Sub-100-fs mode-locked (ML) lasers at approximately 2 μm with average powers exceeding 100 mW are attractive for multiple applications, for example, synchronous pumping of optical parametric oscillators (SPOPOs) operating at wavelengths longer than 5 μm^[1^], mid-infrared (IR) frequency comb generation^[2^], as seed sources for chirped pulse amplification (CPA) laser systems and near-degenerate chirped pulse optical parametric amplification (CPOPA)^[3^], for the generation of high harmonics and soft X-rays^[4^], transparent materials processing^[5^].

The attractive thermo-optical and spectroscopic properties of thulium (Tm³⁺)-doped cubic sesquioxide A₂O₃ (where A = Y, Lu, Sc or their combinations) make them ideally suited for generating high-power femtosecond pulses from passively ML solid-state lasers in the 2-μm spectral region. Using a single-layer graphene saturable absorber (SA), an average power of 270 mW with a relatively long pulse duration of 410 fs was achieved from an ML Tm:Lu₂O₃ ceramic laser^[6^]. A semiconductor saturable absorber mirror (SESAM) ML laser generating 750 mW and 382 fs pulses was described in Ref. [7] using the same material. Watt-level average output power was achieved via Kerr-lens mode-locking (KLM) of a Tm:Sc₂O₃ crystalline laser at 2115 nm with a pulse duration of 298 fs^[8^]. Note that in all these studies, the relatively narrow gain bandwidths of the simple sesquioxides did not support sub-100-fs pulse generation.

Tm³⁺-doped ‘mixed’ sesquioxides (A,B)₂O₃ with compositional disorder inducing inhomogeneous broadening of the absorption and gain spectra are obviously advantageous in the sub-100-fs regime at 2 μm^[9^–11^]. Compared with crystalline sesquioxides, transparent ceramics offer more flexibility owing to the less-challenging fabrication process. The latter features size scalability, overcoming temperature limits of the crystal growth (very high crystal melting temperatures, typically ~2400°C–2500°C) and the potential for creating controlled ‘mixed’ compositions with a specific doping level^[12^,13^]. High-quality, almost pore-free Tm³⁺-doped ‘mixed’ polycrystalline sesquioxides, for example Tm:(Lu,Sc)₂O₃ and Tm:(Lu,Y)₂O₃, are fabricated by the hot isostatic pressing (HIP) sintering method^[13^,14^]. Sub-100-fs ML operation of such a Tm³⁺-doped ‘mixed’ ceramic laser was first demonstrated in 2018: 63-fs pulses with an average power of only 34 mW were generated at 2057.2 nm employing a SESAM^[15^]. Subsequently, shorter pulse durations of 57 fs at 2045 nm and 54 fs at 2048 nm were reported using a single-walled carbon nanotube (SWCNT)-based SA and a SESAM, respectively, with average output power still below 100 mW^[16^,17^]. Figure 1 summarizes the state of the art of sub-100-fs ML solid-state Tm lasers emitting in the 2-μm spectral range^[16^–22^]. An average power of 210 mW was demonstrated in 2019 with an SWCNT-SA ML Tm:LuYO₃ ceramic laser^[16^]. In 2020, a slightly higher power of 222 mW was obtained from a Tm:Sc₂O₃ laser using the KLM technique^[21^], which represents the highest power ever reported from such sub-100-fs ML solid-state Tm lasers. One can recognize that all the average powers higher than 100 mW were obtained by using the above-mentioned sesquioxide materials^[16^,17^,21^], and an obvious trade-off between average power and pulse duration can be seen from all these reported results.

The above results and the superior thermo-optical and improved spectroscopic properties of the Tm³⁺-doped ‘mixed’ polycrystalline sesquioxides motivated us to further explore the feasibility of average power scaling in the sub-100-fs regime. For this purpose, a broadband SA that possesses a low non-saturable loss and high damage threshold at approximately 2 μm is required. Compared with SESAMs, carbon-nanostructure-based SAs, for example graphene^[23^] and SWCNT SAs^[24^], exhibit a broader spectral response and are fabricated by simpler and less expensive techniques. Here, we present the performance of a power-scalable SWCNT-SA ML ‘mixed’ Tm:(Lu,Sc)₂O₃ ceramic laser in the sub-100-fs regime at approximately 2.08 μm.

The high-quality ‘mixed’ Tm:(Lu_2/3Sc_1/3)₂O₃ transparent ceramic used in the experiment was fabricated by the HIP sintering method. The Tm³⁺ doping was 2.8% (atomic fraction) (N_Tm = 8.12 × 10²⁰ cm^–3). A linear X-folded astigmatically compensated resonator was arranged for evaluating the laser performance both in the continuous-wave (CW) and the ML regimes, as illustrated in Figure 2. An uncoated ceramic sample having a thickness of 3 mm and an aperture of 3 mm× 3 mm was mounted on a copper holder with water cooling (coolant temperature: 12°C) and placed between two dichroic folding mirrors, M₁ and M₂ (radius of curvature, RoC = –100 mm), with the Brewster minimum loss condition fulfilled for the laser wavelength. The pump source was a narrow-linewidth CW Ti:sapphire laser tuned to 795 nm emitting linearly polarized radiation. The pump beam was focused into the ceramic using a spherical lens having a focal length of 70 mm to form a waist with beam radii of 30 μm and 77 μm in the sagittal and tangential planes, respectively.

The CW laser performance was investigated with a four-mirror cavity including a plane rear reflector M₃ and a plane-wedged output coupler (OC; without the SWCNT-SA); see Figure 3(a). The measured single-pass pump absorption under lasing conditions was between 57.4% and 58.6%, depending slightly on the OC (0.2%–3%). A maximum power of 755 mW was obtained at an absorbed power of 1.84 W for the 1.5% OC, corresponding to a slope efficiency of 43.6%. The round-trip passive loss was estimated using the Caird analysis^[25^], that is, fitting the measured slope efficiency as a function of the OC reflectivity, giving total round-trip resonator losses of δ = 0.21%, as shown in Figure 3(b). The determined value of δ indicates high optical quality of the transparent ceramic and a well-optimized laser resonator.

To initiate and stabilize a soliton-like ML operation, a transmission-type SWCNT-SA (relying on the first fundamental electronic transition E₁₁ of semiconducting nanotubes for absorption at ~2 μm^[24^]) was employed. The nanotubes were synthesized by the arc-discharge method and the SWCNT/poly(methyl methacrylate) (PMMA) film was spin-coated on a 1-mm-thick fused silica (FS) substrate. The SWCNT-SA exhibited a relatively low non-saturable linear loss of approximately 1%, small saturation fluence of less than 10 μJ/cm², very low modulation depth of less than 0.5% and a slow recovery time constant of approximately 1 ps at approximately 2 μm^[26^]. It was placed at Brewster’s angle in the second cavity beam waist having beam radii of 125 μm and 225 μm in the sagittal and tangential planes, respectively. The latter was created by two concave dispersive mirrors (DMs), DM₁ and DM₂, with RoC of –100 and –50 mm, respectively. The steady-state soliton-like pulses were generated by varying the number of bounces on the DMs (DM₁–DM₄) for negative group delay dispersion (GDD) to balance the self-phase modulation (SPM)^[27^]. All DMs exhibited a GDD of –125 fs² per bounce. The roundtrip material GDD due to the 3-mm thick ceramic sample amounted to approximately –200 fs² at 2.08 μm, estimated by averaging the refractive indices of Lu₂O₃ and Sc₂O₃^[28^]. Additional material GDD of approximately –240 fs² (per round-trip) was introduced by the FS SA substrate.

In addition to the two concave mirrors DM₁ and DM₂, two bounces on the flat DMs (DM₃ and DM₄) were implemented yielding a net round-trip cavity GDD of –875 fs². The ML laser performance was studied by varying the output coupling without changing the cavity length. The latter corresponded to a pulse repetition rate of approximately 82.9 MHz. When applying the 1.5% OC, a self-starting ML operation was achieved with ultimate stability by careful cavity alignment. The central emission wavelength was 2075 nm with a 72 nm FWHM (full width at half maximum). The measured spectrum with its sech²-shaped fit is shown in Figure 4(a). The recorded fringe-resolved autocorrelation trace leads to a deconvolved pulse duration of 65 fs (FWHM) by assuming a sech²-shaped temporal profile, as shown in Figure 4(b), which was only 3.4% longer than the Fourier-transform limit. The average output power amounted to 350 mW for an absorbed pump power of 2.2 W corresponding to an optical conversion efficiency η_opt of 15.9%. The excellent sech²-shaped spectral and temporal profiles indicate soliton ML operation of the Tm:(Lu,Sc)₂O₃ ceramic laser.

Further power scaling in the ML regime was achieved by increasing the OC transmission at the expense of the pulse duration. Indeed, using a 3% OC, the average power reached 486 mW at an absorbed pump power of 2.18 W, which corresponded to η_opt = 22.3%. Figure 5 shows the measured spectrum and fringe-resolved autocorrelation trace. The pulses had a well-fitted sech²-shaped spectrum with an FWHM of 47 nm at 2086 nm and a temporal FWHM of 98 fs, derived from the autocorrelation trace. Assuming a sech²-shaped temporal profile, the resulting time-bandwidth product (TBP) was 0.317, which is evidence for the generation of soliton pulses with a nearly Fourier-limited duration, as expected from the almost perfect fits both in the spectral and in the temporal domains.

The shortest pulses were achieved by reducing the output coupling to 0.5% at the expense of the average power. After extra-cavity linear chirp compensation with a 3-mm-thick polycrystalline ZnS plate (GDD = 465 fs² at 2.08 μm), the pulses were compressed from 66 to 58 fs (eight optical cycles). The average output power amounted to 114 mW for an absorbed pump power of 2.19 W. The ML laser spectrum with a central wavelength of 2076 nm exhibited a significant spectral broadening compared to operation with 1.5% and 3% OC, owing to relatively strong SPM originating from the Tm:(Lu,Sc)₂O₃ ceramic, as shown in Figure 6(a). The on-axis intracavity peak intensity on the ceramic sample reached 292 GW/cm². The pulse duration, which was deconvolved from the measured fringe-resolved autocorrelation trace after compression [see Figure 6(b)], is 20.8% longer than the Fourier-transform limited value of the measured spectrum. We attribute the asymmetric spectral profiles (deviation from the ideal sech²-shaped spectral profile) to the unmanageable intracavity GDD at the long-wave spectral wing, that is, at wavelengths higher than 2.15 μm, and the non-optimized reflection bands of individual cavity mirrors (cf. Figures 4(a) and 6(a)).

The stability in the ML regime of the laser was confirmed by measurements with a radio frequency (RF) spectrum analyser in two frequency span ranges. The recorded fundamental beat note at 82.94 MHz exhibited a high signal-to-noise ratio (SNR) of more than 75 dBc (see Figure 7(a)). The uniform harmonic beat notes in the 1-GHz frequency span (see Figure 7(b)) are evidence for stable steady-state ML operation without any Q-switching and/or multi-pulsing instabilities.

In conclusion, we demonstrated average power scaling of an SWCNT-SA ML ‘mixed’ Tm:(Lu,Sc)₂O₃ ceramic laser maintaining the sub-100-fs regime near 2 μm. Pulses as short as 58 fs were generated at 2076 nm with an average power of 114 mW and a pulse repetition rate of approximately 82.9 MHz. A maximum average output power as high as 486 mW was directly obtained from the ML laser at 2086 nm for a pulse duration of 98 fs, with a conversion efficiency of 22.3%. This represents the highest average output power and conversion efficiency ever reported from any sub-100-fs ML Tm laser. Given the imperfect design of the cavity mirrors, shorter pulse durations would be possible after optimizing the reflection bands of the cavity mirrors, as well as by fine control of the total intracavity GDD over the full spectral bandwidth of the ML laser.