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<strong>Laser</strong>-<strong>Resonator</strong><br />
Dieser Versuch soll einen Einblick in die Arbeiten in einem Optiklabor geben. Der Umgang mit<br />
typischen optischen Komponenten; Konzeption, Aufbau und Justage eines optischen Aufbaus sollen<br />
vermittelt werden.<br />
Im speziellen soll ein bereits vormontierter Titan:Sapphir-<strong>Laser</strong> justiert und somit der <strong>Laser</strong>betrieb<br />
ermöglicht werden. Mit Hilfe der Spektren sollten Charakteristika und Anwendungsgebiete der<br />
verschiedenen <strong>Laser</strong>typen erarbeitet werden.<br />
Wichtig:<br />
Die in diesem Versuch verwendeten <strong>Laser</strong> sind in die <strong>Laser</strong>schutzklasse 4 eingeordnet.<br />
Die Strahlung dieser <strong>Laser</strong> kann zu schweren Verletzungen der Haut und vor allem der Augen<br />
führen (vollständige Erblindung!).<br />
Bereits die diffuse Strahlung ist gefährlich. Bei <strong>Laser</strong>betrieb darf der Praktikumsraum<br />
grundsätzlich nur mit geeigneten Schutzbrillen betreten werden.<br />
Aufgabe 1:<br />
Justieren Sie den Strahl des Helium-Neon-<strong>Laser</strong>s mit Hilfe zweier Spiegel durch zwei Blenden.<br />
Aufgabe 2:<br />
Installieren Sie den Einkoppler und verbinden sie diesen über die Glasfaser mit dem Spektrometer.<br />
Justieren den <strong>Laser</strong>strahl auf den Einkoppler und nehmen Sie das Spektrum des <strong>Laser</strong>lichts auf.<br />
Aufgabe 3:<br />
Bringen Sie, nachdem der Pumplaser eingeschaltet wurde (Betreuer), durch Justage der Spiegel den<br />
Ti:Sa-Aufbau in den <strong>Laser</strong>betrieb.<br />
Aufgabe 4:<br />
Messen Sie das Spektrum des <strong>Laser</strong>s. Wählen Sie durch Justage des Aufbaus verschiedene<br />
<strong>Laser</strong>wellenlängen aus und regen Sie höhere transversale Moden an. Erläutern Sie den Zusammenhang<br />
mit der <strong>Resonator</strong>geometrie.<br />
Aufgabe 5:<br />
Messen und erläutern Sie das Spektrum der Fluoreszenz des Ti:Sa-Kristalls.<br />
Aufgabe 6:<br />
Bestimmen Sie die <strong>Laser</strong>-Schwelle. Optimieren Sie mit Hilfe des Powermeters und der „beam-walk“-<br />
Technik die Ausgangsleistung des <strong>Laser</strong>s. Bestimmen Sie die <strong>Laser</strong>schwelle abermals.<br />
Aufgabe 7:<br />
Diskutieren Sie auf Grundlage der Spektren Anwendungsmöglichkeiten eines Titan:Saphir-<strong>Laser</strong>s und<br />
gehen Sie dabei insbesondere auf den Pulsbetrieb (Modelocking) ein.<br />
Machen Sie sich bitte zur Vorbereitung mit folgenden Begriffen vertraut:<br />
<strong>Laser</strong> (aktives Medium, Besetzungsinversion, <strong>Laser</strong>niveaus, <strong>Resonator</strong>, <strong>Laser</strong>schwelle...),<br />
<strong>Laser</strong>schutz, dielektrischer Spiegel, Spektrometer, Glasfaser, Brewsterwinkel, Frequenzverdopplung,<br />
Modelocking<br />
Literatur z. B.:<br />
Hecht, Optik<br />
Demtröder, <strong>Laser</strong>spektroskopie<br />
Saleh, Fundamentals of Photonics…
Setup and Alignment of a Titan:Sapphire<br />
<strong>Laser</strong><br />
Dr. Christiane Becker, Dr. Nicolas Stenger, Justyna Gansel,<br />
and Fabian Niesler<br />
Karlsruher Institut fuer Technologie<br />
October 28, 2010
1 Safety notes<br />
During this experiment you will use two lasers: a pump laser Verdi V5 and a<br />
Titan:Sapphire (Ti:Sapp) laser. The pump <strong>Laser</strong> can yield a maximal power<br />
of 5 W which is classified as a class 4 laser. That means that direct exposition<br />
of light can damage your skin when the beam is focused. Scattered light<br />
from a reflecting surface can irremediably damage your eyes. That’s why it<br />
is highly recommended to wear safety or alignment goggles. The Ti:Sapp<br />
laser will still yield a power of 0.5 W which classifies it as a class 4 laser too.<br />
It is even more trearterous than the pump laser. Actually the pump laser is<br />
emitting in the green spectrum and hence can be easilly seen by your eyes.<br />
The Ti:Sapp emits around λ = 800 nm, so that the laser beam will be hardly<br />
seen by your eyes. The weak red light you will see is only the small seeable<br />
part of the whole spectrum of the Ti:Sapp. This apparent weakness does<br />
not represent the real intensity of the Ti:Sapp. Scattered light can destroy<br />
irremediably the retina of your eyes.<br />
On top of that the alignment goggles you will use to align the Ti:Sapp are<br />
not protecting your eyes from the red part of the electromagnetic spectrum.<br />
Otherwise you won’t be able to see the light going out of the output coupler<br />
and hence won’t be able to see if the optical resonator is lasing or not.<br />
So please be very careful, don’t look directly into the beam direction of both<br />
lasers. Always wear safety or alignment goggles.<br />
To avoid as much as possible scattered light from reflecting surfaces you<br />
will be asked to get rid of all the jewelry you wear like finger rings, neck<br />
laces, everything that can reflect light into your eyes. Please read carefully<br />
the laser safety documents during the week before the experiment. Your<br />
supervisor will ask you questions on what you’ve learn before you start the<br />
experiment. Before you start the experiment your supervisor will give you<br />
brief instructions on laser safety. Please follow carefully his instructions.<br />
2 Basics of alignment<br />
In this section the basics of optical alignment are described. These fundamental<br />
tools are useful for a broad range of optical setups: <strong>Laser</strong> resonators,<br />
interferometers, autocorrelations, cross-correlations and optical imaging. As<br />
our aim is the setup of a titan:sapphire laser we will focus on laser beam<br />
alignment.<br />
3
Figure 1: Typical situation in a laser laboratory: A laser beam is directed<br />
into a complicated optical setup, containing many mirrors, lenses, delay lines,<br />
prisms,... In case (a) any (absolutely possible) deviation of the initial direction<br />
of the laser beam would result in a complete re-alignment of the optical<br />
setup. In the situation of (b) the beam path is defined by two apertures<br />
(A1, A2) in front of the setup. Only adjustments of mirrors M1 and M2 are<br />
necessary.<br />
2.1 Alignment of a beam through two apertures with<br />
two mirrors<br />
We consider the frequent case where a laser beam is directed into a very<br />
complicated optical setup consisting of many mirrors, lenses, delay lines and<br />
prisms (see Fig. 1). If the beam is steered directly into the optical setup<br />
any - absolutely possible - deviation of the beam direction would cause an<br />
annoying re-alignment of the optical setup (a). Directing the beam through<br />
two apertures with two mirrors however, as seen in part (b), has many advantages:<br />
The course of the laser beam is completely defined by the two<br />
apertures. Hence, the first step before building up a complicated optical<br />
setup is defining the beam path by two apertures in front. Any directional<br />
deviation of the laser beam can be corrected by aligning the beam with the<br />
two mirrors through the two apertures again. It is even very easy to change<br />
the laser source as seen in grey in Fig. 1 (b). You just need two additional<br />
4
mirrors.<br />
Initial alignment procedure<br />
As a general rule, beams should be parallel to the surface of the optical table.<br />
A change of the beam hight should be avoided if ever possible. Furthermore,<br />
deflections by the mirrors by 90 ◦ are preferred. This is not only important<br />
for the sake of clarity and hence for safety, but also to keep track of the<br />
polarization direction of light.<br />
As another general rule, for first alignment choose a weak (< 1 mW) and<br />
visible laser beam. A good choice is for example a Helium-Neon laser with<br />
a wavelength of λ = 633 nm. But be careful and make sure that the laser<br />
power is attenuated below 1 mW with some grey filters! If you want to use<br />
another (stronger) laser source at the end, a configuration as shown in Fig. 1<br />
(b) is meaningful: ”<strong>Laser</strong> 1” is the strong laser, ”laser 2” the alignment laser.<br />
The second mirror of ”laser 2” should be a kinematic mirror so that it can<br />
be removed if ”laser 1” is used.<br />
Placing the mirrors/rough alignment:<br />
1. As beam height we choose the height of the exit of the strong laser.<br />
Mount the week laser in such a way that its exit has the same hight.<br />
2. Place mirror M1’ into the beam path of the week laser as sketched in<br />
Fig. 1 (b). The beam should be centered in the mirror surface.<br />
3. Place mirror M2’ into the beam path of the week laser as sketched in<br />
Fig. 1 (b).It should be a kinematic (removable) mirror. Take care that<br />
the beam hits the mirrors in the center.<br />
4. Adjust the position and orientation of mirror M2’ such that the reflected<br />
beam is roughly above a row of screw holes.<br />
Vertical alignment/definition of the beam height:<br />
1. Take a 90 ◦ alignment tool and mark it at the desired height with a<br />
pencil.<br />
2. Place it in direction of the beam, for higher accuracy as far away as<br />
possible.(Limitations: The length of your arm or available space on<br />
optical table.)<br />
3. Adjust the beam vertically with the second mirror M2’ onto the marking.<br />
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4. Place the 90 ◦ alignment tool into the beam right after mirror M2’.<br />
5. Adjust the beam vertically with the first mirror M1’ onto the marking.<br />
6. Repeat the steps 2 to 5 iteratively unless the beam is parallel to the<br />
surface of the optical table at the desired height.<br />
Horizontal alignment above a row of screw holes:<br />
1. Release carefully the screws that were fixing mirror M2’ on the optical<br />
table.<br />
2. Place the 90 ◦ alignment tool a few centimeters after mirror M2’ such<br />
that the edge is at the middle of a screw hole.<br />
3. Adjust the position (not the orientation!)of M2’ along the axis M1’-<br />
M2’ such that beam hits the edge. Moving mirror M2’ along this axis<br />
ensures that the beam stays centered on its surface.<br />
4. Place the alignment tool as far away as possible in direction of the<br />
beam. The edge should be at the middle of a screw hole in the same<br />
row as in step 2.<br />
5. Adjust the orientation (not the position!) of M2’ horizontally such that<br />
beam hits the edge.<br />
6. Repeat the steps 2 to 5 iteratively unless the beam is aligned above the<br />
row of screw holes.<br />
7. Tighten the screws of mirror M2’ for fixing it on the optical table.<br />
Now we can be sure that our beam is aligned parallel to the table surface at<br />
our desired height and centered above a row of screw holes. This beam path<br />
must be fixed by two apertures. The first should be fixed close to mirror<br />
M2’, the second as far as possible in direction of the beam. For exercise we<br />
can check before if the apertures have exactly the same height.<br />
Adjusting two apertures to exactly the same height:<br />
1. Place one aperture into the beam at a defined position. It is not necessary<br />
to fixe it on the table.<br />
2. Adjust the height of the aperture such that the beam fits the maximally<br />
closed hole.<br />
6
Figure 2: Alignment procedures for defining a beam path with two apertures<br />
and two mirrors (a) or in the rare case with only one effective mirror<br />
(b). Case (a) has to be applied more often, e.g., in ”‘everyday alignment”’.<br />
Case (b) is important for initial alignment above a row of screw holes while<br />
ensuring the beam centered on the mirror surface simultaneously.<br />
3. Remove the first aperture and place the second aperture into the beam<br />
at the same position.<br />
4. Adjust the height of the aperture such that the beam fits the maximally<br />
closed hole.<br />
The two apertures can be screwed in the optical setup now and define the<br />
beam path completely.<br />
Everyday alignment procedure<br />
If the beam path is once defined by two apertures, the everyday alignment<br />
procedure is quite easy. Even if the laser decides every day to change its<br />
direction slightly, it does not matter.<br />
Alignment of a beam through two apertures with two mirrors:<br />
1. Close the second aperture A2 as much as possible.<br />
2. Center the beam on the hole of A2 by adjusting mirror M2’ vertically<br />
and horizontally.<br />
3. Close the first aperture A1 as much as possible.<br />
7
Figure 3: Alignment card with a hole and a slit. The incoming beam (solid<br />
line) passes the hole/slit and is reflected back by a mirror (dashed line). The<br />
spot of the reflected beam should be somewhere near the hole/slit and can<br />
be directed onto the incoming beam by adjusting the mirror vertically and<br />
horizontally.<br />
4. Center the beam on the hole of A1 by adjusting mirror M1’ vertically<br />
and horizontally. Open A1 again afterward.<br />
5. Repeat steps 2 to 4 iteratively unless the beam is perfectly aligned<br />
through the two apertures.<br />
2.2 Aligning a back-reflected beam exactly above the<br />
incoming beam.<br />
In order to build a laser you necessarily need an optical resonator. Therefore<br />
the end mirrors of the resonator have to be aligned such that the beam<br />
impinging onto the end mirror and the reflected beam lay exactly above each<br />
other.<br />
1. Take a white card. Drill an small hole into it or cut a narrow slit at<br />
the edge (see Fig. 3).<br />
2. Center the beam on a mirror perpendicular to the surface.<br />
3. Hold the white card into the beam such that the beam can pass through<br />
the hole (slit). The reflected beam should appear somewhere in the<br />
vicinity of the hole (slit). If you can’t find it put the card closer to the<br />
mirror.<br />
8
4. Adjust the mirror horizontally and vertically that the reflected beam<br />
passes through the hole (slit) backwards.<br />
2.3 Beamwalk<br />
On a later stage of the setup and alignment of the laser it will be necessary<br />
to perform a so called ”beam walk”. The optical resonator might be aligned<br />
perfectly but the crystal is hit on a bad area. Hence the beam must ”walk”<br />
to another spot of the crystal.<br />
1. Monitor the laser power with a power meter. Put your hands on the<br />
two horizontal adjustment screws of the two end mirrors of the optical<br />
resonator.<br />
2. Adjust the first of the screws for maximal power, remember the value<br />
and tilt it a little further in the same direction (power should go down<br />
a little).<br />
3. Adjust the second screw for maximal power. If the power is higher<br />
than in step 2 adjust it a little further in the same direction.<br />
4. Repeat steps 2 and 3 until the maximum possible power is achieved.<br />
Try the beam walk in both directions.<br />
5. Repeat the same procedure using the vertical alignment screws.<br />
9
2.4 Exercises<br />
• Exercise 1<br />
Align the beam of the helium-neon laser above a row of screw holes<br />
at a height of 10 cm. Use a kinematic mirror as second mirror so that<br />
eventually a second laser can be fiddled in afterwards. Apply the alignment<br />
schemes described in section ”Initial alignment procedure”. If<br />
you are content with the result, fixe the beam path by screwing in two<br />
apertures.<br />
• Exercise 2<br />
Practise the ”everyday alignment procedure” with two mirrors and two<br />
apertures a few times.<br />
• Exercise 3<br />
Project the HeNe laser beam on a screen composedv by a beam blocker<br />
and a piece of paper attached on it’s surface. Put the end of the<br />
multimode fiber next to the screen and measure the spectre of the<br />
HeNe.<br />
What can you say about the shape of the HeNe spectrum?<br />
10
3 Setup and alignment of a titan:sapphire laser<br />
The Verdi laser be on ”‘standby mode”’ your supervisor will turn it on for<br />
you. Don’t do it alone.<br />
This section is a ”‘alignment manual”’ for a titan:sapphire laser in continuous<br />
wave (cw) operation. All you need is an energy pump - in our case<br />
a doubled Nd:Yag laser at λ = 532 nm - (What means that the Nd:Yag is<br />
doubled?), a titan:sapphire-crystal, a chiller and water cables for cooling, and<br />
other optical components.<br />
Preliminary considerations<br />
The resonator of a titan:sapphire laser usually has the so called ”Z-configuration”.<br />
Compare figure 2 at the end of this manual with the laser setup in<br />
front of you and identify the different components.<br />
Explain in a few words the role of each component.<br />
Mounting and cleaning the optics<br />
If the dielectric mirrors are polluted with dust try to remove it with a small<br />
blow tool. Remaining dirt has to be removed with lens cleaning paper. Please<br />
ask your supervisor to clean them for you. Don’t try by yourself these components<br />
are very sensitive!<br />
Defining the beam path by two apertures<br />
Use the Helium-Neon laser and align it with two mirrors above a row of screw<br />
holes (see section 2.1). The second mirror should be a kinematic one. Fixe<br />
the beam path by two apertures. Take care that there remains enough space<br />
for two more mirrors that should deflect the strong pump laser through the<br />
same apertures.<br />
Initial alignment of the titan:sapphire laser<br />
Don’t touch the center of the cavity and the Ti:Sapphire crystal!<br />
this parts are very sensitive and expensive!<br />
For the initial alignment the Helium-Neon laser should be used. This not<br />
only minimizes the risk of dangerous reflected and scattered light but also is<br />
more comfortable because no goggles have to be worn.<br />
The beam passes through the focussing lens and the first concave mirror<br />
in the center, propagates through the titan:sapphire crystal right in the middle<br />
and hits the second concave mirror in the center. (Why is the normal<br />
11
to the surface of the Ti:Sapp crystal oriented with a high angle according to<br />
the impiging ray of the pump laser and why do we have inserted a polarizer<br />
before the rasonator of the laser? Hint: it minimizes backreflection on the<br />
surface on the surface) The resonator is in the symmetrical confocal configuration<br />
which ensures a tight focus of the 800 nm mode.<br />
• What is a symmetric confocal configuration? Explain it in a few words.<br />
Why do we use this configuration for the cavity? Discuss the stability<br />
and losses of this resonator geometry with other kind of configurations<br />
like the symmetric concentric one. Don’t enter too much into mathematical<br />
details (For more information look in Optik E.Hecht p.950<br />
or in Fundamentals of photonics B.E.A Saleh p.310). The intensity<br />
profile of the laser beam is directly depending on the geometry of the<br />
resonator. What kind of beam intensity profile would you expect for a<br />
laser composed of two symmetric concave mirrors?<br />
What is the best distance between mirrors and crystal? (Don’t enter in<br />
too much mathematical details, use the notions of optics you’ve learned<br />
in lectures hints: light should make roundtrips in the cavity).<br />
Check now again that the beam is centered on both spherical mirrors and<br />
passes the crystal without hitting the edges. Do it carefully.<br />
As the laser-resonator mirrors are optimized for λ = 800 nm and the<br />
alignment laser has a wavelength of λ = 633 nm, the reflected beams are very<br />
weak. In this case remove some of the grey filters in front of the Helium-Neon<br />
laser for stronger signals.<br />
The beam reflected from the end mirror should be depleted by the first<br />
concave mirror, pass the crystal, hit the second concave mirror at the center<br />
and be reflected again by the output coupler. This reflected beam has to be<br />
centered onto the end mirror of the resonator. Align the beam reflected from<br />
end mirror exactly above the incoming beam as described in section 2.2. Do<br />
exactly the same for the output coupler.<br />
Investigate the 360 ◦ surrounding of the optical setup for unwanted reflections.<br />
Block all of them with a beam blocker. Even if the reflections are quite<br />
weak at the moment be aware that these reflections can be very dangerous<br />
when the strong pump laser is used. For the undeflected pump beam use a<br />
special beam dump specified for blocking high laser powers.<br />
12
Figure 4: Cooling system for pump laser and titan:sapphire crystal.<br />
temperature should be in the range of 18-20 ◦ C.<br />
The<br />
Cooling of the titan:sapphire crystal<br />
Before switching on the pump laser the cooling system for the titan:sapphire<br />
crystal has to be turned on. Check that the chiller is filled with enough clear<br />
(destilled) water. One chiller is sufficient for cooling both, the pump laser<br />
and the crystal. .<br />
Final alignment<br />
Don’t start this section without speaking with your supervisor!<br />
The pump laser Verdi V5 is a class 4 laser even scatterd or reflected light<br />
can damage irremediably your eyes. That’s whay it is strongly recommended<br />
to wear safety or alignment goggles! Your supervisor will help you in these<br />
part, please don’t do anything before talking to your supervisor.<br />
Don’t insert fingers or paper between the focusing lens and the<br />
second concave mirror<br />
The power is there sufficient to burn skin and paper!<br />
Make sure that there is a beam blocker after the output coupler,<br />
insert the grey filter between the output coupler and the beam blocker<br />
The light going out of the output coupler is very treaterous! The<br />
main peak going out of the Ti:Sapp is around λ = 800 nm, so you probably<br />
won’t see it. What you will see is only a small part in the spectrum around<br />
λ = 700 nm. You might think that the intensity is not high but in fact the<br />
power out of the laser is around 0.5 W. It is classified as a class 4 laser. Even<br />
diffused light can damage seriously your eyes. On top of that the alignment<br />
13
goggles are only protecting your eyes around λ = 532 nm. There is no protection<br />
around λ = 800 nm!<br />
Get on the alignment goggles. Your supervisor will switch on the pump<br />
laser. The power (power mode) is now set to the smallest possible value<br />
(P=0.1 W). The beam should be visible inside the crystal via red fluorescence.<br />
Check that the beam passes the crystal without inner reflections at<br />
the borders. For good laser performance it is also important that the losses<br />
in the optical resonator are minimized. Place a white card behind the output<br />
coupling mirror. Increase the laser power to 2-3 W (As usual be carefull to<br />
scattered and reflected light). On the white card a large and strong and<br />
red point should appear, effected by the fluorescence inside the crystal. You<br />
might also see next to the large spot a smaller and weaker one. The stronger<br />
point comes from the first passing through the crystal, the weaker is the<br />
fluorecsnce of the Ti:Sapp crystal backreflected by the end mirror. Align the<br />
end mirror to move the weak spot onto the strong spot unless both points<br />
overlap. Do the same with the output coupler. Now the laser should start<br />
lasing.<br />
• By slightly moving the output coupler verticaly or horizontaly, you<br />
should see appearing the different modes of the resonator (see page 953<br />
in Optik form E.Hecht). Can you explain in a few sentences why you<br />
observe different mode?<br />
Now align the ouput coupler to obtain the TE 00<br />
Shut the beam of the Verdi with a beam blocker as explained by your supervisor.<br />
Close the shutter of the pump laser. Leave the room with the<br />
alignment goggles on your nose and take the security goggles with you. Exchange<br />
the alignment goggles by the security goggles. The security goggles<br />
are protecting your eyes against the green light coming out of the pump laser<br />
and the red light coming out of the Ti:Sapp. During this time your supervisor<br />
will install the powermeter for the rest of the experiment. (Don’t do it<br />
by yourself!) When everything is ready enter to the laser room and proceed<br />
with the rest of the experiment.<br />
Optimization<br />
Once the laser is lasing we can optimize the alignment for maximum power.<br />
Make a beam walk as described in section 2.3 with the two end mirrors of the<br />
optical resonator. With an output coupler of 97% reflectance and an input<br />
14
power of 2.8 W (@ 532 nm) it is possible to obtain 0.4 W output power (@<br />
800 nm). The supervisor will show you how to get more power by adjusting<br />
the center of the cavity. Don’t do it by yourself!<br />
Measurement of the Ti:Sapp spectrum<br />
Place the end of the multimode fiber next to the Ti:Sapp crystal (don’t touch<br />
it! it’s very sensitive). Measure the spectrum of the red fluorescence coming<br />
out of the Ti:Sapp crystal. Insert a beam blocker with a piece of paper<br />
glued on it between the grey filter and the powermeter. Take the end of the<br />
multimode fiber connected to the spectrometer close to the beam blocker.<br />
The scattered light intensity must be sufficient to measure the spectrum of<br />
the Ti:Sapp.<br />
• Compare the spectra from the HeNe, the fluorescence of the Ti:Sapp<br />
and from the lasing spot of the Ti:Sapp. Why is the fluorescence and<br />
the lasing spectra of the Ti:Sapp different?<br />
Why are the spectra of the HeNe and the Ti:Sapp different.<br />
• By slightly moving one degree of liberty of the output coupler, one can<br />
change the lasing mode of the Ti:Sapphire laser. Take two or three<br />
spectra with different modes (frequencies). Determine the frequency<br />
difference between these modes and compare it with the actual length<br />
of the resonator. What can you deduce from this measurement?<br />
• Ti:Sapp lasers are often used in ultra short pulses experiments. To<br />
obtain ultra short light pulses we use a technique called ”‘mode locking”’technique.<br />
Explain in a few sentences what is the mode locking technique.<br />
Explain why the Ti:Sapp laser is appropriate for producing ultra short<br />
pulses by analyzing its spectrum and by comparing it by what you’ve<br />
learned on the mode locking technique.<br />
Additional material to read:<br />
• Eugene Hecht, Optik (4.Auflage), Oldenburg (2005). See Chapter 13,<br />
p. 941 to p. 960.<br />
• Bahaa E. A. Saleh, Malvin Carl Teich, Fundamentals of Photonics,<br />
Wiley (2007). See Chapters 10, 14, and 15.<br />
15