1 Introduction

High-power operation of ultrashort pulse laser sources is highly desirable for a variety of nonlinear optical experiments [1–4]. The Yb-ion-based laser oscillators are well suited for this task. The generation of watt-level sub-100 femtosecond laser pulses directly from the Yb-doped bulk crystal lasers has been reported for Yb:KGW [5–7], Yb:CALGO [8, 9], Yb:CaF2 [10–12], and Yb:Lu2O3 [13] gain media. Such a performance of a mode-locked laser is feasible owing to the propitious properties of the Yb-doped crystals, including fairly broad gain bandwidths, absorption properties suitable for diode pumping, an absence of parasitic losses, and a tolerable level of thermo-optical effects [14–16]. Among the different Yb-doped crystals, the commercially available monoclinic double tungstate crystals of Yb:KGW exhibit favorable properties for generation of high-power sub-100 fs pulses: fairly broad emission bandwidth (~25 nm), high emission cross section (~2.8 × 10−20 cm2 for E//N m polarization), and relatively high thermal conductivity (~3.3 W/m/K) [16]. The generation of high-power ultrashort pulses with a spectrum as broad as the emission bandwidth of the gain medium is still a demanding task. In the high-power regime, the induced nonlinear effects, non-negligible thermal lensing and broad-band group velocity dispersion (GVD) compensation should be carefully addressed. Recently, the generation of 59 fs pulses with 20.2 nm-wide spectrum and output power of 62 mW has been reported from a diode-pumped SESAM-assisted Kerr-lens mode-locked Yb:KGW laser [17].

The conventional design of a mode-locked laser system based on semiconductor saturable absorber mirrors (SESAMs) offers a flexible procedure and provides a reliable and efficient femtosecond laser performance. However, this method is limited in further shortening of the pulse duration owing to the finite recovery time of the absorber which is also susceptible to damage. On the other hand, the Kerr-lens mode locking technique (KLM) enables one to generate shorter pulses due to its inherently fast saturable absorption-like effect, but it requires careful design procedure and does not usually offer self-starting oscillation [18]. A combination of these two techniques (here termed KLAS: Kerr-lens and saturable absorber) can provide a mechanism that benefits from the self-starting operation provided by the SESAM as well as the fast loss modulation and broadband operation of the KLM lasers [5, 6]. Recently, we reported on the development of a high-power sub-100 femtosecond KLAS mode-locked laser based on an InGaAs quantum-dot SESAM (QD-SESAM) [7] as an alternative approach to the widely used quantum-well SESAMs [5, 6]. Such QD-SESAMs exhibit sub-picosecond recovery time, low saturation fluence (10–25 μJ/cm2), and broad-bandwidth operation. The lower saturation fluence of QD-SESAM when compared to the QW counterparts is also beneficial for lowering the intracavity pulse energy required for stable mode locking. These properties make QD-SESAMs promising candidates for the generation of ultrashort laser pulses [19–21].

In this work, we report on the generation of high-power 56 fs pulses from a diode-pumped Yb:KGW laser oscillator based on KLAS mode locking that used a quantum-dot saturable absorber. Using an InGaAs QD-SESAM with 0.5% modulation depth, the laser delivered 56 fs pulses with 1.95 W of average output power at a repetition rate of 77.3 MHz. This corresponds to ~450 kW of peak power. To the best of our knowledge, these are the shortest pulses generated from the monoclinic double tungstate crystals and the shortest ones to date generated with the help of the QD-SESAM structures. Furthermore, the demonstrated pulses exhibited more than one order of magnitude improvement in terms of average power and peak power when compared to the previous Yb-doped lasers operating in sub-60 fs regime with direct diode pumping scheme. Longer pulses with duration of 90 fs and 2.85 W of average power were also generated using high output coupling.

2 Experimental setup

The laser oscillator used a 6 mm-long 1.6 at% doped Yb:KGW crystal (cut along the N g-axis) with antireflection (AR) coatings in a Z-fold cavity (Fig. 1). A fiber-coupled diode laser (100 µm, 0.22 NA) delivered maximum power of 30 W at 980 nm. The pump beam was focused to a spot size of 340 µm in the crystal using two AR-coated achromatic doublets. The absorbed pump power was measured to be around 60%. The laser mode inside the crystal was estimated to be 290 µm in diameter using the ABCD analysis, and it could be gradually increased by adjusting the position of the output coupler mounted on a translation stage. This allowed to introduce the Kerr-lens-induced soft aperturing effect in the mode-locked laser regime owing to the mode size variation with respect to the pump beam waist and a high nonlinear refractive index of the crystal [22]. In the continuous-wave (CW) regime, the laser could deliver up to 6 W of output power using an HR mirror as one of the end mirrors. The laser radiation was polarized along the N m-axis of the crystal. The thermal lensing of the crystal for the operating range of pump power was estimated to be around 100–150 mm of an equivalent focal length [23]. The QD-SESAM (Innolume GmbH) was grown with five pairs of InGaAs quantum-dot layers in the saturable structure and had a 0.5% modulation depth with a saturation fluence of 25 μJ/cm2 [24]. Two Gires–Tournois interferometer mirrors (GTI) were used for compensation of the positive GVD introduced by the laser crystal and optical components, as well as the pulse chirp induced by self-phase modulation (SPM). The total negative GVD of −3200 fs2 per round trip was achieved by two bounces on a −550 and −250 fs2 GTI mirrors (Layertec GmbH). The rest of the cavity mirrors were designed to exhibit low GVD at the laser wavelength (Laseroptik GmbH).

Fig. 1
figure 1

Experimental setup of the mode-locked Yb:KGW laser. AD achromatic ‎doublets, DM ‎dichroic mirror, R1–3 concave mirrors, OC output coupler. R1 = 300 mm, R2 = 300 mm and R3 = 500 mm

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3 Results and discussion

The mode-locked laser operation was initiated using the described QD-SESAM as the end mirror. A stable mode-locked laser operation with spectral bandwidth of 5–8 nm could be realized. The spectral bandwidth of the pulse depended on the pump power and the separation of the output coupler (OC) and the concave mirror R3 (Fig. 1). The output power was maximized for this regime, and the fluence on the absorber was as high as 270 µJ/cm2. The Kerr-lensing effect was then introduced by decreasing the OC-R3 distance using a translation stage. This corresponded to the increase of the laser mode size with respect to the pump beam in the crystal. During this procedure, the laser underwent multi-pulse oscillation and the number of pulses per cavity round trip was reduced as the Kerr-lensing effect became more pronounced. A careful adjustment of the pump power was needed during this transition regime. Once the Kerr-lensing effect became sufficiently strong, a stable single-pulse mode-locked laser operation was obtained. With the incident pump power of 18.3 W, the laser delivered 56 fs pulses with an average output power of 1.95 W at the repetition rate of 77.3 MHz. The full-width at half-maximum (FWHM) spectral bandwidth of the laser was measured to be 20.5 nm with a central wavelength of 1040 nm, as shown in Fig. 2. The time-bandwidth product (TBWP) was 0.335. At this point, the fluence on the saturable absorber was 370 µJ/cm2. No damage of the absorber was observed. The single-pulse oscillation per round trip and absence of Q-switching instabilities were confirmed using a fast oscilloscope/photodetector with a temporal resolution of 100 ps in combination with a wide-range scan (200 ps) autocorrelator [25]. Increasing the pump power resulted in multi-pulse oscillation and eventual cessation of the laser oscillation. The radio frequency (RF) spectrum of the pulse train exhibited high signal-to-noise ratio and the absence of Q-switched mode locking instabilities (Fig. 2c).

Fig. 2
figure 2

a Intensity autocorrelation of the mode-locked laser. Inset a wide-range scan (200 ps). b Spectrum of the mode-locked laser (black dotted curve), the calculated round-trip GVD (blue dotted curve), and the dispersive function D(λ) (upper graph). c RF spectrum of the pulse train. The sech2-shape fits are shown as red solid curves. RBW resolution bandwidth

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The spectrum of the generated pulse was accompanied by a narrow spectral component at 1081 nm which corresponded to the existence of a dispersive wave (Fig. 2b). This dispersive wave, however, was not observed in measurements performed by the oscilloscope and autocorrelator owing to its low intensity and correspondingly long duration. Indeed, the dispersive wave in normal dispersion regime is broadened due to the interplay of SPM and positive GVD at its oscillation wavelength. The net-GVD was calculated based on the available dispersion measurement data of the GTI mirrors, optical components, and the Sellmeier coefficients of an undoped KGW crystal [26]. The calculated positive GVD at the dispersive wave oscillation wavelength (1080 nm) was around +4500 fs2. As it can be seen in Fig. 2b, the total GVD of the cavity rapidly shifted to the normal regime mainly due to the dispersion profile of the −550 fs2 GTI mirror. The spectral energy of the dispersive wave was estimated to be 6.9% of the total spectral energy, and its presence did not deteriorate the long-term stability of the mode-locked laser. The co-existence of dispersive waves with the main mode-locked pulse has been reported and analyzed previously [27–32]. These waves co-propagate with the main pulse and some of the pulse energy is coupled out to the dispersive waves if they are phase-matched. The higher order dispersion coefficients have the substantial effect in this regime. A general phase-matching condition can be expressed as [31]

$$D\left( {{\omega _n}} \right) = \mathop \sum \limits_{m \geqslant 2} \left( {\frac{{{\beta _m}}}{{m!}}{{\left( { - 1} \right)}^m}\omega _n^m} \right) + \frac{{{\beta _2}}}{{2{T^2}}} = \pm 2\pi j,\, j = 0,1,2, \ldots ,$$
(1)

where \({\beta _m} = {\left. {\frac{{{\partial ^m}\phi (\omega )}}{{\partial {\omega ^m}}}} \right|_{{\omega _0}}}\) are dispersion coefficients, \({\omega _0}\) is the carrier frequency, \(\phi (\omega )\) is the phase delay per round-trip, \({\omega _n}\) is the dispersive wave frequency, and \(T = {\raise0.7ex\hbox{$\tau $} \!\mathord{\left/ {\vphantom {\tau {1.76}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{1.76}}\), where \(\tau\) is the FWHM of the mode-locked pulse duration. The dispersion coefficients at carrier frequency (1041 nm) were calculated to be β 2 = −430 fs2, β 3 = −21,451 fs3, and β 4 = −4.84 × 106 fs4 using the net-GVD data. For the measured pulsewidth of \(\tau\) = 56 fs, the dispersive function D (Eq. 1) is plotted in Fig. 2b (upper curve). The resonance condition was satisfied at the wavelength where the observed dispersive wave was present, i.e., \(D\left( {\lambda = 1081\;{\text{nm}}} \right) = - 2\pi .\) Other possible resonance wavelengths at longer or shorter wavelengths in normal GVD regime were not supported by the effective gain of the laser crystal in combination with the increasing loss of the output coupler and dichroic mirror at those wavelengths. To eliminate the dispersive wave, flatter and broader anomalous GVD profile per round-trip for the intended wavelength range is required.

The performance of the laser was also investigated for different GVD and output coupler values (Table 1). The pump power had to be adjusted because of different amount of loss incurred by different numbers of bounces on combinations of GTI mirrors. By increasing the total negative GVD, longer pulses were generated as expected [5]. The dispersive wave was not observed in case of net-GVD of −4800 fs2 mainly due to the narrower spectrum of the laser around 1040 nm. With this value of GVD, higher output power could be extracted from the laser cavity using a higher output coupling without significantly compromising the pulsewidth. For example, 90 fs pulses with 2.85 W of average output power were generated using 10% output coupling and −4800 fs2 GVD.

Table 1 Summary of the mode-locked Yb:KGW laser performance
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Compared to our previous results of KLAS mode-locked Yb:KGW laser with a QD-SESAM [7], the generated pulsewidth was significantly reduced from 90 fs (FWHM = 12.5 nm) to 56 fs (FWHM = 20.5 nm) by decreasing the net-GVD from −4400 to −3200 fs2, respectively. Our results also showed an enhancement in terms of pulse duration compared to the previously reported KLAS mode-locked Yb:KGW laser based on a QW-SESAM, where 67 fs pulses with 3 W of output power were generated [6]. We believe that this can be explained by the increased level of SPM due to a longer crystal as well as lower output coupling. The Q-switching instability was also absent during the mode locking procedure, which was attributed to the lower saturation fluence of QD-SESAM. Interestingly enough, the generated 56 fs pulses are also the shortest produced to date with the help of QD-SESAM absorbers (previously, 86 fs pulses were generated from Cr:forsterite laser [19]).

Higher power regime, however, would require careful compensation of the strong thermal lensing effect in Yb:KGW. A promising candidate for this regime is Yb:CALGO crystal with thermal conductivity coefficient of 6.9 W/m/K and emission bandwidth of 80 nm [33]. For example, the generation of 94 fs pulses with 12.5 W of average output power with SESAM mode locking was reported in [8]. Shorter pulses with duration of 40 fs at lower output power of 1.1 W were also demonstrated in this crystal by Kerr-lens mode locking technique [9]. Another promising Yb-doped laser crystal for generating high-power sub-100 fs pulses is Yb:CaF2 with thermal conductivity coefficient of 6 W/m/K and emission bandwidth of 30 nm [34, 35]. The generation of 48 and 68 fs pulses with output powers of 2.7 and 2.3 W using the Kerr-lens mode locking has been reported in [10, 12], respectively. It should be noted that results presented in [9, 10, 12] were not obtained with directly diode-pumped lasers which greatly reduces their overall efficiency and potential for further power scaling. Therefore, the use of commercially available laser diodes for direct diode pumping is a desired feature due to the reduced cost and complexity of the laser system. A diode-pumped SESAM mode-locked Yb:CaF2 laser was also demonstrated, delivering 87 fs pulses with 1.4 W of output power [11]. A new laser crystal, Yb:Lu2O3, with thermal conductivity of 11 W/m/K and emission bandwidth of 13 nm has also shown its potential in this regime [36] and the generation of 71 fs pulses with 1.09 W of average power was reported in [13]. A comparison of performance of the diode-pumped Yb-lasers in the sub-100 fs regime is shown in Fig. 3. As can be seen, the generated 56 fs pulses with 450 kW of peak power in our work demonstrate more than one order of magnitude higher average and peak powers when compared to the previous sub-60 fs diode-pumped Yb-lasers [37–42]. We believe that such a powerful ultrashort pulse laser source will be attractive for nonlinear frequency conversion into the visible and near-infrared ranges [43–45].

Fig. 3
figure 3

Comparison of sub-100 fs diode-pumped bulk Yb-doped crystal lasers [5–7, 11, 13, 37–42, 46]. Data from [8] are not shown for scaling reasons to better visualize the <90 fs regime. SA saturable absorber, SESAM

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4 Conclusion

In summary, a high-power sub-60 fs Yb:KGW laser based on KLAS mode locking with a QD-SESAM was demonstrated. The laser delivered 56 fs pulses with 1.95 W of average power, which is, to the best of our knowledge, the shortest pulse duration generated from the monoclinic double tungstate crystals and the Yb:KGW crystal in particular. The output average and peak powers were an order of magnitude higher than previously reported values. The QD-SESAM was used to initiate and sustain the pulse generation, while the Kerr-lens mode locking effect was introduced for further pulse duration shortening and stabilization of the single-pulse regime. The spectral bandwidth of the mode-locked laser was 20.5 nm which was near the emission bandwidth limit of the Yb:KGW laser crystal (~25 nm). The pulse duration was limited by the appearance of the dispersive wave at longer wavelength which was caused by the increased level of uncompensated dispersion. This fact and the underutilized emission bandwidth point out to the possibility of generation of even shorter pulses. This can be achieved by more careful dispersion management. At the same time, using a more broad-band emission with the N g-polarization of Yb:KGW [47] or gain media such as Yb:CALGO will be also beneficial. Our preliminary KLAS mode locking results with the latter indicate that the generation of powerful sub-50 fs pulses is possible [48] and will be the subject of future publication. The use of a lower output coupling to reduce the gain [49] can be another route to shorter pulses albeit at the price of a lower output power.