Modelocking of a thin-disk laser with the frequency-doubling nonlinear-mirror technique

We demonstrate a frequency-doubling nonlinear-mirror (NLM) modelocked thindisk laser. This modelocking technique, composed of an intracavity second harmonic crystal in combination with a dichroic output coupler, offers robust operation decoupled from cavity stability (as in semiconductor saturable absorber mirror (SESAM) modelocking) combined with an ultrafast saturable loss and high modulation depth (as in Kerr-lens modelocking (KLM)). With our NLM diode-pumped Yb:YAG thin-disk laser we achieve 21 W of average power at 323-fs pulse duration, which is an order of magnitude shorter than the previously obtained duration with the same technique in bulk lasers. Using these first results, we present a theoretical model for the NLM technique, which accurately predicts its loss modulation properties and the shortest achievable pulse duration without relying on any fitting parameters. Based on this simulation, we expect that the NLM technique will enable thin-disk lasers with average power of more than 100 W, with potentially sub-200 fs pulses. This could potentially solve the pulse duration limitations with SESAM modelocked Yb:YAG thin-disk lasers without imposing strong cavity stability constraints such as in KLM. © 2017 Optical Society of America OCIS codes: (140.0140) Lasers and laser optics; (140.4050) Mode-locked lasers; (140.7090) Ultrafast lasers; (190.7110) Ultrafast nonlinear optics. References and links 1. A. Ancona, S. Döring, C. Jauregui, F. Röser, J. Limpert, S. Nolte, and A. Tünnermann, “Femtosecond and picosecond laser drilling of metals at high repetition rates and average powers,” Opt. Lett. 34(21), 3304–3306 (2009). 2. T. Südmeyer, S. V. Marchese, S. Hashimoto, C. R. E. Baer, G. Gingras, B. Witzel, and U. Keller, “Femtosecond laser oscillators for high-field science,” Nat. Photonics 2(10), 599–604 (2008). 3. T. Nubbemeyer, M. Kaumanns, M. 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Introduction
Femtosecond laser sources with high peak and average power are an indispensable tool for many industrial and scientific applications, including laser precision micromachining and cutting [1], frequency metrology and strong-field physics in attosecond science [2].Laser amplifiers based on the thin-disk, fiber, or Innoslab technology represent the state of the art of high-power ultrafast lasers.They reach kW-level average power with peak powers exceeding the GW level [3][4][5].However, these systems have a substantial level of complexity and, in some cases, non-diffraction-limited beam quality.Modelocked thin-disk laser (TDL) oscillators are an attractive alternative to complicated amplifier systems and combine high output and peak power in a compact table-top MHz oscillator with excellent output beam quality.Moreover, these systems drive experiments at MHz repetition rates [6,7], leading to reduced measurement times, and increased signal-to-noise ratios and photon fluxes [2,8].
Thin-disk lasers offer the highest performance in terms of average power and excellent beam quality among all ultrafast oscillators.Based on the gain material Yb:YAG and modelocked with semiconductor saturable absorber mirrors (SESAMs), they currently achieve up to 275-W average power with 583-fs pulse duration [9] and 80-μJ pulse energy with 1.07-ps pulses [10].Using broadband gain materials such as Yb:CALGO, pulse durations down to sub-50 fs were achieved with SESAM modelocking, however, at the expense of the output power, which stayed below 5 W [11,12].Because of the limited gain bandwidth of Yb-doped materials suitable for high-power operation (Yb:YAG, Yb:LuO), combining shorter pulse durations (sub-500 fs) and high average powers (>100 W) with SESAM-modelocking is a challenging task.This is mainly due to the SESAM's noninstantaneous recovery times, moderate modulation depths, and thermal effects from unsaturated losses and two-photon absorption [13].Ongoing efforts to address these issues include improved strain compensation [14], and different bonding techniques to achieve flatter samples with efficient heat removal [15].Modelocking TDLs with the Kerr-lens technique (KLM) has allowed for shorter pulse durations while maintaining high average power.With the gain material Yb:YAG, this technique resulted in 270 W of average power with 330 fs pulses [16] and 155 W with 140 fs pulses [17].However, these results were limited to pulse energies <15 µJ.Shorter pulses down to sub-50 fs with average power of around 5 W were reported with Yb:YAG [18] and Yb:LuO [19].In general, the KLM technique imposes strict constraints on the cavity design that needs to be operated close to its stability edge.This requirement introduces additional challenges in alignment sensitivity and stability, as it directly couples spatial and temporal effects.Recently, TDLs have also been modelocked with the nonlinear polarization rotation (NPR) technique.Using Yb:YAG as gain material and introducing the required intensity-dependent phase shift for NPR via a long and phase-mismatched intracavity second harmonic generation (SHG) crystal, these oscillators reached up to 44 W with sub-500 fs pulses [20].In this work, we investigate and demonstrate modelocking of a TDL with an alternative technique, the frequency-doubling nonlinear mirror (NLM) [21].In this device, whose operating principles are described in section 2, the combination of a phase-matched SHG crystal and a dichroic output coupling mirror results in a lower effective output coupling rate for high intensity light, thereby providing a saturable reflectivity and enabling modelocked operation.This approach offers a route to overcome the trade-offs in both SESAM and KLM modelocking of high power oscillators.It offers robust operation decoupled from the cavity stability (as in SESAM modelocking), together with an ultrafast saturable loss (as in KLM), while maintaining power scalability.Compared to the NPR technique, a significantly shorter nonlinear crystal can be used, which should be favorable to avoid thermal lensing in future power scaling experiments (for example we use one 0.5-mm-long BBO crystal in the present work, compared with two ~20-mm-long LBO crystals in [20]).Moreover, the NLM technique offers a large and highly flexible modulation depth that scales with the laser output coupling rate.
In Fig. 1(a) we present an overview of the performance of solid-state lasers modelocked with the NLM technique [Fig.1(a)] [22][23][24][25][26]. Additionally, this technique has also been used to assist the cascaded χ (2) lens modelocking process in order to stabilize it and provide selfstarting operation [27].Solid-state NLM-modelocked lasers achieved multi-ps pulse durations at comparatively high repetition rates (~100 MHz), which results in intracavity peak powers below 50 kW.Consequently, tight focusing is needed in order to reach the required intensities to drive the SHG process.This, in turn, makes spatial walk-off effects significant, which limits the efficiency of the process.Longer SHG crystals can be used, which, however, sets a lower limit for the achievable pulse duration in the few-ps-range due to group velocity mismatch (GVM) between the fundamental and its second harmonic [28].
High-power ultrafast TDLs, on the other hand, are well suited for the NLM process as their high peak powers allow for driving the nonlinear process with short crystals, which results in minimized thermal effects, larger bandwidths, and a corresponding short response time of the saturable reflectivity.Additionally, the NLM method is easily power-scalable by increasing the spot size on the SHG crystal.
Here we present a first demonstration of a TDL modelocked by the NLM technique, using a Yb:YAG thin disk.We obtain 21 W of average power with 323-fs pulses and, in another configuration, 28 W with 570-fs pulses.Our proof-of-principle laser reaches more than 1 μJ of pulse energy, which results in more than 3 MW of extracavity peak power.Compared to prior results of NLM modelocking in bulk lasers, we decrease the achieved pulse durations by an order of magnitude [Fig.1(a)].Compared to state-of-the-art TDLs using Yb:YAG as gain medium [Fig.1(b)], this first result reaches pulse durations significantly shorter than those obtained by SESAM-modelocking, and which lie in a range previously only accessible with KLM.
In section 2, we present the operating principles of the NLM technique.In section 3, we discuss the laser experiment.In section 4, we describe in detail our numerical model and use it in order to estimate the shortest pulses achievable with our device.We conclude in section 5 by summarizing the obtained results and envisaging the next generation of NLM modelocked thin-disk lasers with average powers in the 100-W level.The symbols specify the modelocking technique: square for SESAM, circle for KLM, cross for NPR and star for NLM.In the presented results, we reduce the pulse durations achieved with the NLM modelocking technique by an order of magnitude, down to sub-350 fs, at output powers approaching 30 W, which is comparable to pulse durations achieved by state-of-the-art thin-disk oscillators.

NLM operating principles
We show a general schematic of the frequency-doubling NLM technique in Fig. 2(a), consisting of a second-order nonlinear crystal (χ (2) crystal) configured for SHG, in combination with a dichroic output coupler (OC).In Fig. 2(b) we present the evolution of the pulse energy for the fundamental wave (FW) and the second harmonic (SH) inside the χ (2)  crystal, based on the simulation discussed in Sec. 4. The NLM device can be described in three stages: (i) Intracavity laser light [P i in Fig. 2(a)] is directed through an intracavity SHG crystal, where some of this FW light is converted to its SH [in Fig. 2(b) solid red and green curves, refer, respectively, to FW and SH].The SHG crystal is tilted in order to fulfill the phase matching condition (Δk = k SH -2k FW = 0) for the SHG process.
(ii) Both wavelengths travel through a variable length of air ["air space" in Fig. 2(a)] and are reflected from a dichroic OC, which is highly reflective (HR) for the SH and partially reflective for the FW.The transmitted power [P t in Fig. 2(a)] of the FW defines the transmission of the NLM device.
(iii) The beams then pass back through the χ (2) crystal [dashed curves in Fig. 2(b)].The relative phases of the FW and SH are adjusted via the air space in such a way that the reverse process of SHG (i.e., optical parametric amplification, OPA) occurs optimally (Δφ = -π), thereby converting the SH light back to the FW.
Essentially, the NLM modelocking device acts as an OC with intensity-dependent reflectivity and transmission.At higher input intensities, more light is converted to the SH in stage (i).This implies a reduced output coupling rate for the FW, and more total power (FW + SH) being reflected by the OC in stage (ii).Then, by converting the reflected SH back to the FW in stage (iii), there is a higher overall reflectivity for the FW.
To quantify the behavior of the device, we consider the average power of the FW at different positions: P i , P t , and P r refer to the initial intracavity power, the transmitted extracavity power, and the final reflected intracavity power, respectively.We also introduce the corresponding FWHM (full-width at half-maximum) pulse durations, denoted τ i , τ t , and τ r .We then define the following parameters [29][30][31]: ( , ) / ( , ) / .
The parameter R nl indicates the nonlinear reflectivity of the device, T nl the ratio between the intracavity power and the output power of the laser, while κ indicates the pulse-shortening factor, which is related to the modulation bandwidth of the device.The variable I pk is the peak intensity of the incoming beam on the χ (2) crystal, I pk = max(I i (r,t)).

Experiment
In this section, we present the laser cavity used in the presented experiment (Sec.3.1) and the results we obtain with it (Sec.3.2).Then, we discuss how the output pulse parameters depend on the NLM modelocking device configuration (Sec.3.3).

Experimental setup
The laser experiment we present here uses a 230-μm thick, 5-at.%doped Yb:YAG disk, contacted on a CuW heatsink by Dausinger + Giesen GmbH, and mounted in a 24-pass thindisk pump head with a 2.1-mm diameter pump spot.The disk has a wedge of ~0.1 deg between the front and back surface and a non-astigmatic cold radius of curvature of −5.3 m.The disk is diode-pumped up to 160 W at a center wavelength of 936 nm.In Fig. 3(a) we present a schematic of the laser cavity and in Fig. 3(b) the evolution of the 1/e 2 laser mode radius within the oscillator.We designed our cavity to have a double-reflection on the thin disk in order to increase the available gain per roundtrip.The cavity includes a 2.5-mm undoped YAG Brewster plate (BP), which fixes the polarization in the plane of the optical table and provides δ = 6.37 mrad/MW of self-phase modulation (SPM).In a first step, we operate the cavity without the χ (2) crystal, but with the dichroic OC, and we achieve up to 30 W of output power with 33% optical-to-optical efficiency in continuous-wave (cw) singlemode operation (M 2 <1.1).The dichroic OC used for the NLM configuration has 19.7% transmission (R FW = 80.3%) at the FW (1030 nm) and high reflectivity (R SH = 99.9%) at the SH (515 nm).For modelocking, we insert a 500-μm-thick type-1 BBO crystal close to the cavity focus on the OC mirror (beam waist radius of 185 μm), as shown in the inset [Fig.3(c)].The crystal is cut for phase matching at 1030 nm with both faces anti-reflection coated for 1030 nm and 515 nm.We achieve correct phase matching for the SHG process by optimizing the tilt of the BBO crystal while looking at the small green leakage from the OC.For a correct phase offset Δφ between FW and SH for high-efficiency OPA we tune the spacing between the nonlinear crystal and the OC in a range between 5 mm and 8 mm in order to minimize the non-backconverted SH.The modelocking process is initiated by lightly tapping the mounting post of the focusing mirror before the BBO crystal.Flat dispersion-compensating mirrors providing negative group delay dispersion (GDD) are used in the cavity to balance the SPM accumulated in air, the BBO crystal, the BP, and the disk.

Modelocking results
In our optimization of the modelocked operation, we focused on the one hand on reaching the shortest pulse duration, and on the other hand on maximizing the output power.We always optimize the distance between BBO crystal and OC in order to have the maximum backconversion of the SH during the second pass in the BBO crystal.However, by adjusting the SHG phase matching, we adapt the reflectivity saturation and thus obtain the following two configurations: -Short pulse (SP) configuration: the BBO tilt is tuned such that the green leakage through the OC (in cw operation) is maximized, i.e., Δk = 0.This maximize the reflectivity modulation of the NLM device, allowing for the shortest pulses.
-High power (HP) configuration: we slightly phase mismatch the SHG process by reducing the transmitted green light through the OC to ~85% of the maximum value (in cw operation).This reduction of the SHG efficiency corresponds to a phase mismatch |Δk•L| ~0.3π [32].This results in a higher OC rate and lower FW reflectivity, which, in turn, allows for higher output power.
Using an intracavity GDD from the GTI mirrors of −5900 fs 2 per roundtrip, we obtain 323-fs pulses at 21 W of output power in the SP configuration, at a repetition rate of 17.8 MHz.This corresponds to a pulse energy of 1.2 μJ and to more than 3 MW of extracavity peak power.The pulses are supported by an optical spectrum with a FWHM of 4.23 nm [see Fig. 4(a)], which corresponds to a transform-limited duration of 263 fs.The chirp in the pulses could be due to the SHG process, and will be investigated in future work.
In the HP configuration, we could increase the output power up to 28 W at 150 W of pump power, however with substantially longer pulses of 570 fs.In this case, the intracavity GDD is increased to −7000 fs 2 per roundtrip.We ensured clean modelocking in all configurations by obtaining the optical spectrum, the autocorrelation trace and radio frequency spectra.Moreover, by scanning the autocorrelator delay up to 60 ps and acquiring a sampling oscilloscope trace with a 45 GHz bandwidth photodiode we prove single-pulsed operation.The beam quality is assessed by measuring the M 2 of the output beam using a commercially available scanning-slit automatized beam profiler.In all configurations, we obtain a nearly-diffraction-limited beam with an average M 2 = [(M 2 x ) + (M 2 y )]/2 below 1.10.In Fig. 4 we present the diagnostics for the 323 fs pulse, corresponding to the highest peak power.Stable modelocking was observed for several hours in daily operation without any breakdown of modelocking.
The maximum achievable output power in this proof-of-principle experiment is currently limited by the comparatively small pump-spot size on our disk.We chose a maximum pump intensity safety limit of ~5 kW/cm 2 , which restricted the maximum pump power on our disk to 160 W. Additionally, the non-optimal center wavelength of the pump diodes led to our comparatively low optical-to-optical efficiency of 33% in continuous wave single-mode operation and ~19% in modelocked operation.

Experimental investigation of the NLM-modelocking regime
In Figs.5(a) and 5(b) we show the pulse duration and output power versus pump power for three different experimental conditions: two short pulse (SP) configurations with different values of GDD, and one high-power (HP) configuration.In the NLM modelocking technique, the effective OC rate of the cavity varies with the peak intensity in the χ (2) crystal.For a given configuration, increasing the pump power results in a decrease of the effective transmission, which yields a non-linear relation between output power and pump power as we can see in Fig. 5(b).
In order to accurately determine the intensity-dependent OC rate T nl , we employed a photodiode to measure a small FW leakage through an intracavity mirror in order to infer the intracavity power in modelocked operation.We calibrated the ratio between photodiode voltage and intracavity power in cw operation, since in this case the OC rate is equal to the linear transmission of the OC at the laser wavelength.Using the beam waist on the BBO crystal calculated from the cavity design [Fig.3(b)] and the pulse duration retrieved from the autocorrelation trace (assuming a sech 2 pulse), we can estimate the peak intensity on the BBO crystal.The fluctuations in the effective OC transmission from different measurements are within 10%.
In Fig. 5(a) each data point is labelled with the corresponding OC rate for comparison to Fig. 5(c), where we show the effective OC rate versus the peak intensity on the ΒΒΟ crystal.The solid points in Fig. 5(c) represent the same data points presented in Figs.5(a) and 5(b) while the dashed points are additional measurements shown only in Fig. 5(c).For clarity of presentation, these additional points are not shown in Figs.5(a) and 5(b).The solid purple line in Fig. 5(c) is the prediction of our numerical model, which we describe in section 4. The model accurately predicts the behavior of the device.The configurations optimized for high power generally present an effective OC rate slightly higher than the ones optimized for short pulses, and higher than the model (which assumes Δk = 0).This trend is consistent with the fact that in the high-power configuration, the SHG process efficiency is slightly sub-optimal, leading to a less pronounced effect of the NLM of reducing the effective OC transmission.Additionally, our model does not take into account the reflection losses on the BBO, which are <0.5%.These losses will have the effect of slightly reducing the effective OC transmission.
Next, we also investigate the influence of the NLM device on the pulse shaping.For that we compare in Fig. 5(a) the pulse duration achieved in the short-pulse and high-power configuration with the same amount of intracavity GDD (−5900 fs 2 ).The difference between these two configurations clearly indicate that the phase matching substantially influences the pulse duration.Moreover, we compare the pulse durations achieved in the SP configuration for different values of intracavity GDD [in Fig. 5(b) we show −4800 fs 2 and −5900 fs 2 ].The change in GDD only slightly influences the shortest achievable pulse duration.This observation suggests that the leading process in pulse formation is the NLM, rather than the soliton shaping effect.To further test this hypothesis, we fit the experimental data with an exponential function, τ t = cE p -α , where E p is the intracavity pulse energy.We find for α values between 0.5 and 0.8.A conventional soliton shaping mechanism, arising from GDD and SPM, would have α ~1 [33].This deviation from pure soliton shaping suggests that the NLM device dynamics strongly contribute to the pulse formation process.
In the HP configuration, the slightly phase mismatched SHG process leads to a nonnegligible SPM, with its sign depending on the sign of the phase mismatch Δk.This could potentially influence the pulse formation mechanism.However, in these experiments we did not observe any significant change in the modelocking behavior for different signs of the phase mismatch.

Numerical model of the NLM device
In this section, we present a model for the NLM technique (Sec.4.1), demonstrate that it stands in excellent agreement with our experimental results presented in section 3 (Sec.4.2), and predict the next steps needed for scaling the output power and pulse duration of NLM modelocked TDLs.

Description of the model
We base our model on coupled-wave equations which describe the two-stage process, namely SHG on the first pass through the χ (2) crystal, followed by the reverse process of OPA on the return pass.Because of the high intracavity pulse energy involved (>1 μJ), we can use a loose focus (beam waist radius of 185 μm) on a thin BBO crystal (length L = 500 μm), and hence spatial effects such as diffraction and Poynting vector walk-off are negligible.On the other hand, temporal effects (mainly the group velocity mismatch (GVM)) play an important role in limiting the bandwidth of the device [26,28].Indeed the GVM delays the SH pulse with respect to the FW, which leads to a reduced back conversion of the SH to the FW during the second pass in the χ (2) crystal.In our configuration the GVM parameter in the χ (2) crystal corresponds to δ 1,2 = 1/v g SH -1/v g FW = 93 fs/mm [34].For two passes in a 500-μm thick BBO crystal, the total delay sums up to ~100 fs and becomes comparable to the pulse duration, thus it has to be included in our model.By neglecting the spatial effects but including temporal effects to first and second order, we obtain a simplified coupled-wave equations model: We use the following variables: E j : electric field envelope (j = FW or j = SH); n j refractive index; ω j : center frequency; v g : group velocity; d eff : effective nonlinear coefficient of the material [35]; β j : group velocity dispersion parameter; Δk phase mismatch for wavevectors k j = ω j n j / c. ; z: longitudinal position in the crystal; t: delay, in the moving coordinate system relative to the group velocity of the FW.We use Eq. ( 4) to model stages (i) and (iii) of the NLM device, as described in section 2. For stage (i), the SHG process, we solve Eq. ( 4) using as initial conditions a pulse with a temporal sech profile for E FW (t,0), and set E SH (t,0) = 0. We assume perfect phase-matching and therefore set Δk to zero.For stage (ii), we take the output envelopes E FW (t,L) and E SH (t,L), where L is the length of the BBO crystal, and apply the linear reflectivity of the OC (i.e., power reflectivities of R FW = 80.3% for the FW and R SH = 99.9% for the SH).Additionally, we add a phase shift Δφ = -π to the SH.The combination of Δφ = -π and Δk = 0 corresponds to the optimal condition for the back-conversion of the SH to the FW.The resulting envelopes are then used as the input conditions to Eq. ( 4) to model the returning pass (iii), i.e., the OPA process.By performing a series of simulations for different peak intensities on the χ (2) crystal of the incoming pulse (I pk ), we retrieve the behavior of the NLM device for a pulse with a Gaussian intensity profile in space.It is worth noting that this model does not rely on any fitting parameters.

Results of the model: bandwidth considerations
We show the nonlinear reflectivity R nl (I pk, τ i ) as a function of the peak intensity on the BBO crystal I pk for different output pulse durations τ t in Fig. 6(a).The reflectivity modulation is given by the difference between the R FW = 80.3% line (i.e., the linear reflectivity of the OC at 1030 nm) and the R nl curve, defined as in Eq. (1).
The nonlinear reflectivity is significantly reduced for shorter pulse durations, because GVM leads to a reduced temporal overlap between the FW and SH in the second pass through the crystal.This effect results in increased losses of the device.The degradation in performance for shorter pulses corresponds to a limited bandwidth for which this device is able to provide optimal performance.We refer to this limit as modulation bandwidth.It is worthwhile to mention that the phase-matching bandwidth of each one of the single χ (2)  processes (namely SHG and OPA) is significantly larger than the bandwidth of the two processes combined together, because the delay between the FW and SH pulses accumulates through the two processes.
In Fig. 5(c), we showed the corresponding transmission of the NLM T nl , as defined in Eq. ( 2), as a purple solid line.The nonlinear transmission T nl (I pk , τ i ) depends strongly on the pulse peak intensity on the BBO crystal I pk .In contrast to the behavior of R nl , T nl is unaffected by the output pulse duration τ t in the considered range (i.e., for pulses longer than 200 fs).This independence of T nl from τ t is due to the fact that it involves only one pass in the χ (2) crystal and that the bandwidth of the SHG process alone is sufficient for efficient conversion.Thus, in Fig. 5(c) we show only one curve, calculated for a pulse duration of 1 ps, to compare with the experimental values.The good agreement between experiment and theory confirms the validity of our model.
The limitations in the modulation bandwidth of the NLM does not only consist in a reduced nonlinear reflectivity, but translates also into a pulse lengthening effect.Figure 6(b) shows the pulse-shortening parameter, κ, defined as in Eq. ( 3), as a function of the pulse duration transmitted by the NLM.Below a certain pulse duration, the NLM stops acting as a pulse shortener on each round-trip of the cavity.As is clearly visible, this effect is only weakly dependent on the pulse peak intensity on the BBO crystal I pk .Moreover, this threshold point scales with the crystal length.For pulse durations below 300 fs in our experimental configuration, Fig. 6(b) predicts that the NLM causes a pulse lengthening on each round trip.Thus, this transition to κ > 1 likely explains why 300 fs pulse duration was the shortest we could obtain in this experiment, since the NLM (in the configuration used here) acts to lengthen pulses shorter than this.Our model succeeded in predicting both the expected OC rate of the cavity and the shortest achievable pulse duration.Thus, we can use it in the design of the next generation NLM lasers with shorter pulses and higher powers.For example, increasing the nominal transmission of the OC for the FW to 40% instead of 20% would, at the same intensity and BBO crystal length, yield κ = 1 (i.e. the transition between pulse-shortening and pulselengthening) at a pulse duration of ~200 fs, together with an effective OC rate of ~25%.Yb:YAG thin-disk lasers with a similar or even much higher OC rate have already been demonstrated [10,36].Use of a slightly shorter BBO crystal (~300 μm thick) and slightly higher intensity ~90 GW/cm 2 would yield a further reduction in the NLM-limited pulse duration, towards <150 fs pulses.This intensity is still below the BBO crystal damage threshold, based on other demonstrated systems.For instance in [37] a BBO crystal is used in an optical parametric amplifier with peak intensities up to 300 GW/cm 2 (~500-fs pulses at 515 nm).Additionally, the pulse duration supported by the NLM can be reduced even further by GVM compensation techniques.These techniques have already been proposed [38] and demonstrated [26] to increase the modulation bandwidth of the NLM modelocking technique.
As well as offering more favorable pulse shortening, a higher OC rate also reduces the intracavity power demands for a given output power, which is highly favorable for power scaling.Moreover, with the NLM technique, the available modulation depth is approximately proportional to the nominal transmission of the OC for the FW.Thus, going to higher OC rates also increases the modulation depth accordingly, which is beneficial for obtaining short pulses.By scaling the pump spot size on the disk, and the laser spot size on the disk and BBO crystal, we expect that >100 W output powers are well within reach.We expect that the BBO crystal will be able to handle the increased thermal load based on other demonstrated systems, where such crystals are operated with kW-level average power [3].

Conclusion and outlook
We demonstrated the first NLM modelocked TDL, achieving 323-fs pulses at 21 W output power, which corresponds to pulses with >1 μJ pulse energy and >3 MW peak power.A key factor in obtaining this performance was the use of a thin-disk instead of a bulk laser geometry.Indeed the NLM, based on ultrafast nonlinear processes, benefits from high intracavity peak power that is typical of high-power short-pulsed thin disk lasers.Additionally the NLM process is well suited for high-power short-pulsed TDL operation as it provides an easily scalable modulation depth, offers an ultrafast response of the saturable loss (as in KLM), and can be operated in the center of the cavity stability region (as in SESAM modelocking).
We also presented a simple model for the NLM technique that, without any fitting parameters, succeeded in both predicting the effective OC rate and the shortest achievable pulse duration in the presented configuration.Based on our current laser performance and our simulations, we expect this first result to enable a new way towards high-power short-pulsed modelocked thin-disk oscillators in the near future.Increasing the spot size on the disk and simultaneously on the BBO crystal will allow for pumping harder and thus scaling up the average power to the 100-W regime.Employing a shorter crystal and an OC with a higher nominal transmission seems a promising way toward shorter pulses.Additionally, applying broadband gain materials (e.g., Yb:LuO, Yb:CALGO), even shorter pulses could be achieved.By simple adjustment of the χ (2) crystal parameters or material, the technique also holds great promise for long-wavelength TDLs using new thin-disk gain media such as Ho:YAG [39].

Funding
Swiss National Science Foundation (SNSF) project grant numbers 200020_172644.

Fig. 1 .
Fig. 1.(a) Pulse duration and average power of NLM modelocked lasers.(b) Pulse duration and pulse energy of modelocked Yb:YAG TDLs.The symbols specify the modelocking technique: square for SESAM, circle for KLM, cross for NPR and star for NLM.In the presented results, we reduce the pulse durations achieved with the NLM modelocking technique by an order of magnitude, down to sub-350 fs, at output powers approaching 30 W, which is comparable to pulse durations achieved by state-of-the-art thin-disk oscillators.

Fig. 2 .
Fig. 2. (a) Schematic representation of the nonlinear-mirror modelocking (NLM) technique.(b) Evolution of the pulse energy inside the χ (2) crystal.Solid and dashed lines refer, respectively, to the forward and backward pass in the crystal.(OC -output coupler, SHG -second harmonic generation, FW -fundamental wave, SH -second harmonic)

Fig. 3 .
Fig. 3. (a) Schematic representation of the laser cavity.(b) Evolution of the 1/e 2 mode radius.Vertical dashed lines indicate the position of crystals, OC, and end mirror.Labels indicate the curvature of concave mirrors.Inset (c): zoom of mode radius near the OC.(GTIs -dispersive mirrors, BP -Brewster plate)

Fig. 4 .
Fig. 4. Diagnostics for the configuration with the highest peak power (SP configuration, total GDD from the mirrors −5900fs 2 yielding 323 fs pulse duration and 21 W average power).We acquire the diagnostics on the output beam of the laser.(a) optical spectrum, (b) autocorrelation trace, (c) M 2 measure, (d) radio frequency (RF) trace showing the RF comb, (e) RF trace showing the peak at the repetition rate (Res BW = resolution bandwidth), (f) sampling scope trace, in the inset a zoom on a single pulse with a different span.The ripple in the sampling oscilloscope trace is due to the detector.The 1/e 2 beam radius in the M 2 measurement is calculated using the second momentum width (D4σ).The autocorrelation trace and the optical spectrum are fitted with a sech 2 function (red dashed line).(RBW -Resolution bandwidth)

Fig. 5 .
Fig. 5. Characterization of pulse duration (a) and output power (b) versus the pump power.Circles correspond to configurations optimized for short pulses (SP), i.e., Δk = 0; squares to configurations optimized for high power (HP), i.e., the SHG process is slightly detuned from perfect phase matching.(c) Saturable loss effect of the nonlinear mirror.The solid line is the prediction of our model.Solid points: same data shown in in (a) and (b); dashed points: additional data points for the same laser configuration.(GDD -Group delay dispersion)

Fig. 6 .
Fig. 6.Analysis of the performance of the NLM as a function of the output pulse duration τ t and of the peak intensity on the BBO crystal I pk .(a) Saturable reflectivity behaviour: effective reflectivity as a function of I pk for different τ t , (b) pulse shortening factor κ = τ r /τ i as a function of τ t for different I pk .