1. Introduction

High-power/energy femtosecond bulk lasers emitting near 2 µm are significant light sources for frequency expansion through nonlinear optics, such as generation of mid-infrared waves via frequency down conversion including difference-frequency generation (DFG) [1] or optical parametric oscillation/amplification (OPO/OPA) in nonlinear optical crystals that exhibits high nonlinearity but large losses in near-infrared (0.8∼1 µm) region due to lower bandgap [2], and as a “sweet spot” for driving soft X-ray (SXR) via high-harmonic generation (HHG) to push the phase-matched harmonic energy beyond the carbon K-edge [3], as well as next-generation laser-driven plasma accelerator based on big aperture thulium (BAT) laser concept recently proposed by Lawrence Livermore National Laboratory (LLNL), where a large-scale available thulium (Tm³⁺) doped fluoride crystal is chose as amplifier gain for boosting the pulse energy with multi-pulse extraction [4]. In addition, fluoride hosts doped with active holmium (Ho³⁺) ions has been demonstrated alternatively promising candidate for high-gain regenerative amplifier (RA) following with multi-stage booster amplifier to produce 17-GW ultrashort pulses in the 2-µm spectral range [5]. All these amplifier systems based on Tm³⁺/Ho^3 +doped fluoride crystals are benefited from their large-size growth, long excited-state lifetime, and high optical quality. Thus, exploitation of compact, mode-locked femtosecond lasers straightforwardly relying on the Tm³⁺/Ho³⁺ doped fluorides, serving as the gain-profile matched seed source of the aforementioned amplifier systems, defines a direction in the laser field. In comparison with the fiber lasers, solid-state bulk laser exhibits lower excess noise originating from the unwanted amplified spontaneous emission (ASE) and intracavity nonlinearities [6], making it suitable seed sources with carrier-envelope phase (CEP) stabilization.

Up to date, 2-µm Tm/Ho-bulk lasers based on different host materials have been successfully demonstrated in the femtosecond regime, such as cubic sesquioxides [7], disordered CNGG-type garnets [8], calcium rare-earth aluminates CaREAlO₄ (RE = Y, Gd, or their mixture [9] and the most recently developed GdScO₃ crystal [10]. However, for the fluoride hosts doped with Tm³⁺ and/or Ho³⁺ ions the previously reported pulse duration of the mode-locked lasers is still in the picosecond level [11] with a shortest pulse of approximately 0.5-ps [12]. Apart from the low nonlinear refractive index (e.g., n₂ ∼ 0.5 × 10⁻¹³ at 1.06 µm) [13] of fluoride crystals which limits the self-phase modulation (SPM) effects during the mode locking, the short emission wave below 2-µm when doped with single Tm³⁺ ions is another critical limitation for broadening the optical spectrum in the water vapor absorption region. Fortunately, the emission wavelength can be slightly red-shifted above 2 µm simply by co-doping with Ho³⁺ ions, thus enabling to avoid the structured water vapor absorption and shorten the pulse duration [14].

Here, a novel Tm³⁺ and Ho³⁺ co-doped strontium fluoride (SrF₂) crystal, which belongs to cubic system with Fm$\bar{3}$m space group, is employed for mode locking. The cluster effect in this crystal resulted from the substitution of Sr²⁺ ions by rare earth ions can enhance the cross-relaxation process and improve the quantum efficiency [15,16]. In addition, the large-scale available SrF₂ host exhibits broad emission spectrum due to the doped sites in the lattice become inequivalent caused by the charge compensation effects [17], low phonon energy (280 cm^-1 [18]), slightly larger thermal conductivity over the YLF (8.3 versus 7.2 Wm⁻¹K⁻¹ [19,20]), and good mechanical properties. In spite of these advantages, the laser operation based on Tm,Ho:SrF₂ crystals, to the best of our knowledge, has never been studied yet. So, we at first demonstrate the continuous-wave (CW) laser and its wavelength tunability, and thereafter the passive mode locking performance by using a GaSb-based SESAM as saturable absorber (SA). Femtosecond laser (246 fs) without any additional dispersion compensation elements in the cavity has been successfully obtained, the compact configuration with simple structure makes it a potential seed source for large-scale Tm/Ho-fluoride amplimer system in the 2-µm spectral range.

2. Experimental setup

The SrF₂ crystal doped with 3 at.% Tm³⁺ and 0.5 at.% Ho³⁺, was grown by the Czochralski method. Figure 1(a) and (b) shows its absorption and emission spectra, the calculated maximum absorption cross-section (σ_abs) is 5.57 × 10⁻²¹ cm² at 1627 nm, and 8.96 × 10⁻²² cm² at 1700nm which corresponds to the pump wavelength used in the following laser experiment. Since the co-emission of Tm³⁺ (³F₄ →³H₆) and Ho³⁺ (⁵I₇ →⁵I₈) ions and the cluster effect as mentioned above, the luminescence spectrum can span from 1.6 to 2.2 µm with a highest emission peak above 2 µm, the broad emission range in particular with long-wave emission peak enable to avoid the water vapor absorption and thus supporting ultrashort pulses generation at 2 µm.

 

Fig. 1. (a) Absorption spectra of Tm,Ho:SrF₂ crystal; (b) Luminescence spectra of Tm,Ho:SrF₂ crystal and the atmospheric transmittance at normal conditions for a path length of 1 m (HITRAN database, USA model, high latitude, summer, H = 0); (c) Schematic of the mode-locked Tm,Ho:SrF₂ laser. M1-M3: plano-concave mirrors (R_OC = −100 mm); M4: flat rear mirror for CW laser operation; CM1 and CM2: flat chirped mirrors; OC: output coupler; SESAM: Semiconductor Saturable Absorber Mirror; LF: Lyot filter.

Download Full Size | PDF

Figure 1(c) shows the schematic of the Tm,Ho:SrF₂ laser in-band pumped by a Raman-shifted Er:fiber laser with a beam quality (M²-factor) of 1.05 and a maximum output power of ∼5.2 W at 1700nm. An asymmetric X-fold cavity astigmatically compensated by two plano–concave mirrors (M1 and M2, both with a radius of curvature of R_OC = –100 mm) was employed for both the CW and mode locking laser operations. The collimated pump beam was focused with an achromatic lens (L, f = 75 mm), resulting in a waist radius of ∼22 µm. The Tm,Ho:SrF₂ sample with a dimensions of 3 × 3 × 6 mm³ was cut at Brewster’s angle to enforce linearly polarized emission. To mitigate the thermal load, the crystal was wrapped with indium foil and mounted in a copper holder which was water-cooled to 13 °C. By using the ABCD formalism, the beam radius in the crystal was calculated to be 30 µm × 47 µm in the sagittal and tangential planes, respectively. Another plano-concave mirror M3 (R_OC = –100 mm) was used to create a second waist radius of ∼67 µm on the GaSb-SESAM-SA which contains two 8.5-nm-thick InGaAsSb quantum wells and a 50-nm cap layer. The SESAM exhibited a high linear reflectivity (97% at 2080nm) [21,22]. The transmission (T_OC) of the used output coupler (OCs) was 0.5%, 1%, 1.5%, 3%, and 5%. Two identical plane-chirped mirrors (CM1 and CM2) provide a group delay dispersion (GDD) of –125 fs² per bounce for each. A 2-mm-thick home-made Lyot filter (LF) inserted into the cavity at Brewster’s angle was used for wavelength tunning.

3. Results and discussion

3.1 CW and tunable laser operation

Initially, the CW laser performance was investigated with a simply four-mirror cavity. With T_OC = 1.5%, the maximum output power of 580 mW was achieved at 4.2 W pump power, corresponding to a slope efficiency and optical-to-optical efficiency of 37.7% and 17.1%, respectively, as can be seen in Fig. 2(a). The central wavelength exhibited an obvious red-shift from 2060.5 nm to 2096.8 nm [see Fig. 2(b)] with decreasing OC transmission, which is attributed to the enhanced reabsorption effect of the quasi-three-level Ho-laser system [23]. A broad wavelength tunning range of 144.2 nm (1985.3-2129.5 nm) was achieved by inserting the LF into the cavity, as shown in Fig. 2(c). The uniform spectral emission over the full tuning range indicates the potential of the Tm,Ho:SrF₂ crystal for generation of ultrashort laser pulses in the 2-µm spectral range. Some typical optical spectra with normalized intensity can be seen by the inset of Fig. 2(c).

 

Fig. 2. CW laser performance of the Tm,Ho:SrF₂ crystal: input-output dependencies (a) and the corresponding optical spectra (b) for different OCs, η: optical-to-optical efficiency. (c) Wavelength tuning curve of the Tm,Ho:SrF₂ laser with 1% OC at 1.64 W absorbed pump power.

Download Full Size | PDF

3.2 Mode-locked laser operation

Continuous-wave passive mode-locking of the Tm,Ho:SrF₂ laser was studied by employing a GaSb-based SESAM as SA. With T_OC = 0.5%, stable and self-started mode locking were at first studied by applying chirped mirrors (CMs) for intracavity dispersion management, giving a total cavity length of ∼ 1.9 m. By taking into account the group velocity dispersion (GVD) of the Tm,Ho:SrF₂ crystal of approximately –12.3 fs²/mm at 2080nm, the total round-trip GDD amounts to –650 fs², as shown in Fig. 3(a). A maximum average output power of 106 mW was achieved at a pulse repetition rate of ∼88.6 MHz. The optical spectrum is shown in Fig. 3(b), the center wavelength locates at 2078.6 nm with a full width at half maximum (FWHM) of 14.7 nm, corresponding to a measured pulse duration of 322 fs. Since the natural negative dispersion providing by the Tm,Ho:SrF₂ crystal in the 2-µm spectral range, we tested mode-locking laser operation by removing the CMs from the cavity. Stable mode locking was successfully achieved, delivering a maximum average output power of 181 mW and thus a single pulse energy and peak power of ∼2 nJ and 6.3 kW, respectively. Figures 3(b) and (c) show the measured optical spectrum (violet curve) and the intensity autocorrelation trace, respectively. The central wavelength is 2085.6 nm with a spectral FWHM of 16.6 nm, and the pulse duration amounts to 285 fs by assuming a sech²-intensity profile, giving a time-bandwidth product (TBP) of 0.33, very close to the Fourier transform limit. Figure 3(d) shows the typical M²-factor measurement of the output beam at the maximum average power, the M² values in both x- and y-direction are ∼1.3. The recorded far-field beam profile is shown by the inset of Fig. 3(d).

 

Fig. 3. (a) Total round-trip GDD with or without dispersion management elements, i.e., CMs. Optical spectra (b) and the corresponding intensity autocorrelation trace (c) of the mode-locked Tm,Ho:SrF₂ laser with T_OC= 0.5%. (d) A typical M² factor measurement of the laser beam and the corresponding far-field beam profile.

Download Full Size | PDF

Next, mode-locking performance of Tm,Ho:SrF₂ laser was investigated by using a 1% OC. With chirped mirrors (CM1 and CM2) inserting in the cavity for dispersion compensation, the mode-locked laser delivered an average output power of 84 mW, corresponding to a single pulse energy of 0.95 nJ. The optical spectrum centered at 2069.3 nm has a spectral FHWM of 15.5 nm [see the green line in Fig. 4(a)]. The corresponding intensity autocorrelation trace is shown in Fig. 4(b), the pulse duration is 280 fs by assuming a sech²-shaped intensity profile. Similarly, stable mode locking could also be realized without CMs. In this case, the laser generated was 118 mW, corresponding to 1.33 nJ single pulse energy and 4.76 kW peak power. Figures 4(a) and (c) show the measured optical spectrum and the corresponding intensity autocorrelation trace. The optical spectrum centered at 2084.5 nm exhibits a perfect sech²-shaped intensity profile with a FWHM of 20.4 nm. The pulse duration amounts to 246 fs, yielding a TBP of 0.35, close to the Fourier transform limit of the sech²-shaped soliton pulses. The long-scale (15 ps) autocorrelation trace shown by the inset of Fig. 4(c), indicates a single-pulse laser operation without any satellite pulses.

 

Fig. 4. Optical spectra (a) and the corresponding intensity autocorrelation traces (b and c) of the SESAM mode locked Tm,Ho:SrF₂ laser at T_OC = 1% with and without CMs. The inset in (c) shows the intensity autocorrelation trace on a 15 ps time scale.

Download Full Size | PDF

Further pulse shortening into sub-200 fs regime was not achieved due to the following two reasons: I) the SrF₂ host crystal exhibits a much smaller n₂ value in comparison with other commonly used laser materials, e.g., 0.5 × 10⁻¹³ versus 2.5 × 10⁻¹³ for YAG and 5.8 × 10⁻¹³ for Y₂O₃ at 1.06 µm [24]. The smaller n₂ results in a less pronounced nonlinear effect and thus a much weaker self-phase-modulation (SPM) effect to broaden the optical spectrum during mode locking; II) the SPM coefficient is inversely proportional to the laser wavelength [25], again leading to a relative weaker SPM effect at 2 µm compared to that in the 1-µm spectral range.

Finally, an OC with a larger transmission of T_OC = 1.5% was also tested for mode locking. However, stable mode-locked pulse was not achieved and was accompanied by the presence of Q-switching envelope. This is attributed to the smaller pump parameter in this case failing to suppress the Q-switching, where the pump parameter refers to how many times the pump power is above the lasing threshold [26,27].

To further characterize the stability of the mode-locked Tm,Ho:SrF₂ laser, radio frequency (RF) spectra and real-time pulse trains of the shortest pulses were recorded. Figure 5(a) shows the fundamental beat note at ∼88.6 MHz with an extinction ratio of >50 dBc above the noise level. The uniform harmonic beat notes recorded in a 1-GHz frequency span with 300 kHz RBW are shown in the inset of Fig. 5(a), revealing stable steady-state CW mode locking operation. No Q-switching, multi-pulses, or short-term instabilities were observed in the recorded uniform real-time pulse trains on different time scales, as shown in Fig. 5(b).

 

Fig. 5. RF spectra of the mode-locked Tm,Ho:SrF₂ laser: (a) fundamental beat note and (inset)1 GHz span. (b) The typical pulse train on nanosecond and millisecond time scales. RBW, resolution bandwidth.

Download Full Size | PDF

4. Conclusion

Summarizing, CW, wavelength-tunable, and passively mode-locked laser operations of a Tm,Ho:SrF₂ crystal were comprehensively investigated. Without any additional intra- or extra-cavity dispersion compensation elements, mode locking of the Tm,Ho:SrF₂ laser was successfully realized, delivering 246-fs pulses at 2084.5 nm. This femtosecond laser with compact and simple configuration makes it a potential seed source for amplifier systems using large size available and gain profile matched Tm,Ho co-doped fluoride crystals as gain. Further pulse shortening is possible by enhancing the self-phase modulation effect with a high-power pump source, employing an additional Kerr medium with high nonlinear efficiency at a high intracavity power level [28], and optimizing the mixing ratio of Tm³⁺ and Ho³⁺ ions towards a broad gain spectrum through co-emission.