Maciej Kowalczyk
email: m.kowalczyk@pwr.edu.pl

Xuzhao Zhang

Valentin Petrov

Pavel Loiko

Xavier Mateos

Shiyi Guo

Zhengping Wang

Xinguang Xu

Jaroslaw Sotor

Jarosław Sotor

Self-frequency-doubling Yb:CNGS lasers operating in the femtosecond regime

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Introduction

Lasers emitting radiation in the green spectral band have several important emerging applications such as displays [START_REF] Chellappan | Laser-based displays: A review[END_REF] or ranging [START_REF] Mcgarry | NASA's satellite laser ranging systems for the twenty-first century[END_REF]. Moreover, if the radiation is emitted in the form of a high repetition rate train of ultrashort pulses the source can be employed for time-resolved or frequency comb spectroscopy [START_REF] Ideguchi | Adaptive dual-comb spectroscopy in the green region[END_REF]. In case the average power is sufficiently high (> 10-100 mW) such green laser sources can be applied for frequency conversion to wavelength ranges otherwise not accessible by ultrashort pulse lasers: e.g. by second-harmonic generation (SHG) to the UV or by synchronous pumping of optical parametric oscillators to the red part of the spectrum [START_REF] Petrov | Femtosecond nonlinear frequency conversion based on BiB 3 O 6[END_REF]. High repetition rate trains of picosecond or femtosecond pulses are normally generated by passive mode-locking of a continuous-wave (CW) laser where the pulse itself modulates the cavity losses, much faster than an external synchronized modulator. However, implementation of this technique to the Ar + ion laser produced only sub-100-ps pulse durations, not much shorter than active mode-locking, basically limited by the narrow spectral lines in gas lasers [START_REF] Wang | Passive mode locking of the Ar + laser[END_REF]. Solid-state active media lasing in the green exist, e.g. due to the emission of Pr 3+ and Tb 3+ ions or upconversion transitions in Er 3+ -doped crystals, but the corresponding emission bands are also narrow and such passively mode-locked lasers again produced only sub-100-ps pulses [START_REF] Zhang | Laser-diode pumped self-mode-locked praseodymium visible lasers with multi-gigahertz repetition rate[END_REF].

Despite the active development of diode-pumped all-solid-state laser sources operating in the visible, the most frequently used scheme for the generation of green light is still based on frequency-doubling of 1-µm laser radiation in the process of SHG, because such radiation is readily available. This can be realized in crystals exhibiting non-centrosymmetric structure, which provide the necessary χ (2) nonlinearity. Interestingly, some of the non-centrosymmetric crystals which possess sufficient birefringence for angle phase-matching can be also used as host matrices for active ions emitting a fundamental wave around 1 µm, such as neodymium (Nd 3+ ) or ytterbium (Yb 3+ ). This enables one to design a laser, which emits light in the infrared and simultaneously supports SHG in the visible. Intracavity SHG utilizes the higher fundamental intensity and if the laser is mode-locked, the conversion efficiency will be further enhanced due to the increased peak intensity.

This phenomenon was experimentally observed for the first time in 1969 with a Tm 3+ -doped LiNbO 3 crystal operating at 1853 nm [START_REF] Johnson | Coherent emission from rare earth ions in electro-optic crystals[END_REF] and was later termed self-frequency-doubling (SFD). Most adequate SFD host materials are obviously non-centrosymmetric crystals containing passive rare-earth ions, such as Sc, Y, La, Gd or Lu, which can be easily substituted by dopants with the same charge and similar ionic radii. Several such SFD 1-µm Nd lasers have been demonstrated and very efficient CW operation was obtained in a Nd:GdCa 4 O(BO 3 ) 3 (Nd:GdCOB) laser emitting green light with an output power up to 3 W [START_REF] Yu | Efficient high-power self-frequencydoubling Nd:GdCOB laser at 545 and 530 nm[END_REF]. Very recently a slab oscillator based on the same gain medium delivered a record-high power of 17.9 W at 545.5 nm [START_REF] Du | 17.9 W continuous-wave self-frequency-doubled Nd:GdCOB laser[END_REF]. Nevertheless, Nd-based SFD lasers exhibit certain limitations, such as broadband reabsorption of the active ions centered near 530 nm, strongly deteriorating the SHG performance of such sources around their nominal emission wavelength of 1064 nm [START_REF] Yu | Recent advances in self-frequency-doubling crystals[END_REF]. Moreover, neodymium gain media are typically characterized by narrow emission bandwidth, which limits the pulse duration to typically a few picoseconds and hence the peak power that can be achieved in a mode-locked operation. Yet, ultrashort pulse regime is particularly interesting regarding SFD lasers due to the intensity-dependent nature of the SHG process and its interaction with passive mode-locking mechanisms. Moreover, SFD can be employed not only to obtain pulsed visible radiation, but also to introduce negative self-phase modulation based on cascaded χ (2) nonlinearities. This can be exploited for pulse compression [START_REF] Stegeman | χ (2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons[END_REF][START_REF] Phillips | SESAM modelocked Yb:CaGdAlO 4 laser in the soliton modelocking regime with positive intracavity dispersion[END_REF] or Kerr-lens-like mode-locking [START_REF] Zavelani-Rossi | Mode locking by cascading of second-order nonlinearities[END_REF][START_REF] Holmgren | Generation of 2.8 ps pulses by mode-locking a Nd:GdVO 4 laser with defocusing cascaded Kerr lensing in periodically poled KTP[END_REF][START_REF] Mayer | Watt-level 10-gigahertz solid-state laser enabled by self-defocusing nonlinearities in an aperiodically poled crystal[END_REF], while such lasers could also become useful tools in applications requiring femtosecond green pulses.

In contrast to Nd lasers, gain media relying on the Yb 3+ ion are basically free from the above-mentioned limitations. This is due to the absence of reabsorption in the visible band (two-level system) and the intrinsically broader gain bandwidth (originating from strong vibronic coupling) enabling generation of sub-100-fs pulses. Even though the broadband emission of Yb-doped materials represents an essential advantage for tunable SFD, it can also become an obstacle on the way towards efficient frequency-doubling. SHG constitutes losses for the fundamental radiation which are intensity-dependent and in the case of mode-locking will counteract this process in any SFD laser. However, if the spectral acceptance of the SHG process is narrower than the broadband gain of the Yb-doped medium, the emission wavelength might escape from it in order to avoid these losses, which will prevent achieving optimal phasematching. This effect is normally absent in 1-µm SFD Nd lasers where the SHG spectral acceptance can easily cover the entire emission spectrum. The first CW SFD Yb laser was demonstrated in 1999 using an Yb:GdCOB crystal [START_REF] Mougel | Ytterbium-doped Ca 4 GdO(BO 3 ) 3 : an efficient infrared laser and self-frequency doubling crystal[END_REF]. Until now, most of the subsequent studies relied on borate crystals such as the isostructural (monoclinic, optically biaxial) oxyborate Yb:YCa 4 O(BO 3 ) 3 (Yb:YCOB) [17] (6.2 W at 513 nm) or the trigonal (uniaxial) YAl 3 (BO 3 ) 4 (Yb:YAB) [START_REF] Dekker | 1.1 W CW self-frequency-doubled diode-pumped Yb:YAl 3 (BO 3 ) 4 laser[END_REF] (1.1 W at 532 nm). Apart from their relatively high nonlinear coefficients, the calcium rare-earth oxyborates such as YCOB and GdCOB also exhibit extremely broad Yb emission bandwidths, which enabled the generation of 35-fs pulses at 1055 nm with Yb:YCOB [START_REF] Yoshida | Diodepumped mode-locked Yb:YCOB laser generating 35 fs pulses[END_REF].

The majority of the experiments on SFD Yb lasers were devoted to CW operation, including some tunability, and in rare cases Q-switched operation. Only sporadic reports on ultrafast lasers can be found in the literature. The latter include three reports on lasers operating under phase-mismatched SHG crystal orientation using: Yb:GdCOB [START_REF] Druon | Generation of 90-fs pulses from a mode-locked diode-pumped Yb 3+ :Ca 4 GdO(BO 3 ) 3 laser[END_REF] (emitting 90-fs pulses centered at 1045 nm), Yb:YCOB (39-fs pulses at 1049 nm) [START_REF] Gao | Tunable second harmonic generation from a Kerr-lens mode-locked Yb:YCa 4 O(BO3) 3 femtosecond laser[END_REF], and La x Gd y Yb z Sc w (BO 3 ) 4 (x + y + z + w = 4), shortly Yb:LGSB [START_REF] Porębski | Passively modelocked self-frequency doubling Yb:LGSB laser[END_REF] (180-fs pulses at 1070 nm). However, it has to be noted that the second-harmonic (SH) power levels reported in [START_REF] Gao | Tunable second harmonic generation from a Kerr-lens mode-locked Yb:YCa 4 O(BO3) 3 femtosecond laser[END_REF] look highly improbable for the chosen principal crystal cut. To the best of our knowledge, phase-matched SFD in a modelocked Yb laser has been studied only in one publication. In [START_REF] Lederer | Passive mode locking of a self-frequency-doubling Yb:YAl 3 (BO 3 ) 4 laser[END_REF] the authors observed that the SFD mechanism prevented an Yb:YAB laser from standard soliton operation and instead induced generation of strongly chirped picosecond pulses with a total (bidirectional) SH power of 270 mW at 520 nm. Still, soliton mode-locking with a pulse duration of 245 fs could be achieved under slightly phase-mismatched conditions with an average power of 60 mW emitted in the visible. Consequently, there is a lack of comprehensive investigation of the SFD mechanism in the femtosecond regime.

Recently, a novel SFD gain medium, Yb:CNGS (Ca 3 NbGa 3 Si 2 O 14 ; calcium niobium gallium silicate) has been demonstrated [START_REF] Zhang | Growth, thermal and laser properties of a new self-frequency-doubling Yb:CNGS crystal[END_REF]. Yb:CNGS is a langasite-type optically uniaxial (positive) crystal, which belongs to the same trigonal class 32 as YAB and LGSB [START_REF] Zhang | Highly-efficient laser operation of a novel trigonal silicate crystal Yb 3+ :Ca 3 NbGa 3 Si 2 O 14[END_REF][START_REF] Zhang | Crystal growth, low-temperature spectroscopy and multi-watt laser operation of Yb:Ca 3 NbGa 3 Si 2 O 14[END_REF], although it shows different structure (space group P321). While the segregation coefficient for Yb 3+ is unknown, this dopant ion substitutes a different in charge Ca 2+ host-forming cation, which is considered to be the origin of the spectrally broadened bands. The exceptionally broadband emission can potentially match the mode-locked performance of the disordered YCOB/GdCOB [START_REF] Yoshida | Diodepumped mode-locked Yb:YCOB laser generating 35 fs pulses[END_REF] or CaYAlO 4 /CaGdAlO 4 (CALYO/CALGO) crystals [START_REF] Sévillano | 32-fs Kerr-lens mode-locked Yb:CaGdAlO 4 oscillator optically pumped by a bright fiber laser[END_REF][START_REF] Ma | Generation of 30 fs pulses from a diode-pumped graphene mode-locked Yb:CaYAlO 4 laser[END_REF], which enabled generation of the shortest 1-µm pulses to date. Indeed, in our preliminary experiments we generated sub-60-fs pulses tunable between 1055 and 1074 nm, still not limited in duration by the intrinsic emission properties of Yb:CNGS [START_REF] Kowalczyk | Graphene and SESAM mode-locked Yb:CNGS lasers with self-frequency doubling properties[END_REF].

In this work, we present a comprehensive study on an Yb:CNGS laser operating in the mode-locked regime with an emphasis on its SFD properties. In the first part of the paper, we describe the performance of the laser operating in a phase-mismatched SHG configuration.

Here we focus on minimizing the pulse duration at the fundamental wavelength of 1052 nm, achieving a 47-fs pulse width, which could be further compressed extracavity to 40 fs. Moreover, on the basis of computer modelling we show that SFD in this regime leads to generation of two green pulses. The second part of the manuscript is devoted to the investigation of the laser behavior for the case when the SFD effect is maximized. We demonstrate that the mode-locked laser is capable of operating in a standard soliton regime emitting 100-fs pulses at 1046 nm in a configuration close to phase-matching. Under these conditions it generated radiation at 525 nm with a total average power of 66 mW. In order to better describe the mechanism of the SFD phenomenon we compare the experimental results with the outcomes of relevant numerical simulations.

Experimental setup

The schematic of the laser setup is shown in Fig. 1. The active element, 3 at.% Yb:CNGS (the growth charge composition), had a length of 4 mm with an aperture of 3 × 3 mm 2 , and was antireflective (AR) coated both at the fundamental (F) wavelength of 1050 nm and its SH of 525 nm. The crystal was cut for type-I (ee-o) phase-matched SHG at 1064 nm with the angles φ = 90° and θ = 36° in the orthogonal xyz frame where x  a and z  c (a and c are crystallographic axes). Note that type-I phase-matching (for CNGS d eff = d 11 cos 2 θ sin3φ) is a prerequisite for efficient SFD because spatial and temporal walk-off effects are absent between the two input F waves. No cooling of the crystal was provided.

As a pump source we employed a laser diode, which emitted up to 1 W of 979.4 nm radiation. The pump beam was delivered via a single-mode polarization-maintaining fiber and reimaged onto the gain medium with a resulting focal radius of 22 µm and a confocal parameter of 5.2 mm inside the crystal. The pump polarization was aligned as horizontal forming an e-ray inside the crystal, which was placed at a normal incidence between two 100-mm spherical mirrors with its c-axis in the horizontal plane. These mirrors were AR-coated at the pump wavelength, highly-reflective (HR)-coated at the F laser wavelength and provided a transmittance of 65% at the SH of the latter. For mode-locking we adopted a hybrid regime exploiting two types of intensity-dependent loss mechanisms [START_REF] Kowalczyk | High peak power ultrafast Yb:CaF 2 oscillator pumped by a singlemode fiber-coupled laser diode[END_REF]. In order to initiate the pulsed operation we focused the intracavity beam onto a semiconductor saturable absorber mirror (SESAM) with a resulting beam radius of 30 µm (estimated with the ABCD matrix formalism). The finite relaxation time of the SESAM enabled self-starting operation with a pulse duration in the range of 100 fs. Subsequently, we carefully decreased the distance between the SESAM and M 3 mirror pushing the cavity towards the edge of the stability range. This affected the beam size within the gain medium and activated a Kerr-lensing mechanism, further shortening the duration of the generated pulses due to its quasi-instantaneous response. In order to obtain stable mode-locked operation we had to counterbalance the positive group-delay dispersion of the crystal (single-pass GDD = 330/380 fs 2 for o/e(θ = 36°)-ray, respectively [START_REF] Zhang | Growth and optical properties of a new CGG-type laser crystal Nd 3+ :CNGS[END_REF]) and the effect of self-phase modulation (SPM) induced therein. Negative dispersion was introduced with three different Gires-Tournois Interferometer (GTI) mirrors with a single-bounce GDD of -100, -250, and -550 fs 2 (Layertec) used in a double pass. This specific configuration was experimentally optimized regarding the shortest achievable pulse duration. Higher values of negative GDD led to generation of longer pulses, while for insufficient GDD we observed mode-locking in the chirped pulse oscillator regime [START_REF] Kalashnikov | Chirped-pulse oscillators: Theory and experiment[END_REF][START_REF] Kowalczyk | Investigation on dispersion regimes in Yb:KGW solid-state laser[END_REF]. The total physical length of the X-shaped cavity amounted to 190 cm.

Results

Non-phase-matched configuration

Initially, we investigated the laser performance without SHG phase-matching. For this experiment we employed an OC with a transmission of 1% and a SESAM (BATOP) with a finite relaxation time of 1 ps and a modulation depth of 1.2%. The cavity was aligned to enforce lasing with σ polarization (o-ray inside the crystal) in order to exploit the highest gain of the Yb:CNGS crystal [START_REF] Zhang | Crystal growth, low-temperature spectroscopy and multi-watt laser operation of Yb:Ca 3 NbGa 3 Si 2 O 14[END_REF]. This was possible through fine alignment of the overlap with the pump beam due to the spatial walk-off of the two eigen-polarizations inside the crystal (Poynting vectors).

Figure 2 illustrates the performance of the laser operating in the most broadband regime. It was characterized with an optical spectrum analyzer (OSA, AQ6370, Yokogawa) and a SH frequency-resolved optical gating (FROG) device (Mesa Photonics). Emitted spectrum exhibited peak wavelength of 1052 nm and 28 nm full-width-at-half-maximum (FWHM) bandwidth. However, it was strongly broadened in the long wavelength wing. The calculated Fourier-limited pulse duration for the measured spectrum amounts to 36 fs (see Fig. 2b). The FROG-retrieved pulse duration of 47 fs indicated residual chirp, which is confirmed by the spectral phase profile depicted in Fig. 2a. While the phase was almost flat within the main pulse component, the long-wavelength tail was clearly upchirped (the chirp sign was identified by a subsequent measurement after introducing additional GDD of a known value). This was caused by the imperfect dispersion compensation with GTI mirrors characterized with limited spectral band up to approximately 1065 nm. Subsequently, we managed to partially compress the pulses with two extracavity bounces on -250 fs 2 GTI mirrors. This obviously introduced an additional chirp to the main pulse component (see Fig. 2a), but ultimately enabled the reduction of the pulse duration down to 40 fs. It has to be emphasized that an intensity autocorrelation measurement of the pulse duration indicated a slightly shorter value of 38 fs, mainly due to the pulse shape deviation from a fitted sech 2 profile. Additionally, in the inset of Fig. 2b we present a radio-frequency (RF) spectrum of the fundamental beat note at 78.4 MHz. It exhibits a signalto-noise ratio of 70 dB confirming the stability of the mode-locked operation. The average output power emitted from the oscillator amounted to 45 mW. We believe that the achieved reduction of the pulse duration when compared with our previous experiments [START_REF] Kowalczyk | Graphene and SESAM mode-locked Yb:CNGS lasers with self-frequency doubling properties[END_REF] originated mainly from the different crystal sample employed. The normal incidence operation enabled higher intensity resulting in an enhanced SPM contribution that was additionally increased by the longer crystal length. Moreover, we expect that the pulse duration can be further shortened by applying high brightness pumping with, e.g. a fiber laser [START_REF] Sévillano | 32-fs Kerr-lens mode-locked Yb:CaGdAlO 4 oscillator optically pumped by a bright fiber laser[END_REF].

Regardless of the lack of phase-matching conditions for SFD, we observed residual SHG from the fundamental 1050-nm beam. This is due to the type-0 (oo-o) process, involving the single nonlinear coefficient d 11 of CNGS. None of the folding cavity mirrors was HR-coated for 525 nm, therefore the strongest SH signal was registered directly after one of them, mirror M 2 . Figure 3a shows the SH spectrum measured with a CCS100 (Thorlabs) spectrometer. The spectrum exhibited characteristic fringes, which originated from the generation of two interfering SH pulses. Double pulse generation is a direct consequence of the absence of both phase-and group-velocity-matching between the F and SH beams in the process of SFD [START_REF] Manassah | Effects of velocity dispersion on a generated second harmonic signal[END_REF][START_REF] Noordam | Second-harmonic generation of femtosecond pulses: observation of phase-mismatch effects[END_REF][START_REF] Trabs | Spectral fringes in non-phase-matched SHG and refinement of dispersion relations in the VUV[END_REF]. This mechanism is illustrated with the results of 1D numerical modelling performed with the Hussar software [START_REF] Kardaś | Full 3D modelling of pulse propagation enables efficient nonlinear frequency conversion with low energy laser pulses in a single-element tripler[END_REF]. Spatially plane waves were assumed in the model with the spatial walk-off (~1.6°) neglected. While the SFD properties of Yb:CNGS have been investigated previously [START_REF] Zhang | Growth, thermal and laser properties of a new self-frequency-doubling Yb:CNGS crystal[END_REF], the value of the nonlinear coefficient d 11 was not measured. Here, for the purpose of visualization, we used a value determined for a similar isostructural compound, Ca 3 TaGa 3 Si 2 O 14 (CTGS), which amounts to 0.72 pm/V [START_REF] Chen | Crystal growth and characterization of CTGS and Nd:CTGS for self-frequency-doubling applications[END_REF]. The reliability of this value is discussed in the next section devoted to phase-matched SFD. However, for the case of strong phase-and group-velocity mismatch the exact CNGS nonlinearity is unimportant and changing the d 11 value does not introduce any significant modifications to the simulation outcomes. Figures 3c and3d show the evolution of the temporal distribution of the two SH pulses as they propagate along the Yb:CNGS crystal. The time delay is normalized to the position of the F pulse, indicating that one of the green pulses is synchronized with it, while the second one is delayed. This is also demonstrated in Fig. 3b depicting the profile of both F and SH beams at the gain medium exit. The origin of this behavior can be briefly summarized as follows. At the entrance of the crystal the SH starts to build up, but after covering the first coherence length (L coh = 9.5 µm) it converts back to the F (causing the SH pulse energy oscillations visible in the inset of Fig. 3b). Yet, due to different group velocities of the two beams, a trailing edge of the SH component does not overlap temporally with the F beam anymore. Thus, it cannot be back-converted and gets isolated with a relative delay to the F pulse defined by their group-velocity mismatch and the propagation length. Due to the same process, the leading edge of the F pulse constantly generates SH but does not experience any of its back-conversion. Consequently, the SH signal is periodically generated and back-converted as it travels under the envelope of the F pulse. After an initial period, these two mechanisms balance each other and the energy of this SH pulse is stabilized (see inset in Fig. 3b).

Due to the crystal orientation (φ = 0 for an o-ray of the F beam), the SH beam has the same polarization as the driving F radiation (oo-o process). Because the non-phase-matched SHG is obviously not frequency-dependent, it enabled the conversion of the entire spectrum of the sub-50-fs pulses. Simultaneously, it strongly hampered the conversion efficiency, limiting the SH average power to the microwatt level.

Phase-matched configuration

Subsequently, we investigated the laser behavior with maximized SFD effect. For this, the cavity was realigned to enforce lasing of the F beam with π polarization enabling phasematched type-I SHG (ee-o) conditions. While the SFD loss was negligible under phasemismatched conditions, it became crucial for the 1050-nm fundamental radiation as we strongly increased the conversion efficiency. The mode-locked regime was stabilized by the introduced SESAM and Kerr-lensing, which favored high-intensity pulsed operation over CW lasing. Because the SFD is an instantaneous intensity-dependent process, it naturally counteracts the action of the passive mode-locking mechanisms and can eventually destabilize mode-locking. In order to balance this effect, we employed a SESAM with the highest available modulation depth of 2.6% (relaxation time of 500 fs; BATOP). We have indeed observed strong improvement of the mode-locking stability under conditions close to phase-matching, when the SESAM modulation was increased. Moreover, an OC with a transmittance of 0.8% was used to minimize the intracavity losses. Typically, the mode-locked operation was self-starting when the pump power exceeded the threshold of approximately 500 mW. The corresponding average output power of the SH beam measured directly after M 2 was in the range of 1-5 mW. The still low conversion efficiency was associated with the central wavelength of the fundamental laser emission which moved away from the exact phase-matching in order to avoid the SFD loss introduced to the 1-µm F radiation. Subsequently, we changed the effective θ eff angle between the propagation vector and the optical axis of Yb:CNGS by fine-tilting the crystal and/or one of the cavity end mirrors. As θ eff was tuned to maximize the SH output power, we observed two different effects: the increased SFD loss destabilized the mode-locked operation or it resulted in a further shift of the central emission wavelength out of the phase-matched configuration. Consequently, we were not able to achieve mode-locking with perfect phase-matching for the peak wavelength of the fundamental emission. The highest power of the SH beam recorded after M 2 mirror amounted to 21.4 mW. This indicates that the SH power directly after the crystal was equal to 33 mW and the total SH power generated in both directions amounted to 66 mW with 42.8 mW emitted from the cavity. The latter value can be easily increased without affecting the laser performance by employing SH output mirrors (M 1,2 ) with low reflectance in the visible band.

In this configuration the laser was still operating in a stable soliton mode-locking regime emitting 102-fs pulses with 11.8 nm broad spectrum centered at 1046 nm. Figure 4a shows recorded spectrum of the fundamental radiation and an autocorrelation trace with a fit assuming sech 2 pulse profile (obtained with APE PulseCheck). The average output power of the F beam was equal to 40 mW, indicating that the double pass SHG conversion efficiency amounted to roughly 1.3%. Note that this value exceeds the OC losses, but it is still lower than the modulation depth of the employed SESAM. The laser performance has been characterized for the pump power of 950 mW and the mode-locked operation could be sustained for a whole range of pump power levels between ~500 mW -950 mW.

Figure 4b presents the recorded SH spectrum with a central wavelength of 524.9 nm. This means that the crystal was effectively configured for phase-matched SHG at 1049.8 nm, shifted by almost 4 nm from the center of the F spectral peak. This is equivalent to a -0.2° deviation from the optimal phase-matching angle. We have compared the experimental results with the outcomes of the 1D numerical modeling based on the experimental conditions. In contrast to the phase-mismatched case, which was discussed in the previous section, here the nonlinearity of the CNGS crystal is a crucial parameter. First, as the d 11 coefficient is unknown for the studied crystal, we again applied the value measured for CTGS, i.e. d 11 = 0.72 pm/V [START_REF] Chen | Crystal growth and characterization of CTGS and Nd:CTGS for self-frequency-doubling applications[END_REF]. For comparison with the experiment, we used a spatially averaged intensity (1/2 of the peak value) in the 1D model. The simulated SH spectrum for such a nonlinear process (dashed grey line in Fig. 4b) is consistent with the experimental data. The measured spectral bandwidth of the main component amounted to 1.2 nm which agrees with a 1.19-nm acceptance bandwidth calculated for the 4-mm long Yb:CNGS crystal at 525 nm. The Fourier-limited pulse duration for the given bandwidth and a sech 2 pulse profile amounts to 240 fs. Nevertheless, a sech 2 shape cannot be applied for the investigated SFD mechanism, because of the group-velocity-mismatch between the F and SH beams inside the crystal. The SH pulse constantly drains energy from the F pulse, but it also temporally lags behind it as both waves propagate along the crystal. Consequently, the temporal distribution of the generated SH signal strictly depends on its nonlinear interaction with the F component. This can be clearly seen in Fig. 4c, which shows profiles of both beams at the crystal exit. It yields a SH pulse duration (FWHM) of 230 fs, but with a long low-intensity tail, which occurs because of a partial depletion of the F beam. However, the conversion efficiency calculated for the described process amounts to 13.5%, which clearly contradicts the experimentally estimated value of 0.66% for a single pass. Since our simulations show that the spatial walk-off effect has a minor effect on the conversion efficiency under described experimental conditions, we believe that this discrepancy originated from a highly overestimated value of the nonlinear coefficient. A similar conclusion can be found in a previous study on Nd:CNGS [START_REF] Zhang | Diode-pumped passively Q-switched self-frequency-doubled Nd:CNGS laser[END_REF], where the authors estimated the upper limit of the d 11 value to be on the order of 0.46 pm/V. Here, we matched the calculated conversion efficiency to the actually observed level by assuming much lower nonlinear coefficient (d 11 = 0.13 pm/V). The SH pulse shape would be then close to a flat-top (FWHM = 670 fs), due to the negligible depletion of the F beam under these conditions (Fig. 4d). Note that in such a case the pulse duration is defined by the group velocity mismatch and the crystal length. Simultaneously, assuming much lower CNGS nonlinearity does not significantly affect the spectrum (dotted black line in Fig. 4b).

Conclusion

In conclusion, we have realized a mode-locked Yb:CNGS laser operating in the femtosecond regime and studied its SFD properties in configurations without and with SHG phase-matching. When the laser was operated under the conditions preventing efficient nonlinear frequency conversion, it generated pulses centered at 1052 nm with a duration of 47 fs and an average power of 45 mW, which were subsequently compressed extracavity to 40 fs. Note that this achievement still does not exploit the entire gain spectrum of Yb:CNGS, which indicates that this material is one of the most promising novel crystals concerning ultrashort pulse generation near 1 µm. Moreover, we characterized the non-phase-matched SH signal and compared the experimental observations with the outcomes of computer modelling, confirming that this regime results in generation of two ultrashort green pulses. In the second part, we reconfigured the laser in order to enable efficient type-I SHG and maximize the power emitted in the visible band. We were able to tune the central wavelength (1046 nm) of the fundamental radiation down to 4 nm out of optimal phase-matching. In this case, the laser emitted 100-fs soliton pulses with an average power of 40 mW and it simultaneously generated 66 mW of radiation at 525 nm (with ~43 mW emitted from the cavity). On the basis of numerical simulations, we have also studied the relation between the Yb:CNGS nonlinearity and the temporal shape of the SH pulse.

We were unable to achieve perfect phase-matching for the peak wavelength of the infrared radiation. As in all Yb lasers, this can be attributed to the broad gain bandwidth of the crystal, which facilitated spectral shift of the fundamental emission wavelength when the crystal was tilted towards phase-matching, to avoid the losses. This effect can be suppressed by locking the spectrum beneath a broader phase-matching acceptance bandwidth. The latter will require reduction of the crystal thickness to about 1 mm and higher doping level to recover the pump absorption in Yb:CNGS. Another important conclusion from the present study is that low second order nonlinearity (as observed in CNGS) is not a serious limitation in SFD lasers if they operate in the femtosecond regime. Thus sufficiently high conversion efficiency into the visible can be expected with a shorter crystal operating in the gain maximum. The main advantage of Yb:CNGS over similar SFD crystals is its capability to produce very short pulses at the fundamental wavelength, which is expected to result in sub-100-fs durations with sufficient average power in the green in the near future.

Fig. 1 .

 1 Fig. 1. Schematic layout of the Yb:CNGS laser: L 1 -18.4 mm aspheric lens; L 2 -100 mm spherical lens; M 1-3 -100 mm concave spherical mirror; GTI -Gires-Tournois-Interferometer mirror; OCoutput coupler; SESAMsemiconductor saturable absorber mirror; Ffundamental wavelength output; SHsecond harmonic output.

Fig. 2 .

 2 Fig. 2. Performance of the Yb:CNGS laser in the non-phase-matched SFD configuration: optical spectrum recorded with a standard OSA and retrieved from a measured FROG trace; spectral phase with and without extracavity compression (a); FROG-retrieved pulse profile with and without compression compared with the calculated Fourier-limited pulse; temporal phase of the compressed pulses, inset: RF spectrum of the fundamental beat note at 78.4 MHz (b).

Fig. 3 .

 3 Fig. 3. Measured SH spectrum of the Yb:CNGS laser in the non-phase-matched SFD configuration, inset: simulated SH spectrum (a); simulated temporal profile of the fundamental (F) and second harmonic (SH) pulses at the crystal exit, inset: normalized SH pulse energy evolution (b); simulated evolution of the SH signal temporal profile along the crystal (c); the area marked with a dashed line is magnified on (d).

Fig. 4 .

 4 Fig. 4. Performance of the Yb:CNGS laser in the SFD configuration close to phase-matching: optical spectrum, inset: an autocorrelation trace with a fit assuming sech 2 pulses (a); measured second harmonic spectrum compared with the results of the numerical modelling assuming two different values of the d 11 coefficient (b); simulated temporal profile of the F and SH pulses (independently normalized) at the crystal output assuming d 11 = 0.72 pm/V (c) and d 11 = 0.13 pm/V (d).

Acknowledgments

We would like to acknowledge Laser Zentrum Hannover for fabrication of the AR coatings on the Yb:CNGS sample. Moreover, we would like to thank Yicheng Wang (Ruhr University Bochum) for the insightful discussions and Tomasz Kardaś (Fluence) for the help with his software Hussar, which is freely available at www.ufs.edu.pl. The purchase of the FROG equipment was supported by the Foundation for Polish Science within the First TEAM program co-financed by the European Union under the European Regional Development Fund (contract no. POIR.04.04.00-00-434D/17-00).

Funding

National Science Centre (NCN, Poland) (2015/18/E/ST7/00296); National Natural Science Foundation of China (61975096).

Disclosures

The authors declare no conflicts of interest.


Yongguang Zhao

Li I Wang

Weidong Chen
email: weidong.chen@mbi-berlin.de

Pavel Loiko

Yicheng Wang

Zhongben Pan

Hanlin Yang

Wei Jing

Hui Huang

Jiachen Liu

Xavier Mateos

Zhengping Wang

Xinguang Xu

Uwe Griebner

Valentin Petrov

Kerr-lens mode

Keywords:

published or not. The documents may come

Since the first demonstration of sub-100 fs bulk lasers emitting in the 2 μm spectral range in 2017, a Tm:MgWO4 laser mode-locked (ML) by graphene saturable absorber (SA) [1], a remarkable progress has been achieved in this field. Several types of "slow" SAs, such as SEmiconductor Saturable Absorber Mirrors (SESAMs) [2] and single-walled carbon nanotubes (SWCNTs) [3,4] were applied to start and stabilize the soliton type mode-locking [5]. Pulses as short as 54 fs at 2048 nm were generated from a SESAM ML Tm:(Lu,Y)2O3 "mixed" ceramic laser with an average output power of 51 mW [6]. A slightly longer pulse duration of 57 fs was reported using the same gain material and a SWCNT-SA [7].

Kerr-lens mode-locking (KLM) is another, well-established technique, in particular interesting for the 2-μm spectral range where no commercially available SAs exist. It is based on selffocusing in combination with an intracavity aperture. This creates an intensity dependent quasi-instantaneous self-amplitude modulation which acts as an artificial "fast" SA supporting the generation of extremely short pulses down to few fs [8,9]. KLM features: (i) support of broadband operation without the penalty of the non-saturable loss of "slow" SAs [10], and (ii) no operating wavelength limitations inherent to "slow" SAs [11,12].

The challenge of KLM near 2 μm as compared to 1-μm relates to a great extent to the weaker Kerr effect (lower nonlinear refractive index (n2) for a given laser host material) and the associated higher critical power for self-focusing. Normally, tight focusing in the laser gain medium or an extra Kerr material is required to overcome the above-mentioned limitations. Nevertheless the first KLM laser around 2 μm was demonstrated only in 2017 [13][14][15], 8 years after the first passively ML laser using a "slow" SA [16]. The first sub-100-fs KLM Tm laser comprised a Tm:Sc2O3 crystal pumped by a 1611 nm fiber amplifier. It delivered 72-fs pulses at 2108 nm with an average output power of 130 mW [17]. Subsequently, a "slow" SWCNT-SA-assisted KLM operation was also demonstrated and 76-fs were generated at 2037 nm from a Tm:MgWO4 laser [18].

Compared to other Tm 3+ laser host materials, the cubic sesquioxides A2O3 (where A = Y, Lu, Sc or their combination) exhibit a relatively high n2 value favoring KLM operation. Their strong crystal field and large ground-state Stark splitting lead to smooth and broad gain profiles supporting emission far beyond 2 μm, which is exceptional among the Tm 3+ -doped materials. Furthermore, their attractive thermo-mechanical properties favor high average/peak power ML operation [19].

The technology of transparent polycrystalline ceramics not only relaxes the constraint of high melting temperatures for the sesquioxides, but also offers easier elaboration of "mixed"materials which exhibit compositional disorder leading to additional inhomogeneous broadening of the dopant spectral lines. Here, based on the extremely smooth and broad gain profiles of Tm 3+doped "mixed" lutetia-scandia (Lu,Sc)2O3 transparent ceramics in conjunction with their relatively large n2 value we explore the power scalability of sub-100-fs KLM lasers at ~ 2 μm.

Almost pore-free Tm:(Lu2/3Sc1/3)2O3 transparent ceramic with a measured Tm 3+ doping level of 2.8 at.% was fabricated by Hot Isostatic Pressing (HIP) of commercial powders at 1800°C/195 MPa in Ar atmosphere [20]. KLM laser operation was investigated using a five-mirror linear astigmatically compensated X-shaped cavity. The uncoated ceramic sample with an aperture of 3 mm × 3 mm and a thickness of 3 mm was mounted in a watercooled copper holder (coolant temperature: 14℃) and placed at Brewster's angle between two concave dichroic folding mirrors M1 and M2 (RoC = -100 mm). A 795 nm narrow-linewidth continuous-wave (CW) Ti:Sapphire laser was used as a pump source. The pump beam was focused into the ceramic sample by a spherical lens (f = 70 mm) resulting in a beam waist radius of 33 µm × 77 µm in the sagittal and tangential planes, respectively. The corresponding cavity waist radius in the CW mode inside the ceramic sample, estimated by the ABCD formalism, was 30 µm × 57 μm. The cavity was completed by a flat dispersive mirror (DM), a flat rear mirror (M3), and a plane-wedged output coupler (OC), Fig. 1(a). The roundtrip group delay dispersion (GDD) due to the 3-mm thick ceramic sample amounted to -200 fs 2 at 2.08 μm, estimated by averaging the refractive indices of Lu2O3 and Sc2O3 [21]. Taking into account the GDD of the bending DM ( ~ -800 fs 2 per bounce in the spectral range from 2.0 to 2.2 µm) the total round-trip GDD amounted to ~-1850 fs 2 .

The Tm:(Lu,Sc)2O3 ceramic laser was initially characterized in the CW regime with a 0.5% OC. At an absorbed pump power (Pabs) of 1.8 W, a maximum CW output power of 490 mW was achieved The pulse duration was further shortened by using a 0.2% OC while maintaining Pabs = 1.1 W. The average output power dropped to 136 mW, however, the FWHM of the spectrum increased to 70 nm. Scaling of the pump power while maintaining the softaperture KLM regime, was possible up to Pabs = 1.6 W resulting in an average output power of 220 mW. The optical spectrum was further broadened but exhibited a significant deviation from an ideal sech 2 -shape profile, with three distinct peaks at 2081.4, 2181.5 and 2226.7 nm, see Fig. 3(a). Pulses as short as 58 fs were recorded after external linear chirp compensation with a 3-mm thick ZnS ceramic plate (GDD = 465 fs 2 ). This pulse duration is equivalent to 8 optical cycles which was confirmed by recording the fringe-resolved autocorrelation trace, presented in Fig. 3

(b). A long-scale intensity autocorrelation scan (15 ps) is shown in the inset of Fig 3(b)

, confirming a single pulse ML operation without any pedestals or multi-pulses. The deconvolved pulse duration was 13.7% above the Fourier-transform limit, see Fig. 3(a). The peak on-axis laser intensity in the ceramic was ~623 GW/cm 2 . Compared to previous sub-100 fs pulse generation results obtained with Tm-doped mixed sesquioxide ceramics using real SAs [2,6,7], KLM clearly demonstrates average power scalability The KLM pulse train was characterized by a radio frequency (RF) spectrum analyzer. The recorded fundamental beat note at 84.8 MHz exhibited a high extinction ratio of 77 dBc above the noise level, see Fig. 4(a). This, together with the uniform harmonic beat notes shown in For sub-80 fs pulses, the broadband long-wavelength emission extended to ~2.2 μm, see Fig. 2(a) and Fig. 3(a). Given a strong coupling between the electronic transition of Tm 3+ ions and the host material phonons exists, this emission may refer to multiphonon-assisted transitions of the Tm 3+ ions [22,23]. To confirm this hypothesis, we calculated the stimulated emission (SE) cross-section spectrum for the 3 F4 → 3 H6 transition of Tm 3+ ions in the Tm:(Lu,Sc)2O3 ceramic, see Fig. 5(a). According to the Stark splitting of the 3 H6 and 3 F4 Tm 3+ multiplets determined at 10 K, the purely electronic transitions at room temperature (RT) were computed as shown by vertical dashes in Fig. 5(a).

Among them, the longest wavelength is 2099 nm which corresponds to an electronic transition occurring from the lowest Stark level (sub-level) of the 3 F4 multiplet (5683 cm -1 ) to the highest sub-level of the 3 H6 multiplet (919 cm -1 ). The emission at longer wavelengths extending up to 2.3 μm has a vibronic nature Fig. 5. Spectroscopy of Tm:(Lu,Sc)2O3 ceramic: (a) stimulatedemission cross-section, σSE, for the 3 F4 → 3 H6 transition, vertical dashes mark all possible wavelengths of purely electronic Stark transitions, (b) calculated gain cross-section, σgain, spectra for different inversion rates β = N2( 3 F4)/NTm, (c) Raman spectrum, λexc. = 514 nm, numbers denote the peak frequencies in cm -1 ; (d) Derived crystal-field splitting of 3 H6 and 3 F4 multiplets of Tm 3+ ions in C2 sites revealed at 10 K. The red lines illustrate virtual energy-levels due to electron-phonon coupling with the host vibrations participating in laser emission at ~2.1 -2.2 μm. and it determines to a large extent the gain spectra for small inversion rates β, see Fig. 5(b). For very small inversion rates (high finesse cavities), e.g., β = 0.01, the gain cross-section spectrum reveals a smooth and broad profile from 2.1 to 2.3 μm. For slightly higher β, a local peak at ~2.1 μm emerges, spanning from ~2.0 to 2.3 μm, in agreement with our observations in the present KLM Tm:(Lu,Sc)2O3 ceramic laser, cf. Fig. 2(a) and Fig. 3(a).

The measured Raman spectrum of the Tm:(Lu,Sc)2O3 ceramic is shown in Fig. 5(c). Apart from the most intense band at 399 cm -1 , it reveals multiple bands at lower frequencies, 126-344 cm -1 . By adding these vibrations to the higher-lying sub-levels of the 3 H6 ground state (representing an electron-phonon coupling), we obtain a set of densely located virtual energy levels at 768 -1236 cm -1 , as shown in Fig. 5(d). The long-wave emission above 2.1 μm can be thus explained by transitions from the upper laser level ( 3 F4) to one or several of such virtual levels (lower laser level). Full utilization of the vibronic emission in the present ML laser is impossible mainly due to the reflectivity characteristics of the pump mirror M1 and the OC. They limit the spectrum from the long wave side starting from ~2.2 μm and prevent operation in the flat gain region, see Fig. of the laser output through the OC in particular results in a significant deviation from the ideal sech 2 -shape spectral profile indicated by structured satellite peaks around ~2.2 μm, cf. Fig. 2(a) and Fig. 3(a) but also in deviation from the ideal temporal fit, cf. Fig. 3(b). The unmanageable intracavity GDD at the long-wave spectral wing beyond 2.1 μm due to the same cavity elements may also contribute to the formation of such satellites, however the gain at such wavelengths is still provided by vibronic emission. The appearance of such spectral sidebands at the long-wave wing was also observed in other ML Tm-doped sesquioxide lasers when the spectral bandwidths exceeded 60 nm [2,6,7,17]. Alternative gain mechanisms at such long wavelengths suggested in [17] include stimulated Raman scattering and the upper lying 3 H4→ 3 H5 Tm 3+ transition but we have no evidence for such effects in our laser.

In conclusion, we have demonstrated a KLM Thulium sesquioxide laser based on a "mixed" Tm:(Lu,Sc)2O3 transparent ceramic. Using a 0.2% OC, pulses as short as 58 fs, i.e., 8 optical cycles, were generated at ⁓2081 nm. The average output power amounted to 220 mW at a repetition rate of 84.8 MHz. Thus, KLM using other Tm-doped broadband gain media (e.g., disordered or composite ones) and/or a proper cavity design is expected to provide yet shorter pulses near 2 µm, i.e., few optical cycles. The observation of long-wave emission at ~2.2 μm within the ML laser spectrum indicates contribution of Tm 3+ vibronic transitions. Having in mind that such multiphonon-assisted long wavelength emission can be fully resonated it seems advantageous for further spectral broadening and pulse shortening.

Fig. 1 .

 1 Fig. 1. Schematic of the KLM Tm:(Lu,Sc)2O3 ceramic laser (a). Output beam profiles in the CW and ML regimes (b). (M1-M2, dichroic mirrors; DM, dispersive mirror; OC, output coupler; CW, continuous wave; ML, mode-locked).

Fig. 2 .

 2 Fig. 2. KLM Tm:(Lu,Sc)2O3 ceramic laser with TOC = 0.5%. Optical spectrum (a) and interferometric autocorrelation trace (b).at 2088.1 nm with an optical conversion efficiency of 26.8%. KLM operation was established by aligning the resonator towards the edge of the stability region by translating the folding mirror (M2) by several hundreds of micrometers away from the pump mirror (M1) to discriminate the CW regime. KLM was not self-starting. The transition from the CW to the KLM regime was achieved by a slight knock on the flat rear mirror (M3) or the OC. This led to abrupt increase in the average output power from 147 to 247 mW. At Pabs = 1.1 W the corresponding optical conversion efficiency was 22.5%. Figure2shows the recorded optical spectrum and the interferometric autocorrelation trace. The spectrum was centered at 2085.5 nm with a full width at half maximum (FWHM) of 65 nm, Fig.2(a). The autocorrelation trace gives a pulse duration of 71 fs by assuming a sech 2 -shaped temporal profile, see Fig.2(b), which is 22.4% longer than the Fourier-transform limit. A significant change in the recorded far-field beam profile was observed by placing an infrared camera at ~2 m from the OC. The shrinking of the far-field beam diameter from 5.4 (x) mm × 3.7 (y) mm to 3.9 (x) mm × 3.6 (y) mm, as shown in Fig.1(b), is a clear evidence for a soft-aperture Kerr-lens effect and self-focusing inside the ceramic sample. The total cavity length was ~ 1.8 m resulting in a pulse repetition rate of ~84.8 MHz. The peak on-axis laser intensity in the ceramic was estimated to be ~510 GW/cm 2 .The pulse duration was further shortened by using a 0.2% OC while maintaining Pabs = 1.1 W. The average output power dropped to 136 mW, however, the FWHM of the spectrum increased to 70 nm. Scaling of the pump power while maintaining the softaperture KLM regime, was possible up to Pabs = 1.6 W resulting in an average output power of 220 mW. The optical spectrum was further broadened but exhibited a significant deviation from an ideal sech 2 -shape profile, with three distinct peaks at 2081.4, 2181.5 and 2226.7 nm, see Fig.3(a). Pulses as short as 58 fs were recorded after external linear chirp compensation with a 3-mm thick ZnS ceramic plate (GDD = 465 fs 2 ). This pulse duration is equivalent to 8 optical cycles which was confirmed by recording the fringe-resolved autocorrelation trace, presented in Fig.3(b). A long-scale intensity autocorrelation scan (15 ps) is shown in the inset ofFig 3(b), confirming a single pulse ML operation without any pedestals or multi-pulses. The deconvolved pulse duration was 13.7% above the Fourier-transform limit, see Fig.3(a). The peak on-axis laser intensity in the ceramic was ~623 GW/cm 2 . Compared to previous sub-100 fs pulse generation results obtained with Tm-doped mixed sesquioxide ceramics using real SAs[2, 6, 7], KLM clearly demonstrates average power scalability

Fig. 3 .

 3 Fig. 3. KLM Tm:(Lu,Sc)2O3 ceramic laser with TOC = 0.2%. Optical spectrum (a) and interferometric autocorrelation traces of the shortest pulses (b). Inset in (b): simultaneously measured long-scale (±7.5 ps) background-free autocorrelation trace. combined with shortest pulse durations.The KLM pulse train was characterized by a radio frequency (RF) spectrum analyzer. The recorded fundamental beat note at 84.8 MHz exhibited a high extinction ratio of 77 dBc above the noise level, see Fig.4(a). This, together with the uniform harmonic beat notes shown inFig 4(b) indicates highly stable ML operation without any unwanted Q-switched or multiple pulsing instabilities.

  Fig 4(b) indicates highly stable ML operation without any unwanted Q-switched or multiple pulsing instabilities.

Fig. 4 .

 4 Fig. 4. RF spectra of the KLM Tm:(Lu,Sc)2O3 ceramic laser: fundamental beat note (a) and 1-GHz span (b). RBW: resolution bandwidth.

  5(b). The spectral and temporal reshaping

Acknowledgment. Y. Zhao acknowledges financial support from the Alexander von Humboldt Foundation through a Humboldt fellowship.

Funding.

National Natural Science Foundation of China (52032009, 61975208, 62075090, 51761135115, 61850410533, 52072351); Deutsche Forschungsgemeinschaft (PE 607/14-1); Natural Science Foundation of Jiangsu Province (BK20190104); Sino-German Scientist Cooperation and Exchanges Mobility Programme (M-0040); Foundation of President of China Academy of Engineering Physics (CAEP) (YZJJLX2018005); Fundation of Key Laboratory of Research on Chemistry and Physics of Optoelectronic Materials (CAS 2008DP173016).

Disclosures. The authors declare no conflicts of interest

Disclosures. Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.


L I Wang

Weidong Chen
email: chenweidong@fjirsm.ac.cn

Yongguang Zhao

Zhongben Pan

Pavel Loiko

Xavier Mateos

Mircea Guina

Mark Mero

Uwe Griebner

Valentin Petrov

Sub-50-fs pulse generation from a SESAM modelocked Tm,Ho-codoped calcium aluminate laser

We report on sub-50-fs pulse generation from a passively mode-locked Tm,Ho-codoped crystalline laser operating in the 2 μm spectral region. A Tm,Ho:Ca(Gd,Lu)AlO 4 laser delivers pulses as short as 46 fs at 2033 nm with an average power of 121 mW at a pulse repetition rate of ~78 MHz employing a SESAM as a saturable absorber. To the best of our knowledge, this result represents the shortest pulses ever generated from a Tm and/or Ho based solid-state laser. Polarization switching in the anisotropic gain material is observed in the mode-locked regime without any polarization selection elements which is essential for the shortest pulses.

During the last few years there has been a rapid progress in the generation of sub-100-fs pulses in the 2-μm spectral region directly from mode-locked (ML) lasers based on thulium (Tm 3+ ) and/or holmium (Ho 3+ ) doped active media [1]. Apart from direct spectroscopic or diagnostic applications, such high-repetition rate laser sources are important for seeding of ultrafast (chirped-pulse) laser amplifiers and synchronous pumping of optical parametric oscillators operating in the mid-IR spectral range based on nonoxide nonlinear materials with high conversion efficiency [2]. By entering the few optical cycle regime, they can also become a viable alternative to complex and inefficient coherent sources based on optical rectification for seeding of carrier-envelope phase (CEP) stable systems [3]. Ho 3+ -doped laser materials feature the merits of natural emission slightly above 2 μm to overcome the detrimental structured water vapor absorption/dispersion effect below 2 μm, and somewhat higher gain compared to their Tm-doped counterparts. Nevertheless, their spectrally structured gain profiles place limitations on the pulse duration achievable from singly Hodoped ML femtosecond lasers. This problem can be partially resolved by co-doping with Tm 3+ . The gain profiles of Ho 3+ and Tm 3+ in co-doped materials are overlapping, which makes it possible to combine their stimulated emissions and support ultrabroad spectra in the ML regime [4]. Efforts toward exploiting the gain bandwidth of Tm,Ho co-doped bulk gain media resulted in the first sub-100 fs pulse operation in a ML 2-μm solid-state laser in 2018. Using a SEmiconductor Saturable Absorber Mirror (SESAM) as a modelocker, pulses as short as 87 fs with an average power of 27 mW were generated with Tm,Ho:CaYAlO 4 (Tm,Ho:CALYO) [5]. Subsequently, shorter pulses (70 and 67 fs) were obtained with a Tm,Ho co-doped garnet crystal, i.e., Tm,Ho:Ca 3 Li x Nb 1.5+x Ga 3.5-2x O 12 (Tm,Ho:CLNGG), and carbon nanostructures as saturable absorbers (SAs) [6,7]. Finally, a pulse duration of 52 fs at 2015 nm was demonstrated using a Tm,Ho:CaGdAlO 4 (Tm,Ho:CALGO) crystal and a SESAM SA [8].

The above achievements profited from the inhomogeneous spectral broadening of the gain profiles originating from the structural disorder and the related ligand modifications of the host crystals employed. Tetragonal rare-earth calcium aluminates CaLnAlO 4 (Ln = Gd, Y) represent such an extraordinarily disordered host family which is extremely favorable for femtosecond pulse generation. Their structural disorder originates from the second coordination sphere of the laser-active trivalent rare-earth (RE 3+ , e.g., Yb 3+ , Tm 3+ and Ho 3+ ) cations formed by Ca 2+ and Ln 3+ ions Fig. 1. Effective gain cross-section spectra at ~2 μm for the Tm,Ho:CALGLO crystal, β = N( 3 F 4 )/N Tm is the inversion ratio for Tm 3+ ions, the polarization is σ (solid lines) and π (dashed lines).

(due to the charge difference of these ions and the different cationcation distances) [9]. Despite the disordered structure, CaLnAlO 4 still exhibit relatively high thermal conductivity with moderate dependence on the RE 3+ doping concentration [10]. In comparison to the disordered garnets, the polarized absorption and emission of the tetragonal calcium aluminates offer more flexibility in pumping and spectral bandwidth exploitation. Moreover, the structural disorder of the CaLnAlO 4 compounds can be complemented by compositional disorder leading to additional inhomogeneous spectral broadening, smoothing and flattening of the gain profiles of the optically active RE 3+ ions [11]. The latter is achievable by mixing CALGO and CALYO or by Lu-doping of one of them. Such compositional disorder with partial substitution of Gd 3+ by Lu 3+ (a maximum Lu 3+ content of 5.5 at.%) was firstly utilized for Yb 3+doped Ga(Gd,Lu)AlO 4 (Yb:CALGLO) and laser operation both in the continuous-wave (CW) and femtosecond ML regimes was demonstrated [12]. Very recently, we reported on Tm 3+ -doping of this novel mixed host crystal, Tm:CALGLO, its growth, spectroscopy, and CW laser operation [13].

Recently, such Tm,Ho co-doping structurally and compositionally disordered "mixed" co-doped crystal, Tm,Ho:CALGLO, were grown with high optical quality by its growth using the Czochralski method [14]. The measured doping levels were 4.48 at.% Tm 3+ , 0.54 at.% Ho 3+ and 5.51 at.% Lu 3+ , corresponding to a stoichiometric chemical formula of CaGd 0.8947 Lu 0.0551 Tm 0.0448 Ho 0.0054 AlO 4 .

The tetragonal Tm,Ho:CALGLO is an optically uniaxial crystal with two principal polarizations, i.e. E‖c (π-polarization) and E‖a (σ-polarization) with the corresponding refractive indices n e and n o . The calculated gain cross-sections of Tm,Ho:CALGLO for both polarizations with different Tm inversion levels β are shown in Fig. 1. The crystal features an extremely broad and smooth spectral gain profile supporting sub-50-fs pulses. The excellent spectroscopic and thermo-mechanical properties of Tm,Ho:CALGLO are attractive for passively ML operation in the 2-μm spectral region. Implementing a GaSb-based SESAM for mode locking, and broadband dispersive mirrors (DMs) for intracavity group delay dispersion (GDD) management, we report here on the generation of pulses as short as 46 fs, the shortest to date, to the best of our knowledge, for any Tm and/or Ho based solid-state mode-locked laser.

Laser operation was investigated in a X-folded standing-wave cavity without any polarization selecting elements, as shown in Fig. 2. The Tm,Ho:CALGLO crystal was an a-cut cube with an edge of 3 mm which was anti-reflection coated for normal incidence for both the pump and laser wavelengths. It was mounted in a copper holder water-cooled at 12℃, and placed between two dichroic folding mirrors M 1 and M 2 with a Radius of Curvature (RoC) of -100 mm. A third folding mirror (DM 1 , RoC = -100 mm) provided a second cavity beam waist in one of the cavity arms where the SESAM was implemented. The output coupler (OC) terminated the other cavity arm. The radius of the cavity mode in the crystal was estimated to be 30 μm by the ABCD formalism. The Tm,Ho:CALGLO crystal was pumped by a narrow-linewidth CW Ti:sapphire laser tuned to 801.3 nm with its polarization corresponding to π in the crystal to utilize the much higher absorption cross-section [12]. A spherical lens with a focal length of 70 mm focused the pump beam into the crystal yielding a waist radius of 30 μm. The measured single-pass absorption was ~97% under lasing conditions. A maximum CW power of 778 mW was extracted for an absorbed power of 3.09 W using the 3% OC and the SESAM substituted by a plane retroreflector, cf. Fig. 2. The corresponding slope efficiency was ~35.8%. The laser output was π-polarized.

A GaSb-based InGaAsSb quantum wells (QWs) SESAM was applied as a mode-locker. Such a near-surface QW design SESAM has been already successfully applied for the generation of sub-100 fs pulses at ~2 μm [15,16] and the characteristic parameters can be found elsewhere [17]. It was placed at the second beam waist for efficient bleaching of the SA. The estimated radius of this beam waist was ~120 μm. The intracavity GDD was managed by the DMs, one curved (DM 1 ) and several flat (DM 2 -DM 7 ). All DMs exhibited a GDD of -125 fs 2 per bounce. The total negative GDD introduced was varied by the number of bounces on the flat DMs to balance the intracavity material dispersion as well as the positive frequency chirp induced by self-phase modulation (SPM) in ML operation. Three different OCs (3%, 1.5% and 0.5%) were applied. A 3-mm thick ZnS ceramic plate (GDD = 465 fs 2 ) was used for external linear chirp compensation of the extra GDD introduced by the OC substrate (6.35-mm thick infrasil, GDD = -684 fs 2 ).

Initially, ML operation was investigated by applying five bounces (single pass) on the flat DMs (DM 1 -DM 3 ) giving a total round-trip GDD of -1250 fs 2 . Using the 3% OC, stable soliton ML operation was initiated and stabilized by the SESAM for a nominal pump level of 3 W. The laser generated an output power of 320 mW at 2081 nm in π-polarization. The 306-fs pulses, assuming a sech 2 -shape temporal profile, had a sech 2 -fitted spectral FWHM of 15 nm. Optimizing the cavity alignment for shorter pulse durations, we observed substantial broadening of the ML spectrum as well as a blue shift of the central wavelength accompanied by switching to linear σ-polarization. A maximum average power of 332 mW was obtained at optimum alignment for an absorbed pump power of 3.53 W. The measured ML spectrum and the corresponding interferometric autocorrelation trace at this output level are shown in Fig. 3. Almost bandwidth-limited pulses with a duration of 69 fs were achieved while the spectral FWHM was 63 nm. The peak power amounted to 53 kW for a pulse repetition rate of 82.9 MHz. The laser was always self-starting.

Such polarization switching has been reported in a diodepumped high-power Yb:CALGO laser in the CW regime, where the gain cross-sections for the two polarizations are similar in magnitude and hence compete at different inversion rates if the cavity loss is changing owing to the different thermo-optical properties of the laser crystal for π and σ-polarizations [18]. ML lasers are even more for sensitive to cavity losses which supports a similar explanation for the present Tm,Ho:CALGLO laser. We are not aware of any similar observations in a ML solid-state laser. The pulse duration was further reduced to 58 fs by applying the 1.5% OC. As can be expected for a three-level system, the wavelength experienced a slight red-shift, in our case to 2033.2 nm, see Fig. 4, maintaining the σ-polarization. The average power amounted to 191 mW at 82.9 MHz for an absorbed pump power of 3.23 W. In this configuration the estimated pulse duration from the interferometric autocorrelation trace was 45% above the Fourier limit, which means that the intracavity DMs were unable to ensure effective soliton compression, i.e., more negative GDD was required for further shortening of the pulse duration.

The latter was realized using seven instead of five bounces (single pass) on DMs (cf. Fig. 2) resulting in a total round-trip GDD of 1750 fs 2 . The shortest single pulse operation with ultimate stability in this case was achieved using the 0.5% OC, again in σ-polarization. A maximum average power of 121 mW at 78.2 MHz was generated for an absorbed power of 3.78 W. The shortest pulses were characterized using a second-harmonic generation (SHG) frequency-resolved optical gating (FROG) apparatus. The measured and retrieved SHG-FROG traces using a grid size of 512 × 512 points together with the reconstructed spectral and temporal profiles are shown in Figs. 5 (a) and(b). The directly measured spectrum was centered at 2033 nm spanning from 1878 to 2241 nm, in reasonably good agreement with the reconstructed spectrum from the SHG-FROG trace, cf. Fig. 5(c). After external linear chirp compensation with the 3-mm thick ZnS ceramic plate, the retrieved pulse had a FWHM of 47 fs (~7 optical cycles), still ~38% above the Fourier-limit, cf. Fig. 5(d). The retrieved pulse duration was confirmed by an independent measurement of the autocorrelation trace, giving a FWHM of 46 fs, see Fig. 5(e).

The far-field beam profiles for CW and ML operation were recorded with a pyroelectric camera placed at 1.6 m from the OC, see Fig. 6. Almost no changes were observed when switching from the CW to ML operation, easily achievable by slight misalignment. This observation indicates that Kerr-lensing is not the dominant mechanism for mode-locking which is mainly governed by soliton pulse shaping, stabilized by the SESAM. In conclusion, we achieved sub-50 fs pulses in the 2-μm spectral region from a ML laser by exploring Tm,Ho co-doping of the mixed CALGLO crystal. Using a GaSb-based SESAM as a SA pulses as short as 46 fs were recorded, the shortest ever reported for any Tm and/or Ho based solid-state laser. Without any intracavity polarization selective elements, we observed polarization switching related to the anisotropy of the gain medium and triggered by changing the cavity losses (note that the polarization was always linear). Switching from π to σ-polarization was associated with spectral broadening and hence the generation of the shortest pulses. This switching was accompanied by a blue shift of the central wavelength. This regime was readily achievable by minimizing the cavity losses and by careful cavity alignment independent of the OC transmission or the pump level. Note that imposing the σ-polarization simply by the Brewster angle condition for the active medium or taking a c-cut crystal is not practical for the present laser because pumping in π-polarization is much more effective.

Fig. 2 .

 2 Fig. 2. Experimental scheme of the SESAM ML Tm,Ho:CALGLO laser, Lens: focusing lens; M 1 -M 2 : concave mirrors; DM 1 -DM 7 , dispersive mirrors; OC: output coupler; M 3 : plane mirror for CW operation.

Fig. 3 .

 3 Fig. 3. (a) Optical spectrum and (b) interferometric autocorrelation trace of the SESAM ML Tm,Ho:CALGLO laser for Toc = 3%.

Fig. 4 .

 4 Fig. 4. (a) Optical spectrum and (b) interferometric autocorrelation trace of the SESAM ML Tm,Ho:CALGLO laser for Toc = 1.5%.

Fig. 5 .

 5 Fig. 5. SHG-FROG characterization of the shortest pulses from the SESAM ML Tm,Ho:CALGLO laser for Toc = 0.5%. Measured (a) and retrieved (b) SHG-FROG traces; measured and retrieved optical spectrum and its spectral phase (c); Fourier-transform limited (FTL) and retrieved temporal pulse profile and phase (d); measured interferometric autocorrelation trace (e).

Fig. 6 .Fig. 7 .

 67 Fig. 6. ML Tm,Ho:CALGLO laser: far-field beam in (a) CW and (b) SESAM ML regimes. The steady-state pulse train was characterized by a radiofrequency analyzer. Figures 7(a) and (b) show the first beat-note at ~78.2 MHz with a signal-to-noise ratio above 70 dBc and a 1-GHz span, both indicating stable ML operation without any spurious modulations.

Funding. National Natural Science Foundation of China (61975208, 51761135115, 61575199, 61850410533, 62075090, 52032009, 52072351); Deutsche Forschungsgemeinschaft (PE 607/14-1); Sino-German Scientist Cooperation and Exchanges Mobility Program (M-0040); Foundation of the President of China Academy of Engineering Physics (YZJJLX2018005); Foundation of Key Laboratory of Optoelectronic Materials Chemistry and Physics, Chinese Academy of Sciences (2008DP173016); Foundation of State Key Laboratory of Crystal Materials, Shandong University (KF2001).

Disclosures. The authors declare no conflicts of interest. Data Availability. Data supporting the findings presented in this paper are not publicly available at this time but may be obtained from the corresponding author upon reasonable request.


Yongguang Zhao

L I Wang

Weidong Chen
email: chenweidong@fjirsm.ac.cn

Zhongben Pan

Yicheng Wang

Peng Liu

Xiaodong Xu

Ying Liu

Deyuan Shen

Jian Zhang

Mircea Guina

Xavier Mateos

Pavel Loiko

Zhengping Wang

Xingguang Xu

Jun Xu

Mark Mero

Uwe Griebner

Valentin Petrov

SESAM mode-locked Tm:LuYO 3 ceramic laser generating 54-fs pulses at 2048 nm

Mode-locked laser operation near 2.05 μm based on a mixed sesquioxide Tm:LuYO3 ceramic is demonstrated. Continuous-wave and wavelength tunable operation is also investigated. Employing a GaSb-based SESAM as a saturable absorber, a maximum average output power of 133 mW is obtained for a pulse duration of 59 fs. Pulses as short as 54 fs, i.e., 8 optical cycles are generated at a repetition rate of ~78 MHz with an average output power of 51 mW. To the best of our knowledge, this result represents the shortest pulse duration ever achieved from Tm-based solid-state mode-locked lasers.

and high quantum efficiency via a one-for-two cross-relaxation process. These features are attractive in particular for the development of broadband tunable and femtosecond (fs) solidstate lasers in the 2-μm spectral range. Nevertheless, sub-100-fs mode-locked (ML) bulk lasers were not reported until 2017: Using graphene as a saturable absorber (SA), the monoclinic Tm:MgWO 4 crystal delivered 86-fs pulses at 2017 nm [START_REF] Wang | Sub-100 fs Tm:MgWO 4 laser at 2017 nm mode locked by a graphene saturable absorber[END_REF]. Subsequently, single-walled carbon nanotube-based SA (SWCNT-SA) ML lasers using Tm-doped disordered garnets also produced sub-100-fs pulse durations at ~2 μm [START_REF] Wang | 78 fs SWCNT-SA mode-locked Tm:CLNGG disordered garnet crystal laser at 2017 nm[END_REF][START_REF] Pan | Generation of 84-fs pulses from a mode-locked Tm:CNNGG disordered garnet crystal laser[END_REF].

Among the Tm 3+ -doped laser hosts, the cubic (bixbyite structure, space group 3 ) sesquioxides RE 2 O 3 , where RE = Lu, Y and Sc, are of particular interest for sub-100-fs ~2-μm solid-state lasers because of their extremely broad and flat gain spectra extending up to ~2.1 μm due to the strong Stark splitting of the ground state of Tm 3+ ( 3 H 6 , > 800 cm -1 ) in combination with strong electron-phonon interaction and their high thermal conductivity [START_REF] Kränkel | Rare-earth-doped sesquioxides for diode-pumped highpower lasers in the 1-, 2-, and 3-μm spectral range[END_REF]. The first sub-100-fs pulses from a Tm 3+ -doped crystalline sesquioxide laser have been demonstrated with a Kerr-lens ML Tm:Sc 2 O 3 , laser at 2108 nm [START_REF] Suzuki | High quality-factor Kerr-lens mode-locked Tm:Sc 2 O 3 single crystal laser with anomalous spectral broadening[END_REF]. However, the optical quality remains a critical factor for such crystals due to the very high melting point of the RE 2 O 3 compounds (typically 2400 -2500 °C) and possible structural phase transitions in some of them upon cooling [START_REF] Kränkel | Rare-earth-doped sesquioxides for diode-pumped highpower lasers in the 1-, 2-, and 3-μm spectral range[END_REF]. In contrast, ceramic fabrication circumvents such problems due to the relatively low sintering temperature [START_REF] Jing | Synthesis, spectroscopy, and efficient laser operation of "mixed" sesquioxide Tm:(Lu,Sc) 2 O 3 transparent ceramics[END_REF]. Moreover, it is easier to mix isostructural sesquioxide ceramics leading to compositional disorder and broader absorption and gain spectra, the latter being beneficial for the generation of even shorter laser pulses. Sub-10 opticalcycle (63-fs) pulses at 2057 nm were first achieved with a mixed Tm:(Lu,Sc) 2 O 3 ceramic laser using a Semiconductor Saturable Absorber Mirror (SESAM) for mode-locking [START_REF] Wang | Sub-10 optical-cycle passively mode-locked Tm:(Lu 2/3 Sc 1/3 ) 2 O 3 ceramic laser at 2 μm[END_REF]. More recently, pulses as short as 57 fs at 2045 nm were reported for a mixed Tm:LuYO 3 ceramic laser ML by a SWCNT-SA [START_REF] Zhao | SWCNT-SA mode-locked Tm:LuYO 3 ceramic laser delivering 8-optical-cycle pulses at 2.05 µm[END_REF].

The promising spectroscopic features and the previous ML laser results motivated us to further explore the potential of the mixed Tm:(Lu 0.5 Y 0.5 ) 2 O 3 or Tm:LuYO 3 ceramic. This ceramic is synthesized by the hot isostatic pressing (HIP) method at 1700 °C. It exhibits a rather broad absorption band of 26 nm at full width at half-maximum (FWHM) centered at 796.5 nm [START_REF] Zhou | Tm 3+ -doped LuYO 3 mixed sesquioxide ceramic laser: effective 2.05 μm source operating in continuous-wave and passive Q-switching regimes[END_REF], which in fact is a combination of few narrower lines, similar to the composite spectra of Tm:Lu 2 O 3 and Tm:Y 2 O 3 [START_REF] Loiko | Highly efficient, compact Tm 3+ :RE 2 O 3 (RE = Y, Lu, Sc) sesquioxide lasers based on thermal guiding[END_REF]. In the present work, a cubic shape, 3-mm-thick, uncoated Tm:LuYO 3 ceramic sample was used with 3 at.% Tm 3+ -doping (measured small-signal absorption: 66%).

Nowadays SESAMs are the most widely used SAs for ML bulk solid-state lasers that ensure stable and self-starting operation. However, their availability for specific wavelength ranges is limited, in particular around 2 μm. Recent development of SESAM for the 2-μm spectral range has focused on InGaAsSb quantum-wells (QWs) embedded in GaSb in which offset and band-gap can be tailored to encompass a spectral range across 1.9 -3.0 μm. Such 2-μm SESAMs show a fast (few ps) absorption recovery time in particular for the nearsurface design [START_REF] Paajaste | Absorption recovery dynamics in 2 µm GaSb-based SESAMs[END_REF] and an exceptionally broad reflection band of ~ 300 nm due to the use of lattice-matched GaSb/AlAsSb distributed Bragg reflectors (DBRs) [START_REF] Gluth | GaSb-based SESAM mode-locked Tm:YAG ceramic laser at 2 μm[END_REF]. Sub-100-fs pulse ML operation of Tm 3+ doped or Tm 3+ , Ho 3+ co-doped laser materials at ~2 μm using such SESAMs has already been demonstrated [START_REF] Petrov | Sub-100-fs bulk solid-state lasers near 2-micron[END_REF]. In this work, we focus on the study of the mixed Tm:LuYO 3 ceramic as an active medium in combination with a GaSb-based SESAM for ML operation. Nearly transformlimited pulses as short as 54 fs are reported, the shortest pulse duration ever achieved for any Tm-based solid-state laser. Additionally, continuous-wave (CW) tunable laser operation from 1909 to 2019 nm is characterized. The experimental setup is shown in Fig. 1. The ceramic sample was mounted on a water-cooled copper block (coolant temperature: 14 °C) and placed at Brewster's angle between two dichroic folding mirrors M 1 and M 2 . The pump source was a CW narrow-linewidth Ti:Sapphire laser tuned to 795.3 nm. It was focused into the ceramic sample with an f = 70 mm lens to a beam radius of 30 μm. The CW laser performance of the mixed Tm:LuYO 3 ceramic was studied with a standard 4-mirror astigmatically compensated X-type cavity including a plane rear reflector M 3 and a plane-wedged output coupler (OC). The laser cavity mode inside the ceramic sample was estimated using the ABCD formalism giving a waist radius of 30 and 76 μm in the sagittal and tangential planes, respectively.

As can be seen from Fig. 2(a), in the CW laser regime, a maximum output power of 603 mW was obtained for 3% OC transmission at an absorbed pump power of 2.12 W corresponding to a slope efficiency of 33.2%. The single pass pump absorption under lasing conditions depended on the OC and amounted to 62.2% for this OC, revealing some absorption bleaching. The central wavelength changed with T OC from 2060 to 2076 nm, Fig. 2(b). The total round-trip resonator losses (reabsorption losses excluded) were estimated with the Caird analysis by fitting the measured slope efficiency as a function of the OC reflectivity 1-T OC [START_REF] Caird | Quantum electronic-properties of the Na 3 Ga 2 Li 3 F 12 :Cr 3+ laser[END_REF]. The best fit gave = 0.56%, Fig. 2(c). A Lyot filter (3.2-mm-thick quartz birefringent plate) was placed at Brewster's angle close to the OC for wavelength tuning. With the 1.5% OC, an extremely broad tuning range of >200 nm was achieved as shown in Fig. 2(d), limited by the free spectral range of the filter and the reflectivity band of the cavity mirrors. It exceeded the tuning range reported for the Tm:(Lu,Sc) 2 O 3 ceramic under similar conditions by roughly 70 nm [START_REF] Wang | Sub-10 optical-cycle passively mode-locked Tm:(Lu 2/3 Sc 1/3 ) 2 O 3 ceramic laser at 2 μm[END_REF].

For ML operation, M 3 was replaced by a curved chirped mirror CM 1 with RoC = 100 mm in order to create a second intracavity beam waist on the SESAM to increase the fluence for efficient bleaching of the SA. The calculated radius of this beam waist was 120 μm. The GaSb-based SESAM applied in this experiment was analogous to Sample 7, presented in Table 3 of [START_REF] Paajaste | Absorption recovery dynamics in 2 µm GaSb-based SESAMs[END_REF]. Thus it contained two InGaAsSb QWs with a 10 nm barrier placed below the surface (50 nm GaSb cap) which was uncoated. The photoluminescence of the present sample was centered at 2090 nm. For such structures we measured typical recovery times with a fast and a slow component of about 240 fs and 21 ps, respectively [START_REF] Paajaste | Absorption recovery dynamics in 2 µm GaSb-based SESAMs[END_REF], however, the saturable/non-saturable losses and the saturation fluence are still difficult to evaluate.

The intracavity group delay dispersion (GDD) was optimized by two extra plane CMs (CM 2 and CM 3 ) in the other cavity arm, changing the number of bounces. All CMs had a GDD of -125 fs 2 per bounce. Applying 3, 5 and 7 bounces (single pass) on the plane CMs, the total round-trip GDD amounted to -887, -1387 and -1887 fs 2 , respectively (including the contribution of the ceramic sample: -137 fs 2 , estimated by averaging the refractive index for Y 2 O 3 and Lu 2 O 3 [START_REF] Zelmon | Temperature-dependent Sellmeier equations for rareearth sesquioxides[END_REF]). For three of the OCs (T OC = 1.5%, 0.5% and 0.2%), stable and selfstarting sub-100-fs pulse generation was obtained, however, only for 5 bounces on the CMs. : fitted pulse duration (FWHM).

Based on this cavity configuration, pulses as short as 69 fs with an average output power of 133 mW (for an absorbed pump power of 1.68 W) were obtained directly from the ML laser with T OC = 1.5%. The geometrical cavity length was ~1.92 m which resulted in a pulse repetition rate of ~78 MHz. The spectrum of the ML laser, recorded with a resolution of 0.5 nm, was centered at 2040.5 nm and had a sech 2 -fitted FWHM of 75 nm, as shown in Fig. 3. The observed satellite at longer wavelengths is associated with leakage through the OC whose transmission drastically increases at ~2200 nm. In fact, it does not present an artefact but is a kind of pulse shaping mechanism which alleviates a trend towards multi-pulse instability in the ML regime due to excessive intracavity energy for the given negative GDD. It could be ideally suppressed in future experiments by optimized characteristics of the OC. However, achieving yet broader reflectivity bands for such an OC, is indeed a technological challenge.

The envelopes of the recorded interferometric autocorrelation trace in Fig. 4(a) were well fitted assuming a sech 2 -shaped pulse with a duration of 69 fs (FWHM), equivalent to 10 optical cycles. The resulting time-bandwidth product amounted to 0.373 indicating some residual chirp. The latter was eliminated by additional external compression using a 3-mm-thick ZnS polycrystalline plate. A pulse duration as short as 59 fs was achieved, confirmed by the measured interferometric autocorrelation trace in Fig. 4(b), representing 9optical-cycle pulses. Due to the unaltered spectrum, the timebandwidth product dropped to 0.319 indicating almost bandwidth limited pulses.

The pulse duration was further shortened by reducing the OC transmission to 0.5% at the expense of the average output power. Thus, the shortest pulses directly generated from the self-starting ML laser had a FWHM duration of 66 fs. At ultimate stability, the average output power amounted to 51 mW for 1.5 W of absorbed pump power. The corresponding spectrum was centered at 2048 nm with a sech 2 -fitted FWHM of 82 nm. The slightly chirped pulses with a time-bandwidth product of 0.387 were externally compressed with the same 3mm-thick ZnS plate. Their characterization included interferometric autocorrelation and SHG-FROG (secondharmonic generation frequency-resolved optical gating) with a 1-mm-thick type-I LiNbO 3 crystal. Assuming a sech 2 pulse shape, the autocorrelation measurement (Fig. 5) gave a pulse duration of 54 fs representing 8 optical cycles by counting the fringes. The absence of post-or pre-pulses was confirmed by a measurement on a 15-ps time span (inset Fig. 5). The FROG results are summarized in Fig. 6. The measured FROG spectrogram was reconstructed with an error of 0.0048 on a 128 ⨯128 grid, Fig. 6(a) and (b). The retrieved FROG spectrum with a FWHM of 82 nm, centered at 2048 nm, is shown in Fig. 6(c). It coincides almost perfectly with the one independently measured with a spectrometer, except for the small satellite at longer wavelengths. A pulse duration of 55 fs was derived from the FROG retrieval as shown in Fig. 6(d), in excellent agreement with the independently measured τ Δ autocorrelation trace; cf. Fig. 5. The residual linear chirp parameter was derived from a parabolic fit to the spectral phase leading to ±100 fs 2 . It was not possible to determine the sign with a suitable substrate because of the small chirp value. The time-bandwidth product after compression (0.316) was indicative of Fourier-limited pulses.

Compared to the experimental conditions in [START_REF] Zhao | SWCNT-SA mode-locked Tm:LuYO 3 ceramic laser delivering 8-optical-cycle pulses at 2.05 µm[END_REF], stronger self-phase modulation can be expected in the present work due to the higher intracavity intensity in the ceramic sample (~50 GW/cm 2 on-axis for the shortest pulses). The same is true for the spatial Kerr-lens effect. Concerning the origin and role of the spectral satellite at longer wavelengths, cf. Fig. 3 and Fig. 6(c), it shall be emphasized that the drop in the OC reflectivity is associated with abrupt variation of its GDD. However, the same is true also for the CMs around 2200 nm. In fact, from experiments using a different OC design, which ensured extended reflectivity at longer wavelengths, it seems that a similar, though much weaker in amplitude satellite is still present, and thus its origin might be related to higher order dispersion near 2200 nm. However, a stronger satellite occurring for an OC with a narrower reflection band as the one employed in the present work seems to stabilize the soliton regime in this laser where the intracavity GDD can be optimized only in a discrete manner, ultimately contributing to the achievement of the shortest pulse duration. Figure 7 shows the measured radio frequency (RF) spectra of the fundamental beat note at ~78 MHz with a resolution bandwidth (RBW) of 300 Hz and a 1-GHz-wide span (RBW: 10 kHz) to verify the stability of the ML laser for the shortest pulse operation. The very high extinction of 76 dBc and the absence of any spurious modulation are evidences for stable CW-ML operation of the mixed Tm:LuYO 3 ceramic laser. In conclusion, we present a detailed investigation of CW, tunable and mode-locked laser operation of a mixed sesquioxide Tm:LuYO 3 ceramic laser at ~2 μm. Using the same gain medium and GDD compensation scheme, it was possible to directly compare mode-locking initiated by a SESAM and a SWCNT-SA [START_REF] Zhao | SWCNT-SA mode-locked Tm:LuYO 3 ceramic laser delivering 8-optical-cycle pulses at 2.05 µm[END_REF]. The pulse duration of 54 fs achieved in the present work by using a GaSb-based SESAM as a SA, represents the shortest pulse ever reported for any Tm-based bulk solid-state laser. It demonstrates that a resonant-type SA can be equally good or even better for mode-locking of such femtosecond lasers. Whereas from previous studies it is known that such SESAMs typically show slower response, larger modulation depths and lower non-saturable losses compared to SWCNT-SAs [START_REF] Petrov | Sub-100-fs bulk solid-state lasers near 2-micron[END_REF], the present results indicate that these characteristic parameters are not of crucial importance and can vary in quite broad ranges, see Table 1 in [START_REF] Petrov | Sub-100-fs bulk solid-state lasers near 2-micron[END_REF]. Finally, we note that while Tm-fiber lasers have produced slightly shorter pulse durations, this was only the case after external compression in a prism pair [START_REF] Nomura | Sub-50-fs pulse generation from thuliumdoped ZBLAN fiber laser oscillator[END_REF] while the oscillator itself operated in the chirped pulse regime, delivering pulse durations of the order of 1 ps.

Fig. 1 .

 1 Fig. 1. Setup of the ML Tm:LuYO3 laser: M1-M2: concave folding mirrors (RoC = 100 mm), M3: rear mirror in CW operation; CM1-CM3, chirped mirrors; OC: output coupler.

T

  OC = 0.2%, η = 11.5%T OC = 0.5%, η = 17.3%T OC = 1.5%, η = 28.3% T OC = 3%, η = 33.2%Output power [mW]Absorbed pump power[mW]

  Fig. 2. CW laser performance of the mixed Tm:LuY2O3 ceramic for different OCs (a); laser spectra (b); slope efficiency as a function of the OC reflectivity ROC=1-TOC (c); and spectral tuning range obtained with a Lyot filter (d).

Fig. 3 .Fig. 4 .

 34 Fig.3. Spectrum of the ML Tm:LuY2O3 ceramic laser using TOC=1.5% (left axis) and OC reflectivity ROC=1 -TOC (right axis).

Fig. 5 .

 5 Fig. 5. Interferometric autocorrelation trace of the shortest pulses from the ML Tm:LuYO3 ceramic laser obtained with TOC = 0.5%. The fit assumes a sech 2 -pulse shape. Inset: noncollinear autocorrelation trace on a time span of 15 ps.

Fig. 6 .

 6 Fig. 6. SHG FROG characterization for the shortest pulses of the Tm:LuYO3 ceramic laser (TOC = 0.5%): Measured (a) and retrieved (b) FROG traces; retrieved and measured spectra, and retrieved spectral phase (c); retrieved temporal intensity profile and phase (d).

Fig. 7 .

 7 Fig. 7. Radio frequency spectra of the ML mixed Tm:LuYO3 sesquioxide ceramic laser: 1-GHz span (a) and fundamental beat note (b).

Funding.

  National Natural Science Foundation of China (61975208, 51761135115, 61575199, 61850410533); Deutsche Forschungsgemeinschaft (PE 607/14-1); Laserlab-Europe (654148); Natural Science Foundation of Jiangsu Province (SBK2019030177); Sino-German Scientist Cooperation and Exchanges Mobility Programme (M-0040); China Academy of Engineering Physics (CAEP) (YZJJLX2018005); Fund of Key Laboratory of Optoelectronic Materials Chemistry and Physics, Chinese Academy of Sciences (2008DP173016) and China Scholarship Council (CSC) (201704910363).

Acknowledgments. Y. Zhao acknowledges financial support from the Alexander von Humboldt Foundation through a Humboldt fellowship. M. Guina acknowledges A. Härkönen and R. Koskinen for assistance with SESAM fabrication.

Disclosures. The authors declare no conflicts of interest.