Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Multipass amplifiers with self-compensation of the thermal lens

Open Access Open Access

Abstract

We present an architecture for a multipass amplifier based on a succession of optical Fourier transforms and short propagations that shows a superior stability for variations of the thermal lens compared to state-of-the-art 4f-based amplifiers. We found that the proposed multipass amplifier is robust to variations of the active medium dioptric power. The superiority of the proposed architecture is demonstrated by analyzing the variations of the size and divergence of the output beam in the form of a Taylor expansion around the design value for variations of the thermal lens in the active medium. The dependence of the output beam divergence and size is investigated also for variations of the number of passes, for aperture effects in the active medium, and as a function of the size of the beam on the active medium. This architecture makes efficient use of the transverse beam filtering inherent in the active medium to deliver a beam with excellent quality (TEM00).

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Multipass amplifiers are used for the generation of the currently highest laser pulse energies and average powers [16]. Oscillators, regenerative amplifiers, and multipass amplifiers are limited in pulse energy by the damage of optical components induced by the high intensity. Multipass amplifiers possess a higher damage threshold compared to laser oscillators and regenerative amplifiers due to the absence of intracavity enhancement and nonlinear crystals [7,8]. Optical damage can be avoided by increasing the laser beam size, but this typically increases the sensitivity of the beam propagation and output beam characteristics (size and divergence) to the active medium thermal lens. The active medium design and material choice can be optimized to decrease the thermal lens, e.g., in thin-disk lasers [912]. Still, the higher pump powers and the increased beam size needed for energy and power scaling make the thermal lens in the active medium the most severe limitation to overcome [6,13,14]. For these reasons an optical layout has to be chosen that minimizes the changes of the beam propagation for variations of the thermal lens of the active medium.

Commonly, relay imaging (4f-imaging) from active medium to active medium is used to realize a multipass amplifier where the output power is independent of the thermal lens of the active medium because the beam is imaged from pass to pass [15]. The 4f-design exhibits various advantages: it sustains equal beam size at each pass on the active medium independent of the dioptric power of the active medium and independent of the beam size at the active medium. Moreover, numerous passes can be realized with only a few optical elements [1626]. Yet, this design does not represent the optimal solution for a multipass amplifier because the phase front curvature of the beam after propagation through this optical system depends strongly on variations of the active medium dioptric power.

In this paper, we present a novel multipass architecture whose propagation from pass to pass is given by a succession of Fourier transforms and short propagations. The working principle, the practical implementation, and the advantages in terms of stability to variations of dioptric power (thermal lens) and aperture effects of the active medium are detailed.

2. THERMAL LENS AND APERTURE EFFECTS

In this section, we briefly review well-known facts and various definitions needed in the following sections.

When a laser beam crosses the pumped active medium, it is amplified and it experiences a position-dependent optical phase delay (OPD) that distorts its phase front curvature. When simulating the propagation of the laser beam, this distortion can be mostly accounted for by approximating the active medium with a spherical lens [27,28] that can be easily described within the ABCD-matrix formalism [29].

The position-dependent gain (and absorption in the unpumped region) can be approximated by an average gain per pass and a position-dependent transmission function that shows a gradual transition from maximal transmission (including gain) on the optical axis to zero transmission far from the axis. This position-dependent gain is commonly referred to as “soft aperture.” In this study we consider only Gaussian beams in the fundamental mode and we approximate the super-Gaussian aperture of the pumped active medium as the Gaussian aperture. This approximation is justified because the Fourier transform (that underlies the here-presented designs) converts the high-frequency spatial distortions of the beam caused by the super-Gaussian aperture into a halo of the fundamental mode that is eliminated in the next pass at the active medium. Therefore, the beam propagating in the amplifier shows only minor higher-order distortions from the fundamental mode so that the description of the super-Gaussian aperture can be effectively accomplished using a Gaussian aperture [30]. In fact, a Gaussian aperture transforms a Gaussian input beam into a Gaussian output beam [31]. The relation between the 1/e2-radii of the input (win) and output (wout) beams takes the simple form

wout2=win2+W2,
where W2 is the 1/e2-radius of the intensity transmission function of the Gaussian aperture [31,32]. This simple behavior of a Gaussian aperture acting on a Gaussian beam (TEM00-mode) can be captured into an ABCD-matrix for Gaussian optics as [30,31,3336]
Maperture=[10iλπW21],
where λ is the wavelength of the laser beam.

An active medium (AM) usually exhibits both a lens effect (position-dependent OPD) and an aperture effect (position-dependent gain). These can be merged into a single ABCD-matrix describing the active medium MAM=Mlens·Maperture, where Mlens is the ABCD-matrix of a thin spherical lens. The product of these two ABCD-matrices becomes

MAM=[10V1]·[10iλπW21]=[10ViλπW21],
where V is the dioptric power of the active medium. In Eq. (3) we have assumed that the length of the active medium is negligible, i.e., that the length of the active medium is much smaller than the Rayleigh length of the beam. This assumption is generally well justified for high-power lasers given the large beam waists they have at the active medium.

The similarity of MAM and Mlens allows us to define a complex dioptric power V˜ (V˜C) of the active medium as

V˜=V+iλπW2.
Its real part V is the “standard” dioptric power (focusing–defocusing effects), while the imaginary part accounts for the Gaussian aperture. The real part can be articulated as a sum of various contributions
V=Vunpumped+Vthermal=Vunpumped+Vthermalavg+ΔV,
where Vunpumped is the dioptric power of the unpumped active medium and Vthermal the dioptric power related to the pumping of the active medium (thermal lens effect). The latter can be expressed by a known average value Vthermalavg and an unknown deviation ΔV from this average value that might depend among others on running conditions and imperfection of the active medium due to the manufacture process.

In Sections 37, for simplicity, but without loss of generality, we assume that Vunpumped+Vthermalavg=0. In Section 8, when realistic implementations of multipass amplifiers are presented, we relax this assumption. Moreover, in the various plots presented in this paper we have fixed the value of the aperture size to be W=4win. For comparison, in some figures we also present results for W= to highlight the aperture effects.

A laser mode size of win0.7Rp, where Rp is the radius of the super-Gaussian pump spot, is typically used in the thin-disk laser community for efficient laser operation in the fundamental mode. The above choice of a Gaussian aperture with W=4win rests upon the fact that it produces a similar reduction of the fundamental mode size and a similar reduction of the fundamental mode transmission compared to a super-Gaussian aperture fulfilling the relation win0.7Rp [30].

3. STATE-OF-THE-ART MULTIPASS AMPLIFIERS

The commonly used state-of-the-art multipass amplifiers are based on 4f-relay imaging (4f) from active medium to active medium [1525] so that in these amplifiers the beam proceeds as a succession of propagations

AM4fAM4fAM4fAM4fAM.
The geometrical layout and the corresponding propagation of a laser beam through a 4f-segment is given in Fig. 1(a). By concatenating, for example, six of such propagations, the 6-pass amplifier of Fig. 1(b) can be realized.

 figure: Fig. 1.

Fig. 1. (a) Scheme of the laser beam propagation from active medium to active medium through a 4f-imaging segment. The 4f-segment is given by a free propagation of distance f, a focusing optics with focal length f, a free propagation with length 2f, a second focusing element with focal length f, and a free propagation of length f. The vertical magenta lines represent the position of the active medium; the vertical black lines indicate the position of the optic with focal length f. The black curves represent the beam size evolution along the optical axis z. (b) 6-pass amplifier and corresponding beam size evolution along the propagation axis realized by concatenating five 4f-imaging stages and assuming a Gaussian aperture at the active medium of W=4win. The black curves show the beam size evolution for an active medium dioptric power having the design value, i.e., V=0. The red and blue curves show the propagations (beam size evolution) for V=±140f. The gray curves represent the beam evolution for V=0 and W=. The discontinuity of the waist size at the gain medium is caused by the (Gaussian) aperture effect of the finite pump region.

Download Full Size | PPT Slide | PDF

It can be demonstrated that the 4f-imaging warrants the relation win,N=wout,N1 [15]. Here, we defined win,N as the size of the beam incident on the Nth pass at the active medium and wout,N as the size of the beam departing from the Nth pass at the active medium after amplification. In the absence of aperture effects (W=) in the active medium wout,N=win,N. Hence, in the absence of aperture effects the beam size is identically reproduced at each pass on the active medium independent of the size of the laser beam. This property, together with the simplicity of the implementation (many passes using few optical elements), are the main advantages of the 4f-based multipass architecture. However, for nonvanishing aperture effects (W) the beam size is decreased when passing the active medium wout,N<win,N [see Eq. (1)]. Because the 4f-imaging reproduces the beam win,N+1=wout,N the beam size is continuously decreased at each pass wout,N<wout,N+1 as is visible in Fig. 1(b).

By considering the various curves presented in Fig. 1(b) another, even more crucial, drawback of the 4f-based architecture emerges, namely, that the divergence of the output beam strongly depends on variations of the dioptric power ΔV of the active medium.

The output beam characteristics and their dependence on variations of ΔV can be derived by making use of the ABCD-matrix and complex beam parameter formalism [33]. The complex beam parameter q is defined as

1q=1Riλπw2,
where R is the radius of curvature of the phase front and w is the 1/e2-radius of the TEM00 Gaussian beam. In this framework the complex beam parameter at the output of an optical system (qout) can be computed knowing the ABCD-matrix of the optical system and the complex beam parameter at its input (qin) using the relation [33]
qout=Aqin+BCqin+D.
The ABCD-matrix describing the Gaussian beam propagation from the first pass to the last pass of an N-pass amplifier having (N1) 4f-imaging propagations reads
M4f,N=[(1)N10(1)N·N·ΔV˜(1)N1].
The complex beam parameter of the output beam just after the last pass can be obtained by applying Eq. (7) to the ABCD-matrix of Eq. (8). Its Taylor expansion around qin for small variations of ΔV˜ takes the form
qout,N=qin+Nqin2ΔV˜+N2qin3ΔV˜2+N3qin4ΔV˜3+.
Notably, this expansion shows a linear dependence of qout,N on variations of ΔV˜, implying a sensitivity of the output beam characteristics also to small variations of ΔV˜. In addition, the linear dependence in N indicates that there is an accumulation of aperture and lens effects at each pass though the active medium [see the increase of beam divergence and decrease of beam size at each pass in Fig. 1(b)].

From Eq. (9) it is possible to extract the phase front curvature and size of the output beam. When aperture effects are neglected (W=) they are given by

wout,N=win,
Rout,N1=NΔV.
While the output beam size does not depend on variations of the dioptric power ΔV, the phase front curvature of the output beam shows the above-mentioned accumulation of the dioptric power deviation ΔV, leading to an increasing deviation from the design value of Rout,N1=0 with an increasing number of passes. This implies a strong dependence of the output beam divergence to variations of the operational conditions.

When aperture effects are included, the beam size right after the Nth pass on the active medium shrinks with increasing N as

wout,Nwin=1win2N2W2+3win4N28W45win6N316W6+.
Here, for simplicity and to better discern the dependence of wout,N on the aperture size W we have assumed that V=ΔV=0.

Imaging properties of the 4f-scheme, also distortions of the OPD beyond what is accounted for by the spherical lens, as well as distortions caused by the deviation from a purely Gaussian aperture, are accumulated at each pass. Thus, while propagating in the 4f-based multipass amplifier the beam shows increasing mode deformation (beyond the TEM00-mode) resulting in an output beam with decreased beam quality and increased dependency on running conditions [1,37].

For 4f-based amplifiers there are two methods to reduce the accumulation of phase front distortions. The first is by changing the distance between the two lenses used for the imaging [see Fig. 1(a)] [18,38] so that their separation departs from 2f. To put it in another way, the distance between the focusing elements of the 4f-propagation can be adjusted to preserve the q-parameter also for a curved active medium [39]. The second approach is by realizing the N-pass 4f-amplifier as a succession of 2N 4f-segments so that between each pass on the active medium there is an intermediate image of the active medium. At the position of this intermediate image, a deformable mirror can be placed adjusted to produce an opposite phase front distortion compared to the active medium [1]. These methods are particularly suited to compensate for nonzero values of the sum Vunpumped+Vavg. For time-dependent variations of ΔV, a time-dependent correction of the distance or of the dioptric power of the deformable mirror would be necessary, making the system significantly more complex. Especially difficult to be compensated are fast variations that might occur during the pulsed amplification process [38]. Contrarily, the compensation achieved in the Fourier-based amplifier architecture presented in this work is passive and thus well suited also for fast variations of ΔV.

4. FROM 4F-IMAGING TO A DOUBLE FOURIER TRANSFORM WITH FILTERING

In some realizations of multipass amplifiers based on 4f-imaging [15,23,4043], the problematic accumulations of beam distortions at each pass have been suppressed by placing tight apertures (pinholes) in the focus (center) of the 4f-imaging segments as shown in Fig. 2(a). Mode filtering is thus achieved at the cost of output efficiency. In these designs the 4f-propagation is split into a 2f-propagation, an aperture, and a second 2f-propagation. The 2f-propagations act as optical Fourier transforms, while the pinhole filters the beam components beyond the fundamental Gaussian mode.

 figure: Fig. 2.

Fig. 2. Schemes showing the transition from a 2-pass amplifier based on 4f-imaging with mode cleaning achieved with a pinhole in part (a), to a 4-pass amplifier based on a double optical Fourier transform with mode filtering achieved through the soft apertures of the pumped active medium in part (b). The optical Fourier transform is realized by the sequence: free propagation of length F, focusing element with focal length F, followed by a free propagation of length F. The same notation as in Fig. 1 is used.

Download Full Size | PPT Slide | PDF

These schemes indicate a way of how to modify the 4f-imaging propagation to reduce the accumulation of beam deformations, namely, by using optical Fourier-transform propagations to transport the beam from pass to pass and by using the aperture available in the active medium itself as a mode cleaner. In this new scheme, the pinhole of Fig. 2(a) is replaced by the active medium (more precisely two passes in the active media) as shown in Fig. 2(b) that exhibits an intrinsic soft aperture. Hence, the active medium acts not only as gain medium but also as mode cleaner, maximizing the gain for the fundamental mode. For comparison, a 4f-based 4-pass amplifier has similar aperture losses for the fundamental mode as the multipass amplifier of Fig. 2(b), but it does not provide mode cleaning. Multipass amplifiers based on this succession of Fourier propagations and passes at the gain medium featuring a soft aperture will be evaluated in the following sections.

5. 2-PASS AMPLIFIER WITH FOURIER TRANSFORM PROPAGATIONS

In this section, we investigate the properties of a Fourier-based 2-pass amplifier as sketched in Fig. 3(b). Here, the beam crosses first the active medium, propagates through an optical segment acting as an optical Fourier transform, and then passes the active medium a second time. The properties of this system are compared to the 2-pass amplifier shown in Fig. 3(a), which is based on a 4f-imaging propagation.

 figure: Fig. 3.

Fig. 3. Scheme and corresponding beam size evolution along the optical axis z for a 2-pass amplifier based on 4f-imaging in part (a) and on an optical Fourier transform in part (b). It was assumed that W=4win, and the same notation as in Fig. 1 is used. Similar to Fig. 1(b), the Gaussian aperture related to the finite pump region causes the discontinuity of the beam size at the gain medium.

Download Full Size | PPT Slide | PDF

To quantify the sensitivity to variations of ΔV˜ of the beam leaving the 2-pass amplifier we first evaluate the corresponding ABCD-matrix. The ABCD-matrix of the 2-pass amplifier MFourier,2 based on the Fourier transform results from the product

MFourier,2=MAM·MFourier·MAM
=[F·ΔV˜FF2·ΔV˜2+1FF·ΔV˜],
where MFourier is the ABCD-matrix of the optical Fourier transform with A=D=0, B=F, C=1/F, with F being the focal length of the optics (lens or curved mirror) used to realize the Fourier transform when ΔV˜=ΔV+iλ/πW2.

By combining Eq. (14) with Eq. (7) we can deduce the complex beam parameter that is replicated from the input plane (just before the first pass) to the output plane (just after the second pass) qout=qin. The solution reads

qstable=iF1(F·ΔV˜)2.
Therefore, unlike the 4f-imaging that can reproduce any beam size for any value of f, the Fourier transform can reproduce the size of the input TEM00 beam at its output only provided that the complex parameter of the input beam fulfills the condition qin=qstable. Note that in this case the output beam size equals the input beam size only when the number of passes in the active medium is even.

When designing multipass amplifiers the pragmatic choice for the input beam is to assume that the active medium has no dioptric power and no aperture effects (V=ΔV=0 and W=), i.e., ΔV˜=0. In this case, the stability condition given in Eq. (15) simplifies to qstable=iF so that our practical choice for the input beam parameter is

qin=iF.
Using Eq. (6), this condition can be re-expressed as
win=λFπ.
It is evident from this equation that the focal length F needed to realize the Fourier transform reproducing the size of the beam from active medium to active medium depends on the desired beam size at the active medium.

The benefits of the Fourier transform can be evinced by following the beam propagation shown in Fig. 3(b). The beam size of the input beam win,1 is reduced by the soft aperture with W of the active medium so that wout,1<win,1. The smaller beam is, however, converted by the Fourier transform into a larger beam win,2>win,1 [see Fig. 3(b)]. At the second pass through the active medium, this larger beam is reduced by the aperture wout,2<win,2 so that the resulting beam has roughly the size of the input beam wout,2win,1. There is thus a counteracting interplay between the reduction of the beam size caused by the aperture, and the increase of the beam size related with the Fourier transform that stabilizes the beam size close to the value expressed by Eq. (17) so that similar beam sizes are reproduced at each pass. Because of this compensation, variations of the width W of the soft aperture do not significantly affect the output beam size so that a precise knowledge of the aperture effect is not needed when designing Fourier-based multipass systems.

For an analogous compensation mechanism, the Fourier-based 2-pass amplifiers exhibit output beam sizes and divergences that are insensitive to variations of ΔV [see Fig. 3(b)]. Indeed, an active medium with focusing dioptric power turns the entering collimated beam into a converging beam, but the following Fourier transform converts this converging beam into a diverging beam. At the second pass, the focusing dioptric power of the active medium essentially cancels the divergence of the impinging beam. In such a way, the beam leaving the 2-pass amplifier has similar size and divergence as the collimated input beam. An analogous compensation occurs for an active medium with defocussing dioptric power.

Summarizing, there is a counteraction between the Fourier transform and the active medium that results in output beam characteristics only weakly dependent on variations of ΔV˜. The reduced sensitivity to variations of ΔV of the Fourier-based compared to the 4f-based amplifier can be clearly appreciated by comparing the divergences of the output beams in Figs. 3(a) and 3(b). The 4f-imaging leads to an accumulation of the lens effects from pass to pass, while the Fourier transform leads to a substantial compensation of these lens effects. This compensation applies also for other deformations of the phase front occurring at the active medium beyond the spherical distortion already accounted in V.

The complex parameter of the outgoing beam after propagation along the 2-pass amplifier can be calculated from Eq. (7) and the ABCD-matrix elements of Eq. (14). By assuming an input beam parameter as given in Eq. (16), we find that the complex parameter of the output beam for small variations of ΔV˜ takes the form

qout,2=iF+iF3ΔV˜2F4ΔV˜3F6ΔV˜5+
after a Taylor expansion around qin=iF.

Remarkably, in this case qout,2 depends only quadratically on variations of the complex-valued dioptric power ΔV˜. This is in sharp contrast to the linear dependence observed in Eq. (9) for the amplifier based on 4f-imaging. In other words, the output beam for the 2-pass Fourier-based amplifier in first order does not depend on ΔV˜ so that the output beam characteristics such as phase front curvature (given by radius Rout,2) and beam size wout,2 are very insensitive to small variations of the dioptric power and aperture effects of the active medium.

The beam size wout,2 and the phase front curvature Rout,2 obtained from qout,2 are shown in blue in Figs. 4(a) and 4(b), respectively, for variations of the dioptric power ΔV and aperture size of W=4win. Similar plots are given in Figs. 4(c) and 4(d) for W= to highlight the role of the aperture. When comparing these blue curves with the red dashed curves, which represent the output beam characteristics for the 4f-based 2-pass amplifier, it becomes evident that for a 4f-based amplifier the output beam size strongly depends on W and that the output divergence strongly depends on ΔV. Oppositely, the Fourier-based multipass amplifier has output characteristics insensitive to small variations of ΔV and W.

 figure: Fig. 4.

Fig. 4. Size wout,2 and phase front curvature Rout,21 of the output beam leaving the 2-pass amplifiers of Fig. 3 for variations of the active medium dioptric power ΔV. The top row assumes W=4win, and in the bottom one W=. The blue curves represent the results for the Fourier-based amplifier of Fig. 3(b), while the dashed red curves represent the results for the 4f-based amplifier of Fig. 3(a). In both cases it was assumed that qin=qstable. For comparison, in gray are given wstable(ΔV) and Rstable1(ΔV) corresponding to the complex beam parameter given in Eq. (15).

Download Full Size | PPT Slide | PDF

Assuming no aperture effects (W=), the Taylor expansions of the output beam characteristics take the form

wout,2win=1+12F2ΔV218F4ΔV4+,
Rout,21=F2ΔV3+F4ΔV5F6ΔV7+F8ΔV9+
with win satisfying Eq. (17). The insensitivity of the output beam properties to small variations of the active medium dioptric power is manifested graphically in Fig. 4 by the flat behavior of the blue curves around ΔV=0. Mathematically it shows in the absence of a linear term in ΔV in Eq. (19) and by the absence of both liner and quadratic terms in ΔV in Eq. (20).

It is also interesting to investigate how the Gaussian aperture of the active medium affects the output beam size. Assuming that V=ΔV=0, we find that the output beam size takes the simple form

wout,2win=1+win42W4win88W8+win1216W12+.
Hence, the relative change of the output beam size caused by the aperture is in leading order dependent on win4/2W4 compared to win2/W2 for the 4f-based 2-pass amplifier [see Eq. (12)]. In other words, aperture effects minimally impact the size of the output beam of a Fourier-based multipass amplifier as long as win/W1.

The dependence of the phase front radius Rout,21 on aperture effects has also been investigated. Similar to the 4f-based amplifier, also in this case the phase front radius (divergence) of the beam leaving the amplifier, for V=0, does not depend on the aperture size W.

6. 4-PASS AMPLIFIERS WITH FOURIER TRANSFORM PROPAGATIONS

In this section, we consider the 4-pass amplifier based on optical Fourier transforms obtained by concatenating two of the optical segments of Fig. 3(b). The resulting propagation follow the sequence

AMFourierAMAMFourierAM,
as sketched in Fig. 5(a). We assumed here that the propagation between the second and the third pass on the active medium is so short that it can be neglected. This can either be realized with a propagation that is physically short compared to the Rayleigh length of the beam [see Fig. 5(a)] or as sketched in Fig. 5(b) by inserting 4f-imaging between the second and the third pass that per definition has a vanishing effective optical length (B=0 for the ABCD-matrix of a 4f-imaging propagation). In this case, the propagation in the 4-pass amplifier follows the sequence
AMFourierAM4fAMFourierAM.
The complex parameter of the output beam can be obtained following a similar procedure as in the previous section and can be approximated by a Taylor expansion in ΔV˜ as
qout,4=iF+2F4ΔV˜34iF5ΔV˜44F6ΔV˜5+.
Notably in this equation, there are no linear and no quadratic terms in ΔV˜. Indeed, the lowest order affecting the output beam parameter depends on the third power of ΔV˜. The output beam parameters are thus even less sensitive to small variations of the thermal lens and aperture effects compared to the 2-pass Fourier-based amplifiers [compare Eqs. (22)–(18)].

 figure: Fig. 5.

Fig. 5. Two types of 4-pass amplifiers both based on two optical Fourier transforms. In (a), there is physically short free propagation between the second and third pass. In (b), 4f-imaging is used to obtain propagation with zero effective length between the second and third pass. The same notation as in Fig. 1 is used. The gray-shaded region indicates the 4f-imaging segment. The discontinuity of the beam size due to the aperture at the active medium is visible.

Download Full Size | PPT Slide | PDF

The size and divergence of the output beam for ΔV variations can be obtained by combining Eq. (22) with Eq. (6). Assuming for simplicity that W= we find

wout,4win=1+2F4ΔV42F8ΔV8+,
Rout,41=2F2ΔV34F4ΔV58F6ΔV7+.
The insensitivity of wout,4 to variations of the active medium dioptric power around V=0 roots from its ΔV4-dependence, to be compared to the ΔV3-dependence of the 2-pass Fourier-based amplifier, and the ΔV-dependence of the 4f-based amplifiers. Differently, the decreased sensitivity of Rout,41 relative to Rout,21 to small variations of the active medium dioptric power roots in a better cancellation between the ΔV3 and the ΔV4 terms.

A plot of wout,4 and Rout,41 for variations of ΔV is shown in blue in Fig. 6 and compared with the results given in dashed red for a 4f-based amplifier with 4 passes and same beam size. For the Fourier-based amplifier the “stability region,” where the impact of ΔV variations to the output beam characteristics is small, increases with the number of passes while it decreases for 4f-based amplifiers (compare Fig. 6 with Fig. 4).

 figure: Fig. 6.

Fig. 6. Similar to Fig. 4, but for amplifiers with four passes. The blue curves represent the output beam characteristics of both layouts of Fig. 5. The red dashed curves represent the output characteristics of the 4f-amplifier design.

Download Full Size | PPT Slide | PDF

7. MULTIPASS AMPLIFIER WITH A LARGE NUMBER OF PASSES

Following the reasoning of the above sections, an amplifier with a large number of passes (N=8,12,16,) inheriting the same insensitivity to variations of the active medium lens and aperture effects can be realized by concatenating several of the 4-pass segments presented in Fig. 5.

An example of an 8-pass amplifier modeled according to this scheme is shown in Fig. 7. Size and phase front curvature of the output beam for an 8-pass and a 16-pass amplifier as a function of ΔV are shown in Figs. 8 and 9, respectively. The accumulation of lens and aperture effects in the 4f-based amplifiers becomes striking when considering the red dashed curves in these figures. In such multipass designs, the size of the output beam wout becomes significantly smaller than the input beam size win, while the phase front curvature 1/Rout of the output beam becomes increasingly sensitive to variations of ΔV (large slope of the red curves).

 figure: Fig. 7.

Fig. 7. 8-pass amplifier realized by concatenating two 4-pass amplifiers of Fig. 5(a). The same notation as in Fig. 1 has been used.

Download Full Size | PPT Slide | PDF

 figure: Fig. 8.

Fig. 8. Similar to Fig. 4, but for an 8-pass amplifier as given in Figs. 7 and 11. The black dashed lines represent the maximally allowed deviations for vanishing aperture effects given by Eqs. (25) and (26).

Download Full Size | PPT Slide | PDF

 figure: Fig. 9.

Fig. 9. Similar to Fig. 8, but for a 16-pass amplifier.

Download Full Size | PPT Slide | PDF

Contrarily, in the Fourier-based amplifiers the output beam characteristics show an oscillatory behavior around the design value for variations of ΔV. For vanishing aperture effects this oscillation is bound (see black dashed lines in Figs. 8 and 9) by the following relations:

win<wout,N(ΔV)<wstable2(ΔV)/win,
F2ΔV2<Rout,N1(ΔV)<F2ΔV2,
where wstable(ΔV) and Rstable1(ΔV) are the size and phase front radius obtained from Eq. (15) represented by the gray curves in Figs. 8 and 9. A nonvanishing aperture in the active medium leads to a damping of this oscillatory behavior so that the output beam characteristics approach the design value corresponding to the complex beam parameter qstable given in Eq. (15). In this case the gray curves represent the output beam characteristics for an infinite number of passes. A similar damping related with aperture effects has been discussed in detail also in the context of multipass oscillators [44].

The Taylor expansion of the complex beam parameter after a propagation through a Fourier-based 8-pass amplifier is

qout,8=iF+4F4ΔV˜3+16iF5ΔV˜440F6ΔV˜5+,
to be compared with the beam parameter after a 32-pass propagation
qout,32=iF+16F4ΔV˜3+256iF5ΔV˜42720F6ΔV˜5.
From these equations, the corresponding output beam sizes and phase front curvatures can be deduced for variations of ΔV. Assuming W= the results are
wout,8win=1+8F4ΔV432F6ΔV6+,
wout,32win=1+128F4ΔV410752F6ΔV6+,
Rout,81=4F2ΔV340F4ΔV5+32F6ΔV7+,
Rout,321=16F2ΔV32720F4ΔV5+132992F6ΔV7.
Similar to the Fourier-based 4-pass amplifiers, the output beam waist and divergence of the 8-, 16-, 32-pass amplifiers depend in lowest order on ΔV4 and ΔV3, respectively. The coefficients in front of ΔV4 and ΔV3 increase with the number of passes but still the maximal deviation from the design value (gray curves) is bound by the relations of Eqs. (25) and (26).

Alike previous sections we have investigated the dependence of the output beam size on the aperture size W. Assuming for simplicity that we are in the center of the “stability region” (V=ΔV=0) we find that

wout,8win=12win6W6+8win8W8+,
wout,32win=18win6W6+128win8W8+,
and that the phase front curvature of the output beam does not depend on the aperture size. Unlike the behavior for a 4f-based amplifier, the beam waist is converging toward the values of Eq. (15). The converging behavior that is apparent in the top panels of Figs. 8 and 9 does not obviously manifest from the Taylor expansions of Eqs. (27)–(34).

8. PRACTICAL REALIZATION

The Fourier-based multipass amplifiers sketched in the previous sections show excellent output beam stability for variations of V˜ but their practical implementation as such leads to long propagation lengths. In fact, the large mode size at the active medium needed for high-power and high-energy operation requires the use of large focal lengths F:

F=πwin2λ.
This result was obtained by solving Eq. (17) for F. For example, a beam size at the active medium of 1 mm requires F=3m for λ=1030nm so that each Fourier transform is 6 m long.

At the same time, it is challenging to realize an active medium with vanishing dioptric power V=Vunpumped+Vthermalavg=0 at the desired operational conditions as assumed in previous sections.

The realization of the Fourier transform propagation using two pairs of Galilean telescopes solves both these issues: it shortens the physical propagation length and allows for the use of active media with nonvanishing dioptric power. However, the focal lengths and the positions of the mirrors forming the telescope pairs must be chosen so that the propagations from active medium to active medium correspond approximatively to a Fourier transform, i.e., their ABCD-matrices must have the form A=D=0 and B=1/C=F.

In the thin-disk lasers sector it is customary to use thin disks (active media) with a focusing focal length (fAM). Therefore, as shown in Fig. 10(a), the active medium itself can be used as curved mirror to realize the Galilean telescopes. To fully define the layout of the Fourier transform, we need to further assume the position of the defocusing optical elements (lens or mirrors) forming the telescope pairs. In the layout shown in Fig. 10(a), it was assumed that these defocusing elements were placed at a distance 0.25L after and before the active media, where L is the distance from active medium to active medium. Under these assumptions, we find that the telescopic pair act as a Fourier transform when the focal length f of these defocusing elements fulfill the relation

f=12(4fAM+L)L3L8fAM+L28LfAM+32fAM2.
The resulting equivalent value of F takes then the form
F=fAM32(fAM/L)28fAM/L+1+4fAM/L(4fAM/L1)2.
As can be seen from Fig. 10(b), the ratio F/L, which describes the physical shortening factor of the Fourier transform length due to the implementation of the Galilean telescopes, rapidly increases with decreasing the fAM/L ratio. Thus, a small value of fAM/L via Eqs. (35) and (37) leads to a large beam size at the active medium, even for a short physical propagation length L.

 figure: Fig. 10.

Fig. 10. (a) Scheme of the optical Fourier transform from active medium to active medium obtained using two Galilean telescopes. The active medium itself (vertical lines at z=0 and z=1) acts as the focusing element of the telescopes with focal length fAM. The defocusing elements (cyan vertical lines) of the telescopes have focal length f given by Eq. (36) and are placed at a distance 0.25L from the active medium, where L is the distance between the two passes in the active medium. The beam size (w) evolution in the Fourier transform segment is given for three different values of the active medium focal length: fAM=L (solid), fAM=0.5L (dashed), and fAM=0.3L (dotted). (b) Effective focal length F of the Fourier transform as a function of the active medium focal length fAM expressed in units of L.

Download Full Size | PPT Slide | PDF

In the practical implementation, however, there is a limit in the minimal value of the focal length fAM given by the optical damage at the defocusing elements and the laser-induced breakdown in air. Indeed the beam sizes at the defocusing elements and in the focus of the telescopic system decrease with decreasing fAM.

We conclude by sketching the optical layout and the corresponding beam size evolution for two 8-pass Fourier-based amplifiers realized with the above-described Galilean telescopes. In these designs the active medium that has a focusing dioptric power V is also utilized as the focusing element of the Galilean telescope. In Fig. 11(a), the propagation from active medium to active medium follows the sequence

AMFourierAMLAMFourierAML,
where L is a short propagation distance compared to the Rayleigh length of the beam at the active medium, while in Fig. 11(b) the propagation from active medium to active medium follows the sequence
AMFourierAM4fAMFourierAM4f,
i.e., an alternation between Fourier- and 4f-propagations. The optical properties of the output beam for both these sequences corresponding to the two amplifier layout of Fig. 11 are shown in Fig. 8.

 figure: Fig. 11.

Fig. 11. (a) Scheme of an 8-pass Fourier-based amplifier obtained by concatenating two 4-pass amplifiers of Fig. 5(a). Each Fourier transform has been shortened using two Galilean telescopes. The active medium is also part of the Galilean telescope. Between two Fourier transforms, there is a short propagation of length L. (b) Similar to (a), but in this case the 8-pass amplifier is based on Fig. 5(b). Between each Fourier transform there is a 4f-imaging (indicated by the gray shaded area). The same notation as in Fig. 1 is used.

Download Full Size | PPT Slide | PDF

The shortening of the propagation due to the insertion of telescopes can be better appreciated with a numerical example. A large focal length of F=90m [see Eq. (35)] is needed to realize a multipass amplifier based on the scheme of Fig. 7 (without telescopes), having a beam size win=5.4mm and a wavelength of λ=1030nm. Assuming the short propagation length is L=1m the total length of the 8-pass amplifier would be Ltotal=720m. Using the layout of Fig. 11(a), the same beam size at the active medium can be obtained for an active medium with focal length fAM=1m and a defocusing element with focal length f=150mm placed at a distance of 861 mm. In this way the distance AM-Fourier-AM is reduced to 3.445 m (instead of 180 m). Assuming that L=1m the total length of the 8-pass amplifier is reduced to Ltotal=16.8m (instead of 720 m). Because this telescope reduces the beam size in the midplane of the Fourier transform to w=0.57mm, optical damage issues have to be considered. Yet, this beam size is significantly larger than the size of w=0.06mm in the focal plane of a 4f-imaging with f=1000mm.

9. CONCLUSION

Numerous studies have investigated the influence of the active medium thermal lens on resonator (oscillator) eigenmodes [33,45]. Oscillator designs have been developed that mitigate this influence, reducing the dependence of the oscillator performance and output beam characteristics to variations of the thermal lens of the active medium. However, similar studies have not (or insufficiently) been undertaken for multipass amplifiers. This might be associated with the fact that the 4f-relay imaging, that is commonly used when realizing multipass amplifiers, offers two obvious advantages. The first is that its imaging properties reproduce the same transverse intensity profile (size) from pass to pass independent of the size and shape of the beam and independent of the active medium dioptric power. The second is that several passes can be implemented with only few optical elements. Less obvious and known are the disadvantages. The first is that the beam size is reproduced only for a vanishing aperture effect at the active medium. Second, there is a pile up of phase front distortions at each pass on the active medium that strongly affects the output beam divergence and the beam quality. Imaging-based amplifiers are thus well suited for low-power lasers where the thermal lens is small but become less apt for high-power lasers with good output beam quality.

Here, we have presented a multipass amplifier architecture based on a succession of optical Fourier propagations. Contrary to the 4f-imaging the layout of this Fourier transform propagation needs to be designed to match the desired beam size at the active medium. Moreover, the implementation of this architecture requires one additional mirror for every pass, making it more complex compared to the 4f-based layouts. However, the implementation of these minor additional complexities is rewarded with the compensation of the thermal lens effects occurring in this architecture, which significantly decreases the sensitivity of size and divergence of the output beam to variations of the dioptric power and aperture effects of the active medium. Therefore, this architecture overcomes present energy- and power-scaling limitations related with the thermal lens effect in the active medium. Furthermore, the mode filtering that naturally occurs from the interplay between the Fourier transform propagations and the soft aperture of the active medium provides excellent beam quality with high efficiency.

We found that the output beam size and phase front radius of a Fourier-based multipass system are less sensitive to variations of the active medium thermal lens than a single-pass amplifier. Hence, from the point of view of the stability to thermal lens effects, it is advantageous to realize amplifiers as multipass amplifiers where the propagating beam is redirected several times to the same active medium. Various active media can be utilized provided they have identical or similar dioptric power. The multipass architecture presented here is thus particularly suited for thin-disk lasers where the gain per pass is small and multiple passes are required. An example of such a multipass amplifier realized according to this architecture is presented in Refs. [46,47], where the disk is acting as active medium, soft aperture, and focusing mirror of the Galilean telescopes used to realize the Fourier transform.

We want to point out that the here-presented architecture can be used in other contexts as well. For example, a recent development in Faraday insulators reduced the thermal lens effect resulting in TEM00 up to 400 W average power [48,49]. However, commercially available laser systems already provide output powers exceeding 10 kW [50]. In the laser system at advanced LIGO the focusing thermal lens effect of terbium gallium granate used in the Faraday rotator was compensated using a plate of deuterated potassium dihydrogen phosphate exhibiting a defocusing thermal lens [51]. Following our design [as presented in Fig. 3(b)] the effective thermal lens of the Faraday rotator can be almost canceled (see Fig. 4) without additional transmissive elements simply by splitting the rotator in two halves and by implementing a Fourier transform between them.

Funding

Swiss National Science Foundation (SNF 200021_165854); H2020 European Research Council (ERC) (ERC CoG. #725039, ERC StG. # 279765); ETH Research Grant (ETH-35 14-1); ETH Femtosecond and Attosecond Science and Technology (ETH-FAST) (NCCR MUST).

REFERENCES

1. S. Keppler, C. Wandt, M. Hornung, R. Bödefeld, A. Kessler, A. Sävert, M. Hellwing, F. Schorcht, J. Hein, and M. C. Kaluza, “Multipass amplifiers of POLARIS,” Proc. SPIE 8780, 87800I (2013). [CrossRef]  

2. J. Körner, J. Hein, M. Kahle, H. Liebetrau, M. Kaluza, M. Siebold, and M. Loeser, “High-efficiency cyrogenic-cooled diode-pumped amplifier with relay imaging for nanosecond pulses,” Proc. SPIE 8080, 80800D (2011). [CrossRef]  

3. J. Körner, J. Hein, and M. C. Kaluza, “Compact aberration-free relay-imaging multi-pass layouts for high-energy laser amplifiers,” Appl. Sci. 6, 353 (2016). [CrossRef]  

4. R. Jung, J. Tümmler, and I. Will, “Topic 1: High average power disk laser,” 2016, https://www.mbi-berlin.de/de/research/projects/1.2/topics/1_power_disk_laser/.

5. M. Siebold, “PENELOPE, Helmholtz-Zentrum Dresden-Rossendorf e. V,” 2016, https://www.hzdr.de/db/Cms?pNid=2098.

6. J.-P. Negel, A. Loescher, A. Voss, D. Bauer, D. Sutter, A. Killi, M. A. Ahmed, and T. Graf, “Ultrafast thin-disk multipass laser amplifier delivering 1.4 kW (4.7 mJ, 1030 nm) average power converted to 820 W at 515 nm and 234 W at 343 nm,” Opt. Express 23, 21064–21077 (2015). [CrossRef]  

7. F. Butze, M. Larionov, K. Schuhmann, C. Stolzenburg, and A. Giesen, “Nanosecond pulsed thin disk Yb:YAG lasers,” in Advanced Solid-State Photonics (TOPS) (2004), p. 237.

8. M. D. Martinez, J. K. Crane, L. A. Hackel, F. A. Penko, and D. F. Browning, “Optimized diode-pumped Nd:glass prototype regenerative amplifier for the national ignition facility (NIF),” Proc. SPIE 3267, 234–242 (1998). [CrossRef]  

9. A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994). [CrossRef]  

10. U. Brauch, A. Giesen, M. Karszewski, C. Stewen, and A. Voss, “Multiwatt diode-pumped Yb:YAG thin disk laser continuously tunable between 1018 and 1053 nm,” Opt. Lett. 20, 713–715 (1995). [CrossRef]  

11. C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW CW thin disc laser,” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000). [CrossRef]  

12. R. Peters, “Ytterbium-doped sesquioxides as highly efficient laser materials,” Ph.D. thesis (Department Physik der Universität Hamburg, 2009).

13. V. Chvykov, H. Cao, R. Nagymihaly, M. P. Kalashnikov, N. Khodakovskiy, R. Glassock, L. Ehrentraut, M. Schnuerer, and K. Osvay, “High peak and average power Ti:sapphire thin disk amplifier with extraction during pumping,” Opt. Lett. 41, 3017–3020 (2016). [CrossRef]  

14. A. Vaupel, N. Bodnar, B. Webb, L. Shah, M. Hemmer, E. Cormier, and M. Richardson, “Hybrid master oscillator power amplifier system providing 10 mJ, 32 W, and 50 MW pulses for optical parametric chirped-pulse amplification pumping,” J. Opt. Soc. Am. B 30, 3278–3283 (2013). [CrossRef]  

15. J. T. Hunt, J. A. Glaze, W. W. Simmons, and P. A. Renard, “Suppression of self-focusing through low-pass spatial filtering and relay imaging,” Appl. Opt. 17, 2053–2057 (1978). [CrossRef]  

16. P. Georges, F. Estable, F. Salin, J. P. Poizat, P. Grangier, and A. Brun, “High-efficiency multipass Ti:sapphire amplifiers for a continuous-wave single-mode laser,” Opt. Lett. 16, 144–146 (1991). [CrossRef]  

17. J. Wojtkiewicz and C. G. Durfee, “High-energy, high-contrast, double-confocal multipass amplifier,” Opt. Express 12, 1383–1388 (2004). [CrossRef]  

18. E. Kaksis, G. Almási, J. A. Fülöp, A. Pugžlys, A. Baltuška, and G. Andriukaitis, “110 mJ 225 fs cryogenically cooled Yb:CaF2 multipass amplifier,” Opt. Express 24, 28915–28922 (2016). [CrossRef]  

19. H. Plaessmann, S. A. Ré, J. J. Aionis, D. L. Vecht, and W. M. Grossman, “Multipass diode-pumped solid-state optical amplifier,” Opt. Lett. 18, 1420–1422 (1993). [CrossRef]  

20. P. Lundquist, S. Sarkisyan, E. A. Wilson, R. M. Copenhaver, H. Martin, and S. McCahon, “Off axis walk off multi-pass amplifiers,” U.S. patent 12954387 (24 November 2010).

21. H. Plaessmann, W. Grossman, and T. Olson, “Multi-pass light amplifier,” U.S. patent 08079640 (18 November 1992).

22. S. Erhard, A. Giesen, and C. Stewen, “Laser amplifier system,” U.S. patent 10208664 (5 February 2000).

23. A. M. Scott, G. Cook, and A. P. G. Davies, “Efficient high-gain laser amplification from a low-gain amplifier by use of self-imaging multipass geometry,” Appl. Opt. 40, 2461–2467 (2001). [CrossRef]  

24. D. N. Papadopoulos, A. Pellegrina, L. P. Ramirez, P. Georges, and F. Druon, “Broadband high-energy diode-pumped Yb:KYW multipass amplifier,” Opt. Lett. 36, 3816–3818 (2011). [CrossRef]  

25. S. Banerjee, K. Ertel, P. D. Mason, P. J. Phillips, M. Siebold, M. Loeser, C. Hernandez-Gomez, and J. L. Collier, “High-efficiency 10 J diode pumped cryogenic gas cooled Yb:YAG multislab amplifier,” Opt. Lett. 37, 2175–2177 (2012). [CrossRef]  

26. J. Neuhaus, D. Bauer, J. Zhang, A. Killi, J. Kleinbauer, M. Kumkar, S. Weiler, M. Guina, D. H. Sutter, and T. Dekorsy, “Subpicosecond thin-disk laser oscillator with pulse energies of up to 25.9 microjoules by use of an active multipass geometry,” Opt. Express 16, 20530–20539 (2008). [CrossRef]  

27. L. M. Osterink and J. D. Foster, “Thermal effects and transverse mode control in a Nd:YAG laser,” Appl. Phys. Lett. 12, 128–131 (1968). [CrossRef]  

28. W. Koechner, “Thermal lensing in a Nd:YAG laser rod,” Appl. Opt. 9, 2548–2553 (1970). [CrossRef]  

29. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966). [CrossRef]  

30. K. Schuhmann, “The thin-disk laser for the 2S–2P measurement in muonic helium,” Ph.D. thesis (Institute for Particle Physics and Astrophysics, ETH Zürich, 2017).

31. A. Siegman, Lasers (University Science Books, 1986).

32. J. M. Eggleston, G. Giuliani, and R. L. Byer, “Radial intensity filters using radial birefringent elements,” J. Opt. Soc. Am. 71, 1264–1272 (1981). [CrossRef]  

33. H. Kogelnik, “On the propagation of Gaussian beams of light through lenslike media including those with a loss or gain variation,” Appl. Opt. 4, 1562–1569 (1965). [CrossRef]  

34. M. S. Bowers, “Diffractive analysis of unstable optical resonators with super-Gaussian mirrors,” Opt. Lett. 17, 1319–1321 (1992). [CrossRef]  

35. L. C. Andrews and W. B. Miller, “Single-pass and double-pass propagation through complex paraxial optical systems,” J. Opt. Soc. Am. A 12, 137–150 (1995). [CrossRef]  

36. V. L. Kalashnikov, I. G. Poloyko, V. P. Mikhailov, and D. von der Linde, “Regular, quasi-periodic, and chaotic behavior in continuous-wave solid-state Kerr-lens mode-locked lasers,” J. Opt. Soc. Am. B 14, 2691–2695 (1997). [CrossRef]  

37. M. Pittman, S. Ferré, J. Rousseau, L. Notebaert, J. Chambaret, and G. Chériaux, “Design and characterization of a near-diffraction-limited femtosecond 100-TW 10-Hz high-intensity laser system,” Appl. Phys. B 74, 529–535 (2002). [CrossRef]  

38. F. Friebel, A. Pellegrina, D. N. Papadopoulos, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Diode-pumped Yb: CaF2 multipass amplifier producing 50 mJ with dynamic analysis for high repetition rate operation,” Appl. Phys. B 117, 597–603 (2014). [CrossRef]  

39. J. Neuhaus, “Passively mode-locked yb:yag thin-disk laser with active multipass geometry,” Ph.D. thesis (Universität Konstanz, 2009).

40. A. Sullivan, H. Hamster, H. C. Kapteyn, S. Gordon, W. White, H. Nathel, R. J. Blair, and R. W. Falcone, “Multiterawatt, 100-fs laser,” Opt. Lett. 16, 1406–1408 (1991). [CrossRef]  

41. P. Rambo, J. Schwarz, M. Kimmel, and J. L. Porter, “Development of high damage threshold laser-machined apodizers and gain filters for laser applications,” High Power Laser Sci. Eng. 4e32 (2016). [CrossRef]  

42. S. Banerjee, K. Ertel, P. D. Mason, P. J. Phillips, M. De Vido, J. M. Smith, T. J. Butcher, C. Hernandez-Gomez, R. J. S. Greenhalgh, and J. L. Collier, “DiPOLE: a 10 J, 10 Hz cryogenic gas cooled multi-slab nanosecond Yb:YAG laser,” Opt. Express 23, 19542–19551 (2015). [CrossRef]  

43. T. J. Yu, S. K. Lee, J. H. Sung, J. W. Yoon, T. M. Jeong, and J. Lee, “Generation of high-contrast, 30 fs, 1.5 PW laser pulses from chirped-pulse amplification Ti:sapphire laser,” Opt. Express 20, 10807–10815 (2012). [CrossRef]  

44. K. Schuhmann, K. Kirch, and A. Antognini, “Multi-pass resonator design for energy scaling of mode-locked thin-disk lasers,” Proc. SPIE 10082, 100820J (2017). [CrossRef]  

45. V. Magni, “Resonators for solid-state lasers with large-volume fundamental mode and high alignment stability,” Appl. Opt. 25, 107–117 (1986). [CrossRef]  

46. A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009). [CrossRef]  

47. K. Schuhmann, M. A. Ahmed, A. Antognini, T. Graf, T. W. Hänsch, K. Kirch, F. Kottmann, R. Pohl, D. Taqqu, A. Voss, and B. Weichelt, “Thin-disk laser multi-pass amplifier,” Proc. SPIE 9342, 93420U (2015). [CrossRef]  

48. K. T. Stevens, W. Schlichting, G. Foundos, A. Payne, and E. Rogers, “Promising materials for high power laser isolators,” Laser Technik J. 13, 18–21 (2016). [CrossRef]  

49. Electro-Optics Technology, Inc., “Pavos ultra series,” 2018, http://www.eotech.com/content/userfiles/Pavos%20Ultra-Rotators%20and%20Isolators.pdf.

50. IPG Photonics Corporation, “High power CW fiber lasers,” https://www.ipgphotonics.com/en/products/lasers/high-power-cw-fiber-lasers.

51. V. Zelenogorsky, O. Palashov, and E. Khazanov, “Adaptive compensation of thermally induced phase aberrations in Faraday isolators by means of a DKDP crystal,” Opt. Commun. 278, 8–13 (2007). [CrossRef]  

References

  • View by:

  1. S. Keppler, C. Wandt, M. Hornung, R. Bödefeld, A. Kessler, A. Sävert, M. Hellwing, F. Schorcht, J. Hein, and M. C. Kaluza, “Multipass amplifiers of POLARIS,” Proc. SPIE 8780, 87800I (2013).
    [Crossref]
  2. J. Körner, J. Hein, M. Kahle, H. Liebetrau, M. Kaluza, M. Siebold, and M. Loeser, “High-efficiency cyrogenic-cooled diode-pumped amplifier with relay imaging for nanosecond pulses,” Proc. SPIE 8080, 80800D (2011).
    [Crossref]
  3. J. Körner, J. Hein, and M. C. Kaluza, “Compact aberration-free relay-imaging multi-pass layouts for high-energy laser amplifiers,” Appl. Sci. 6, 353 (2016).
    [Crossref]
  4. R. Jung, J. Tümmler, and I. Will, “Topic 1: High average power disk laser,” 2016, https://www.mbi-berlin.de/de/research/projects/1.2/topics/1_power_disk_laser/ .
  5. M. Siebold, “PENELOPE, Helmholtz-Zentrum Dresden-Rossendorf e. V,” 2016, https://www.hzdr.de/db/Cms?pNid=2098 .
  6. J.-P. Negel, A. Loescher, A. Voss, D. Bauer, D. Sutter, A. Killi, M. A. Ahmed, and T. Graf, “Ultrafast thin-disk multipass laser amplifier delivering 1.4 kW (4.7 mJ, 1030 nm) average power converted to 820 W at 515 nm and 234 W at 343 nm,” Opt. Express 23, 21064–21077 (2015).
    [Crossref]
  7. F. Butze, M. Larionov, K. Schuhmann, C. Stolzenburg, and A. Giesen, “Nanosecond pulsed thin disk Yb:YAG lasers,” in Advanced Solid-State Photonics (TOPS) (2004), p. 237.
  8. M. D. Martinez, J. K. Crane, L. A. Hackel, F. A. Penko, and D. F. Browning, “Optimized diode-pumped Nd:glass prototype regenerative amplifier for the national ignition facility (NIF),” Proc. SPIE 3267, 234–242 (1998).
    [Crossref]
  9. A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).
    [Crossref]
  10. U. Brauch, A. Giesen, M. Karszewski, C. Stewen, and A. Voss, “Multiwatt diode-pumped Yb:YAG thin disk laser continuously tunable between 1018 and 1053 nm,” Opt. Lett. 20, 713–715 (1995).
    [Crossref]
  11. C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW CW thin disc laser,” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).
    [Crossref]
  12. R. Peters, “Ytterbium-doped sesquioxides as highly efficient laser materials,” Ph.D. thesis (Department Physik der Universität Hamburg, 2009).
  13. V. Chvykov, H. Cao, R. Nagymihaly, M. P. Kalashnikov, N. Khodakovskiy, R. Glassock, L. Ehrentraut, M. Schnuerer, and K. Osvay, “High peak and average power Ti:sapphire thin disk amplifier with extraction during pumping,” Opt. Lett. 41, 3017–3020 (2016).
    [Crossref]
  14. A. Vaupel, N. Bodnar, B. Webb, L. Shah, M. Hemmer, E. Cormier, and M. Richardson, “Hybrid master oscillator power amplifier system providing 10 mJ, 32 W, and 50 MW pulses for optical parametric chirped-pulse amplification pumping,” J. Opt. Soc. Am. B 30, 3278–3283 (2013).
    [Crossref]
  15. J. T. Hunt, J. A. Glaze, W. W. Simmons, and P. A. Renard, “Suppression of self-focusing through low-pass spatial filtering and relay imaging,” Appl. Opt. 17, 2053–2057 (1978).
    [Crossref]
  16. P. Georges, F. Estable, F. Salin, J. P. Poizat, P. Grangier, and A. Brun, “High-efficiency multipass Ti:sapphire amplifiers for a continuous-wave single-mode laser,” Opt. Lett. 16, 144–146 (1991).
    [Crossref]
  17. J. Wojtkiewicz and C. G. Durfee, “High-energy, high-contrast, double-confocal multipass amplifier,” Opt. Express 12, 1383–1388 (2004).
    [Crossref]
  18. E. Kaksis, G. Almási, J. A. Fülöp, A. Pugžlys, A. Baltuška, and G. Andriukaitis, “110 mJ 225 fs cryogenically cooled Yb:CaF2 multipass amplifier,” Opt. Express 24, 28915–28922 (2016).
    [Crossref]
  19. H. Plaessmann, S. A. Ré, J. J. Aionis, D. L. Vecht, and W. M. Grossman, “Multipass diode-pumped solid-state optical amplifier,” Opt. Lett. 18, 1420–1422 (1993).
    [Crossref]
  20. P. Lundquist, S. Sarkisyan, E. A. Wilson, R. M. Copenhaver, H. Martin, and S. McCahon, “Off axis walk off multi-pass amplifiers,” U.S. patent12954387 (24November2010).
  21. H. Plaessmann, W. Grossman, and T. Olson, “Multi-pass light amplifier,” U.S. patent08079640 (18November1992).
  22. S. Erhard, A. Giesen, and C. Stewen, “Laser amplifier system,” U.S. patent10208664 (5February2000).
  23. A. M. Scott, G. Cook, and A. P. G. Davies, “Efficient high-gain laser amplification from a low-gain amplifier by use of self-imaging multipass geometry,” Appl. Opt. 40, 2461–2467 (2001).
    [Crossref]
  24. D. N. Papadopoulos, A. Pellegrina, L. P. Ramirez, P. Georges, and F. Druon, “Broadband high-energy diode-pumped Yb:KYW multipass amplifier,” Opt. Lett. 36, 3816–3818 (2011).
    [Crossref]
  25. S. Banerjee, K. Ertel, P. D. Mason, P. J. Phillips, M. Siebold, M. Loeser, C. Hernandez-Gomez, and J. L. Collier, “High-efficiency 10 J diode pumped cryogenic gas cooled Yb:YAG multislab amplifier,” Opt. Lett. 37, 2175–2177 (2012).
    [Crossref]
  26. J. Neuhaus, D. Bauer, J. Zhang, A. Killi, J. Kleinbauer, M. Kumkar, S. Weiler, M. Guina, D. H. Sutter, and T. Dekorsy, “Subpicosecond thin-disk laser oscillator with pulse energies of up to 25.9 microjoules by use of an active multipass geometry,” Opt. Express 16, 20530–20539 (2008).
    [Crossref]
  27. L. M. Osterink and J. D. Foster, “Thermal effects and transverse mode control in a Nd:YAG laser,” Appl. Phys. Lett. 12, 128–131 (1968).
    [Crossref]
  28. W. Koechner, “Thermal lensing in a Nd:YAG laser rod,” Appl. Opt. 9, 2548–2553 (1970).
    [Crossref]
  29. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
    [Crossref]
  30. K. Schuhmann, “The thin-disk laser for the 2S–2P measurement in muonic helium,” Ph.D. thesis (Institute for Particle Physics and Astrophysics, ETH Zürich, 2017).
  31. A. Siegman, Lasers (University Science Books, 1986).
  32. J. M. Eggleston, G. Giuliani, and R. L. Byer, “Radial intensity filters using radial birefringent elements,” J. Opt. Soc. Am. 71, 1264–1272 (1981).
    [Crossref]
  33. H. Kogelnik, “On the propagation of Gaussian beams of light through lenslike media including those with a loss or gain variation,” Appl. Opt. 4, 1562–1569 (1965).
    [Crossref]
  34. M. S. Bowers, “Diffractive analysis of unstable optical resonators with super-Gaussian mirrors,” Opt. Lett. 17, 1319–1321 (1992).
    [Crossref]
  35. L. C. Andrews and W. B. Miller, “Single-pass and double-pass propagation through complex paraxial optical systems,” J. Opt. Soc. Am. A 12, 137–150 (1995).
    [Crossref]
  36. V. L. Kalashnikov, I. G. Poloyko, V. P. Mikhailov, and D. von der Linde, “Regular, quasi-periodic, and chaotic behavior in continuous-wave solid-state Kerr-lens mode-locked lasers,” J. Opt. Soc. Am. B 14, 2691–2695 (1997).
    [Crossref]
  37. M. Pittman, S. Ferré, J. Rousseau, L. Notebaert, J. Chambaret, and G. Chériaux, “Design and characterization of a near-diffraction-limited femtosecond 100-TW 10-Hz high-intensity laser system,” Appl. Phys. B 74, 529–535 (2002).
    [Crossref]
  38. F. Friebel, A. Pellegrina, D. N. Papadopoulos, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Diode-pumped Yb: CaF2 multipass amplifier producing 50 mJ with dynamic analysis for high repetition rate operation,” Appl. Phys. B 117, 597–603 (2014).
    [Crossref]
  39. J. Neuhaus, “Passively mode-locked yb:yag thin-disk laser with active multipass geometry,” Ph.D. thesis (Universität Konstanz, 2009).
  40. A. Sullivan, H. Hamster, H. C. Kapteyn, S. Gordon, W. White, H. Nathel, R. J. Blair, and R. W. Falcone, “Multiterawatt, 100-fs laser,” Opt. Lett. 16, 1406–1408 (1991).
    [Crossref]
  41. P. Rambo, J. Schwarz, M. Kimmel, and J. L. Porter, “Development of high damage threshold laser-machined apodizers and gain filters for laser applications,” High Power Laser Sci. Eng. 4e32 (2016).
    [Crossref]
  42. S. Banerjee, K. Ertel, P. D. Mason, P. J. Phillips, M. De Vido, J. M. Smith, T. J. Butcher, C. Hernandez-Gomez, R. J. S. Greenhalgh, and J. L. Collier, “DiPOLE: a 10 J, 10 Hz cryogenic gas cooled multi-slab nanosecond Yb:YAG laser,” Opt. Express 23, 19542–19551 (2015).
    [Crossref]
  43. T. J. Yu, S. K. Lee, J. H. Sung, J. W. Yoon, T. M. Jeong, and J. Lee, “Generation of high-contrast, 30 fs, 1.5 PW laser pulses from chirped-pulse amplification Ti:sapphire laser,” Opt. Express 20, 10807–10815 (2012).
    [Crossref]
  44. K. Schuhmann, K. Kirch, and A. Antognini, “Multi-pass resonator design for energy scaling of mode-locked thin-disk lasers,” Proc. SPIE 10082, 100820J (2017).
    [Crossref]
  45. V. Magni, “Resonators for solid-state lasers with large-volume fundamental mode and high alignment stability,” Appl. Opt. 25, 107–117 (1986).
    [Crossref]
  46. A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
    [Crossref]
  47. K. Schuhmann, M. A. Ahmed, A. Antognini, T. Graf, T. W. Hänsch, K. Kirch, F. Kottmann, R. Pohl, D. Taqqu, A. Voss, and B. Weichelt, “Thin-disk laser multi-pass amplifier,” Proc. SPIE 9342, 93420U (2015).
    [Crossref]
  48. K. T. Stevens, W. Schlichting, G. Foundos, A. Payne, and E. Rogers, “Promising materials for high power laser isolators,” Laser Technik J. 13, 18–21 (2016).
    [Crossref]
  49. Electro-Optics Technology, Inc., “Pavos ultra series,” 2018, http://www.eotech.com/content/userfiles/Pavos%20Ultra-Rotators%20and%20Isolators.pdf .
  50. IPG Photonics Corporation, “High power CW fiber lasers,” https://www.ipgphotonics.com/en/products/lasers/high-power-cw-fiber-lasers .
  51. V. Zelenogorsky, O. Palashov, and E. Khazanov, “Adaptive compensation of thermally induced phase aberrations in Faraday isolators by means of a DKDP crystal,” Opt. Commun. 278, 8–13 (2007).
    [Crossref]

2017 (1)

K. Schuhmann, K. Kirch, and A. Antognini, “Multi-pass resonator design for energy scaling of mode-locked thin-disk lasers,” Proc. SPIE 10082, 100820J (2017).
[Crossref]

2016 (5)

P. Rambo, J. Schwarz, M. Kimmel, and J. L. Porter, “Development of high damage threshold laser-machined apodizers and gain filters for laser applications,” High Power Laser Sci. Eng. 4e32 (2016).
[Crossref]

J. Körner, J. Hein, and M. C. Kaluza, “Compact aberration-free relay-imaging multi-pass layouts for high-energy laser amplifiers,” Appl. Sci. 6, 353 (2016).
[Crossref]

V. Chvykov, H. Cao, R. Nagymihaly, M. P. Kalashnikov, N. Khodakovskiy, R. Glassock, L. Ehrentraut, M. Schnuerer, and K. Osvay, “High peak and average power Ti:sapphire thin disk amplifier with extraction during pumping,” Opt. Lett. 41, 3017–3020 (2016).
[Crossref]

E. Kaksis, G. Almási, J. A. Fülöp, A. Pugžlys, A. Baltuška, and G. Andriukaitis, “110 mJ 225 fs cryogenically cooled Yb:CaF2 multipass amplifier,” Opt. Express 24, 28915–28922 (2016).
[Crossref]

K. T. Stevens, W. Schlichting, G. Foundos, A. Payne, and E. Rogers, “Promising materials for high power laser isolators,” Laser Technik J. 13, 18–21 (2016).
[Crossref]

2015 (3)

2014 (1)

F. Friebel, A. Pellegrina, D. N. Papadopoulos, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Diode-pumped Yb: CaF2 multipass amplifier producing 50 mJ with dynamic analysis for high repetition rate operation,” Appl. Phys. B 117, 597–603 (2014).
[Crossref]

2013 (2)

2012 (2)

2011 (2)

D. N. Papadopoulos, A. Pellegrina, L. P. Ramirez, P. Georges, and F. Druon, “Broadband high-energy diode-pumped Yb:KYW multipass amplifier,” Opt. Lett. 36, 3816–3818 (2011).
[Crossref]

J. Körner, J. Hein, M. Kahle, H. Liebetrau, M. Kaluza, M. Siebold, and M. Loeser, “High-efficiency cyrogenic-cooled diode-pumped amplifier with relay imaging for nanosecond pulses,” Proc. SPIE 8080, 80800D (2011).
[Crossref]

2009 (1)

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

2008 (1)

2007 (1)

V. Zelenogorsky, O. Palashov, and E. Khazanov, “Adaptive compensation of thermally induced phase aberrations in Faraday isolators by means of a DKDP crystal,” Opt. Commun. 278, 8–13 (2007).
[Crossref]

2004 (1)

2002 (1)

M. Pittman, S. Ferré, J. Rousseau, L. Notebaert, J. Chambaret, and G. Chériaux, “Design and characterization of a near-diffraction-limited femtosecond 100-TW 10-Hz high-intensity laser system,” Appl. Phys. B 74, 529–535 (2002).
[Crossref]

2001 (1)

2000 (1)

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW CW thin disc laser,” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).
[Crossref]

1998 (1)

M. D. Martinez, J. K. Crane, L. A. Hackel, F. A. Penko, and D. F. Browning, “Optimized diode-pumped Nd:glass prototype regenerative amplifier for the national ignition facility (NIF),” Proc. SPIE 3267, 234–242 (1998).
[Crossref]

1997 (1)

1995 (2)

1994 (1)

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).
[Crossref]

1993 (1)

1992 (1)

1991 (2)

1986 (1)

1981 (1)

1978 (1)

1970 (1)

1968 (1)

L. M. Osterink and J. D. Foster, “Thermal effects and transverse mode control in a Nd:YAG laser,” Appl. Phys. Lett. 12, 128–131 (1968).
[Crossref]

1966 (1)

1965 (1)

Ahmed, M. A.

Aionis, J. J.

Almási, G.

Amaro, F. D.

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Andrews, L. C.

Andriukaitis, G.

Antognini, A.

K. Schuhmann, K. Kirch, and A. Antognini, “Multi-pass resonator design for energy scaling of mode-locked thin-disk lasers,” Proc. SPIE 10082, 100820J (2017).
[Crossref]

K. Schuhmann, M. A. Ahmed, A. Antognini, T. Graf, T. W. Hänsch, K. Kirch, F. Kottmann, R. Pohl, D. Taqqu, A. Voss, and B. Weichelt, “Thin-disk laser multi-pass amplifier,” Proc. SPIE 9342, 93420U (2015).
[Crossref]

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Baltuška, A.

Banerjee, S.

Bauer, D.

Bigot, E. L.

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Biraben, F.

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Blair, R. J.

Bödefeld, R.

S. Keppler, C. Wandt, M. Hornung, R. Bödefeld, A. Kessler, A. Sävert, M. Hellwing, F. Schorcht, J. Hein, and M. C. Kaluza, “Multipass amplifiers of POLARIS,” Proc. SPIE 8780, 87800I (2013).
[Crossref]

Bodnar, N.

Bowers, M. S.

Brauch, U.

U. Brauch, A. Giesen, M. Karszewski, C. Stewen, and A. Voss, “Multiwatt diode-pumped Yb:YAG thin disk laser continuously tunable between 1018 and 1053 nm,” Opt. Lett. 20, 713–715 (1995).
[Crossref]

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).
[Crossref]

Browning, D. F.

M. D. Martinez, J. K. Crane, L. A. Hackel, F. A. Penko, and D. F. Browning, “Optimized diode-pumped Nd:glass prototype regenerative amplifier for the national ignition facility (NIF),” Proc. SPIE 3267, 234–242 (1998).
[Crossref]

Brun, A.

Butcher, T. J.

Butze, F.

F. Butze, M. Larionov, K. Schuhmann, C. Stolzenburg, and A. Giesen, “Nanosecond pulsed thin disk Yb:YAG lasers,” in Advanced Solid-State Photonics (TOPS) (2004), p. 237.

Byer, R. L.

Camy, P.

F. Friebel, A. Pellegrina, D. N. Papadopoulos, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Diode-pumped Yb: CaF2 multipass amplifier producing 50 mJ with dynamic analysis for high repetition rate operation,” Appl. Phys. B 117, 597–603 (2014).
[Crossref]

Cao, H.

Chambaret, J.

M. Pittman, S. Ferré, J. Rousseau, L. Notebaert, J. Chambaret, and G. Chériaux, “Design and characterization of a near-diffraction-limited femtosecond 100-TW 10-Hz high-intensity laser system,” Appl. Phys. B 74, 529–535 (2002).
[Crossref]

Chériaux, G.

M. Pittman, S. Ferré, J. Rousseau, L. Notebaert, J. Chambaret, and G. Chériaux, “Design and characterization of a near-diffraction-limited femtosecond 100-TW 10-Hz high-intensity laser system,” Appl. Phys. B 74, 529–535 (2002).
[Crossref]

Chvykov, V.

Collier, J. L.

Contag, K.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW CW thin disc laser,” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).
[Crossref]

Cook, G.

Copenhaver, R. M.

P. Lundquist, S. Sarkisyan, E. A. Wilson, R. M. Copenhaver, H. Martin, and S. McCahon, “Off axis walk off multi-pass amplifiers,” U.S. patent12954387 (24November2010).

Cormier, E.

Crane, J. K.

M. D. Martinez, J. K. Crane, L. A. Hackel, F. A. Penko, and D. F. Browning, “Optimized diode-pumped Nd:glass prototype regenerative amplifier for the national ignition facility (NIF),” Proc. SPIE 3267, 234–242 (1998).
[Crossref]

Davies, A. P. G.

Dax, A.

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

De Vido, M.

Dekorsy, T.

Doualan, J.-L.

F. Friebel, A. Pellegrina, D. N. Papadopoulos, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Diode-pumped Yb: CaF2 multipass amplifier producing 50 mJ with dynamic analysis for high repetition rate operation,” Appl. Phys. B 117, 597–603 (2014).
[Crossref]

Druon, F.

F. Friebel, A. Pellegrina, D. N. Papadopoulos, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Diode-pumped Yb: CaF2 multipass amplifier producing 50 mJ with dynamic analysis for high repetition rate operation,” Appl. Phys. B 117, 597–603 (2014).
[Crossref]

D. N. Papadopoulos, A. Pellegrina, L. P. Ramirez, P. Georges, and F. Druon, “Broadband high-energy diode-pumped Yb:KYW multipass amplifier,” Opt. Lett. 36, 3816–3818 (2011).
[Crossref]

Durfee, C. G.

Eggleston, J. M.

Ehrentraut, L.

Erhard, S.

S. Erhard, A. Giesen, and C. Stewen, “Laser amplifier system,” U.S. patent10208664 (5February2000).

Ertel, K.

Estable, F.

Falcone, R. W.

Ferré, S.

M. Pittman, S. Ferré, J. Rousseau, L. Notebaert, J. Chambaret, and G. Chériaux, “Design and characterization of a near-diffraction-limited femtosecond 100-TW 10-Hz high-intensity laser system,” Appl. Phys. B 74, 529–535 (2002).
[Crossref]

Foster, J. D.

L. M. Osterink and J. D. Foster, “Thermal effects and transverse mode control in a Nd:YAG laser,” Appl. Phys. Lett. 12, 128–131 (1968).
[Crossref]

Foundos, G.

K. T. Stevens, W. Schlichting, G. Foundos, A. Payne, and E. Rogers, “Promising materials for high power laser isolators,” Laser Technik J. 13, 18–21 (2016).
[Crossref]

Friebel, F.

F. Friebel, A. Pellegrina, D. N. Papadopoulos, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Diode-pumped Yb: CaF2 multipass amplifier producing 50 mJ with dynamic analysis for high repetition rate operation,” Appl. Phys. B 117, 597–603 (2014).
[Crossref]

Fülöp, J. A.

Georges, P.

Giesen, A.

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW CW thin disc laser,” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).
[Crossref]

U. Brauch, A. Giesen, M. Karszewski, C. Stewen, and A. Voss, “Multiwatt diode-pumped Yb:YAG thin disk laser continuously tunable between 1018 and 1053 nm,” Opt. Lett. 20, 713–715 (1995).
[Crossref]

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).
[Crossref]

F. Butze, M. Larionov, K. Schuhmann, C. Stolzenburg, and A. Giesen, “Nanosecond pulsed thin disk Yb:YAG lasers,” in Advanced Solid-State Photonics (TOPS) (2004), p. 237.

S. Erhard, A. Giesen, and C. Stewen, “Laser amplifier system,” U.S. patent10208664 (5February2000).

Giuliani, G.

Glassock, R.

Glaze, J. A.

Gordon, S.

Graf, T.

K. Schuhmann, M. A. Ahmed, A. Antognini, T. Graf, T. W. Hänsch, K. Kirch, F. Kottmann, R. Pohl, D. Taqqu, A. Voss, and B. Weichelt, “Thin-disk laser multi-pass amplifier,” Proc. SPIE 9342, 93420U (2015).
[Crossref]

J.-P. Negel, A. Loescher, A. Voss, D. Bauer, D. Sutter, A. Killi, M. A. Ahmed, and T. Graf, “Ultrafast thin-disk multipass laser amplifier delivering 1.4 kW (4.7 mJ, 1030 nm) average power converted to 820 W at 515 nm and 234 W at 343 nm,” Opt. Express 23, 21064–21077 (2015).
[Crossref]

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Grangier, P.

Greenhalgh, R. J. S.

Grossman, W.

H. Plaessmann, W. Grossman, and T. Olson, “Multi-pass light amplifier,” U.S. patent08079640 (18November1992).

Grossman, W. M.

Guina, M.

Hackel, L. A.

M. D. Martinez, J. K. Crane, L. A. Hackel, F. A. Penko, and D. F. Browning, “Optimized diode-pumped Nd:glass prototype regenerative amplifier for the national ignition facility (NIF),” Proc. SPIE 3267, 234–242 (1998).
[Crossref]

Hamster, H.

Hänsch, T. W.

K. Schuhmann, M. A. Ahmed, A. Antognini, T. Graf, T. W. Hänsch, K. Kirch, F. Kottmann, R. Pohl, D. Taqqu, A. Voss, and B. Weichelt, “Thin-disk laser multi-pass amplifier,” Proc. SPIE 9342, 93420U (2015).
[Crossref]

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Hein, J.

J. Körner, J. Hein, and M. C. Kaluza, “Compact aberration-free relay-imaging multi-pass layouts for high-energy laser amplifiers,” Appl. Sci. 6, 353 (2016).
[Crossref]

S. Keppler, C. Wandt, M. Hornung, R. Bödefeld, A. Kessler, A. Sävert, M. Hellwing, F. Schorcht, J. Hein, and M. C. Kaluza, “Multipass amplifiers of POLARIS,” Proc. SPIE 8780, 87800I (2013).
[Crossref]

J. Körner, J. Hein, M. Kahle, H. Liebetrau, M. Kaluza, M. Siebold, and M. Loeser, “High-efficiency cyrogenic-cooled diode-pumped amplifier with relay imaging for nanosecond pulses,” Proc. SPIE 8080, 80800D (2011).
[Crossref]

Hellwing, M.

S. Keppler, C. Wandt, M. Hornung, R. Bödefeld, A. Kessler, A. Sävert, M. Hellwing, F. Schorcht, J. Hein, and M. C. Kaluza, “Multipass amplifiers of POLARIS,” Proc. SPIE 8780, 87800I (2013).
[Crossref]

Hemmer, M.

Hernandez-Gomez, C.

Hornung, M.

S. Keppler, C. Wandt, M. Hornung, R. Bödefeld, A. Kessler, A. Sävert, M. Hellwing, F. Schorcht, J. Hein, and M. C. Kaluza, “Multipass amplifiers of POLARIS,” Proc. SPIE 8780, 87800I (2013).
[Crossref]

Hugel, H.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW CW thin disc laser,” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).
[Crossref]

Hügel, H.

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).
[Crossref]

Hunt, J. T.

Indelicato, P.

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Jeong, T. M.

Julien, L.

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Kahle, M.

J. Körner, J. Hein, M. Kahle, H. Liebetrau, M. Kaluza, M. Siebold, and M. Loeser, “High-efficiency cyrogenic-cooled diode-pumped amplifier with relay imaging for nanosecond pulses,” Proc. SPIE 8080, 80800D (2011).
[Crossref]

Kaksis, E.

Kalashnikov, M. P.

Kalashnikov, V. L.

Kaluza, M.

J. Körner, J. Hein, M. Kahle, H. Liebetrau, M. Kaluza, M. Siebold, and M. Loeser, “High-efficiency cyrogenic-cooled diode-pumped amplifier with relay imaging for nanosecond pulses,” Proc. SPIE 8080, 80800D (2011).
[Crossref]

Kaluza, M. C.

J. Körner, J. Hein, and M. C. Kaluza, “Compact aberration-free relay-imaging multi-pass layouts for high-energy laser amplifiers,” Appl. Sci. 6, 353 (2016).
[Crossref]

S. Keppler, C. Wandt, M. Hornung, R. Bödefeld, A. Kessler, A. Sävert, M. Hellwing, F. Schorcht, J. Hein, and M. C. Kaluza, “Multipass amplifiers of POLARIS,” Proc. SPIE 8780, 87800I (2013).
[Crossref]

Kao, C. Y.

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Kapteyn, H. C.

Karszewski, M.

Keppler, S.

S. Keppler, C. Wandt, M. Hornung, R. Bödefeld, A. Kessler, A. Sävert, M. Hellwing, F. Schorcht, J. Hein, and M. C. Kaluza, “Multipass amplifiers of POLARIS,” Proc. SPIE 8780, 87800I (2013).
[Crossref]

Kessler, A.

S. Keppler, C. Wandt, M. Hornung, R. Bödefeld, A. Kessler, A. Sävert, M. Hellwing, F. Schorcht, J. Hein, and M. C. Kaluza, “Multipass amplifiers of POLARIS,” Proc. SPIE 8780, 87800I (2013).
[Crossref]

Khazanov, E.

V. Zelenogorsky, O. Palashov, and E. Khazanov, “Adaptive compensation of thermally induced phase aberrations in Faraday isolators by means of a DKDP crystal,” Opt. Commun. 278, 8–13 (2007).
[Crossref]

Khodakovskiy, N.

Killi, A.

Kimmel, M.

P. Rambo, J. Schwarz, M. Kimmel, and J. L. Porter, “Development of high damage threshold laser-machined apodizers and gain filters for laser applications,” High Power Laser Sci. Eng. 4e32 (2016).
[Crossref]

Kirch, K.

K. Schuhmann, K. Kirch, and A. Antognini, “Multi-pass resonator design for energy scaling of mode-locked thin-disk lasers,” Proc. SPIE 10082, 100820J (2017).
[Crossref]

K. Schuhmann, M. A. Ahmed, A. Antognini, T. Graf, T. W. Hänsch, K. Kirch, F. Kottmann, R. Pohl, D. Taqqu, A. Voss, and B. Weichelt, “Thin-disk laser multi-pass amplifier,” Proc. SPIE 9342, 93420U (2015).
[Crossref]

Kleinbauer, J.

Knowles, P. E.

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Koechner, W.

Kogelnik, H.

Körner, J.

J. Körner, J. Hein, and M. C. Kaluza, “Compact aberration-free relay-imaging multi-pass layouts for high-energy laser amplifiers,” Appl. Sci. 6, 353 (2016).
[Crossref]

J. Körner, J. Hein, M. Kahle, H. Liebetrau, M. Kaluza, M. Siebold, and M. Loeser, “High-efficiency cyrogenic-cooled diode-pumped amplifier with relay imaging for nanosecond pulses,” Proc. SPIE 8080, 80800D (2011).
[Crossref]

Kottmann, F.

K. Schuhmann, M. A. Ahmed, A. Antognini, T. Graf, T. W. Hänsch, K. Kirch, F. Kottmann, R. Pohl, D. Taqqu, A. Voss, and B. Weichelt, “Thin-disk laser multi-pass amplifier,” Proc. SPIE 9342, 93420U (2015).
[Crossref]

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Kumkar, M.

Larionov, M.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW CW thin disc laser,” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).
[Crossref]

F. Butze, M. Larionov, K. Schuhmann, C. Stolzenburg, and A. Giesen, “Nanosecond pulsed thin disk Yb:YAG lasers,” in Advanced Solid-State Photonics (TOPS) (2004), p. 237.

Lee, J.

Lee, S. K.

Li, T.

Liebetrau, H.

J. Körner, J. Hein, M. Kahle, H. Liebetrau, M. Kaluza, M. Siebold, and M. Loeser, “High-efficiency cyrogenic-cooled diode-pumped amplifier with relay imaging for nanosecond pulses,” Proc. SPIE 8080, 80800D (2011).
[Crossref]

Liu, Y. W.

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Loescher, A.

Loeser, M.

S. Banerjee, K. Ertel, P. D. Mason, P. J. Phillips, M. Siebold, M. Loeser, C. Hernandez-Gomez, and J. L. Collier, “High-efficiency 10 J diode pumped cryogenic gas cooled Yb:YAG multislab amplifier,” Opt. Lett. 37, 2175–2177 (2012).
[Crossref]

J. Körner, J. Hein, M. Kahle, H. Liebetrau, M. Kaluza, M. Siebold, and M. Loeser, “High-efficiency cyrogenic-cooled diode-pumped amplifier with relay imaging for nanosecond pulses,” Proc. SPIE 8080, 80800D (2011).
[Crossref]

Ludhova, L.

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Lundquist, P.

P. Lundquist, S. Sarkisyan, E. A. Wilson, R. M. Copenhaver, H. Martin, and S. McCahon, “Off axis walk off multi-pass amplifiers,” U.S. patent12954387 (24November2010).

Magni, V.

Martin, H.

P. Lundquist, S. Sarkisyan, E. A. Wilson, R. M. Copenhaver, H. Martin, and S. McCahon, “Off axis walk off multi-pass amplifiers,” U.S. patent12954387 (24November2010).

Martinez, M. D.

M. D. Martinez, J. K. Crane, L. A. Hackel, F. A. Penko, and D. F. Browning, “Optimized diode-pumped Nd:glass prototype regenerative amplifier for the national ignition facility (NIF),” Proc. SPIE 3267, 234–242 (1998).
[Crossref]

Mason, P. D.

McCahon, S.

P. Lundquist, S. Sarkisyan, E. A. Wilson, R. M. Copenhaver, H. Martin, and S. McCahon, “Off axis walk off multi-pass amplifiers,” U.S. patent12954387 (24November2010).

Mikhailov, V. P.

Miller, W. B.

Moncorgé, R.

F. Friebel, A. Pellegrina, D. N. Papadopoulos, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Diode-pumped Yb: CaF2 multipass amplifier producing 50 mJ with dynamic analysis for high repetition rate operation,” Appl. Phys. B 117, 597–603 (2014).
[Crossref]

Moschuring, N.

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Mulhauser, F.

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Nagymihaly, R.

Nathel, H.

Nebel, T.

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Negel, J.-P.

Neuhaus, J.

Nez, F.

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Notebaert, L.

M. Pittman, S. Ferré, J. Rousseau, L. Notebaert, J. Chambaret, and G. Chériaux, “Design and characterization of a near-diffraction-limited femtosecond 100-TW 10-Hz high-intensity laser system,” Appl. Phys. B 74, 529–535 (2002).
[Crossref]

Olson, T.

H. Plaessmann, W. Grossman, and T. Olson, “Multi-pass light amplifier,” U.S. patent08079640 (18November1992).

Opower, H.

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).
[Crossref]

Osterink, L. M.

L. M. Osterink and J. D. Foster, “Thermal effects and transverse mode control in a Nd:YAG laser,” Appl. Phys. Lett. 12, 128–131 (1968).
[Crossref]

Osvay, K.

Palashov, O.

V. Zelenogorsky, O. Palashov, and E. Khazanov, “Adaptive compensation of thermally induced phase aberrations in Faraday isolators by means of a DKDP crystal,” Opt. Commun. 278, 8–13 (2007).
[Crossref]

Papadopoulos, D. N.

F. Friebel, A. Pellegrina, D. N. Papadopoulos, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Diode-pumped Yb: CaF2 multipass amplifier producing 50 mJ with dynamic analysis for high repetition rate operation,” Appl. Phys. B 117, 597–603 (2014).
[Crossref]

D. N. Papadopoulos, A. Pellegrina, L. P. Ramirez, P. Georges, and F. Druon, “Broadband high-energy diode-pumped Yb:KYW multipass amplifier,” Opt. Lett. 36, 3816–3818 (2011).
[Crossref]

Payne, A.

K. T. Stevens, W. Schlichting, G. Foundos, A. Payne, and E. Rogers, “Promising materials for high power laser isolators,” Laser Technik J. 13, 18–21 (2016).
[Crossref]

Pellegrina, A.

F. Friebel, A. Pellegrina, D. N. Papadopoulos, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Diode-pumped Yb: CaF2 multipass amplifier producing 50 mJ with dynamic analysis for high repetition rate operation,” Appl. Phys. B 117, 597–603 (2014).
[Crossref]

D. N. Papadopoulos, A. Pellegrina, L. P. Ramirez, P. Georges, and F. Druon, “Broadband high-energy diode-pumped Yb:KYW multipass amplifier,” Opt. Lett. 36, 3816–3818 (2011).
[Crossref]

Penko, F. A.

M. D. Martinez, J. K. Crane, L. A. Hackel, F. A. Penko, and D. F. Browning, “Optimized diode-pumped Nd:glass prototype regenerative amplifier for the national ignition facility (NIF),” Proc. SPIE 3267, 234–242 (1998).
[Crossref]

Peters, R.

R. Peters, “Ytterbium-doped sesquioxides as highly efficient laser materials,” Ph.D. thesis (Department Physik der Universität Hamburg, 2009).

Phillips, P. J.

Pittman, M.

M. Pittman, S. Ferré, J. Rousseau, L. Notebaert, J. Chambaret, and G. Chériaux, “Design and characterization of a near-diffraction-limited femtosecond 100-TW 10-Hz high-intensity laser system,” Appl. Phys. B 74, 529–535 (2002).
[Crossref]

Plaessmann, H.

Pohl, R.

K. Schuhmann, M. A. Ahmed, A. Antognini, T. Graf, T. W. Hänsch, K. Kirch, F. Kottmann, R. Pohl, D. Taqqu, A. Voss, and B. Weichelt, “Thin-disk laser multi-pass amplifier,” Proc. SPIE 9342, 93420U (2015).
[Crossref]

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Poizat, J. P.

Poloyko, I. G.

Porter, J. L.

P. Rambo, J. Schwarz, M. Kimmel, and J. L. Porter, “Development of high damage threshold laser-machined apodizers and gain filters for laser applications,” High Power Laser Sci. Eng. 4e32 (2016).
[Crossref]

Pugžlys, A.

Rabinowitz, P.

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Rambo, P.

P. Rambo, J. Schwarz, M. Kimmel, and J. L. Porter, “Development of high damage threshold laser-machined apodizers and gain filters for laser applications,” High Power Laser Sci. Eng. 4e32 (2016).
[Crossref]

Ramirez, L. P.

Ré, S. A.

Renard, P. A.

Richardson, M.

Rogers, E.

K. T. Stevens, W. Schlichting, G. Foundos, A. Payne, and E. Rogers, “Promising materials for high power laser isolators,” Laser Technik J. 13, 18–21 (2016).
[Crossref]

Rousseau, J.

M. Pittman, S. Ferré, J. Rousseau, L. Notebaert, J. Chambaret, and G. Chériaux, “Design and characterization of a near-diffraction-limited femtosecond 100-TW 10-Hz high-intensity laser system,” Appl. Phys. B 74, 529–535 (2002).
[Crossref]

Salin, F.

Sarkisyan, S.

P. Lundquist, S. Sarkisyan, E. A. Wilson, R. M. Copenhaver, H. Martin, and S. McCahon, “Off axis walk off multi-pass amplifiers,” U.S. patent12954387 (24November2010).

Sävert, A.

S. Keppler, C. Wandt, M. Hornung, R. Bödefeld, A. Kessler, A. Sävert, M. Hellwing, F. Schorcht, J. Hein, and M. C. Kaluza, “Multipass amplifiers of POLARIS,” Proc. SPIE 8780, 87800I (2013).
[Crossref]

Schlichting, W.

K. T. Stevens, W. Schlichting, G. Foundos, A. Payne, and E. Rogers, “Promising materials for high power laser isolators,” Laser Technik J. 13, 18–21 (2016).
[Crossref]

Schnuerer, M.

Schorcht, F.

S. Keppler, C. Wandt, M. Hornung, R. Bödefeld, A. Kessler, A. Sävert, M. Hellwing, F. Schorcht, J. Hein, and M. C. Kaluza, “Multipass amplifiers of POLARIS,” Proc. SPIE 8780, 87800I (2013).
[Crossref]

Schuhmann, K.

K. Schuhmann, K. Kirch, and A. Antognini, “Multi-pass resonator design for energy scaling of mode-locked thin-disk lasers,” Proc. SPIE 10082, 100820J (2017).
[Crossref]

K. Schuhmann, M. A. Ahmed, A. Antognini, T. Graf, T. W. Hänsch, K. Kirch, F. Kottmann, R. Pohl, D. Taqqu, A. Voss, and B. Weichelt, “Thin-disk laser multi-pass amplifier,” Proc. SPIE 9342, 93420U (2015).
[Crossref]

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

F. Butze, M. Larionov, K. Schuhmann, C. Stolzenburg, and A. Giesen, “Nanosecond pulsed thin disk Yb:YAG lasers,” in Advanced Solid-State Photonics (TOPS) (2004), p. 237.

K. Schuhmann, “The thin-disk laser for the 2S–2P measurement in muonic helium,” Ph.D. thesis (Institute for Particle Physics and Astrophysics, ETH Zürich, 2017).

Schwarz, J.

P. Rambo, J. Schwarz, M. Kimmel, and J. L. Porter, “Development of high damage threshold laser-machined apodizers and gain filters for laser applications,” High Power Laser Sci. Eng. 4e32 (2016).
[Crossref]

Schwob, C.

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Scott, A. M.

Shah, L.

Siebold, M.

S. Banerjee, K. Ertel, P. D. Mason, P. J. Phillips, M. Siebold, M. Loeser, C. Hernandez-Gomez, and J. L. Collier, “High-efficiency 10 J diode pumped cryogenic gas cooled Yb:YAG multislab amplifier,” Opt. Lett. 37, 2175–2177 (2012).
[Crossref]

J. Körner, J. Hein, M. Kahle, H. Liebetrau, M. Kaluza, M. Siebold, and M. Loeser, “High-efficiency cyrogenic-cooled diode-pumped amplifier with relay imaging for nanosecond pulses,” Proc. SPIE 8080, 80800D (2011).
[Crossref]

Siegman, A.

A. Siegman, Lasers (University Science Books, 1986).

Simmons, W. W.

Smith, J. M.

Stevens, K. T.

K. T. Stevens, W. Schlichting, G. Foundos, A. Payne, and E. Rogers, “Promising materials for high power laser isolators,” Laser Technik J. 13, 18–21 (2016).
[Crossref]

Stewen, C.

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW CW thin disc laser,” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).
[Crossref]

U. Brauch, A. Giesen, M. Karszewski, C. Stewen, and A. Voss, “Multiwatt diode-pumped Yb:YAG thin disk laser continuously tunable between 1018 and 1053 nm,” Opt. Lett. 20, 713–715 (1995).
[Crossref]

S. Erhard, A. Giesen, and C. Stewen, “Laser amplifier system,” U.S. patent10208664 (5February2000).

Stolzenburg, C.

F. Butze, M. Larionov, K. Schuhmann, C. Stolzenburg, and A. Giesen, “Nanosecond pulsed thin disk Yb:YAG lasers,” in Advanced Solid-State Photonics (TOPS) (2004), p. 237.

Sullivan, A.

Sung, J. H.

Sutter, D.

Sutter, D. H.

Taqqu, D.

K. Schuhmann, M. A. Ahmed, A. Antognini, T. Graf, T. W. Hänsch, K. Kirch, F. Kottmann, R. Pohl, D. Taqqu, A. Voss, and B. Weichelt, “Thin-disk laser multi-pass amplifier,” Proc. SPIE 9342, 93420U (2015).
[Crossref]

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

Vaupel, A.

Vecht, D. L.

von der Linde, D.

Voss, A.

K. Schuhmann, M. A. Ahmed, A. Antognini, T. Graf, T. W. Hänsch, K. Kirch, F. Kottmann, R. Pohl, D. Taqqu, A. Voss, and B. Weichelt, “Thin-disk laser multi-pass amplifier,” Proc. SPIE 9342, 93420U (2015).
[Crossref]

J.-P. Negel, A. Loescher, A. Voss, D. Bauer, D. Sutter, A. Killi, M. A. Ahmed, and T. Graf, “Ultrafast thin-disk multipass laser amplifier delivering 1.4 kW (4.7 mJ, 1030 nm) average power converted to 820 W at 515 nm and 234 W at 343 nm,” Opt. Express 23, 21064–21077 (2015).
[Crossref]

U. Brauch, A. Giesen, M. Karszewski, C. Stewen, and A. Voss, “Multiwatt diode-pumped Yb:YAG thin disk laser continuously tunable between 1018 and 1053 nm,” Opt. Lett. 20, 713–715 (1995).
[Crossref]

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).
[Crossref]

Wandt, C.

S. Keppler, C. Wandt, M. Hornung, R. Bödefeld, A. Kessler, A. Sävert, M. Hellwing, F. Schorcht, J. Hein, and M. C. Kaluza, “Multipass amplifiers of POLARIS,” Proc. SPIE 8780, 87800I (2013).
[Crossref]

Webb, B.

Weichelt, B.

K. Schuhmann, M. A. Ahmed, A. Antognini, T. Graf, T. W. Hänsch, K. Kirch, F. Kottmann, R. Pohl, D. Taqqu, A. Voss, and B. Weichelt, “Thin-disk laser multi-pass amplifier,” Proc. SPIE 9342, 93420U (2015).
[Crossref]

Weiler, S.

White, W.

Wilson, E. A.

P. Lundquist, S. Sarkisyan, E. A. Wilson, R. M. Copenhaver, H. Martin, and S. McCahon, “Off axis walk off multi-pass amplifiers,” U.S. patent12954387 (24November2010).

Wittig, K.

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).
[Crossref]

Wojtkiewicz, J.

Yoon, J. W.

Yu, T. J.

Zelenogorsky, V.

V. Zelenogorsky, O. Palashov, and E. Khazanov, “Adaptive compensation of thermally induced phase aberrations in Faraday isolators by means of a DKDP crystal,” Opt. Commun. 278, 8–13 (2007).
[Crossref]

Zhang, J.

Appl. Opt. (6)

Appl. Phys. B (3)

M. Pittman, S. Ferré, J. Rousseau, L. Notebaert, J. Chambaret, and G. Chériaux, “Design and characterization of a near-diffraction-limited femtosecond 100-TW 10-Hz high-intensity laser system,” Appl. Phys. B 74, 529–535 (2002).
[Crossref]

F. Friebel, A. Pellegrina, D. N. Papadopoulos, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, and F. Druon, “Diode-pumped Yb: CaF2 multipass amplifier producing 50 mJ with dynamic analysis for high repetition rate operation,” Appl. Phys. B 117, 597–603 (2014).
[Crossref]

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365–372 (1994).
[Crossref]

Appl. Phys. Lett. (1)

L. M. Osterink and J. D. Foster, “Thermal effects and transverse mode control in a Nd:YAG laser,” Appl. Phys. Lett. 12, 128–131 (1968).
[Crossref]

Appl. Sci. (1)

J. Körner, J. Hein, and M. C. Kaluza, “Compact aberration-free relay-imaging multi-pass layouts for high-energy laser amplifiers,” Appl. Sci. 6, 353 (2016).
[Crossref]

High Power Laser Sci. Eng. (1)

P. Rambo, J. Schwarz, M. Kimmel, and J. L. Porter, “Development of high damage threshold laser-machined apodizers and gain filters for laser applications,” High Power Laser Sci. Eng. 4e32 (2016).
[Crossref]

IEEE J. Quantum Electron. (1)

A. Antognini, K. Schuhmann, F. D. Amaro, F. Biraben, A. Dax, A. Giesen, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C. Y. Kao, P. E. Knowles, F. Kottmann, E. L. Bigot, Y. W. Liu, L. Ludhova, N. Moschuring, F. Mulhauser, T. Nebel, F. Nez, P. Rabinowitz, C. Schwob, D. Taqqu, and R. Pohl, “Thin-disk Yb:YAG oscillator-amplifier laser, ASE, and effective Yb:YAG lifetime,” IEEE J. Quantum Electron. 45, 993–1005 (2009).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “A 1-kW CW thin disc laser,” IEEE J. Sel. Top. Quantum Electron. 6, 650–657 (2000).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (2)

Laser Technik J. (1)

K. T. Stevens, W. Schlichting, G. Foundos, A. Payne, and E. Rogers, “Promising materials for high power laser isolators,” Laser Technik J. 13, 18–21 (2016).
[Crossref]

Opt. Commun. (1)

V. Zelenogorsky, O. Palashov, and E. Khazanov, “Adaptive compensation of thermally induced phase aberrations in Faraday isolators by means of a DKDP crystal,” Opt. Commun. 278, 8–13 (2007).
[Crossref]

Opt. Express (6)

S. Banerjee, K. Ertel, P. D. Mason, P. J. Phillips, M. De Vido, J. M. Smith, T. J. Butcher, C. Hernandez-Gomez, R. J. S. Greenhalgh, and J. L. Collier, “DiPOLE: a 10 J, 10 Hz cryogenic gas cooled multi-slab nanosecond Yb:YAG laser,” Opt. Express 23, 19542–19551 (2015).
[Crossref]

T. J. Yu, S. K. Lee, J. H. Sung, J. W. Yoon, T. M. Jeong, and J. Lee, “Generation of high-contrast, 30 fs, 1.5 PW laser pulses from chirped-pulse amplification Ti:sapphire laser,” Opt. Express 20, 10807–10815 (2012).
[Crossref]

J. Neuhaus, D. Bauer, J. Zhang, A. Killi, J. Kleinbauer, M. Kumkar, S. Weiler, M. Guina, D. H. Sutter, and T. Dekorsy, “Subpicosecond thin-disk laser oscillator with pulse energies of up to 25.9 microjoules by use of an active multipass geometry,” Opt. Express 16, 20530–20539 (2008).
[Crossref]

J. Wojtkiewicz and C. G. Durfee, “High-energy, high-contrast, double-confocal multipass amplifier,” Opt. Express 12, 1383–1388 (2004).
[Crossref]

E. Kaksis, G. Almási, J. A. Fülöp, A. Pugžlys, A. Baltuška, and G. Andriukaitis, “110 mJ 225 fs cryogenically cooled Yb:CaF2 multipass amplifier,” Opt. Express 24, 28915–28922 (2016).
[Crossref]

J.-P. Negel, A. Loescher, A. Voss, D. Bauer, D. Sutter, A. Killi, M. A. Ahmed, and T. Graf, “Ultrafast thin-disk multipass laser amplifier delivering 1.4 kW (4.7 mJ, 1030 nm) average power converted to 820 W at 515 nm and 234 W at 343 nm,” Opt. Express 23, 21064–21077 (2015).
[Crossref]

Opt. Lett. (8)

U. Brauch, A. Giesen, M. Karszewski, C. Stewen, and A. Voss, “Multiwatt diode-pumped Yb:YAG thin disk laser continuously tunable between 1018 and 1053 nm,” Opt. Lett. 20, 713–715 (1995).
[Crossref]

H. Plaessmann, S. A. Ré, J. J. Aionis, D. L. Vecht, and W. M. Grossman, “Multipass diode-pumped solid-state optical amplifier,” Opt. Lett. 18, 1420–1422 (1993).
[Crossref]

V. Chvykov, H. Cao, R. Nagymihaly, M. P. Kalashnikov, N. Khodakovskiy, R. Glassock, L. Ehrentraut, M. Schnuerer, and K. Osvay, “High peak and average power Ti:sapphire thin disk amplifier with extraction during pumping,” Opt. Lett. 41, 3017–3020 (2016).
[Crossref]

M. S. Bowers, “Diffractive analysis of unstable optical resonators with super-Gaussian mirrors,” Opt. Lett. 17, 1319–1321 (1992).
[Crossref]

D. N. Papadopoulos, A. Pellegrina, L. P. Ramirez, P. Georges, and F. Druon, “Broadband high-energy diode-pumped Yb:KYW multipass amplifier,” Opt. Lett. 36, 3816–3818 (2011).
[Crossref]

S. Banerjee, K. Ertel, P. D. Mason, P. J. Phillips, M. Siebold, M. Loeser, C. Hernandez-Gomez, and J. L. Collier, “High-efficiency 10 J diode pumped cryogenic gas cooled Yb:YAG multislab amplifier,” Opt. Lett. 37, 2175–2177 (2012).
[Crossref]

P. Georges, F. Estable, F. Salin, J. P. Poizat, P. Grangier, and A. Brun, “High-efficiency multipass Ti:sapphire amplifiers for a continuous-wave single-mode laser,” Opt. Lett. 16, 144–146 (1991).
[Crossref]

A. Sullivan, H. Hamster, H. C. Kapteyn, S. Gordon, W. White, H. Nathel, R. J. Blair, and R. W. Falcone, “Multiterawatt, 100-fs laser,” Opt. Lett. 16, 1406–1408 (1991).
[Crossref]

Proc. SPIE (5)

K. Schuhmann, K. Kirch, and A. Antognini, “Multi-pass resonator design for energy scaling of mode-locked thin-disk lasers,” Proc. SPIE 10082, 100820J (2017).
[Crossref]

K. Schuhmann, M. A. Ahmed, A. Antognini, T. Graf, T. W. Hänsch, K. Kirch, F. Kottmann, R. Pohl, D. Taqqu, A. Voss, and B. Weichelt, “Thin-disk laser multi-pass amplifier,” Proc. SPIE 9342, 93420U (2015).
[Crossref]

M. D. Martinez, J. K. Crane, L. A. Hackel, F. A. Penko, and D. F. Browning, “Optimized diode-pumped Nd:glass prototype regenerative amplifier for the national ignition facility (NIF),” Proc. SPIE 3267, 234–242 (1998).
[Crossref]

S. Keppler, C. Wandt, M. Hornung, R. Bödefeld, A. Kessler, A. Sävert, M. Hellwing, F. Schorcht, J. Hein, and M. C. Kaluza, “Multipass amplifiers of POLARIS,” Proc. SPIE 8780, 87800I (2013).
[Crossref]

J. Körner, J. Hein, M. Kahle, H. Liebetrau, M. Kaluza, M. Siebold, and M. Loeser, “High-efficiency cyrogenic-cooled diode-pumped amplifier with relay imaging for nanosecond pulses,” Proc. SPIE 8080, 80800D (2011).
[Crossref]

Other (12)

R. Jung, J. Tümmler, and I. Will, “Topic 1: High average power disk laser,” 2016, https://www.mbi-berlin.de/de/research/projects/1.2/topics/1_power_disk_laser/ .

M. Siebold, “PENELOPE, Helmholtz-Zentrum Dresden-Rossendorf e. V,” 2016, https://www.hzdr.de/db/Cms?pNid=2098 .

F. Butze, M. Larionov, K. Schuhmann, C. Stolzenburg, and A. Giesen, “Nanosecond pulsed thin disk Yb:YAG lasers,” in Advanced Solid-State Photonics (TOPS) (2004), p. 237.

R. Peters, “Ytterbium-doped sesquioxides as highly efficient laser materials,” Ph.D. thesis (Department Physik der Universität Hamburg, 2009).

P. Lundquist, S. Sarkisyan, E. A. Wilson, R. M. Copenhaver, H. Martin, and S. McCahon, “Off axis walk off multi-pass amplifiers,” U.S. patent12954387 (24November2010).

H. Plaessmann, W. Grossman, and T. Olson, “Multi-pass light amplifier,” U.S. patent08079640 (18November1992).

S. Erhard, A. Giesen, and C. Stewen, “Laser amplifier system,” U.S. patent10208664 (5February2000).

K. Schuhmann, “The thin-disk laser for the 2S–2P measurement in muonic helium,” Ph.D. thesis (Institute for Particle Physics and Astrophysics, ETH Zürich, 2017).

A. Siegman, Lasers (University Science Books, 1986).

J. Neuhaus, “Passively mode-locked yb:yag thin-disk laser with active multipass geometry,” Ph.D. thesis (Universität Konstanz, 2009).

Electro-Optics Technology, Inc., “Pavos ultra series,” 2018, http://www.eotech.com/content/userfiles/Pavos%20Ultra-Rotators%20and%20Isolators.pdf .

IPG Photonics Corporation, “High power CW fiber lasers,” https://www.ipgphotonics.com/en/products/lasers/high-power-cw-fiber-lasers .

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1.
Fig. 1. (a) Scheme of the laser beam propagation from active medium to active medium through a 4 f -imaging segment. The 4 f -segment is given by a free propagation of distance f , a focusing optics with focal length f , a free propagation with length 2 f , a second focusing element with focal length f , and a free propagation of length f . The vertical magenta lines represent the position of the active medium; the vertical black lines indicate the position of the optic with focal length f. The black curves represent the beam size evolution along the optical axis z . (b) 6-pass amplifier and corresponding beam size evolution along the propagation axis realized by concatenating five 4 f -imaging stages and assuming a Gaussian aperture at the active medium of W = 4 w in . The black curves show the beam size evolution for an active medium dioptric power having the design value, i.e., V = 0 . The red and blue curves show the propagations (beam size evolution) for V = ± 1 40 f . The gray curves represent the beam evolution for V = 0 and W = . The discontinuity of the waist size at the gain medium is caused by the (Gaussian) aperture effect of the finite pump region.
Fig. 2.
Fig. 2. Schemes showing the transition from a 2-pass amplifier based on 4 f -imaging with mode cleaning achieved with a pinhole in part (a), to a 4-pass amplifier based on a double optical Fourier transform with mode filtering achieved through the soft apertures of the pumped active medium in part (b). The optical Fourier transform is realized by the sequence: free propagation of length F , focusing element with focal length F , followed by a free propagation of length F . The same notation as in Fig. 1 is used.
Fig. 3.
Fig. 3. Scheme and corresponding beam size evolution along the optical axis z for a 2-pass amplifier based on 4 f -imaging in part (a) and on an optical Fourier transform in part (b). It was assumed that W = 4 w in , and the same notation as in Fig. 1 is used. Similar to Fig. 1(b), the Gaussian aperture related to the finite pump region causes the discontinuity of the beam size at the gain medium.
Fig. 4.
Fig. 4. Size w out , 2 and phase front curvature R out , 2 1 of the output beam leaving the 2-pass amplifiers of Fig. 3 for variations of the active medium dioptric power Δ V . The top row assumes W = 4 w in , and in the bottom one W = . The blue curves represent the results for the Fourier-based amplifier of Fig. 3(b), while the dashed red curves represent the results for the 4 f -based amplifier of Fig. 3(a). In both cases it was assumed that q in = q stable . For comparison, in gray are given w stable ( Δ V ) and R stable 1 ( Δ V ) corresponding to the complex beam parameter given in Eq. (15).
Fig. 5.
Fig. 5. Two types of 4-pass amplifiers both based on two optical Fourier transforms. In (a), there is physically short free propagation between the second and third pass. In (b),  4 f -imaging is used to obtain propagation with zero effective length between the second and third pass. The same notation as in Fig. 1 is used. The gray-shaded region indicates the 4 f -imaging segment. The discontinuity of the beam size due to the aperture at the active medium is visible.
Fig. 6.
Fig. 6. Similar to Fig. 4, but for amplifiers with four passes. The blue curves represent the output beam characteristics of both layouts of Fig. 5. The red dashed curves represent the output characteristics of the 4 f -amplifier design.
Fig. 7.
Fig. 7. 8-pass amplifier realized by concatenating two 4-pass amplifiers of Fig. 5(a). The same notation as in Fig. 1 has been used.
Fig. 8.
Fig. 8. Similar to Fig. 4, but for an 8-pass amplifier as given in Figs. 7 and 11. The black dashed lines represent the maximally allowed deviations for vanishing aperture effects given by Eqs. (25) and (26).
Fig. 9.
Fig. 9. Similar to Fig. 8, but for a 16-pass amplifier.
Fig. 10.
Fig. 10. (a) Scheme of the optical Fourier transform from active medium to active medium obtained using two Galilean telescopes. The active medium itself (vertical lines at z = 0 and z = 1 ) acts as the focusing element of the telescopes with focal length f AM . The defocusing elements (cyan vertical lines) of the telescopes have focal length f given by Eq. (36) and are placed at a distance 0.25 L from the active medium, where L is the distance between the two passes in the active medium. The beam size ( w ) evolution in the Fourier transform segment is given for three different values of the active medium focal length: f AM = L (solid), f AM = 0.5 L (dashed), and f AM = 0.3 L (dotted). (b) Effective focal length F of the Fourier transform as a function of the active medium focal length f AM expressed in units of L .
Fig. 11.
Fig. 11. (a) Scheme of an 8-pass Fourier-based amplifier obtained by concatenating two 4-pass amplifiers of Fig. 5(a). Each Fourier transform has been shortened using two Galilean telescopes. The active medium is also part of the Galilean telescope. Between two Fourier transforms, there is a short propagation of length L . (b) Similar to (a), but in this case the 8-pass amplifier is based on Fig. 5(b). Between each Fourier transform there is a 4 f -imaging (indicated by the gray shaded area). The same notation as in Fig. 1 is used.

Equations (42)

Equations on this page are rendered with MathJax. Learn more.

w out 2 = w in 2 + W 2 ,
M aperture = [ 1 0 i λ π W 2 1 ] ,
M AM = [ 1 0 V 1 ] · [ 1 0 i λ π W 2 1 ] = [ 1 0 V i λ π W 2 1 ] ,
V ˜ = V + i λ π W 2 .
V = V unpumped + V thermal = V unpumped + V thermal avg + Δ V ,
AM 4 f AM 4 f AM 4 f AM 4 f AM .
1 q = 1 R i λ π w 2 ,
q out = A q in + B C q in + D .
M 4 f , N = [ ( 1 ) N 1 0 ( 1 ) N · N · Δ V ˜ ( 1 ) N 1 ] .
q out , N = q in + N q in 2 Δ V ˜ + N 2 q in 3 Δ V ˜ 2 + N 3 q in 4 Δ V ˜ 3 + .
w out , N = w in ,
R out , N 1 = N Δ V .
w out , N w in = 1 w in 2 N 2 W 2 + 3 w in 4 N 2 8 W 4 5 w in 6 N 3 16 W 6 + .
M Fourier , 2 = M AM · M Fourier · M AM
= [ F · Δ V ˜ F F 2 · Δ V ˜ 2 + 1 F F · Δ V ˜ ] ,
q stable = i F 1 ( F · Δ V ˜ ) 2 .
q in = i F .
w in = λ F π .
q out , 2 = i F + i F 3 Δ V ˜ 2 F 4 Δ V ˜ 3 F 6 Δ V ˜ 5 +
w out , 2 w in = 1 + 1 2 F 2 Δ V 2 1 8 F 4 Δ V 4 + ,
R out , 2 1 = F 2 Δ V 3 + F 4 Δ V 5 F 6 Δ V 7 + F 8 Δ V 9 +
w out , 2 w in = 1 + w in 4 2 W 4 w in 8 8 W 8 + w in 12 16 W 12 + .
AM Fourier AM AM Fourier AM ,
AM Fourier AM 4 f AM Fourier AM .
q out , 4 = i F + 2 F 4 Δ V ˜ 3 4 i F 5 Δ V ˜ 4 4 F 6 Δ V ˜ 5 + .
w out , 4 w in = 1 + 2 F 4 Δ V 4 2 F 8 Δ V 8 + ,
R out , 4 1 = 2 F 2 Δ V 3 4 F 4 Δ V 5 8 F 6 Δ V 7 + .
w in < w out , N ( Δ V ) < w stable 2 ( Δ V ) / w in ,
F 2 Δ V 2 < R out , N 1 ( Δ V ) < F 2 Δ V 2 ,
q out , 8 = i F + 4 F 4 Δ V ˜ 3 + 16 i F 5 Δ V ˜ 4 40 F 6 Δ V ˜ 5 + ,
q out , 32 = i F + 16 F 4 Δ V ˜ 3 + 256 i F 5 Δ V ˜ 4 2720 F 6 Δ V ˜ 5 .
w out , 8 w in = 1 + 8 F 4 Δ V 4 32 F 6 Δ V 6 + ,
w out , 32 w in = 1 + 128 F 4 Δ V 4 10752 F 6 Δ V 6 + ,
R out , 8 1 = 4 F 2 Δ V 3 40 F 4 Δ V 5 + 32 F 6 Δ V 7 + ,
R out , 32 1 = 16 F 2 Δ V 3 2720 F 4 Δ V 5 + 132992 F 6 Δ V 7 .
w out , 8 w in = 1 2 w in 6 W 6 + 8 w in 8 W 8 + ,
w out , 32 w in = 1 8 w in 6 W 6 + 128 w in 8 W 8 + ,
F = π w in 2 λ .
f = 1 2 ( 4 f AM + L ) L 3 L 8 f AM + L 2 8 L f AM + 32 f AM 2 .
F = f AM 32 ( f AM / L ) 2 8 f AM / L + 1 + 4 f AM / L ( 4 f AM / L 1 ) 2 .
AM Fourier AM L AM Fourier AM L ,
AM Fourier AM 4 f AM Fourier AM 4 f ,

Metrics

Select as filters


Select Topics Cancel
© Copyright 2022 | Optica Publishing Group. All Rights Reserved