1. IRAQI JOURNAL OF APPLIED PHYSICS
All Rights Reserved ISSN (printed) 1813-2065, (online) 2309-1673 Printed in IRAQ 9
Tayyab Imran1
Mukhtar Hussain2
Using Frequency Resolved
Optical Gating for
Optimization of Thermal
Lensing Compensated
Ti:Sapphire Femtosecond
Laser System
1
Department of Physics and
Astronomy,
College of Science,
King Saud University,
P.O. Box 2454,
Riyadh 11541,
SAUDI ARABIA
2
Department of Physics,
Govt. College University Faislabad,
Sahiwal, PAKISTAN
We report the characterization and optimization of thermal lensing compensated
high peak power Ti:Sapphire femtosecond laser system, 4.0mJ pulse energy
operating at 1-kHz repetition rate. Thermal lensing is compensated by employing
convex folding mirrors and Peltier coolers while thermal eigenmode post-
amplifier has introduced to retain the amplified laser pulse beam on the
amplifier crystal. Single-shot second harmonic generation (SHG) frequency-
resolved optical gating (FROG) diagnostic technique is employed to characterize
the output compressed laser pulses. FROG image is monitored by charged-
couple device (CCD) attached to the personal computer and optimization of the
laser system is observed by FROG image in real time. Grating detuning is carried
out in the compressor to optimize the minimum possible pulse duration and pulse
of 30 fs duration is measured at the zero detuning scale.
Keywords: Ultrafast lasers; Ti:Sapphire laser; Chirped pulse amplification; Optical gating
1. Introduction
A swift advancement in the development of high
average peak power laser systems have been
observed in recent years [1-5]. The high peak power
laser systems have become quite important in
various experimental applications such as high
harmonics generations (HHG), white-light
continuum (WLC), plasma and optical field
ionization [6-8]. High peak power laser system
needs high power pump laser beam to pump the
crystal in the amplifier. This high pump power in
amplifiers induced the thermal effect in amplifying
crystal which leads to the distortion in the amplified
pulses that ultimately reduce the efficiency of the
amplifier. To perform experiments, it is essentially
required to characterize and optimize the spectral
and temporal evolution of thermal lensing
compensated laser systems.
Different diagnostics techniques have been
employed to characterize the high power
femtosecond laser systems such as auto-correlation
[9,10], spectral phase interferometry for direct
electric-field reconstruction (SPIDER) [11], and
frequency resolved optical gating (FROG) [12-16].
The autocorrelation technique fails to provide
information about the phase of the pulse therefore
the shape of temporal profile is guessed before to
make experimental measurement, on the other hand
SPIDER technique can provide spectral and
temporal information but the experimental setup is
quite complicated and difficult to align. The FROG
technique which can be described as a spectrally
resolved auto-correlation measurement, simple in
setup and efficient to characterize the spectral and
temporal evolution of the femtosecond pulses. There
are different versions of FROG diagnostic
techniques [14], the most sensitive version of FROG
is second harmonic generation (SHG) FROG.
Further it can be a categorized into multi-shot
FROG and single-shot FROG. In this article, we
explain and investigate the characterization and
optimization of thermal lensing compensated high
power Ti:Sapphire femtosecond laser system
operating at 1-kHz repetition rate by employing
SHG-FROG technique.
2. Femtosecond laser system
A Ti:Sapphire femtosecond laser system
operating at 1-kHz repetition rate consist of an
oscillator, a grating stretcher, multi pass pre-
amplifier, post-amplifier, and a grating compressor.
The block diagram of femtosecond laser system is
shown in Fig. (1), femtosecond pulses which are
generated from a mode locked femtosecond
Ti:Sapphire laser oscillator in the long cavity
arrangement running at 27 MHz repetition rate [17].
The laser pulses from the oscillator are stretched to
220 ps in 1400 grooves/mm ruling grating stretcher
[18]. Pulses are made to pass through Faraday
rotator to block the back reflection and backward
amplified spontaneous emission (ASE) from the
amplifier. The pulses are then sent to 8-pass pre-

2. IJAP, vol. (11), no. (3), July-September 2015, pp. 9-12
10 © Iraqi Society for Alternative and Renewable Energy Sources and Techniques (I.S.A.R.E.S.T.)
amplifier where the pulse train is extracted from the
amplifier after four passes which are selected by a
Pockel’s cell at 1-kHz repetition rate. The extracted
pulse is directed again to pre-amplifier to complete
the remaining 4-passes where pulse energy raises up
to 1.2 mJ. The output pulses from the pre-amplifier
are further directed to post-amplifier after passing
through the second Pockel’s cell, which improve the
contrast ratio and minimize the ASE emerges out
from the pre-amplifier. Finally the output pulse
energy reaches up to 7.0 mJ at the output of the
second amplifier [19].
When a high power laser is used as a pump
source, thermal lensing arises which is induced by
heating of Ti:Sapphire crystal of the amplifier which
results distortion of wave fronts of laser pulses that
reduces the focusing stability of laser spot.
Therefore, for adequate amplification efficiency and
good beam quality, one has to compensate the
thermal lensing [5, 20]. At the constant value of
input pumping power, the simple convex mirror or
lens can be used in order to compensate the thermal
lensing [21,22]. To compensate the thermal lensing,
we employed convex folding mirrors and the Peltier
cooler that is installed to lower the temperature of
the crystal up to -40°C. The Peltier cooler is
attached with the copper block on which the crystal
is mounted. By cooling the Ti:Sapphire crystal,
thermal conductivity increases and change in
refractive index per unit temperature decreases
which results the decrease of thermal lensing [23].
Further, to compensate the thermal lensing effects,
thermal eigenmode type 4-pass post-amplifier [12,
20] introduced to keep the beam size of the
amplified laser pulses on the crystal. The output
pulses of the post-amplifier are made to double pass
through a pair of parallel 1480 grooves/mm ruling
gratings compressor, and compressed pulse of 4.0
mJ obtained at the output.
Fig. (1) Schematic setup of 1-kHz repetition rate Ti:Sapphire femtosecond laser system: FR (Faraday Rotator), PC (Pockel’s Cell)
3. Results and Discussion
The frequency resolved optical gating (FROG)
technique [14] has been used for the characterization
of femtosecond laser pulses in time and frequency
domains simultaneously [14,24]. We employed the
most sensitive single-shot second harmonic
generation (SHG) FROG diagnostic technique to
align, characterize and optimize the high power
laser system. The experimental scheme of the
FROG setup is shown in Fig. (2). Compressed
pulses after the compressor is split up into two
identical pulses by using 50% beam splitter, these
pulses are line-focused by using cylindrical mirror,
the focused pulses are then recombined in a 100 µm
thick BBO (Beta Barium Borate) type nonlinear
crystal. The splitted pulses are line focused with a
small angle of 2° to accomplish single-shot FROG
configuration [25,26]. The overlapping beam with
small angle geometry in the nonlinear crystal
reduces the phase mismatching, but shortened the
measurable temporal range.
The output pulse from the nonlinear crystal is
spectrally resolved by a 150 grooves/mm ruling
grating and captured by a CCD camera. This
captured image is called the FROG trace or image.
To retrieve the information from FROG trace,
commercial FROG software (Femtosecond, Inc.) is
used. The FROG software algorithm uses the input
experimental data, starting with an initial guess
value, a better and closer guess is generated through
iterative Fourier transform algorithm, which
approaches the correct electric field. After running
number of iterations the FROG error decides the
reliability of the retrieval process [24].

3. IRAQI JOURNAL OF APPLIED PHYSICS
All Rights Reserved ISSN (printed) 1813-2065, (online) 2309-1673 Printed in IRAQ 11
Fig. (2) Schematic of FROG diagnostic to characterize the
laser pulses
The FROG trace or image is a two-dimensional
spectrogram, which has a delay time axis and a
wavelength axis. By using the FROG algorithm, the
intensity and phase profiles of the test pulse can be
retrieved from the experimental FROG trace, which
may provide complete information about the test
pulse in terms of intensity and phase profile. As in
our experimental setup, SHG-FROG trace can be
expressed as [12-16,25,26].
𝐼 𝐹𝑅𝑂𝐺(𝜔, 𝜏) = |∫ 𝐸(𝑡)𝐸(𝑡 − 𝜏)𝑒𝑥𝑝(𝑖𝜔𝑡)𝑑𝑡
∞
−∞
|
2
(1)
FROG error G(k) [24,25] is a root mean square
average across the trace which is difference of
experimental FROG trace and the retrieved FROG
trace.
𝐺(𝑘)
= √
1
𝑁2
∑ |𝐼 𝐹𝑅𝑂𝐺(𝜔𝑖, 𝜏𝑗) − 𝐼 𝐹𝑅𝑂𝐺
(𝑘)
(𝜔𝑖, 𝜏𝑗)|
2
𝑁
𝑖,𝑗=1 (2)
Where IFROG(i,j) and I(k)
FROG(i,j) are
representing the experimental and retrieved FROG
traces respectively, which are always normalized to
a peak of unity. The information of the femtosecond
pulse retrieved from the FROG trace is considered
to be reliable if FROG error is below than the noise
level of the experimental trace [23-25]. A two
dimensional FROG trace is retrieved from the
measured trace (Fig. 3) by running a number of
iterations using FROG software (Femtosecond,
Inc.). From the two dimensional FROG trace,
retrieved temporal and spectral evolution of the
compressed pulse was plotted, which reveals
temporal and spectral phase variations. From the
retrieved plots we observe, the FWHM of retrieved
temporal profile is 30 fs with relatively flat temporal
phase variations, which changes about 1 radians
peak to peak as shown in Fig. (3a).
Similarly retrieved spectral profile shows that
the phase distortion is less than 1 radian over the
bandwidth of 70 nm, as shown in Fig. (3b). The
FROG error for 256 X 256 trace was G=0.0028,
which is considerably low.
(a)
(b)
Fig. (3) (a) Retrieved temporal profiles of amplified laser
pulses, inset FROG trace, (b). Retrieved spectral profiles of
amplified laser pulses
At the compressor end of the laser system, the
optimized output spectrum is shown in Fig. (4a), the
efficiency of a laser pulse was optimized by
adjusting the incident angle into the grating and the
separation between gratings. We have adjusted the
grating separation in the compressor in order to
compensate the second and third group delay
dispersion and to optimize the minimum possible
pulse duration [23]. As it can be seen in Fig. (4b),
by detuning the grating, pulse duration changes
correspondingly, it is observed that the change in
pulse duration is very small when grating detuned
between -50 to 50 µm and the pulse duration has a
minimum (~30fs) at the zero detuning scale. These
results conclude the characterization and
optimization of the thermal lensing compensated
high peak power 1-kHz repetition rate femtosecond
laser system.

4. IJAP, vol. (11), no. (3), July-September 2015, pp. 9-12
12 © Iraqi Society for Alternative and Renewable Energy Sources and Techniques (I.S.A.R.E.S.T.)
(a)
(b)
Fig. (4) (a) Optimized output spectrum of the femtosecond
laser system, (b). Grating detuning to optimize the
compressor for minimum possible pulse duration
4. Conclusion
A thermally compensated Ti:Sapphire based
high power femtosecond laser system, 4.0mJ energy
per pulse, 30fs pulse duration operating at 1-kHz
repetition rate has been described, characterized and
optimized. Long cavity oscillator used as front end
of femtosecond laser system because of broadband
spectrum, low ASE and long interval between
pulses. To compensate the thermal lensing, convex
folding mirrors and Peltier cooler was used to cool
down the Ti:Sapphire crystal of the amplifier and
thermal eigenmode post-amplifier was introduced to
overcome the thermal lensing effects by keeping the
beam size of the amplified laser pulses on the
amplified crystal. Sensitive SHG-FROG single-shot
technique was employed to characterize the
thermally compensated femtosecond laser system.
The detuning of grating compressor vs pulse
duration was studied to optimize the compressor for
minimum possible pulse duration.
Acknowledgment
The authors acknowledge this research was
carried out at Korea Advanced Institute of Science
and Technology (KAIST), South Korea. One of the
author would also like to greatly acknowledge the
support of Prof. Dr. Nam Chang Hee and senior
fellow Dr. Jae Hee Sung.
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