1. Introduction

Ultrafast solid-state lasers operating near 2 µm with relatively high average powers are attractive for a wide range of applications, such as synchronous pumping of optical parametric oscillators (SPOPOs) to produce mid-IR wavelengths [1], generation of mid-IR frequency combs for time-resolved molecular spectroscopy in the molecular fingerprint region [2], industrial processing of transparent materials [3], and free-space optical communication [4]. To date, singly Tm$^{3+}$- or Tm$^{3+}$,Ho$^{3+}$ co-doped gain media with hosts such as cubic sesquioxide, disordered CNGG-type garnets, calcium rare-earth aluminates (CaREAlO$_{4}$ with RE = Y or Gd) and monoclinic tungstates, have been exploited as promising candidates for 2-µm mode-locked lasers in the femtosecond regime [5]. In comparison, the cubic sesquioxides (RE$_{2}$O$_{3}$, where RE = Lu, Y, Sc, or their mixture) combine superior thermo-mechanical properties, relatively low photon energies [6], and broad and smooth gain spectra [7], making them attractive for high-average-power ultrafast lasers in the 2-µm spectral range. Moreover, the strong ground-state splitting of Tm$^{3+}$ ions in the sesquioxides enables laser emission extending up to 2.1 µm, thus avoiding the structured water vapor absorption and supporting stable femtosecond pulse generation in this wavelength region [8]. In fact, nearly all the sub-100-fs mode-locked bulk Tm-lasers with average powers exceeding 100 mW relied on crystalline or ceramic type sesquioxides hosts [5].

Figure 1 summarizes the progress in 2-µm sub-picosecond solid-state lasers based on sesquioxides host materials, including single crystals [9–16] and polycrystalline ceramics [17–25]. A clear trade-off between pulse duration and average output power can be seen from the summary. For sub-100-fs pulses the average powers are relatively low with a highest value of 486 mW from a 98-fs Tm:LuScO$_{3}$ ceramic laser [25]. In this case further power scaling was limited by the available power of the employed Ti-sapphire laser. Commercially available AlGaAs laser diodes at $\sim$ 790 nm can provide much higher pump powers but exhibit low brightness [26]. The beneficial two-for-one cross-relaxation excitation process in Tm$^{3+}$ for the 790-nm laser pumping can provide in principle a nearly 200% quantum yield [27], however, a high Tm-doping concentration is required [28] which is inevitably accompanied by thermal problems. An alternative approach is direct in-band pumping ($^{3}$H$_{6}$ $\rightarrow$ $^{3}$F$_{4}$ transition in Tm$^{3+}$) by using a fiber laser, which combines the high brightness of the single-mode emission and a low quantum defect. For example, by using a Er,Yb-fiber master oscillator power amplifier (MOPA) at 1611 nm as a pump source, longer pulses ($\sim$ 300 fs) with an average power up to 1 W has been obtained from a Kerr-lens mode-locked Tm:Sc$_{2}$O$_{3}$ crystalline laser [12], indicating the average power scalability potential of in-band pumping for the femtosecond mode-locked lasers.

 

Fig. 1. Progress in femtosecond mode-locked 2-µm Tm sesquioxide lasers. Open symbols represent crystalline active media and filled symbols correspond to transparent ceramics. LuO (Lu$_{2}$O$_{3}$), ScO (Sc$_{2}$O$_{3}$), LuScO (LuScO$_{3}$), LuYO (LuYO$_{3}$), SWCNT: Single-walled carbon nanotube saturable absorber, SESAM: Semiconductor saturable absorber mirror, KLM: Kerr-lens mode-locking.

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From the point of view of material availability with good optical quality, the growth of crystalline sesquioxides is still a challenge due to their high melting temperature (> 2400 $^{\circ }$C [6]). In comparison, polycrystalline sesquioxide transparent ceramics can be easily fabricated by hot isostatic pressing at a lower sintering temperature ranging from 1300 $^{\circ }$C to 1850 $^{\circ }$C [29], thus making them attractive for large-size active elements or “mixed” ceramics [30,31] which exhibit inhomogeneous gain spectra broadening caused by compositional disorder [20,22]. As shown in Fig. 1, apart from one case of using a combination of different crystal and ceramic [16], all sub-10-optical-cycle (sub-70-fs) pulses were produced from such “mixed” sesquioxide ceramic lasers pumped by a Ti-sapphire laser at around 795 nm [20–25].

Here, we study the performance of the SESAM mode-locked Tm-doped “mixed” (Lu and Sc) sesquioxide ceramic laser in-band pumped by a high-brightness Raman fiber laser at 1627 nm. More than 1-W average output power has been achieved with a pulse duration of 280 fs at 2060 nm, which is comparable or even superior to the previously reported 2-µm Tm mode-locked lasers based on sesquioxide crystals.

2. Nonlinear refractive index measurement and laser setup

Nonlinear refractive index ($n_{2}$) associated with Kerr self-focusing in space and self-phase modulation (SPM) in the time domain, is a critical factor in mode-locking for ultrashort pulse generation. Therefore, in the present work we first evaluated $n_{2}$ for the specific ceramic by using the Z-scan technique. The “mixed” (Lu$_{2/3}$Sc$_{1/3}$)$_{2}$O$_{3}$ ceramic doped with 2.8 at.% Tm$^{3+}$ was fabricated by hot isostatic pressing at 1800 $^{\circ }$C. A 1-mm thick sample with an aperture of 3 $\times$ 3 mm$^{2}$ was used for the $n_{2}$ measurement. The laser source was a femtosecond optical parametric amplifier (OPA, Orpheus, Light Conversion) tunable near 2 µm (160-fs pulse duration by assuming a Gaussian pulse profile and 100 kHz repetition rate). Figure 2 shows the measured transmittance curve employing the closed-aperture Z-scan method. With the fitted phase-change parameter of the incident beam [32], $n_{2}$ was calculated to be 4.66 $\times$ 10$^{-20}$ m$^{2}$/W taking into account the weak linear absorption coefficient of 0.15 cm$^{-1}$ at 2 µm. This value is higher than that of 3.3 $\times$ 10$^{-20}$ m$^{2}$/W for the Tm:Lu$_{2}$O$_{3}$ crystal [17].

 

Fig. 2. Closed-aperture Z-scan curve of a 1-mm thick Tm:(Lu$_{2/3}$Sc$_{1/3}$)$_{2}$O$_{3}$ ceramic at 2 µm.

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Figure 3(a) shows the experimental setup of the SESAM mode-locked Tm:(Lu,Sc)$_{2}$O$_{3}$ ceramic laser. The pump source was a 1627-nm Er,Yb Raman fiber laser with a measured beam propagation factor ($M^{2}$) of 1.08. As shown in Fig. 3(b), the 1627-nm pump wavelength is very close to the absorption peak (1621 nm) of the $^{3}$H$_{6} \rightarrow ^{3}$F$_{4}$ transition, corresponding to an absorption cross-section of $\sim$ 4 $\times$ 10$^{-21}$ cm$^{2}$ [33]. By using a spherical lens with a focal length of $f$ = 75 mm, the pump beam was focused on the ceramic sample with a beam waist radius of 22 µm. An astigmatically compensated $X$-shaped cavity with two flat chirped mirrors (CM1 and CM2) in the longer arm terminated by a flat-wedged output coupler (OC), was employed to study the laser performance. Each chirped mirror provides a group delay dispersion (GDD) of $\sim$ –125 fs$^{2}$ per bounce at 2.08 µm, and the optimum bounce number per mirror in this work was 2 per round trip. The uncoated ceramic sample with dimensions of 3 $\times$ 3 $\times$ 3 mm$^{3}$ was placed in the cavity at Brewster’s angle. The simulated laser beam radius on the ceramic was 32 µm $\times$ 57 µm in the sagittal and tangential planes, respectively. To mitigate the thermal load, the sample was wrapped in indium foil and water-cooled to 14 $^{\circ }$C through a Cu-holder. The dichroic folding mirrors, M1, M2 and M3, were plano-concave mirrors with radius of curvature of $R_{OC}$ = –100 mm. A GaSb-based SESAM contained two InGaAsSb quantum wells (8.5-nm thickness) and a 50-nm cap layer [34], was employed for starting and stabilizing the mode-locking, and the calculated beam radius was $\sim$ 50 µm on it. Two OCs with transmissions ($T_{OC}$) of 1.5% and 3% were used for laser operation, respectively.

 

Fig. 3. (a) Experimental setup of the SESAM mode-locked Tm:(Lu,Sc)$_{2}$O$_{3}$ ceramic laser in-band pumped by a Raman fiber laser at 1627 nm, and (b) the absorption cross-sections of the Tm:(Lu,Sc)$_{2}$O$_{3}$ ceramic for the $^{3}$H$_{6}$ $\rightarrow$ $^{3}$F$_{4}$ transition and the optical spectrum of pump laser. (M1-M3: cavity mirrors; CM1-CM2: chirped mirrors; RM1-RM4: reflective mirrors; DM: dichroic mirror; OC: output coupler; PM: power meter; OSA: optical spectrum analyzer).

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3. Results and discussions

By using a flat retro-reflecting mirror to replace M3, continuous-wave (CW) laser operation was studied first without the SESAM and chirped mirrors in the cavity. At the highest incident pump power of 4.1 W, the ceramic absorption measured under lasing conditions with $T_{OC}$ = 3% was 68.3%, i.e., the absorbed pump powers was 2.8 W. A maximum CW output power of 1.03 W was achieved, corresponding to a slope efficiency with respect to the absorbed power of 41.8%. Thereafter, mode-locking was studied by inserting the SESAM and CMs into the cavity, leading to a physical cavity length of 1.7 m. Taking into account the group velocity dispersion (GVD) of the 3-mm thick ceramic sample that was estimated from the Sellmeier equations of Lu$_{2}$O$_{3}$ and Sc$_{2}$O$_{3}$ [35], the total round-trip GDD [see Fig. 4(a)] amounted to $\sim$ –750 fs$^{2}$ at 2.08 µm. With the 3% OC, the highest average output power of 1.02 W at 86.5 MHz repetition rate was achieved from the self-starting femtosecond mode-locked Tm:(Lu,Sc)$_{2}$O$_{3}$ ceramic laser, yielding a single pulse energy of 11.8 nJ. The corresponding laser efficiency with respect to the absorbed pump power amounted to 36.4%. The almost unchanged output power compared to the CW regime, is an indication of extremely low non-saturable losses of the used SESAM. Further power scaling was limited only by the available pump power. A 5% OC was tested for power scaling but failed to ensure stable mode-locking. Nevertheless, the average power achieved with the 3% OC is comparable to the maximum value of 1 W reported from a Tm:Sc$_{2}$O$_{3}$ crystalline laser at 95 MHz [12], confirming the potential of transparent sesquioxide ceramics for power scalability of 2-µm femtosecond mode-locked bulk lasers. The measured optical spectrum, with a central wavelength of 2060 nm, is shown in Fig. 4(a). Fitting the spectral profile with a sech$^{2}$-function gives a FWHM (full width at half maximum) of 16 nm.

 

Fig. 4. Optical spectrum (a), autocorrelation trace (b), and the recorded pulse trace (c) of the SESAM mode-locked Tm:(Lu,Sc)$_{2}$O$_{3}$ ceramic laser with $T_{OC}$ = 3%. The solid red curve in (a) represents the total round-trip GDD. Inset in (b): the corresponding long-scale ($\pm$ 8 ps) autocorrelation trace. Inset in (c): the pulse train recorded on a millisecond time scale at the highest average power.

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Figure 4(b) shows the measured noncollinear autocorrelation trace at the highest average power. By assuming a sech$^{2}$ pulse intensity profile, the pulse duration amounted to 280 fs, thus leading to a time-bandwidth product (TBP) of 0.317, which is an indication of transform-limited pulses. The long-scale autocorrelation trace shown by the inset of Fig. 4(b), proves a single pulse operation of the mode-locked Tm:(Lu,Sc)$_{2}$O$_{3}$ ceramic laser without any temporal satellites. The pulse train recorded on a nanosecond time scale is shown in Fig. 4(c), indicating a good pulse-to-pulse stability with an amplitude noise of less than $\pm$ 0.45%. Obviously, the mode-locked laser operated at a repetition rate of 86.5 MHz, i.e., the cavity fundamental frequency without harmonic mode-locking effects. Moreover, steady-state mode-locked operation without any signs of unwanted Q-switching envelope fluctuations was confirmed from the measured pulse train on a long-term (10 ms) time scale.

Shorter pulses were generated with the 1.5% OC. At an absorbed pump power of 2.07 W, the average output power of the mode-locked laser dropped to 300 mW for a repetition rate of 86.6 MHz, thus giving a pulse energy of $\sim$ 3.5 nJ. However, the spectral FWHM increased to 69 nm due to the enhanced SPM effect. The SPM coefficient calculated from the measured $n_{2}$ is closed to that deduced from the soliton area theorem [36], $\sim$ 1.7 $\times$ 10$^{-7}$ W$^{-1}$, indicating that mode-locking took place in the soliton regime. As shown in Fig. 5(a), the corresponding optical spectrum with a central wavelength at 2076 nm was well fitted by a sech$^{2}$-function. For comparison, the “gray” area shown as a background represents the calculated gain cross section of the Tm:(Lu,Sc)O$_{3}$ ceramic for a population inversion parameter of $\beta$ = 0.05 [33]. The pulse duration of around 10-optical cycles was confirmed by the fringe-resolved interferometric autocorrelation trace [see Fig. 5(b)], which exhibited a peak-to-background ratio of exactly 8:1. By assuming a sech$^{2}$ pulse shape, both envelopes were well fitted, indicating chirp-free pulses with a FWHM duration of 66 fs. The resulting TBP was calculated to be again 0.317, very close to the Fourier-transform limit. Single pulse operation without satellites was confirmed again by measuring the noncollinear autocorrelation trace on a long time scale [see the inset in Fig. 5(b)]. In this case, the peak on-axis laser intensity in the ceramic was estimated to be 110 GW/cm$^{2}$. Finally, the stability of the mode-locking regime was characterized by recording the real-time pulse trains on different time scales [see Fig. 5(c)]. The uniform pulse train without obvious amplitude fluctuations and Q-switching envelope modulations indicated stable, steady-state mode-locking.

 

Fig. 5. Optical spectrum (a), interferometric autocorrelation trace (b), and the typical pulse train on a nanosecond time scale (c) of the shortest pulses generated with $T_{OC}$ = 1.5%. The “gray” area in (a) represents the calculated gain cross-section for a population inversion parameter of $\beta$ = 0.05. Insets in (b) and (c): noncollinear autocorrelation trace on a long time scale of $\pm$ 8 ps, and the pulse train on a millisecond time scale.

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4. Conclusions

Summarizing, we have experimentally demonstrated the power scalability of the femtosecond mode-locked ceramic laser in the 2-µm spectral range, by employing a Tm-doped “mixed” sesquioxide transparent ceramic which was in-band pumped by a Er,Yb Raman fiber laser at 1627 nm. Watt-level average power was achieved with a laser efficiency of 36.4%, which is comparable to the crystalline laser [12] and represents the highest power level ever reported from Tm- or Tm,Ho femtosecond mode-locked bulk lasers. Further power scaling seems to be possible just through improvement of the available pump power. Nevertheless, the demonstrated watt-level femtosecond laser is an ideal seed source for further amplification, and in particular suitable for direct amplification in the so-called single-crystal fibers (fiber-like, thin-crystal rods which exhibit both the advantages of fiber geometry structure and crystalline properties [37]), without the chirped-pulse amplification (CPA) process [38]. In addition, sub-70-fs pulses have also been demonstrated based on enhanced SPM effect, but at the expense of the average output power. The results obtained in the present work are an evidence for the potential of the rare-earth doped “mixed” sesquioxide ceramics in both power scalable femtosecond lasers and few-optical-cycle pulses generation. Moreover, the feasibility of large-size active element fabrication makes such ceramics promising candidates for implementation in high-power ultrafast thin-disk and slab lasers or amplifiers.