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Ultrafast Optics
Laboratory exercise in
Advanced Optics and Lasers VT 2015
Computer exercises about modelocking
How to create 100 fs light pulses
How to measure short laser pulses
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Introduction
The shortest event created my man is a compressed laser pulse
from a modelocked laser.
The shortest visible laser pulse that has been created lasted for 4 fs (when this
is written in June 2003). During 4 fs, light travel 1200 nm. These short laser
pulses have a wavelength of about 800 nm. This corresponds to a period time
of 2.7 fs. (Light pulses in the ultraviolet spectral range with a sub-femtosecond
pulse duration (<100 as) has been created by a process known as high-order
harmonic generation).
During the lab, we will not work with pulses that are quite that short. We will
be working with pulses that last for about 100 fs.
The fastest available electronic detector has a temporal resolution of about 300
fs. Not even this detector would be suitable for measuring the duration of the
pulses we create during this lab. We will instead use the shortest event
available (The laser pulse itself) and measure its duration using
autocorrelation.
Modelocking is a relatively abstract concept. We will during the lab attempt to
visualize modelocking through a few computer exercises.
The material in the lab manual is intended to give an overview of the material
needed to benefit from the lab. It may be a good idea to read chapter 15.4D in
Saleh&Teich about modelocking.
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Modelocking and short pulses
In order for pulses to be short, many frequency components must
be available. (Heisenberg’s uncertainty principle) But how is the
pulse duration effected by the relative phase of these frequency
components?
Longitudinal modes
Two conditions determine the frequency components available to build up a
wide frequency spectrum.
The first is the resonance condition for a standing wave:
n=L or expressed in frequency =nc/2L
The second one is the spectral bandwidth of the laser. The laser bandwidth is
mainly limited by the gain profile of the amplifying medium.


In a cavity consisting only of a gain medium, end mirror and output coupler,
all modes are oscillating in random phase. By introducing additional
components in the cavity, it is possible to phase-lock these modes to each
other. Depending on the method by which the phases are locked one refers to
either active or passive modelocking. When the phase difference between the
modes is constant, the modes are oscillating in phase and interfere
constructively. If we add the E-fields from the standing modes, the sum as
function of time will be a short pulse propagating back and forth in the cavity.
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Active modelocking (Saleh&Teich 615-620)
In active modelocking, an external rf-field is applied to an acousto-optic
modulator in the cavity. The rf-frequency is chosen so that the sidebands that
are generated match the frequency separation between adjacent lasermodes (rf:
=2c/). This gives a preference for the modes to oscillate in phase.
Passive modelocking (Saleh&Teich 615-620)
When considering passive modelocking, it is easier to think in the temporal
domain. The idea behind passive modelocking is to introduce a medium in the
cavity, which has high losses for low intensities and low losses for high
intensities. An example of such an element is a saturable absorber. For short
pulses structures the losses are low. When the medium is pumped the
population in the ground state is lowered which makes the absorption decrease
and thereby the losses. If the laser pulse duration is short, relaxation to the
ground state does not occur while the pulse lasts.
If on the other hand the laser operates at low intensities providing CW
radiation the population in the upper state has time to relax and we have a
constant high population in the ground state and high absorption.
This is the way a saturable absorber gives preference to short pulses, which are
obtained when the cavity modes are oscillating in phase.
Passive Kerrlens modelocking (Saleh&Teich 619)
At low intensities, the refractive index (for a given wavelength) is constant. At
high intensities, the refractive index vary by n=n1+n2I. Due to the fact that the
laser has a spatial intensity variation, the refractive index will be larger in the
center of the beam, where the intensity is the highest. This makes the crystal
appear like a lens (referred to as a Kerr lens). A Kerr lens can be used to create
losses for CW radiation, whereas the losses for high intensity pulses obtained
by modelocking are minimal. Thus, a Kerr lens can be used for passive
modelocking. It is common that the Kerr lensing in the amplifying medium is
used. The amplifying medium is used both to obtain gain and to obtain
modelocking.
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Titanium sapphire
crystal
Aperture
Low intensities
large losses
Laser beam
x
n=n1+n2I
I
High intensity
small losses
The beams spatial profile creates the "Kerr lens"
Dispersion compensation (Saleh&Teich 184-186)
Due to dispersion, different frequency components propagate with different
velocities in any material. In solids, like different types of glass, crystals etc.
the effect can be substantial. In nearly all materials, shorter wavelengths
propagate slower than longer wavelengths. This phenomenon is known as
positive group velocity dispersion (GVD). The consequence of this is that a
short pulse consisting of many wavelengths is prolonged in time. In order to
compensate for this something with negative group velocity dispersion is
needed. Negative GVD means that short wavelengths propagate a shorter
optical path. This can be obtained with the prism arrangement shown below.
Prism pair with negativ group velocity dispersion
Short wavelengths are deflected more
P2
P1
Longer wavelengths travel a longer optical path
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laser in
Titanium sapphire
Titanium sapphire has an energy level diagram, which is typical for solid laser
materials (four level laser). The unique properties of this material are a broad
absorption band, which can be pumped by fixed-frequency lasers and a wide
lower laser level. The bandwidth over which laser can be obtained is wide
enough to allow for 3 fs long pulses. The absorption band has its peak at
around 500 nm and the emission spectrum is peaked at around 800 nm. Since
the absorption and emission bands are well separated, there are minimal losses
due to reabsorption of the laser radiation.
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Relaxation
3
Pump
Lasing
500 nm
800 nm
4
Relaxation
1
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Equipment
The Ti:Al2O3 laser (The titanium sapphire laser)
Note; The set-up will vary from one year to the other. Please read it as an
orientation without paying too much attention to detail.
The titanium sapphire laser is built from 7 components (+an additional lens to
focus the pump radiation). See the figure below.
OC
CM1
CM2
P2
L
pump from Nd-laser
C
M
P1
P1,P2 prisms
CM1, CM2 curved mirror, krökt spegel
(these are transparent for the pump radiation)
M mirror, spegel
C crystal, kristall
OC output coupler utkopplingsspegel
L lens for the pump laser
The components include two plane end mirrors, two prisms to give a negative
GVD, two spherical mirrors surrounding the amplifying medium. The
titanium sapphire crystal works as gain medium as well as a Kerr lens.
When the laser is optimized for CW operation (not modelocked) the two
curved mirrors are placed symmetrically around the titanium sapphire crystal.
They are placed such that the focus from the crystal is imaged a few meters
behind the end mirrors. (The curved mirrors are slightly more than one focal
length away from the center of the crystal.)
This is for the same reason that curved mirrors often are used in lasers, the
g1*g2 product should be less than 1 in order for the laser to be stable! (More
on this in Saleh&Teich chapter 10.2)
When the laser is optimized for modelocked operation, one of the curved
mirrors is moved forward. The spatial profile of the laser inside the crystal is
no longer optimally matched to the pump volume defined by the green light
from the pump laser.
The movement of the curved mirror is compensated for, by the Kerr lens, as
soon as the laser is modelocked. The laser is optimized for short modelocked
pulses. Expressed in terms of the stability diagram, the laser is closer to an
unstable region when the laser is not modelocked. In addition the laser spatial
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profile in the gain medium has a better overlap with the pumped volume in
modelocked operation compared to CW operation.
The laser in the lab has been set up in this way, but when the titanium sapphire
crystal is pumped, lasing will start where the gain is highest (a small number
of modes at the peak of the gain medium). The laser emits CW radiation, but
since a number of modes are present and interference may occur, the intensity
will vary slightly with a random temporal structure. (Compare to what you
observe in the computer exercises.)
By introducing a phase perturbation in the system, many of the modes may
randomly get the same phase. When this occurs, an intensity spike is obtained.
(Compare to the computer exercises.) When this happens, the titanium
sapphire crystal will start to work as a Kerr lens. For lower intensity radiation
in between the spikes, the losses will be large. In the temporal domain, we
observe that the randomly generated pulse will start take over as its losses are
lower. In the frequency domain this means that we have obtained a number of
laser modes which are oscillating in phase.
The autocorrelator
The autocorrelator consists of two laser beams with k-vectors Ka and
Kbwhich cross at a small angle in a frequency doubling crystal. The
geometry can be chosen such that the two generating and the generated beam
with double frequency fulfill either of the phase-matching conditions.
(Ka+Ka=Ka2) or (Kb+Kb=Kb2). To express this differently, both of them
give rise to frequency doubled radiation. It is however also to obtain
phasematching by the condition Ka+Kb=Kab2This frequency doubled
radiation propagates in a direction, which is defined by the vector sum
Ka+KbThis means that the generated beam propagates in between the two
generating beams. For a pulsed laser, this third beam can be generated only if
the generated beams are temporally overlapped in the crystal. A sketch of an
autocorrelator is shown below.
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PMT
M mirrors
BS beam splitter
KDP Frequency doubling crystal
PMT Photo multiplier tube
M1
KDP
20 Hz 1mm
M2
M4
BS
M3
Manually adjustable
The autocorrelator
The beam is split up into two equally strong pulses, which are delayed by
propagating different paths in the two arms of the autocorrelator. Then they
are spatially overlapped in the crystal. By moving one of the mirrors in the
autocorrelator they can also be temporally overlapped. By moving the
scanning mirror around the point where a temporal overlap is obtained, it is
possible to determine the temporal structure by measuring the intensity as
function of the mirror position. The only thing one needs to know to calibrate
the autocorrelator is the speed of light in air.
Mathematically we can express the signal as S() = (t-)*I(t) , where I(t) is
the pulse shape and  is the delay between the pulses. The integral above is
known as the autocorrelation function. This has been a mathematical tool long
before the duration of laser pulses was measured with autocorrelators.
The spectrometer
The laser beam is incident on a slit. Diffraction yields a divergent beam, which
illuminates the grating. The 1st order is imaged onto the output plane of the
spectrometer. The output plane hits a 1-dimensional readout camera which is
connected to an oscilloscope.
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The power meter
The power meter has a build-in thermo-resistor. This is mounted in a
connection similar to a Wheatstone’s bridge. The thermo-resistor gives a
measure of the temperature and thereby the absorbed average power.
The photo diode
The diode is made from a semi-conductor material. Free carriers are created by
the optical field. These are accelerated through the potential difference
generated by a 9V battery. The current generated by the carriers is measured
over a 50 ohm resistor.
The oscilloscope
A digital oscilloscope Tektronix (TDS 724) will be used. It has an analog
bandwidth of 500 MHz and a digital sampling rate of 1 Gsample/s. Four
signals are connected. The signal from the photodiode monitoring the pulse
train (CH2). The signal controlling the wave generator which determine the
position of tone of the mirrors in the autocorrelator (EXT1) and the signal
from the detector in the autocorrelator (CH1). The fourth signal is the signal
from the spectrometer (EXT2).
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Practical laboratory exercises
Computer exercise
The program MODES.exe visualizes a number of standing modes in a cavity.
How are the frequencies related to each other?
At the bottom you can see the absolute value of the sum of E-field
Describe what you see!
Modify the settings! Describe what happens!
Describe what you see in terms of the concept of modelocking.
The program modlas.exe is designed around two windows. The first show the
frequency composition and the second the temporal structure.
Using the menus, you can set the laser bandwidth, the cavity length, the
frequency width of a single laser mode and the phase relationship between the
modes. Hint: If you click inside a window, you can read the time (frequency)
and intensity for this time (frequency).
Set a short cavity length of about 0.1 m.
How is the pulse shape influenced by the number of modes? (For a given
cavity length this is coupled to the spectral width).
How does the number of modes influence the pulse duration?
How does the cavity length influence the distance between pulses?
How does the spectral shape influence the temporal structure?
What happens when phases are set to random? Can “pulse-like” structures
occur? How is this connected to the start-up of the titanium sapphire laser?
What happens with well-defined phases but random amplitudes?
Which are more important, controlling phases or amplitudes?
What happens with equal amplitudes and a chirped pulse?
What is chirp? What importance can it have to the mode-locking process?
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Laboratory work using the laser
Use safety goggles for 800 nm! Do not touch the green beam!
Do not insert objects into the beam (In particular the green beam)!
Stand up in the laboratory!
Remove watches, rings and other shiny objects!
When the pump laser is turned on, the titanium sapphire laser will start to emit
laser radiation.
Make sure that the laser beam is blocked (i.e. by a power meter)!
The instructor will show you how to modelock the laser.
What happens to the output power as the laser is modelocked? Why?
The curved mirror CM2 focus the spontaneous emission from the crystal.
Measure the distance from the focus to the end mirror. (The supervisor will
tell you the distance from the crystal to the end mirror). You can now compare
this which is near the stability limit to your FRED simulation.
The supervisor will move CM2 to a new position about 1 mm more away from
the crystal. Measure the output power. Are we in a more stable or unstable
regime for the CW radiation? Is it possible to modelock the laser? Explain!
The supervisor will move CM2 back and modelock the laser.
Observe the temporal structure of the laser radiation using a photodiode and
the oscilloscope. (Modelocked and not modelocked.)
What happens to the temporal structure when the laser is modelocked? How
does this compare to the results from the computer exercises?
What information can we obtain from the temporal structure?
Observe the spectrum using the spectrometer. What happens to the spectral
width as the laser is modelocked?
Measure the spectral width!
How short pulses are it (in principle) possible to get from the laser?
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When looking for a signal with the autocorrelator, how carefully must the arm
lengths be adjusted?
Compare the autocorrelator to the sketch in the manual. Identify the different
components. Scan the adjustable arm until you observe a signal that depends
on both beams.
Start the wave generator and study the signal using the oscilloscope. How can
we calibrate the time scale?
What is the width of the autocorrelation function? What is our pulse duration?
(Assume a Gaussian shape).
Compare the pulse duration to what you calculated from the spectral shape.
Is the pulse Fourier limited?
How is it possible to obtain even shorter pulses?
What is the peak power?
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Preparation problems
Solve these problems before the lab
1.
The shortest pulse was 3.4 fs in duration. Assuming a Gaussian
pulse shape, how wide was the pulse in the frequency plane?
2.
With help from the figure showing the autocorrelator,
determine how much the temporal delay between the pulses is
changed as the mirror M2 is moved 30 m.
3.
4.
Fourier transform the gaussian E=E0exp(-(t/T)2+it) (or find it
in a table). What is the FWHM in the temporal and frequency
domain respectively? The product of these full widths at half
maximum is referred to as the “time-bandwidth product”. What
is it for a Gaussian? In the laboratory we observe the intensity
(not the e-field). How does the result compare to the value
given by Saleh&Teich pages 938-939? Do you want to modify
your result from problem 1?
The shape of the autocorrelation signal S(t   I  t    d
may make you associate with a convolution (faltning in
Swedish) integral. We want to measure the pulse duration and
pulse shape. We can do that by measuring the autocorrelation
signal. Autocorrelation means that the pulse is convoluted with
itself. What is the relation between the FWHM of the
autocorrelation signal to that of the pulse? Assume a Gaussian
pulse shape. Hint: F(g*h)= F(g)F(h), F denote the Fourier
transform, * denotes an operation called convolution. (If you
don’t know what a convolution is – skip this problem)
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5.
6.
A modelocked titanium sapphire laser emits a beam with
300 mW average power at 800 nm. The wavelength width is
25 nm. (FWHM in intensity). The optical path length between
the end mirrors is 1.8 m. What is the peak power in the pulses?
Make suitable assumptions!
How many modes are locked in the laser in problem 5?
Additional reading
Saleh & Teich: Fundamentals of photonics
2nd edition
Modelocking (15.4D), pages 615-620
Group Velocity & Group Velocity Dispersion, pages 184-186
Measurement of Intensity Autocorrelation, pages 1002-1003
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