Esrom Kifle

Pavel Loiko

Carolina Romero

Javier Rodríguez

Vázquez De Aldana

Magdalena Aguiló

Francesc Díaz

Patrice Camy

Uwe Griebner

Valentin Petrov

Xavier Mateos
email: xavier.mateos@urv.cat

Watt-level ultrafast laser inscribed Thulium waveguide lasers

We report on the first watt-level ultrafast laser inscribed Thulium waveguide (WG) lasers. Depressed-index buried channel WGs with a circular cladding (type III) are produced in monoclinic Tm 3+ :KLu(WO 4 ) 2 crystals. Laser operation is achieved under conventional ( 3 H 6 → 3 H 4 ) and in-band ( 3 H 6 → 3 F 4 ) pumping. In the former case, employing a Raman fiber laser emitting at 1679 nm as pump, the continuous-wave Tm channel WG laser generated 1.37 W at 1915-1923 nm with a record-high slope efficiency of 82.7% (with respect to the absorbed pump power), a threshold of only 17 mW and a spatially single-mode output with linear polarization. The WG propagation losses were 0.2±0.3 dB/cm. Passive Q-switching of Tm channel WG lasers is achieved using Cr 2+ :ZnS and Cr 2+ :ZnSe saturable absorbers. With Cr 2+ :ZnS, record-short pulses of 2.6 ns/6.9 μJ at a repetition rate of 8.0 kHz were generated. The developed WGs are promising for compact GHz mode-locked lasers at ~2 μm.

Introduction

Waveguide (WG) lasers represent an important component of integrated photonic circuits [START_REF] Marshall | Laser written waveguide photonic quantum circuits[END_REF]. They are compatible with optical fibers and various on-chip devices leading to applications in the fields of optical sensing, on-chip spectroscopy, microfluidics, telecom, medicine and soft material processing. According to their geometry, active WGs can be classified into planar and channel devices. In planar WG lasers, the mode confinement by index-guiding is ensured only in one direction (orthogonal to the plane of the active layer) [START_REF] Mackenzie | Dielectric solid-state planar waveguide lasers: a review[END_REF]. In channel WGs, it is provided in two directions leading to a well-defined index profile and, typically, singletransverse-mode operation [START_REF] Chen | Optical waveguides in crystalline dielectric materials produced by femtosecond-laser micromachining[END_REF]. Channel WGs have the benefits of small mode areas leading to high intracavity light intensity, low laser threshold, good spatial beam quality and high efficiency due to the good overlap of pump and laser modes. Practical advantages include also their compact and robust design, and compatibility with fiber technology.

The eye-safe spectral range of ~2 μm contains absorption lines of several relevant bio-and atmospheric molecules such as H 2 O, CO 2 , N 2 O or NH 3 . Thus, channel WG lasers emitting continuous-wave (CW) and pulsed laser radiation at these wavelengths are of particular interest for bio-sensing, on-board ice sensing and wind mapping, as well as surgery of soft tissues [START_REF] Scholle | 2 μm laser sources and their possible applications[END_REF]. Such compact lasers can be also used as seed sources for WG and fiber amplifiers. Typically, laser emission at ~2 μm in WG lasers is achieved using trivalent rare-earth ions such as Thulium (Tm 3+ ) [START_REF] Rameix | An efficient, diode-pumped, 2 μm Tm:YAG waveguide laser[END_REF] or Holmium (Ho 3+ ) [START_REF] Mcdaniel | Operation of Ho:YAG ultrafast laser inscribed waveguide lasers[END_REF]. WG lasers emitting above 2 μm based on Chromium (Cr 2+ ) doped chalcogenides (ZnS, ZnSe) are known as well [START_REF] Macdonald | Ultrabroad midinfrared tunable Cr:ZnSe channel waveguide laser[END_REF].

The Thulium ion (electronic configuration: [Xe]4f 12 ) features emission at ~2 μm on the the 3 F 4 → 3 H 6 4f-4f transition [START_REF] Stoneman | Efficient, broadly tunable, laser-pumped Tm:YAG and Tm:YSGG cw lasers[END_REF]. Due to the typically large Stark splitting of the ground-state ( 3 H 6 ) and strong electron-phonon coupling located at the end of the lanthanide series, Tm 3+ doped materials feature broad emission spectra. A conventional way to excite Tm 3+ ions is to use the intense 3 H 6 → 3 H 4 transition, Fig. 1(a), spectrally located at ~0.8 μm. Furthermore, the phonon-assisted cross-relaxation (CR) energy-transfer process that becomes efficient even at moderate Tm 3+ doping levels [START_REF] Van Dalfsen | Thulium channel waveguide laser with 1.6 W of output power and ~80% slope efficiency[END_REF], Tm 1 ( 3 H 4 ) + Tm 2 ( 3 H 6 ) → Tm 1 ( 3 F 4 ) + Tm 2 ( 3 F 4 ), leads to two excitations into the upper laser level thus enhancing the laser slope efficiency over the Stokes limit and reducing the heat load. Efficient Tm WG lasers based on conventional pumping using high-brightness pump sources (e.g., Ti:Sapphire lasers) are known [START_REF] Van Dalfsen | Thulium channel waveguide laser with 1.6 W of output power and ~80% slope efficiency[END_REF][START_REF] Bolanos | Tm:LiYF 4 planar waveguide laser at 1.9 μm[END_REF]. Van Dalfsen et al. reported on a Tm 3+ :KY(WO 4 ) 2 channel WG laser delivering up to 1.5-1.6 W at 1840 nm with a slope efficiency η of 75-81% [START_REF] Van Dalfsen | Thulium channel waveguide laser with 1.6 W of output power and ~80% slope efficiency[END_REF]. The disadvantages of the conventional pumping scheme are the limited power scaling capabilities and poor integration with fiber technology. High-power AlGaAs laser diodes with a suitable emission wavelength, widely used in bulk Tm lasers, have not been implemented in efficient single-transverse-mode Tm channel WG lasers so far. The latter is related to the lack of high brightness laser diodes around 800 nm, i.e., with multi Watt emission in the transversal single mode. (a) Energy level scheme of Tm 3+ in monoclinic KLu(WO 4 ) 2 crystal [START_REF] Silvestre | Thulium doped monoclinic KLu(WO 4 ) 2 single crystals: growth and spectroscopy[END_REF] showing relevant processes: red and green arrowspump and laser transitions, CRcross-relaxation, NRnon-radiative relaxation, Rradiative relaxation, ETUenergy-transfer upconversion; (b) absorption cross-section, σ abs , spectra for the 3 H 6 → 3 H 4 and 3 H 6 → 3 F 4 transitions of Tm 3+ in KLu(WO 4 ) 2 [START_REF] Petrov | Growth and properties of KLu(WO 4 ) 2 , and novel ytterbium and thulium lasers based on this monoclinic crystalline host[END_REF]. The pump wavelengths are indicated by the vertical lines. The light polarization is E || N p and E || N m .

Another pumping scheme for the Tm 3+ ion (called resonant or in-band pumping) refers to a direct excitation to the upper laser level ( 3 F 4 ). This scheme can result in high laser efficiency even at moderate Tm 3+ concentrations. The only limiting factor here is the phonon-assisted energy-transfer upconversion (ETU), Tm 1 ( 3 F 4 ) + Tm 2 ( 3 F 4 ) → Tm 1 ( 3 H 6 ) + Tm 2 ( 3 H 4 ), a process opposite to the CR, which depopulates the upper laser level. However, for low Tm 3+ doping levels, the ETU rates are weak. As a pump source for in-band pumping, one can use Raman fiber lasers operating at ~1.7 μm. Efficient bulk in-band-pumped Tm lasers are known [START_REF] Antipov | Highly efficient 2 μm CW and Q-switched Tm 3+ :Lu 2 O 3 ceramics lasers in-band pumped by a Raman-shifted erbium fiber laser at 1670 nm[END_REF][START_REF] Yao | Highly efficient Tm:CaYAlO 4 laser in-band pumped by a Raman fiber laser at 1.7 μm[END_REF]. W. Yao et al. developed a Tm 3+ :CaYAlO 4 laser delivering 6.8 W at 1968 nm with η ≈ 56% [START_REF] Yao | Highly efficient Tm:CaYAlO 4 laser in-band pumped by a Raman fiber laser at 1.7 μm[END_REF]. There is only one report about an in-band-pumped Tm 3+ :LiYF 4 waveguide laser generating 2.05 W at 1881 nm with η = 78.3% [START_REF] Loiko | In-band pumping of Tm:LiYF 4 channel waveguide: a power scaling strategy for ~2 μm waveguide lasers[END_REF]. However, due to the weaker crystal-field in fluorides, it was not possible to operate this laser above 1.9 μm.

For the fabrication of Tm channel WG lasers, different methods have been used such as Liquid Phase Epitaxy (LPE) [START_REF] Rameix | An efficient, diode-pumped, 2 μm Tm:YAG waveguide laser[END_REF][START_REF] Rivier | Tm:KY(WO 4 ) 2 waveguide laser[END_REF][START_REF] Bolaños | Continuous-wave and Q-switched Tm-doped KY(WO 4 ) 2 planar waveguide laser at 1.84 µm[END_REF][START_REF] Kifle | Tm:KY 1-x-y Gd x Lu y (WO 4 ) 2 planar waveguide laser passively Q-switched by single-walled carbon nanotubes[END_REF] with subsequent microstructuring by reaction ion (Ar + ) beam etching [START_REF] Van Dalfsen | Efficient KY 1-x-y Gd x Lu y (WO 4 ) 2 :Tm 3+ channel waveguide lasers[END_REF] or, recently, by diamond-saw dicing [START_REF] Loiko | Watt-level Tm:LiYF 4 channel waveguide laser produced by diamond saw dicing[END_REF][START_REF] Kifle | Diamond saw dicing of thulium channel waveguide lasers in monoclinic crystalline films[END_REF], direct bonding [START_REF] Mackenzie | 15 W diode-side-pumped Tm:YAG waveguide laser at 2 μm[END_REF], ion diffusion [START_REF] Shepherd | 1.9-μm operation of a Tm:lead germanate glass waveguide laser[END_REF] or reactive co-sputtering [START_REF] Li | High-power thulium lasers on a silicon photonics platform[END_REF]. Only LPE-based Tm channel WG lasers have featured watt-level output performance so far, see Table 1. In recent years, another method for the fabrication of photonic microstructures in transparent dielectric materials has emerged, namely femtosecond Direct Laser Writing (fs-DLW) [START_REF] Chen | Optical waveguides in crystalline dielectric materials produced by femtosecond-laser micromachining[END_REF][START_REF] Gattass | Femtosecond laser micromachining in transparent materials[END_REF], also referred as Ultrafast Laser Inscription (ULI). It is based on the formation of a strongly localized, permanent and thermally stable variation of the refractive index (n) in the material volume by a tightly focused fs laser radiation. The light-guiding is then ensured by a refractive index difference Δn between the laser damage tracks and the unmodified (bulk) material. The Δn can be both positive (guiding within the damage tracks, type I structures, typically observed in glasses [START_REF] Davis | Writing waveguides in glass with a femtosecond laser[END_REF]) or negative (guiding between the damage tracks, type II or type III structures) depending on the material.

Fs-DLW has the advantages of short fabrication time, high precision, a great variety of the three-dimensional WG geometries and available materials (glasses, crystals or ceramics), moderate propagation losses and it is relatively simple from the technological point of view. So far, fs-DLW has been implemented for the fabrication of type II or type III channel WGs in thulium-doped glasses [START_REF] Lancaster | Fifty percent internal slope efficiency femtosecond direct-written Tm 3+ :ZBLAN waveguide laser[END_REF][START_REF] Lancaster | Versatile largemode-area femtosecond laser-written Tm:ZBLAN glass chip lasers[END_REF] and cubic crystals / ceramics [START_REF] Ren | Mid-infrared waveguide lasers in rareearth-doped YAG[END_REF][START_REF] Morris | 1.9 μm waveguide laser fabricated by ultrafast laser inscription in Tm:Lu 2 O 3 ceramic[END_REF], Table 1. D. Lancaster et al. achieved the best results in terms of output power using a Tm 3+ -doped ZBLAN glass WG with conventional pumping around 800 nm, namely 205 mW at ~1890 nm with η = 67% [START_REF] Lancaster | Versatile largemode-area femtosecond laser-written Tm:ZBLAN glass chip lasers[END_REF]. The WG propagation losses were 0.4±0.2 dB/cm. However, the obtained results are inferior compared to LPE-based WGs. The objective of the present work is to assess the potential of fs-DLW for producing active WGs with Tm doping capable of delivering Watt-level output at ~2 μm with high laser efficiencies. We have employed both conventional and in-band pumping schemes. The latter has never been applied to fs-DLW Tm WGs before.

We utilized one of the advantages of fs-DLW: its applicability to various materials including low-symmetry (anisotropic) crystals. By preserving the crystallinity of the unmodified material (acting as a core), compared to the damage tracks (acting as a cladding) [START_REF] Kifle | Femtosecond-laser-written hexagonal cladding waveguide in Tm:KLu(WO 4 ) 2 : µ-Raman study and laser operation[END_REF], we were able to explore the beneficial anisotropic spectroscopic properties of lowsymmetry crystals. In particular, we used the monoclinic potassium lutetium double tungstate, Tm 3+ :KLu(WO 4 ) 2 , which is known for efficient bulk laser operation at ~2 μm in the continuous-wave [START_REF] Mateos | Efficient 2μm continuous-wave laser oscillation of Tm 3+ :KLu(WO 4 ) 2[END_REF][START_REF] Serres | Diode-pumped microchip Tm:KLu(WO 4 ) 2 laser with more than 3 W of output power[END_REF], passively Q-switched [START_REF] Segura | Passive Q-switching of the diode pumped Tm 3+ :KLu(WO 4 ) 2 laser near 2-µm with Cr 2+ :ZnS saturable absorbers[END_REF][START_REF] Loiko | Subnanosecond Tm:KLuW microchip laser Q-switched by a Cr:ZnS saturable absorber[END_REF][START_REF] Serres | Tm:KLu(WO 4 ) 2 microchip laser Q-switched by a graphene-based saturable absorber[END_REF] and mode-locked [START_REF] Schmidt | Femtosecond pulses near 2 µm from a Tm:KLuW laser mode-locked by a single-walled carbon nanotube saturable absorber[END_REF] regimes. Thindisk lasers based on this laser material are also known [START_REF] Vatnik | Efficient thin-disk Tm-laser operation based on Tm:KLu(WO 4 ) 2 /KLu(WO 4 ) 2 epitaxies[END_REF]. The crystal features intense and broad spectral bands (absorption and emission) with polarized light, easy Tm 3+ doping, strong CR and weak luminescence quenching [START_REF] Petrov | Growth and properties of KLu(WO 4 ) 2 , and novel ytterbium and thulium lasers based on this monoclinic crystalline host[END_REF]. It is thus very attractive for both conventional and in-band pumping; see the polarized absorption cross-section, σ abs , spectra for the 3 H 6 → 3 H 4 and 3 H 6 → 3 F 4 transitions in Fig. 1(b).

KLu(WO 4 ) 2 belongs to the crystal family of monoclinic double tungstates (MDTs) with a general chemical formula KRE(WO 4 ) 2 (abbreviated: KREW, where RE = Gd, Y or Lu is a host-forming cation). So far, these crystals were recognized as excellent laser host materials for doping with such rare-earth ions (RE 3+ ) as Yb 3+ [START_REF] Lagatsky | Diode-pumped CW lasing of Yb:KYW and Yb:KGW[END_REF][START_REF] Liu | Efficient high-power laser operation of Yb:KLu(WO 4 ) 2 crystals cut along the principal optical axes[END_REF][START_REF] Loiko | Sub-nanosecond Yb:KLu(WO 4 ) 2 microchip laser[END_REF][START_REF] Serres | Prospects of monoclinic Yb:KLu(WO 4 ) 2 crystal for multi-watt microchip lasers[END_REF][START_REF] Griebner | Passively mode-locked Yb:KLu(WO 4 ) 2 oscillators[END_REF], Tm 3+ [START_REF] Mateos | Efficient 2μm continuous-wave laser oscillation of Tm 3+ :KLu(WO 4 ) 2[END_REF][START_REF] Serres | Diode-pumped microchip Tm:KLu(WO 4 ) 2 laser with more than 3 W of output power[END_REF][START_REF] Segura | Passive Q-switching of the diode pumped Tm 3+ :KLu(WO 4 ) 2 laser near 2-µm with Cr 2+ :ZnS saturable absorbers[END_REF][START_REF] Loiko | Subnanosecond Tm:KLuW microchip laser Q-switched by a Cr:ZnS saturable absorber[END_REF][START_REF] Serres | Tm:KLu(WO 4 ) 2 microchip laser Q-switched by a graphene-based saturable absorber[END_REF][START_REF] Schmidt | Femtosecond pulses near 2 µm from a Tm:KLuW laser mode-locked by a single-walled carbon nanotube saturable absorber[END_REF][START_REF] Gaponenko | Thermal lensing and microchip laser performance of N g -cut Tm 3+ :KY(WO 4 ) 2 crystal[END_REF] and Ho 3+ [START_REF] Loiko | In-band-pumped Ho:KLu(WO 4 ) 2 microchip laser with 84% slope efficiency[END_REF][START_REF] Jambunathan | Growth, spectroscopy and laser operation of Ho:KY(WO 4 ) 2[END_REF][START_REF] Loiko | Microchip laser operation of Tm,Ho:KLu(WO 4 ) 2 crystal[END_REF][START_REF] Mateos | Holmium thin-disk laser based on Ho:KY(WO 4 ) 2 /KY(WO 4 ) 2 epitaxy with 60% slope efficiency and simplified pump geometry[END_REF]. The advantages of RE 3+ -doped MDTs are the following: (i) high RE 3+ doping levels (up to stoichiometric compositions) with minimum lattice distortions; (ii) ordered structure, i.e., a single crystallographic site for the RE 3+ ions (C 2 ), (iii) long RE 3+ -RE 3+ interatomic distances leading to a weak luminescence quenching; (iv) high luminescence quantum yields and weak non-radiative relaxation from the emitting states of the considered RE 3+ ions; (v) strong anisotropy of optical and spectroscopic properties for polarized light; (vi) Raman activity. As for the thermal properties, the thermal conductivity of MDT is moderate (κ ~ 3.5 Wm -1 K -1 for KLu(WO 4 ) 2 ) [START_REF] Silvestre | Thermal properties of monoclinic KLu(WO 4 ) 2 as a promising solid state laser host[END_REF]. The thermo-optical effects in MDTs can be greatly suppressed owing to their "athermal" behavior [START_REF] Loiko | Thermal-lens-driven effects in N g -cut Yb-and Tm-doped monoclinic KLu(WO 4 ) 2 crystals[END_REF][START_REF] Loiko | Thermal lensing study and athermal directions in flashlamp-pumped Nd:KGd(WO 4 ) 2 laser crystal[END_REF], i.e., a mutual compensation of contributions to the variation of the optical path length arising from the negative thermo-optic coefficients (dn/dT < 0) [START_REF] Loiko | Thermo-optic dispersion formulas for monoclinic double tungstates KRe(WO 4 ) 2 where Re = Gd, Y, Lu, Yb[END_REF] and positive thermal expansion [START_REF] Loiko | Detailed characterization of thermal expansion tensor in monoclinic KRe(WO 4 ) 2 (where Re = Gd, Y, Lu, Yb)[END_REF]. These properties lead to a weak, positive and nearly spherical thermal lens for certain crystal orientations with a reduced effect on the laser mode [START_REF] Loiko | Characterization of the thermal lens in 3 at.% Tm:KLu(WO 4 ) 2 and microchip laser operation[END_REF][START_REF] Loiko | Thermal lensing in Yb:KLu(WO 4 ) 2 crystals cut along the optical indicatrix axes[END_REF][START_REF] Loiko | Polarization-anisotropy of thermal lens in Yb:KY(WO 4 ) 2 laser crystal under high-power diode pumping[END_REF][START_REF] Yumashev | Thermal stress and end-bulging in monoclinic crystals: The case study of double tungstates[END_REF][START_REF] Loiko | All-space existence and dispersion of athermal directions in monoclinic KY(WO4)2[END_REF].

Prior to the present work, there existed studies on ultrafast laser written channel WGs in monoclinic double tungstate crystals (see Section 3.4). In particular, fs-DLW buried channel WGs in the monoclinic Tm 3+ :KLu(WO 4 ) 2 crystal were first reported in [START_REF] Kifle | Femtosecond-laser written Tm:KLu(WO 4 ) 2 waveguide lasers[END_REF].

Direct laser writing and waveguide laser setup

Fabrication and characterization of waveguides

As a gain material, we used the monoclinic (sp. gr. C 6 2h -C2/c) Tm 3+ :KLu(WO 4 ) 2 crystal (shortly Tm:KLuW). It was grown by the Top-Seeded Solution Growth (TSSG) Slow-Cooling method using potassium ditungstate (K 2 W 2 O 7 ) as a solvent and a [010]-oriented seed [START_REF] Petrov | Growth and properties of KLu(WO 4 ) 2 , and novel ytterbium and thulium lasers based on this monoclinic crystalline host[END_REF]. The Tm 3+ doping level was 3 at.% (ion density: N Tm = 2.15×10 20 cm -3 ). Tm:KLuW is an optically biaxial crystal and it was oriented in the frame of the mutually orthogonal optical indicatrix axes N p , N m and N g (the corresponding refractive indices follow the relation n p < n m < n g ). A rectangular sample was cut for light propagation along the N g -axis (N g -cut) to utilize the advantageous thermo-optical [START_REF] Loiko | Thermal-lens-driven effects in N g -cut Yb-and Tm-doped monoclinic KLu(WO 4 ) 2 crystals[END_REF][START_REF] Loiko | Characterization of the thermal lens in 3 at.% Tm:KLu(WO 4 ) 2 and microchip laser operation[END_REF] and spectroscopic [START_REF] Silvestre | Thulium doped monoclinic KLu(WO 4 ) 2 single crystals: growth and spectroscopy[END_REF] properties for this crystal orientation. The sample thickness (t) was 3.00 mm and its aperture was 3.10(N m )×2.85(N p ) mm 2 . Its input, output and top surfaces were polished to laser-grade quality (prior to the inscription of the WGs) and remained uncoated. Depressed-index buried channel WGs with a circular cladding were fabricated in bulk Tm:KLuW crystals by fs-DLW [START_REF] Kifle | Femtosecond-laser written Tm:KLu(WO 4 ) 2 waveguide lasers[END_REF], see the scheme in Fig. 2(a). As a laser source, we used a Ti:Sapphire regenerative amplifier (Spitfire, Spectra-Physics) delivering 120 fs pulses at a central wavelength of 795 nm with a repetition rate of 1 kHz. The pulse energy incident on the sample was attenuated using a set of a half-wave (λ/2) plate, a calibrated neutral density filter and a linear polarizer. A 40× microscope objective (numerical aperture: N.A. = 0.65) was used to focus the femtosecond laser radiation into the sample through the polished top face (N m ×N g ). To produce the damage tracks, the sample was translated in the horizontal direction (along the N g -axis) with a speed of 400 µm/s. The incident pulse energy on the sample was ~ 57 nJ. The damage tracks were continuous and they were written through the entire sample length thus reaching the polished input and output surfaces. No repolishing of the sample end-facets was applied after completing the fs-DLW process. The polarization of the femtosecond radiation (E || N m ) was orthogonal to the writing direction [START_REF] Kifle | Femtosecond-laser-written hexagonal cladding waveguide in Tm:KLu(WO 4 ) 2 : µ-Raman study and laser operation[END_REF] to avoid anisotropic effects related to the birefringence of MDTs. The writing parameters were optimized in a set of previous test experiments.

The photograph of the sample during fs-DLW is shown in Fig. 3. The line scan procedure was repeated at different depths and lateral positions of the crystal to fabricate a barrel-shaped WG, Fig. 2(b). It consisted of an unmodified core surrounded by a ring-shaped cladding (diameter: 40 μm) containing 48 damage tracks. The bottom-up writing approach was implemented to ensure that the incoming pulses are not blocked or distorted by the previously written tracks. The axis of the WG was located at a depth of ~120 µm below the crystal surface. The tracks had a lateral separation of 2 μm. Their size was ~1×6 μm 2 along the horizontal and vertical directions.

The end-facet and top-surface of the sample were inspected using a confocal laser microscope (model LSM 710, Carl Zeiss) equipped with a blue laser diode (λ = 405 nm) and a polarizer, Fig. 4. All the studies were performed in transmission mode with polarized light. When observing the end-facet, a dark ring of damage tracks below the crystal surface representing the cladding is seen, Fig. 4(a). No cracks surrounding the cladding are visible for the selected pulse energy. The inner part of the WG is darker because of the scattering at the damage tracks. Similarly, observing the WG from the top crystal surface, Fig. 4(b), a dark barrel-shaped cladding is visible in the pristine bulk volume. The cladding has a periodic netlike surface. The modification of the material in the irradiated regions was confirmed by μ-Raman spectroscopy. This method is well suited to characterize the structural modifications induced by the fs pulses and to study the integrity of the inherent crystal structure at the WG core. For the mapping, a Renishaw inVia Reflex confocal Raman microscope equipped with an Ar + laser (λ exc = 514 nm) and a 50× Leica objective was used. A set of a λ/2 plate and a polarizer were used to determine the polarization state of the incident and scattered light. The measurement geometry was ( ) g jk g , where j, k = p, m for the overview polarized Raman spectra, Fig. 5, and( ) g mm g for the μ-Raman mapping. Here and below, we use the Porto's notations [START_REF] Damen | Raman effect in zinc oxide[END_REF] for polarized Raman spectroscopy, i.e., For the μ-Raman mapping, we selected the most intense vibration of KLuW, centered at ~907 cm -1 and assigned as ν(W-O)/ν 1 (internal mode) [START_REF] Petrov | Growth and properties of KLu(WO 4 ) 2 , and novel ytterbium and thulium lasers based on this monoclinic crystalline host[END_REF]. It is related to the W-O stretching vibrations in the distorted WO 6 octahedrons. During the measurement, a high precision motorized 3D-stage was used to control the position of the sample. Initially, the end-facet of the WG was aligned to be at the focus of the laser. The sample was translated by ~15 µm (the measurement was performed slightly below the surface). The Wire 3.5TM software was used. The Raman spectra were taken with a spatial resolution of ~0.4 µm and a spectral resolution of ~1 cm -1 over the desired area (140 (N p ) × 140(N m ) µm 2 ). The Raman peak was fitted using the Lorentz profile yielding the peak height (intensity), the peak position (Raman shift) and the peak width. The 2D plots of these parameters created the desired maps, Fig. 6.

In the core region, the crystalline quality of the material is well preserved, as indicated by almost unchanged Raman response as compared to that from the pristine bulk crystal surrounding the WG. Thus, fs-DLW is expected to maintain the beneficial anisotropic optical and spectroscopic properties of the crystal. For the irradiated regions forming the depressedindex cladding, a decreased Raman intensity, broadening of the peak and a shift of its position to higher frequencies are observed. These findings are an indication of a partial amorphization of the material (a decrease in its crystallinitya degree of structural order, i.e., the lack of lattice defects, imperfections and structure disorder). The existence of a residual anisotropic stress field is evident from the observed phonon energy shift outside the WG cladding [START_REF] Nguyen | Heuristic modelling of laser written mid-infrared LiNbO 3 stressed-cladding waveguides[END_REF], see Fig. 6(a). This stress field leads to the stress-induced birefringence via the photo-elastic effect [START_REF] Yumashev | Photo-elastic effect, thermal lensing and depolarization in acut tetragonal laser crystals[END_REF] and favors the polarization response of the WG. For Tm 3+ :KLuW, because of the anisotropy of its spectroscopic properties, it is desirable to work (both in absorption and emission) with light polarization E || N m . The corresponding refractive index of the bulk (undoped) KLuW crystal is n m = 1.9927 at the wavelength of 1.9 μm [START_REF] Loiko | Refined orientation of the optical axes as a function of wavelength in three monoclinic double tungstate crystals KRE(WO 4 ) 2 (RE = Gd, Y or Lu)[END_REF]. This value is calculated using the Sellmeier formulas based on the experimental data on the dispersion of the principal refractive indices. The latter were determined in [START_REF] Loiko | Refined orientation of the optical axes as a function of wavelength in three monoclinic double tungstate crystals KRE(WO 4 ) 2 (RE = Gd, Y or Lu)[END_REF] by the minimum deviation method using oriented prisms. For the fabricated micro-structures, the waveguiding properties were ensured by a decrease of the refractive index in the cladding, Δn = n claddingn core ≈ -0.6×10 -3 [START_REF] Kifle | Femtosecond-laser-written hexagonal cladding waveguide in Tm:KLu(WO 4 ) 2 : µ-Raman study and laser operation[END_REF]. In [START_REF] Kifle | Femtosecond-laser-written hexagonal cladding waveguide in Tm:KLu(WO 4 ) 2 : µ-Raman study and laser operation[END_REF], this value was estimated at the wavelength of ~1.84 μm using the measured laser mode divergence out of a buried channel WG inscribed in a 3 at.% Tm:KLuW crystal. Thus, the fabricated WGs are classified as type III fs-DLW structures (or depressed-cladding WGs, contrary to another known geometry also based on depressed refractive index, type II, but relying on a double-track scheme and a stress-induced refractive increase at the waveguide core) [START_REF] Chen | Optical waveguides in crystalline dielectric materials produced by femtosecond-laser micromachining[END_REF].

Depressed-cladding WGs were first reported by Okhrimchuk et al. for Nd 3+ :YAG crystals [START_REF] Okhrimchuk | Depressed cladding, buried waveguide laser formed in a YAG:Nd 3+ crystal by femtosecond laser writing[END_REF][START_REF] Okhrimchuk | Low loss depressed cladding waveguide inscribed in YAG:Nd single crystal by femtosecond laser pulses[END_REF]. Later, such structures were fabricated in various materials doped with various RE 3+ ions, such as (i) Nd 3+ [START_REF] Liu | Continuous wave laser operation in Nd:GGG depressed tubular cladding waveguides produced by inscription of femtosecond laser pulses[END_REF][START_REF] Okhrimchuk | 11-GHz waveguide Nd: YAG laser CW mode-locked with single-layer graphene[END_REF][START_REF] Liu | Femtosecond laser inscribed cladding waveguides in Nd:YAG ceramics: Fabrication, fluorescence imaging and laser performance[END_REF][START_REF] Salamu | Laser emission from diode-pumped Nd:YAG ceramic waveguide lasers realized by direct femtosecond-laser writing technique[END_REF][START_REF] Pavel | Diode-laser pumping into the emitting level for efficient lasing of depressed cladding waveguides realized in Nd:YVO 4 by the direct femtosecond-laser writing technique[END_REF] and (ii) Yb 3+ [START_REF] Jia | Efficient waveguide lasers in femtosecond laser inscribed double-cladding waveguides of Yb:YAG ceramics[END_REF][START_REF] Palmer | High slope efficiency and high refractive index change in direct-written Yb-doped waveguide lasers with depressed claddings[END_REF][START_REF] Yi. Ren | Switchable single-dualwavelength Yb,Na:CaF 2 waveguide lasers operating in continuous-wave and pulsed regimes[END_REF], both applied for laser emission at ~1 μm; (iii) Er 3+ [START_REF] Moglia | Efficient upconversion-pumped continuous wave Er 3+ :LiLuF 4 lasers[END_REF][START_REF] Khurmi | Ultrafast pulse generation in a mode-locked Erbium chip waveguide laser[END_REF][START_REF] Lancaster | Er 3+ active Yb 3+ Ce 3+ co-doped fluorozirconate guided-wave chip lasers[END_REF], the laser operation was achieved in the visible, at ~0.55 μm, using an upconversion pumping scheme, and in the near-infrared, at ~1.5 μm; Pr 3+ [START_REF] Liu | Femtosecond-laser micromachined Pr:YLF depressed cladding waveguide: Raman, fluorescence, and laser performance[END_REF][START_REF] Khurmi | Visible laser emission from a praseodymiumdoped fluorozirconate guided-wave chip[END_REF], for red laser emission at ~0.6-0.7 μm; Ho 3+ [START_REF] Lancaster | Efficient 2.9 μm fluorozirconate glass waveguide chip laser[END_REF][START_REF] Lancaster | 2.1 μm waveguide laser fabricated by femtosecond laser direct-writing in Ho 3+ ,Tm 3+ :ZBLAN glass[END_REF][START_REF] Mcdaniel | Operation of Ho:YAG ultrafast laser inscribed waveguide lasers[END_REF], for near-mid-infrared emissions at ~2.1 μm and ~2.9 μm. The results for Tm 3+ -doped type III WGs are discussed in the Introduction section. Moreover, such a WG geometry was implemented for transition-metal-doped (e.g., Cr 4+ , Cr 2+ , Fe 2+ ) materials used both as saturable absorbers [START_REF] Okhrimchuk | Waveguide-saturable absorber fabricated by femtosecond pulses in YAG:Cr 4+ crystal for Q-switched operation of Yb-fiber laser[END_REF] and gain media [START_REF] Macdonald | Efficient mid-infrared Cr:ZnSe channel waveguide laser operating at 2486 nm[END_REF][START_REF] Lancaster | Mid-infrared laser emission from Fe: ZnSe cladding waveguides[END_REF].

Laser set-up

The scheme of the WG laser is shown in Fig. 7. The WG sample was mounted on a passivelycooled glass (BK7) holder. The linear laser cavity was composed of a flat pump mirror (PM) coated for high transmission (HT) at the pump wavelengths (T = 96% at 0.80 μm and 93% at 1.68 μm) and for high reflection (HR) at 1.87-2.30 μm, and a set of flat output couplers (OCs) with transmission T OC = 1.6%...50% at the laser wavelength. Operation without an OC (relying solely on the Fresnel reflection from the uncoated WG facet, equivalent to T OC = 89%) was also studied. We have also employed a short-pass OC coated for HT at 1.80-1.96 μm with T OC of 2% at 2.02-2.12 μm, to enforce laser oscillation above 2 μm. For CW operation, both PM and OC were placed as close as possible to the crystal with minimum air gaps. No index-matching liquid was used. Such liquids, under high pump power, might burn and damage the WG end-facets or induce coating damage to the mirrors. Thus, for the CW laser, the geometrical cavity length was 3.0 mm. Two pump sources were applied. The first source for conventional pumping the 3 H 6 → 3 H 4 transition was a CW Ti:Sapphire laser (model 3900S, Spectra Physics) delivering up to 3.2 W at λ P = 802 nm (emission bandwidth: Δλ P < 0.2 nm) with M 2 ≈ 1. The second source for in-band pumping the 3 H 6 → 3 F 4 transition was a home-made Raman fiber laser (RFL) [START_REF] Thouroude | Linearly-polarized high-power Raman fiber lasers near 1670 nm[END_REF] delivering up to 4.45 W at 1679 nm (Δλ P = 1 nm) with M 2 ≈ 1. Both lasers were linearly polarized. The pump was focused into the crystal using a spherical uncoated CaF 2 lens (focal length: f = 40 mm, transmission at the pump wavelengths: T = 93.8±0.3%) resulting in a pump spot size at the input WG facet 2w P = 30±5 μm. The pump polarization was E || N m .

For the Ti:Sapphire laser, the pump coupling efficiency into the WG, η coupl = P coupl /P inc , was determined from pump-transmission experiments at 830 nm (out of Tm 3+ absorption) to be 77.1±1% (Fresnel losses at the uncoated WG input facet taken into account). The pump absorption at 802 nm, η abs,NL = P abs /P coupl , was determined in a similar manner under nonlasing conditions at incident pump powers corresponding to the laser threshold P th for each OC (we assumed that under lasing conditions, η abs,L ≈ η abs,NL (P th )). It amounted to 81-85±1%, depending on the OC. Similar values were obtained from a rate-equation model accounting for the ground-state bleaching and CR. Note that the small-signal pump absorption calculated from the spectroscopic parameters, η abs,0 = 1exp(-σ P abs N Tm t) = 97.5%. Here, σ P abs = 5.75×10 -20 cm 2 , cf. Fig. 1(b). Thus, the pump absorption in the WG was bleached.

For the RFL, we assumed a similar value of η coupl . The pump absorption was taken at its small-signal limit, η abs,0(1-pass) = 50.8% (σ P abs = 1.10×10 -20 cm 2 , Fig. 1(b)), not to overestimate the laser slope efficiency. Because of the high reflectivity of the OCs at ~1.68 μm, the pumping was in double-pass. Thus, the total pump absorption, η abs,0(2-pass) = 56.1±1%.

For the passive Q-switching experiments, a transmission-type SA was inserted between the crystals and the OC at a normal incidence with minimum air gaps.

The laser output after the OC was collimated using a spherical CaF 2 lens (f = 15 mm). A cut-off filter (FEL 900, Thorlabs) was used to filter out the residual pump. The emission spectra were measured using an optical spectrum analyzer (OSA, model AQ6375B, Yokogawa) equipped with a low-OH multimode optical fiber (core diameter: 200 μm, N.A. = 0.50, length: 2 m) from Thorlabs. The laser radiation was coupled into the fiber using an uncoated CaF 2 lens (f = 40 mm). The spectral sensitivity of the OSA-based set-up was calibrated using a quartz iodine lamp with a known spectral power distribution. The beam profile was captured using a FIND-R-SCOPE near-IR camera. The output facet of the WG was reimaged onto the camera using a short focal length CaF 2 lens (f = 15 mm). The pump and laser radiation were selected by a proper long-pass / short-pass filter. A scale calibration for the camera was provided by illuminating the WG with near-IR light revealing the cladding with a known size. We also used a 1951 USAF resolution test target (R1DS1, Thorlabs) placed on the position of the WG output facet to verify the scale calibration for the camera. The pulsed output was detected with a fast InGaAs photodetector (model UPD-5N-IR2-P, Alphalas, rise time: <200 ps) and an 8 GHz digital oscilloscope (DSA70804B, Tektronix).

Saturable absorbers

For the passive Q-switching experiments, several SAs based on Cr 2+ -doped chalcogenides (ZnS and ZnSe) were used. They are well-known for passive Q-switching of bulk Tm lasers [START_REF] Tsai | Q-switched 2-µm lasers by use of a Cr 2+ :ZnSe saturable absorber[END_REF][START_REF] Yu | Compact passively Q-switched diodepumped Tm:LiLuF 4 laser with 1.26 mJ output energy[END_REF][START_REF] Faoro | Passively Q-switched Tm:YLF laser[END_REF]. They provide (i) a broad and intense absorption in the near-IR related to the 5 T 2 → 5 E( 5 D) transition of Cr 2+ ions in tetrahedral (T d ) sites, Fig. 8(a); (ii) high ground-state absorption (GSA) cross-sections, σ GSA , (iii) low excited-state absorption and (iv) acceptable laser-induced damage threshold (LIDT) [START_REF] Mirov | Progress in mid-IR lasers based on Cr and Fe-doped II-VI chalcogenides[END_REF][START_REF] Sorokina | Cr 2+ -doped II-VI materials for lasers and nonlinear optics[END_REF][START_REF] Loiko | Saturable absorption properties at 1.54 µm of Cr 2+ :ZnS prepared by thermal diffusion at hot isostatic pressing[END_REF]. At the laser wavelength of ~1.84 μm, the σ GSA are 0.62×10 -18 cm 2 (for Cr 2+ :ZnS) and 0.95×10 -18 cm 2 (for Cr 2+ :ZnSe).

The thickness of the SAs (t SA ) was about 1.0 and 2.2 mm for Cr 2+ :ZnSe and Cr 2+ :ZnS, respectively, and their small-signal (unsaturated) transmission at 1.84 μm T SA was 98.0...64.3%, Fig. 8(b). Both faces of the SAs were AR-coated at the laser wavelength to reduce the insertion losses. The passive Q-switching experiments were performed using the conventional pumping at 800 nm in order to avoid excessive heating of the SA by the residual (non-absorbed) pump that may lead to unstable operation. Only OCs with high transmission (T OC = 20% and 50%) were used to avoid damage to the optical components due to the high intracavity laser fluence.

Continuous-wave lasers

Conventional pumping

At first, we used conventional pumping (to the 3 H 4 state, λ P = 802 nm). The input-output characteristics of the Tm WG laser are shown in Fig. 9(a). For the "standard" OCs, the maximum output power reached for T OC = 50%, 1.07 W at 1828-1855 nm with a slope efficiency η of 62.4% (with respect to the absorbed pump power, P abs ). The laser threshold was at P abs = 170 mW and the optical-to-optical conversion efficiency η opt was 38.3% (vs. the incident pump power, P inc ). For lower output coupling, the laser performance gradually deteriorated.

The laser emission spectra are shown in Fig. 9(b). They are broad and contain multiple lines due to (i) the broad gain spectra of Tm 3+ :KLuW and (ii) etalon (Fabry-Perot) effects at the crystal-mirror interfaces. As the output coupling decreased, the central laser wavelength experienced a red-shift due to the quasi-three-level nature of the 3 F 4 → 3 H 6 Tm 3+ laser transition exhibiting reabsorption losses [START_REF] Petrov | Growth and properties of KLu(WO 4 ) 2 , and novel ytterbium and thulium lasers based on this monoclinic crystalline host[END_REF]. For the lowest T OC = 1.6%, the emission was at 1887-1921 nm. For T OC < 5%, the laser operated at ~1.90 μm and for higher T OC , it jumped to ~1.84 μm. This agrees with the gain spectra of Tm 3+ :KLuW for E || N m , Fig. 10.

Without an OC (effective T OC of 89%), the WG laser-generated an output power of 130 mW at ~1834 nm with a notably increased laser threshold of 335 mW and much lower η = 17.5%, see Fig. 9(c,d). This is attributed to significantly higher upconversion losses associated with high Tm 3+ inversion ratios β = N 2 ( 3 F 4 )/N Tm . Indeed, high β is needed to compensate for the cavity losses in this case leading to enhanced ETU. With a short-pass OC, we achieved an output power of 350 mW at 1994-2032 nm with η = 35.0%, Fig. 9(c,d). The laser threshold was relatively high, 310 mW. The longest wavelength of a purely electronic transition 3 F 4 → 3 H 6 for Tm 3+ :KLuW is 1948 nm (corresponding to a transition between the Stark sub-levels with energies 5663 and 530 cm -1 , i.e., the lowest and the highest ones in the corresponding multiplets) [START_REF] Silvestre | Thulium doped monoclinic KLu(WO 4 ) 2 single crystals: growth and spectroscopy[END_REF]. The observed wavelengths are attributed to vibronic interaction (the electron-phonon coupling) with the low-energy phonons of the KLuW lattice, cf. Fig. 5 [START_REF] Loiko | Vibronic thulium laser at 2131 nm Q-switched by single-walled carbon nanotubes[END_REF]. Such vibronic emissions have been previously observed only in bulk Tm lasers [START_REF] Loiko | Vibronic thulium laser at 2131 nm Q-switched by single-walled carbon nanotubes[END_REF][START_REF] Cornacchia | Efficient, diode-pumped Tm 3+ :BaY 2 F 8 vibronic laser[END_REF][START_REF] Loiko | Monoclinic Tm:MgWO 4 crystal: Crystal-field analysis, tunable and vibronic laser demonstration[END_REF]. For all studied OCs, the laser output was linearly polarized (E || N m ); the polarization was naturally selected by the gain anisotropy, Fig. 10(a) [START_REF] Petrov | Growth and properties of KLu(WO 4 ) 2 , and novel ytterbium and thulium lasers based on this monoclinic crystalline host[END_REF]. The output power dependencies were linear indicating weak thermal effects. This was confirmed by applying a quasi-CW pumping (duty cycle: 1:2). No thermal fracture of the crystal around the written WGs was observed. The produced damage tracks were stable under the high-power laser irradiation and the associated heating.

For both pump and laser wavelengths, we analyzed the mode profiles at the WG output facet, Fig. 11. The pump mode, Fig. 11(a), is well confined within the cladding and it is slightly multimode. There is a weak leakage of the pump mode through the ring of the damage tracks. The laser mode, Fig. 11(b), is confined within the cladding, and the corresponding 1D intensity profiles along the horizontal (along the polarization, || N m ) and vertical (|| N p ) directions are nearly Gaussian, see Fig. 11(c) (goodness of the fit: R 2 > 0.99). The mode diameters (at the 1/e 2 intensity level) are 2w L = 41.9±2 μm and 39.4±2 μm, respectively. Thus, a good overlap between the pump and laser modes is observed.

The measured M 2 x,y factors of the laser mode were below 1.3.

In-band pumping

The CW laser experiments were extended to in-band pumping (to the 3 F 4 state, λ P = 1679 nm). The input-output characteristics are shown in Fig. 12(a). The maximum output power reached 1.37 W at 1915-1923 nm with a slope efficiency η of 82.7% (vs. the absorbed pump power) and the laser threshold was as low as P abs = 17 mW. The optical-to-optical efficiency η opt was 74.8% (vs. the incident pump power). For lower output coupling, the slope efficiency gradually decreased. Contrary to the case of conventional pumping, for T OC > 20%, the laser performance slightly deteriorated. This is attributed to the effect of ETU, see Fig. 1(a). For all OCs, the laser emission was linearly polarized (E || N m ). Neither damage of the WG nor thermal roll-over in the output dependencies were observed. Typical laser emission spectra for the in-band pumped Tm WG laser are shown in Fig. 12(b). They differ from those recorded with conventional pumping, Fig. 9(b). For low T OC < 10%, the emission was within two spectral bands centered at ~1.92 and 1.95 μm, e.g., at 1908-1921 nm and 1940-1948 nm for T OC = 1.6%. For higher output coupling, only the short-wavelength emission band was observed. For the maximum T OC = 50%, the laser emission was within three spectral bands centered at ~1.85, 1.92 and 1.95 μm. These spectral features agree well with the gain spectra of Tm 3+ :KLuW [START_REF] Petrov | Growth and properties of KLu(WO 4 ) 2 , and novel ytterbium and thulium lasers based on this monoclinic crystalline host[END_REF]. For the in-band pumping, the pump and laser mode profiles were similar. The laser mode at the output WG facet is presented in Fig. 13(a). It is more symmetric compared to the case of conventional pumping, Fig. 11(b), and more confined within the cladding. The 1D intensity profiles are well fitted with a Gaussian distribution (R 2 > 0.99), yielding mode diameters 2w L of 31.6±2 μm and 36.3±2 μm along the horizontal and vertical directions, respectively. These values are lower compared to the case of conventional pumping, indicating weaker interaction with the cladding and, potentially, lower propagation losses (see Section 3.3). The M 2

x,y factors of the laser mode were as low as 1.1.

Discussion

Let us consider the slope efficiency of the Tm WG lasers. First, we estimate the WG propagation losses for both pumping schemes using the Caird analysis [START_REF] Caird | Quantum electronic properties of the Na 3 Ga 2 Li 3 F 12 :Cr 3+ laser[END_REF] modified for the case of high output coupling [START_REF] Morris | 1.9 μm waveguide laser fabricated by ultrafast laser inscription in Tm:Lu 2 O 3 ceramic[END_REF]:

, ) / 2 + )(1 (1/ = 1/ OC 0     (1)
where γ =ln(1 -L), L is the internal loss per pass, γ OC =ln(1 -T OC ), and η 0 is the intrinsic slope efficiency. The plots of the inverse of the slope efficiency, 1/η, vs. inverse of the outputcoupling loss, 1/γ OC , are shown in Fig. 14. Their linear fits yield the η 0 and L parameters. For the Caird analysis to be meaningful, the laser wavelength (more precisely, the Stokes efficiency λ P /λ L ) should be constant for all OCs [START_REF] Caird | Quantum electronic properties of the Na 3 Ga 2 Li 3 F 12 :Cr 3+ laser[END_REF]. In our case, the blue-shift of λ L with increasing output coupling is minor with respect to λ P . For the conventional pumping (considering the data for T OC ≤ 50%), η 0 = 74.2±7% and the WG propagation losses δ loss = 4.34L/t = 1.3±0.3 dB/cm, in agreement with [START_REF] Kifle | Femtosecond-laser written Tm:KLu(WO 4 ) 2 waveguide lasers[END_REF]. For the inband pumping, η 0 = 85.5±7% and δ loss = 0.2±0.3 dB/cm. Both δ loss values are specified at the laser wavelength of ~1.9 μm. The much lower propagation losses in the latter case are attributed to (i) weaker overlap of the pump and laser modes with the WG cladding, Fig. 13(a), and (ii) lower fractional heat loading under in-band pumping leading to weaker heat dissipation in the WG and, consequently, weaker thermo-optic effects such as stressinduced depolarization losses or diffraction losses caused by the thermal lens. The effect of lower δ loss is visible in the emission spectra, as longer wavelengths are generated in the inband pumped laser, Fig. 12(b), indicating smaller inversion ratios β.

The upper limit for the slope efficiency η of a quasi-three-level solid-state laser is [START_REF] Van Dalfsen | Thulium channel waveguide laser with 1.6 W of output power and ~80% slope efficiency[END_REF]:

, • • L St, q OC mode        (2)
where η mode is the mode overlap efficiency;

η OC = ln[1 -T OC ]/ln[1 -T OC )•(1 -2L)]
is the outcoupling efficiency (2L is the roundtrip passive loss); η q is the pump quantum efficiency; η St,L = λ P /λ L is the Stokes efficiency under lasing conditions. For this analysis, we assume an outcoupling corresponding to the best laser performance and use the WG propagation losses values determined above.

Let us first consider conventional pumping (λ P = 802 nm). From the measured pump and laser modes, Fig. 11(c), we calculate η mode = 93±5%. From the determined δ loss value, we derive η OC = 88.1%. The pump quantum efficiency in this case is determined mostly by the CR which depends on the Tm doping concentration: for the given N Tm , η q = 1.75 [START_REF] Mateos | Efficient micro-lasers based on highly-doped monoclinic double tungstates[END_REF]. Finally, η St,L is 4.36%, so that η ≤ 62.5% which agrees well with our results. More details about the pump quantum efficiency for Tm 3+ ions can be found elsewhere [START_REF] Loiko | Stochastic model of energy-transfer processes among rare-earth ions. Example of Al 2 O 3 :Tm 3+[END_REF].

For the case of in-band pumping (λ P = 1679 nm), a similar analysis is performed yielding the following values: η mode >99%, η OC = 94.5%, η q ≈ 1 (assuming weak ETU) and η St,L = 87.4%. As a result, η is ≤ 82.6%, again in agreement with our observations. Thus, the higher slope efficiency for the in-band pumped Tm WG laser is due to (i) better overlap between the pump and laser modal profiles, (ii) lower associated intracavity losses and (iii) much higher Stokes efficiency, well exceeding that for the conventional pumping even under efficient CR process. Further discussion about the in-band pumping can be found in a recent study [START_REF] Llamas | Ultrafast laser inscribed waveguide lasers in Tm:CALGO with depressed-index cladding[END_REF].

The upper limit of the slope efficiency for conventional pumping is set by η q determined by CR, and, consequently, by the Tm doping level (3 at.%). Higher η q approaching its limit (2) is expected in highly-doped (≥8 at.% Tm) samples. However, in our fs-DLW experiments using highly doped crystals the obtained quality of the WGs was low. This low quality is most probably due to the overlap of the writing central wavelength (795 nm) with the Tm 3+ absorption ( 3 H 6 → 3 H 4 ) inducing serious damage to the crystal. This limitation is however absent under in-band pumping where low-doped crystals can be used still leading to a high laser slope efficiency.

The threshold of an in-band pumped quasi-three-level laser can be calculated as [100]:

. 2

w t N k h P       + + =  (3)
Here, h is the Planck constant, ν P is the pump frequency, k Σ is the total loss coefficient, k Σ = k OC + k loss , where k OC = -ln(1 -T OC )/2t and k loss = -ln(1 -2L)/2t represent the outcoupling and passive losses, respectively, σ L abs = 0.17×10 -20 cm 2 and σ L SE = 1.36×10 -20 cm 2 are the absorption and stimulated-emission cross-sections of Tm 3+ :KLuW at the laser wavelength λ L ≈ 1.92 μm [START_REF] Petrov | Growth and properties of KLu(WO 4 ) 2 , and novel ytterbium and thulium lasers based on this monoclinic crystalline host[END_REF], respectively, the term σ L abs N Tm stands for the reabsorption losses and τ Tm = 0.275 ms [START_REF] Petrov | Growth and properties of KLu(WO 4 ) 2 , and novel ytterbium and thulium lasers based on this monoclinic crystalline host[END_REF] is the upper laser level ( 3 H 4 ) lifetime. Finally, Eq. ( 3) yields P th = 19 mW, in good agreement with our experimental result.

For the designed lasers, the confocal parameter of the pump beams is comparable with the crystal thickness: 2z R was about a few mm (in the crystal) for the conventional and in-band pumping. Thus, one may argue about a bulk (non-waveguiding) regime of laser operation. It is known that the thermal lens in N g -cut Tm:KLuW crystal is positive [START_REF] Serres | Diode-pumped microchip Tm:KLu(WO 4 ) 2 laser with more than 3 W of output power[END_REF] and it supports lasing in a plano-plano cavity. However, when the position of the pump beam was moved out of the WG into the bulk crystal, no laser emission was observed. Moreover, the size of the laser mode was clearly determined by the WG cladding (the estimated radius of the laser mode defined solely by the thermal lens is ~60 μm). Finally, no lasing in the bulk regime is expected without the OC.

Fs-DLW double tungstate waveguide lasers

Let us discuss the previous results on fs-DLW of optical waveguides in MDT crystals. The Tm:KLuW crystal is a representative of this crystal family.

The laser-active WGs were based on MDT crystals doped with Yb 3+ and Nd 3+ (at ~1 μm), Er 3+ (at ~1.5 μm) and Tm 3+ and Ho 3+ ions (at ~2 μm). A summary of the laser performances (output power and slope efficiency) of the fs-DLW MDT WG lasers is shown in Fig. 15. Liu et al. also reported laser operation in such WGs under Ti:Sapphire laser pumping at 808 nm. The Nd WG laser-generated 33 mW at 1065 nm with η = 41.4% and the WG propagation losses were as high as 2 dB/cm (at the laser wavelength) [110]. The estimated refractive index change (decrease) due to fs-DLW was -2.9×10 -3 at the wavelength of ~1 μm (in the damage tracks), as determined from the measured numerical aperture of the waveguide [110].

Erbium WGs. The only report on ~1.5 μm MDT waveguide laser was based on fs-DLW type III buried channel WG in 1 at.% Er:KLuW. The WG laser diode-pumped at 981 nm generated 8.9 mW at 1533.6 nm with a slope efficiency of 20.9% [111]. The laser output was linearly polarized (E || N m ).

Thulium WGs. In the first work on ~2 μm fs-DLW MDT waveguides, Kifle et al. reported on type III buried channel WGs in 3 at.% Tm:KLuW with a circular and hexagonal cladding [START_REF] Kifle | Femtosecond-laser written Tm:KLu(WO 4 ) 2 waveguide lasers[END_REF]. Under Ti:Sapphire laser pumping at 802 nm, the WG with a circular cladding generated output power of 46 mW at 1912 nm corresponding to a slope efficiency of 15.2%. The same authors studied the WGs with a hexagonal (optical lattice-like) cladding in more detail in [START_REF] Kifle | Femtosecond-laser-written hexagonal cladding waveguide in Tm:KLu(WO 4 ) 2 : µ-Raman study and laser operation[END_REF], including the emission properties at ~2 μm, micro-Raman spectroscopy and improved laser behavior. An estimation of the refractive index change of -0.6×10 -3 and the propagation losses of 1.2 ± 0.3 dB/cm at the wavelength of ~1.84 μm were provided. Furthermore, the power scaling of Tm WG laser with a circular cladding was also demonstrated [112], yielding 247 mW at 1849.6 nm with a slope efficiency of 48.7%. The Tm WG lasers operated at the fundamental transverse mode. In [START_REF] Kifle | Passively Q-switched femtosecond-laser-written thulium waveguide laser based on evanescent field interaction with carbon nanotubes[END_REF], type III surface channel WG geometry (with a halfring cladding) was implemented for Tm:KLuW. Finite element method simulations of the surface WG accounting for various processes contributing to the refractive index change (damage and stress-optic index changes) have been performed. The refractive index change at sub-μm tracks was estimated from this analysis to be Δn = -0.01 + 0.0017i at the wavelength of ~1.85 μm [START_REF] Kifle | Passively Q-switched femtosecond-laser-written thulium waveguide laser based on evanescent field interaction with carbon nanotubes[END_REF]. Note that the estimated real part of the complex refractive index, Re(Δn), is higher than the value obtained from the measured numerical aperture of a similar waveguide [START_REF] Kifle | Femtosecond-laser-written hexagonal cladding waveguide in Tm:KLu(WO 4 ) 2 : µ-Raman study and laser operation[END_REF].

Holmium WGs. The only report on fs-DLW Ho:MDT WGs was based on buried channel type III WGs fabricated in 5 at.% Ho:KGdW [113]. The Ho WG laser was in-band pumped by a bulk Tm laser at 1960 nm and it generated 212 mW at 2055 nm with a slope efficiency of 67.2%. The WG propagation losses were 0.94±0.2 dB∕cm (at the laser wavelength). Micro-Raman and micro-luminescence mapping of the WG end-facet were also reported. In both Tm and Ho fs-DLW WG lasers, the output was linearly polarized (E || N m ) [112,113]. For Ho WG, it was spatially multimode [113].

Passively Q-switched lasers

Laser performance

Passive Q-switching was performed using conventional pumping at 802 nm exclusively, as already mentioned, because of the SA absorption at the in-band pumped wavelength around 1680 nm. We started with the Cr 2+ :ZnSe SA having the smallest modulation depth (T SA = 98.0%) and, thus, the lowest insertion losses. The pump power was limited to P abs ≈ 1.15 W since above this level the pulse stability degraded due to significant heating of the SA by the non-absorbed pump power. The input-output dependencies of the passively Q-switched (PQS) Tm WG laser are shown in Fig. 16(a). The maximum average output power was 434 mW at 1838 nm with a slope efficiency η = 48.9% (for T OC = 50%). The laser threshold was at P abs = 265 mW. Considering the output power achieved in the CW mode (at the same pump level), the Q-switching conversion efficiency η conv was 67.9%. For lower outcoupling (T OC = 20%), the laser generated only 284 mW at ~1850 nm with η = 29.7% and higher η conv = 80.2%.

Typical laser emission spectra are shown in Fig. 16(b). For higher outcoupling, the spectrum is narrower due to stronger competition of laser lines saturating the SA. The relatively high Q-switching conversion efficiencies and the minor change of the laser wavelength with respect to the CW regime are evidence for relatively low insertion loss of the SA. For both OCs, the laser emission was linearly polarized (E || N m ). The pulse duration (defined as FWHM) Δτ p and the pulse repetition frequency (PRF) were determined directly and the pulse energy was calculated, E out = P out /PRF (P outaverage output power). The dependence of these pulse characteristics on the pump power is illustrated in Fig. 17 (for the Cr 2+ :ZnSe SA with T SA = 98.0%). Better pulse characteristics were observed for higher outcoupling: the pulse duration / energy reached 8.2 ns / 7.0 μJ at the maximum pump power for T OC = 50%. The Δτ p and E out values showed only a weak dependence on the pump level contrary to the PRF which increased almost linearly, from 5 to 62 kHz. As a result, the peak power P peak = E out /Δτ p reached 0.85 kW.

Effect of the saturable absorber modulation depth

To investigate the effect of the modulation depth, we compared Cr 2+ :ZnS and Cr 2+ :ZnSe SAs with different small-signal transmission T SA . The PQS laser performance was studied at a reference pump power of P abs = 0.80 W (well above the laser threshold whilst below the range of instabilities caused by the residual pump) using the high-transmission output coupler, T OC = 50%. The laser characteristics for the studied SAs are summarized in Table 2. With the decrease of the small-signal SA transmission from 98.0% to 64.3%, the average output power gradually decreased from 244 to 55 mW (thus, the Q-switching conversion efficiency dropped from 61.7% to 13.9%) because SAs with smaller transmission introduced higher insertion losses. The laser wavelength for all SAs was at ~1838 nm. Because of the high inversion ratios β, the gain spectrum of Tm 3+ :KLuW features a local maximum at ~1.84 μm [START_REF] Petrov | Growth and properties of KLu(WO 4 ) 2 , and novel ytterbium and thulium lasers based on this monoclinic crystalline host[END_REF]. Thus, no wavelength blue-shift is expected even for greatly increased intracavity losses. Regarding the pulse characteristics, the pulse duration notably shortened with decreasing T SA , from 9.3 down to 2.6 ns, Fig. 19(a), representing a record-short value for any passively Q-switched WG laser at ~2 μm. This behavior is typical for PQS solid-state lasers. Corresponding oscilloscope traces of the single Q-switched pulses are shown in Fig. 19(c). The pulse energy was, however, weakly dependent on T SA , Fig. 19(b), reaching 6.9 μJ for the SA with the highest optical density (T SA = 64.3%). The latter may originate from the heating of the SA by the residual pump radiation. As a result, the peak power for this SA was as high as 2.66 kW. The PRF decreased with decreasing T SA , from 41.0 to 8.0 kHz related to the corresponding drop of the average output power. The oscilloscope traces of the pulse trains for the Cr 2+ :ZnS SAs are shown in Fig. 20 indicating stable PQS operation without any signs of multi-pulse generation. For optically dense Cr 2+ :ZnS SAs, compared to Fig. 18(b),(c), the intensity instabilities were higher but still below 20%.

Discussion

According to the relation between the recovery time of initial absorption τ rec and the characteristic time of formation of a single Q-switched pulse, Δτ, typically in the ns-range, the SAs employed in PQS solid-state lasers are classified as "fast" (τ rec << Δτ) and "slow" (τ rec >> Δτ). Cr 2+ -doped chalcogenides (ZnS and ZnSe) are classical "slow" SAs for PQS ~2 μm lasers. They allow obtaining either high pulse energies (up to mJ) [START_REF] Yu | Compact passively Q-switched diodepumped Tm:LiLuF 4 laser with 1.26 mJ output energy[END_REF] or very short pulses (down to sub-ns) [START_REF] Loiko | Subnanosecond Tm:KLuW microchip laser Q-switched by a Cr:ZnS saturable absorber[END_REF] while operating at low repetition rates (few kHz) because τ rec for these materials is about 5-6 μs [START_REF] Mirov | Progress in mid-IR lasers based on Cr and Fe-doped II-VI chalcogenides[END_REF] (associated with the lifetime of the 5 E( 5 D) Cr 2+ state).

"Slow" SAs feature a weak dependence of the PQS laser pulse characteristics (energy and duration) on the pump power if the following criterion is satisfied [114]:

. 1

SA AE L SE L abs GSA  + = A A X    (4)
Here, A AE and A SA are the laser mode areas in the active element and in the SA, respectively (A AE ≈ A SA for the WG lasers). For the Cr 2+ :ZnS and Cr 2+ :ZnSe SAs, at the laser wavelength of 1.84 μm, X are 17 and 26, respectively (here, σ L abs = 1.38×10 -20 cm 2 and σ L SE = 3.67×10 -20 cm 2 [START_REF] Petrov | Growth and properties of KLu(WO 4 ) 2 , and novel ytterbium and thulium lasers based on this monoclinic crystalline host[END_REF]). Thus, the proposed laser design is suitable for efficient "slow" SA passive Qswitching. Now let us determine the intracavity fluence on the SA [115]:

. π

Here, T OC is the transmission of the output coupler, E out is the output pulse energy, w L is the radius of the intracavity laser mode and the factor "2" indicates a nearly Gaussian laser mode. For the SAs made of Cr 2+ :ZnSe (T SA = 98.0%) and Cr 2+ :ZnS (T SA = 96.7%) yielding the lowest pulse energies, F in = 2.4 J/cm 2 and 2.9 J/cm 2 , respectively. These values have to be compared with the saturation fluence of the SAs, F S = (hν L )/σ GSA , where ν L is the laser frequency. The latter amount to F S = 0.17 J/cm 2 and 0.11 J/cm 2 , respectively. Thus, all SAs are fully bleached.

During the passive Q-switching experiments, no damages of the SAs nor the WG were observed. The latter allows estimating a lower limit of the laser induced damage threshold (LIDT) for Cr 2+ -doped chalcogenides for ns-pulses at a wavelength of ~2 μm. Considering the maximum F in values obtained on our experiments, LIDT ≥3.3±0.5 J/cm 2 for both materials. This value agrees well with a recent report [START_REF] Loiko | Saturable absorption properties at 1.54 µm of Cr 2+ :ZnS prepared by thermal diffusion at hot isostatic pressing[END_REF].

The pulse characteristics (duration / energy) were calculated using a model of a quasithree level laser material and a "slow" SA [116,117]. The results are shown in Fig. 19(a),(b). Both the predicted trends for the pulse characteristics and their values agree with the experiment.

In Table 3, we summarized the results on passively Q-switched Tm WG lasers reported so far [START_REF] Bolaños | Continuous-wave and Q-switched Tm-doped KY(WO 4 ) 2 planar waveguide laser at 1.84 µm[END_REF][START_REF] Kifle | Tm:KY 1-x-y Gd x Lu y (WO 4 ) 2 planar waveguide laser passively Q-switched by single-walled carbon nanotubes[END_REF][START_REF] Kifle | Passively Q-switched femtosecond-laser-written thulium waveguide laser based on evanescent field interaction with carbon nanotubes[END_REF][START_REF] Kifle | Femtosecond-laser written Tm:KLu(WO 4 ) 2 waveguide lasers[END_REF]112,[118][119][120][121][122]. Two classes of SAs were implemented, namely, "fast" and "slow" ones. The latter group comprises of Cr 2+ -doped chalcogenides (ZnS, ZnSe) while the former one contains various nanostructures, such as graphene (a single layer of carbon atoms arranged in a honeycomb lattice, a representative 2D material [123,124]), single-walled carbon nanotubes (SWCNTsrolled sheets of graphene [125]), transition metal dichalcogenides (TMDs, MoS 2 [126,127]) and topological insulators (TIs, Bi 2 Te 3 [128]). The TMDs and TIs are the graphene-inspired 2D materials containing few weakly interacting atomic layers. The thulium WG lasers Q-switched by nanostructure-based SAs typically operated at low average output powers (limited by the thermal effects in the SA [129]) and at high repetition rates (hundreds of kHzfew MHz) determined by their low modulation depth (e.g., ~1.5% for a single layer of carbon atomsgraphene [130]). As a result, the pulse energy was about tens to hundreds nJ and the pulse durations were in the μs range (except of configurations where it was reduced due to the short cavity length and, hence, short roundtrip time). Furthermore, the slope efficiency of such lasers was low indicating the need for further optimization of insertion losses in such nanostructures. However, they still can be considered as a cheap and broadband alternative to Semiconductor Saturable Absorber Mirrors (SESAMs) [131].

The only previous report on Cr 2+ :ZnS Q-switching of a Tm WG laser presented moderate pulse characteristics (pulse duration / energy: 1.2 μs / 120 nJ) corresponding to a low average output power of 1.2 mW with a slope efficiency of about 3%. In the present work, we fully explore the potential of Cr 2+ -doped chalcogenides as "slow" SAs by reaching simultaneously high pulse energies (for WG lasers, namely few μJ), short pulse durations (few ns) and, thus, record-high peak powers. Furthermore, the good thermal properties of ZnS and ZnSe allowed for power scaling reaching record-high average output powers for this type of lasers. Note that this operation regime corresponded to low repetition rates (few tens kHz).

Conclusion

To conclude, femtosecond Direct Laser Writing is a powerful method to fabricate singlemode active (Tm 3+ -doped) channel waveguides. We have extended this method to anisotropic crystals for highly efficient and power-scalable laser emission at ~2 μm. Using two different pump schemes, conventional pumping around 800 nm relying on cross-relaxation and in-band pumping at 1678 nm, we demonstrated for the first time watt-level continuous-wave output from a Tm channel WG laser produced by fs-DLW. For the latter pump scheme, the output power reached 1.37 W at 1915-1923 nm with a record-high slope efficiency of 82.7% almost approaching the Stokes limit, while the laser threshold was as low as 17 mW. The laser output was spatially single-mode with a naturally-selected linear polarization. The estimated WG propagation losses were relatively low, 0.2±0.3 dB/cm at the wavelength of ~1.9 μm, and comparable to the LPE-based WGs due to the weak leakage of the pump / laser modes through the WG cladding and reduced thermal effects under in-band pumping.

In-band pumping of fs-DLW Tm channel WGs using ~1.7 μm Raman fiber lasers (RFLs) represents an efficient strategy for high-power integrated light sources at ~2 μm. A proper design of the RFL wavelength will help to reach higher pump absorption (which was ensured in the present work by double-pass pumping). Moreover, by applying dielectric coatings to the WG facets, direct fiber-to-waveguide light coupling can be implemented.

The combination of fs-DLW single-mode Tm channel WGs and Cr 2+ -doped chalcogenides (ZnS or ZnSe) acting as "slow" saturable absorbers represents an efficient way to generate few ns-long pulses at kHz-range repetition rates. Such compact and robust PQS WG lasers can be used as seed sources for further amplification. We achieved the shortest pulses (2.6 ns) and the highest peak power (2.66 kW) ever extracted from a PQS WG laser at ~2 μm.

The good power scalability, low internal losses and spatially single-mode output make the developed WGs interesting for mode-locked WG lasers operating at high repetition rates (GHz-range) [132][133][134][135]. In particular, the studied gain material, Tm:KLu(WO 4 ) 2 , is known for its smooth and broad emission spectra at ~2 μm utilized in mode-locked bulk lasers [START_REF] Schmidt | Femtosecond pulses near 2 µm from a Tm:KLuW laser mode-locked by a single-walled carbon nanotube saturable absorber[END_REF]. To ensure low mode-locking thresholds, the WG length should be increased up to 1-2 cm which has been already realized in our writing experiments.

Another interesting direction applying Tm channel WG lasers is the extension of their emission wavelength well beyond 2 μm (into the shortwave-and midwave-infrared spectral range). One way is the use of vibronic laser emission, as demonstrated in the present work. An alternative is the laser operation on the 3 H 4 → 3 H 5 laser transition at ~2. 3 μm [136,137].

Fig. 1 .

 1 Fig. 1. (a) Energy level scheme of Tm 3+ in monoclinic KLu(WO 4 ) 2 crystal [11] showing relevant processes: red and green arrowspump and laser transitions, CRcross-relaxation, NRnon-radiative relaxation, Rradiative relaxation, ETUenergy-transfer upconversion; (b) absorption cross-section, σ abs , spectra for the 3 H 6 → 3 H 4 and 3 H 6 → 3 F 4 transitions of Tm 3+ in KLu(WO 4 ) 2 [12]. The pump wavelengths are indicated by the vertical lines. The light polarization is E || N p and E || N m .

Fig. 2 .

 2 Fig. 2. (a) Femtosecond Direct Laser Writing of channel buried waveguides in a bulk Tm:KLuW crystal; (b) illustration of the geometry of a depressed-index waveguide with a circular cladding (type III structure, end-facet view).

Fig. 3 .

 3 Fig. 3. Photograph of a Tm:KLuW sample under femtosecond Direct Laser Writing. The red laser serves as a laser pointer.

Fig. 4 .

 4 Fig. 4. Confocal laser microscope images of a buried channel waveguide in Tm:KLuW produced by femtosecond Direct Laser Writing: (a) end-facet view, (b) top view. Transmission mode, λ = 405 nm, polarized light: (a) P || N p , (b) P || N g .

  the indices i and l stand for the directions of propagation of the excitation and the back-scattered (detected) light, respectively, and the indices j and k indicate the corresponding polarization states. For simplicity, we use the labels p, m, g for the optical indicatrix axes N p , N m , N g , respectively.

Fig. 5 .

 5 Fig. 5. Polarized Raman spectra of the 3 at.% Tm:KLuW crystal. The measurement geometry is ( ) g jk g for j, k = p, m (Porto's notations), λ exc = 514 nm.

Fig. 6 .

 6 Fig. 6. Micro-Raman mapping of a polished end-facet of the depressed-cladding buried channel WG in Tm:KLuW produced by femtosecond Direct Laser Writing: measuring the high gain 907 cm -1 phonon mode: (a) peak frequency, (b) peak width (full width at half-maximum -FWHM) and (c) peak intensity. Measurement geometry: g(mm)g (Porto's notations), λ exc = 514 nm. WG diameter: 40 μm.

Fig. 7 .

 7 Fig. 7. Scheme of the Tm channel waveguide laser: Llenses, PMpump mirror, OCoutput coupler, SAsaturable absorber, Fcut-off filter.

Fig. 8 .

 8 Fig. 8. (a) Ground-state-absorption (GSA) cross-section, σ GSA , spectra of Cr 2+ :ZnS and Cr 2+ :ZnSe (this work); (b) the small-signal transmission (T SA ) spectra of the studied SAs. The vertical lines indicate the laser wavelength.

Fig. 9 .

 9 Fig. 9. Continuous-wave Tm channel WG laser with conventional pumping (λ P = 802 nm): (a,c) input-output dependencies, ηslope efficiency; (b,d) typical laser emission spectra, P abs = 1 W. The laser polarization is E || N m .

Fig. 10 .

 10 Fig. 10. Emission properties of Tm 3+ ions in KLuW at ~2 μm (the 3 F 4 ↔ 3 H 6 transition): (a) stimulated-emission (SE) cross-sections, σ SE , for light polarizations E || N m and E || N p ; (b) gain cross-sections, σ g = βσ SE -(1-β)σ abs , for light polarization E || N m and various inversion ratios β = N 2 ( 3 F 4 )/N Tm , N 2 is the population of the upper laser level.

Fig. 11 .

 11 Fig. 11. Mode analysis of the Tm channel WG laser (conventional pumping): (a,b) 2D intensity profiles of the (a) pump mode at 802 nm and (b) laser mode at ~1840 nm, red circleposition of the WG cladding; (c) 1D intensity plots along the horizontal (|| N m ) and vertical (|| N p ) directions, symbolsexperimental data, curves -Gaussian fits. The laser polarization is horizontal. T OC = 50%, P abs = 1.0 W.

Fig. 12 .

 12 Fig. 12. Continuous-wave Tm channel WG laser with in-band pumping (λ P = 1679 nm): (a) input-output dependencies, ηslope efficiency; (b) typical laser emission spectra, P abs = 1 W. The laser polarization is E || N m .

Fig. 13 .

 13 Fig. 13. Mode analysis of the thulium channel waveguide laser (in-band pumping): (a) 2D intensity profile of the laser mode at ~1950 nm, red circleposition of the WG cladding; (b) 1D intensity plots along the horizontal (|| N m ) and vertical (|| N p ) directions, symbolsexperimental data, curves -Gaussian fits. The laser polarization is horizontal. T OC = 50%, P abs = 0.9 W.

Fig. 14 .

 14 Fig. 14. Caird analysis of the intracavity losses for Tm channel WG lasers with conventional (in red) and in-band pumping (in blue): the plots show the inverse of the slope efficiency, 1/η, vs. the inverse of the output-coupling losses, 1/γ OC , circlesexperimental data, line -their fit.

Fig. 15 .

 15 Fig. 15. Summary of the output performance of continuous-wave waveguide lasers produced in rare-earth-doped monoclinic double tungstate (MDT) crystals by fs direct laser writing: (a) slope efficiency η vs. the absorbed pump power; (b) output power; (c) propagation losses δ loss . As for passive (undoped) crystals, Eaton et al. observed Raman gain around the fs laser inscribed damage tracks in KGdW [101]. Ytterbium WGs. Bain et al. reported on type II buried channel WGs (with a double-track geometry) fabricated in 5 at.% Yb:KGdW and Yb:KYW crystals [102]. The WG propagation losses were in the range 1.9-3.9 dB/cm. The Yb:KGdW WG laser-generated an output power of 18.6 mW at 1023 nm with η = 9.3% (vs. the absorbed pump power). The pump source was a single-mode fiber-coupled 980 nm InGaAs laser diode. Later, the same authors reported on micro-Raman spectroscopy of such waveguides by monitoring several characteristic Raman bands [103]. The authors concluded that the densification of the double-oxygen WOOW bridges in the lattice is responsible for the refractive index change around the irradiated regions. Borca et al. reported on passive waveguiding in type I and type II buried channel WGs in 2 at.% Yb:KYW; an estimation of δ loss = 2-2.5 dB/cm at ~1 μm was provided [104]. de Mendívil et al. implemented fs laser writing for material removal of LPE-grown "mixed" Yb 3+ -doped MDT films [105,106]. The WG propagation losses and the laser performance were governed mostly by the LPE method. The maximum output power was 100 mW at 1001 nm with a very high η = 78% [105]. Bae et al. reported on type III surface channel WGs (with

Fig. 16 .

 16 Fig. 16. Passively Q-switched Tm channel WG laser (conventional pumping at 802 nm): (a) input-output dependencies, ηslope efficiency; (b) typical laser emission spectra measured at the maximum P abs . The laser polarization is E || N m . SA: Cr 2+ :ZnSe with T SA = 98.0%.

Fig. 17 .

 17 Fig. 17. Characteristics of the passively Q-switched Tm channel WG laser (conventional pumping at 802 nm): (a) pulse duration (FWHM), (b) pulse repetition frequency (PRF), (c) pulse energy. SA: Cr 2+ :ZnSe, T SA = 98.0%.The oscilloscope traces of the shortest Q-switched pulses achieved with both studied OCs are shown in Fig.18(a). The pulses have a nearly Gaussian temporal shape. Typical pulse trains of the PQS Tm WG laser corresponding to a PRF of 9.3 and 31 kHz are shown in Fig.18(b),(c). The latter confirms the excellent stability of the PQS operation with a measured pulse-to-pulse r.m.s. timing jitter of <5% and intensity instabilities in the pulse train of <10%.The mode profile of the PQS laser was similar to that of the CW one, cf. Fig. 11(b).

Fig. 18 .

 18 Fig. 18. Oscilloscope traces of (a) the shortest single Q-switched pulses and (b) pulse trains at a PRF of 9.3 kHz and 31 kHz (T OC = 50%) for the passively Q-switched Tm channel WG laser. SA: Cr 2+ :ZnSe with T SA = 98.0%.

Fig. 19 .

 19 Fig. 19. Tm channel WG laser passively Q-switched by Cr 2+ :ZnS and Cr 2+ :ZnSe SAs with different small-signal transmission T SA : (a) pulse duration, (b) pulse energy and (c) the corresponding oscilloscope traces. Panels (a),(b): symbolsexperimental data, curvesnumerical modeling. T OC = 50%, P abs = 0.8 W.

Fig. 20 .

 20 Fig. 20. Oscilloscope traces of the pulse trains from the Tm channel WG lasers passively Qswitched by Cr 2+ :ZnS SAs with different small-signal transmission: T SA = (a) 86.7%, (b) 75.8%, (c) 69.2% and (d) 64.3%. P abs = 0.8 W, T OC = 50%.

Table 1 . Output Characteristics* of Thulium Channel Waveguide Lasers Fabricated by Liquid Phase Epitaxy (LPE) and Femtosecond Direct Laser Writing (DLW) Method

 1 Pthlaser threshold, ηslope efficiency (vs. absorbed pump power), Poutoutput power, λLlaser wavelength, ηcouplpump coupling efficiency. The best results are selected from multiple reports on the same material.

	LPE	Tm:KY(WO4)2 794	50	1.5-1.6 81-75 1840	90	[9]
		Tm:LiYF4	783	70	1.30	80	1880	87	[20]
			1679	12	2.05	78.3 1881	86.5	[15]
	DLW	Tm:ZBLAN	792	12	0.21	67	1890	79	[28]
		Tm:Y3Al5O12	800	312	0.09	27	1985	20	[29]
		Tm:Lu2O3	796	50	0.08	7	1942	40	[30]
		Tm:KLu(WO4)2 802	52	0.17	37.8 1847	83	[31]
			802	170	1.07	62.4 1828-1855 77.1	**
			1679	17	1.37	82.7 1915-1923 ~77	**
	*λP -pump wavelength,

Material λP, nm Pth, mW Pout, W η, % λL, nm ηcoupl, % Ref. **This work.

Table 2 . Output Characteristics* of Passively Q-switched Thulium Channel Waveguide Lasers**

 2 Eoutpulse energy, PRFpulse repetition frequency, Ppeakpeak power. Bold numbers correspond to the best results. **At a reference Pabs = 0.80 W, for TOC = 50%.

	SA	TSA,	Pout,	ηconv,	Δτp,	Eout,	PRF,	Ppeak,
		%	mW	%	ns	μJ	kHz	kW
	Cr 2+ :ZnSe 98.0	244	61.7	9.3	6.0	41.0	0.64
	Cr 2+ :ZnS	86.7	177	44.8	5.8	5.1	34.7	0.88
		75.8	113	28.6	3.7	6.0	18.8	1.63
		69.2	74	18.7	3.1	7.1	10.4	2.30
		64.3	55	13.9	2.6	6.9	8.0	2.66
	*Pout -average output power, ηconv -Q-switching conversion efficiency, Δτp -pulse
	duration,

Table 3 . An Overview of Passively Q-switched Thulium Waveguide Lasers Reported So Far*

 3 Poutaverage output power, λLlaser wavelength, ηslope efficiency, Δτppulse duration, Eoutpulse energy, PRFpulse repetition frequency. Bold numbers correspond to the best results.

	Gain	SA	Pout,	λL,	η,	Δτp,	Eout,	PRF,	Ref.
	material		mW	nm	%	ns	nJ	kHz
	LPE-based
	Tm:KYW	Cr 2+ :ZnS	1.2	1.845 ~3	1200	120	10	[17]
		graphene	6.5	1.832 9	195	5.8	1130 [118]
			26.7	1.834 11.3 98	21	1270 [119]
		SWCNTs	45.6	1.835 22.5 83	33	1390 [18]
	Fs-DLW
	Tm:ZBLAN graphene	6	~1.9	~5	2760	240	25	[120]
		Bi2Te3	16.3	1.88	1.3	1400	370	44.1 [121]
	Tm:YAG	graphene	6.5	1.944 ~2	<500	9.5	684	[122]
	Tm:KLuW	SWCNTs	10.3	1.841 3.8	50	7	1480 [60]
			150	1.847 34.6 98	106	1420 [31]
		graphene	24.9	1.845 9.3	88	18	1390 [112]
		MoS2	22.1	1.843 8.5	73	18	1580 [112]
		Cr 2+ :ZnSe 430	1.838 48.9 8.2	7.0×10 3 61.6 This work
		Cr 2+ :ZnS	55.4	1.833 -	2.6	6.9×10 3 8	This work
	*

Acknowledgments

E. K. acknowledges financial support from the Generalitat de Catalunya under grants 2016FI_B00844, 2017FI_B100158, and 2018FI_B200123. This work was supported by French Agence Nationale de la Recherche (ANR) through the LabEx EMC3 project FAST-MIR, the European Community funds FEDER and the Normandie region. P.L. thanks Ms. Daria Maliarova for the help with the illustrations.

Funding

Spanish Government, MINECO (MAT2016-75716-C2-1-R (AEI/FEDER,UE), FIS2017-87970-R); Junta de Castilla y León (SA287P18); Generalitat de Catalunya (2017SGR755).


Pavel Loiko

Mengting Chen

Josep Maria Serres

Magdalena Aguiló

Francesc Díaz

Haifeng Lin

Ge E Zhang

Lizhen Zhang

Zhoubin Lin

Patrice Camy

Shi-Bo Dai

Zhenqiang Chen

Yongguang Zhao

L I Wang

Weidong Chen
email: chenweidong@fjirsm.ac.cn

Uwe Griebner

Valentin Petrov

Xavier Mateos

Spectroscopy and high-power laser operation of a monoclinic Yb 3+ :MgWO 4 crystal

Recently, monoclinic wolframite-type ((Fe,Mn)WO4, sp. gr. P2/c) magnesium tungstate crystals, MgWO4, have emerged as promising host materials for doping with rare-earth ions (RE 3+ ) [1][2][3]. They belong to the crystal family of monoclinic transition metal monotungstates M 2+ WO4 (where M = Mg, Zn, Mn, Fe, Ni, etc.) [4]. So far, MgWO4 (a = 4.6889 Å, b = 5.6753 Å, c = 4.9289 Å, β = 90.726° [5]) crystals were mostly studied for scintillators and for doping with transition-metal ions, e.g., Cr 3+ [5,6]. MgWO4 exhibits good thermomechanical properties (high thermal conductivity <κ> of 8.7 W/(mK) [7] and low anisotropy of thermal expansion: αa = 11.22, αb = 8.09 and αc = 8.77 [10 -6 K -1 ] [3]). These properties are superior compared to another well-known crystal family of monoclinic double tungstates, KLn(WO4)2 [8], for which <κ> ≈ 3.5 W/mK and the thermal expansion tensor shows a significant anisotropy [9]. Besides, RE 3+ -doped MgWO4 shows attractive spectroscopic properties (broad and intense emission bands for polarized light, large Stark splitting, high luminescence quantum yield and Raman activity) [1][2][3]. These advantages originate from the low-symmetry structure and the substantial difference in ionic radii of the RE 3+ dopants and the host-forming Mg 2+ cations [10].

Regarding laser operation of RE 3+ -doped MgWO4 crystals, previous studies focused mostly on the spectral range of ~2 μm using thulium (Tm 3+ ) [2,[10][11][12] and holmium (Ho 3+ ) [3] ion doping. A diode-pumped continuous-wave (CW) Tm 3+ :MgWO4 laser generated 3.09 W at 2022-2034 nm with a slope efficiency η of 50% [11]. A graphene mode-locked (ML) Tm 3+ :MgWO4 laser delivered 86 fs pulses at 2017 nm featuring a bandwidth of 53 nm at a repetition rate of 76 MHz [12].

For laser emission at ~1 μm, ytterbium (Yb 3+ ) ion doping holds a huge potential. This is because Yb 3+ has a simple energy-level scheme eliminating the unwanted energy-transfer processes and leading to high Stokes pump efficiency and weak heat loading [13]. The larger Stark splitting of the ground-state ( 2 F7/2) (as compared to Nd 3+ ) is a prerequisite for broader emission at ~1 μm. So far, the growth and preliminary spectroscopy of Yb 3+ :MgWO4 crystal were reported [1,14]. A semiconductor saturable absorber mirror (SESAM) ML Yb 3+ :MgWO4 laser delivered 125 fs pulses at 1065 nm at a repetition rate of 117 MHz [15].

In this work, we report a detailed room-and low-temperature polarization-resolved spectroscopy of Yb 3+ :MgWO4 paving the way towards its highly-efficient and high-power diode-pumped laser operation. We consider this work as a first step towards high-power mode-locked bulk and thin-disk lasers based on Yb 3+ :MgWO4.

The 1.25 at.% Yb 3+ :MgWO4 crystal was grown by the Top-Seeded Solution Growth (TSSG) method using Na2WO4 as a solvent [1,3]. Its structure (monoclinic, sp. gr. C 4 2h -P2/c) [16] was confirmed by using X-ray powder diffraction. In MgWO4, the Yb 3+ ions are replacing the Mg 2+ ones in a single type of sites (Wyckoff position: 2f, site symmetry: C2, VI-fold oxygen coordination in distorted [Mg|YbO6] polyhedra), Fig. 1(b). Charge compensation is provided by Na + cations entering from the melt [3]. The corresponding ionic radii are RYb = 0.868 Å, RMg = 0.72 Å and RNa = 1.02 Å. The concentration of Yb 3+ ions in the crystal NYb was 1.82×10 20 cm -3 (as determined by Inductively Coupled Plasma Atomic Emission Spectroscopy). Note that the increase of Yb 3+ doping level is mainly limited by the heterovalent doping mechanism; this would also lead to the deteriorated thermal properties of the crystal.

Monoclinic Room-temperature (RT, 293 K) absorption, σabs, cross-sections corresponding to the 2 F7/2 → 2 F5/2 transition are shown in Fig. 2(a) for the principal light polarizations E || Np, Nm and Ng. The maximum σabs is 6.16×10 -20 cm 2 at 974.0 nm (the zero-phonon line, ZPL, at RT) and the corresponding full width at half maximum (FWHM) of the absorption peak is 5.6 nm (for E || Ng). The stimulated-emission (SE) cross-sections, σSE, were calculated using a combination of the Füchtbauer-Ladenburg (F-L) equation [17] based on the measured luminescence spectra, and the reciprocity method (RM) [18] based on the determined Stark splitting). The maximum σSE reaches 6.2×10 -20 cm 2 at 1056.7 nm for E || Nm. Yb 3+ :MgWO4 exhibits a strong anisotropy of the SE cross-sections at this wavelength: σSE(m) : σSE(g) = 3.7 and σSE(m) : σSE(p) = 5.5, which is a prerequisite for a linearly polarized laser emission. From the luminescence spectra (measured with λexc = 972 nm), the emission bandwidth is 18.7 nm (E || Nm) and >50 nm (structured spectrum, E || Ng). Yb 3+ :MgWO4 exhibits a single-exponential luminescence decay with a lifetime τlum of 366 μs, as measured for a powdered sample to avoid radiation trapping. The 2 F5/2 → 2 F7/2 transition of Yb 3+ represents a quasithree-level laser scheme with reabsorption. The polarized Raman spectra of an Nm-cut Yb 3+ :MgWO4 crystal are shown in Fig. 4 for the m(ij)m, where i, j = p, g, configurations (using Porto's notation). The excitation wavelength is λexc = 514 nm. The most intense vibration is observed at 915.7 cm -1 (the FWHM of the Raman band is 15.0 cm -1 ) and assigned to symmetric stretching W-O vibrations ν1(A1g) in the WO6 octahedra [2]. Yb 3+ :MgWO4 is promising for self-Raman frequency conversion. To resolve the Stark splitting of Yb 3+ multiplets, the absorption and luminescence spectra were measured in the temperature range of 6-300 K, Fig. 5. For Yb 3+ ions in C2 symmetry sites, there is a total of 2J + 1 Stark sub-levels for each 2S+1 LJ multiplet, numbered as 0..3 for 2 F7/2 and 0'..2' for 2 F5/2. The interpretation of the Stark transitions was carried out accounting for the Raman spectra. The energy-level scheme of Yb 3+ ions in MgWO4 is shown in Fig. 6(a). The ZPL (the transition between the lowest sub-levels of both multiplets) has an energy EZPL = 10275 cm -1 . The partition functions for the lower and upper multiplets are Z1 = 1.352 and Z2 = 1.469, respectively (Z1/Z2 = 0.920). The total Stark splitting of the ground-state, ΔE( 2 F7/2) = 765 cm -1 , exceeds that in other known tungstate crystals [8,19], Fig. 6(b). For the RE 3+ ions, the barycenter of any 2S+1 LJ 4f n multiplet shows a linear variation vs. the barycenter of any other isolated multiplet, which is expressed as a barycenter plot [20], see Fig. 6(c). The barycenter energies <E( 2 F5/2)> and <E( 2 F7/2)> for Yb 3+ :MgWO4 agree well with this plot.

In Table 1, we compare the emission properties of Yb 3+ :MgWO4 with other well-known tungstate laser crystals, namely, monoclinic (sp. gr. C2/c) Yb 3+ :KLu(WO4)2 [8] and tetragonal disordered (sp. gr. I41/a) Yb 3+ :NaY(WO4)2 [21]. Yb 3+ :MgWO4 has higher SE crosssections, while its gain bandwidths are comparable to those of monoclinic double tungstates. *λem -emission wavelength, Δλg -gain bandwidth (β = 0.1), σSE -SE cross-section, τlum -reabsorption-free luminescence lifetime.

For laser experiments, a rectangular sample was cut from the 1.25 at.% Yb 3+ :MgWO4 crystal for light propagation along the Np optical indicatrix axis (Np-cut). It had a thickness of 3.1 mm and an aperture of 4×4 mm 2 . This crystal orientation was selected because it gives access to the high-gain light polarization (E || Nm). The uncoated crystal was mounted in a Cu-holder using Indium foil for better thermal thermal contact from all lateral sides. The holder was cooled to ~14 °C by circulating water. The crystal was inserted in a compact plano-plano (microchip-type) laser cavity, Fig. 7, formed by a flat pump mirror (PM) coated for high transmission (HT) at 0.88-0.99 μm and for high reflection (HR) at 1.02-1.23 μm, and a set of flat output couplers (OCs) with a transmission TOC of 0.5%...10% at the laser wavelength. Both the PM and the OC were placed close to the crystal with minimum air gaps, so that the geometrical cavity length was ~3.1 mm. The microchip laser concept benefits from a robust and compact design and good cavity stability. The Np-cut Yb 3+ :MgWO4 crystal generated a maximum output power of 18.2 W at ~1056 nm with a slope efficiency η of ~89% (vs. the absorbed pump power Pabs), Fig. 8(a). The laser threshold was at Pabs = 0.54 W and the optical-to-optical efficiency ηopt amounted to 33.7% (vs. the pump power incident on the crystal). All these values are specified for TOC = 10%. The laser output was linearly polarized (E || Nm) and the polarization was intrinsically selected by the gain anisotropy, Fig. 2(b). For all studied OCs, the emission wavelength was ~1.06 μm, Fig. 3(a), in agreement with the gain spectra. A slight blue-shift of the laser wavelength with increasing output coupling was detected, Fig. 8(b), and ascribed to the quasi-three-level nature of the Yb 3+ laser scheme exhibiting reabsorption at the laser wavelength. The laser operation in the plano-plano cavity was supported by a positive (focusing) thermal lens. For TOC < 10%, power scaling was limited by a thermal roll-over probably because of too high intracavity laser intensity. The determined laser slope efficiency gives an estimation of the roundtrip passive loss L of 0.35% (loss coefficient: δloss = 0.0056 cm -1 ). No crystal fracture was observed up to at least Pabs = 22.5 W (limited by the available pump).

In Table 2, we compare the output characteristics of compact diode-pumped lasers based on Yb 3+ -doped oxide crystals and reported recently. The superior laser results achieved with Yb 3+ :MgWO4 compared to previous studies with other tungstate crystals, Yb 3+ :NaY(WO4)2 and Yb 3+ :KLu(WO4)2, are attributed to its better thermo-mechanical properties. crystals, Yb 3+ :NaY(WO4)2 and Yb 3+ :KLu(WO4)2, are attributed to its better thermo-mechanical properties. *Pout -output power, λL -laser wavelength; Pth -threshold pump power, η -slope efficiency (vs. absorbed pump power); **This work.

To conclude, monoclinic Yb 3+ :MgWO4 is a promising crystal for compact, highly-efficient and high-power lasers at ~1 μm thanks to a combination of attractive thermal and spectroscopic properties. We report on the first laser operation of Yb 3+ :MgWO4 in a microchip-type laser cavity yielding >18 W of linearly polarized output at ~1.06 μm with slope efficiency (88.8%) almost approaching the Stokes limit, ηSt = λP/λL = 91.7%. This is attributed to weak non-radiative relaxation, low optical losses and good modematching provided by the positive thermal lens for the selected crystal orientation and the results achieved in this work represent a record for Yb 3+ -doped tungstate laser crystals.

Fig. 1 .

 1 Fig. 1. (a) Orientation of the optical indicatrix axes (Np, Nm and Ng) in monoclinic Yb:MgWO4 crystal: a, b and c -crystallographic axes, C2 -2fold symmetry axis; (b) crystal structure in projection to the a-c plane.

  Yb 3+ :MgWO4 is optically biaxial (point group 2/m). At the wavelength of ~1 μm, the principal refractive indices are np = 1.97, nm = 2.03 and ng = 2.13±0.02 according to the np < nm < ng convention. One of the optical indicatrix axes (Nm) coincides with the C2 symmetry axis (the b-axis) and other two (Np and Ng) are lying in the orthogonal mirror plane (the a-c plane), Fig. 1. The angle Np^c = 37.1°, measured within the obtuse angle β.

Fig. 2 .Fig. 3 .

 23 Fig. 2. RT (a) absorption, σabs, and (b) stimulated-emission, σSE, crosssection spectra of Yb 3+ in monoclinic MgWO4 for E || Np, Nm and Ng. Thus, gain cross-sections, σgain = βσSE -(1 -β)σabs, where β = N2( 2 F5/2)/NYb is the inversion ratio, and N2 is the upper laser level population, are calculated to predict the spectral properties of laser emission, see Fig. 3 for E || Nm and E || Ng. For E || Nm, a local peak in the gain spectra is observed at ~1057 nm and the gain bandwidth Δλg is 15.1 nm (FWHM, for β = 0.1). For E || Ng, a similar behavior is observed while the gain spectra are broader, Δλg = 26.1 nm.

Fig. 4 .

 4 Fig. 4. Polarized Raman spectra for Yb 3+ :MgWO4 for the m(xy)m configurations (Porto's notation), numbers indicate the Raman frequencies in cm -1 .

Fig. 5 .

 5 Fig. 5. Low temperature spectroscopy of Yb:MgWO4: (a) absorption spectra for E || Nm; (b) luminescence spectra for E || Ng, λexc = 972 nm. The "+" marks indicate Stark transitions.

Fig. 6 .

 6 Fig. 6. Stark splitting of Yb 3+ multiplets in MgWO4: (a) Energy-level scheme, numbers indicate the energy in cm -1 , Z1(2) are the partition functions; (b) Stark splitting of Yb 3+ in tungstate crystals: MgWO4, KLu(WO4)2 [8], NaGd(WO4)2 [19] (C2 and S4 -Yb 3+ site symmetries); (c) barycenter plot [20] for Yb 3+ ions showing the result for MgWO4.

Fig. 7 .

 7 Fig. 7. (a) Scheme of the compact diode-pumped Yb 3+ :MgWO4 laser: LD -laser diode, PM -pump mirror, OC -output coupler; (b) typical profile of the laser beam in the far-field (the beam ellipticity originates from the astigmatic thermal lens), Pabs ≈ 10 W.

Fig. 8 .

 8 Fig. 8. Diode-pumped compact Yb 3+ :MgWO4 laser: (a) input-output dependences, η -slope efficiency; (b) typical laser emission spectra. The crystal orientation is Np-cut, the laser polarization is E || Nm.

Table 1 . Spectroscopic Properties* of Yb 3+ in Tungstate Crystals

 1

	Crystal	Site λ em ,	Δλ g ,	σ SE ,	τ lum ,	Ref.
			nm	nm	10 -20 cm 2	μs
	NaY(WO 4 ) 2 S 4	1018(π)	33.9(π)	1.38(π)	309 [21]
			1024(σ)	25.9(σ)	0.86(σ)
	KLu(WO 4 ) 2 C 2	1026.7(m)	20.2(m)	2.6(m)	275 [8]
			1041.2(p)	28.0(p)	1.3(p)
	MgWO 4	C 2	1056.7(m)	15.1(m)	6.25(m)	366 *
			1056.6(g)		1.68(g)

Table 2 . Output Characteristics* of Compact Diode-Pumped Ytterbium Lasers Based on Oxide Crystals Reported So Far

 2

	Crystal	Yb,	P out ,	λ L ,	P th ,	η,	Ref.
		at.%	W	nm	W	%
	Yb:LuVO 4	1.5	8.3	1031	2.6	80 [22]
	Yb:CaGdAlO 4	8	7.79	~1061	2.0	84 [13]
	Yb:LuAlO 3	2	9.6	1041	~1.5	74 [23]
	Yb:NaY(WO 4 ) 2	4.8	5.2	1045	1.20	50 [24]
	Yb:KLu(WO 4 ) 2	5.2	11.0	~1045	0.61	80 [25]
	Yb:MgWO 4	1.25	18.2	~1056	0.54	89 **
	Yb:Ca 4 GdO(BO 3 ) 3	10	18.2	1032	~1	70 [26]
	Yb:YAl 3 (BO 3 ) 4	5.6	10.6	1042	0.79	72 [27]
	Yb:Lu 3 Ga 5 O 12	7.1	8.97	1040	1.22	75 [28]

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

Disclosures. The authors declare no conflicts of interest.

Funding. National Natural Science Foundation of China (61975208, 51761135115, 61850410533, 61575199, 61875199); 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); Spanish Government, MINECO (MAT2016-75716-C2-1-R (AEI/FEDER,UE); Generalitat de Catalunya (2017SGR755).