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DEVELOPMENT AND CHARACTERIZATION OF A HIGH AVERAGE POWER, SINGLE-
STAGE REGENERATIVE CHIRPED PULSE AMPLIFIER
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
To my family
Graduate school has been an extremely enriching experience dispelling my naivety in more
ways than one.
I owe a great deal to my mentor Dr. David Reitze for his guidance and encouragement that
saw me through these past six years in graduate school. Not only did he acquaint me with the
rudiments of ultrafast lasers, but he also helped me gain a deep insight and perspective into this
field. I very much appreciate Dr. Reitze's treatment of his graduate students as junior colleagues.
It is encouraging as well as challenging reminding me always of my discerning decision of
joining his research team.
I am grateful to my committee members Profs. Hagen, Tanner, Stanton and Kleiman for
serving on my supervisory committee and for all their advice and suggestions. I would also like
to thank Prof. Nicolo Omenetto for agreeing to serve on my committee at an extremely short
notice and was patient enough to read through my thesis and spot typos in just two days!
My sincere gratitude also goes to my fellow graduate students Jinho Lee, Shengbo Xu and
Xiaoming Wang for all their help and for creating a pleasant environment in the laboratory. I
would like to thank Dr. Yoonseok Lee and Pradeep Bhupathi for their ideas and suggestions
about cryogenics and vacuum systems and also for all the stycast that they so willingly made for
me! Bill Malphurs and Marc Link from the machine shop deserve special mention for their
brilliant imagination and craftsmanship. Many thanks go to Luke Williams for letting me benefit
from his expertise in thermodynamics and CAD designing software. I am extremely grateful to
the support staff in the Physics department, Jay Horton, Don Brennan and many more for lending
a helping hand whenever I needed one. I thank Darlene Latimer and Nathan Williams for all
their assistance during times of distress! I would also like to thank all the folks in Tanner Lab
and Hebard Lab for letting me borrow sundry items and equipment from their laboratories from
time to time.
I wish to thank my friends Ronojoy Saha, Karthik Shankar, Aparna Baskaran, Naveen
Margankunte from the physics department and many others in Gainesville for providing respite
from the trials and tribulations of graduate school with countless Friday nights filled with revelry!i
Finally I wish to thank my parents and my siblings for their unconditional support and
patience over all these years and the undaunted faith they have in me. Last but not least, a great
deal of credit goes to Rajkeshar Singh who, although my husband of just two years, has been my
best buddy for almost a decade now. I definitely do not envision myself here today if it were not
TABLE OF CONTENTS
ACKNOWLEDGMENT S .............. .................... iv
LI ST OF T ABLE S ............ ...... ._ .............. viii..
LI ST OF FIGURE S .............. .................... ix
AB S TRAC T ......_ ................. ..........._..._ xiii..
1 INTRODUCTION .............. ...............1.....
2 ULTRASHORT PULSE GENERATION AND CHARACTERIZATION ............... .... ...........9
2.1 Relationship between Duration and Spectral Width ................. ............................9
2.2 Time Bandwidth Product ................. ...............12................
2.3 Dispersion ................. ...............14.................
2.4 Nonlinear Effects ................. ............... ...............16......
2.4.1 Second Order Susceptibility ................. ......... ...............16. ....
2.4.2 Third Order Susceptibility ................. ......... ...............18. ....
18.104.22.168 Nonlinear index of refraction ................. ........._. ....... 18..... ...
22.214.171.124 Kerr lens effect ............ ..... ._ ...............19..
126.96.36.199 Self phase-modulation .....__.....___ ..........._ .............2
2.5 Summary ............ ..... ._ ...............22....
3 DESIGN AND CONSTRUCTION OF A HIGH AVERAGE POWER, SINGLE STAGE
CHIRPED PULSE AMPLIFIER ............ ..... ._ ...............23...
3.1 Introducti on ............... .... .....__ .. ...............23..
3.2 Why Chirped Pulse Amplifieation? ............ .....__ ....._ ...........2
3.3 Ti: Sapphire as Gain Medium ............ ..... ._ ...............26..
3.4 M ode-locked Laser ............ ..... ._ ...............28...
3.5 Dispersion .............. .... .._ ...............31...
3.6 Pulse Stretching and Recompression............... .............3
3.7 Ti: Sapphire based Laser Amplifier............... ...............3
3.7. 1 Process of Amplifieation ............ ..... ._ ...............41.
3.7.2 Types of Amplifiers ............ ..... ._ ...............42..
3.8 Pulse Shaping............... .. ..............4
3.9 Ultrashort Pulse Measurement............... ..............4
3.10 Chirped Pulse Amplifier system ............ ......__ ...............49.
3.11 Summary ............ ..... ._ ...............50....
4 THERMAL EFFECTS IN HIGH POWER LASER AMPLIFIER ................. ............... ....52
4.1 Introducti on ................. ...............52........... ....
4.2 Theoretical Background.................. .............5
4.3 Methods to Reduce Thermal Effects .................. ...............61..
4.4 Liquid Nitrogen Cooled Ti Al203 Laser Amplifier ................. ................. ........ 64
4.5 Construction of a Regenerative Amplifier Cavity ........._._........__. ........._......66
4.6 Measurement of Thermal Lens ........._.___..... .___ ...............68...
4.7 Calculation of Thermal Lens ................. ....... ... .............7
4.8 Direct Measurement of the Optical Path Deformations ........._._. ..... ._.__............76
4.9 Effects of Thermal Aberrations on Beam Shape .............. ...............78....
4.10 Summary ............ ..... .._ ...............80...
5 CHARACTERIZATION AND OPTIMIZATION OF HIGH AVERAGE POWER CPA......82
5.1 Amplifier Performance .............. ...............82....
5.1.1 Average Power, Pulse Energy .............. ...............82....
5.1.2 Spatial Beam quality............... ...............83
5.1.3 Spectral Characteristics .............. .. ...............85
5.1.4 Shot-to-shot Pulse Energy Characterization.................. ..........8
5.2 Design Considerations for Single Stage Cryogenic CPA System ........._..... ..............88
5.3 Compensation of Modal Astigmatism ............__......__ ...._ ...........9
5.4 Summary ............ ..... ._ ...............94....
6 CONCLUSION ............ ..... ._ ...............95....
A FREQUENCY RESOLVED OPTICAL GATING (FROG) .................. ................9
B ACOUSTO-OPTIC PROGRAMMABLE DISPERSIVE FILTER ................. ................. 105
B.1 Bragg diffraction of light by Acoustic waves ................. ...............105.............
B.2 Amplitude and Phase control using an AOPDF............... ...............107.
LI ST OF REFERENCE S ................. ...............111................
BIOGRAPHICAL SKETCH ................. ...............120......... ......
LIST OF TABLES
2-1 Time bandwidth product for different pulse shapes (Figure 2-4)..........._ ... ...............1 3
4-1 Quantitative estimate of thermal effects in sapphire............... ...............56
4-2 Thermal properties of sapphire at 300 and 77 oK. .............. ...............65....
5-1 Performance of the CPA system ................. ...............88.............
LIST OF FIGURES
1-1 High Harmonic generation in Ar gas. .............. ...............4.....
1-2 A sheet of invar micromachined with (a) 10 nsec pulses and (b) 100-fs pulses ..................5
1-3 Schematic of surface spectroscopy (a) and a typical Sum-frequency Generation
spectra (b)............... ...............6...
2-1 Evolution of a plane monochromatic wave in time (a) and a plane wave with
Gaussian amplitude modulation in time (b) ................. ...............10...............
2-2 Fourier transform of the (a) cosine function in Figure 2-1(a) and (b) Gaussian
function in Figure 2-1 (b)............... ...............10..
2-3 Time evolution of a Gaussian electric Hield with a quadratic chirp (b = 10) on it.............12
2-4 Intensity profie for a Gaussian pulse (solid blue curve), hyperbolic secant (dashed
blue curve) and a lorentzian (red curve). ............. ...............14.....
2-5 Schematic relationship between phase and group velocities for a transparent
2-6 Geometry of second-harmonic generation (a) and schematic energy level diagram (b).
2-7 Geometry (a) and schematic of third order generation (b). ................ ............ .........18
2-8 Schematic representation of the Kerr lensing effect ........__............_. ........._.._. ...20
2-9 Schematic of Self-phase modulation. ............. ...............22.....
3-1 A schematic representation of a Chirped Pulse Amplifier system. ............. ..................25
3-2 Absorption and emission spectra for Ti: sapphire. ............. ...............26.....
3-3 Self-mode-locked Ti: sapphire laser oscillator. ............. ...............27.....
3-4 Generation of ultrashort pulses by the mechanism of mode locking. ........._.._... ..............28
3-5 Oscillator spectrum as measured by a fiber spectrometer and its Fourier transform.........30O
3-6 A Gaussian pulse possessing (a) linear chirp (#"(mi,)) on it and (b) qluadratic chirp
(#"'(mi,)) on it. ......____ ...._ ....._ ...._ .... ......._ ..................33
3-7 Dispersive delay lines .............. ...............34....
3-8 Prism delay line............... ...............36..
3-9 Schematic of the stretcher layout. Oscillator pulses of duration ~20 fs are stretched to
~ 200 ps without any chromatic aberrations. ............. ...............38.....
3-10 Spectrum measured from the oscillator and after propagation through the pulse
stretcher ................. ...............38.................
3-11 Effect of gain narrowing in amplifiers, the red curve is the fundamental laser
spectrum and the blue curve is after five passes through the laser medium. .....................42
3-12 Schematic representation of a multipass amplifier system. ............... ...................4
3-13 A schematic representation of the regenerative amplifier in our laboratory. ................... .44
3-14 Amplified pulse spectrum shows a FWHM of 33-nm. Inset, blue curve is the shaped
oscillator spectrum using an AOPDF, which yielded an amplified bandwidth of 33-
nm, obtained from the original oscillator spectrum (red curve). ............. ....................46
3-15 Experimental auto-correlator set up. ........... .....__ ...............48..
3-16 FROG: (a) experimental spectrogram, (b) Retrieved spectrogram with a Frog error of
0.002, (c) 43 fs pulsewidth and (d) spectrum from the retrieved Frog trace. ....................48
3-17 Schematic representation of CPA. ............. ...............50.....
4-1 Simulation of the resultant temperature gradient in an end pumped Ti Al203 laSer rod
at room temperature when pumped by 70 W of 532 nm laser light. ............. .................52
4-2 Refractive index changes to a crystal incident with 80 W of pump beam. The thermal
gradient causes optical path deformation for a beam traveling along the : -axis.............. 53
4-3 Radially curved end-faces due to increase in temperature caused due to absorption of
incident pump beam. .............. ...............54....
4-4 Brewster cut Ti sapphire crystal. ............. ...............62.....
4-5 Dependence of (a) Thermal dispersion (dn dT) (Feldman et al., 1978) and (b)
Thermal conductivity ic (Holland, 1962) of Ti sapphire with temperature. ....................66
4-6 CAD drawings depicting (a) Vacuum dewar assembly and (b) copper crystal holder......68
4-7 Boundary temperature rise as pump power is increased when lasing action is
inhibited (red points) and when the cavity is lasing (blue points). The lines are guides
to the eye. .............. ...............68....
4-8 Measured thermal lens and thermal power for the two transverse axes; the boundary
temperature was measured to be 87 K at zero pump power and 103 K at 55 W of
pump power. ............. ...............70.....
4-9 Cavity stability parameter as a function of measured thermal lens. ............. ..................70
4-10 Computed temperature profile in a 6 mm long, 5 mm diameter Brewster-cut Ti:
sapphire crystal single end-pumped by 50 W in a 0.4 mm pump spot waist radius for
and absorption corresponding tO GabsL = 2.2 and a boundary temperature of 103 K........73
4-11 Plots (a,b) are the corresponding AOPD as a function of the transverse coordinates,
for the computed temperature profile in figure (3-6) ................. ................. ........ 74
4-12 Comparison of experimentally measured thermal lens powers (squares) against
numerically predicted values using finite element analysis (circles) and an analytical
expression for thermal lensing (triangles)............... ..............7
4-13 Spatial interference pattern in the Michelson interferometer recorded in a CCD
camera as a function pump power. ............. ...............76.....
4-14 Measured OPD compared with the FEA calculated for three different boundary
conditions. There is excellent agreement with a boundary temperature of
Tb = 103"K at higher pump powers. ............. ...............77.....
4-15 Beam shape as a function of repetition rate. Increasing the repetition rate of the pump
beam introduces modal distortions. ............. ...............78.....
4-16 M2 meaSurement for an uncompressed amplified beam of average power 5W at 5
5-1 Amplified output power as a function of pump repetition rate (square points)
measured before compression; the red-line is a guide to the eye. ............. ...................82
5-2 Amplified v/s pump pulse energy with increasing repetition rate. ................. ...............83
5-3 Measured M2 for an uncompressed amplified beam of average power of 9 W at 8
5-4 Amplified spectrum (blue-curve) for the corresponding oscillator spectrum (red
curve) as measured using a fiber spectrometer. .............. ...............85....
5-5 Emission spectra for Ti: sapphire. ............. ...............86.....
5-6 Free-running spectrum for the regenerative amplifier cavity at 5 k
5-7 Shot-to-shot pulse energy measured for more than 600, 000 shots. ................ ...............87
5-8 Histogram of the amplified output pulse energy. The black dots are the
experimentally measured data with 20 bins and the red curve is a Gaussian fit to the
data. .............. ...............88....
5-9 Thermally induced optical path difference versus crystal length for a Eixed radius of
2.5 mm for Tboundar=103 oK (left axis) and Tboundary=77 OK (right axis). ..........................90
5-10 Thermally induced optical path difference versus crystal radius for a fixed length of
6 mm for Tboundar=103 oK (left axis) and Tboundary=77 OK (right axis) .............. ...............91
5-11 3 -mirror folded astigmatically compensated cavity ................. .............................93
A-1 Schematic of the experimental set up of the FROG apparatus in our laboratory. ...........101
A-2 Raw SHG-FROG spectrograms recorded using (a) 150 g/mm and (b) 300 g/mm
grating. The horizontal axis is the wavelength axis and the vertical axis is the delay
axis. ............. ...............102....
A-3 Raw SHG-FROG spectrograms indicating (a) unfiltered (b) filtered traces. The
horizontal axis is the wavelength axis and the vertical axis is the delay axis. .................1 03
B-1 Bragg vector diagram and physical configuration for (a) retreating and (b) oncoming
sound waves. ................. ................. 107........ ....
B-2 Schematic of the AOPDF ..........._ ..... ..__ ...............108.
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
DEVELOPMENT AND CHARACTERIZATION OF A HIGH AVERAGE POWER, SINGLE-
STAGE REGENRATIVE CHIRPED PULSE AMPLIFIER
Chair: David Reitze
Major Department: Physics
Ultrashort pulses have revolutionized the field of optical science making it possible to
investigate highly nonlinear processes in atomic, molecular, plasma and solid-state physics and
to access previously unexplored states of matter. Although ultrashort pulses make an extremely
useful tool, the generation of these highly energetic but short pulses is by no means trivial.
Amplified ultrashort pulses are generated by the technique of chirped pulse amplification (CPA).
Pulses with peak powers of the order of 1012 W from the CPA lasers when focused down to a
surface area that correspond to a few square-microns generates high intensities capable of
ionizing the medium or generate spectacular non-linear electromagnetic phenomena.
This dissertation details the design, fabrication and complete characterization of a high
average power, high repetition rate, and single-stage chirped pulse amplifier system capable of
delivering 40-45 fs pulses in the milli-joule range at multikilohertz repetition rate. In order to
achieve millijoule level pulses from a single amplifier stage, the CPA systems need to be
pumped with high average power sources. This introduces a host of thermal issues and thermal
management then becomes necessary to increase the efficiency of such systems. In this work, we
have carried out a systematic investigation of the thermal loading effects in a high average power,
regenerative CPA system. We experimentally characterize the thermal aberrations using a variety
of different techniques interferometryy, pump-probe thermal lens power, and M2 analysis). We
compute the temperature distribution, the optical path deformations (OPDs) and the
corresponding thermal lens focal powers using Finite Element Analysis (FEA) for different
pumping conditions. The validation of the experimental results with the FEA model allowed us
to use the model to design an effective regenerative amplifier cavity that is stable over a wide
range of thermal lens focal length and hence over a wide range of repetition rates. The model
could also predict optimal pumping conditions for minimizing thermal aberrations for a variety
of geometries and pumping schemes.
The regenerative amplifier is capable of generating 40-45 fs, ~ ImJ pulses at 5 kHz
repetition rate and ~ 300 CIJ at 12 k
pulse energy) in the shot-to-shot pulse energy and good beam quality (average M~2 Of 1.42 at 5
Light is everywhere in the world. It has always been a carrier of information: from the real
world to our brains through our eyes. Our vision defines a sense of perception, which in turn
governs the way we look at the world. With the help of modern instruments, light has enabled us
to see closely and understand phenomena beyond our limited visibility. From scrutinizing
astronomical obj ects thousands of light years away from us to delving into the microscopic world,
light has in many ways helped us achieve the impossible.
Much of this achievement witnessed accelerated growth after the invention of lasers, which
have undoubtedly been one of the greatest inventions in the history of science. Since their arrival
in the 1960s (Maiman, 1960) they have found themselves useful in almost all areas of science
today. Barely years after the first laser was demonstrated DeMaria and coworkers (1966)
generated ultrashort pulses which were picoseconds long from a modelocked Nd: glass laser.
Atomic and molecular processes occur on time scales as short as a few picoseconds (10-12 SOCS)
to a few femtoseconds (10-"5 secs). The generation of short laser pulses has made it possible to
observe such effects with very high temporal resolution. The shorter the pulse duration, the
greater are the prospects of investigating highly nonlinear processes in atomic, molecular, plasma
and solid-state physics and gain access to previously unexplored states of matter.
Through the 1970s picosecond pulses were generated from flash lamp pumped solid state
materials such as ruby, Nd: glass and Nd: YAG using passive modelocking schemes such as
saturable absorbers in the laser cavity. But the major drawbacks of these systems were the large
fluctuations in the shot-to-shot output from the laser, and the instability of the saturable dye
solution whose quality degraded with exposure to light. As a result focus shifted from solid state
gain medium to organic dye lasers which were capable of generating pulses shorter than 10-ps.
The field of ultrafast laser development has seen rapid progress since the generation of
high quality sub-picosecond (0.1-ps) laser pulses by Richard Fork, Benjamin Greene and Charles
Shank in 1981. Pulse durations quickly dropped to the femtosecond regime (Shank et al., 1982)
using colliding pulse modelocked lasers. With the invention of solid state laser material such as
Ti3+ doped sapphire (Ti: Al203) by P. F. Moulton (1986) renewed interest in solid state lasers as
they offered higher stored energies and unlimited operating and 'shelf' lifetimes as compared to
organic dye liquids.
The discovery of self-modelocked Ti: sapphire lasers by Spence et al in 1991
revolutionized the field of ultrafast laser development. It now became possible to generate pulses
as short as 5 fs (Jung, et al., 1997; Morgner et al., 1999) directly from a laser oscillator without
the use of saturable absorbers. These table top lasers easily generate peak power levels of the
order of a few megawatts (106 W) (Huang et al., 1992a; 1992b; Asaki et al., 1993).
Ultrashort pulses allow for fast temporal resolution. One now has the capability to 'freeze'
motion of fast moving electrons and molecules, facilitating the study of molecular dissociation
dynamics, complex chemical reaction dynamics, etc. thus paying way for the field of
femtochemistry (Zewail, 1996), which deals with the nature of transition states and their control.
Following the development of milli-joule level picosecond pulses by Strickland and
Mourou in 1985, it became possible to generate millijoule level femtosecond pulses via the
technique of Chirped Pulse Amplification. This saw an increase in peak power by six orders of
magnitude 1012W)over those generated by the Ti: sapphire laser oscillators. Current table top
laser systems can generate peak powers in the petawatt range (10'5W) (Perry et al., 1999;
Pennington et al., 2000, Kitagawa et al., 2004).These lasers have found a variety of applications
over the past decade and continue to do so as our understanding develops.
Peak powers of a megawatt are however insufficient for many experiments. Several
nonlinear optical processes like high harmonic generation, ultrashort surface science, generation
of extreme ultraviolet radiation (EUV) (to name a few) are limited by the availability of
ultrashort pulse energies and the average flux, making it necessary to amplify pulses from a self-
mode-locked Ti: sapphire oscillators. The technique of chirped pulse amplification has
progressed significantly since the amplified picosecond pulses from the system developed by
Strickland and Mourou (1985). Amplification of ultrashort pulses by a factor of 106 to generate
peak powers in excess of 1012 W (1 TW) at a repetition rate of 10 Hz was easily achieved (Maine
et al., 1988; Kimetec et al., 1991; Sullivan et al., 1991; Zhou et al., 1995; Chambaret et al., 1996).
S. Backus et al. (2001) extended the chirped pulse amplification technique to generate millijoule
level, femotsecond pulses at multikilohertz repetition rate in a single stage chirped pulse
amplifier system. Advantages of liquid nitrogen cooled Ti: sapphire crystal (Moulton, 1986;
Schulz and Henion, 1991) were incorporated into a multipass amplifier cavity.
The advent of such high intensity, ultrafast lasers has facilitated many experiments in
'high-field' science. Matter exposed to intense ultrashort laser light undergoes ionization as the
electronic wave packet is set free to oscillate in a laser electric field that is strong enough to
overcome the effective binding potential. Nobel gases such as neon, argon, etc. when exposed to
such intense electric fields, ionize generating electromagnetic waves at much higher frequencies.
Also free electrons in plasma can be accelerated over 100 MeV in a space of only a few
millimeters (Umstadter, 2001) using strong laser electric fields. As a specific example, millijoule
level amplified pulses are essential for non-linear processes such as generating sub-nanometer
range radiation, which are harmonics of the fundamental laser beam (L'Huillier and Balcou 1993;
Bartels et al., 2000; Reitze et al., 2004). When a high-energy ultrashort laser pulse is tightly
focused the intensities created corresponds to an electric field that often exceeds the binding
energy of a valence electron to the core of a noble gas atom. Within the first laser period the
ej ected electron from the parent ion is accelerated and it may return to the parent ion with a finite
probability releasing harmonics that are coherent, directional and shorter in duration as compared
to the driving laser pulse (Figure 1-1). Coherent soft and hard X-rays produced due to the
harmonic up-conversion are used to conduct frequency interferometry in the ultraviolet to probe
thin solid films and dense plasmas (Salieres et al., 1999; Descamps et al., 2000) and study
electron transport dynamics in semiconductors (Rettenberger et al., 1997).
20 25 30 35 40
matuerials thatudrgo fbic ratedn mic rostrcue using fe 6mto 0-secn a0nd ioscn pulses s1
muc eteril tha n thgos parodcaed mcotcue using nanseodan iosecond pulses (iXeta.197VodrLind e
al., 1997). Such fast 'cold' ablation technique where the solid is changed directly to the gas
phase is highly desirable as it reduces effects caused by heat conduction and interaction of the
pulse with the ablated material.
In addition, amplified ultrashort pulses can further be compressed to sub-10 fs duration by
self-phased modulation of these pulses in hollow core waveguides and pulse compression
(Steinmeyer et al., 1999). Harmonics generated by such short and intense pulses give rise
coherent x-rays with pulse duration as short as 10-1 s (100 attoseconds) (Paul et al., 2001;
Hentschel et al., 2001) to study electronic state transition processes that occur faster than
Figure 1-2: A sheet of invar micromachined with (a) 10 nsec pulses and (b) 100-fs pulses.
(http://www. cmxr. com/Indu stri al/Handb ook/Chapter7 .htm)
Femtosecond pulses with high energy and faster repetition rates are also utilized to perform
surface non-linear spectroscopy (Ostroverkhov et al., 2005; Liu et al., 2005). As a second order
nonlinear optical effect, second harmonic generation and sum-frequency generation are
forbidden under the electric-dipole approximation in media with inversion symmetry. But at the
surface or an interface this symmetry is necessarily broken. Thus non-linear surface spectroscopy
is surface specific. As described in Figure 1-3 (a), two laser beams at frequencies my~ and @2~ When
mixed at an interface generate surface-specific sum frequency (or second harmonic,
when mi, = mi, ) output in transmission or reflection. The signal is proportional to the square of the
nonlinear susceptibility j' ms) = my + m,: of the interface. Scanning m, over the vibrational
resonances of the molecules or adsorbates on the surface, gives rise to a vibrational spectrum,
which is unique to that particular surface/interface. When mi, and mi, are high energy pulses
derived from a high brightness femtosecond chirped pulse amplifier, the peaks in the vibration
spectra are well enhanced making it possible to detect surface abnormalities with ease.
Figure 1-3: ~ Schemaic-~ of surac spcrsoy()adatpclSmfeunyGnrto
spo,~ ectra (b).[ernd with permisonfo Supriee l,(91]
An ntese ltrshot lserpule a aailbletody, ithpea poers> 1 Wcm r
capable~ ofgnrtn lcrcfed ta xes f1"Vccnpoueawk fpam
A voume, w-Sherea is h avlnt of sra pe thesop lase randia tionscapal oum frq c generatinatoeond
pulses and electron bunches (Naumova et al., 2004; Ness et al., 2005). These laser-based
radiation sources may someday be used for cancer radiotherapy and as injectors into
conventional accelerators, which are critical tools for x-ray and nuclear physics research.
The above examples present but a few of the applications of ultrafast lasers in physics,
materials science, and chemistry. There is an ever-increasing need for ultrashort pulses at high
pulse energies and faster repetition rates driven by these applications. The generation of these
pulses is by no means trivial: the simultaneous requirement of high pulse energies (> 1 mJ) and
high repetitions rates (> 5 k
then becomes the key to the operation of these highly pumped lasers. Improved thermal
properties of sapphire at 77 oK (Moulton, 1986) allows for much efficient extraction of energy
from the crystal in an amplifier making it possible to achieve millijoule pulses at k
rates in a single amplifier stage (Backus et al., 2001). Lowering the crystal temperature way
below the ambient only reduces and does not eliminate the deleterious thermal effects. Thus in
order to increase the overall efficiency of the chirped pulse amplifier system an extensive
thermal analysis and characterization of the crystal in the amplifier becomes inevitable as it
provides a better understanding of these thermal effects.
In this thesis we develop and characterize a high average power, single-stage, chirped
pulse amplifier system that generates 40-45-fs pulses with pulse energies close to a 1mJ at 5 k
repetition rate. We present a systematic investigation of the thermal loading effects in such
amplifier systems. We experimentally characterize thermal aberrations in a regenerative
amplifier using a variety of techniques. Using Finite Element Analysis (FEA) we compute the
temperature distributions, optical path deformations (AOPD) and corresponding thermal focal
lengths for a variety of pumping conditions. Excellent agreement between the FEA modeling and
the experimental results allow us to predict optimal pumping conditions for minimizing thermal
aberrations that could further increase the efficiency of the system. The usage of the acousto-
optic programmable dispersive filter (AOPDF) as a pulse shaper makes this a unique and a
compact system capable of delivering ultrashort pulses in the millijoule range. High brightness
sources such as this is ideally suited for high harmonic generation which is essential for the
generation of attosecond pulses, plasma generation and acceleration of free electrons in plasma.
Applications such as femtosecond micromachining and surface characterization using nonlinear
frequency conversion techniques will benefit from the amplifier's high average powers for the
high signal-to-noise measurements via lock-in detection.
The layout of the dissertation is as follows: in Chapter 2 we discuss the principles of
ultrashort pulse generation and characterization. The design and construction of the various
components of a high average power, single-stage chirped pulse amplifier is described in detail
in Chapter 3. Chapter 4 deals with issues relating to the design, modeling and characterization of
the host of thermal effects in a regenerative CPA system. The experimentally measured results
are validated numerically using Finite Element Analysis (FEA). The characterization and the
optimization of the pulses from the amplifier system are elaborated in Chapter 5 along with
techniques that can further improve the efficiency of the CPA system. Finally we conclude in
ULTRASHORT PULSE GENERATION AND CHARACTERIZATION
Before we begin to delve into the details of the construction and performance of a high
average power chirped pulse amplification system, it is beneficial to understand more about the
fundamentals of generation and characterization of femtosecond pulses. This chapter discusses
the various aspects of femtosecond pulses that are extremely crucial to the work described in this
Beginning with a mathematical relationship between pulse width and the spectral
bandwidth the chapter discusses dispersion of broad bandwidth pulses. Principles of nonlinear
effects such as the second and third order effects that are crucial for pulse characterization and
the generation of ultra board brand sources respectively are discussed in the Einal sections of this
2.1 Relationship between Duration and Spectral Width
A plane monochromatic wave of frequency 4i, (Figure 2-1 (a)) has an infinite spread in the
E (t) = Re (E, exp (iw,t)) (2.1)
A light pulse can be generated from a sinusoidal electric field as in equation (2.1) by multiplying
it with a bell shaped function for the amplitude modulation. Choosing a Gaussian function the
above equation then transforms as
E(t)= Re E, exp (-Tft+ im,t) (2.2)
The time evolution of equation (2.2) is shown in Figure 2-1(b). r is the shape factor of the
Gaussian envelope. The spectral content of the two kinds of light pulses can be obtained by
performing a Fourier transform to the temporal domain. Figure 2-2 (a) and (b) are the numerical
Fourier transforms for the cosine and the Gaussian function in equations (2.1) and (2.2).
The monochromatic plane wave oscillates with a single frequency 4i~ whereas the Fourier
transform of the Gaussian function is also a Gaussian, with the width proportional to r .
Figure 2-1: Evolution of a plane monochromatic wave in time (a) and a plane wave with
Gaussian amplitude modulation in time (b).
Figure 2-2: Fourier transform of the (a) cosine function in Figure 2-1(a) and (b) Gaussian
function in Figure 2-1 (b).
From the empirical relationship between the spectral width and the pulse duration of the
pulse, we can now derive a more formal relation (Seigman, pp.331). For a Gaussian electric field
as in equation (2.2), the instantaneous intensity can be expressed as
Ift)- = Elt) 2 = E2 ep- (41n, 2)1 t (2.3)
where r is the duration of the pulse measured at half the maximum intensity and is known as the
Full Width at Half Maximum (FWHM).
r, = Ju2(2.4)
The Gaussian spectrum in frequency is the Fourier transform of equation (2.2)
E (mi) = exp ( ~) (2.5)
The power spectrum of the Gaussian pulse can be written in the same form as the instantaneous
intensity as in equation (2.3)
IS) E ()2= Bp-(1n ) (2.6)
The FWHM bandwidth of the Gaussian pulse is
Af = (2.7)
If in equation(2.2) C = (a ib), where b is known as the chirp factor, then the pulsewidth r,
and Af, undergo the following modification
Incorporating the E in the expression for electric field equation(2.2), in the time domain
E (t) = E, exp(-at )exp i met + bt 1]
E (t) ac exp ig, (t)]
40, (t) = mi,t + bt2 (2.10)
is the time varying phase of the Gaussian pulse. An instantaneous phase gives rise to an
instantaneous frequency 0i,.
For the Gaussian pulse described above this instantaneous frequency is given as
m,(t) = mil,t+ bt = 4i, + 2bt (2.12)
Thus a Gaussian pulse with a time-varying instantaneous linear frequency is known as
being chirped with the parameter b being a measure of this chirp. Figure 2-3 demonstrates a
chirped Gaussian pulse.
Figure 2-3: Time evolution of a Gaussian electric field with a quadratic chirp (b = 10O) on it.
2.2 Time Bandwidth Product
The product of pulsewidth and spectral bandwidth is known as the time bandwidth product
(TBP). Multiplying equations (2.4) and (2.7) we get
Afpr, = -_ 0.44 (2.13)
According to the uncertainty relation the time bandwidth product for a Gaussian pulse cannot be
less than 0.44. Chirp on a Gaussian pulse increases the TBP.
~ (2 1n 2 fb 2 fb 2
Af r= x +I- ~0.44 x 1+ (2.14)
Thus for a Gaussian pulse the minimum TBP is 0.44 and such a pulse is known as
'transform-limit' as the linear chirp-factor b = 0 .
The TBP depends on the shape of the pulse and the definitions of Af and At (rms, FWHM,
etc.). The table below compares the TBP for 3 fundamental pulse shapes suitable for laser beams,
for other forms of intensity profiles such as square, triangular, exponential etc. the reader is
urged to refer Sala et al (1980).
Table 2-1: Time bandwidth product for different pulse shapes (Figure 2-4)
Pulse Shape Intensity I(t) Afe At dit rdc
Hyperbolic Secant = sech2X 0.3148
Lorentzian 1 0.2206
Note: Adapted from Sala et al. (1980).
Figure 2-4: Intensity profile for a Gaussian pulse (solid blue curve), hyperbolic secant (dashed
blue curve) and a lorentzian (red curve).
Ultrashort pulses, with its broad spectral content undergo dispersion as they propagate in
air, materials, etc. Dispersion is said to occur when the phase velocity of the wave depends on its
frequency (Born and Wolf). The vacuum dispersion relation is given as: m,= ck where 0i is the
angular frequency of the radiation, k is the wave number and c is the velocity of light in free
space. For such a dispersion relation the phase velocity (v, and the group velocity vg) are the
same. In a dispersive medium, the dielectric constant is a function of frequencye(mi) with the
consequence that v, + vg Different components of the wave travel with different speeds and tend
to change phases with respect to one another. An ultrashort pulse propagating through such a
media will undergo changes in its shape ultimately leading to temporal broadening.
Figure 2-5: Schematic relationship between phase and group velocities for a transparent
medium (v < v ).
The electric field of an ultrashort pulse, in the frequency domain is given by equation (2.5).
After the beam propagates through a distance x its spectrum is modified accordingly as
E(B) = E, (w)exp +ik (w)x] (2.15)
where k (m) = n/cul is a frequency dependent propagation constant, with n2 being the refractive
index of the medium. If the propagation constant k (mi) is a slowly varying function of a ,: it can
expanded in a Taylor series expansion about a central frequency mi, as long as As I .
dk 1 8 k 2 1 8 k 3
8m ~2!8 3! Sm"'
The frequency dependent propagation constant k (mi) will modify the pulse as it propagates
through the medium. Substituting the above expression in equation (2.15)
E m)= x -k,(m -ikx m- ,)- k~ ( -m) +.. (2.17)
where, k'= (8k/8m/co~ csandk" = (8k/8d~),0= ,,. The temporal evolution of such a pulse can be
obtained by a Fourier transform of its spectral shape (Rulliere, pp.33).
E(t)= 1 E(w)exp(-imt)ds (2.18)
E (t = xp s, t- F(x)t -(2.19)
The first term in the exponent produces a time delay by an amount x/v:, after propagation though
a distance x The quantity v, (c,) = (m/k)0 is the phase velocity of each of the plane wave
components of the pulse in the medium. vg (e ) = (d'k/dw)l is known as the group velocity and
determines the speed of the pulse in the medium. For cases where el, 0i, vg < v and the
pulse is said to undergo normal dispersion. Now F(x) =1/ + 2ik~x, where" = d/de v, (mc)l
is known as the group velocity dispersion. Figure 2-5 is a schematic of the dispersion effect in a
medium with a dispersion relation m = ck (c() Thus the equation (2.19) demonstrates that a short
pulse propagating through a transparent medium undergoes delay, a broadening of its pulse
duration accompanied by a frequency chirp.
2.4 Nonlinear Effects
2.4.1 Second Order Susceptibility
Light intensities generated by an ultrashort pulse can change optical properties of the
medium that they pass through. The intensity dependent changes to the optical properties of the
material constitute nonlinear optics. Many of these nonlinear optical effects tend to be useful
while generating and characterizing ultrashort pulses.
On expanding the polarization in a Taylor series expansion
P = X' E + X'mEE + X'3EEE +... (2.20)
The first term in the above equation is the linear term whereas it's the higher-order terms that
account for the nonlinear optical effects.
Second-order optical effect or second harmonic generation (SHG) is caused due to the second
order susceptibility term Xc: It is characterized by the second-order polarization P(2 (t) .
Pm' (t) = X'mEE*~ (2.21)
Two photons of frequency ai combine in a medium to give rise to a single photon of
frequency 2mi (Figure 2-6). But the process of second harmonic generation is dependent on the
orientation of the crystal axis and the polarization of the incoming light. If the medium posses an
inversion symmetry, X(2 vanishes uniformly over the bulk of the medium. SHG in such cases
can be observed either at an interface or on the surface of the medium. For an impinging
intensity I(mi) of frequency ai with a propagation constant k, the intensity of the second
harmonic signal I(2mu) with the propagation constant k, = 2k, through a nonlinear crystal of
length Iis given as (Boyd)
I (2m) ='Z 2~~1 I2 (0)~ l2)] (2.22)
where, Ak = k, 2k, is known as the wavevector mismatch. The SHG process is most efficient
for the perfect phase matched condition where Ak = 0 .
Figure 2-6: Geometry of second-harmonic generation (a) and schematic energy level diagram (b).
As the SHG signal for a given crystal length, orientation and polarization of the incoming
light is directly dependent on its intensity, it is extensively used to measure the pulsewidth of an
ultrashort pulse as described in detail in appendix A.
The second order susceptibility is also responsible for a variety of other effects that involve
3 photons such as the sum-frequency generation (SFG) where two incoming photons of
frequency my~ and ai~ combine in a nonlinear crystal and generate a signal at the sum
frequency 03,= my,+m ~. Difference frequency generation (DFG) is a process where the two
incoming photons generate a signal at the difference frequency 03~ = mi~ my~ where 0i~ > 0i, The
satisfaction of the phase marching condition Ak = k, + k, k, determines the efficiency of all
these process within a non-centrosymmetric crystal.
2.4.2 Third Order Susceptibility
Three photons mix to generate third order nonlinear effects due to the third order
susceptibility X(3) term equation(2.20). The third order polarization term can be written as
P(3) __ (3)I.E
Some of the third order effects include third harmonic generation (as in Figure 2-7) where
three photons of frequency ai combine to generate a photon of frequency 3m ,. Unlike the second
order effect, the third order effect can occur in any media irrespective of the symmetry and can
also occur in liquids and amorphous materials such as fused silica.
The number of effects increases as the order of nonlinearity increases. The primary focus
of this chapter will be to discuss the effects related to generation and characterization of
Figure 2-7: Geometry (a) and schematic of third order generation (b).
188.8.131.52 Nonlinear index of refraction
The intensity of the ultrashort pulse in a medium changes its optical properties. The third
order polarization in equation (2.23) when combined with the linear polarization term becomes
P = '1'E + 3. g(3)I.E = X, E(m)
where, Xpt = X(1 + 3.g(3)1
where I = E2 is the intensity of the incident ultrashort pulse. The second order term can be
made to vanish in the above equation due to symmetry conditions in the crystal. For a
centrosymmetric medium X(2) VaHishes and for non-centrosymmetric medium the second order
effects can be eliminated by orienting the crystal in such a way so as to satisfy the phase
matching condition only for X(3) effects. The refractive index of the material is defined
as: n2 = 1+4. 3 c. Substituting for X74, the refractive index can be expressed as
n2 = 1+c4nXrf c +12.:? IE(co) 2 (2.25)
The refractive index of a material, when a high intensity laser beam is incident on it, can also be
described by the following relation
n2 = no0 +n12 IE 2 (2.26)
where no and n2 are the linear and nonlinear index of refraction respectively.
Comparing the relations (2.25) and(2.26), one can obtain expressions for no andn2
n0 = 1+ 4g 111/2
For an ultrashort pulse the intensity is a function of both space and timelI(r, t) Both the spatial
and temporal dependence of intensity leads to interesting effects such as Kerr lens effect, self-
phase modulation, self-focusing, filamentation etc. Effects that lead to the generation of
ultrashort pulses are discussed in the following sections.
184.108.40.206 Kerr lens effect
The spatial intensity profile of a Gaussian laser beam propagating in a X(3) material is
I(r)=exp(-gr ) (2.28)
The refractive index of the material also gains a spatial gradient given as
n2(r) = nlo +nI2(r.) (2.29)
This generates a refractive index gradient as in Figure 2-8 that follows the gradient in the
intensity profile of the incident ultrashort pulse. For a nonlinear index of refractionn, > 0, the
refractive index is greater at the center of the medium as compared to the sides. The amount of
nonlinear phase accumulated by the ultrashort pulse as it passes through this graded index
2xi 2xi 2xi
O(r) = n,1ol- n IIl(r) = -0o Y n I(r) (2.30)
This effect similar to a static lens, increases the focal power of the material due to the spatial
variation in the phase of a traversing beam such that beam focuses into the material. This effect
known as Kerr lens effect is of utmost importance in understanding self mode-locked Ti:
sapphire laser oscillators.
Figure 2-8: Schematic representation of the Kerr lensing effect. The KLM effect leads to the self-
focusing of the intense ultrashort pulses.
220.127.116.11 Self phase-modulation
The temporal profile of a Gaussian pulse incident on a X3 material is
Ir) t = x (2.31)
Thus the refractive index is then transformed as
n(t) = no + n2,I 0 Xp (2.32)
The time varying intensity leads to a time varying refractive index as the pulse propagates
dn dl t 2 ii2 t
dt = 2 dt ~r x 722 (2.33)
An instantaneous refractive index brings about a change in the total phase ( = -2xinl/Al)
accumulated by a pulse or a phase delay as it propagates through such a medium.
2xi 2xi 2xi
O(t)= nol n 0 21(t) (2.34)
where ii is the vacuum wavelength of the carrier and nolis the optical length traversed by the
pulse. This generates a time varying shift in frequency
dO 2xi dl
mi(t) -m n
dt jl dt
A plot of Am ~(t) (Figure 2-9) shows that the leading edge of the pulse shifts towards the
lower frequencies ('red' shift) and the trailing edge shits towards higher frequencies ('blue' shift),
generating an overall increase in the bandwidth of the pulse.
Although the spectral content of the pulse is increased as it passes through such a crystal
the temporal structure remains unaltered by the self-focusing effect. But natural dispersion
occurring within the crystal tends to broaden the pulse.
Ti: sapphire-based laser oscillators make use of the Kerr-lensing effect to generate pulse as
short as 6-fs (Jung et al., 1997) directly from an oscillator which is described in detail in the
23500 -50 0 50 100
Figure 2-9: Schematic of Self-phase modulation. (a) A Gaussian pulse propagating through a
nonlinear system undergoes self focusing effect (b) which gives rise to additional
frequency components which when compensated for material dispersion generates a
We briefly discussed in this chapter the essential theoretical background needed to
understand the various nonlinear process such as the generation of femtosecond lasers through
the Kerr lensing effect. Also processes such as the second harmonic generation which is a
commonly used tool to characterize ultrashort pulse widths, were discussed in considerable detail.
More on the technique of measuring ultrashort pulses are elaborated in Appendix A at the end of
DESIGN AND CONSTRUCTION OF A HIGH AVERAGE POWER, SINGLE STAGE
CHIRPED PULSE AMPLIFIER
Strickland and Mourou (1985) developed the first ultrashort laser in the year 1985, capable
of delivering millijoule pulses at picosecond time scales (2x10-12 Secs) at a wavelength of 1.06
Clm, by the technique of chirped pulse amplification. Ultrashort pulses by definition support a
large spectral bandwidth(Av~r= const) Amplification of ultrashort pulses enforces certain
minimum requirements on an amplifier system. First, the amplifier bandwidth must be wide
enough to accommodate the spectral bandwidth of the seed or the un-amplified pulses. As a wide
range of Fourier components is required to produce an ultrashort pulse, a gain medium with a
narrow emission bandwidth could not possibly support ultrashort pulses. The central wavelength
l, of the seed pulses must efficiently extract the stored energy in the amplifying medium, i.e the
fluence of a pulse must be close to the saturation fluence of the amplifying gain medium
J,, = hu/a, where o, is the gain cross-section of the gain medium. Finally the peak intensities
generated within the amplifier must be well below a certain critical level above which nonlinear
effects as discussed in chapter 2 can distort both the spatial and the temporal profile of the
amplified beam and in some cases can damage the optical components within an amplifier as
3.2 Why Chirped Pulse Amplification?
While amplifying femtosecond pulses, the phase shift experienced by a propagating
ultrashort pulse in an amplifying medium can be both linear and nonlinear
hToal =,ZI nl~ (n, + n,I(r, t))1
Ai A (3.1)
The linear phase 2n.,;-7~/Al arises due to the linear index of refractionn,. The nonlinear phase
shift arises from the nonlinear response (distortion) of the electron cloud surrounding an ion
subjected to an intense electric field. As can be seen from equation (3.1), the peak intensities
associated with an ultrashort pulse introduce additional phase delay (n,2 > 0) and therefore
experience enhanced nonlinearities, which are manifested both in temporal as well as spatial
distortions of the laser pulse. One can calculate the nonlinear phase accumulated by an ultrashort
pulse along an optical path L as (Koechner, 1976)
2Oz i= nIrtd (3.2)
where n, is the nonlinear index of refraction of the lasing medium and I (r, t) is the instantaneous
pulse intensity within the amplifier cavity. A peak value of 5 for the nonlinear phase Oz (for
historical reasons also known as the 'B integral') corresponds to a critical intensity (Maine et al.,
1988) above which only high spatial frequencies are preferentially amplified, reducing the
spectral bandwidth of the amplified pulses that ultimately results in longer pulses. As noted in
the previous chapter a host of nonlinear effects are associated with the spatial as well as the
temporal variation of the intensity of an ultrashort pulse. And if the accumulated nonlinear phase
exceeds this critical value, the ultrashort beam becomes distorted due to these nonlinear
processes (Boyd, 2003). Thus keeping the amount of nonlinear phase that an ultrashort pulse can
gather, much below the threshold value is of utmost importance in amplifying these pulses to
high energy levels.
Given a suitable gain media like Ti3+:Al203 (which shall be discussed in the following
section), the technique of chirped pulse amplification circumvents the generation of excess
amplified intensities capable of damaging amplifier materials or causing nonlinear effects. Figure
3-1 illustrates a schematic of a chirped pulse amplification system.
This technique relies on increasing the duration of the pulse being amplified by introducing
a controlled amount of dispersion ('chirping' the beam) and then optically compressing (Treacy,
1969; Martinez, 1987; Martinez, et al.,1984) the amplified beams to its original pulse duration.
Fs-Laser I M Stretcher I Amplifier 1 Compressor *
Figure 3-1: A schematic representation of a Chirped Pulse Amplifier system. The pulse cartoons
represent the temporal structure of the pulse at each stage in the amplification process.
Temporally lengthening (or 'stretching') the pulses reduces the peak intensity, enabling
efficient energy extraction from the amplifier gain media by distributing the total energy content
of the pulse over a broader time scale. Chirped pulse amplification becomes particularly useful
for amplifiers utilizing solid-state gain media with high stored energy densities (1--10 J/cm2)
well above the damage threshold of several optical components, in order to efficiently extract the
entire stored energy in the gain media.
The following sections contain an in depth discussion of the various components of a
single stage, CPA system in our laboratory.
3.3 Ti: Sapphire as Gain Medium
Ultrashort pulse amplification needs very broadband gain media. Femtosecond amplifiers
in the past relied heavily on broadband laser dyes and excimer gain mediums as the amplifying
material (Ippen and Shank, 1986; Downer et al., 1984; Knox et al., 1984). Due to the low
saturation fluences offered by these media, the amplified output powers were severely limited by
the size of the amplifying medium. But solid-state media such as Nd: glass, Cr3+ doped BeAl204
(Alexandrite), Cr3+ and Ti3+ doped Al203 (Sapphire) not only posses much higher stored energies
(~ 1J/cm2) but also display extremely broad emission bandwidths to support ultrashort pulses
---Absorption \ -Fluorescence
400 500O 600 700 800 9100
Figure 3-2: Absorption and emission spectra for Ti: sapphire. [Adapted from Rulliere (1998)].
Of all the solid state materials available, Ti3+ doped Al203 (COmmonly referred to as Ti:
sapphire) emerged to be the most promising material (Moulton, 1986). The early nineties saw a
boom in the use of Ti: sapphire as an active medium to produce femtosecond pulses due a
number of its features that were desirable as a laser host material. With a damage threshold of 8-
10 J/cm2 (COmparable with metals), high saturation fluence of 0.9 J/cm2, a peak gain cross-
section og of 2.7 x 10-19 /cm2 (Backus et al., 1998) and an extremely broad gain bandwidth of
230 nm (Moulton, 1986), there is little doubt as to why Ti: sapphire is a favorite among
femtosecond-laser developers! Ti: sapphire exhibits a peak absorption maximum at 500 nm.
Figure 3-2 indicates the absorption and emission bandwidths for Ti3+ doped Al203. With the
availability of high average power diode-pumped solid-state lasers, such as the frequency
doubled Nd: YAG and Nd: YLF laser source (laser emission at 532 nm), Ti: sapphire quickly
became the obvious choice in the development of table-top terawatt sources (Backus et al., 2001).
P, 8I~00 nm, 30 fs
2 n/e~n nPump Laser
Ti: Al Os L
Figure 3-3: Self-mode-locked Ti: sapphire laser oscillator. The cavity is formed by a high
reflecting mirror (HR) and an output coupler (OC). The pump beam is focused on to
the crystal which is placed in a sub-resonator formed by mirrors M1 and M2.
Dispersion compensation is achieved by prisms P1 and P2.
There has been a tremendous amount of progress in the generation of femtosecond pulses
since the construction of the first self mode-locked Ti: sapphire laser by Spence et al. in 1991
generating 60-fs pulses. With further improvisations to their optical design (Figure 3-3), it
became possible to generate pulses as short as 6 fs (Jung et al., 1997) directly from a laser
oscillator. Short pulses were achieved by the process of Kerr-Lens mode-locking (discussed in
the previous chapter), wherein an inherent nonlinearity of the Ti: sapphire crystal was creditably
exploited, which is yet another reason why Ti: sapphire is the most revered material for
ultrashort pulse generation!
3.4 Mode-locked Laser
Mode-locking is the essential mechanism to generate pulses from a laser oscillator. A laser
cavity allows oscillation only for di screet resonance frequencies that sati sfy the
condition = mc/2L where cis the velocity of light and L is the length of the laser cavity and
m is an integer. The longitudinal modes of a laser cavity oscillate freely and the output intensity
consists of different modes with no specific phase relation with respect to each other and the
laser is said to be operating in a 'continuous wave' or cw mode. These modes which initially
possess random phases, when forced to oscillate with a well defined phase constitutes a pulse
and the laser is then said to be lasing in a pulsed mode with a finite bandwidth spectrum as in
Mode-locking in dye lasers and in certain solid state media was achieved either by an
external modulation (active mode-locking) or by placing saturable absorbing medium in the laser
cavity (passive mode-locking).
Figure~ ~ 3-:Gneain futrsot uss yte ehnimo md ocig
Ti: sapphire laser does not require either extrnatmlatino strbl borest
Fgu 34 enerateo o ultrashort pulses. Thi ise knowns asse f mode-locking. A icse ntepeiu
chapter, an intensity dependent variation of the refractive index of the Ti: sapphire crystal,
arising from a non-uniform power density distribution in Gaussian beams gives rise to an
intensity dependent phase-shift that leads to the generation of multiple modes within the
oscillator cavity. The amplitude of the short pulse is modulated in such a way that intense pulses
experience less loss than weaker pulses and can therefore sustain within the cavity.
Figure 3-3 is a schematic of a self-mode-locked Ti: sapphire laser oscillator. The laser
cavity is formed by two plane mirrors, one a high reflecting mirror (HR) and an output coupler
(OC) which is partly transmitting. The Ti: sapphire crystal is placed in a sub resonating cavity
formed by two identical spherical mirrors of radii of curvature 10-cm, which are dichroic in
nature, transmitting 532-nm and reflecting 800-nm. Two fused silica prisms placed in the longer
arm of this asymmetric cavity provide the phase compensation necessary to achieve mode
locking. The Ti: sapphire crystal is pumped by a 5 W Coherent Verdi which is a diode pumped
Nd: YVO4 laSer system.
The refractive index of sapphire varies with the intensity of the incident pulse
as n = no + n2I(r) The crystal behaves like a converging lens asn2 > 0 The Kerr lensing effect
in conjunction with the self-focusing of the laser beam within the crystal gives rise to the
broadening of the spectral content of the pulse.
Although the spectral content of the pulse is increased as it passes through the Ti: sapphire
crystal the temporal structure remains unaltered by the self-focusing effect. But natural
dispersion occurring within the crystal tends to broaden the pulse. The prism pair inside the
oscillator cavity generates negative dispersion to compensate for the positive dispersion
introduced by the crystal (Martinez et al., 1984; Fork et al., 1984), enabling the generation of
femtosecond pulses from the oscillator. Careful balancing of the self-phase modulation effects
and the group velocity dispersion due to the prism pair causes all the modes in the oscillator to
have the same optical path length through the crystal, forcing them to oscillate in phase to
generate a train of mode-locked pulses with a repetition rate 1 aR where zR is the round trip time
around the cavity.
The peak intensities inside the Ti: sapphire crystal must be high enough to induce
nonlinearity but well below a critical level, which can distort the beam within the cavity. In order
to favor the high intensity pulsed operation of the laser over the continuous-wave (cw) mode, old
designs of the Ti: sapphire oscillator used a hard aperture blocking out the large waist modes that
correspond to low intensity levels.
Figure;8 3-5:LZ ~ Osiltrsetu s esrdb ie p ecrmtran t orertasom
Inst s hecacuatd empra pofle(tmpra bndwdt o 1 f) ssmig
consant haseacrss te enire pecral andwdth
Fi The m-.odltos inathemesre spectrum as ered an ariactoh fiber spectrometer. The itempora roiler wrans
calulaed nfrset fitrn the meascured sepecrum w oith a avtzky-orl a sooting funto and then perfoming
aninereourertransfr on the arsmoothedetr spectrum.adidh
stroking the prism next to the high reflecting mirror. The oscillator routinely generates 300-400-
mW mode-locked pulses at the repetition rate of 90 MHz (defined by the cavity length), centered
at 800-nm and a full width of half-maximum bandwidth (FWHM) of 80-90-nm, an average pulse
energy of 2-5 nJ depending on the alignment. A pair of razor edges that form a slit allows tuning
of the mode locked spectrum. In order to stabilize the laser in the mode locked state, the Ti:
sapphire crystal is maintained at a constant temperature of 20 oC by a circulating water chiller.
Also for prolonged stability, the laser is isolated from the environment by enclosing it in a
protective case. Due to the absence of an external compensator to generate transform limit pulses
from the oscillator, the temporal FWHM is always greater than calculated as in the inset of
The seed pulses from the oscillator are then introduced into a pulse stretcher to temporally
broaden the pulses before they can be inj ected into the amplifier.
The phenomenon of dispersion is very important to the Hield of ultrafast optics. As
ultrashort pulses, with their broad spectral content undergo dispersion as they propagate in air,
materials, etc., dispersion management then becomes the key to developing really short pulses.
As previously noted, dispersion is said to occur when the phase velocity of the wave depends on
its frequency (Born and Wolf). Different components of the wave travel with different speeds
and tend to change phases with respect to one another. An ultrashort pulse propagating through
such a medium will undergo changes in its shape ultimately leading to temporal broadening. The
electric field of an ultrashort pulse is represented in the frequency domain as
E~m)= E~) ex (iq(m))(3.3)
where E(co)is the amplitude modulation for a finite beam and #(0) is the phase of each of the
frequency components present in the beam. If the spectral phase #(0) is a slowly varying
function of ai (this does not hold true in regions of 'anomalous dispersion' where n~i) varies
rapidly over narrow intervals of mi) then it can expanded in a Taylor series expansion about a
central frequency mio.
8 ~1 82~ 2
(m) = + (0 G (C( -~ o)? +- (m G) +... (3.4)
8m 2!cm 802 3! 3
where 8 /80i, 82 l~i2 and 83 l~i3 are the derivatives of phase with respect to frequency and
are known as group delay, second-order dispersion or group velocity dispersion (GVD), third-
order dispersion (TOD), fourth-order dispersion (FOD) and so on. The variation of the group
delay r = 80/80i with frequency is
From the above expression, it is clear that the #"(mo), known as frequency-sweep rate linearly
chirps the pulse and #"(mo~) generates a quadratic chirp on the pulse, etc. Figure 3-6 (a) and (b)
illustrate a Gaussian pulse with a second-order and third order phase on it that generates a linear
and quadratic chirp on it respectively.
For pulses that undergo normal dispersion in materials, the phase change is given
by ma, (mi) = La,n(mi) m/~c Thus longer wavelength components in the pulse travel faster than the
shorter wavelength components i.e 'red' travels faster than 'blue', introducing a positive chirp. A
pulse compressor then becomes inevitable to compensate for this positive chirp.
The management of spectral phase is thus of utmost importance in the design of a chirped
pulse amplifier system. The next section deals with the broadening or the chirping of the pulses
in order to effectively amplify them in an amplifier and their recompression back to femtosecond
Figure 3-6: A Gaussian pulse possessing (a) linear chirp (#"(co,)) on it and (b) quadratic chirp
(#"'(w,)) on it.
3.6 Pulse Stretching and Recompression
As an ultrashort pulse propagates through the different optical components in an amplifier
cavity, the material dispersion accumulated must be compensated for in order to achieve shorter
pulse durations. Also in order to reduce the risk of damaging the amplifier components and to
keep the amount of accumulated non-linear phase [equation(3.2)] well below the threshold level,
femtosecond pulses obtained from the Ti: sapphire oscillators must be temporally broadened
before they can be injected into an amplifier. Also, in order to generate ultrashort pulses in a
mode-locked Ti: sapphire oscillator it becomes necessary to compensate for the group velocity
dispersion (GVD) such that all the spectral components of the pulse can travel with the same
group velocity around the oscillator cavity. Thus dispersive components become an integral part
of a chirped pulse amplifier system.
Pulse stretching can simply be accomplished by material dispersion. As beams traverse
through material they tend to broaden temporally owing to normal dispersion. But for most
materials significant lengths are needed to achieve stretch factors of 104 which are required to
amplify nanojoule level femtosecond pulses to the millijoule level. In addition, one cannot avoid
beam distortions due to the increased B-integral.
Figure 3-7: Dispersive delay lines. (a): A pair of anti-parallel gratings forms a pulse compressor
(Treacy, 1969) and (b) Pulse stretcher formed by anti-parallel gratings with a unit
magnifieation telescope between them by Martinez et al. (1984).
In 1969 E. B. Treacy showed an extremely clever way of broadening pulses in time by
using an anti-parallel grating pair (Figure 3-7(a)). Significant stretch factors could be achieved
with this arrangement, although as originally conceived the Treacy configuration was designed
to produce negative group delay dispersion that could compensate for positive material
dispersion. The grating pair disperses the spectrum of the pulse, such that the 'blue' edge of the
spectrum travels faster than the 'red' edge through the grating arrangement. The first grating
serves the purpose of dispersing the spectral content of the pulse and hence the negative GVD,
and the second grating recollimates the different wavelengths. Martinez (1987) designed a
compressor with dispersion opposite to that of the Treacy's design (Figure 3-7(b)). A telescope
placed between a pair of anti-parallel gratings modified the effective length between them
yielding positive group velocity besides providing a high magnification yielding compression
factors as high as 3000.
The phase shift across the spectrum of the pulse as the beam propagates though the grating
pair can be calculated as (Treacy, 1969)
where Lg is the perpendicular distance between the gratings, 7 is the incidence angle, B is the
angle between the incident and the diffracted beams, ii is the central wavelength of the spectrum
of the pulse and d is the grating constant. One can derive the group velocity dispersion (GVD)
from the above equation
824 87 4;~cL,/cos(7-6)
The expression for GVD for the Martinez stretcher (Figure 3-7 (b)) is the same as eq.(3.7)
except with an opposite sign. The above expression is for a single pass through the grating pair.
The beams are made to pass once again through the arrangement to remove the wavelength
dependent spatial walk-off, by reflecting them off a retro-reflector or a pair of mirrors used in a
roof geometry. Due to the ease of their construction the stretcher and the compressor are
designed in such a way as to exactly reproduce the input pulse temporally.
Martinez et al. (1984), showed that negative GVD can also be generated from a pair of
prisms arranged in parallel. While the reflective grating geometry as in Figure 3-7 (b) is not an
easily adjustable design the prism arrangement in Figure 3-8 provides both low loss as well as
tunability from negative to positive values of GVD and hence is incorporated into the mode-
locked Ti: sapphire oscillator to compensate for the varying pulse GVD which is alignment
dependent. It is based on the idea that wavelength dependent phase delay caused by angular
dispersion always yields negative GVD.
Figure 3-8: Prism delay line. A pair of parallel prisms generates negative GVD that can be varied
by changing the distance between the prisms (Martinez, 1984; Fork, 1984).
In the Figure 3-8, the optical path between the points A and B is
A = ~c/mi = nL eos B (3.8)
The GVD term is given as
d2 A'3 dA8
dei, 27r c2 dA1
Substituting for A from equation (3.8) in equation (3.9) and calculating the GVD along the
direction of the wave vector (6 = 0) yields
dA dn d 3.0
-2d1 = n d L (3.10
The above expression yields a negative GVD regardless of the sign of the term d8/dAl The first
prism, as in the case for the grating pair, causes the angular dispersion and the second prism
serves to recollimate the different wavelengths. The net dispersion is also easily adjustable by
translating one of the prisms normal to the incident beam without altering the optical alignment.
This allows for the introduction of material dispersion without changing the negative GVD.
For amplified pulse duration < 35-40 fs, getting rid of the residual phase over a large
spectral bandwidth becomes a formidable task due to the mismatch of the compressor i.e when it
is not able to compensate completely the chirp introduced in the stretching and the amplification
process. The all-refractive stretcher design by Martinez et al. (1987) introduces strong chromatic
aberrations (a wavelength component that diffracts from the first grating at an angle of 6 must
arrive at the second grating at the same angle) inevitably causing a mismatch between the
dispersive delay lines in a CPA. A. Offner (US Patents, 1971) came up with an all-reflective
triplet combination that reduces the effects of chromatic aberration. When used as a stretcher,
this design makes it possible to recompress amplified pulse to near transform-limit. The Offner
triplet consists of a single grating and the refractive unit magnification lens telescope in the
traditional stretcher design by Martinez is replaced with two concentric spherical mirrors, one
concave and the other convex. The use of spherical mirrors reduces the aberrations to only
spherical order, which in turn are further reduced owing to the fact that the ratio of their radii of
curvature is two and they are of opposite signs. Although any deviation of the grating from the
center of curvature (Gill and Simon, 1983) of the two mirrors, causes astigmatism leading to
degradation in the temporal pulse profile.
Cheriaux et al. used a slightly modified version of the Offner triplet in their stretcher
design for their CPA system (1996). Although they had to place the grating out of the plane of
curvature for stretching purposes, the spherical aberrations as a result of this arrangement were
calculated to be very small such that the temporal shape of the pulses remained unchanged. Their
calculations also indicated that the spherical aberrations were significantly less severe than a
slight misalignment of the components in Offner's triplet design. Further improvisation to the
stretcher design by Cheriaux et al., (1996) M. B. Mason et al. (2000) came up with an all-
reflective doublet geometry (Figure 3-9) that lets the diffraction grating lie at the aberration-free
position in a stretcher configuration, enabling nearly perfect recompression of the broadened
pulses. It has the capability of achieving large stretch factors with over-sized optics while totally
eliminating any aberrations to the pulses.
Input Mirror, R= 120-cm
Convex Mirror Plane
R- 101-cm Mirror
Figure 3-9: Schematic of the stretcher layout. Oscillator pulses of duration ~20 fs are stretched to
~ 200 ps without any chromatic aberrations.
Figure 3-10: Spectrmm measured from the oscillator and after propagation through the pulse
stretcher. Spectral clipping on the red side of the spectrmm is due to insufficient width
of the optics in stretcher.
The stretcher in our CPA system uses the Mason doublet design to achieve stretch factors
as high as 104. The pulses from the oscillator are broadened to ~200-ps. Pulses are incident into
the stretcher at an angle of 8.240 (close to Littrow angle). We use an 8-inch diameter concave
mirror of radius of curvature of 120-cm to set a band-pass limit of ~100 nm on the spectrum of
the seed pulses. A convex mirror of radius of curvature 101-cm is placed about 70-cm from the
concave mirror. This arrangement produces an effective length (Lg, as in eq.(3.7)) of 121-cm. A
schematic of the stretcher setup is given in Figure 3-9. Some spectral clipping (Figure 3-10) is
observed in spite of the use of large optics in the stretcher.
For ideal compensation the incident angles and the effective lengths for the stretcher and
compressor must be close. But the incident angle for the compressor in our setup is 180 and the
effective length is about 125 cm. This is to account for the material dispersion and the higher
order dispersion terms added to the total phase of the pulse due to the amplification process.
3.7 Ti: Sapphire based Laser Amplifier
Amplifying femtosecond pulses in the milli-joule range was once only possible using dye-
amplifiers (Knox, 1988). Ti: sapphire based regenerative amplifier was first introduced in 1991
by J. Squier, et al. following the introduction of Ti: sapphire based laser oscillators by Spence et
al. (1991). These systems demonstrated a two-fold increase in the pulse energies. Also due to
their wide tunability and low background as compared to the dye amplifiers, it was possible to
generate more than 2 W of average power from Ti: sapphire amplifiers at a repetition rate of 10
repetition rate pump lasers, low repetition rate systems soon grew more popular as pulse energies
as high as a joule were available at a repetition rate of 10 Hz (Sullivan et al., 1991; Zhou et al.,
1995). A few millijoules of amplified pulse energy were attainable at 1 k
(Vailliancourt et al., 1990; Backus et al., 1995). When high average power pump sources
became available, pumping water-cooled Ti: sapphire crystal in the amplifier cavity generated
huge thermal loading which then limited the pulse energies to a few micro-joules in high
repetition rate CPA systems. As the pump power is increased to achieve large amplification
factors, the residual heat in the Ti: sapphire crystal gives rise to deleterious effects that influence
pulse energies and mode quality, limiting the overall efficiency of the system. Specifically, the
thermal gradient generated within the crystal due to the pump beam, consequently gives rise to a
gradient in the index of refraction of sapphire that causes the crystal to act as a positive lens (De
Franzo and Pazol, 1993; Moulton, 1986).
Moulton (1986) and later Schulz and Henion (1991) observed that the thermal properties of
sapphire improved upon cooling to 93 OK. They noted that calculations of the thermo-optic
aberrations indicated an increase in the output power capabilities of a Ti: sapphire laser by 200
times at 77 oK than at room temperature. Several groups have since developed high brightness,
high repetition rate ultrafast laser systems which mitigate or circumvent these thermal effects.
Backus et al. (2001) produced a millijoule level, femtosecond single-stage multi-pass chirped
pulse amplifier at 7 kHz repetition rate utilizing cryogenically (LN2) COoled Ti:sapphire crystal.
By cooling the crystal to temperatures near 77 K, a forty-fold increase in the thermal
conductivity (Touloukain et al., 1973; Holland, 1962) and five-fold reduction in the temperature
dependent refractive index term (dn/dT) at low temperatures (Feldman et al., 1978) is obtained.
Zhavoronkov and Korn (2004) demonstrated single-stage regenerative Ti: sapphire amplification
at multi-kilohertz repetition rate to powers of 6.5 W at 20 k
210 K and a cavity design that takes into account the strong astigmatic thermal loading of the Ti:
sapphire rod. Zhou, et al. (2005) have used two stages to avoid large thermal loading present in
single-stage systems to generate 7 W of average power at a repetition rate of 5 k
3.7.1 Process of Amplification
Optical amplification occurs in a medium where the equilibrium configuration of the
system comprises of its atoms or molecules in a state with higher energy content as compared to
the ground state of the system. This electronic exchange between the two energy states is
achieved by an external pump source. Amplifieation occurs when an electromagnetic wave of
appropriate frequency passes through such an 'inverted' medium, resulting in a release of
photons as the atoms drop back to a lower energy state, thereby extracting energy from the
system. The gain of the amplifying medium is defined as the ratio of the output intensity to that
of the input intensity. For a gain curve or emission line shape goof a laser medium of lengthL,
the gain in energy through a single pass is expressed as
Go = ez^(3.11)
go = no
where n is the population density in the upper energy level of the system and o is the gain cross
section. For successive passes through the amplifying medium, the energy content in the seed
pulse grows exponentially. This exponential increase in the gain with increasing paths through a
laser medium with limited gain bandwidth leads to narrowing of the amplified spectrum as the
central portion of the spectrum experiences more gain as compared to the spectral components
on the wings. Figure 3-11 (which is a schematic) illustrates an amplified pulse that undergoes
gain narrowing in the amplifier upon multiple round trips within the laser cavity. To circumvent
this, the amplifying medium should have a very broad gain bandwidth, such that in spite of the
gain narrowing effect, the amplified pulse bandwidth is still quite significant.
Just as the amplified bandwidth depends on the gain narrowing effect, the gain saturation
effects in the amplifier limit the maximum energy of the amplified pulse. As the energy of the
input pulse increases with each pass through the amplifying medium, the number of photons
extracting energy from the medium becomes comparable to the population density in the upper
level of the host material. Consequentially the amplifier's gain falls lowering the energy of the
amplified pulses after it reaches the peak attainable gain in the cavity.
For a homogeneously broadened medium, the gain saturation is expressed as
g = (3.12)
1 + E Es~t
where, go is the small signal gain coefficient, E is the signal fluence and Es, is the fluence of the
This effect is less pronounced for materials with large saturation fluence such as the Ti:
sapphire (Es,,t= 0.9 J/cm2). While gain narrowing determines the amplified bandwidth and hence
the pulse duration, gain saturation effect determines the pulse energy and these effects often
dictate the type of amplifiers (either regenerative or multipass) one may need.
Figure 3-11: Effect of gain narrowing in amplifiers, the red curve is the fundamental laser
spectrum and the blue curve is after five passes through the laser medium.
3.7.2 Types of Amplifiers
Amplifiers can be classified into two broad categories: Multipass and Regenerative
In a multipass amplifier as in Figure 3-12 (the exact geometry may vary from system to
system) (LeBlanc et al., 1993; Zhou et al., 1994; Backus et al., 1995; 2001; Lenzer et al., 1995)
the seed pulse is made to pass through the gain medium just a few times and each time it follows
a different path through the laser medium everytime. For media with a high gain co-efficient and
where the pump power is not an issue, the multipass system is often the best scheme of
amplification. One can get around the effects of gain narrowing with just a few roundtrips within
the multipass amplifier cavity while achieving a high output power. This configuration limits the
amount of gain that can be extracted from the medium and hence is suitable only when the
energy of the input pulse is high enough to begin with.
Figure 3-12: Schematic representation of a multipass amplifier system. The seed pulses pass the
gain medium several times but through a different path each time.
On the other hand a regenerative amplifier allows one to achieve very high gain factors on
the order of 105-106 (Wynne et al., 1994; Barty et al., 1996; Zhavoronkov et al., 2004;
Ramanathan et al., 2006). Hence pulse energies of the order of a millijoule can be realized with
input seed pulse energy as low as a few nanojoules, as is obtained from a mode-locked Ti:
sapphire oscillator. Figure 3-13 is a schematic representation of the regenerative amplifier in our
lab. One of the main advantages of a regenerative amplifier is it's a laser cavity configuration
which determines the spatial profile and the pointing of the amplified beam. It is capable of
delivering highly energetic pulses with excellent beam quality. Although one of its major
drawbacks is that due to the high gain per pass and since the number of passes is usually large to
obtain high factors of amplification, the effect of gain narrowing restricts the bandwidth of the
amplified pulses. In addition, amplified spontaneous emission can deplete the gain faster than the
seed pulse. Thus systems that generate ultrashort pulses in the 1-10 mJ range often use a high
gain preamplifier followed by one or two power amplification stages.
M, Ti:sapp Pump Beam 1/4
Figure 3-13: A schematic representation of the regenerative amplifier in our laboratory. The seed
pulses are injected through a Faraday Isolator (FI) and reflected off a Thin film
Polarizer (TFP). The pockel cell (PC) and the h/4 waveplate confine the seed pulses
for ~250 ns (15-16 roundtrips) in a cavity formed by mirrors M1 and M2. The
amplified output is obtained through the other exit in the FI.
But with the advent of high average power pump lasers such as the diode pumped solid
state lasers, using high thermal conductivity crystals such as the Ti: sapphire, it is now possible
to generate millij oule level pulses at k
2001; Zhavoronkov and Korn, 2004; Ramanathan et. al., 2006).
The effects of gain narrowing and gain saturation could be curbed to a certain extent by
shaping the spectral amplitude of the seed pulses before injection into the amplifier cavity or
during the amplification process. For positively chirped pulses in the amplifier, the leading edge
or the 'red' edge of the pulse spectrum can experience a higher gain as compared to the 'blue' or
the trailing edge of the spectrum. In the past etalons were placed within the amplifier cavity to
compensate for the gain narrowing effects. Barty et al (Barty et al., 1996) used 3-Clm thick air
spaced etalon in their regenerative amplifier cavity to obtain a ~15% increase in the amplified
bandwidth thereby measuring 18 fs pulses on compression. Specialized filters have been used in
the amplifier cavity to generate spectrally dependent losses such that the maximum gain around
800-nm is reduced and distributed over the wings of the gain curve. Bagnoud and Salin (2000)
used a 580-Clm thick birefringent filter to increase the spectra of the amplified pulses from 30-nm
to ~50-nm. More recently Takada et al (2006) designed a multilayer dielectric fi1m to introduce
losses near the peak of the gain curve of Ti: sapphire, generating 12-fs pulses directly from a
they rely on gain losses to increase the bandwidth of the amplified pulses.
3.8 Pulse Shaping
Pulse shaping techniques wherein an input pulse with a slight 'lean' in its spectral content
towards the wings of the gain curve could offset the gain narrowing effect and lead to broader
bandwidth with low pulse energy losses. Spatial light modulators (SLM) that serve as amplitude
and or phase masks when placed in a zero-dispersion standard 4f stretcher, serves as a pulse
shaping devise for ultrashort pulses (Omenetto et al., 2001; Efimov and Reitze, 1998; Efimov et
al., 1995). The SLM placed in the Fourier plane between the two lenses of the stretcher setup as
in Figure 3-7(b), allows one to write complex amplitude and phase masks that when applied to
an ultrashort pulse can generate arbitrary amplitude and phase profile.
Verluise et al (2000) demonstrated an acousto-optic programmable dispersive filter
(AOPDF) or commonly known as the Dazzler as a pulse shaping device. Unlike the SLM pulse
shapers, the dazzler is based on the acousto-optic interaction and does not need to be placed in a
Fourier plane of a zero dispersion stretcher setting, making it a highly compact device. When
placed between the stretcher and the amplifier, the dazzler can pre-compensate for gain
narrowing and saturation effects in the amplifier. Pittman et al (2002) applied spectral and phase
correction to the pre-amplified pulses using the dazzler to generate an amplified bandwidth of 51
nm. Figure 3-14 indicates an optimally shaped input pulse spectrum with the dazzler that
generates the broadest bandwidth pulses from our amplifier. For more on the principles of
operation of the dazzler system, consult Appendix B.
,,.,Waveengt (~nm) Lm
Figure 3-14: Amplified pulse spectrum shows a FWHM of 33-nm. Inset, blue curve is the shaped
oscillator spectrum using an AOPDF, which yielded an amplified bandwidth of 33-
nm, obtained from the original oscillator spectrum (red curve).
3.9 Ultrashort Pulse Measurement
Since electronic devices have response times that span a few nanoseconds to few
picoseconds, they cannot be used to measure the temporal characteristics of an ultrashort pulse.
In order to measure an event as short as few femtoseconds, we need a probe that is either shorter
or the same duration as the event itself. The only way then to measure a femtosecond pulse, is to
use the pulse to measure itself! The most common method to measure ultrashort pulse has been
the auto-correlation method devised by Maier et al. (1966). The ultrashort pulse to be measured
is split into two using a 50-50-beam splitter. The optical set up is similar to the Michelson
Interferometer where one of the beams traverses a fixed path length through one of the arms of
the interferometer and is known as the reference beam, the probe beam on the other hand passes
through a delay stage (Figure 3-15). The two beams are then focused and spatially overlapped
on to a nonlinear crystal that generates a second harmonic generation (SHG) signal. The SHG
signal which is twice the frequency of the fundamental beams is then measured as a function of
the delay time z between the two pulses. The field envelope of the second harmonic signal is
then the product of the electric fields of the two pulses
EG (t, z) ac E (t) E(t r) (3.13)
If the two beams have an intensity distribution as I(t) and I(t z), the auto-correlation of the
two pulses is
-> It,(r) c CI (t)I(t r)dt(.4
The measured auto-correlation signallI,(r) then gives us an estimate of the duration of the
measured ultrashort pulse. It is evident from the above equation that the auto-correlation
technique cannot uniquely determine the temporal phase structure of the pulse. For a given
intensity profile as measured by the auto-correlation technique, one can construct several
different pulses with different phase structures (Chung and Weiner, 2001).
To be able to determine the temporal phase of the pulse, one needs to know the frequency
domain phase of the pulse along with its magnitude. But as the auto-correlation yields only the
Fourier-transform magnitude, it represents a classic case of the unsolvable 1-D phase retrieval
problem (Akutowicz, 1956; 1957).
Figure 3-15: Experimental auto-correlator set up. The pulse to be measured is split into two; the
pulses that are delayed with respect to each other are focused on a SHG crystal and
measured in a detector.
Experimental FROG trace Retrieved FROG trace
time (s) Wa elengh (nm
Figure~ ~ ~ 3-6 FRG a xeietlsecrga,()Rtivdsecrga ihaFo ro
of002 c 3f uswdt n d pcrmfo h reree Frgtae
In the eal 190s Trbn an ae(93 rsre omketepaertrearbe
a -iesoa n heeni ol il acuaeifrmto bu the phs of thulea
well~~~~~~~~~~~~~ (Strk 197.Ti ehiu nw steFeqec eovdOtclGtn FO)
spectallyresovd h SH siga in anat-orltradtepcrga bandte
uniuel deemnstetmorlplewdhadth orsodn haeb sn hs
retrieval algorithm. The spectrogram is a 2-dimensional representation of the pulse as a function
of frequency and time delay(S'(m, )) For a more detailed explanation of this technique refer to
appendix A at the end of this dissertation.
Figure 3-16 (a) and (b) is the experimental and retrieved FROG traces respectively for a
compressed pulse from the CPA system in our laboratory and (c) and (d) is the retrieved
temporal and spectral profie with the phase structure in the respective domains for a 43-fs pulse.
3.10 Chirped Pulse Amplifier system
The single stage chirped pulse amplifier system in our laboratory (Figure 3-17) employs a
Coherent Corona laser, capable of generating 12-mJ pulses at an average power of 80 W at a
repetition rate that can be varied from 1-25 k
30 fs pulses from a home-built Ti: sapphire oscillator is stretched to ~200 ps before inj section into
the amplifier. The crystal in the regenerative amplifier is placed in a cryogenic vacuum chamber
and cooled to 87 oK by the use of liquid nitrogen. Two Faraday isolators placed in the beamline
prevent the backtracking of the amplified pulses into the oscillator. Two spherical mirrors of
radii of curvature 1 and 2m (high damage threshold custom coating from Rocky Mountain Inc.)
form the regenerative amplifier cavity. The seed pulses are introduced into the amplifier via
reflection off a thin film polarizer (Alpine Research Optics). A sol-gel coated Pockels cell (KD P)
and a quarter waveplate combination help retain the amplified pulses for ~240-ns (15-16
roundtrips) within the amplifier cavity. The Pockels cell helps switch the amplified pulses out of
the amplifier. The crystal is double pumped with roughly a total of 60 W of 532-nm light from
both sides. An average amplified power of 6 W (1.2 mJ pulse energy) at 55 W of pump power
and 9 W (1.8 mJ pulse energy) at 80 W of pump power at 5 k
pulses are then magnified by an 8f-telescope system before compression to minimize the risk of
damage to the compressor gratings. The energy of the compressed pulses drops to 0.7 mJ and 1.3
mJ at 55 W and 80 W of pump power respectively due to an efficiency of about 70%, of the
The amplifier exhibits a variety of temperature related effects such as thermal lensing,
thermal birefringence, and stress. Thermal management within the amplifier cavity is of utmost
importance in developing a high power, high repetition rate CPA. The next chapter is hence
devoted to the understanding of these issues and some techniques adopted to develop a state-of-
the-art CPA system.
Ti: Al O, Oscillator
~2 mJ,Q 45 fs M
Clryogenic Vacuum chamber PC 4
Figure 3-17: Schematic representation of CPA.
This chapter was devoted to the discussion of the design and construction of the various
components that make a chirped pulse amplifier system in our laboratory. Since the system is a
single-stage amplifier, the Ti: sapphire crystal is pumped with a high average power pump
source that gives rise to deleterious thermal issues. The following chapter characterizes these
temperature related effects and its effect on the performance of the amplifier.
THERMAL EFFECTS IN HIGH POWER LASER AMPLIFIER
As discussed briefly in the previous chapter, temperature related effects in the regenerative
amplifier cavity causes detrimental effects to its performance. This chapter is dedicated to
discussing these effects in detail and the steps undertaken to mitigate them to increase the overall
efficiency ofthe system.
Figure 4-1: Simulation of the resultant temperature gradient in an end pumped Ti Al203 laSer rod
at room temperature when pumped by 70 W of 532 nm laser light. Courtesy Jinho
The output of a Ti sapphire (Ti: Al203) laSer when pumped by 80 W of frequency- doubled
Nd: YAG laser of wavelength 532 nm Apump,,) giVCS rise to a laser output peaked at 800 nm
(iasmg,). Ti: sapphire has a wide absorption band in the green spectral region with significant
absorption at 532-nm (figure2-2) due to which it absorbs 85-90% of the incident pump light (the
absolute absorption is dependent on the doping levels of Ti3+ in Sapphire). The quantum defect or
the Stokes shift which is the energy difference between the pump photon and the lasing photon
'7( = Aasmg ipurmp) i S deposited as heat in the crystal. The radial intensity dependence of the beamn
is translated into a spatial temperature gradient along the transverse axes in the crystal. This
results in a 'hot' area at the center of the crystal as compared to its edges. As an example of the
severity of this effect, Figure 4-1 is a numerical simulation of the temperature rise within a
crystal whose boundary is maintained at room temperature, when a Gaussian beam of 532-nm
source at an average power of 70 W is incident on it. For the sake of simplicity a 6-mm long and
2.5-mm radius cylindrically symmetric crystal was assumed for the simulation which was
performed using a Finite Element Analysis package by Comsol Multiphysics or commonly
referred to as Femlab. The spot size of the pump beam on the crystal was 500-Clm and the
absorption parameter a, L was 2.2. As Figure 4-1 indicates the center of the crystal is about 150
oK above room temperature. This spatial variation in the temperature along the two transverse
radial axes alters the refractive index leasing to the following thermal effects (Koechner, 1976)
Figure 4-2: Refractive index changes to a crystal incident with 80 W of pump beam. The thermal
gradient causes optical path deformation for a beam traveling along the : -axis.
1. Thermo-optic effect: The temperature gradient in the crystal changes the refractive
index of the laser material along the axes perpendicular to the propagation axis'z' as in
Figure 4-2. A laser beam traversing through the crystal experiences a change in the
optical path length (OPD) due to the position dependent refractive index n2 (r, z) .
AOPD = A~d:= A~d:(4.1)
where AT = T (r, z) T (r,, z, ), An, is the temperature dependence of refractive index.
2. Thermo-elastic deformations (Thermal Expansion): The heat generated by the
absorption expands and leads to radially curved end-faces because of the heat generated
temperature gradients. The former effect does not affect the focal characteristics of the
crystal, but the thermal gradients generate increased focal power (Figure 4-3). This end-
face curvature causes a change in the optical path length of a transmitting laser beam.
AOPD, = a A Td: (4.2)
where a is the thermal expansion co-efficient.
Figure 4-3: Radially curved end-faces due to increase in temperature caused due to absorption of
incident pump beam.
3. Elasto-optic effect: The temperature distribution T (r) also causes the center of the
crystal to expand more rapidly as compared to the cooler outer edges. This generates
mechanical stress in laser rod as the center is constrained by the edges of the crystal.
The optical path length changes induced due to this effect is given as
AOPD,, = 'An,,d: (4.3)
where Ane, is the photo-elastic coefficients of the crystal.
Thus, the total optical path difference can be calculated as
AOPD = AOPD, + AOPDe + AOPDe (4.4)
These various thermal effects coupled with the fact that thermal constants of
sapphire (a,r, dn/dT) are functions of temperature, induce modal distortions in the lasing beam,
which restrict the output power from the amplifier cavity besides distorting the shape of the
beam. Table 4-1 gives a quantitative comparison of these thermal effects in sapphire indicating
that the elasto-optic effects can be safely neglected while calculating the net thermal effects in
the Ti: Al203 CryStal (Lawrence, 2003). The comparison made in Table 4-lassumes that the heat
incident on the crystal is absorbed uniformly over the entire length of the crystal whose radius R
is much larger than the beam diameter a Considering only radial heat flow between the points
r = 0 tor = mi, the temperature differences where there is no appreciable change in the thermal
constants of the crystal is thus calculated as
sT = A T[ -a ATa (4.5)
=w K (27ts~ih)
where, Pa is the absorbed power by a crystal of length h r is the thermal conductivity.
Integrating this quantity over the entire length of the crystal yields
3Tdz = a(4.6)
The relative strengths of the various thermal effects can now be calculated and compared
as equation (4.6) indicates that r/PJ3Td~z is a constant for any material for small changes in
In order to achieve beam quality close to the diffraction limit and higher amplified pulse
energies, these optical distortions in the cavity must be eliminated as much as possible. In the
past, numerous methods have been proposed that can lower these distortions (Schulz and Henion,
1. Pumping the crystal at lower powers such that the available heat limits the thermal
distortions in the system.
2. Using a slab geometry for the crystal rather than a cylindrical rod design in the amplifier
(Koechner, 1976) reduces the heat flow to a one-dimensional problem, which then
simplifies the removal of heat.
3. Reducing the quantum defect n (which may be defined as i4 1,,,li,,, or i4 ,, 1,,,,,, by
pumping the crystal with a higher wavelength source (Moulton, 1986).
Table 4-1: Quantitative estimate of thermal effects in sapphire.
Thermo-optic effect 1
Thermal expansion 0.8
Elasto-optic effect 0.2
Note Adapted from Lawrence (2003)
For several reasons, the above mentioned measures cannot be easily implemented when
designing high average power systems. Pumping the crystal at lower powers reduces the output
power of the amplifier. Although a slab geometry produces lower optical distortions, is it found
(Miyake et al., 1990) that the cylindrical rod geometry for Ti: Al203 prOduces higher powers
when cooled to liquid nitrogen temperature. Besides a slab geometry can also give rise to various
parasitic modes that can lower the useful stored energy in the crystal (Koechner, 1976). Special
coatings to suppress these parasitic modes and to enhance the thermal coupling to the cooling
unit can add to the cost and the design complexities of slabs. In addition slab geometries are not
easily implementable in regenerative amplifier systems.
The heat generated in the crystal is given by the product of the amount of heat absorbed by
the crystal and the quantum defect(H = P, x 77). Pumping Ti: Al203 at 600 nm instead of 500 nm
reduces the quantum defect by a factor of two (Schulz, 1991). In order then, to achieve the same
absorbed power at 600 nm, the concentration of Ti3+ ions has to be increased in the crystal as, the
absorption coefficient of Ti: Al203 is lower for 600 nm as compared to 500 nm (figure 2-2)
(Moulton, 1986). Thus high quality crystals must be used to limit losses due to the absorption of
the crystal at the lasing wavelength. Most significantly the availability of high-powered pump
sources at 600-nm restricts operation at this regime.
This prompts a more detailed study and analysis of the two most damaging thermal effects
in Ti: Al203 to gain a better understanding of the problem so as to be able to suggest remedial
4.2 Theoretical Background
As explained above, refractive index changes of Ti: sapphire with incident pump beam
leads to optical distortions. These changes can be separated into temperature- and stress-
n(r) = no + An(r), + An(r), (4.7)
where n (r) is the radial variation of refractive index; no is the index at the center of the laser rod
and Anz(r),~ and An (r.) are the temperature and stress dependent coefficients of refractive index
respectively. Ignoring the effects of the stress-dependent changes (Lawrence, 2003) as per
explanation above, n (r) can be expressed as
An~),= T~r -T~o) = AT(x, v y, z) (4.8)
This results in an OPD change as given in equation (4.1).
As sapphire exhibits peak absorption at 532-nm, there usually is some physical distortion of the
flatness of the rod ends that result in a change of the optical path length of a laser beam that
traverses through it. This deviation can be calculated as
L(r) = aoLoA T(r) (4.9)
where, so is the coefficient of expansion and La is the original length of the laser crystal. This
results in an OPD change as per equation (4.2) Thus the transverse optical path difference for
propagation along the z-direction can be written in general as
AOPD(x, y)= (n[T(x, y,z)]-1)dz (4.10)
Expanding n and dz in powers ofAT, using equation (4.8) and (4.9) equation (4. 10) becomes
AOPD(x, y) (no +~ -AT 1)(dz + ao ATdz)
L L L(4.11)
= n ATdzo +I naoTdzo coTdzo +(no -1) +O([AT]2)
Neglecting the constant term and terms in(AT)2, the integrated optical path length is then given
AOPD~x~y)= +a(n -1)I AT(x. y.z~dz (.2
\dT U I(.2
Analytical solutions to the above equation for cylindrically symmetric crystal geometry can be
obtained by solving the steady-state heat diffusion equation with the appropriate boundary
-V *[KcVT(x, y, z)] = Q
M. E. Innocenzi et al. (1990) solved the heat diffusion equation for an axially heated cylinder
with a thermally conductive boundary at the periphery. For an incident pump beam that is
Gaussian in nature, the steady state temperature difference is calculated as
aabs n exp(-aoz) r02:: 2r0P2 : 2r2 (.4
AT(r, z)= x In +l 2 E1 2(.4
where, 14 is the incident pump power, aab s I the absorption coefficient that results in the
heating, w, is 1/e2 radius of the Gaussian pump beam, ro is the radius and r is the thermal
conductivity of the laser rod. The expression for AT(r,z) can be obtained by neglecting
E, 132r0,2m ,;as it mall for most practical cases andl epuandi~ng E, 12r2/m2 (Abramawitz andl
Stegun, 1965) as a power series and retaining only the terms quadratic in r. Plugging it into
equation (4.1) (their calculations do not include the thermal expansion of the crystal) yields the
resultant phase change or the transmitting laser beam of wavelength ii through the crystal
A # = AOPD(r)
2i7y (dn/dT) 245
Af = 2 [1- eXp(-aabs)]r
comparing the above equation to the phase changes that occur in a lens like medium with a
quadratic variation in its refractive index (Kogelnik, 1965)
A # = (4.16)
where, f is the effective focal length. Comparing equation (4.15) with equation (4.16) the
effective focal length for the laser rod can be written as
f= ~i 1 (4.17)
th n (dn/dT) 1 -exp(-aabsn)
This effect known as thermal lensing because it alters the modal properties of a beam that
transmits through it, just like a static lens but unlike a static lens, it's dynamic in nature due to its
implicit dependence on pump power. In an amplifier cavity formed by two spherical end mirrors,
this effect can destabilize the cavity as the modal properties of the lasing beam starts to exhibit
the same dynamism as the thermal lens in the crystal for various pump power levels. A positive
value of dn/dT for a material generates a converging thermal lens and a negative value
generates a diverging lens. Although the above equation is calculated for a cylindrical crystal
pumped with a continuous laser source, we can nevertheless use it to obtain an estimate of the
focal length for a Brewster cut Ti sapphire crystal pumped with a pulsed laser source (Coherent,
Corona). The thermal constants for sapphire at room temperature are: ic = 0.33 W/cm2 (Holland,
1962), dn/dT = 1.28 x10 /K (Feldman et al., 1978). For a crystal with its boundaries at room
temperature and pumped with 60W of green light with a spot of 500-Clm on the crystal and a
constant pump absorption-length product, absL = 2.2 yields a thermal lens of focal length
f, = 4cm !
To increase the thermal lens focal length or conversely to decrease the thermal lens power
(defined asl/,), the pump power can be decreased or alternatively the pump spot size on the
crystal can be increased. Recalculating the focal length for a pump spot of radius 1-mm and a
decreased incident pump power of 30 W, increases the focal length to ~ 30-cm. Although
reducing the pump power increases f,, but this necessarily decreases the amplified output power.
Since a high overlap integral between the pump spot and the lasing beam spot sizes on the crystal
is required for efficient energy extraction from the Ti: sapphire in the amplifier. This integral is a
maximum when the pump beam is smaller or equal to the amplified beam. Increasing the spot
size my~ of the pumping beam may alter the overlap integral, again bringing about a reduction in
the extracted energy from the amplifier.
Thus to be able to achieve high average amplified power from a regenerative Ti sapphire
amplifier cavity the thermal lens effect needs to be either eliminated (ideal solution) or at least
minimized (practical solution).
4.3 Methods to Reduce Thermal Effects
In the past, researchers have used various methods to reduce thermal effects in their laser
systems. A quick review through some of these measures brings about a deeper understanding of
The most intuitive method of eliminating or reducing thermal effects in a laser cavity
would be to introduce a diverging lens in the beam path to compensate for the induced positive
or converging thermal lens generated by the crystal. Due to the variable nature and broad range
of the thermal lens, a fixed focal length passive optical element cannot compensate for a range of
incident pump powers. Also such an optical element will change the beam diameter on the
crystal with each pass, increasing modal distortions in the laser beam.
Salin et al. (1998) introduced the concept of thermal eigenmode amplifiers. A thermally-
loaded multipass amplifier is equivalent to a series of lenses separated by a distance L that
corresponds to the beam round trip length inside the cavity. An unfolded resonator with two
spherically curved mirrors with radii of curvature 2 fherm, With the crystal at the center is
equivalent to a series of lenses of focal length ftherm Separated by a distance L. An eigenmode of
this resonator, calculated from the paraxial Gaussian beam propagation relations, reproduces
itself for each round trip, which for a multipass is equivalent to re-imaging the beam onto itself
after each pass. If the input beam has the same size and characteristics of the eigenmode of the
resonator then the amplified output beam characteristics are similar to those of the input beam
producing diffraction limited amplified pulses. This is suitable when the incident pump power is
maintained at a constant value, as any change in this parameter causes a change in the focal
length thus changing L This is also based on the assumption that the host medium is cylindrical,
such that the thermal lens is mostly spherical over the entire pump beam diameter and the length
between the successive passes is a constant. A Brewster cut rod (Figure 4-4) instead of a
cylindrical laser rod generates an aspherical thermal lens and it then becomes difficult to
calculate the thermal eigenmode accurately. MacDonald et al. (2000) have reduced the thermal
lensing effect in diode-pumped Nd: YAG laser with multiple composite rods. These rods had
undoped end caps to remove the part of thermal lens formed due to the bending of the end faces
of the laser rod.
Zhavoronkov and Korn (2004) thermoelectrically cooled a 3-cm Ti sapphire crystal in a
three-mirror astigmatic regenerative amplifier cavity to 210 OK that took into account the huge
positive thermal loading of the sapphire rod. Their single-stage, multi-kilohertz laser was able to
generate 6.5 W of average amplified power at 20 k
were obtained, the thermal and thermo-optical constants did not differ significantly from their
room temperature values, and it is likely that higher order spatial aberrations were present in the
Q =60.5 2.
Figure 4-4: Brewster cut Ti sapphire crystal.
Zhou X et al. (2005) used two multipass amplification stages after a regenerative amplifier
cavity in order to avoid large thermal loading present in single-stage systems. They were able to
generate 7W of average amplified output at a repetition rate of 5 k
to solve the thermal-loading problem in their CPA system, managing multiple amplifier stages
can get cumbersome.
An often used technique to reduce thermal lensing in high power continuous wave
Nd:YAG laser systems (Graf et al., 2001; Wyss et al., 2002; Mueller et al., 2002) can be
incorporated to compensate for thermal effects in single-stage high repetition rate systems. The
idea is to use self-compensating (adaptive) methods to thermo-optically compensate for the
thermal lens effects that change with changing power. This technique essentially uses adaptive
optical devices such as self-adjusting lenses within the laser cavity that can compensate for every
single pass of the lasing beam through the cavity. A material with a negative thermal dispersion
coefficient is placed in the cavity that generates a power dependent thermal lens that
compensates for the positive dn/dT induced by the temperature gradient in the laser crystal. Th.
Graf et al. (2001) were the first to successfully use an adaptive negative thermal lens to
compensate for the positive thermal lens in a transversely diode-pumped Nd: YAG laser rod. The
compensating element must absorb a small fraction of the incident laser power and hence should
posses a strong thermal dispersion dn/dT to effectively compensate for the positivedn/dT This
technique has also been extended to correct thermally induced optical path length changes
induced by absorption of transmissive optical components such as electro-optic modulators and
Faraday isolators, of gravitational wave interferometer (Mueller et al., 2002).
We attempted to extend the concept of thermo-optical compensation to our regenerative
amplifier. Curing gels or index matching fluids such as the OCF-446 (Nye Opticals) possesses
the combined advantages of solid materials (no convection) with a strong negative dn/dT With
a negative thermal dispersion value as high as 3.5 x 10-4 o -1 and a large expansion co-efficient
of 8 x 10-4 it seems like an ideal candidate as a compensating material with the added advantage
of low absorption at the lasing wavelength of 800-nm (< 2x 10-4 O/o/pm). Although numerical
simulations by Jinho Lee seem to suggest that the thermo-optical compensation method should
work for an OCF thickness of ~ 3mm for a pump power of 80 W, but preliminary experiments
have revealed the high intracavity peak powers in the regenerative amplifier cavity causes
damage to the cell containing OCF 446. It is not clear from these experiments if the damage
occurred to the cell holding the OCF or if the OCF itself burns due to the absorption at the lasing
wavelength. Redesigning the cavity taking into consideration the OCF or changing the location
of the OCF could potentially solve this problem but has not yet been experimentally verified and
could possibly be one of the avenues that could further be explored to increase the efficiency of
the present amplifier system.
Meanwhile the most efficient and convenient means of reducing thermal effects in Ti
sapphire laser crystal in a chirped pulse amplifier is by cooling it to cryogenic temperatures
(liquid nitrogen temperature (770K) or below) (Moulton, 1986; Schulz and Henion, 1991).
Sapphire exhibits excellent thermal properties on cooling to low temperatures. The next section
delves on how the thermal properties of sapphire can be exploited to reduce the temperature
4.4 Liquid Nitrogen Cooled Ti Al203 Laser Amplifier
P.F. Moulton (1986) was the first to demonstrate the advantages of cooling the sapphire
laser crystal to liquid nitrogen temperature in a quasi cw laser. He reported an increase in the
output power of the laser from 45 mW to 150 mW when the crystal was cooled to 80 OK. He
attributed this effect to an increase in the thermal conductivity of sapphire with decreasing
temperature. This idea was then extended by Schulz and Henion (1991) where they investigated
the effects of thermal loading on a single-transverse-mode of Ti: sapphire laser cooled to 93 OK
and reported a reduction in the thermo-optical refractive index changes by more than two orders
of magnitude. They realized an output power from the Ti: sapphire laser that was 200 times
larger at 77 oK than at room temperature!
Table 4-2: Thermal properties of sapphire at 300 and 77 oK.
Property At 300 oK At 77 oK
Thermal conductivity it 0.33 W cm K- 10 Wcm K-
Thermal dispersion dn dT 1.28 x 10-5 K1 0.19 x 105 K-1
Thermal expansion co- 5.0 x 10-6 K-1 0.34 x 10-6 K-1
Note: Adapted from Schulz and Henion (1991).
Table 4-2 compares the thermal properties of Ti sapphire at room temperature and liquid
nitrogen temperature. Figure 4-5 (a) and (b) show the variation of thermal conductivity r and
dn/dT with temperature, the key parameters in minimizing thermal distortions.
The thermal lens focal length as given by equation (4.17) is directly proportional to the
ratio r/(du/dT) Figure 4-5 indicates that as the temperature is decreased, the thermal
conductivity rises steeply, and the coefficient of refractive index with temperature decreases
thereby making the ratio of thermal conductivity to dn/dT increase with increasing temperature.
This leads to a decreasing thermal power (or an increasing thermal lens focal length). Backus et
al. (2001) were able to generate 13 W of amplified output power at 7 k
cryogenically cooled single-stage multipass amplifier with good beam quality (measured M2 Of
1.2 and 1.36 along the X and Y axis).
We can now calculate the effective thermal lens focal length [equation (4.17)] of a Ti
sapphire crystal at LN2 temperature using the constants in Table 4-2 for an input pump power of
60 W and a spot size of 500-ypm as mentioned above. On doing so, an f, of ~8m is obtained!
Thus we find that there is a tremendous decrease in the thermal lens power of about two orders
of magnitude on cooling the crystal to 77 oK!
50 100 150 200 250 300 350 400 450
Figure 4-5: Dependence of (a) Thermal dispersion (dn dT) (Feldman et al.,1978) and (b) Thermal
conductivity ic (Holland, 1962) of Ti sapphire with temperature.
In order to design an effective regenerative amplifier cavity we accurately need to know
the positive thermal lens generated by the crystal with changing pump power. We have made a
very detailed study of this, which is elaborated in the remaining sections of this chapter. The next
section deals with the construction of a regenerative chirped pulse amplifier since all the
experiments and numerical calculation on thermal analysis were performed on this high average
power CPA system.
4.5 Construction of a Regenerative Amplifier Cavity
The entire below mentioned discussion has been based on the current amplifier system in
our CPA and this section delves into the details of the construction of this amplifier.
A 5-mm diameter and 6-mm long Ti sapphire crystal is the host material in our
regenerative amplifier cavity. The crystal is cooled to 87 oK in a vacuum chamber that' s placed
underneath a liquid nitrogen dewar. The vacuum chamber was designed after extensive
consultations with our in-house mechanical engineer Luke Williams. The LN2 dewar is separated
from the crystal by a thin copper wall of thickness ~100-Clm. The crystal is held in a copper
holder, and a 127-Clm Indium foil is sandwiched between the crystal and the thin copper wall for
better thermal contact between with the LN2 in the dewar. A thermocouple placed along one of
the edges of the crystal senses the temperature of the crystal at all times. The temperature sensor
has an in-built relay circuit to automatically facilitate the turning off of the pump laser when the
crystal temperature exceeds 185 oK. Figure 4-6 is a CAD drawing of the vacuum chamber-
dewar assembly in our CPA system. As can be seen in the Figure 4-6 (a), the vacuum can has 2
extended arms on either side with brewster windows on it as entrance and exit for both the pump
beam and the amplified IR beam. A view-port right in front of the crystal allows one to position
the pump beams on the crystal. Figure 4-6 (b) is the copper holder in which the Ti sapphire
crystal is placed.
This particular assembly generates almost 0.6 OC rise in temperature per Watt rise in the
pump power (Figure 4-7). At zero watts of pump power the crystal temperature as measured by
the thermocouple is 90 oK. With almost 65 W of pump power at 5 k
temperature rises to about 127 oK when the lasing action within the regenerative amplifier cavity
is inhibited and 108 oK when the cavity is in the lasing mode. The higher temperature rise when
the cavity is not lasing is due to the absorption of fluorescence by the thermocouple which is
considerably decreased during the lasing action. This allows for continuous operation of the
regenerative amplifier to repetition rates as high as 12 k
= cavity lsn
0 10 20 30 40 50 60 70
0.3 mJ at 12 k
amplified pulses (Figure 4-15).
Figure 4-6: CAD drawings depicting (a) Vacuum dewar assembly and (b) copper crystal holder.
Drawings by Luke Williams.
Pump Power (W)
Figure 4-7: Boundary temperature rise as pump power is increased when lasing action is
inhibited (red points) and when the cavity is lasing (blue points). The lines are guides
to the eye.
4.6 Measurement of Thermal Lens
A laser beam transmitted through a material that acts as a thermal lens undergoes modal
changes in its divergence angle relative to the input beam. By measuring these changes, one can
estimate the thermal lens power of the material. The design of an optimum regenerative amplifier
cavity necessitates the need to characterize accurately the thermal lens in the Ti sapphire crystal.
To be able to measure the thermal lens in our laboratory we used a He-Ne laser to probe
the Ti: sapphire crystal as a function of pump power. The He-Ne laser was mode matched to the
pump beam spot on the crystal. The changes in the divergence angle of the beam after traversing
the crystal were determined for a series of pump powers by measuring the position dependent
spot sizes with a CCD camera. By comparison with the He-Ne beam waist position at zero pump
power, the measured waist positions for the non-zero pump powers enabled us to calculate the
thermal lens focal length within the thin-lens approximation using the ABCD matrix formulation.
In Figure 4-8 is plotted the measured thermal lens power for the two transverse axes as a
function of power. For a pump power of about 50-55 W the measured thermal lens focal length is
about 1.1 m along the vertical axis on the crystal and 0.2-0.3 m along the horizontal axis. The
asymmetry in the thermal lens is immediately evident as the thermal lens power along the
horizontal axis rises much sharply as compared to the vertical axis.
An effective amplifier is one where the cavity maintains stability over a wide range of
thermal lens power. The ABCD formalism was used in which the crystal was treated as a thin
spherical lens. The cavity stability or the g-parameter was calculated for various combinations
and permutations of the radii of curvature of the two end mirrors and the distance between them.
The most suitable cavity was one that exhibited stability (-1<; g<;-1) for a large range of thermal
lens, where 'g' is the stability factor. This essentially translates as minimum changes to the spot
size of the amplified beam on the crystal. The regenerative amplifier cavity currently being used
is 2-m long, comprised of two spherical mirrors of radii of curvature 1-m and 2-m. Figure 4-9 is
a plot of the g-parameter calculated for different values of thermal lens power using the ABCD
4.5 -1 Y-Axis
4.0 -1 o
E 3.5 -I /
15 20 25 30 35 40 45 50 55 60
Pump Power W
Figure 4-8: Measured thermal lens and thermal power for the two transverse axes; the boundary
temperature was measured to be 87 K at zero pump power and 103 K at 55 W of
0 1 2 3 4
Thermal Lens focal length (m)
Figure 4-9: Cavity stability parameter as a function of measured thermal lens.
From the above plot, it's clear that the cavity is most stable for a thermal lens focal length
values from 0.6-m to 5-m. Also the calculated laser beam spot size (1/e radius) on the crystal
shows a variation of about 15% from its minimum value of 343-pLm at about 1-m thermal lens
focal length. The imaging system of the pump beam on the crystal let us vary the pump spot
from a 1/e radius of 200-Clm to 800-Clm. This ensures a good overlap of the pump beam with the
varying mode sizes of the amplified beam on the crystal, for a great range of pump powers.
In order to validate the thin lens approximation in calculating the thermal lens of the
crystal as a function of pump power, we invoke the simple lens maker' s formula for the effective
focal length for both thin and thick lenses.
1 ---1 1 (nzens no)d
Phlck lens 0'L)
fthlck R 4 nzensR,
where nzens and no are the refractive index of the lens medium and the medium in which the lens
is placed. R, and R2 are the radii of curvature of the two curved surfaces of the lens of thickness
d The difference in the thermal lens power resulting from the thin lens and the thick lens
treatment of the sapphire crystal is given as
For a Ti: sapphire of thickness d = 6mm in vacuum and with refractive index, n =s1.76 and
assuming R, = 0.5m and R2 = -lm the change in the focal length is 3.4 x 10-3. Due to the
insignificant difference between the two treatments of the crystal thermal lens, it suffices to use
just the thin lens approximation in all the calculations using the measured modal changes with
4.7 Calculation of Thermal Lens
Although cooling to 77 oK brings about a drastic reduction in the thermal lens power of the
crystal, it is in practice difficult to achieve boundary temperatures close to the LN2 temperature
when pumping with high laser powers. For a 6-mm thick Brewster-cut sapphire crystal the thin
lens approximation does not accurately describe the thermal lens. Hence to validate the use of the
thin lens approximation, we compared the measured thermal lens power with that obtained from
a Finite Element Analysis (FEA). An accurate knowledge of the temperature gradient inside the
crystal determines the thermal lens accurately.
The temperature gradient is obtained by solving the heat diffusion equation (4.13) with the
appropriate boundary conditions. For cylindrically symmetric geometries, pumped with
continuous sources, analytical solutions to the heat equation are intuitive (Quetschke et al., 2006).
Analytical solutions have also been obtained for crystals pumped with pulsed sources (Lausten
and Balling, 2003), however the crystal geometry was again a cylindrically symmetric one. For
more complicated geometries such as Brewster cut crystals (Figure 4-4) numerical methods are
needed to calculate the temperature gradient inside the crystal. Additionally, the physical
quantities in these equations (a, c, dn/dT) are temperature and therefore spatially dependent, and
not analytically tractable. Hence we use a finite element analysis package (Comsol Multi-Physics)
to model the pump pulse-induced temperature changes and numerically integrate equation (4.12)
to compute AOPD Calculations by Jinho Lee show that for a Brewster-cut geometry the source
term on the RHS of the 3-D heat equation (4. 13) takes the form
2Pa, 2o L, xx
Q2~~) cosy ex 2 -a 8r) 2COSB,2 2 _- abs L
O~xFr) mo +2 cos 8, cos 8,
where P is the incident laser power, aabis ISthe absorption coefficient for the pump, mi is the
pump waist (1/e in field), L is the crystal length, and 8,,, are the incident and refracted angles in
the crystal, respectively. Even though the pump source is pulsed the steady state equation
perfectly describes the situation as the thermal relaxation constant for Ti: sapphire laser rod is
measured to be ~0.5-secs (Ito et al., 2002) which is much longer than the repetition rate of the
laser. Therefore, for pump repetition rates of > 1 k
of the thermal gradient.
x 10 11
5 5 1106
x~~ 103 x 109 104
Horizontal Axis Crystal length (m)
Figure 4-10: Computed temperature profie in a 6 mm long, 5 mm diameter Brewster-cut Ti:
sapphire crystal single end-pumped by 50 W in a 0.4 mm pump spot waist radius for
and absorption corresponding to adb = 2.2 and a boundary temperature of 103 K.
The geometry (shown in Figure 4-10) consists of a 3D-tilted cylinder corresponding to our
Brewster cut crystal. Temperature dependent thermo-optical and mechanical constants were
obtained from Touloukain et al. (1973) and Holland (1962) were fitted over 50 300 K. The
absorption at the Ti: sapphire emission wavelength was not included as this has a negligible
effect on the temperature for Ti: sapphire crystals with high Eigures of merit
(FOM~ = as,,,,,/as,,,,,, = 200; a being the absorption coefficient). The boundary conditions were
specified as a temperature T, along the barrel of cylinder as either a Eixed or variable temperature
(corresponding to contact with the bath) and on the ends as dT/dni = const (corresponding to the
radiation). This allowed us to explore more physically realistic scenarios in our amplification
--q dratic lfit
fs1ea a s
system. Calculating the temperature profile within the crystal, we can now estimate the changes
in the optical path length or AOPD through the crystal.
The simulated AOPD were calculated for an ideal thin lens of the same focal length f~~ in
vertical and the horizontal transverse dimensions as that obtained from the simulated temperature
gradient within the crystal (Figure 4-11)The experimentally measured thermal lens values from
the previous section were then compared to the thermal lens values obtained from the computed
(a) Hron axis -=-cal uated OPD
-10 -q dratic 1it
a-400 ,., ~f-en as" u
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
crystal radius (mm)
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
crystal radius (mm)
Figure 4-11: Plots (a,b) are the corresponding AOPD as a function of the transverse coordinates,
for the computed temperature profile in figure (3-6).
These values were also compared with the analytical solution to thermal lens focal length
[equation(4.17)] derived by Innocenzi et al. (1990), associated with the phase changes that occur
inside a cylindrical laser rod due to temperature dependent refractive index An (r, z).Figure 4-12,
is a plot of the measured thermal lens focal lens power as a function of pump power, compared
with the values obtained from the FEA calculations and the expression (4.17) The ic and
dn/dT values used in equation (4. 17) corresponded to the maximum computed temperature rise
at the center of the crystal at each pump power. While the FEA calculations agree reasonably
well with the measured values along the vertical crystal axis and quite well along the horizontal
axis, the focal lens power calculated from Innocenzi's analytical equation significantly
underestimates the lens power along both axes.
0. a rical Axit
fmnite eleme it method
S10 20 30 40 50
% Pump Power (W)
(b6 ) Horizontal Axis
1. rit element mto
10 20 30 40 50
Pump Power (W)
Figure 4-12: Comparison of experimentally measured thermal lens powers (squares) against
numerically predicted values using finite element analysis (circles) and an analytical
expression for thermal lensing (triangles). Formula derived from Innocenzi et al
The underestimation by the analytical expression is somewhat surprising, since treating
r and dn/dT as a constant over the entire crystal volume underestimates the effective thermal
conductivity and over estimates dn/dT since r ( dn/dT ) increases (decreases) as the
temperature decreases away from the beam propagation axis. However, equation (4.17) neglects
the physical expansion of the crystal, which can increase the thermal lens power by a factor of
1.8 over a pure thermo-optic lens (Lawrence, 2003). Nonetheless, the FEA lens power estimates
agree with experimental data when using boundary temperatures consistent with the
experimentally measured boundary temperature values.
This present regenerative amplifier cavity designed with the above measured thermal lens
measurement and the FEA analysis has been performing exceptionally well producing average
powers as high as 9 W (before compression) when pumped with 80 W of green light at 5 k
4.8 Direct Measurement of the Optical Path Deformations
To directly measure the pump induced path length changes and further corroborate our
simulations, the LN2 COoled Ti: sapphire crystal was placed in one of the arms of a Michelson
interferometer. A single frequency 1064-nm Nd: YAG laser (Lightwave Corporation NPRO) was
split into two arms with the crystal in one arm and free space through the other. The interference
pattern was recorded as a function of power on the WinCam CCD beam analyzer. Figure 4-13 is
the recorded spatial interference pattern as a function of pump power.
PPMP=OW PPM = 6W PPM = 22W
PUP= 41W PPM = 54W PPM = 56W
Figure 4-13: Spatial interference pattern in the Michelson interferometer recorded in a CCD
camera as a function pump power.
The zero intensity frame corresponds to zero path difference at 0 W of pump power. As the
pump power was gradually increased, the change in the intensity of the interference pattern
indicated the increase in the OPD through the crystal. Figure 4-14 is the measured optical path
difference obtained from the recorded interference pattern, in the crystal as a function of pump
600 +--T = 93
-T~ = 103K 3
500 -T =13
Experlliental oi tical
400 pt 1frn
3 0 10 2 30 4 50 0
Fiue41:Maue PD coprdwt h E acltdfrtredfeetbudr
Tb ~ ~ ~ ~ ~ Pm = 03K thihe pm pwes
At the highest pump power (56 W), a AOPD of 350 nm +/- 80 nm was measured (or
approximately 0.45 Ai at 800 nm), decreasing as the pump power was lowered. The intensity
fluctuation of the NPRO laser (102 103) as well as path fluctuations caused by acoustic
perturbation of the interferometer optics most likely caused the large error bars at lower pump
powers. Experimentally, a boundary temperature of 93K was recorded at the boundary for zero
pump power. As the pump power was increased to 55 W, a boundary temperature rise of 20K
was recorded, but a fraction of this rise was experimentally attributed to the absorption of
scattered Ti: sapphire fluorescence by the thermocouple; only a portion of the experimentally
recorded temperature rise was due to physical heating at the boundary. Thus, we simulated the
AOPD for a range of constant boundary temperatures Tb displayed in Figure 4-14. At the
highest pump powers, we see good agreement between the predicted and measured optical path
length for Tb =103"K (corresponding to 10 OK rise on the boundary), although the data and
simulations deviate somewhat at lower temperatures and most severely at the lowest temperature.
As expected, the AOPD is less severe as the boundary temperature is reduced due primarily to
the strong temperature dependence of ic. Figure 4-10 and Figure 4-11displays the computed
temperature rise and AOPD for a particular boundary temperature Tb = 103"K respectively.
4.9 Effects of Thermal Aberrations on Beam Shape
5kHz, EF 1.56 ml 6kMz, Er=1.44 ml 7k~, Er=1.44 ml SkMz, 57-0.96 ml
Figure 4-15: Beam shape as a function of repetition rate. Increasing the repetition rate of the
pump beam introduces modal distortions.
The spatial quality of the amplified beam is highly sensitive to temperature changes within
the crystal. The amplified beam shapes were measured using a WinCamD-UCM CCD beam
analyzer after ample attenuation Figure 4-15 is a far field measurement of the spatial profile of
the beam with increasing repetition rates.
As the pump power is increased the temperature within the crystal increases leading to
increased spatial distortions to the beam profile. The boundary temperature as measured by a
thermocouple on the crystal rose from 103 oK at 5 k
repetition rate. Astigmatism due to the geometry of the crystal is evident in the elliptical shape of
(a) Ve tical A> is
the amplified beam even at a repetition rate of 5 k
was measured (5W output power) using the beam analyzer by attenuating it suitably and
focusing with a 1 m focal length lens.
;0 -40 0 40
40 0 40
Figure 4-16: M2 meaSurement for an uncompressed amplified beam of average power 5W at 5
A common measure for the beam quality is known as M It is defined as the ratio of
divergence of the amplified beam to the divergence of an ideal Gaussian beam of equal beam
M' = OR"measured
where 00R, and Inteasured are the waist and the divergence respectively of the laser beam of
unknown quality and me~ and 0Gaussan are the waist and the divergence of a fundamental laser
mode (TEMoo mode). The transverse profile of the beam (mi)R, ) WaS measured as a function of
the propagation distance using a CCD camera. If mi)R, = )~ then
M = easuect(4.22)
These results are shown in Figure 4-16. We observed that at lower repetition rates (5 k
corresponding to 5 W average power, the amplified beam M2 ValUeS deviated from the ideal
TEMoo mode by a factor of only 1.62 and 1.14 in the vertical and the horizontal axes respectively.
The thermal astigmatism of the crystal geometry is evident in the measured M2 value (a ratio of
1.42 in the divergence angle along the two axes). For higher repetition rates (8 k
amplified power output of 9W and a boundary temperature T, = 108"K ) this ratio increased
further to 1.73 (measured M2 ValUeS of 2.12 and 1.22 in the vertical and the horizontal axes
respectively). The rise in the astigmatism of the beam shape can be attributed to the changes in
the temperature related thermal constants for sapphire crystal as the boundary temperature
increases at higher repetition rates.
Summarizing the contents of this chapter, we detailed the various temperature related
effects in a high average power laser system and more specifically to liquid nitrogen cooled Ti:
sapphire crystal in a regenerative chirped pulse amplifier. We thoroughly characterized these
thermal effects using both experimental techniques (such as interferometry, M~ analysis and
measurement of focal power) as well as Finite Element Analysis. These measurements helped us
in designing a suitable cavity for the regenerative amplifier that generates 5 W of 40fs, amplified
output. The good agreement between the measurements and the numerical methods allowed us to
extend the numerical methods to predict an optimal cavity configuration to further minimize
these thermal aberrations which are detailed along with the present status of the amplifier in the
CHARACTERIZATION AND OPTIMIZATION OF HIGH AVERAGE POWER CPA
Having fully investigated the fundamental aspects of designing and constructing a chirped
pulse amplifier and the thermal issues inherent with high powered systems in prior chapters, this
chapter concentrates on the characterization and performance of the amplifier and discusses
methods to further enhance its efficiency.
5.1 Amplifier Performance
5.1.1 Average Power, Pulse Energy
The cryogenic amplifier cavity based on the extensive thermal analysis is capable of
delivering 9 W of amplified power at 5 k
lis a plot of the measured average output power as a function of the pump laser' s repetition rate.
4 5 6 9 10 11 12 13
Repetition Rate ktz
Figure 5-1: Amplified output power as a function of pump repetition rate (square points)
measured before compression; the red-line is a guide to the eye.
As the repetition rate is increased the output power of the system drops. This drop
coincides with the drop in the pulse energy of the pump laser (from 14.7 to 6 mJ). The boundary
temperature around the crystal increases from 110 oK at 5 k
indicates the amplified and the pump pulse energy with increasing repetition rate. The efficiency
of the regenerative amplifier (defined as Eamph~fiedlEpump ,) is approximately 14% at 5 k
drops to 5% at 12 k
which no lasing action is observed as the cavity ceases to be stable. By altering the cavity g-
parameter, the amplifier can be made operational for repetition rates above 12 k
amplified output power of 4.5 W is generated at 12 k
recovered from the compressor. This could easily go up by the usage of gratings with improved
efficiency in the compressor setup.
Repetition Rate (kd~z)
Figure 5-2: Amplified v/s pump pulse energy with increasing repetition rate. Amplified pulse
energy is indicated by the red points and the pump pulse energy by the blue points.
The solid lines are guides to the eye
5.1.2 Spatial Beam quality
The increasing thermal loading effects as a result of the increasing repetition rate also
bring about degradation of the spatial profile of the amplified beam as in Figure 4-15. This is
evident in the measured M~ of the beam at 8 k
chapter, M~ is a measurement of deviation of a laser mode from the fundamental TEMoo mode.
A boundary temperature of 115 oK was recorded for an input pump power of 75 W at 8 k
M2 Value Of 1.22 and 2.12 was recorded in the vertical and the
An average output power of 9 W uncompressedd) was obtained.
12nn 1- aucal i
lo \I *
repetition rate. A measured
horizontal axes respectively.
-120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120
Figure 5-3: Measured M2 for an uncompressed amplified beam of average power of 9 W at 8
The ratio of the divergence angle along the 2 axes is thus 1.73, which is a nearly 22%
increase from its value at 5 k
If the only source of astigmatism in the cavity is due to the Brewster crystal geometry, then
increasing the repetition rate should have little or no effect to beam astigmatism. But the rise in
the astigmatism of the beam shape with increasing pump power can be attributed to the changes
in the temperature related thermal constants for sapphire crystal as the boundary temperature
increases at higher repetition rates. Figure 5-3 is a plot of the measured M2 along the two
transverses axes plotted along with the respective divergence for a Gaussian beam of same waist.
5.1.3 Spectral Characteristics
The bandwidth of the amplified pulse is 25-30 nm (without any amplitude shaping)
depending on the bandwidth of the seed pulses. The amplified spectrum is shifted to the 'blue'
end of the spectrum as compared to the oscillator spectrum (Figure 5-4).
0.8- -w r l10.8
700 7 0 740 760 7240 800 8 0 840 860 8140 900
Figure 5-4: Amplified spectrum (blue-curve) for the corresponding oscillator spectrum (red
curve) as measured using a fiber spectrometer.
Figure 5-5 is the emission spectra for Ti: sapphire at two different boundary temperatures:
87 oK and 300 oK. We observe that the emission spectrum is narrower at a crystal temperature of
87 oK than at room temperature. As the oscillator spectrum (Figure 5-4) is red-shifted with
respect to the emission spectrum the gain of the amplifier (Figure 5-5) is pulled to the bluer edge
of the spectrum due to which the amplified spectrum peaks at 780-nm as compared to 820-nm
for the oscillator spectrum. The spectrum for the free-running laser for the regenerative amplifier
cavity confirms the reason for this spectral shift towards the blue end (Figure 5-6). By reshaping
the oscillator spectrum as in figure 3-14 using the dazzler towards the blue end not only increases
the amplified output power from the regenerative amplifier but also reduces the amount of time
the seed pulse needs to stay within the cavity to be able to extract gain from the crystal. This is
since the gain of the sapphire crystal peaks at 775-nm (Figure 5-5), sculpting the spectrum of the
7 0 740 760 780 800 820 840
Figure 5-6: Free-running spectrum for the regenerative amplifier cavity at 5 k
seed pulse towards the bluer edge of the spectrum leads to efficient extraction of the energy by
the seed pulse from the crystal that in turn leads to a reduction in the number of roundtrips the
seed pulse needs to make to be able to gain the same amount of energy as a pulse with its
spectrum shifted towards the red-edge.
The amplified spectrum in Figure 5-4 generates 40-45 fs compressed pulses in a grating
based compressor with an efficiency of about 60%.
Figure 5-5: Emission spectra for Ti: sapphire.
800 900 1000 1100