Generation of 35-fs pulses from a Kerr lens mode-locked Yb:Lu_2O_3 thin-disk laser

We investigate Kerr lens mode locking of Yb:Lu2O3 thin-disk laser oscillators operating in the sub-100-fs regime. Pulses as short as 35 fs were generated at an average output power of 1.6 W. These are the shortest pulses directly emitted from a thin-disk laser oscillator. The optical spectrum of the 35-fs pulses is almost 3 times broader than the corresponding emission band of the gain crystal. At slightly longer pulse duration of 49 fs, we achieve an average power of 4.5 W. In addition, 10.7 W are obtained in 88-fs pulses, which is twice higher than the previous power record for ultrafast thin-disk lasers generating pulses shorter than 100 fs. Our results prove that Kerr lens mode-locked Yb:Lu2O3 thin-disk lasers are a promising technology for further average power and pulse energy scaling of ultrafast high-power oscillators operating in the sub-100-fs regime. © 2017 Optical Society of America OCIS codes: (140.4050) Mode-locked lasers; (140.3538) Lasers, pulsed; (140.7090) Ultrafast lasers; (140.3615)


Introduction
Following the demonstration of the first mode-locked thin-disk laser (TDL) oscillator more than fifteen years ago [1], tremendous progress in the area of power scaling has been achieved [2]. In this period, the field of mode-locked TDLs has evolved into being the leading technology for high power and high pulse energy ultrafast laser oscillators. State-of-the-art ultrafast TDLs emit up to 275 W of output power [3,4] and 80 μJ of pulse energy [5] with several hundred femtoseconds pulse durations. Such performance has enabled TDLs to directly drive applications which previously required the use of complex amplifier systems [6][7][8]. However, reducing the pulse duration of high-power oscillators is a major challenge. The first TDL emitting sub-100-fs pulses has been demonstrated only in 2012 [9] and even today, the power levels in this regime are limited to 5 W [9,10] (see Fig. 1). Therefore, external nonlinear pulse compression is applied for many applications in areas such as high field science and frequency comb generation. This introduces an additional stage of complexity to the system which may reduce the beam quality, power level and temporal pulse profile. Overcoming the trade-off between output power and pulse duration by providing compact and simple laser oscillators delivering hundreds of watts and tens of micro-joules in sub-100-fs pulses will simplify many existing experiments and open new application areas. Overview of sub-170-fs mode-locked thin-disk lasers based on Yb-doped materials [9][10][11][12][13][14][15][16][17]. The results presented in this article are highlighted with star symbols. The green area spotlights the desired performances of ultrafast oscillators to directly drive applications such as high field science and frequency comb generation.
Initially, all ultrafast TDLs were passively mode-locked using a semiconductor saturable absorber mirror (SESAM, [18]). Besides self-starting pulsed operation and simplicity of the cavity design, the combination of TDLs and SESAMs enables power scalability of the modelocked performance of the laser [2]. Following the demonstration of the first Kerr lens modelocked (KLM) TDL [19], similar scaling laws were demonstrated for this alternative mode locking technique resulting in average output powers up to 270 W in 330-fs pulses utilizing Yb:Y 3 Al 5 O 12 (Yb:YAG) [4]. Recently, 140-fs pulses were generated directly from a KLM Yb:YAG thin-disk oscillator at an average output power of 155 W and an optical-to-optical efficiency of 29% [17]. This pulse duration is more than three times shorter than any Yb:YAG SESAM mode-locked TDL [2]. Mode locking of TDLs via the Kerr lensing mechanism enables high modulation depth as well as instantaneous response time of the selfamplitude modulation. While Yb:YAG may be the best choice for high (average) output power, its gain bandwidth of 9 nm (FWHM) does not support pulses shorter than 120 fs. In order to achieve mode-locked operation with pulse durations shorter than 100 fs, numerous TDL using Yb-doped laser materials with broader gain bandwidths have been developed [20]. In this way, the minimum pulse duration was successfully reduced from initially hundreds of femtoseconds to 49 fs, which were obtained from a SESAM mode-locked Yb:CaGdAlO 4 (Yb:CALGO) TDL [10,14]. Most of the recently demonstrated Yb-based broadband gain materials are still in an early phase of thin-disk development, suffering from growth defects and non-optimized disk processing technologies. Moreover, many of them exhibit comparably low thermal conductivity due to their disordered nature. All of these factors hinder further power scaling at the moment. Until recently, all TDLs generating record-short pulses were based on SESAM mode locking. In 2015, pulses as short as 49 fs with 33 nm optical bandwidth have been obtained from a KLM Yb:YAG TDL [15]. This result relied on spectral broadening of the pulses utilizing additional spectral components generated due to SPM well beyond the gain limitation [21]. Although the output power of 3.5 W was moderate, this result clearly indicates that KLM is a promising approach for achieving even The disk was initially tested in continuous-wave (cw) operation in a linear multimode (MM) cavity consisting of a flat output coupler (OC) with a transmission T OC of 1.8% and the HR coated backside of the disk, separated by ≈7 cm. The beam radius of the fundamental mode on the gain crystal was estimated to be 360 μm, thus the laser operation was highly multi-mode given the pump spot diameter of 2.8 mm. In such a configuration, highest efficiencies can be expected due to an improved overlap of the top-head pump profile and the laser beam compared to a diffraction limited Gaussian beam. As shown in Fig. 3, a cw output power of 137 W was obtained under 209 W of incident pump power. The optical-tooptical efficiency amounted to 66% and the slope efficiency was 81%. These values are close to the best reported results with this gain material in the thin-disk configuration [22]. In order to avoid damage, we limited the pump intensity on the disk to ≈3.5 kW/cm 2 even though no hints for degradation of the laser efficiency were observed even at highest pump powers. In the next step, we built a 3 m long linear cavity supporting fundamental transverse mode (FM) operation following a similar design as the one reported in [25]. The disk and a concave curved mirror (CM) (RoC = 3 m) are placed between two flat end mirrors, of which one is partially transmissive and used as an OC. In this configuration where the disk is used as a folding mirror, the laser beam passes four times per roundtrip (RT) through the gain crystal which leads to a twice higher gain and consequently a twice larger optimal output coupling rate compared to the multi-mode cavity. The lasing performance in cw operation was evaluated for different output coupling rates (see Fig. 3). The estimated laser mode to pump diameter ratio was around 80% and the beam quality factor M 2 was measured to be below 1.2 in all experiments, confirming fundamental mode operation of the laser. At T OC = 3.6%, 122 W were emitted with an optical-to-optical efficiency approaching 60% and a high slope efficiency of 70%. The near field mode profile of the laser at this output power is depicted in the inset of Fig. 3. These results reveal that this particular disk exhibits high growth and manufacturing quality and is well suited for further mode-locking experiments.

Results of the laser experiments in mode-locked operation
For mode-locked operation, we modified the cavity similar to [19] in order to favor pulsed operation by applying the Kerr effect as depicted in Fig. 4. A 2-mm-thick undoped YAG plate is placed under Brewster's angle in the focal region between the two concave mirrors (CM2 and CM3), which have both a RoC of 400 mm. This Brewster plate (BP) ensures linear polarization of the laser beam and serves as the Kerr medium for the mode-locking mechanism. The beam spot radius inside the BP is estimated to be 90 µm × 150 µm in sagittal and tangential planes. A water-cooled pinhole placed in front of an end mirror serves as a hard aperture for KLM. The intra-cavity group delay dispersion (GDD) is adjusted by several dispersive mirrors for the soliton formation. The pulsed operation is generally initiated by a gentle knock on the laser table. The cavity length of the resonator is 2.5 m, which results in a 61 MHz repetition rate of the generated pulses. The resonator is operated in ambient air and has a footprint of only 80 cm × 40 cm. In our work, we focused on optimizing the laser for shortest pulse duration and highest average output power in the sub-100-fs regime. For this purpose, we studied the influence of critical laser parameters in one general cavity configuration, keeping the cavity design and the concave mirrors around the Kerr element constant. We investigated the mode locking performance for varying output coupling rate, intra-cavity dispersion, and hard aperture diameter. For each configuration, the pump power was set to the level delivering the minimum pulse duration in stable fundamental mode locking. At slightly higher pump power, a cw breakthrough was typically observed in the optical spectrum. In this way, stable mode locking was obtained for a large variety of laser parameters. The transverse beam quality M 2 was measured in several mode-locked configurations and was always below 1.05. Table 1 summarizes the mode-locked performance and laser parameters for a few representative configurations.  show the optical spectra and the gain at an inversion level of 0.3 for reference, as well as the intensity autocorrelation traces with the corresponding fit to the autocorrelation of a sech 2 function for the three configurations. The side peaks observed in the spectra of the short pulses carry only a minor fraction of the power and are associated with dispersive waves, similar to the sidebands observed in previous work [14,24]. Moreover, the output coupler transmission increases by more than a factor of two at the edges of the spectrum. The radio frequency spectrum and sampling oscilloscope trace of the shortest pulses are shown in Figs. 5(c) and 5(d). The 88-fs and 49-fs configurations achieve an average power of 10.7 and 4.5 W, respectively. The shortest pulse duration of 35 fs has been achieved at an output power of 1.6 W. For this pulse duration measurement, an extra-cavity dispersive mirror with negative group delay dispersion of −250 fs 2 was used to compensate for the material dispersion of the output coupler mirror and for the propagation in air. For all configurations, we confirmed fundamental single pulse mode-locked operation of the laser with a 180-ps long-range autocorrelation and a fast 18.5-ps photodiode in combination with a 40-GHz sampling oscilloscope as shown in Fig. 5(c).
This result demonstrates pulses 4 times shorter than previously achieved from a SESAM mode-locked Yb:Lu 2 O 3 TDL [11] and 50% shorter than obtained in bulk geometry with the same gain material [24]. For reaching shorter pulse durations, we observed general trends in agreement with previous reported studies on mode-locking with fast saturable absorbers [17,29,30]. Operating at a moderate level of introduced negative dispersion of −1000 fs 2 up to −2000 fs 2 per roundtrip enabled shortest pulse durations. Pulses became instable at lower GDD values, while for higher values, the minimum achievable pulse duration increased. Other critical parameters are output coupling rate and hard aperture diameter. To optimize pulse durations, it was important to reduce the output coupling rate while at the same time decreasing the aperture size. This allows maximizing the modulation depth of the self-amplitude modulation, enabling stable mode-locking operation even in a regime with strong gain narrowing of the pulses. In this context, it should be noted that the optical bandwidth of the 35-fs pulses is almost 3 times broader than the FWHM of the emission cross section of the gain crystal.

Conclusion and outlook
We studied the minimum pulse durations achievable in soliton mode-locking with a TDL based on the broadband gain material Yb:Lu 2 O 3 and KLM for various configurations of output coupling rate, intra-cavity dispersion, and hard aperture diameter. This work presents the shortest pulses and the highest power with sub-100-fs pulses directly emitted from a thindisk laser oscillator. In order to reach shortest pulse durations, the total negative intra-cavity dispersion needs to be minimized and the modulation depth of the saturable absorber has to be maximized by selecting a low degree of output coupling and adapting the hard aperture diameter. The efficiency in mode-locked operation is currently below 10% but we expect that further optimization of the cavity design in combination with mode-locking parameters for lower non-saturable losses should enable higher values. Furthermore, in 2014, Brons et al. showed that scaling the intra-cavity peak power is feasible by enlarging the spot size on the Kerr medium [4], eventually leading to a significant increase of the output power of the laser. As a next step towards power scaling of sub-100-fs lasers, we will perform a similar study on an Yb:Lu 2 O 3 -based KLM oscillator. We expect that an increase of the spot size in the Kerr medium in combination with a larger pump area on the disk and multi-pass on the laser crystal will enable significantly higher output powers and pulse energies, making this source even more attractive for numerous experiments. Our work shows that Yb:Lu 2 O 3 is one of the most promising gain materials for power-scaling of sub-100-fs TDL oscillators towards several hundred watts of output power.