3. Power scaling in KLM oscillators

For power scaling of soliton mode-locked oscillators both the nonlinear and the thermal instabilities need to be considered. A thin-disk gain medium is in both cases an ideal solution. The predominantly one-dimensional heat flow within the thin gain medium minimizes thermal lensing and the low peak intensities in the large but thin disk minimize the nonlinear phase shift. Unlike the usual bulk KLM oscillators [44], high power thin-disk KLM oscillators require that the role of the gain and Kerr-medium are separated to distinct intra-cavity elements. This way it is possible to keep the mode size on the thin-disk large and to tune the nonlinear phase shift nearly independently by means of an additional Kerr-medium (see Figure 4a).

losses are essential for average power and peak power scaling. Thus, in 2014, quickly after the first demonstration of thin-disk KLM [33] up to 270 W average power from a KLM thin-disk laser were demonstrated [7] (also see Figure 2b). The utilized thin-disk technology remains the key component for high average power operation for both Kerr-lens and SESAM modelocking techniques. While the first demonstrator of a KLM thin-disk oscillator [33] relied on a copper mounted thin-disk the record performances approaching 300 W output were achieved with a thin-disk contacted to a diamond heat sink [7]. The superior heat-conductivity of diamond in combination with a suitable contacting technique [46] allow both larger pump intensities as well as thinner disks to be used which helps to reduce thermal lensing and

Another important aspect is thermal lenses in the oscillator elements. KLM oscillators require an increased sensitivity to the Kerr-lens to initiate mode-locking and retain a strong selfamplitude modulation (SAM) effect. This higher sensitivity is achieved by adjusting the resonator close to the edge of stability [48, 49] where, however, not only the sensitivity to the Kerrlens but also to any thermal lens inside the resonator is increased. In particular, the Kerrmedium material has a very pronounced influence on the oscillator behavior. For intra-cavity average power levels larger than 500 W, the use of fused silica plates is difficult at best, exhibiting strong thermal lensing. This is observable, e.g., by shifting the Kerr-medium under CW irradiation along the beam-axis and monitoring the mode-size change. Suitable alternatives are found in sapphire (46 W m�<sup>1</sup> K�<sup>1</sup> [50]), crystalline quartz (10 W m�<sup>1</sup> K�<sup>1</sup> [50]) or YAG (13 W m�<sup>1</sup> K�<sup>1</sup> [50]) materials, all having a significantly higher thermal conductivity than

Furthermore, highly dispersive mirrors were found to exhibit additional thermal lensing and to prevent average power scaling [47, 51, 52]. However, after a few attempts in manufacturing of those mirrors, it was possible to identify a multilayer design showing no thermal effects and still providing significant dispersion levels around �3000 fs<sup>2</sup> within 10 nm spectral bandwidth [53]. Another thermal lens suppression method implies the use of substrates with higher

The pulses traveling inside the KLM oscillator cannot take on arbitrary pulse energy E and width T but have to obey the well known soliton propagation law. It is assumed that soliton

s

with the group delay dispersion (GDD) β<sup>2</sup> and the nonlinear self-phase modulation (SPM) coefficient γ. The pulse can retain its shape when the frequency chirp due to SPM is canceled by (anomalous) dispersion of opposite sign. Pulses with a peak-power smaller or larger than P<sup>0</sup> do not meet this condition. If the peak-power is too small, the pulses are dispersed and if it

ffiffiffiffiffiffiffiffi ∣β2∣ γP<sup>0</sup>

T ¼

thermal conductivity and (or) lower thermal expansion coefficients [54, 55].

mode-locking is stable at a certain peak power level P<sup>0</sup> [56] then

). With a sapphire Kerr-plate more than 1.2 kW, stable average

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(1)

aspherical aberrations [47].

fused silica (1.4 W m�<sup>1</sup> K�<sup>1</sup>

3.2. Peak power scaling: general aspects

power could be demonstrated inside the KLM oscillator.

### 3.1. Average power scaling

One of the crucial advantages of KLM compared to semiconductor saturable absorbers is nearly negligible linear and nonlinear absorption inside of a dielectric Kerr-medium. SESAMs normally exhibit non-saturable losses and multiphoton absorption [45]. Such low absorption

Figure 4. (a) Oscillator sketch. TD: thin-disk; OC: output-coupler; HD: highly dispersive mirrors; F1,2: focusing mirrors; KM: Kerr-medium; HA: hard aperture and (b) a photo of a 100 W-level thin-disk oscillator in a compact monolithic aluminum housing. Photo credit: Kilian Fritsch.

losses are essential for average power and peak power scaling. Thus, in 2014, quickly after the first demonstration of thin-disk KLM [33] up to 270 W average power from a KLM thin-disk laser were demonstrated [7] (also see Figure 2b). The utilized thin-disk technology remains the key component for high average power operation for both Kerr-lens and SESAM modelocking techniques. While the first demonstrator of a KLM thin-disk oscillator [33] relied on a copper mounted thin-disk the record performances approaching 300 W output were achieved with a thin-disk contacted to a diamond heat sink [7]. The superior heat-conductivity of diamond in combination with a suitable contacting technique [46] allow both larger pump intensities as well as thinner disks to be used which helps to reduce thermal lensing and aspherical aberrations [47].

Another important aspect is thermal lenses in the oscillator elements. KLM oscillators require an increased sensitivity to the Kerr-lens to initiate mode-locking and retain a strong selfamplitude modulation (SAM) effect. This higher sensitivity is achieved by adjusting the resonator close to the edge of stability [48, 49] where, however, not only the sensitivity to the Kerrlens but also to any thermal lens inside the resonator is increased. In particular, the Kerrmedium material has a very pronounced influence on the oscillator behavior. For intra-cavity average power levels larger than 500 W, the use of fused silica plates is difficult at best, exhibiting strong thermal lensing. This is observable, e.g., by shifting the Kerr-medium under CW irradiation along the beam-axis and monitoring the mode-size change. Suitable alternatives are found in sapphire (46 W m�<sup>1</sup> K�<sup>1</sup> [50]), crystalline quartz (10 W m�<sup>1</sup> K�<sup>1</sup> [50]) or YAG (13 W m�<sup>1</sup> K�<sup>1</sup> [50]) materials, all having a significantly higher thermal conductivity than fused silica (1.4 W m�<sup>1</sup> K�<sup>1</sup> ). With a sapphire Kerr-plate more than 1.2 kW, stable average power could be demonstrated inside the KLM oscillator.

Furthermore, highly dispersive mirrors were found to exhibit additional thermal lensing and to prevent average power scaling [47, 51, 52]. However, after a few attempts in manufacturing of those mirrors, it was possible to identify a multilayer design showing no thermal effects and still providing significant dispersion levels around �3000 fs<sup>2</sup> within 10 nm spectral bandwidth [53]. Another thermal lens suppression method implies the use of substrates with higher thermal conductivity and (or) lower thermal expansion coefficients [54, 55].

## 3.2. Peak power scaling: general aspects

3. Power scaling in KLM oscillators

3.1. Average power scaling

96 High Power Laser Systems

aluminum housing. Photo credit: Kilian Fritsch.

For power scaling of soliton mode-locked oscillators both the nonlinear and the thermal instabilities need to be considered. A thin-disk gain medium is in both cases an ideal solution. The predominantly one-dimensional heat flow within the thin gain medium minimizes thermal lensing and the low peak intensities in the large but thin disk minimize the nonlinear phase shift. Unlike the usual bulk KLM oscillators [44], high power thin-disk KLM oscillators require that the role of the gain and Kerr-medium are separated to distinct intra-cavity elements. This way it is possible to keep the mode size on the thin-disk large and to tune the nonlinear phase

One of the crucial advantages of KLM compared to semiconductor saturable absorbers is nearly negligible linear and nonlinear absorption inside of a dielectric Kerr-medium. SESAMs normally exhibit non-saturable losses and multiphoton absorption [45]. Such low absorption

Figure 4. (a) Oscillator sketch. TD: thin-disk; OC: output-coupler; HD: highly dispersive mirrors; F1,2: focusing mirrors; KM: Kerr-medium; HA: hard aperture and (b) a photo of a 100 W-level thin-disk oscillator in a compact monolithic

shift nearly independently by means of an additional Kerr-medium (see Figure 4a).

The pulses traveling inside the KLM oscillator cannot take on arbitrary pulse energy E and width T but have to obey the well known soliton propagation law. It is assumed that soliton mode-locking is stable at a certain peak power level P<sup>0</sup> [56] then

$$T = \sqrt{\frac{|\beta\_2|}{\gamma P\_0}}\tag{1}$$

with the group delay dispersion (GDD) β<sup>2</sup> and the nonlinear self-phase modulation (SPM) coefficient γ. The pulse can retain its shape when the frequency chirp due to SPM is canceled by (anomalous) dispersion of opposite sign. Pulses with a peak-power smaller or larger than P<sup>0</sup> do not meet this condition. If the peak-power is too small, the pulses are dispersed and if it is too high, several instabilities can occur. Commonly observed instabilities are the splitting into two or more pulses per roundtrip period or the appearance of additional CW-background radiation. This equation describes well the case not only when pulses travel in lossless media such as fibers or a passive resonator but also catches the dilemma of power-scaling in modelocked oscillators.

The pulse energy of a soliton can be increased, e.g., by introducing larger values of the GDD. New coating methods allow introducing GDD on the order of 100,000 fs<sup>2</sup> with highly dispersive mirrors [7, 30, 57]. However, the larger chirp from the strong dispersion is automatically compensated by a pulse-duration growth that leaves the peak power constant. This way highest pulse energies were generated and extracted from SESAM mode-locked oscillators at the expense of longer pulses [28, 30].

The second important variable in Eq. (1) is the reduction of the SPM parameter which depends on the effective mode-area Aeff inside the oscillator elements of thickness d and nonlinear refractive index n2. Interestingly, a contribution of air to the SPM parameter cannot be neglected anymore at a certain intra-cavity peak power and cavity length.

$$
\gamma \propto \frac{d \, n\_2}{A\_{\text{eff}}} \tag{2}
$$

expect to increase the peak power favorably by the factor N<sup>2</sup>

expected, quadratic scaling of the peak power.

results are summarized in Figure 5.

that SAM also stays constant. This condition, however, is not necessarily fulfilled. Unfortunately, the decisive SAM parameters of a certain KLM resonator such as modulation-depth or saturation-power are not easily measurable and even simulations appear challenging due to the coupling between temporal and spatial extent of the pulses. The dependence of SAM on the resonator geometry therefore gives an experimentally observed deviation from the initially

The geometrical power scaling concept was applied experimentally as published in earlier work of the authors [7, 8]. The KLM oscillators were operated in air both under normal and reduced pressure environments. For the scaling experiments in work [7], all parameters except the pump power were kept constant. Four passes of the laser mode through the Yb:YAG thindisk (TRUMPF Laser GmbH) per roundtrip allowed to couple out large fractions of the intracavity power (21% transmission of the output coupler). The mode size inside the 1 mm thick sapphire Kerr-plate was varied by successively exchanging the mirrors F1,2 to have R1, <sup>2</sup> ranging from 300 to 900 mm. The resulting peak power increased proportionally to R1, 2. These

As described previously, the soliton peak-power is fairly invariant under a change of the intracavity GDD. However, the changes in pulse energy and duration can be substantial and give flexibility in the design parameters. This is demonstrated in Figure 5b, where the GDD in the thin-disk KLM oscillator was varied from �18,000 to �48,000 fs<sup>2</sup> by exchanging dispersive

Figure 5. (a) Summary of the data from the geometrical KLM power-scaling approach. The waist radius in the Kerrmedium, growing with R1,2, is approximated from ABCD-matrix calculations and (b) experimental example of intra cavity peak power and pulse duration when the total oscillator second order anomalous dispersion (GDD) is increased.

. A necessary condition for this is

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A decrease of γ is therefore directly coupled to the resonator geometry, regardless of whether SESAM or a Kerr-lens is used for mode-locking. The thin-disk gain medium favors large beam areas and short crystal lengths for average power scaling which implies also the minimization of the SPM-coefficient γ. Most state of the art, mode-locked thin-disk lasers are operated in a vacuum or reduced pressure environment to further decrease γ [8, 28, 36]. SESAM modelocked oscillators are especially sensitive to SPM since their modulation-depth and -speed is intrinsically limited for high-power operation. Current limitations to power scaling in such oscillators are assumed to originate partly from the residual nonlinearity in the mirror coatings [45]. KLM oscillators on the other hand appear to have a much higher tolerance to nonlinear phase shifts being attributed to the achievable large modulation depth as well as the near instantaneous response time of the Kerr-nonlinearity. Thus, fairly large peak-powers can be generated even under normal atmosphere [7].

#### 3.3. Geometrical approach to peak power scaling

Increasing the peak-power in KLM oscillators appears straightforward using a geometrical approach. A fair assumption is that the main contribution to the pulse nonlinear phase shift originates from the interaction in the Kerr-medium. Therefore, in an oscillator where all parameters such as dispersion, self-amplitude modulation, losses, pulse duration, etc. are fixed and only the mode area in the Kerr-medium is increased, the peak power should increase linearly with Aeff . This is not in contradiction with the soliton condition as stated in Eq. (1). The Kerr-medium is located in the beam waist of a focusing arrangement as seen in Figure 4. The mode radius wkerr in the Kerr-medium is linearly dependent on the curvature radius R1, <sup>2</sup> of the focusing arrangement mirrors F1 and F2. Therefore, varying R1,<sup>2</sup> by a factor N, one would expect to increase the peak power favorably by the factor N<sup>2</sup> . A necessary condition for this is that SAM also stays constant. This condition, however, is not necessarily fulfilled. Unfortunately, the decisive SAM parameters of a certain KLM resonator such as modulation-depth or saturation-power are not easily measurable and even simulations appear challenging due to the coupling between temporal and spatial extent of the pulses. The dependence of SAM on the resonator geometry therefore gives an experimentally observed deviation from the initially expected, quadratic scaling of the peak power.

is too high, several instabilities can occur. Commonly observed instabilities are the splitting into two or more pulses per roundtrip period or the appearance of additional CW-background radiation. This equation describes well the case not only when pulses travel in lossless media such as fibers or a passive resonator but also catches the dilemma of power-scaling in mode-

The pulse energy of a soliton can be increased, e.g., by introducing larger values of the GDD. New coating methods allow introducing GDD on the order of 100,000 fs<sup>2</sup> with highly dispersive mirrors [7, 30, 57]. However, the larger chirp from the strong dispersion is automatically compensated by a pulse-duration growth that leaves the peak power constant. This way highest pulse energies were generated and extracted from SESAM mode-locked oscillators at

The second important variable in Eq. (1) is the reduction of the SPM parameter which depends on the effective mode-area Aeff inside the oscillator elements of thickness d and nonlinear refractive index n2. Interestingly, a contribution of air to the SPM parameter cannot be

> <sup>γ</sup><sup>∝</sup> d n<sup>2</sup> Aeff

A decrease of γ is therefore directly coupled to the resonator geometry, regardless of whether SESAM or a Kerr-lens is used for mode-locking. The thin-disk gain medium favors large beam areas and short crystal lengths for average power scaling which implies also the minimization of the SPM-coefficient γ. Most state of the art, mode-locked thin-disk lasers are operated in a vacuum or reduced pressure environment to further decrease γ [8, 28, 36]. SESAM modelocked oscillators are especially sensitive to SPM since their modulation-depth and -speed is intrinsically limited for high-power operation. Current limitations to power scaling in such oscillators are assumed to originate partly from the residual nonlinearity in the mirror coatings [45]. KLM oscillators on the other hand appear to have a much higher tolerance to nonlinear phase shifts being attributed to the achievable large modulation depth as well as the near instantaneous response time of the Kerr-nonlinearity. Thus, fairly large peak-powers can be

Increasing the peak-power in KLM oscillators appears straightforward using a geometrical approach. A fair assumption is that the main contribution to the pulse nonlinear phase shift originates from the interaction in the Kerr-medium. Therefore, in an oscillator where all parameters such as dispersion, self-amplitude modulation, losses, pulse duration, etc. are fixed and only the mode area in the Kerr-medium is increased, the peak power should increase linearly with Aeff . This is not in contradiction with the soliton condition as stated in Eq. (1). The Kerr-medium is located in the beam waist of a focusing arrangement as seen in Figure 4. The mode radius wkerr in the Kerr-medium is linearly dependent on the curvature radius R1, <sup>2</sup> of the focusing arrangement mirrors F1 and F2. Therefore, varying R1,<sup>2</sup> by a factor N, one would

(2)

neglected anymore at a certain intra-cavity peak power and cavity length.

locked oscillators.

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the expense of longer pulses [28, 30].

generated even under normal atmosphere [7].

3.3. Geometrical approach to peak power scaling

The geometrical power scaling concept was applied experimentally as published in earlier work of the authors [7, 8]. The KLM oscillators were operated in air both under normal and reduced pressure environments. For the scaling experiments in work [7], all parameters except the pump power were kept constant. Four passes of the laser mode through the Yb:YAG thindisk (TRUMPF Laser GmbH) per roundtrip allowed to couple out large fractions of the intracavity power (21% transmission of the output coupler). The mode size inside the 1 mm thick sapphire Kerr-plate was varied by successively exchanging the mirrors F1,2 to have R1, <sup>2</sup> ranging from 300 to 900 mm. The resulting peak power increased proportionally to R1, 2. These results are summarized in Figure 5.

As described previously, the soliton peak-power is fairly invariant under a change of the intracavity GDD. However, the changes in pulse energy and duration can be substantial and give flexibility in the design parameters. This is demonstrated in Figure 5b, where the GDD in the thin-disk KLM oscillator was varied from �18,000 to �48,000 fs<sup>2</sup> by exchanging dispersive

Figure 5. (a) Summary of the data from the geometrical KLM power-scaling approach. The waist radius in the Kerrmedium, growing with R1,2, is approximated from ABCD-matrix calculations and (b) experimental example of intra cavity peak power and pulse duration when the total oscillator second order anomalous dispersion (GDD) is increased.

the increase of nonlinear phase acquired in gas. Thus, the contribution of air relative to that from the bulk Kerr-medium becomes significant. This is potentially harmful as (i) the pulsestability becomes more dependent on air-fluctuations due to the coupling to SAM and SPM (ii) the oscillator SAM cannot be optimized independently anymore by positioning of the Kerr-

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This effect can only be counteracted by evacuating or decreasing the pressure of the atmosphere in the oscillator. A rough estimation of the fractional contribution of the bulk Kerrmedium to total nonlinear phase-shift, depending on waist-size of the cavity-mode and differ-

For these reasons, it was necessary to reduce the atmospheric pressure in the oscillator from [8] to about 150 mbar for stable operation whereas the effect of evacuation proved negligible in the short-R1, <sup>2</sup> oscillators [7]. The total nonlinear phase-shift acquired in the reduced-pressure oscillator with R1, <sup>2</sup> being 2 m was approximately 0.6 rad. In that case, the contribution of air to

Although the geometrical peak power scaling concept described here exhibits a seemingly linear dependence of the intra-cavity peak-power on the mode size in the Kerr-medium, it is very interesting to further verify this dependence for even larger mode sizes and higher intra-

Figure 7. Estimated contribution of the Kerr-plate to the total nonlinearity γ, originating from both the solid Kerr-plate

and the air inside the oscillator. It is plotted for different air-pressures.

medium as the atmosphere begins contributing to the mode-shaping.

the total nonlinear phase-shift can be estimated to stay favorably below 10%.

ent pressure levels is depicted in Figure 7.

cavity peak powers.

Figure 6. (a) Spectral broadening and spectral shift for different Kerr-medium positions with respect to the focus and (b) intra-cavity peak power for different Kerr-medium positions. The saturation-power of the SAM is also estimated from ABCD-calculations and plotted.

mirrors. In particular example, the intra-cavity pulse energy increased from 32 to 57 μJ while the pulse duration also increased from 210 to 330 fs showing little effect on the peak power.

Soliton mode locking with strong self-phase modulation allows the direct generation of pulses approaching the spectral gain bandwidth of the laser-medium. SPM plays a key role in replenishing those spectral components of the pulse which do not see sufficient net amplification from the gain emission spectrum. A reasonably small value of the intra-cavity dispersion as well as a strong self-amplitude modulation is necessary to reach this regime. In a KLM oscillator combining a fairly low roundtrip GDD of 12,000 fs2 as well as a sapphire plate of 5 mm thickness, 140 fs pulses could be generated with a high optical-to-optical efficiency of 29%. The oscillator operated with a focusing section incorporating mirrors R1,<sup>2</sup> with 2 m curvature. This allowed an intra-cavity peak-power level of more than 400 MW with more than 60 MW output peak power. These results are in a good agreement with the linear powerscaling curve in Figure 5a.

The SAM is quite sensitive to the position of the Kerr-medium within the focus of F1,2. Simulations show that mostly the saturation power is affected which intuitively follows from the change of intensity in the medium. Data taken for a Kerr-medium being translated through the focus are displayed in Figure 6. It is evident that both the spectral bandwidth and the peakpower increase while the Kerr-medium position is shifted out of the focus. A factor of nearly 2 could thus be gained in intra-cavity peak-power, from near 200 MW to more than 400 MW. Beyond this point mode-locking could not be observed.

#### 3.4. Influence of atmosphere

The relatively short ( 5 m) KLM oscillators with R1,<sup>2</sup> up to 1 m are fairly insensitive to pressure changes of the encompassing air and most of the nonlinear phase-shift is acquired in the Kerr-medium. The increase of Rayleigh distance for weaker focusing (longer R1, 2) leads to the increase of nonlinear phase acquired in gas. Thus, the contribution of air relative to that from the bulk Kerr-medium becomes significant. This is potentially harmful as (i) the pulsestability becomes more dependent on air-fluctuations due to the coupling to SAM and SPM (ii) the oscillator SAM cannot be optimized independently anymore by positioning of the Kerrmedium as the atmosphere begins contributing to the mode-shaping.

This effect can only be counteracted by evacuating or decreasing the pressure of the atmosphere in the oscillator. A rough estimation of the fractional contribution of the bulk Kerrmedium to total nonlinear phase-shift, depending on waist-size of the cavity-mode and different pressure levels is depicted in Figure 7.

For these reasons, it was necessary to reduce the atmospheric pressure in the oscillator from [8] to about 150 mbar for stable operation whereas the effect of evacuation proved negligible in the short-R1, <sup>2</sup> oscillators [7]. The total nonlinear phase-shift acquired in the reduced-pressure oscillator with R1, <sup>2</sup> being 2 m was approximately 0.6 rad. In that case, the contribution of air to the total nonlinear phase-shift can be estimated to stay favorably below 10%.

Although the geometrical peak power scaling concept described here exhibits a seemingly linear dependence of the intra-cavity peak-power on the mode size in the Kerr-medium, it is very interesting to further verify this dependence for even larger mode sizes and higher intracavity peak powers.

mirrors. In particular example, the intra-cavity pulse energy increased from 32 to 57 μJ while the pulse duration also increased from 210 to 330 fs showing little effect on the peak power.

Figure 6. (a) Spectral broadening and spectral shift for different Kerr-medium positions with respect to the focus and (b) intra-cavity peak power for different Kerr-medium positions. The saturation-power of the SAM is also estimated from

Soliton mode locking with strong self-phase modulation allows the direct generation of pulses approaching the spectral gain bandwidth of the laser-medium. SPM plays a key role in replenishing those spectral components of the pulse which do not see sufficient net amplification from the gain emission spectrum. A reasonably small value of the intra-cavity dispersion as well as a strong self-amplitude modulation is necessary to reach this regime. In a KLM oscillator combining a fairly low roundtrip GDD of 12,000 fs2 as well as a sapphire plate of 5 mm thickness, 140 fs pulses could be generated with a high optical-to-optical efficiency of 29%. The oscillator operated with a focusing section incorporating mirrors R1,<sup>2</sup> with 2 m curvature. This allowed an intra-cavity peak-power level of more than 400 MW with more than 60 MW output peak power. These results are in a good agreement with the linear power-

The SAM is quite sensitive to the position of the Kerr-medium within the focus of F1,2. Simulations show that mostly the saturation power is affected which intuitively follows from the change of intensity in the medium. Data taken for a Kerr-medium being translated through the focus are displayed in Figure 6. It is evident that both the spectral bandwidth and the peakpower increase while the Kerr-medium position is shifted out of the focus. A factor of nearly 2 could thus be gained in intra-cavity peak-power, from near 200 MW to more than 400 MW.

The relatively short ( 5 m) KLM oscillators with R1,<sup>2</sup> up to 1 m are fairly insensitive to pressure changes of the encompassing air and most of the nonlinear phase-shift is acquired in the Kerr-medium. The increase of Rayleigh distance for weaker focusing (longer R1, 2) leads to

scaling curve in Figure 5a.

ABCD-calculations and plotted.

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3.4. Influence of atmosphere

Beyond this point mode-locking could not be observed.

Figure 7. Estimated contribution of the Kerr-plate to the total nonlinearity γ, originating from both the solid Kerr-plate and the air inside the oscillator. It is plotted for different air-pressures.

#### 3.5. Intensity noise and CEP stabilization

Since power-fluctuations can be enhanced in nonlinear processes like SPM, high-harmonic generation, difference frequency generation or optical parametric amplification it is necessary that the pulses generated from the oscillator are as noiseless as possible. It is not obvious that high-power oscillators, especially those with long cavities, can be as silent as usual low power bulk KLM oscillators. Concerns were also raised by some that high-power KLM oscillators would also suffer from instabilities since the initiation of mode-locking requires a setup close to the cavity stability limit. State of the art KLM thin-disk oscillators deliver more than 100 W average power and, thus, are by two orders of magnitude more powerful than usual KLM bulk oscillators. For instance, the oscillator described in the previous section [8] delivers 150 W average and 60 MW peak power.

2.1 W [59]. So far, CEP stabilization of high average and peak power oscillators was demonstrated only for KLM thin-disk oscillators resulting in sub-300 mrad out-of-loop noise and output average powers in the 40–50 W range. This was achieved by implementing two CEP control methods, namely intra-cavity loss control by means of an acousto-optic modulator (AOM) [5] and pump-diode control by means of dual-wavelength pumping [60]. Very recently, a new intra-cavity loss modulation approach comprised of an AOM simultaneously acting as a Kerr-medium was implemented [61]. This resulted in the highest average power CEP stabilized laser delivering over 100 W output power and over 30 MW peak power. This approach seems to be scalable by at least an order of magnitude in terms of peak power making it a

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Even though the geometrical scaling-procedure enables near 100 MW pulses directly from KLM oscillators, it relies on a substantial intra-cavity peak- and average power increase. This raises the demands on the coating damage thresholds during stressful events such as the transition to mode locking. The elevated intra-cavity average powers of more than 1 kW also require careful selection of the utilized materials to prevent thermal lensing instabilities. Complementary to the intra-cavity power-scaling, it is possible to boost the oscillator output by enlarging the output-coupling ratio. This concept has been realized with a mode-locked thin-disk oscillator in [62] for the first time using an imaging multi-pass configuration. Up to 72% of the circulating power were extracted from the SESAM mode-locked oscillator in [30] resulting in 145 W average power output while the intra-cavity value was only 200 W. The short interaction length in the thin disk cannot replenish such high power-loss during a single roundtrip which needs to be overcome by an increased number of beam-passes through the

The number of disk passes cannot be made arbitrarily high, however, since any thermal lens in the disk is accumulated, giving rise to a narrowing of the cavity-stability zones with respect to the pump power. While this effect has obviously not hindered comprehensive implementation in an oscillator-cavity working at the center of the stability-zone [30], it is not as obvious that the same can be done for KLM-cavities that are more sensitive to the presence of thermal lenses. However, recently a first demonstration of this multi-pass concept in a thin-disk KLM oscillator was realized with six double passes through the thin disk per round-trip resulting in 130 W average and 20 MW peak output power [63]. With respect to a reference oscillator, the peak power did not drop when increasing the output-coupling ratio to 30%, rendering it an

All oscillators presented (see Table 1) were mode locked in the anomalous dispersion regime providing bandwidth limited, unchirped pulses with a well behaved temporal phase.

method of choice for the next-generation CEP-stabilized KLM thin-disk oscillators.

disk, e.g., with an imaging multi-pass cell (20 passes realized in [30]).

encouraging result towards scaling the output coupling ratio to 50%.

4.2. Positive dispersion regime

4. Discussion

4.1. Further power scaling opportunities

The intensity noise of this oscillator was characterized (see Figure 8). Measurement of the laser output with an RF-signal analyzer reveals that nearly all of the noise is generated in the lowfrequency band below 10 kHz. This can be attributed to both technical noise such as watercooling, pump-source or air-turbulences as well as gain-relaxation dynamics. The latter lies in the lower kHz range due to the approximately 1 ms upper state lifetime of Yb:YAG. An intensity noise of 0.3% rms deviation in the 1 Hz–1 MHz window is typical for KLM thin-disk oscillators. At slightly reduced power levels even better values can be measured on a daily basis. These intensity-noise values are comparable to commercial Ti:Sapphire oscillators and promise good results for CEP stabilization of high peak and average power thin-disk oscillators.

Many advanced scientific applications such as high precision spectroscopy in the XUV-VUV range or attosecond pulse generation require the lasers to be CEP stabilized. Obviously, the demonstration of CEP stabilization of femtosecond thin-disk oscillators is an important step towards enabling these applications with a compact, transportable thin-disk oscillator source. Moreover, a low intensity noise is a critically important prerequisite for the CEP stabilization demonstration. The first carrier envelope offset frequency stabilization of a femtosecond thindisk oscillator was demonstrated with a KLM thin-disk oscillator providing a remarkably high average power of 45 W and a peak power over 4 MW [58]. A similar demonstration followed with a SESAM mode-locked thin-disk oscillator, providing a moderate output power of only

Figure 8. (a) RF signal around the repetition rate of the oscillator with 60 MW output peak power. Small sidebands are visible more than 75 dB below the signal and (b) low-frequency noise performance.

2.1 W [59]. So far, CEP stabilization of high average and peak power oscillators was demonstrated only for KLM thin-disk oscillators resulting in sub-300 mrad out-of-loop noise and output average powers in the 40–50 W range. This was achieved by implementing two CEP control methods, namely intra-cavity loss control by means of an acousto-optic modulator (AOM) [5] and pump-diode control by means of dual-wavelength pumping [60]. Very recently, a new intra-cavity loss modulation approach comprised of an AOM simultaneously acting as a Kerr-medium was implemented [61]. This resulted in the highest average power CEP stabilized laser delivering over 100 W output power and over 30 MW peak power. This approach seems to be scalable by at least an order of magnitude in terms of peak power making it a method of choice for the next-generation CEP-stabilized KLM thin-disk oscillators.
