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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 />

5


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

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