Thin-Disk Yb:YAG Oscillator-Amplifier Laser, ASE, and Effective Yb ...

IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 45, NO. 8, AUGUST 2009 993 

Thin-Disk Yb:YAG Oscillator-Amplifier Laser, 

ASE, and Effective Yb:YAG Lifetime 

Aldo Antognini, Karsten Schuhmann, Fernando D. Amaro, François Biraben, Andreas Dax, Adolf Giesen, 

Thomas Graf, Theodor W. Hänsch, Paul Indelicato, Lucile Julien, Cheng-Yang Kao, Paul E. Knowles, 

Franz Kottmann, Eric Le Bigot, Yi-Wei Liu, Livia Ludhova, Niels Moschüring, Françoise Mulhauser, 

Tobias Nebel, François Nez, Paul Rabinowitz, Catherine Schwob, David Taqqu, and Randolf Pohl 

Abstract—We report on a thin-disk Yb:YAG laser made from a 

-switched oscillator and a multipass amplifier delivering pulses 

of 48 mJ at 1030 nm. The peculiar requirements for this laser are 

the short delay time ( SHH ns) between electronic trigger and optical 

output pulse and the time randomness with which these triggers 

occur (with trigger to next trigger delay I S ms). Details 

concerning the oscillator dynamics (-switching cycle, intensity stabilization), 

and the peculiar amplifier layout are given. Simulations 

of the beam propagation in the amplifier based on the Collins integral 

and the measured aspherical components of the disk reproduce 

well the measured beam intensity profiles (with higher order 

intensity moments) and gains. Measurements of the thermal lens 

and ASE effects of the disk are also presented. A novel method to 

deduce the effective Yb:YAG upper state lifetime (under real laser 

operation and including ASE effects) is presented. That knowledge 

is necessary to determine gain and stored energy in the active 

medium and to understand the limiting factors for energy scaling 

of thin-disk lasers. 

Index Terms—Amplified spontaneous emission (ASE), Collins 

integral, diode-pumped laser, effective Yb:YAG lifetime, multipass 

amplifier, oscillator, prelasing, -switch, thermal lens, thin-disk 

laser. 

Manuscript received August 28, 2008; revised January 20, 2009. Current version 

published July 15, 2009. 

A. Antognini, T. W. Hänsch, N. Moschüring, T. Nebel, and R. Pohl are with 

the Max–Planck–Institut für Quantenoptik, 85748 Garching, Germany (e-mail: 

Aldo.Antognini@psi.ch). 

K. Schuhmann and A. Giesen are with Technologiegesellschaft für Strahlwerkzeuge 

mbH, 70178 Stuttgart, Germany. 

F. D. Amaro is with the Departamento de Fisica, Universidade de Coimbra, 

3000 Coimbra, Portugal. 

F. Biraben, P. Indelicato, L. Julien, E. Le Bigot, F. Nez, and C. Schwob are 

with Laboratoire Kastler Brossel,École Normale Supérieure et Université P. et 

M. Curie, 75252 Paris, CEDEX 05, France. 

A. Dax is with the Physics Department, Yale University, New Haven, CT 

06520-8121 USA. 

T. Graf is with IFSW — Institut für Strahlwerkzeuge, Universität Stuttgart, 

70569 Stuttgart, Germany. 

C.-Y. Kao and Y.-W. Liu are with the Physics Department, National Tsing 

Hua University, Hsinchu 300, Taiwan. 

P.E. Knowles, L. Ludhova and F. Mulhauser are with the Département de 

Physique, Université de Fribourg, 1700 Fribourg, Switzerland. 

F. Kottmann and D. Taqqu are with the Paul Scherrer Institute, 5232 Villigen–PSI, 

Switzerland. 

P. Rabinowitz is with the Department of Chemistry, Princeton University, 

Princeton, NJ 08544–1009 USA. 

Color versions of one or more of the figures in this paper are available online 

at http://ieeexplore.ieee.org. 

Digital Object Identifier 10.1109/JQE.2009.2014881 

0018-9197/$25.00 © 2009 IEEE 

I. MOTIVATION 

L 

ASER spectroscopy of the Lamb shift ( energy 

difference) in muonic hydrogen ( ) is being 

performed at the Paul Scherrer Institute in Switzerland to 

determine the root mean square (rms) proton charge radius 

with precision [1]–[4]. A multistage laser system was 

developed to provide pulses of 0.2 mJ energy tunable at 6- m 

wavelength, which corresponds to the transition 

wavelength. It consists of a frequency-doubled -switched 

Yb:YAG thin-disk laser ( nm), a CW injection-seeded 

pulsed titanium-sapphire laser, and a Raman cell [5]. In this 

letter, we report on the -switched operation of a Yb:YAG 

thin-disk oscillator laser and thin-disk multipass amplifier 

developed for this experiment. The more unusual requirements 

for the thin-disk laser operation are the short delay ( ns) 

between trigger signal and optical output and the temporal 

randomness with which the triggers occur. The minimum delay 

time between two pulses (laser dead time) has to be ms 

or shorter, and the laser has to deliver 90 mJ at 1030 nm. The 

thin-disk laser we developed is composed of two parallel systems 

each consisting of an oscillator and a multipass amplifier 

as shown in Fig. 1. After frequency doubling with two LBO 

crystals in series for each system, the amplifier pulses are then 

used to pump the titanium-sapphire laser. 

II. INTRODUCTION 

In the past decade, Yb:YAG gain media have garnered interest 

because of the long fluorescence lifetime ( ms [6]), high 

doping concentration (no concentration quenching up to 30 at.% 

[7]), and the ease of pumping via commercially available highpower 

InGaAs laser diodes. Yb:YAG lasers (1030 nm) pumped 

with InGaAs diodes (940 nm) have a very small quantum defect, 

no excited state absorption, and no up-conversion, resulting in 

reduced waste heat production and enhanced efficiency. However, 

only in combination with the thin-disk technology [9], 

[10], which avoids some difficulties arising from the quasi-fourlevel 

energy scheme at room temperature, is it possible to capitalize 

on the advantages of Yb:YAG as a gain medium. The 

thin-disk technology permits effective cooling (thus high power 

pumping is possible), yet suffers only small thermal lensing 

and depolarization effects (from thermally induced stress birefringence). 

The long fluorescence lifetime and its related small 

stimulated emission cross section (2 cm [6]) are beneficial 

for high-energy storage per unit pump power but results 

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994 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 45, NO. 8, AUGUST 2009 

Fig. 1. Schematic view of the thin-disk laser system for the muonic hydrogen 

Lamb shift experiment. Two fiber-coupled diode lasers of 450 and 900 W emitting 

at 940 nm are used to continuously pump the -switched oscillators and 

the multipass amplifiers, respectively, which deliver pulses at 1030 nm of 35-ns 

pulse width. 

Fig. 2. Thin-disk laser principle. The thin-disk with the back side HR-coated 

for both pump (940 nm) and laser (1030 nm) wavelength is soldered on a water 

cooled heat sink. The fiber coupled diode light is imaged onto the disk. The 

parabolic mirror and the folding prisms lead to a 12-pass pump scheme. The 

fluorescence light exiting the beveled surface of the disk is absorbed by a water 

cooled aperture. 

in a large saturation fluence of J cm . As drawbacks, 

the low gain of the medium and relatively low optical damage 

threshold of the disk (few J cm ) make it difficult to extract the 

stored energy efficiently. An oscillator-amplifier scheme was 

thus chosen. The oscillator is operated in the CW prelasing 

mode prior to trigger, guaranteeing a short delay time between 

the electrical trigger and optical pulse output. The multipass amplifier 

boosts the pulse energy to fulfill the design requirements. 

Two fiber-coupled diode lasers (with 600- and 1000- m fiber 

core diameter and NA ) of 450 and 900 W emitting at 

940 nm were used to continuously pump the oscillators and the 

amplifiers, respectively. The output beam from each fiber was 

split into two beams of roughly equal power, and each beam 

pumped one of the four laser head disks. A schematic view of 

the laser head is shown in Fig. 2. Efficient absorption of the 

pump light required a multipass scheme (relay imaging) since 

the 0.2-mm disk thickness had only small absorption per pass 

(NB: all through this paper, disks of 12-mm diameter, 0.2-mm 

thickness, and 7 at.% doping concentration have been used). 

By using a parabolic mirror (32-mm focal length), four prisms 

acting as retro-reflectors, and the disk-mirror itself [11], 12 

double-passes of the pump beam through the laser crystal were 

realized. The thin-disk crystal was anti-reflection (AR)-coated 

at the front side and high-reflection (HR)-coated at the rear 

side for both pump and laser wavelengths. The rear side was 

Fig. 3. (a) Optical layout of the -switched thin-disk oscillator laser where 

PC is the Pockels-cell and TFP the thin film polarizer. The pulse is extracted 

through the TFP when the polarization is correspondingly rotated. (b) Principle 

arrangement of the PC switching. Prior to trigger, one PC cathode is at ground 

whilst the other is controlled by the feedback loop voltage … stabilizing the 

circulating power. Then, one after the other, the PC cathodes are switched to 

high voltage … . 

soldered onto a water-cooled heat sink with a coolant temperature 

maintained at 10 C. The thin-disk acts therefore as an 

amplifying mirror in a laser cavity and its rear side coating 

enables multipass pumping. One of the main advantages of 

the thin-disk technology when compared with conventional 

designs is the small phase distortion of the reflected beam 

at the disk-mirror arising from thermally induced spherical, 

and aspherical, lens effects. Nevertheless, although small, that 

distortion is nonvanishing and must be accounted for in the 

laser cavity design, especially for multipass amplifiers where 

large beams and long beam paths are involved. 

III. -SWITCHED OSCILLATOR 

The thin-disk oscillator shown in Fig. 3(a) consists of a 1-mlong 

cavity which includes a telescope forming a mm 

spot size at the disk position. 1 During each round trip, the circulating 

light is reflected twice at the mirror disk, which means 

that it crosses the gain medium four time, increasing the gain 

per unit time. The interference between the two beams at the 

disk is reduced by a fix -plate placed in front of the disk, 

which also serves as a window for the laser head. The other main 

components are a thin-film polarizer (TFP) acting as a polarization-dependent 

outcoupler, a second adjustable -plate, and a 

Pockels-cell (PC) with BBO crystal. Their interaction controls 

the -switching dynamics and is characterized by the following 

steps. 

• CW pumping and lasing: the disk is continuously pumped 

by the diode light (225 W pump power with an rms pump 

radius of 0.67 mm) and the oscillator is lasing close to 

threshold (output power of W) with the largest possible 

TFP transmission, i.e., high transmission solution for the 

output coupler at the given output power. The transmission 

is a function of the -plate rotation angle relative to the 

preferential direction defined by the TFP (and the voltage 

difference between the two PC cathodes, see below). 

• Trigger: when the laser is triggered, the cavity is closed by 

having the PC rotate the polarization of the light circulating 

between the flat end-mirror and the TFP such that the TFP 

becomes a high reflector. This is done by applying a high 

voltage (HV) close to the quarter-wave voltage to the first 

1 When the beam is Gaussian the radius � of the Ia� intensity drop is specified. 

For a beam deviating from a Gaussian shape the rms radius � is specified. 

It is related to the spot size � via � aP� . The pump spots are usually 

more flat-top-shaped. The FWHM of a flat-top profile is related to the rms radius 

via FWHM aP � Q � . 


ANTOGNINI et al.: THIN-DISK YB:YAG OSCILLATOR-AMPLIFIER LASER, ASE, AND EFFECTIVE YB:YAG LIFETIME 995 

Fig. 4. Light intensity circulating in the oscillator cavity measured with a photodiode 

for two -switch cycles when pulses of (a) 0.1 mJ and (b) 10 mJ are 

extracted. Prior to trigger, the laser operates in CW prelasing mode (A). Then 

a trigger occurs and a pulse is extracted (B). Cavity closure and pulse build-up 

(190 ns) are not visible in this time scale. The laser is off whilst population inversion 

recovers (C). The bottom figure shows an undershoot typical of diode 

saturation caused by the pulse. Spiking occurs when the recovering population 

inversion reaches levels which permit lasing but can be suppressed by the feedback 

loop regulating … [see Fig. 3(b)]. When the laser is triggered, the input of 

the PI controller is switched to set value until reactivation at time (D). Without 

active feedback, the spiking undergoes a “natural” damping with a time constant 

longer than that provided by the active control. 

PC electrode: kV [Fig. 3(b)]. The applied 

HV compensates the polarization rotation occurring at the 

-plate. 

• Pulse build-up: within the closed cavity, losses are small 

( per round trip), resulting in a fast amplification of 

the circulating power. 

• Cavity dumping: the circulating power is then extracted 

from the cavity when the second PC cathode is raised to 

the same HV as the first electrode. Extracted pulses have 

energies which scale with the cavity closure time [up to 12 

mJ and 35-ns pulse lengths (FWHM)]. 

• Back to stable CW conditions: after pulse extraction some 

time is needed to reestablish the baseline population inversion 

(CW pumping). After ms the CW prelasing 

reaches the same behaviour as prior to trigger. In the meantime, 

the PC electrodes recover—on a s time scale—to 

their initial value. The laser is ready to accept the next 

trigger. 

This millisecond-timescale dynamics are depicted in Fig. 4 

where the power circulating in the cavity during a -switch 

cycle is shown. As visible from the figure, before approaching 

its steady-state value, the laser exhibits relaxation oscillation 

(spiking). Pronounced spiking occurs since the upper state 

lifetime is much longer than the photon lifetime in the cavity 

and it is accentuated by the quasi-four-level nature of the active 

medium. 

Optical damage to the disk is avoided by extracting the pulse 

from the cavity before saturation occurs. Fluctuations of the circulating 

power in the CW prelasing regime thus results in fluctuations 

of the extracted pulse energy, so stabilization of the 

prelasing power is mandatory. The circulating power is monitored 

by a photodiode positioned behind a cavity mirror and 

its level is stabilized to a constant value using a PI feedback 

loop ( V) acting on one PC cathode to control the 

cavity losses; see Fig. 3(b). This active stabilization considerably 

reduces the spiking; see Fig. 4, leading to a shorter laser 

dead time, as well as stabilizing the circulating power, leading 

to predictable and stable pulse energy even with the stochastic 

nature of the triggering. To prevent a large departure from the 

value prior to trigger, the PI controller integral component 

is held at the pre-trigger output value whilst the laser is below 

threshold. 

From the laser dynamics plot of Fig. 4 it should be clear that 

pulse-to-pulse delays down to 1.1 ms may be reached. This is 

confirmed by the direct measurement of the extracted pulse energy 

as a function of the repetition rate: no energy decrease per 

pulse is seen up to repetition rates of 850 Hz. This indicates that 

the effective lifetime of the Yb:YAG upper state (in real operational 

conditions) is considerably smaller than the spontaneous 

lifetime of 1 ms given in the literature (cf. Section VI). 

The CW prelasing of the oscillator (at 1.3 W output power) 

guarantees that a large number of photons (1 ) circulate 

in the cavity prior to a triggered pulse formation. This shortens 

from 600 to 200 ns the time required for a closed cavity to reach 

the extracted pulse energy, which, for a 10-mJ pulse, is equivalent 

to 5 photons. When the oscillator operates close to 

laser threshold only one mode is present in the cavity at a given 

time, so proper cavity design can force the prelasing to occur 

at the cavity fundamental mode (measured ). If the 

cavity fundamental mode at the disk position is too small relative 

to the pump spot size, competition between higher order 

eigenmodes occurs resulting in transversal mode hopping which 

in turn leads to unstable laser operation. Consequently, the oscillator-amplifier 

scheme was required by the fact that there is no 

stable prelasing operation for multimode lasers enabling larger 

cavity modes and thus high pulse energies. 

In summary, the oscillator routinely delivers pulses of 12 mJ 

energy at repetition rates up to 850 Hz. The factors limiting the 

maximum energy are the optical damage of the disk coating and 

amplified spontaneous emission (ASE) effects discussed extensively 

in Section VI. The pulse energy may be varied simply by 

changing the cavity closure time (cf. Fig. 16). The CW pumping 

and the small thermal lens effects ensure that the pulse spatial 

profiles do not depend on the pulse energy and pulse-topulse 

delay time. A gain of 1.25 per reflection at the disk-mirror 

is measured, by measuring an exponential gain coefficient of 

0.069 ns for a cavity with 6.5 ns round-trip time and 2% 

losses. The total delay between trigger and optical output is 

ns, the sum of the time required for the PC to switch 

after receiving the trigger (60 ns) and the required cavity closure 

time (190 ns for a 12-mJ pulse). 

IV. MULTIPASS AMPLIFIER 

The multipass thin-disk amplifier was made from multiple instances 

of one intrinsically stable optical segment formed by 

the disk and two curved mirrors ( , ). Fig. 5 shows how 

a 12-pass amplifier was realized by concatenating 12 segments 

in series. The key to realize the beam routing was the introduction 

of an array of 24 mirrors, which allowed the independent 

alignment of each pass on the disk and folded the beam path 



Fig. 5. Schematic of the beam routing for a 12-pass amplifier. (a) The optical 

path sequence proceeds 1-disk-2-u -3-disk-4-u -5-disk-6-u -7-FFF where 

u —u defines the optically stable segment. The distance between mirror 

array and disk is 84 cm. (b) Working principle of the mirror array. The 24 flat 

reflectors (designated with number 1–24) guide the beam for 12 passes. Starting 

from 1 the beam reaches 2 after reflection at the disk (whose projection is shown 

by the circle). The beam then arrives at 3 by reflection at u (whose projection 

is shown by the hexagon). Following this sequence the beam progressively 

explores all the mirrors of the array. A second mirror u is necessary in order 

to access the two external mirror rows. (c) Photograph of the mirror array. The 

orientation of each reflector can be varied to adjust each pass individually. The 

scale is given by the 25.4-mm mirrors. 

into a smaller volume. In the following we discuss the properties 

of the amplifier as realized and compare them to a classical 

4-f propagation. 

For the analysis of the beam propagation in the amplifier, the 

24 flat mirror of array may be neglected and the discussion given 

by how the beam develops along its propagation axis ( -axis). 

Consider first the design of the stable “cavity” segment, which 

must be stable for the disk lens effect. The lens effect varies 

from disk to disk and depends on running parameters such as 

pump beam size and intensity, and cooling water temperature 

and flow. For stability, the variable disk lens should only minimally 

influence the eigenmode size at the disk position. For a 

disk with vanishing focal power we choose the following segment 

design: a concave mirror ( mm) at , 

the disk with lens at m and a convex mirror 

( mm) at m. The size of the eigenmode 

inside the resonator is shown in Fig. 6 for variations of the disk 

focal power. As is well visible from Fig. 6(a), only at the convex 

mirror ( ) position does the eigenmode size strongly depend 

on variations of the disk lens power. This is acceptable since 

the optical damage threshold of the mirror coating is one order 

of magnitude higher than for the disk, and because at the mirror 

no beam-size-dependent complex effects (amplification/absorption, 

aspherical terms) occur. The eigenmode size as a function 

of the disk lens is plotted in Fig. 6(b) and may be considered 

as a stability diagram [12]. For any disk focal power , and 

for any mode size at the disk ( mm), a segment can be 

designed whose stability diagram is centered around . 

The 12-pass amplifier was realized by simply concatenating 

12 such segments. Fig. 7 shows the evolution of the beam size 

Fig. 6. (a) Spot size � of the amplifier segment fundamental eigenmode formed 

by a concave mirror u (‚ a SHHH mm) at � aH, the disk with lens � at � a 

IXQ m and a convex mirror u (‚ a 0PHHH mm) at � aQXV m. The various 

curves are associated with different lens power Ia� (m ) of the disk. (b) The 

eigenmode size as a function of the disk lens power at the disk, u and u . The 

amplifier segment is designed so that the measured disk lens power of Ia� a 

H diopters is in the center of the stability region. When the unstable region is 

reached, the eigenmode size at the disk position varies strongly (increases) as 

visible from (a). 

Fig. 7. Beam propagation in the amplifier assuming the laser remains in its 

fundamental mode, for an amplifier layout which is a concatenation of optically 

stable segments (a); with 4-f classical propagation (b). The vertical continuous 

lines represent the disk position, whereas the dashed lines are those of u , u , 

and the imaging optics, respectively. Besides the propagation for the optimized 

amplifier layout with Ia� a H m , two additional beam propagations are 

shown with the disk lens power varied by 6HXHP m . Note the stability of the 

beam spot size at the disk positions. The 4-f propagation is constrained to have 

similar minimal beam spot size as the beam in (a). 

for propagation in the amplifier including the effect of small disk 

lens power variations for both our configuration and a classical 

4-f scheme. Here, it was assumed that the laser beam stays in its 

fundamental mode for the whole propagation. 

To achieve regular propagation, i.e., beam propagation in 

the amplifier with beam profiles corresponding to the segment 

eigenmodes, the beam had to be correctly coupled into the 

amplifier. A three mirror telescope, whose layout and properties 

are depicted in Fig. 8, was used to match the oscillator 

beam into the amplifier. The telescope gives the independent 

freedoms to fine tune both the spot size and the divergence of 

the beam entering the amplifier. 

The choice of the given amplifier arrangement was motivated 

by the lower sensitivity of the generated laser beam on disk lens 



Fig. 8. Design and properties of the telescope coupling the oscillator beam into 

the amplifier. (a) Optical layout where � a IHHH mm, � a 0ISH mm and 

� a USH mm. The distance from the last mirror to the disk equals � .By 

varying the distance v , the beam size at the disk position may be adjusted and 

moving v controls its divergence. (b), (c) Beam spot size and divergence at the 

disk as a function of the distance v and v . 

Fig. 9. Spot size (a) and divergence (b) of the beam exiting the amplifier as a 

function of the disk lens power for different cases: the concatenation of optical 

stable segments (S), the concatenation of optical stable segments with a complex 

disk focal power accounting for a Gaussian aperture given by the gain profile 

(S+A), and a 4-f propagation. The chosen large aperture (� aSXU mm) 

strongly increases the beam stability. 

variations when compared to a classical 4-f scheme. Spot size 

and divergence of the exit beam are presented for comparison in 

Fig. 9 for both the given amplifier and the classical 4-f propagation. 

The stability of our amplifier configuration as visible in 

the figure is further enhanced by the aperture effect associated 

with the gain/absorption in the disk. On the contrary, the aperture 

effect in a 4-f configuration would reduce the beam size at 

the disk position after every pass. The aperture effect may be 

approximately included in our Gaussian beam propagation by 

replacing the lens at the disk-mirror with a complex lens given 

by where is the wave vector and 

the aperture waist (the aperture is assumed to be Gaussian). In 

addition, when constrained to have similar minimal beam sizes 

as in the segment, the 4-f propagation exhibits longer beam path, 

i.e., longer laser delay. However, it must be stressed that the 4-f 

configuration would show a beam profile at the disk position 

which is not affected by the lens effects associated with the disk, 

which would very much simplify the amplifier construction (see 

below). 

For completeness, a brief remark about pointing stability 

is necessary: when correctly implemented, i.e., with an even 

Fig. 10. Beam profiles for the 9th to 12th passes in the amplifier measured at the 

disk position. The even passes show a Gauss-like shape whereas the odd passes 

are more ring-like. The pump spot profile is plotted for comparison (dashed 

line). 

Fig. 11. Odd passes beam profiles for various disks and amplifier layouts. 

number of mirrors per round-trip 2 (disk included), the 4-f 

configuration shows a pointing stability superior to the chosen 

concatenation of segments. We gave priority to thermal lens stability 

and optical damage threshold (maximizing waists) rather 

than pointing stability arguments. Note that the sensitivity to 

misalignment (pointing instability) scales with the beam waist 

whereas the stability range for variation of the medium lens 

power is proportional to [12]. 

Starting from the above given theoretical layout based on the 

assumption that the laser beam propagates only in its fundamental 

mode, a time-consuming experimental optimization of 

the amplifier parameters (distances, radius of curvature of the 

mirrors, coupling) was necessary in order to achieve stable beam 

propagation. The optimization accounted for the uncertainty related 

to the radius of curvature of the disk-mirror, and especially 

for the production of higher-order intensity moments excited by 

the aspherical components of the disk-mirror. As an example, 

Fig. 10 shows a sequence of measured laser profiles at the disk 

position from the 9th to the 12th pass. Higher order intensity moments 

are excited, and the intensity profiles follow a succession 

of Gauss-like (even passes) and ring-like (odd passes) shapes. 

Fig. 11 shows a selection of images taken during the alignment 

procedures for different disks and amplifier layouts to indicate 

the variety of possible odd-pass profiles. Profiles with hot-spots 

were avoided for they decrease the maximum output energy at 

which disk rupture occurs. 

Higher order beam propagation may be described by the 

Collins integral [14]. It has been demonstrated that as long as 

the paraxial approximation of the beam holds, the beam propagation 

is determined by the ABCD-elements of the ray matrix 

not only for the fundamental mode but also for higher-order 

intensity moments [17], [18]. In addition to the optical layout 

given by the ABCD-elements, the simulation of the amplifier 

beam propagation requires the knowledge of the complex 

2 The misalignment instability caused by an odd number of mirrors is well 

shown in [13, Fig. 6a]. 



Fig. 12. (a) Space resolved gain �@�A for a reflection at the disk-mirror for 

several pump power densities and a pump spot of 4-mm diameter (FWHM). 

The measurement was made by imaging the laser beam at the disk position 

into a CCD-camera for the pumped and unpumped case. (b) Topography of the 

disk–mirror effective surface �@�A measured interferometrically. 

intensity gain for a beam reflected at the disk-mirror 

which may be written as 

where is the gain amplitude accounting for amplification 

in the pumped region, and absorption in the unpumped region, 

respectively (soft aperture effects), and is 

the optical phase difference associated with an amplification-reflection 

at the disk-mirror. The describes the phase 

difference accumulated for (infinitesimally-small) beams being 

reflected at different positions on the disk-mirror. It relates 

to the effective surface topography profile of the 

disk-mirror via 

where is the wavelength (normal beam incidence assumed). 

The term “effective” accounts for the fact that the originates 

not only from a curvature of the disk’s HR coating, but 

also from spatial variations of the Yb:YAG optical length (cf. 

Section V). Measurements of and are shown in Figs. 12 and 

17. 

The propagation of the electric field in the amplifier was 

simulated by concatenating Collins integrals accounting for the 

transit of the beam between two successive passes in the disk, 

with complex amplification processes accounting for the disk 

described by a multiplication of the beam’s electric field with 

. The link between the electric fields of a beam propagating 

from plane 1 to plane 2 described by the ABCD-matrix 

is given by the Collins integral [14] 

where and are the electric fields at the input and output 

of the optical system, respectively, are the space coordinates, 

and . 

Fig. 13 shows the simulated beam profiles at the disk position 

issued by using even-parity function fits for the measured 

and , and the amplifier layout associated with 

the beam profiles of Fig. 10. The observed alternation between 

Gauss-like and ring-like profiles as well as the measured gain 

(1) 

(2) 

(3) 

Fig. 13. Simulated beam intensity profiles at the disk position for the multipass 

amplifier. The overall gain for 12 passes is 6.4. 

are well reproduced by the simulations. A more precise comparison 

with the measured profiles is shown in Fig. 14. The 

small deviations may be attributed to several factors: imperfect 

laser alignment, deviation of from an even-parity and radial 

symmetric function, nonperpendicular beam incidence on 

the disk (which varies slightly from pass to pass), and - 

length variations (which also change slightly from pass to pass). 

Simulations give evidence that the excitation of higher order intensity 

moments has to be mainly attributed to the disk-mirror 

asphericity , defined as any deviation of from a 

polynomial of second order in : 

whereas and its related soft aperture effects are of 

minor importance. Fig. 15 demonstrates the sensitivity of the 

profiles and total amplifier gain when the aspherical terms 

associated with the disk-mirror are varied. Although all 

profiles have been generated with the same disk spherical lens 

described by the second order terms in (and the same 

amplifier layout), the gain and the profiles change dramatically 

when are varied. The amplifier design which assumes 

Gaussian beam propagation and has thus to 

be strongly modified in order to achieve stable beam propagation. 

It is worth noticing that for a 4-f configuration the phase 

front of the beam leaving the disk is given (ignoring some small 

gain/absorption related effects) by , where 

is the number of passes on the disk. Thus, the higher 

order components increase linearly with the number of passes 

for the 4-f configuration whereas they saturate for our amplifier 

choice as inferred from Fig. 13. 

Energy scalability with pump spot diameter—increasing the 

pump power at constant pump intensity—is limited mainly by 

ASE (cf. Section VI). The limitation set by ASE is even more severe 

for pulsed operation at low repetition rates ( kHz) than 

for CW operation. Another limiting factor driving performance 

is the optical damage of the disk, mainly by coating ablation following 

energy absorption. Taking into account these constraints 

we designed an amplifier with a pump rms radius of 1.15 mm 

and 3.5 kW cm pump power density. Small-signal gains up to 

7 have been measured for the 12-pass amplifier for beam spot 

rms mm at the disk position. This corresponds 

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Fig. 14. Simulated (line) and measured (dots) intensity profiles from the 9th to 

the 12th pass. 

Fig. 15. Intensity profiles of the 11th pass for various disk-mirror aspherical 

components which are shown in the inset. All the profiles have been produced 

with the same amplifier layout and � @�Y �A. 

Fig. 16. (a) Amplifier and oscillator output energy as a function of the oscillator 

cavity closure time. (b) Amplifier gain as a function of its input energy. Note 

that for this disk the optical rupture threshold was not reached. 

to a small-signal gain of 1.18 per reflection (double-pass). Amplifier 

and oscillator pulse energy as a function of the oscillator 

cavity closure time are plotted in Fig. 16 together with the resulting 

amplifier gain as a function of its input energy. As may 

be inferred from this figure there is the potential to further increase 

the pulse energy if allowed by the optical damage. The 

disk oscillator-amplifier system delivers pulses with energy of 

48 mJ at 1030 nm for repetition rates up to 850 Hz, within a 

delay of 400 ns after the electronic trigger. This satisfies all 

the requirements for the measurement of the muonic hydrogen 

Lamb shift. 

Fig. 17. (a) �@�Y �A for an unpumped disk. The laser beam impinges from the 

bottom to the effective profile acting as a mirror. (b) �@�Y �A for the same disk 

pumped with 3.5 kWacm and 4-mm diameter. (c) �@�A for various pump power 

densities given in kWacm . For clarity of representation, the various plots have 

been vertically shifted. (d) Total disk lens power Ia� for four disks as a function 

of the pump power density resulting from fitting �@�Y �A with � @�Y �A in 

the range �Y � P ‘0IY I“ mm. The solid circles deviate from the typical behavior 

due to flaws during disk production presently undetectable before the disks are 

put into operation. (e) Pure thermal-induced aspherical components of the profiles 

in (c). They are the remnants of the fits of the curves in (c) after subtraction 

of the profile at zero-pumping. 

V. LENS EFFECT AND ASPHERICAL TERMS OF THE DISK 

A Michelson interferometer was used to measure the 

space-resolved associated with a reflection of a laser 

beam (with 1030 nm wavelength and 1 W power) at the 

disk-mirror. The disk-mirror was placed in one of the interferometer 

arms, whereas in the other, a flat mirror (slightly 

tilted) served as reference. The interference stripe analysis 

indicates that for an unpumped disk the profile usually 

corresponds to a concave mirror as shown in Fig. 17(a). The 

concave curvature is the result of the internal tensile stress of 

the HR-coatings and the stress induced by the soldering of 

the disk to the heat sink. When the disk is pumped there is an 

axial heat flux (perpendicular to the disk surface) resulting in 

an axial temperature gradient. Closer to the heat sink, the disk 

temperature is lower giving rise to smaller thermal expansion 

than at the front side of the disk. The stress related to different 

thermal expansion (in radial direction) of the rear and front 

side causes a mechanical bending of the disk-mirror towards 

a more convex value with increasing pump power as shown in 

Fig. 17(b) and (c). A complete description of the various effects 

modifying requires finite elements simulations [9] and 

is beyond the scope of this article. However, we can briefly list 

the various physical contributions: 

• caused by the above described mechanical bending 

related with the different thermal expansion between the 



rear and front sides of the disk in radial direction. It produces 

convex lens values and dominates over all the following 

contributions. 

• originating from the thermal expansion in axial direction. 

A primitive model which assumes a flat-top temperature 

profile in radial direction with a temperature difference 

K leads to profile height difference between 

pumped and unpumped region of 

nm where K [15] is the linear thermal 

expansion coefficient, [16] the Yb:YAG refractive 

index and mm the disk thickness. It shifts the 

disk lens to more concave values. 

• arising from the temperature dependence of . 

With K between two different position on the 

disk, it follows that nm 

where K [15] is the thermo-optical 

coefficient. It leads to more concave values. 

• associated with a change in population difference 

between upper and lower Yb:YAG manifold in 

the pumped and unpumped region. With a polarizability 

difference cm between upper and 

lower manifold and for cm we estimate 

[19] nm. It 

contributes to more concave values. 

The effective radii of curvature of the disk-mirrors are obtained 

by fitting the measured ’s with a polynomial function of 

second order in . The zero order accounts for an irrelevant 

global shift of the mirror surface, the first order compensates 

the tilt of the reference mirror and the second order is used to 

extract the lens power. The extracted effective lens power as a 

function of the pump power density is shown for several disks 

in Fig. 17(d). By subtracting the zero-pumping profile from the 

pumped one the “pure” thermal lensing effect can be extracted. 

Effective thermal lens powers of m have 

been measured when pumping with 3 kW cm and an rms radius 

of 1.15 mm. The fits remnants for the profiles in (c) after 

subtraction of the profile at zero-pumping, are shown in (e) 

and correspond to the pure thermal-induced aspherical components. 

The thermal-induced asphericity turns out to increase 

with pump power density and to be localized at the border of the 

pumped region. 

VI. ASE AND EFFECTIVE LIFETIME OF YB:YAG 

The pumped region of a disk has a peculiar geometry due to 

the large aspect ratio (radius to thickness ), resulting in a 

larger ASE when compared to a classical rod/slab crystal design. 

Spontaneously emitted photons are amplified for an average 

distance whereas a reflected laser beam for a distance 

. A reflected laser beam experiences thus a gain which 

is times smaller than the gain 

experienced by a spontaneously emitted photon, where is the 

intensity gain coefficient. For the specific amplifier-disk characteristics 

( cm , mm, mm), this ratio is 

approximately 10. Additionally, total internal reflection (TIR) of 

the ASE radiation occurring at the disk borders may redirect the 

Fig. 18. Schematic view of the disk (white) and pump region (gray) geometry 

with an example of ray tracing for a spontaneously emitted photon. For the 

beveled disks the ASE photons leave the disk when they reach the beveled region. 

TIR stands for total internal reflection and % IH is the beveling angle. 

The disk thickness is � aHXP mm and the pump diameters are P� aRmm and 

P� aPXQ mm for the amplifier and oscillator respectively. 

photon into the pumped region (see Fig. 18) leading to a further 

amplification or even to parasitic oscillation in the disk itself. 3 In 

order to reduce this back-reflection the disks are beveled, since 

TIR at the beveled surface decreases the incidence angle of the 

photon at next reflection. When the angle is smaller than the TIR 

angle the photon escapes from the disk. This escape efficiency 

increases with decreasing angle (see Fig. 18). However, the 

usable disk front surface is reduced by the beveling process. An 

angle is chosen in order to accommodate both effects. 

A water-cooled ring is introduced as depicted in Fig. 2 to absorb 

the exiting fluorescence. Some 35% (150 W at running 

conditions) of the pump power absorbed in the disk is subsequently 

absorbed in the water cooled aperture. In the absence of 

the water-cooled ring, the extracted fluorescence would cause 

thermo-induced mechanical distortion, optical coating damage 

and temperature gradients in the laser head. These temperature 

gradients would generate irregular air circulation and thus induce 

laser pointing instability via the temperature dependence 

of the air refractive index. 

ASE depletes the population inversion and thus lowers the 

gain. The relatively high gain achieved in the amplifier has been 

possible only with beveled disks. The amplification of the spontaneously 

emitted photon increases with the pump spot diameter. 

This is because both the path length in the pumped region 

and the probability that a photon crosses the pumped region 

multiple times (following TIR at the disk border) increases with 

diameter. 

An interesting way to quantify these ASE effects is to introduce 

the concept of the “effective lifetime” of the Yb:YAG 

upper state. The increase of the total relaxation rate from the 

upper state population induced by the amplification process for 

the spontaneously emitted photons is included in the definition 

of the effective lifetime. We have developed a method to deduce 

the effective lifetime based on the measurement of the resonance 

behaviour of the oscillator cavity since the resonance width depends 

on the effective lifetime. To measure the resonance the oscillator 

cavity is excited and its reaction is recorded as a function 

of the excitation frequency. Excitation of the oscillator cavity 

3 An additional source of ASE is given by photons which escape from the disk 

front side and propagate along the pump optics (see Fig. 2). These photons are 

thus imaged several times onto the pumped region and experience amplification. 

This effect is estimated to be 10% of the total ASE. 



Fig. 19. Measured (squares) and fitted (line) oscillator resonances for the internal 

circulating power. (a) In-phase component. (b) Quadrature component. 

Both resonances are simultaneously fitted with (15) and (16). 

occurs by slightly modulating the PC, generating a small modulation 

of the cavity losses. The intensity of both transmitted and 

circulating power are recorded with photodiodes as a function 

of the modulation frequency. The photodiode signals are then 

fed to a lock-in amplifier (phase sensitive detector) whose reference 

is given by the signal used to excite the PC. The lock-in 

amplifier outputs the amplitudes (dc signals) of the in-phase and 

quadrature (90 degrees out-of-phase) components. By varying 

the reference signal frequency, resonance curves as shown in 

Fig. 19 are obtained. 

A model for these resonances is given in the following. Consider 

the ASE rate 

where is the population difference between the 

initial (excited) and final laser transition states, the emission 

cross section, the spontaneous lifetime of the upper state and 

, constants. describes the spontaneous emission rate 

from the upper state, whereas the parenthesis describes the first 

order expansion of the spatially averaged gain for spontaneously 

emitted photons. This gain is proportional to the population inversion 

density, the cross section ( ), and a geometrical 

factor ( , respectively, ). We can define the effective lifetime 

as 

Since ASE plays an important role, it has to be included in the 

rate equations describing the laser dynamics given by the evolution 

of the population inversion and the evolution of the 

power circulating in the cavity : 

with the total Yb ion density, the 

pumping rate, the total cavity losses and a constant. The 

first term on the right side of (7) accounts for ASE, the second 

for stimulated emission, and the third for repumping. The first 

(5) 

(6) 

(7) 

(8) 

term on the right side of (8) accounts for the power losses 

( photon lifetime ). The first step is to solve these 

equations for the steady state regime ( , ). 

Then we consider a small perturbation of the steady-state 

regime achieved by modulating the cavity losses at a frequency 

as 

This leads to small deviations ( ) of the steady state values 

( ). Inserting (9) in (7) and (8) leads to a differential 

equation of second order equivalent to a driven resonance in 

classical mechanics: 

where 

whose solution takes the form 

with 

(9) 

(10) 

and (11) 

(12) 

(13) 

(14) 

and a function independent of . is the 

in-phase component, i.e., in phase with the excitation, whereas 

represents the quadrature component. In order to account 

for phase delays arising from the electronic setup which lead to 

a rotation in the complex plane of in-phase and quadrature components, 

the resonance curves of Fig. 19 have been simultaneously 

fitted with 

for Fig. 19(a) (15) 

for Fig. 19(b) (16) 

where are constants, and from the resulting fit parameters the 

effective lifetime is extracted. One of the necessary input constants 

is the lifetime at zero-pumping. Because of radiation trapping 

[6], [20], which was neglected in the above equations, there 

is a difference between the spontaneous and the zero-pumping 

lifetime. Radiation trapping is caused by the reabsorption of 

the fluorescence light in the active medium itself originating 

from the non-negligible population of the lower state associated 

with the 1030 nm transition. However, radiation trapping 

may be included simply by substituting with an effective 

lifetime at zero-pumping . We estimate that at our conditions 

radiation trapping increases the fluorescence effective 

lifetime at zero-pumping from ms [8] to 

ms. Nevertheless, the effective lifetimes extracted from the 

resonance fits show a negligibly small dependence on the used 

value of the effective lifetime at zero-pumping. As illustrated in 

Fig. 20, the effective lifetime shows a strong dependence on the 

pump power density. For disks with 7 at. % doping, the effective 

lifetime is reduced from 1.06 ms (not measured here) for 



Fig. 20. Effective upper state lifetime of Yb:YAG as a function of the pump 

power density for 0.67-mm rms radius and 7 at. % (not beveled) disk. A lifetime 

of 1.06 ms at zero-pumping accounting for radiation trapping is used. 

no population inversion to ms when pumped with 

4.6 kW cm power density, a pump rms radius of 0.67 mm and 

laser eigenmode size at the disk position of mm. 

The extracted effective lifetime can be used to deduce the 

small intensity gain coefficient related to a single reflection 

gain at the disk-mirror with and the stored 

energy in the pumped region. Let us consider the disk 

prior to pulse extraction, when only the pumping process and 

the above described ASE effects have to be accounted for. The 

rate equation governing the upper-manifold population 

(17) 

where pump power , pump wavelenth , and pump efficiency 

can be solved for constant and steady-state conditions 

to give 

The 1030-nm lasing transition inversion is given by 

(18) 

(19) 

where is the lower manifold population, ( at 300 K, 

69% at 400 K) and ( at 300 K, at 400 K) is the 

fractional population of the metastable and terminal Stark level 

[21]. By inserting , the gain takes the form 

(20) 

where is the dynamic cross section, related to the measured 

effective stimulated cross section cm 

by [21]. Comparing the measured 

small-signal intensity gain per reflection at the disk mirror of 

( mm) with that predicted by (20) gives us 

a way to determine the pump efficiency . By inserting 

W, cm , nm, ms 

and cm , it turns out that . The 

fraction of pump light that is back-reflected after the 12-pass 

pump scheme is measured to be , resulting in a pump 

efficiency of , which is in agreement with 

the above given result. 

Fig. 21. Gain exponent P�� as a function of the pump power density. The 

points are obtained from (20) by inserting the ( of Fig. 20, aHXVW and approximately 

accounting for the temperature dependence of � and � . The energy 

stored in the pumped volume inferred from (21) is also given. The squares 

represent gain coefficient per pass extracted from gain measurements (� a IXPS 

for 4.6 kWacm and � aHXHPI mm). 

The gain deduced from (20) is plotted as a function of the 

pump power density in Fig. 21. The same figure also shows the 

energy stored in the pumped volume which is given by [22] 

with (21) 

where J cm [21] is the gain medium saturation 

fluence. The extractable energy is related to the stored energy via 

a factor describing the overlap of the oscillator mode (Gaussian 

beam with rms radius of 0.5 mm) with the pump region (quasiflat-top 

profile with rms radius of 0.67 mm) and depends also 

on interference effects at the disk-mirror. 

As is well visible from the figure, the drop in effective lifetime 

connected with ASE leads to gain saturation and stored energy 

saturation. Moreover, for 4.6-kW cm pump power density, a 

pump power back-reflection of only 10% is measured, and no 

ground-state pump bleaching is observed being the ratio of excited 

state population to total dopant density of . 

With a pump rms radius of 0.67 mm the heat flow in the disk is 

already mainly one-dimensional. Overheating of the disk thus 

does not represent any limitation in energy scaling because an 

increase of the pump spot surface at constant pump intensity issues 

the same disk temperature (both heat production and heat 

flow scales with the surface). 

We conclude that the energy scaling of thin-disk lasers operated 

at low repetition rates ( kHz) 4 is limited mainly by ASE 

effects and not by available pump power, overheating, or pump 

absorption inefficiency. 

VII. CONCLUSION 

We have developed a diode-pumped thin-disk Yb:YAG laser 

composed from an oscillator and an amplifier delivering 48-mJ 

4 Note that ASE effects are strongly reduced for operation at higher repetition 

rates (b IH kHz) or in the CW regime (at high output efficiency). At low repetition 

rates, prior to the pulse formation, the population inversion is given only 

by the pumping and the ASE effect (see (17)), whereas in the CW regime the 

population inversion is determined by stimulated emission. In order to increase 

the laser efficiency, thin-disk lasers operating in the CW regime are usually operated 

with outcoupler transmissions from 1 to 3%. As can be inferred from (8), 

in the CW regime the population inversion is given by x a va� . Thus, a low 

transmission outcoupler implies low x , which leads via (5) to reduced ASE 

losses. 



pulses only 400 ns after a randomly occurring laser trigger. The 

light output is stable for stochastic triggers occurring between 

0 and 850 Hz (minimum pulse separation 1.1 ms). Two parallel 

systems (each composed of an oscillator and amplifier), 

have been built and operated (at reduced energy output, i.e., 

2 25 mJ) at close to 100% uptime for more than 10 days in 

August 2007 in an accelerator environment at the beam 

line at the Paul Scherrer Institute. 

The -switched oscillators deliver pulses up to 12 mJ energy 

each and 35 ns pulse length at 1030 nm, with pulse-to-pulse 

delay times down to 1.1 ms and delay times between trigger and 

optical pulse output of 250 ns. Such a short delay, which is one 

unusual requirement related to our experiment, is achieved by 

designing a relatively short oscillator cavity and operating the 

oscillator prior to trigger in CW prelasing mode close to lasing 

threshold. 

After the 12-pass amplifiers, the pulse energies reach 48 mJ 

in each system. Instead of the classical 4-f beam propagation, 

the amplifier is conceived as a concatenation of optically stable 

segments. This choice is motivated by the smaller sensitivity of 

the beam waist and the divergence at the amplifier output for a 

variation of the disk lens. In addition, the beam path length is 

shorter when compared to the 4-f configuration. The propagation 

of the laser beam in the amplifier including the formation 

of higher order intensity moments has been experimentally and 

theoretically explored. The Collins integral, measured space-resolved 

gain and optical phase delay for a beam reflected at the 

disk-mirror are used to simulate the propagation in the amplifier. 

The main source for the higher-order intensity moments is the 

asphericity of the disk-mirror profile. The real amplifier layout 

leading to optimal gain and beam spot size at the disk position 

(total amplifier gain up to seven with beam spot rms radii of 

1.1 mm for each pass) differs strongly from the layout based on 

Gaussian beams and the disk-mirror approximated with a spherical 

lens. To increase the gain and the stored energy the disks are 

beveled. The beveling reduces the amplification of the spontaneously 

emitted photons inside the disk resulting in a reduced 

ASE-induced depletion of the upper state population, notably 

for large pump spot sizes. 

The ASE-induced depletion is quantified by measuring the 

oscillator resonance whose width depends on the ASE rate and 

is represented in terms of the effective lifetime of the Yb:YAG 

upper state. It is measured that due to ASE the effective lifetime 

drops from 1.06 ms at zero-pumping to ms at 

4.6 kW cm and pump rms radius of 0.67 mm. The measured 

effective lifetime is used to determine the gain and the stored 

energy in the disk as a function of the pump power density. It is 

found that for the used thin-disk technology and at low repetition 

rate ( kHz) pulsed mode operation, the ASE represents the 

main limiting factor for energy scalability with pump spot diameter 

(increasing the pump power at constant pump intensity). 

Possible increase of performance may thus be reached by using 

thin-disks bonded with undoped YAG caps [23] or thicker disks. 

Additionally, adaptive mirrors may be used to control the beam 

shape at the disk position in order to increase the optical damage 

threshold, reduce diffraction losses, and increase the overlap between 

pump and laser beam (flat-top beam shape). 

ACKNOWLEDGMENT 

The authors would like to thank A. Austerschulte, 

A. Michalowski, H. Brückner, K. Linner, W. Simon, 

J. Häusermann, F. Dausinger, M. Müller, B. Rippstein, 

R. Vögeli, C. Kramer, M. Strittmatter, G. Villano, R. Binder, 

R. Greschner, Y. Yalcin, C. Stolzenburg, M. Larionov, 

J. Speiser, D. Kuntze, B. Weichelt, A. Allmendinger, F. Butze, 

F. Manfred, T. Metzger, C. Y. Teisset, L. Simons, V. Markushin, 

M. Storni, Z. Hochman, M. Horisberger, the PSI workshop, the 

PSI Hallendienst, the MPQ workshop, and F. R. Lechner. 

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Aldo Antognini was born in Switzerland in 1976. He graduated in physics from 

the ETH, Zürich, Switzerland, in 2001 and the Ph.D. degree in atomic physics 

from the Ludwig-Maximilians-University, Munich, Germany, in 2005. 

Since September 2001, he has been with the group of T. W. Hänsch at the 

Max-Planck-Institute of Quantum Optics, Garching, Germany. In 2006, he went 

to Stuttgart, Germany, to collaborate with the A. Giesen group at the Institut für 

Strahlwerkzeuge to develop a thin-disk laser for the muonic hydrogen Lamb 

shift experiment. He is currently engaged with the spectroscopy of muonic hydrogen 

and the development of the required laser system. 

Karsten Schuhmann was born in Germany in 1974. He received the degree in 

physics from the University of Frankfurt, Frankfurt, Germany, in 2002. 

Then, he joined the Lasers Development Department of the Institut für 

Strahlwerkzeuge, Stuttgart, Germany, where he worked mainly on development 

of high-power disk-lasers and interferometric evaluation. In 2006, he started 

to develop a thin-disk laser for the muonic hydrogen Lamb shift experiment. 

Since 2007, he has continued his research at the Technologiegesellschaft für 

Strahlwerkzeuge mbH, Stuttgart. 

Fernando D. Amaro received the Diploma in physics and the M.S. degree from 

Coimbra University, Coimbra, Portugal, in 2003 and 2006, respectively, where 

he is currently working toward the Ph.D. degree in the field of ion blocking on 

gaseous detectors. 

François Biraben received the doctorat d’etat degree in atomic physics from 

the Pierre and Marie Curie University. 

He is Directeur de Recherche at CNRS. He is deputy director of the Kastler 

Brossel laboratory. His research interests are in the metrology of hydrogen atom 

and the measurement of fundamental constants. 

Andreas Dax received the Ph.D. degree in physics from the University of Bonn, 

Bonn, Germany, in 1992. 

Currently, he is a Project Associate with the University of Tokyo, Tokyo, 

Japan. His field of activity is in high-resolution laser spectroscopy currently of 

exotic atoms at CERN. 

Adolf Giesen received the Ph.D. degree from the University of Bonn, Bonn, 

Germany, in 1982. 

He then joined the Institute of Technical Physics at DLR (the German 

Aerospace Center) in Stuttgart. He worked on RF-excited CO -lasers before 

moving to the Institut für Strahlwerkzeuge, University of Stuttgart. Stuttgart, 

Germany. He then worked on thin-disk lasers (in collaboration between the 

University of Stuttgart and DLR). Since 2007 he has been the director of the 

Institute of Technical Physics at the German Aerospace Center (DLR). 

Dr. Giesen was the recipient of the Berthold Leibinger Preis in 2002 and with 

the Rank Prize in 2004 for the invention and his work on thin disk lasers. 

Thomas Graf was born in Switzerland in 1966. He received the physics degree 

and the Ph.D. degree from the University of Bern, Bern, Germany, in 1993 and 

1996, respectively. 

After 15 months of research at Strathclyde University, Glasgow, U.K., he was 

appointed head of the High-Power Lasers and Material Science Group in April 

1999 at the Laser Department of the Institute of Applied Physics, University 

of Bern, where he was awarded the venia docendi in 2001 and where he was 

appointed to Assistant Professor in 2002. In 2004, he was appointed Professor 

and Director of the Institut für Strahlwerkzeuge (IFSW) at the University of 

Stuttgart, Stuttgart, Germany. He is engaged in high-power all-solid-state laser 

systems, laser beam shaping, and laser applications in manufacturing. 

Dr. Graf served as a board member of the Swiss Society for Optics and Microscopy 

from 2001 to 2007, is a board member of the European Optical Society, 

and is a regular member of the Optical Society of America and the German 

Wissenschaftliche Gesellschaft Lasertechnik e.V., WLT (Scientific Society for 

Laser Technology). 

Theodor W. Hänsch was born in Heidelberg, Germany. He received the Ph.D. 

degree in laser physics from the University of Heidelberg in 1969. 

He is currently a Director with the Max-Planck-Institute of Quantum Optics, 

Garching, Germany, and Carl Friedrich von Siemens Professor with the Department 

of Physics of the Ludwig- Maximilians-University, Munich, Germany. In 

1970, he joined A. L. Schawlow at Stanford University as a Postdoctoral Fellow. 

Two years later, he accepted a faculty appointment with the Stanford Physics 

Department, where he worked as a Full Professor from 1975 until he returned 

to his native Germany in 1986. In 1974, Hänsch and Schawlow made a seminal 

proposal for laser cooling of atomic gases. Twenty-five years later, Hänsch and 

his Munich team were the first to realize Bose–Einstein condensation on a microfabricated 

atom chip. 

Dr. Hänsch was corecipient of the Physics Nobel Prize (with J. L. Hall) in 

2005 for their contributions to the development of laser-based precision spectroscopy, 

including the optical frequency comb technique. 

Paul Indelicato was born in 1958. He received the Ph.D. degree in physics from 

the Pierre and Marie Curie University, Paris 6, Paris, France, in 1987. 

He is a Director of Research at CNRS, director of the Kastler Brossel laboratory, 

and head of the Energy Matter, Universe pole of the Science Directorate 

of the Pierre and Marie Curie University. He has been Associate Researcher 

with the University of Virginia in 1989–1990, Guest scientist at NIST during 

1987–1990, and was elected Fellow of the American Physical Society in 2003. 

He currently works on experimental and theoretical studies of highly charged 

ions and exotic atoms. 

Lucile Julien received the “doctorat d’Etat” degree in atomic physics from the 

Pierre and Marie Curie University, Paris 6, Paris, France. 

She is a Professor with Pierre and Marie Curie University, where she is Director 

of the Master of Physics Department. 

Cheng-Yang Kao was born in Taiwan in 1977. He received the M.S. degree 

in physics from National Central University, Taiwan, in 2002. He is currently 

working toward the Ph.D. degree at the National Tsing Hua University, Hsinchu, 

Taiwan. His doctoral research focuses on the production of the ultracold polar 

molecule 39 K Rb in magneto-optical trapping (MOT) using photoassociation 

method. 

He has continued to study physics with Prof. Y.-W. Liu at National Tsing 

Hua University. 

Paul E. Knowles was born in Nova Scotia, Canada. He received the Ph.D. degree 

in nuclear physics from the University of Victoria, Victoria, BC, Canada, 

in 1996. 

Following several years of muon-related research (e.g., weak interactions and 

muonic Lamb shift), he changed domains. He is currently Maitre-Assistant with 

the University of Fribourg, Fribourg, Switzerland, working in atomic physics, 

more precisely laser-pumped alkali vapor magnetometers. 



Franz Kottmann received the Ph.D. degree in physics from ETH, Zurich, 

Switzerland, in 1982. 

He is a Senior Researcher of particle physics with the Paul Scherrer Institute, 

Villigen, Germany. Since 1999, he has been a cospokesperson on the laser-spectroscopic 

measurement of the muonic hydrogen Lamb shift. 

Eric Le Bigot received the Ph.D. degree in atomic physics from the Pierre and 

Marie Curie University, Paris 6, France. 

He is an Associate Researcher with CNRS. His current research includes 

X-ray precision spectroscopy of highly charged ions, with applications to X-ray 

standards and to the test of fundamental theories. 

Yi-Wei Liu received the Ph.D. degree from Oxford University, Oxford, U.K. 

He is an Associate Professor with National Tsing-Hau University, Hsinchu, 

Taiwan, and his research is on the laser spectroscopy of simple atomic system 

and the interaction of ultracold hetero-nuclear atoms. 

Livia Ludhova was born in Slovakia in 1973. She received the undergraduate 

and Ph.D. degrees in geology and the degree in physics from Comenius University, 

Bratislava, Slovakia, in 1996, 1999, and 2001, respectively, and the Ph.D. 

degree in physics from Fribourg University, Fribourg, Switzerland, in 2005. Her 

doctoral work in physics focused on muonic hydrogen Lamb shift experiment. 

Currently, she is a Postdoctoral Fellow with the Istituto Nazionale di Fisica 

Nucleare, Milan, Italy, working in the field of neutrino physics (Borexino experiment). 

Nils Moschüring is currently working toward the Diploma in physics at the 

Ludwig-Maximilians-University, Munich, Germany. 

He has a heightened interest in quantum optics, solid-state physics, and computer 

science. 

Françoise Mulhauser received the Ph.D. degree in nuclear physics from the 

University of Friborg, Switzerland. 

After many years of experimental research in nuclear physics and weak interactions, 

she started a new career as a Nuclear Physicist with the International 

Atomic Energy Agency (IAEA), promoting the peaceful application of nuclear 

sciences in developing countries. 

Dr. Mulhauser was the corecipient, as staff of the IAEA, of the Nobel Peace 

Prize in 2005 

Tobias Nebel was born in 1976. He received the Diploma from the University of 

Munich, Munich, Germany, in 2004. He is currently working toward the Ph.D. 

degree at the Max-Planck-Institute of Quantum Optics. 

In 2004, he joined the Max-Planck-Institute of Quantum Optics, where he is 

currently working on the Lamb shift in muonic hydrogen towards his doctoral 

degree. He has studied physics in Augsburg, Germany, Vancouver, BC, Canada, 

and Munich. 

François Nez received the “doctorat d’Etat” degree in atomic physics from the 

Pierre and Marie Curie University, Paris 6, France. 

He is a Junior Researcher with CNRS and member of the CODATA task group 

on Fundamental Constant. His current research activities are in high-resolution 

spectroscopy, cold atoms, and fundamental constant measurement. 

Paul Rabinowitz was born in Brooklyn, NY, in 1935. He received the B.S. 

degree from Brooklyn College, Brooklyn, NY, the M.S. degree from New York 

University, and the Ph.D. degree from the Polytechnic Institute of Brooklyn, all 

in physics. 

He joined TRG Inc. as a Research Physicist in 1959 and was involved in 

the early development of lasers and laser applications. In 1967, he joined the 

Polytechnic Institute of Brooklyn and directed laboratory work in quantum 

electronics, featuring laser frequency stabilization and saturated resonance 

spectroscopy. He joined Exxon Research and Engineering in 1974, where he 

worked on the development of laser isotope separation techniques and high 

power broadly tunable Raman lasers that were used for interfacial nonlinear 

optical spectroscopy. In 1996, he joined the Chemistry Department, Princeton 

University, Princeton, NJ, and has worked on the development of resonators and 

applications for CRDS (cavity ring-down spectroscopy) to the measurement 

of trace gaseous species. He holds 10 patents and is author or coauthor of 52 

scientific publications. 

Dr. Rabinowitz is a Fellow of the Optical Society of America and a member 

of the American Physical Society. 

Catherine Schwob is Associate Professor and Researcher with the University 

Pierre et Marie Curie, Paris, France. She has worked several years on high-resolution 

spectroscopy and fundamental constant measurement. Her new activity 

field deals with quantum optics in nano-objects. 

David Taqqu received the Ph.D. degree in physics from ETH, Zurich, Switzerland, 

in 1972. 

He is a Senior Researcher in particle physics with the Paul Scherrer Institute, 

Villigen, Switzerland. His recent research activities cover the development of 

low-energy muon beam lines and the spectroscopy of muonic atoms. 

Randolf Pohl was born in Munich, Germany, in 1970. He received the degree in 

physics from the Technical University of Munich in 1997 and the Ph.D. degree 

from ETH, Zurich, Switzerland, in 2001, both in physics. 

From 1997 to 2005, he studied the long-lived PS state in muonic hydrogen 

at the Paul Scherrer Institute, Villigen, Switzerland. He is currently with the 

Max-Planck-Institute of Quantum Optics, Garching, Germany, with the aim to 

measure the Lamb shift in muonic hydrogen. He is the Co-Spokesman of the 

Muonic Hydrogen Lamb Shift Collaboration.

Thin-Disk Yb:YAG Oscillator-Amplifier Laser, ASE, and Effective Yb ...

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