulsed,
which is roughly 30 nm, and the tunability of the OPO, it is difficult to quantify the exact
amount of light that is being absorbed by the crystal at any given moment. Even though
the transmission losses are far from ideal, mitigation strategies for dealing with some level
83
of absorbed laser light will be necessary for any applications where the scaling of average
power is of interest. It will be shown in Sec. 6.3 that there is a direct relationship between
the intracavity power and the presence of thermal effects.
Due to the complex relationship between the signal and the idler and their
respective bandwidths, the most useful metric to relate the average power with the absorbed
light was the short-wave IR (SWIR) power. This value was calculated as the sum of the
amplified and returned signal beam and the exiting idler power. The signal beam, which is
resonated through the OPO cavity, sees the crystal twice during one round-trip: once during
the amplification stage and again when the beam is headed toward the output coupler.
During this time, the idler passes through the crystal only once and is not resonated in the
cavity. With measurement values of the idler’s average power, the output power of the
OPO and the known transmission of the output coupler, a total contribution of near 2 µm,
could be calculated.
The SWIR power is the only contributing factor to the heat dissipated in the crystal.
Although the average power of the pump light is considerable, the absorption is less than
0.5%. With the cavity blocked, thermal measurements of the crystal were made at
increasing pump powers, and even in the absence of active cooling, no measurable change
in the crystal temperature was observed. This suggested that any heating of the crystal was
the result of the near-2-µm light from the signal and idler beams.
6.1.2 Active Cooling of the OPO
As mentioned above, a TEC was used to actively cool the BiBO crystal during
operation. It was necessary to removing the dissipated heat from the crystal was necessary
for high power operation. Images of the setup are shown in Fig. 4.9, and a more detailed
schematic of the device is shown in Fig. 6.1.
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Figure 6.1: Schematic of the thermoelectric cooler (TEC) and heat sink for the BiBO crystal
shown from the side (not drawn to scale).
The 5 5 8.4-mm BiBO crystal is held in place by a small plastic clamp that is
mechanically connected to the large-area aluminum plate, which is connected to a
kinematic mount for tip and tilt control of the crystal. The unpolished crystal face was
placed on a thin layer of chemically etched indium foil that ensures good thermal contact
between the BiBO and the TEC. The TEC was a Peltier module (CP0.8-127-06L, Laird
Technologies) and actively transferred heat from the crystal to a 6 12 12-mm aluminum
block. A thermistor was attached to the block to monitor the temperature and was
connected to a home-built controller for the TEC. The current sent to the TEC from the
controller was varied to achieve a stable temperature, which could be set to within 0.1°C
at a range between 10°C to 50°C. The signal beam was placed vertically in the middle of
the crystal to ensure proper clearance of the beam from the crystal mount regardless of
changes to the alignment. The beam was place roughly 1.5 mm from the edge of the crystal
to give additional usable space in the event of damage. Although placing the beam closer
to the cooling surface may have helped with cooling, the size of the beam was a concern
for creating a uniform temperature distribution.
As shown in Fig. 5.5 the falloff in efficiency for pump powers that exceeded 30 W
signified a change in the behavior of the system at high intracavity powers. Thermal
management became a prime concern when the output power was compared with the
85
optimal temperature setting of the TEC. As stated above, to initiate lasing, the TEC was
set to a temperature of 29.8°C, which was slightly above the 24.2°C room temperature . Of
course, the laser could have been operated with a slightly different angle between the pump
and the crystal axis to initiate lasing, but it was found that this was the optimal method for
achieving maximum power over the full range of available pump powers. The initial
temperature setting allowed for maximum output power at the lasing threshold. As the
pump power was increased, the TEC operating temperature had to be reduced to maximize
the output power, as shown in Fig. 6.2.
Figure 6.2: The relationship between the TEC temperature setting and the signal power
shows how the temperature had to be reduced to obtain optimal power of the OPO output.
When an optimal TEC temperature was found, the laser could achieve stable
operation for pump powers of less than 30 W. This suggested that the bulk temperature of
the crystal was constant and that the TEC could adequately remove the dissipated heat from
the crystal. However, if lasing was stopped for any reason (e.g., cavity length mismatch
between the pump and OPO), the temperature of the TEC had to be reset to achieve lasing
again. This behavior heavily suggested that local heating effects require that the bulk
temperature of the crystal be reduced to achieve adequate phase matching at higher powers.
86
Furthermore, the falloff in efficiency at higher powers suggested that the TEC was unable
to adequately cool the crystal. This is supported by the optimal temperature setting of the
TEC for output powers exceeding 2.5 W. For the full range of signal powers, the TEC
could maintain the temperature setting of the controller. However, output powers beyond
2.5 W (which is the point where the efficiency falls off significantly) required only a small
decrease in the TEC temperature for optimal output powers. This can be explained for by
local heating effects that could no longer be adequately compensated for by active cooling;
it was not a result of the TEC having insufficient enough power to draw out the total heat
dissipated from the crystal.
Tuning the angle of the crystal relative to the pump beam was a viable, although
problematic, alternative to actively cooling the crystal. Practically, this made it difficult to
handle the high-powered reflections of the pump beam. At maximum power, the reflected
pump beam had an average power of 7.5 W from the reflection of the front and back
surfaces of the crystal. This reflected beam had to be captured by a beam dump, which was
placed near the turning mirror before the 1.5-m ROC pump mirror. As can be seen in Fig.
4.7, the available clearance was quite small, so large adjustments to the crystal angle were
avoided unless absolutely necessary. Angle tuning the crystal was tested in conjunction
with actively cooling the crystal. It was found that angle tuning the crystal could not
improve the OPO performance for powers where the efficiency had begun to decrease.
6.2 Measurement of Thermal Properties
6.2.1 Thermal Camera Selection and Image Acquisition
To investigate suspicions mentioned in the previous section, thermal images were
taken of the crystal while operating the OPO. Images were taken with an HT THT45
compact thermal camera. This device is a relatively inexpensive handheld microbolometer
array that allows one to take detailed thermal images of the crystal. Higher-resolution
cameras were available at a greatly increased cost were found to be unnecessary for the
needs of this investigation.
87
Obtaining images with enough resolution to capture the fine details of the thermal
gradient was critical for modeling thermally induced effects. The camera had to be placed
as close to the crystal as possible within the minimum focusing distance of the device. The
tight beam clearance and limited space in the plane of the crystal created additional
constraints on the optimal placement of camera. The best location was determined to be
130-mm away from the front face of the crystal (the side from which the pump beam
arrives) slightly above the plane of the crystal. A variable focus lens was available in the
unit and was used to focus the front face of the crystal. The height difference between the
camera and crystal was chosen such that thermal radiation from the surface of the indium
foil was not reflected off the front face of the crystal.
Thermal calibration of the crystal was important for obtaining accurate temperature
measurements. It was found that temperature values were highly dependent on the
emissivity of the material, which was a variable that could be changed both during image
acquisition or in post-processing using the THTLink software package provided with the
hardware. Images were calibrated by heating and cooling the crystal using both the TEC
and a hot plate and then measuring the front face of the crystal to determine the correct
emissivity value that would have the software accurately predict the steady state
temperature of the crystal for different images.
6.2.2 Preparation of Thermal Images for Data Analysis
Importing the data to MATLAB was necessary to adequately analyze the thermal
properties of the crystal. Although the THTLink software was a powerful tool for
investigating the thermal images, it lacked the flexibility needed to extensively investigate
the thermal impact on the OPO cavity. Several steps were necessary to prepare the images
before they could be used to analyze the thermal properties of the crystal.
First, the images taken were saved to a jpg file format that be could analyzed using
THTLink. This program was necessary to pull the metadata from the image, including the
temperature’s relation to the image’s colormap as well as various material information
88
(e.g., emissivity). All images were uploaded into THTLink, which allowed for the color
scale to be set to a given temperature range. An appropriate scale was chosen after
analyzing a given data set so that fine details were easy to observe. These modified images
were then saved by the program into a separate jpg file as a grayscale image. By knowing
the temperature range of the grayscale, the jpg file could be imported into MATLAB with
a known temperature scale that allowed for further analysis. Due to the exportation of files
in this manner, an interpolation of the thermal data was performed, giving a higher
resolution of the thermal gradients than was possible with the initial images taken.
Before data could be analyzed, it was necessary to rescale and crop the images.
Rescaling was necessary due to the angle of the camera relative to the crystal face. For
thermal images to be more representative of the physical dimensions of the crystal, the
height of each image was changed so that the height of the crystal in the images was equal
to the width. The result produced square images of the crystal face that could be easily
scaled to the physical dimensions provided by the manufacturer.
Although the signal beam never moved relative to the crystal face, there were slight
changes between individual pictures due to the manual image acquisition as mentioned
above. To more easily compare the images, they were cropped so that only the crystal face
was visible. In greyscale, this process was difficult to do, however when the images were
colored, it was much easier to crop. Therefore, duplicates of each image were made for
both color and greyscale. The scaled images were then cropped in color mode and the
cropping dimensions relative to the entire picture were applied to the grayscale images.
The final images were then saved as new files ready to be imported to MATLAB.
6.2.3 Final Thermal Images
It would be useful to first interpret a sample thermal image to understand the key
features before using this data to understand the dynamics of the OPO. An example of the
final thermal images after they were calibrated and uploaded to MATLAB is shown in Fig.
6.3. The heat distribution caused by the signal and idler beam is shown schematically in
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Fig. 6.3(a) along with the relative location of the TEC. Although these two beams start in
the same location there is a small spatial separation as they exit the crystal due to the
noncollinear pump/signal interaction. Figure 6.3(b) shows a sample thermal image where
local heating effects from the SWIR power are evident. Preliminary investigation showed
that the surface of the crystal closest to the TEC was much cooler than the temperature
around the beam, reinforcing the suspicion that the local heating effects played a significant
role in the cavity’s behavior.
Figure 6.3: (a) Schematic of the front face of the BiBO crystal. The crystal’s dimensions
are 5 × 5 mm. The locations of the signal and idler beam are shown by the solid and dashed
red circles, respectively. (b) Sample thermal image showing the local heating effects from
the presence of these two beams [179].
6.3 Impact of Internal Power on the Thermal Gradient
As mentioned in Sec. 6.1, at higher powers the impact of the falloff in efficiency
was likely related to the thermal gradient. With a method in place to take thermal images
of the crystal face, it was of interest to measure the thermal gradient as a function of the
SWIR power. Figure 6.4 shows thermal images are shown with the corresponding SWIR
power.
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Figure 6.4: Thermal images of the front face of the BiBO crystal during OPO operation
with the corresponding short-wavelength IR (SWIR) power. Each image was taken after
optimizing the thermoelectric cooler (TEC) temperature for maximum output power [179].
At low powers, it is evident that local heating is not a problem. The TEC can control
the temperature of the BiBO crystal and optimize the signal power without creating a
thermal gradient. As the SWIR begins to increase, significant local heating occurs around
the signal and idler beams. At 23.7 W SWIR power, the slope efficiency of the cavity has
not yet fallen off, yet one can see the onset of local heating effects. As the SWIR power
approaches maximum, the thermal gradient becomes more pronounced, which directly
corresponds to the falloff in efficiency at higher powers.
The thermal gradient was of critical importance for understanding the falloff in
efficiency at higher powers. As will be shown in the following sections, the thermal
gradient causes a change in the index of the material, which affects phase matching and
cavity dynamics through thermal lensing.
6.4 Thermally Induced Phase-Matching Errors
Temperature has a significant effect on critically phase-matched systems [142]. The
maximum change observed in the crystal temperature over the available power in the OPO
was 4.8°C. This corresponds to an optimal change in the phase-matching angle of 1.78
mrad at degeneracy, which is significant compared to the angular acceptance of the OPO,
which was calculated to be 3.04 mrad [163]. An additional complication is the spatially
varying index, which causes a complicated gain profile across the beam area from non-
uniform phase matching. To investigate this complication, thermal images were taken at
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different output powers while the OPO was running and used to determine the effect of
local heating on the phase matching, which is shown in Fig. 6.5.
In this figure, thermal images were used to calculate a 2-D profile of the index using
the thermo-optic dispersion formula for the BiBO crystal [163]. The index values were
then used calculate the phase matching that is typically done for simple 1-D models. It was
useful to understand the reduction of gain at higher powers by investigating the impact of
the thermal gradient on the phase matching. This was done by comparing the phase
matching for different center wavelengths of the signal beam and how that was affected for
different output powers.
Figure 6.5: Thermal images of the front face of the BiBO crystal during OPO operation
with the corresponding SWIR power. Each image was taken after optimizing the TEC
temperature for maximum output power. The circle shows the 1/e2 diameter of the beam
area [180].
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The impact of the thermal profile varies significantly over the tunability of the
OPO. Near threshold, the 4.5 W SWIR power does not produce a strong thermal gradient,
which leads to a uniform phase-matching profile across the tunability of the OPO, as shown
in Figs. 6.5(a), 6.5(d), and 6.5(g). Here the metric of phase matching is the commonly used
sinc2 (∆𝑘𝐿
2) function that directly relates the phase matching to the maximum-available
parametric gain [61]. In Figs. 6.5(b), 6.5(e), and 6.5(h) the incident SWIR power on the
crystal has risen to 23.7 W, where the local heating becomes apparent. Figures 6.5(c),
6.5(f), and 6.5(i) show the most-pronounced thermal gradient, which occurs at maximum
output power. Although higher output powers could be obtained with more pump power,
the increase in the thermal gradient suggests that the slope efficiency would continue to
decline because of the unmitigated thermal effects.
The center wavelength of the signal beam, which can be tuned over a range of
roughly 200 nm, changes the phase matching when a strong thermal gradient is present. As
shown in Figs. 6.5(a)–6.5(c), the phase-matching gradient does not significantly change
despite the increasing thermal gradient in the crystal. The minimum value of the sinc2
function over the beam area is 0.77, suggesting the OPO is well phase matched near the
degenerate wavelength of 2060 nm [56]. This is not too surprising considering how flat the
phase matching curve is near degeneracy, as shown in Fig. 4.4. For wavelengths away from
degeneracy, the phase matching degrades as the SWIR power is increased. This makes
sense since the phase matching curve changes more rapidly as a function of the angle
between the pump and crystal axis, which will shift as the temperature changes. Figures
6.5(g)–6.5(i) show that when the center wavelength is at 2150 nm, the beam is no longer
adequately phase matched at high powers. The most obvious method for resolving this
problem would be to either rotate the crystal to achieve the optimal pump angle or to
operate the TEC at a different temperature to optimize performance at this wavelength.
The phase-matching gradient at wavelengths away from degeneracy suggested that
this effect could not be eliminated entirely. The total change in the sinc2 function over the
cross section of the beam is 0.23, 0.25, and 0.29 for Figs 6.5(c), 6.5(f), and 6.5(i),
93
respectively. At high powers, the tunability of a BiBO-based OPO will inevitably be
limited as the phase matching becomes unsuitable for broadband operation.
6.5 Power Limitations from Thermal Lensing
In addition to thermally induced phase-matching difficulties, the temperature
gradient of the crystal along the cross section of the beam induces thermal lensing. It is
well known that these types of thermal effects can create a thermal lens through a gradient
index, resulting in spherical aberration of the wavefront, index variation through the
photoelastic effect, and mechanical stress that results in the bulging of the crystal’s end
faces [181-183]. For this investigation, we focus only on the lensing contribution of the
thermally induced gradient index, which was shown to be the most dominant factor for
thermal lensing present in the cavity.
The impact thermal lensing creates two separate problems that interfere with the
gain of the cavity. In this cavity, introducing a thermal lens changes the beam size at the
crystal as well as the wavefront curvature of the beam. A change in the beam radius creates
an imperfect overlap between the pump and signal beams. This can decrease the gain when
the cavity mode (signal beam) gets larger or smaller. In the case where the signal beam is
larger than the pump, the signal beam will have a higher intensity near the center, even for
non-saturated amplification. This will result in either the propagation of higher-order
modes within the cavity (and therefore loss of beam quality) or the loss of efficiency
because of the amplification of higher-order modes that are not resonated in the cavity
[169, 170]. In the case where the signal beam is smaller than the pump, the signal beam is
unable to utilize the total available pump energy, resulting in a lower efficiency than when
the modes are perfectly matched [60].
The wavefront also creates a reduction in the available gain, which is determined
by the angular acceptance of the crystal. When the beam focus shifts away from the crystal,
the wavefront’s radius of curvature (ROC) begins to decrease. As this occurs, the
94
components of the beam’s spatial frequency distribution that exceed the angular acceptance
of the system will not be adequately phase matched, reducing the system’s efficiency [184].
Normally, both factors are negligible by ensuring the pump and signal beams are
of equal size and at focus inside the crystal. With the introduction of the thermal lens, both
factors can negatively affect the available gain, thereby reducing the system’s efficiency,
which contributes to the falloff at higher powers, as shown in Fig. 5.5. These quantities are
difficult to quantify precisely without extensive modeling of the pump depletion (temporal
and spatial), changes in the cavity mode, and phase-matching errors. Since this extensive
characterization was outside the scope of this investigation, a simpler model was developed
that assumed the thermal gradients, measured at the face of the crystal, were constant along
the length of the crystal. This model was tested by comparing predictions of the cavity
mode size to the measurements made as the power was varied.
The spatially varying refractive index across the beam was calculated from the
thermal gradient measurements using temperature-dependent Sellmeier coefficients for
BiBO [142]. The second-order coefficient of a fourth-order polynomial fit was used to
calculate the refractive power of the thermal lens using [56]
𝑓 ≈ 1/𝑛max𝑘𝑑, (6.1)
where d is the length of the crystal, nmax is the highest component of the index of the crystal
along the polynomial fit, and k is defined by the paraxial approximation of the index:
𝑛 = 𝑛max(1 −𝑘𝑟2
2). (6.2)
In this approximation, higher orders of the polynomial were ignored. The calculation was
performed separately for both the x and y axes of the beam. The impact of the thermal lens
on the beam size and ROC at the crystal was calculated using an ABCD model [177].
Measurements were made to verify the model’s predictions over a range of SWIR
powers. First, the cavity was reconfigured by swapping the positions of M3 and the OC
95
shown in Fig. 4.7. This made it possible to measure the output beam at a location that was
predicted to be more sensitive to thermal lensing. Figure 6.6(a) compares direct
measurements of the output-beam size (solid lines for x and y axes) and the predictions
from the ABCD model that were derived from thermal measurements (dots). The
agreement suggests that, despite the simplicity of the model, an analysis based on thermal
images can be used to understand the impact of the thermal lens on the cavity.
Figure 6.6: (a) The measured radius (solid line) of the output beam compared against the
SWIR power on the crystal in the alternative cavity configuration for the x and y (blue and
red, respectively) dimensions of the beam. The predicted beam size from the measured
thermal gradient is also shown (dots). (b) The calculated beam size and (c) wavefront ROC
at the nonlinear crystal over the full range of incident power for the x and y dimensions of
the beam (blue and red), respectively [180].
With the ABCD model, thermal images were used to predict the cavity mode size
and the ROC at the crystal as a function of the SWIR power, as shown in Figs. 6.6(b) and
6.6(c), respectively. Figure 6.6(b) shows that the beam size increases as the power of the
cavity rises. The thermal gradient is higher along the y direction, in part because the thermal
conductivity is approximately 60% that of the x direction. The thermal conductivity was
calculated to be 18.4 Wm–1K–1 and 11.8 Wm–1K–1 for the x and y directions, respectively
[164], leading to a stronger thermal lens that produces astigmatism and a non-Gaussian mode
profile at high powers. The ROC, as shown in Fig. 6.6(c), also changes significantly as the
SWIR power is increased. This occurs because the cavity design is not perfectly symmetric
about the crystal; therefore, the introduction of a lensing element causes the position of cavity
beam waist to shift.
96
Although the loss gain was not quantified for this investigation, there is a
remarkable connection between thermally induced cavity dynamics calculated from the
thermal effects and the loss of efficiency. Figure shows this correlation directly by
comparing the OPO power and calculated spot size against the pump power. Near 25 W of
pump power, the calculated cavity mode begins to change rapidly, occurring at the same
pump power at which the slope efficiency falls off. Independent measurements determined
the spot size and output power, yet the strong correlation between them suggests that this
simple technique of imaging the thermal properties of the crystal can be a strong tool for
predicting the cause of gain reduction in parametric devices.
Figure 6.7: Correlation between the signal power (black) and calculated beam-spot size at
the crystal for different pump powers. The dashed line shows the slope efficiency of 14%
before thermal effects begin to take effect at 30 W of pump power [180].
97
7 Outlook and Conclusions
7.1 Summary
A cw-pumped Yb:YAG thin-disk laser constructed as a scalable pump source for
an ultrafast OPO was described in Chap. 3. The basic principles of operation were
explained and the process of scaling this technology to higher pulse intensities was
explored. The laser could produce 45 W of average power with pulse durations of 1.0-ps
and pulse energies exceeding 6 µJ. The suitability of this laser as a pump source for a
parametric device was investigated, and the beam quality and stability were shown to be
suitable for the goals of this investigation.
Chapter 4 presented the design of an ultrafast OPO utilizing a high-average-power
thin-disk pump laser. Multiple crystals were investigated as a gain medium for providing
scalable ultrafast pulses in the IR. The reasons for choosing BiBO can be summarized as
an optimization of available gain, technological maturity and transparency range.
Unanticipated absorption near the operational wavelengths of the OPO were observed with
new transparency measurements of commercially available BiBO crystals. The use of a
noncollinear interaction geometry was explained, and optimization of AR coatings for an
oscillator with high average power was explored. Multiple designs of the OPO cavity were
discussed and alignment strategies for extended cavities were considered. An ABCD
analysis showed that the folded cavity design could be extended to longer lengths using
telescopic image relays, ultimately achieving high pulse energies.
Chapter 5 described the characterization and results of the OPO. The pulse duration
and measurements of the spectrum showed that the output pulses were heavily chirped. It
was shown that the pulse duration was nearly constant for different output powers. The
temporal stability of the free-running OPO was investigated and showed that the noise
98
present in the pump laser was amplified in the OPO. Methods to improve the temporal
stability with automated electronics were discussed. The efficiency and scalability of the
OPO were characterized, showing that there was room for improvement in the efficiency
compared to other BiBO-based OPO’s and that higher powers could have been achieved if
thermal limitations could had been overcome. The beam quality was also measured and, as
expected, was near diffraction limited.
The limitations to the output power were investigated by characterizing the thermal
properties of the nonlinear crystal in Chap. 6. Although exceptionally high average powers
were obtained with the OPO, limitations of the system used to actively cool the crystal
were explored. This was done by mapping the 2-D change in the refractive index as a
function of SWIR power through thermal images of the nonlinear crystal. The impact of
the thermal gradient on both the phase-matching properties at different wavelengths and
the induced thermal lens was explored. Uniform phase matching over the cross section of
the beam was severely limited at wavelengths away from degeneracy at higher powers.
Thermal-lensing effects were shown to shift the beam waist away from the nonlinear
crystal. A strong correlation between changes in the cavity dynamics and the decrease in
efficiency was observed. Although the impact of the thermal gradient on the gain of the
OPO was not quantified, the method employed showed a meaningful connection between
the thermal properties and the falloff in efficiency near the maximum-available pump
power in the OPO.
7.2 Outlook
This section, a brief outlook for potential improvements to the OPO constructed for
this investigation and recent related technological advancements. Some of the most
promising areas for improvement will be discussed, including optimization of the signal
pulse’s duration, improvements to the pump laser’s power/energy, active jitter stabilization
techniques, thermal management for the OPO crystal, and enhancements to the OPO cavity
design.
99
7.2.1 OPO Pulse Duration
One of the most immediate places for improvement with the current system is the
optimization of pulse duration. External pulse compression is a commonly employed
technique to minimize the duration when the pulse coming out of the cavity is chirped. In
this study, dispersion was designed to be nearly uniform across the tunability of the OPO
but not optimized for near-zero dispersion for the output pulses. External pulse
compression was not employed due to the large tuning bandwidth of the OPO and the
additional costs from broadband pulse compression near 2 µm. From the pulse
measurements shown in Chap. 5, the TBP was measured to be 0.928 (from a minimum of
0.315 for a sech2 pulse) suggesting that the duration of the output pulses could be reduced
to ~170 fs; however, the minimum-achievable pulse duration is not clear. Higher-order
dispersion effects could easily increase the pulse length, and since no measurement of the
spectral phase was made it is difficult to predict the shortest pulse duration that could be
obtained. Improving the pump source is another strategy that could be used to reduce the
pulse duration.
7.2.2 Pump-Laser Power and Energy
There are several ways the pump laser could be upgraded as a pump source for an
ultrafast OPO. Direct improvements to the pulse energy have already been obtained from
a thin-disk laser with a similar design and identical core components. The pulse energy
could be improved by increasing the number of passes in the cavity. An active multipass
cavity using 11 passes (instead of the 6 used here) would nearly double the available pulse
energy without sacrificing the average power of both the pump and the signal [98].
Additional improvements to Yb:YAG thin-disk lasers have been made, including removing
astigmatism with a unique multipass cavity geometry, using KLM to initiate mode-locking
instead of a SESAM for shorter pulses and increasing cw-pump power to achieve higher
average powers for ultrafast pulses [38, 97].
Other thin-disk materials have been investigated to improve the bandwidth
available from a Yb:YAG. Recently, Yb:Lu2O3 was used to achieve pulse durations as
100
short as 142 fs with an average power of 7 W [185], Yb:LuScO3 achieved sub-100-fs pulses
[186], and Yb:CALGO reached 62 fs with a sub 10 W average powers [187]. Although
the average power of Yb:YAG is still significantly higher, it is reasonable to expect that
the power scalability of these devices will lead to pulses with several tens of microjoules
and hundreds of watts over average power in the near future.
7.2.3 Timing-Jitter Stabilization
The temporal stability and timing jitter could be improved in both the OPO and
TDML. In the TDML the method of improvement is straightforward. Of the options
reviewed, the best solution is to lock the TDML to an external crystal rf signal generator.
A commercially available solution was found through TEM Messtechnik but was not
employed in this test-bed study. The repetition rate of the most-stable multipass
configuration was 7.08 MHz. The TDML could be locked to a crystal oscillator generating
a frequency of 212.5 MHz (30th harmonic of the TDML’s repetition rate). This was an
affordable choice that also reduced the requirements of the locking circuit.
The circuit would control three types of motion to compensate for rapid changes in
the cavity and long-term drift. High-frequency drift could be compensated for with a short
stroke (2-µm), large-bandwidth lead zirconate titanate (PZT) mount attached to the optical
mount of one of the end mirrors. Low-frequency noise could be similarly compensated for
using a PZT with a longer stroke (12-µm). For long term drift, one of the end mirrors could
be mounted to a linear micrometer if the PZTs could not compensate for the change in
cavity length, which was expected due to the hundreds of microns in drift observed during
operation. The three-axis motion control would significantly reduce the phase noise for
nearly all frequencies below 15 kHz, greatly reducing the temporal jitter of the laser.
Due to the potential of misalignment from these controls a slave cavity would be
required to prevent damage to the thin disk. A slave cavity can be placed inside the TDML
by using a variable output coupler in a simple linear cavity arranged so that the loss for that
cavity would be higher than the TDML but would lase if alignment problems from the
101
main cavity created significant losses. Exceptional care would be required when installing
the timing stability system to avoid the introduction of power fluctuations from minor
alignment changes, which would not be monitored by the locking circuit.
Improving the temporal jitter for the OPO is slightly more complicated. Since the
wavelength of an OPO will change with the cavity length within a certain tolerance, locking
the OPO to an external frequency source is inadequate to ensure stable operation. An
alternative cavity stabilization approach based on wavelength fluctuations was first
demonstrated in a synchronously pumped dye laser [188]. Two photodiodes were used to
monitor the intensity on both sides of a spectrally dispersed beam, and their voltage
difference was used to adjust the cavity length in a simple electronic circuit. Although
limitations of this technology due to errors in finely structured spectra were present, it was
successfully implemented for femtosecond OPO’s to reduce temporal jitter [189].
This method was improved using of a one-dimensional position-sensitive detector
that allowed continuous monitoring of the OPO wavelength, independent of the incident
power level and shape of the pulse spectrum [190]. This technique has been successfully
utilized in ultrafast OPO’s, greatly improving their temporal stability [175]. The
implantation of this technology would be relatively straightforward in a 2-µm OPO,
although careful choice of a detector would be required or a portion of the output would
have to be frequency doubled to use as a signal for the control circuit.
An additional improvement could be a redesign of the OPO’s enclosure. The OPO
was exposed to lab environment without a full enclosure or environmental controls.
Implementing independent temperature and humidity controls would reduce instabilities
caused by sporadic air flow in the cavity and would result in more-reliable, long-term
operation. Another improvement that would be highly desirable is an upgrade to the
thermal management system.
102
7.2.4 Thermal Management of Nonlinear Crystals
As discussed in Chap. 6, limitations of the system used to actively cool the crystal
led to a loss in potential power. Multiple strategies could be employed to improve the
thermal management in this system, aside from different choices in the nonlinear crystal or
improvements to the manufacturing process. Devising ways to mitigate the types of thermal
effects discussed in the previous chapter will be of great importance as the power of
ultrafast OPO’s is scaled to the maximum-available power of various pump sources.
One strategy would be to place the beams closer to the interface between the TEC
and the nonlinear crystal. This commonly employed technique ensures that the heat
diffusion occurs very close to the location where heat is generated; however, this is
typically done for beams sizes much smaller than were required for this system. For this
investigation, a beam size of 570 µm was used while most OPO’s use a beam radius of less
than 100 µm inside the crystal. As seen in Fig. 6.4(e) the thermal gradient of the crystal
temperature near the cooling interface changes rapidly at a 1-mm distance. It is quite
possible that placing the cavity mode closer to the cooling surface would lead to an
irregular thermal gradient. It is unclear if this new gradient would cause nonuniform (and
thus suboptimal) phase matching over the beam surface or induce aberrations into the
beam.
Another method to improve the thermal management would be to actively cool
every non-optical surface of the crystal (i.e., surround the crystal). In this study, the TEC
drew heat only from the bottom face of the crystal. Looking again at Fig. 6.4(e), near the
maximum available power, a few details in the thermal distribution show the disadvantages
of drawing heat from just one side. Near the cooling surface the temperature of the crystal
is a few degrees cooler than top of the crystal. Neglecting the local heating near the beam,
the temperature across the crystal face is not uniform. If heat was dissipated from every
non-optical surface, it would likely reduce the thermal gradient across the beam. It would
be possible to create a metal housing with indium foil on the four sides of the crystal,
similar to the device used in this study. Additionally, a TEC could be attached to each side
103
of the housing, which would improve heat extraction in four directions. Although this
would improve the bulk cooling of the nonlinear crystal, it is uncertain how much it would
reduce the effect of local heating. Since this would be relatively easy to implement, it would
be worth investigating.
Other cooling strategies have recently been investigated for other parametric
devices that could possibly be used in this system to achieve higher powers. One promising
technique was the atomic bonding of a material with high thermal conductivity to the
optical surfaces of the nonlinear crystal. This technique was recently employed in an
optical parametric amplifier using a BBO crystal bonded to actively cooled sapphire plates
[191, 192]. Modifications to this approach would be necessary for it to be used in the BiBO
based OPO. To prevent Fresnel reflections between the cooling surface and the nonlinear
crystal, the indices of the two materials must be nearly identical (which is the case for BBO
and sapphire). An alternative material would have to be identified for this technique to be
extended to other nonlinear crystals, especially BiBO where the index was significantly
higher, in this orientation, than BBO.
7.2.5 Cavity Design
Other strategies could be employed that mitigate the result of the thermal effects
rather than prevent them. The calculated effects of the thermal gradient give insight into
the best methods to compensate for thermal lensing and phase-matching errors. Thermal
lensing had a large effect on imperfect pump/signal mode overlap and changes to the ROC
of the signal beam, leading to suboptimal gain. Phase-matching limitations from the
thermal gradient had a significant effect on wavelengths away from degeneracy, suggesting
that improvements to the width of the phase-matching curve would provide the maximum
benefit to the thermal limitations.
Thermally induced phase-matching errors can be mitigated by decreasing the
crystal length or increasing the noncollinear angle between the pump and signal beams.
The 8.4-mm crystal length chosen for this investigation optimized the gain without limiting
104
the bandwidth necessary for sub-100-fs pulses. Sufficient gain was available with
significantly shorter crystals (< 1 mm) using beams with smaller radii to achieve high
intensities. Due to the high energies in this system, small beam sizes led to a risk of damage.
The damage threshold of BiBO has not been well studied, however, and was based on
reports from other BiBO-based systems and the crystal vendor. Recent reports suggest that
ultrafast pulse intensities of 20 GW/cm2 [193] are possible in BiBO, suggesting that the
crystal length could be significantly reduced to accommodate broader phase matching
using a smaller beam radius.
The results of the thermal analysis highlight multiple strategies available to reduce
the impact of the thermal lensing. The increase in the ROC of the signal beam and the size
of the beam radius indicate that the beam waist was shifting away from the nonlinear
crystal. For this system, the shift of the beam radius was strictly due to the asymmetry of
the cavity. Since the cavity is longer on one side of the crystal than the other, the
introduction of an optical element with variable power causes a shift in the beam waist.
This can be mitigated in two ways: first, the cavity could be redesigned so that it is perfectly
symmetric around the nonlinear crystal. The cavity changes from the thermal lens would
then have a negligible effect on the position of the beam waist. This would require a careful
selection of the mirrors to achieve a completely symmetric design that could also have a
cavity length equal to the pump. A second option would be the incorporation of a variable
telescope. Previous systems with a large thermal load could implement such a device to
compensate for the thermally induced changes. A well-aligned variable telescope would
allowone to make changes during laser operation that would not interfere with the cavity
alignment and would maintain a constant beam waist in the gain medium. Due to the critical
alignment restrictions of this cavity, the former strategy is preferable to the latter, but either
method could be employed.
105
7.3 Conclusions
In this study, the construction and characterization of a scalable ultrafast OPO have
been presented. A high-average-power Yb:YAG thin-disk laser was constructed, capable
of producing 1.0-ps pulses at 1030 nm with a repetition rate of 7.08 MHz and average
powers exceeding 45 W. This laser was used to pump a high-energy, extended-cavity
femtosecond BiBO OPO. Using a noncollinear interaction geometry, the OPO could
produce 455-fs pulses at 7.08 MHz from 1.99 to 2.20 µm with energies up to 350 nJ with
a stable output. Even higher energies would be obtainable at the cost of efficiency and
stability, although the potential of even more power was available if thermally induced
limitations were overcome.
Despite the limitations of this system, what was accomplished in this investigation
was still quite impressive. The system described here achieved the highest pulse energy to
date (under stable performance) from any watt-class synchronously pumped ultrafast OPO.
These pulse energies belong to a class of OPO’s pumped by cutting-edge laser sources,
which are scalable to powers and pulse energies well beyond what was used in any of these
investigations. There have been no reports of a BiBO-based OPO with pulse energies
higher than reported here. Additionally, to the best of our knowledge, no femtosecond
oscillator operating beyond 2 µm has achieved energies greater than those reported here.
This research is another example of the potential from scalable ultrafast OPO’s that
have been constructed in recent years. Systems built in the past decade showcase the
potential of such devices, proving high-intensity pulses with high average powers from a
simple system, capable of operating over a wide range of wavelengths not traditionally
obtainable from other oscillators. The performance of these OPO’s come without any
significant change in classical design principles, but by strategic utilization of modern
technology to obtain pulse energies previously unavailable to OPO’s. With improvements
to the pulse energy and average power of pump sources for parametric devices, this trend
will continue to grow and open new doors for applications that can be solved by OPO’s.
106
While the system described in this work represents several landmarks in
performance, it is certainly work that could only be built on the shoulders of giants. So
much of the effort that has come before has made such a great contribution to the scientific
community that the work described here seems like a drop in the pond. Only after countless
hours toiling with the difficulties of designing and building one of these devices was the
author truly able to appreciate the dedication required to become an OPO expert. I can only
hope that the work presented here will be as important to others as previous work has been
to me, and that the results obtained in this research will aid in increasing the potential of
these devices.
107
References
1. R. Kingston, "Parametric amplification and oscillation at optical frequencies," Proceedings of the
Institute of Radio Engineers 50, 472-& (1962).
2. S. Akhmanov and R. Khokhlov, "Concerning one possibility of amplification of light waves," Sov.
Phys. JETP 16, 252-257 (1963).
3. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between Light
Waves in a Nonlinear Dielectric," Physical Review 127, 1918-1939 (1962).
4. J. Giordmaine and R. C. Miller, "Tunable Coherent Parametric Oscillation in LiNb O 3 at Optical
Frequencies," Physical Review Letters 14, 973 (1965).
5. R. Byer, M. Oshman, J. Young, and S. Harris, "Visible CW parametric oscillator," Applied
Physics Letters 13, 109-111 (1968).
6. R. Smith, J. Geusic, H. Levinstein, J. Rubin, S. Singh, and L. Van Uitert, "Continuous optical
parametric oscillation in Ba2NaNb5O15," Applied Physics Letters 12, 308-310 (1968).
7. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).
8. K. Burneika, M. Ignatavicius, V. Kabelka, A. Piskarskas, and A. Stabinis, "Parametric light
amplification and oscillation in KDP with mode-locked pump," IEEE Journal of Quantum
Electronics 8, 574-574 (1972).
9. M. Becker, D. Kuizenga, D. Phillion, and A. Siegman, "Analytic expressions for ultrashort pulse
generation in mode‐locked optical parametric oscillators," Journal of Applied Physics 45, 3996-
4005 (1974).
10. E. Cheung and J. Liu, "Theory of a synchronously pumped optical parametric oscillator in steady-
state operation," JOSA B 7, 1385-1401 (1990).
11. E. Cheung and J. Liu, "Efficient generation of ultrashort, wavelength-tunable infrared pulses,"
JOSA B 8, 1491-1506 (1991).
12. C. Fallnich, B. Ruffing, T. Herrmann, A. Nebel, R. Beigang, and R. Wallenstein, "Experimental
investigation and numerical simulation of the influence of resonator-length detuning on the output
power, pulse duration and spectral width of a cw mode-locked picosecond optical parametric
oscillator," Applied Physics B: Lasers and Optics 60, 427-436 (1995).
13. R. Laenen and T. Roth, "Numerical study and experimental results for a synchronously pumped
optical parametric oscillator in the saturation regime," JOSA B 14, 454-459 (1997).
108
14. G. Gale, M. Cavallari, and F. Hache, "Femtosecond visible optical parametric oscillator," JOSA B
15, 702-714 (1998).
15. D. Edelstein, E. Wachman, and C. Tang, "Broadly tunable high repetition rate femtosecond optical
parametric oscillator," Applied Physics Letters 54, 1728-1730 (1989).
16. Q. Fu, G. Mak, and H. Van Driel, "High-power, 62-fs infrared optical parametric oscillator
synchronously pumped by a 76-MHz Ti: sapphire laser," Optics letters 17, 1006-1008 (1992).
17. J. Dudley, D. Reid, M. Ebrahimzadeh, and W. Sibbett, "Characteristics of a noncritically
phasematched Ti: sapphire pumped femtosecond optical parametric oscillator," Optics
communications 104, 419-430 (1994).
18. G. Gale, M. Cavallari, T. Driscoll, and F. Hache, "Sub-20-fs tunable pulses in the visible from an
82-MHz optical parametric oscillator," Optics letters 20, 1562-1564 (1995).
19. K. C. Burr, C. Tang, M. A. Arbore, and M. M. Fejer, "Broadly tunable mid-infrared femtosecond
optical parametric oscillator using all-solid-state-pumped periodically poled lithium niobate,"
Optics letters 22, 1458-1460 (1997).
20. C. McGowan, D. Reid, Z. Penman, M. Ebrahimzadeh, W. Sibbett, and D. Jundt, "Femtosecond
optical parametric oscillator based on periodically poled lithium niobate," JOSA B 15, 694-701
(1998).
21. D. T. Reid, J. M. Dudley, M. Ebrahimzadeh, and W. Sibbett, "Ti: Sapphire Pumped Femtosecond
Optical Parametric Oscillator Exhibiting Soliton Formation," Journal of Modern Optics 41, 1231-
1242 (1994).
22. D. Reid, J. Dudley, M. Ebrahimzadeh, and W. Sibbett, "Soliton formation in a femtosecond
optical parametric oscillator," Optics letters 19, 825-827 (1994).
23. K. Puech, L. Lefort, and D. Hanna, "Broad tuning around degeneracy in a singly resonant
synchronously pumped parametric oscillator by means of a diffraction grating," JOSA B 16, 1533-
1538 (1999).
24. M. V. O’Connor, M. A. Watson, D. P. Shepherd, and D. C. Hanna, "Use of a birefringent filter for
tuning a synchronously pumped optical parametric oscillator," Applied Physics B: Lasers and
Optics 79, 15-23 (2004).
25. S. Marzenell, R. Beigang, and R. Wallenstein, "Synchronously pumped femtosecond optical
parametric oscillator based on AgGaSe2 tunable from 2 μm to 8 μm," Applied Physics B: Lasers
and Optics 69, 423-428 (1999).
26. T. Lang, T. Binhammer, S. Rausch, G. Palmer, M. Emons, M. Schultze, A. Harth, and U.
Morgner, "High power ultra-widely tuneable femtosecond pulses from a non-collinear optical
parametric oscillator (NOPO)," Optics express 20, 912-917 (2012).
27. M. Ghotbi, A. Esteban-Martin, and M. Ebrahim-Zadeh, "Tunable, high-repetition-rate,
femtosecond pulse generation in the ultraviolet," Optics letters 33, 345-347 (2008).
109
28. A. Esteban-Martin, V. Ramaiah-Badarla, V. Petrov, and M. Ebrahim-Zadeh, "Broadband, rapidly
tunable Ti: sapphire-pumped BiB 3 O 6 femtosecond optical parametric oscillator," Optics letters
36, 1671-1673 (2011).
29. C. McGowan, D. Reid, M. Ebrahimzadeh, and W. Sibbett, "Femtosecond pulses tunable beyond 4
μm from a KTA-based optical parametric oscillator," Optics communications 134, 186-190
(1997).
30. S. McCahon, S. Anson, D.-J. Jang, and T. F. Boggess, "Generation of 3–4-μm femtosecond pulses
from a synchronously pumped, critically phase-matched KTiOPO 4 optical parametric oscillator,"
Optics letters 20, 2309-2311 (1995).
31. C. Cleff, J. Epping, P. Gross, and C. Fallnich, "Femtosecond OPO based on LBO pumped
by a frequency-doubled Yb-fiber laser-amplifier system for CARS spectroscopy," Applied Physics
B 103, 795-800 (2011).
32. C. W. Rudy, A. Marandi, K. A. Ingold, S. J. Wolf, K. L. Vodopyanov, R. L. Byer, L. Yang, P.
Wan, and J. Liu, "Sub-50 fs pulses around 2070 nm from a synchronously-pumped, degenerate
OPO," Optics Express 20, 27589-27595 (2012).
33. D. Reid, M. Ebrahimzadeh, and W. Sibbett, "Efficient femtosecond pulse generation in the visible
in a frequency-doubled optical parametric oscillator based on RbTiOAsO 4," JOSA B 12, 1157-
1163 (1995).
34. M. Jankowski, A. Marandi, C. Phillips, R. Hamerly, K. Ingold, R. Byer, and M. Fejer,
"Femtosecond Temporal Simulton Formation in Optical Parametric Oscillators," in Nonlinear
Optics, (Optical Society of America, 2017), NTu1B. 3.
35. , retrieved https://www.ape-berlin.de/sites/default/files/OPO%20X.pdf.
36. P. Russbueldt, T. Mans, J. Weitenberg, H. Hoffmann, and R. Poprawe, "Compact diode-pumped
1.1 kW Yb: YAG Innoslab femtosecond amplifier," Optics letters 35, 4169-4171 (2010).
37. T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A.
Tünnermann, "Femtosecond fiber CPA system emitting 830 W average output power," Optics
letters 35, 94-96 (2010).
38. D. Bauer, I. Zawischa, D. H. Sutter, A. Killi, and T. Dekorsy, "Mode-locked Yb: YAG thin-disk
oscillator with 41 µJ pulse energy at 145 W average infrared power and high power frequency
conversion," Optics express 20, 9698-9704 (2012).
39. J. Brons, V. Pervak, E. Fedulova, D. Bauer, D. Sutter, V. Kalashnikov, A. Apolonskiy, O. Pronin,
and F. Krausz, "Energy scaling of Kerr-lens mode-locked thin-disk oscillators," Optics letters 39,
6442-6445 (2014).
40. O. H. Heckl, J. Kleinbauer, D. Bauer, S. Weiler, T. Metzger, and D. H. Sutter, "Ultrafast Thin-
Disk Lasers," in Ultrashort Pulse Laser Technology (Springer International Publishing, 2016), pp.
93-115.
41. T. Lamour, L. Kornaszewski, J. Sun, and D. Reid, "Yb: fiber-laser-pumped high-energy
picosecond optical parametric oscillator," Optics express 17, 14229-14234 (2009).
110
42. T. P. Lamour and D. T. Reid, "650-nJ pulses from a cavity-dumped Yb: fiber-pumped ultrafast
optical parametric oscillator," Optics express 19, 17557-17562 (2011).
43. J. Tate, T. Auguste, H. Muller, P. Salieres, P. Agostini, and L. DiMauro, "Scaling of wave-packet
dynamics in an intense midinfrared field," Physical review letters 98, 013901 (2007).
44. S. Hädrich, J. Rothhardt, M. Krebs, S. Demmler, A. Klenke, A. Tünnermann, and J. Limpert,
"Single-pass high harmonic generation at high repetition rate and photon flux," Journal of Physics
B: Atomic, Molecular and Optical Physics 49, 172002 (2016).
45. T. Südmeyer, S. Marchese, S. Hashimoto, C. Baer, G. Gingras, B. Witzel, and U. Keller,
"Femtosecond laser oscillators for high-field science," Nature Photonics 2, 599-604 (2008).
46. X. Zhou, P. Ranitovic, C. Hogle, J. Eland, H. Kapteyn, and M. Murnane, "Probing and controlling
non-Born-Oppenheimer dynamics in highly excited molecular ions," Nature Physics 8, 232-237
(2012).
47. C. B. Schaffer, A. Brodeur, J. F. García, and E. Mazur, "Micromachining bulk glass by use of
femtosecond laser pulses with nanojoule energy," Optics letters 26, 93-95 (2001).
48. T. M. Taczak and D. K. Killinger, "Development of a tunable, narrow-linewidth, cw 2.066-μm
Ho: YLF laser for remote sensing of atmospheric CO 2 and H 2 O," Applied optics 37, 8460-8476
(1998).
49. K. Scholle, E. Heumann, and G. Huber, "Single mode Tm and Tm, Ho: LuAG lasers for LIDAR
applications," Laser Physics Letters 1, 285 (2004).
50. K. Scholle, S. Lamrini, P. Koopmann, and P. Fuhrberg, "2 µm laser sources and their possible
applications," (2010).
51. R. W. Boyd, Nonlinear optics (Academic press, 2003).
52. J. Feinberg, "Self-pumped, continuous-wave phase conjugator using internal reflection," Optics
letters 7, 486-488 (1982).
53. R. Boyd, Contemporary nonlinear optics (Academic Press, 2012).
54. N. Kukhtarev, V. Markov, and S. Odulov, "Transient energy transfer during hologram formation
in LiNbO3 in external electric field," Optics Communications 23, 338-343 (1977).
55. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of nonlinear optical crystals
(Springer, 2013), Vol. 64.
56. N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Gue, G. Jaeger, A. Muller, and A. Migdall,
"Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,"
Optical Engineering 39, 1016-1024 (2000).
57. W. Koechner, Solid-state laser engineering (Springer, 2013), Vol. 1.
58. S. A. Akhmanov and R. Khokhlov, "New developments in non-linear optics," Physics-Uspekhi 11,
394-402 (1968).
111
59. S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, "Optics of femtosecond laser pulses,"
Moscow Izdatel Nauka (1988).
60. G. Cerullo and S. De Silvestri, "Ultrafast optical parametric amplifiers," Review of Scientific
Instruments 74, 1 (2003).
61. M. M. Fejer, G. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic
generation: tuning and tolerances," IEEE Journal of Quantum Electronics 28, 2631-2654 (1992).
62. E. Lim, M. Fejer, and R. Byer, "Second-harmonic generation of green light in periodically poled
planar lithium niobate waveguide," Electronics Letters 25, 174-175 (1989).
63. A. Scavennec, "Mismatch effects in synchronous pumping of the continuously operated mode-
locked dye laser," Optics Communications 17, 14-17 (1976).
64. J. Sun, B. J. Gale, and D. T. Reid, "Dual-color operation of a femtosecond optical parametric
oscillator exhibiting stable relative carrier-envelope phase-slip frequencies," Optics letters 31,
2021-2023 (2006).
65. M. Rodwell, T. Baer, B. Kolner, K. Weingarten, and D. Bloom, "Reduction of timing fluctuations
in a mode-locked Nd: YAG laser by electronic feedback," Optics letters 11, 638-640 (1986).
66. M. J. Rodwell, D. M. Bloom, and K. J. Weingarten, "Subpicosecond laser timing stabilization,"
IEEE Journal of Quantum Electronics 25, 817-827 (1989).
67. G. Kennedy, R. Grant, W. E. Sleat, and W. Sibbett, "Amplitude noise reduction of a coupled-
cavity mode-locked NaCl: OH− color-center laser by active synchronization," Optics letters 18,
208-210 (1993).
68. P. Beaud, W. Hodel, B. Zysset, and H. Weber, "Ultrashort pulse propagation, pulse breakup, and
fundamental soliton formation in a single-mode optical fiber," IEEE journal of quantum
electronics 23, 1938-1946 (1987).
69. Sellmeier, "Zur Erklärung der abnormen Farbenfolge im Spectrum einiger Substanzen," Annalen
der Physik 219, 272-282 (1871).
70. I. Malitson, "Interspecimen comparison of the refractive index of fused silica*," Josa 55, 1205-
1209 (1965).
71. R. Fork, O. Martinez, and J. Gordon, "Negative dispersion using pairs of prisms," Optics letters 9,
150-152 (1984).
72. R. L. Fork, C. B. Cruz, P. Becker, and C. V. Shank, "Compression of optical pulses to six
femtoseconds by using cubic phase compensation," Optics letters 12, 483-485 (1987).
73. E. Treacy, "Compression of picosecond light pulses," Physics Letters A 28, 34-35 (1968).
74. E. Treacy, "Optical pulse compression with diffraction gratings," IEEE Journal of quantum
Electronics 5, 454-458 (1969).
75. G. Steinmeyer, "Femtosecond dispersion compensation with multilayer coatings: toward the
optical octave," Applied optics 45, 1484-1490 (2006).
112
76. R. Szipöcs, C. Spielmann, F. Krausz, and K. Ferencz, "Chirped multilayer coatings for broadband
dispersion control in femtosecond lasers," Optics letters 19, 201-203 (1994).
77. A. Tikhonravov and M. Trubetskov, "Modern status and prospects of the development of methods
of designing multilayer optical coatings," Journal of Optical Technology 74, 845-850 (2007).
78. F. Gires and P. Tournois, "Interferometre utilisable pour la compression dimpulsions lumineuses
modulees en frequence," COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L
ACADEMIE DES SCIENCES 258, 6112-& (1964).
79. I. Sorokina, A. Cassanho, H. Jenssen, R. Szipöcs, E. Sorokin, and E. Wintner, "Prismless
passively mode-locked femtosecond Cr: LiSGaF laser," Optics letters 21, 1165-1167 (1996).
80. R. Stolen and A. Ashkin, "Optical Kerr effect in glass waveguide," Applied Physics Letters 22,
294-296 (1973).
81. J.-C. M. Diels, J. J. Fontaine, I. C. McMichael, and F. Simoni, "Control and measurement of
ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy," Applied Optics 24,
1270-1282 (1985).
82. D. J. Kane and R. Trebino, "Characterization of arbitrary femtosecond pulses using frequency-
resolved optical gating," IEEE Journal of Quantum Electronics 29, 571-579 (1993).
83. V. Wong and I. A. Walmsley, "Analysis of ultrashort pulse-shape measurement using linear
interferometers," Optics letters 19, 287-289 (1994).
84. C. Dorrer and I. A. Walmsley, "Accuracy criterion for ultrashort pulse characterization techniques:
application to spectral phase interferometry for direct electric field reconstruction," JOSA B 19,
1019-1029 (2002).
85. A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, "Scalable concept for diode-
pumped high-power solid-state lasers," Applied Physics B: Lasers and Optics 58, 365-372 (1994).
86. C. J. Saraceno, F. Emaury, C. Schriber, A. Diebold, M. Hoffmann, M. Golling, T. Südmeyer, and
U. Keller, "Toward millijoule-level high-power ultrafast thin-disk oscillators," IEEE Journal of
Selected Topics in Quantum Electronics 21, 106-123 (2015).
87. J.-P. Negel, A. Voss, M. A. Ahmed, D. Bauer, D. Sutter, A. Killi, and T. Graf, "1.1 kW average
output power from a thin-disk multipass amplifier for ultrashort laser pulses," Optics letters 38,
5442-5445 (2013).
88. C. J. Saraceno, F. Emaury, O. H. Heckl, C. R. Baer, M. Hoffmann, C. Schriber, M. Golling, T.
Südmeyer, and U. Keller, "275 W average output power from a femtosecond thin disk oscillator
operated in a vacuum environment," Optics express 20, 23535-23541 (2012).
89. C. Teisset, M. Schultze, R. Bessing, M. Haefner, S. Prinz, D. Sutter, and T. Metzger, "300 W
picosecond thin-disk regenerative amplifier at 10 kHz repetition rate," in Mid-Infrared Coherent
Sources, (Optical Society of America, 2013), JTh5A. 1.
90. C. J. Saraceno, F. Emaury, C. Schriber, M. Hoffmann, M. Golling, T. Südmeyer, and U. Keller,
"Ultrafast thin-disk laser with 80 μJ pulse energy and 242 W of average power," Optics letters 39,
9-12 (2014).
113
91. P. Lacovara, H. Choi, C. Wang, R. Aggarwal, and T. Fan, "Room-temperature diode-pumped Yb:
YAG laser," Optics letters 16, 1089-1091 (1991).
92. S. Ricaud, A. Jaffres, K. Wentsch, A. Suganuma, B. Viana, P. Loiseau, B. Weichelt, M. Abdou-
Ahmed, A. Voss, and T. Graf, "Femtosecond Yb: CaGdAlO 4 thin-disk oscillator," Optics letters
37, 3984-3986 (2012).
93. K. S. Wentsch, L. Zheng, J. Xu, M. A. Ahmed, and T. Graf, "Passively mode-locked Yb 3+: Sc 2
SiO 5 thin-disk laser," Optics letters 37, 4750-4752 (2012).
94. C. J. Saraceno, O. H. Heckl, C. R. Baer, M. Golling, T. Südmeyer, K. Beil, C. Kränkel, K.
Petermann, G. Huber, and U. Keller, "SESAMs for high-power femtosecond modelocking: power
scaling of an Yb: LuScO 3 thin disk laser to 23 W and 235 fs," Optics express 19, 20288-20300
(2011).
95. T. Südmeyer, C. Kränkel, C. R. E. Baer, O. H. Heckl, C. J. Saraceno, M. Golling, R. Peters, K.
Petermann, G. Huber, and U. Keller, "High-power ultrafast thin disk laser oscillators and their
potential for sub-100-femtosecond pulse generation," Applied Physics B 97, 281-295 (2009).
96. K. Beil, C. J. Saraceno, C. Schriber, F. Emaury, O. H. Heckl, C. R. Baer, M. Golling, T.
Südmeyer, U. Keller, and C. Kränkel, "Yb-doped mixed sesquioxides for ultrashort pulse
generation in the thin disk laser setup," Applied Physics B 113, 13-18 (2013).
97. J. Neuhaus, D. Bauer, J. Zhang, A. Killi, J. Kleinbauer, M. Kumkar, S. Weiler, M. Guina, D. H.
Sutter, and T. Dekorsy, "Subpicosecond thin-disk laser oscillator with pulse energies of up to 25.9
microjoules by use of an active multipass geometry," Optics express 16, 20530-20539 (2008).
98. J. Neuhaus, J. Kleinbauer, A. Killi, S. Weiler, D. H. Sutter, and T. Dekorsy, "Pulse energies
exceeding 13 microjoules from a passively mode-locked Yb: YAG thin-disk oscillator by use of a
self-imaging active multipass geometry," in Conference on Lasers and Electro-Optics, (Optical
Society of America, 2008), CFB1.
99. A. Killi, K. Wallmeroth, T. Vethake, and V. Kuhn, "Cooling disk lasers," (Google Patents, 2016).
100. A. Giesen and J. Speiser, "Fifteen years of work on thin-disk lasers: results and scaling laws,"
IEEE Journal of Selected Topics in Quantum Electronics 13, 598-609 (2007).
101. J. Neuhaus, "Passively mode-locked Yb: YAG thin-disk laser with active multipass geometry,"
(PhD thesis, University Konstanz, 2009).
102. W. F. Krupke, "Ytterbium solid-state lasers. The first decade," IEEE Journal of Selected Topics in
Quantum Electronics 6, 1287-1296 (2000).
103. S. Reuter, Numerische Modellierung und experimentelle Charakterisierung der physikalischen
Eigenschaften von modengekoppelten Femtosekunden-Yb: YAG-und Yb: KGW-lasern (Cuvillier,
2004).
104. T. Y. Fan, "Heat generation in Nd: YAG and Yb: YAG," IEEE Journal of Quantum Electronics
29, 1457-1459 (1993).
114
105. V. V. Ter-Mikirtychev and V. A. Fromzel, "Directly single-diode-pumped continuous-wave Yb
3+: YAG laser tunable in the 1047–1051-nm wavelength range," Applied optics 39, 4964-4969
(2000).
106. C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, "A 1-kW CW thin disc laser," IEEE
Journal of selected topics in quantum electronics 6, 650-657 (2000).
107. R. C. Powell, Physics of solid-state laser materials (Springer Science & Business Media, 1998),
Vol. 1.
108. O. Antipov, D. Bredikhin, O. Eremeykin, A. Savikin, E. Ivakin, and A. Sukhadolau, "Electronic
mechanism for refractive-index changes in intensively pumped Yb: YAG laser crystals," Optics
letters 31, 763-765 (2006).
109. S. Chénais, F. Balembois, F. Druon, G. Lucas-Leclin, and P. Georges, "Thermal Lensing in
Diode-Pumped Ytterbium Lasers-Part II: evaluation of quantum efficiencies and thermo-optic
coefficients," IEEE journal of quantum electronics 40, 1235-1243 (2004).
110. A. M. Scott, G. Cook, and A. P. Davies, "Efficient high-gain laser amplification from a low-gain
amplifier by use of self-imaging multipass geometry," Applied optics 40, 2461-2467 (2001).
111. M. Kumkar, "Laser amplification system," US Pat 6765947(2006).
112. T. Petersen and J. Bromage, "Intracavity Chirped-Pulse Amplification for High-Energy Ultrafast
Optical Parametric Oscillators," in Frontiers in Optics, (Optical Society of America, 2012),
FM4G. 3.
113. H. Kogelnik and T. Li, "Laser beams and resonators," Applied Optics 5, 1550-1567 (1966).
114. P. French, "The generation of ultrashort laser pulses," Reports on Progress in Physics 58, 169
(1995).
115. F. Kartner, I. Jung, and U. Keller, "Soliton mode-locking with saturable absorbers," IEEE Journal
of Selected Topics in Quantum Electronics 2, 540-556 (1996).
116. F. Kärtner and U. Keller, "Stabilization of solitonlike pulses with a slow saturable absorber,"
Optics letters 20, 16-18 (1995).
117. R. Paschotta and U. Keller, "Passive mode locking with slow saturable absorbers," Applied
Physics B: Lasers and Optics 73, 653-662 (2001).
118. O. Martinez, R. Fork, and J. P. Gordon, "Theory of passively mode-locked lasers including self-
phase modulation and group-velocity dispersion," Optics letters 9, 156-158 (1984).
119. U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger,
N. Matuschek, and J. A. Der Au, "Semiconductor saturable absorber mirrors (SESAM's) for
femtosecond to nanosecond pulse generation in solid-state lasers," IEEE Journal of selected topics
in QUANTUM ELECTRONICS 2, 435-453 (1996).
120. A. Kost and E. M. Garmire, Nonlinear optics in Semiconductors (Academic press, 1999), Vol. 58.
121. U. Keller, "Recent developments in compact ultrafast lasers," Nature 424, 831-838 (2003).
115
122. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, "Sensitive
measurement of optical nonlinearities using a single beam," IEEE journal of quantum electronics
26, 760-769 (1990).
123. M. Sheik-Bahae, J. Wang, R. DeSalvo, D. Hagan, and E. Van Stryland, "Measurement of
nondegenerate nonlinearities using a two-color Z scan," Optics letters 17, 258-260 (1992).
124. E. Van Stryland, M. Sheik-Bahae, A. Said, and D. Hagan, "Characterization of nonlinear optical
absorption and refraction," Progress in crystal growth and characterization of materials 27, 279-
311 (1993).
125. E. W. Van Stryland and M. Sheik-Bahae, "Z-scan measurements of optical nonlinearities,"
Characterization techniques and tabulations for organic nonlinear materials 18, 655-692 (1998).
126. J. Wang, M. Sheik-Bahae, A. Said, D. J. Hagan, and E. W. Van Stryland, "Time-resolved Z-scan
measurements of optical nonlinearities," JOSA B 11, 1009-1017 (1994).
127. R. Fluck, R. Häring, R. Paschotta, E. Gini, H. Melchior, and U. Keller, "Eyesafe pulsed microchip
laser using semiconductor saturable absorber mirrors," Applied physics letters 72, 3273-3275
(1998).
128. M. Haiml, R. Grange, and U. Keller, "Optical characterization of semiconductor saturable
absorbers," Applied Physics B: Lasers and Optics 79, 331-339 (2004).
129. A. Schlatter, S. C. Zeller, R. Grange, R. Paschotta, and U. Keller, "Pulse-energy dynamics of
passively mode-locked solid-state lasers above the Q-switching threshold," JOSA B 21, 1469-
1478 (2004).
130. U. Keller, D. Miller, G. Boyd, T. Chiu, J. Ferguson, and M. Asom, "Solid-state low-loss
intracavity saturable absorber for Nd: YLF lasers: an antiresonant semiconductor Fabry–Perot
saturable absorber," Optics letters 17, 505-507 (1992).
131. C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, "Q-switching stability
limits of continuous-wave passive mode locking," JOSA B 16, 46-56 (1999).
132. J. A. Der Au, D. Kopf, F. Morier-Genoud, M. Moser, and U. Keller, "60-fs pulses from a diode-
pumped Nd: glass laser," Optics letters 22, 307-309 (1997).
133. F. Kurtner, J. A. Der Au, and U. Keller, "Mode-locking with slow and fast saturable absorbers-
what's the difference?," IEEE Journal of Selected Topics in Quantum Electronics 4, 159-168
(1998).
134. A. Siegman, "Wow to (Maybe) Measure Laser Beam Quality," (1998).
135. A. E. Siegman, "Defining, measuring, and optimizing laser beam quality," in OE/LASE'93: Optics,
Electro-Optics, & Laser Applications in Science& Engineering, (International Society for Optics
and Photonics, 1993), 2-12.
136. S. Kimura and C. Munakata, "Measurement of a Gaussian laser beam spot size using a boundary
diffraction wave," Applied Optics 27, 84-88 (1988).
116
137. R. Pantell, "The laser oscillator with an external signal," Proceedings of the IEEE 53, 474-477
(1965).
138. A. Tyazhev, D. Kolker, G. Marchev, V. Badikov, D. Badikov, G. Shevyrdyaeva, V. Panyutin, and
V. Petrov, "Mid-infrared optical parametric oscillation in the wide-bandgap BaGa 4 S 7 nonlinear
crystal," in Lasers and Electro-Optics (CLEO), 2012 Conference on, (IEEE, 2012), 1-2.
139. Y. Peng, X. Wei, W. Wang, and D. Li, "High-power 3.8μm tunable optical parametric oscillator
based on PPMgO:CLN," Optics Communications 283, 4032-4035 (2010).
140. G. Marchev, F. Pirzio, A. Agnesi, G. Reali, V. Petrov, A. Tyazhev, P. G. Schunemann, and K. T.
Zawilski, "1064nm pumped CdSiP2 optical parametric oscillator generating sub-300 ps pulses
near 6.15μm at 1–10 kHz repetition rates," Optics Communications 291, 326-328 (2013).
141. V. Petrov, "Frequency down-conversion of solid-state laser sources to the mid-infrared spectral
range using non-oxide nonlinear crystals," Progress in Quantum Electronics 42, 1-106 (2015).
142. J. Rothhardt, S. Demmler, S. Hädrich, T. Peschel, J. Limpert, and A. Tünnermann, "Thermal
effects in high average power optical parametric amplifiers," Optics letters 38, 763-765 (2013).
143. M. H. Dunn and M. Ebrahimzadeh, "Parametric generation of tunable light from continuous-wave
to femtosecond pulses," Science 286, 1513-1517 (1999).
144. Y.-R. Shen, "The principles of nonlinear optics," New York, Wiley-Interscience, 1984, 575 p.
1(1984).
145. D. Reid, M. Ebrahimzadeh, and W. Sibbett, "Noncritically phase-matched Ti: sapphire-pumped
femtosecond optical parametric oscillator based on RbTiOAsO 4," Optics letters 20, 55-57 (1995).
146. L. R. Marshall and A. Kaz, "Eye-safe output from noncritically phase-matched parametric
oscillators," JOSA B 10, 1730-1736 (1993).
147. L. E. Myers, R. Eckardt, M. Fejer, R. Byer, W. Bosenberg, and J. Pierce, "Quasi-phase-matched
optical parametric oscillators in bulk periodically poled LiNbO 3," JOSA B 12, 2102-2116 (1995).
148. L. Lefort, K. Puech, S. Butterworth, Y. Svirko, and D. Hanna, "Generation of femtosecond pulses
from order-of-magnitude pulse compression in a synchronously pumped optical parametric
oscillator based on periodically poled lithium niobate," Optics letters 24, 28-30 (1999).
149. S. C. Kumar and M. Ebrahim-Zadeh, "High-power, fiber-laser-pumped, picosecond optical
parametric oscillator based on MgO: sPPLT," Optics express 19, 26660-26665 (2011).
150. A. Dubietis, R. Butkus, and A. P. Piskarskas, "Trends in chirped pulse optical parametric
amplification," IEEE Journal of selected topics in quantum electronics 12, 163-172 (2006).
151. J. Rothhardt, S. Demmler, S. Hädrich, J. Limpert, and A. Tünnermann, "Octave-spanning OPCPA
system delivering CEP-stable few-cycle pulses and 22 W of average power at 1 MHz repetition
rate," Optics express 20, 10870-10878 (2012).
152. S. Banerjee, N. Umemura, and K. Kato, "Sellmeier and thermo-optic dispersion formulas for
AgGa (S1-xSex) 2 with application in mid-IR generation," in Lasers and Applications in Science
and Engineering, (International Society for Optics and Photonics, 2006), 610314-610314-610316.
117
153. E. Cheung, J. Liu, K. Koch, and G. T. Moore, "Measurements of second-order nonlinear optical
coefficients from the spectral brightness of parametric fluorescence," Optics letters 19, 168-170
(1994).
154. D. Armstrong, W. Alford, T. Raymond, and A. Smith, "Absolute measurement of the effective
nonlinearities of KTP and BBO crystals by optical parametric amplification," Applied optics 35,
2032-2040 (1996).
155. D. Eimerl, S. Velsko, L. Davis, and F. Wang, "Progress in nonlinear optical materials for high
power lasers," Progress in Crystal Growth and Characterization of Materials 20, 59-113 (1990).
156. H. Hellwig, J. Liebertz, and L. Bohatý, "Linear optical properties of the monoclinic bismuth
borate BiB3O6," Journal of Applied Physics 88, 240-244 (2000).
157. V. Badikov, D. Badikov, G. Shevyrdyaeva, A. Tyazhev, G. Marchev, V. Panyutin, V. Petrov, and
A. Kwasniewski, "Phase‐matching properties of BaGa4S7 and BaGa4Se7: Wide‐bandgap
nonlinear crystals for the mid‐infrared," physica status solidi (RRL)-Rapid Research Letters 5, 31-
33 (2011).
158. V. Kemlin, P. Brand, B. Boulanger, P. Segonds, P. G. Schunemann, K. T. Zawilski, B. Ménaert,
and J. Debray, "Phase-matching properties and refined Sellmeier equations of the new nonlinear
infrared crystal CdSiP 2," Optics letters 36, 1800-1802 (2011).
159. N. Pylneva, N. Kononova, A. Yurkin, G. Bazarova, and V. Danilov, "Growth and non-linear
optical properties of lithium triborate crystals," Journal of crystal growth 198, 546-550 (1999).
160. L. Cheng, L.-T. Cheng, J. Bierlein, F. Zumsteg, and A. Ballman, "Properties of doped and
undoped crystals of single domain KTiOAsO4," Applied physics letters 62, 346-348 (1993).
161. J. D. Bierlein, "Potassium Titanyl Phosphate (KTP): Properties, Recent Advances and New
Applications," in 1989 Orlando Symposium, (International Society for Optics and Photonics,
1989), 2-12.
162. S. Das, G. C. Bhar, S. Gangopadhyay, and C. Ghosh, "Linear and nonlinear optical properties of
ZnGeP 2 crystal for infrared laser device applications: revisited," Applied optics 42, 4335-4340
(2003).
163. N. Umemura, S. Banerjee, K. Miyata, F. Tanno, and K. Kato, "Thermo-optic dispersion formula
for BiB3O6," in Quantum Electronics and Laser Science Conference, (Optical Society of
America, 2005), JTuC18.
164. R. Riedel, J. Rothhardt, K. Beil, B. Gronloh, A. Klenke, H. Höppner, M. Schulz, U. Teubner, C.
Kränkel, and J. Limpert, "Thermal properties of borate crystals for high power optical parametric
chirped-pulse amplification," Optics express 22, 17607-17619 (2014).
165. T. Petersen, J. Zuegel, and J. Bromage, "High-average-power, 2-μm femtosecond optical
parametric oscillator synchronously pumped by a thin-disk, mode-locked laser," Optics Express
25, 8840-8844 (2017).
166. P. N. Gavryushkin, L. I. Isaenko, A. P. Yelisseyev, V. A. Gets, and O. S. Il’ina, "Growth,
Morphology and Optical Properties of γ-BiB3O6Single Crystals," Crystal Growth & Design 12,
75-78 (2011).
118
167. P. Wright and B. Cockayne, "The organometallic chemical vapour deposition of ZnS and ZnSe at
atmospheric pressure," Journal of Crystal Growth 59, 148-154 (1982).
168. C. Nabors, S. Yang, T. Day, and R. Byer, "Coherence properties of a doubly resonant monolithic
optical parametric oscillator," JOSA B 7, 815-820 (1990).
169. S. Brosnan and R. Byer, "Optical parametric oscillator threshold and linewidth studies," IEEE
Journal of Quantum Electronics 15, 415-431 (1979).
170. R. Paschotta, "Beam quality deterioration of lasers caused by intracavity beam distortions," Optics
Express 14, 6069-6074 (2006).
171. E. Hecht, "Optics, 4th," International edition, Addison-Wesley, San Francisco 3(2002).
172. N. Bloembergen, "Role of cracks, pores, and absorbing inclusions on laser induced damage
threshold at surfaces of transparent dielectrics," Applied optics 12, 661-664 (1973).
173. J. Dobrowolski, A. Tikhonravov, M. K. Trubetskov, B. T. Sullivan, and P. Verly, "Optimal single-
band normal-incidence antireflection coatings," Applied optics 35, 644-658 (1996).
174. T. Petersen and J. Bromage, "Thin-Disk Pumped, High-Average-Power, 2.06-µm BiB 3 O 6
Femtosecond Optical Parametric Oscillator," in Laser Science, (Optical Society of America,
2015), LTh4I. 6.
175. T. P. Lamour, J. Sun, and D. T. Reid, "Wavelength stabilization of a synchronously pumped
optical parametric oscillator: optimizing proportional-integral control," The Review of scientific
instruments 81, 053101 (2010).
176. V. Shcheslavskiy, V. Yakovlev, and A. Ivanov, "High-energy self-starting femtosecond Cr 4+: Mg
2 SiO 4 oscillator operating at a low repetition rate," Optics letters 26, 1999-2001 (2001).
177. H. Kogelnik, "On the propagation of Gaussian beams of light through lenslike media including
those with a loss or gain variation," Applied Optics 4, 1562-1569 (1965).
178. L. Pedrotti, "SJ Leno M," Pedrotti Leno S. Pedrotti, Frank “Introduction to Optics third edition”
p17-25 (2007).
179. T. Petersen, J. Zuegel, and J. Bromage, "High-Energy Infrared Femtosecond Optical Parametric
Oscillator Synchronously Pumped by a Thin-Disk Laser," in Advanced Solid State Lasers,
(Optical Society of America, 2016), ATu1A. 6.
180. T. Petersen, J. D. Zuegel, and J. Bromage, "Thermal effects in an ultrafast BiB3O6 optical
parametric oscillator at high average powers," Applied Optics 56, 6923-6929 (2017).
181. M. J. Riedl, Optical design fundamentals for infrared systems (SPIE press, 2001), Vol. 48.
182. H. Kogelnik, "Imaging of optical modes—resonators with internal lenses," Bell Labs Technical
Journal 44, 455-494 (1965).
183. W. Koechner, "Thermal lensing in a Nd: YAG laser rod," Applied optics 9, 2548-2553 (1970).
119
184. I. Jovanovic, B. J. Comaskey, and D. M. Pennington, "Angular effects and beam quality in optical
parametric amplification," Journal of Applied Physics 90, 4328-4337 (2001).
185. C. J. Saraceno, S. Pekarek, O. H. Heckl, C. R. Baer, C. Schriber, M. Golling, K. Beil, C. Kränkel,
G. Huber, and U. Keller, "Self-referenceable frequency comb from an ultrafast thin disk laser,"
Optics express 20, 9650-9656 (2012).
186. C. J. Saraceno, O. H. Heckl, C. R. Baer, C. Schriber, M. Golling, K. Beil, C. Kränkel, T.
Südmeyer, G. Huber, and U. Keller, "Sub-100 femtosecond pulses from a SESAM modelocked
thin disk laser," Applied Physics B 106, 559-562 (2012).
187. A. Diebold, F. Emaury, C. J. Saraceno, C. Schriber, M. Golling, T. Südmeyer, and U. Keller, "62-
fs pulses from a SESAM modelocked Yb: CALGO thin disk laser," in Advanced Solid State
Lasers, (Optical Society of America, 2013), AF3A. 2.
188. J. Chesnoy and L. Fini, "Stabilization of a femtosecond dye laser synchronously pumped by a
frequency-doubled mode-locked YAG laser," Optics letters 11, 635-637 (1986).
189. M. D. Dawson, T. F. Boggess, A. L. Smirl, and D. Maxson, "Cavity-length detuning effects and
stabilization of a synchronously pumped femtosecond linear dye laser," Optics letters 13, 126-128
(1988).
190. D. Butterworth, S. Girard, and D. Hanna, "A simple technique to achieve active cavity-length
stabilisation in a synchronously pumped optical parametric oscillator," Optics communications
123, 577-582 (1996).
191. C. Rothhardt, J. Rothhardt, A. Klenke, T. Peschel, R. Eberhardt, J. Limpert, and A. Tünnermann,
"BBO-sapphire sandwich structure for frequency conversion of high power lasers," Optical
Materials Express 4, 1092-1103 (2014).
192. J. Rothhardt, C. Rothhardt, M. Müller, A. Klenke, M. Kienel, S. Demmler, T. Elsmann, M.
Rothhardt, J. Limpert, and A. Tünnermann, "100 W average power femtosecond laser at 343 nm,"
Optics letters 41, 1885-1888 (2016).
193. F. Geier, J. Pupeikis, H. Geiseler, N. Ishii, T. Kanai, and J. Itatani, "Generation of Carrier-
Envelope Phase-Stable 8.1-fs Infrared Pulses at 20 kHz in a BiB 3 O 6-based Optical Parametric
Amplifier," in Advanced Solid State Lasers, (Optical Society of America, 2016), ATh1A. 2.
