We report on the first investigation of a passive mode-locking Nd:LuLiF4 laser at 1047 nm with semiconductor saturable absorber mirror. The maximal average output power of 1.21 W was obtained with a slope efficiency of 10.8%, under an incident pump power of 12.6 W. The pulse duration of 5.1 ps and a spectral width of 0.45 nm were obtained with a repetition rate of 40 MHz. This corresponds to the single pulse energy of 30.3 nJ and the peak power of 5.93 kW.
© 2015 Optical Society of America
Ultrafast all-solid-state lasers operating in the infrared spectral regions provide a cost-effective solution for various applications compatible with moderate average powers, such as nonlinear microscopy, optical coherence tomography, medical treatment, and scientific research. Within an all-solid-state ultrafast laser technology, semiconductor saturable absorber mirrors (SESAMs), especially those with quantum-well structures, have been widely used for passive mode-locking because of its advantages of compact, fast, and cover band gaps from the visible to the infrared [1–3]. Pulse durations range from picoseconds to a few femtoseconds, depending on the laser media and the parameters of the saturable absorber. Nd-doped host materials have already been employed as laser gain media working at passive mode-locking with SESAMs. The pulse durations of 2.8 ps, 6.8 ps, and 2.8 ps for Nd:YLF, Nd:YAG, and Nd:YVO4 have been reported [4,5].
Compared with oxides, fluoride crystals are more attractive owing to their high transparency in a wide wavelength range and low phonon energy which reduces non-radiative relaxation between adjacent energy levels. A new fluoride crystal, LuLiF4, like its isomorphs YLF, has been emerged as a new promising diode-pumped laser crystal. The Nd:LuLiF4 (Nd:LLF) crystal has several advantages such as negative thermal dependence of refractive index, which can lead to a weak thermal lens, and strong spectral anisotropy for polarized absorption and emission. And the Nd:LLF crystal is evaluated to determine whether compositional wavelength tuning would be practical, that is, changing the laser wavelength by a partial-to-total substitution of Lu for Y in the laser material. The laser operations of Nd:LLF material are based on the strong transitions and manifolding with nominal wavelengths of 1.05 and 1.32 μm, respectively [6–8]. Though, Nd:LLF has a smaller emission cross-section (17.3 × 10−20 cm2 for π polarization) at 1047 nm and a higher upper-state lifetime (489 μs)  compared with Nd:YVO4, requiring careful design of the laser resonator to avoid Q-switching instabilities.
The Nd:LLF laser performances have been investigated by several groups. A laser-diode-pumped continuous wave (CW) Nd:LLF laser has been reported by Kaminskii et al. with 150 mW output power at 1047 nm in 1993 . In 2011, Li et al. presented a 1047 nm wavelength Nd:LLF laser with maximal CW output power of 1.3 W . And the diode-pumped 910 nm CW laser of Nd:LLF crystal was investigated by Zhao et al. in 2012 . Wang et al. demonstrated 808 nm diode-pumped tunable continuous wave and passively Q-switched Nd:LLF laser with monolayer graphene in 2015 . Meanwhile, efficient CW dual-wavelength laser at 1314 and 1321 nm and passively Q-switched Nd:LLF laser with V:YAG was also reported in 2013 . One can see that the investigations on the Nd:LLF crystal are mainly focused on CW and passively Q-switched laser performance. To the best of our knowledge, there is no investigation on passive mode-locking Nd:LLF laser with a semiconductor saturable absorber mirror at 1047 nm.
In this paper, we have experimentally investigated 792 nm diode-pumped passively mode-locked Nd:LLF laser performance with a SESAM for the first time. The 5.1 ps pulse duration was obtained with the repetition rate of 40 MHz. The maximum average output power of 1.21 W was achieved at an incident pump power of 12.6 W. A single pulse energy and a peak power were calculated to be 30.25 nJ and 5.93 kW, respectively.
Resonator design to prevent Q-switching instabilities
For easy to occur Q-switching instabilities in mode-locked operation, the design of such a laser is challenging because of the low emission cross section of gain medium . In order to suppress Q-switching mode-locking (QML), the intra-cavity pulse energy needs to surpass the critical pulse energy which can be given by 
The saturation fluence of the gain medium is defined as
Due to the low emission cross-section of Nd:LLF, the resonator cavity needs to be carefully designed to avoid Q-switching instabilities. Generally, higher intra-cavity pulse energies help to prevent QML, which can be obtained by operating at lower repetition rate or higher average output power. Meanwhile, smaller spot size in the gain medium or on the SESAM, and more passes through the gain material per round trip also help to avoid Q-switching instabilities. The intra-cavity pulse energy and peak power need to be well below the damage threshold of the SESAM to prevent the saturable absorber from optical damage. As shown in Fig. 1, a five-mirror W-shape resonator with a total cavity length of 375 cm was employed to reduce the repetition rate and increase the longitudinal mode which is favorable for stable continuous wave mode-locked operation. The lengths of the four cavity arms L1, L2, L3, and L4 were carefully optimized to be 70.5, 93.5, 200, and 11 cm, respectively. Using the ABCD transfer matrix, the estimated mode radii in the gain medium and on the SESAM were 94 and 27 μm, thus the critical intra-cavity pulse energy was 64 nJ calculated by Eq. (1).
The schematic setup for passive mode-locking laser with a SESAM is depicted in Fig. 1. The flat mirror M1 was high-reflection (HR) coated at 1047 nm. M2 and M3 were HR coated at 1047 nm with radii of curvature of 1000 and 200 mm, respectively. A flat mirror with the transmission of T = 4% was employed as output coupler (OC). The cavity parameters were designed in principle to satisfy mode matching with the pump beam and the proper spot size on the SESAM. In order to minimize astigmatism of the laser system, the M2, M3, and OC were arranged as small folded angles as possible. The high-quality a-cut Nd:LLF crystal with Nd-doping concentration of 1 at. % was grown by the Czochralski method, with a dimension of 3 × 3 × 6 mm3. The two faces of the crystal were polished and antireflection (AR)-coated at 792 nm and 1047 nm. The pump source comes from a 30 W fiber-coupled 792-nm laser diode. The fiber core is 200 µm in core diameter with a numerical aperture (NA) of 0.22. The pump beam was focused into the laser crystal by the focusing optics with a beam radius of ~100 µm. The central wavelength of pump source can be slightly adjusted by changing the temperature to match the Nd:LLF absorption peak near 792 nm. To efficiently cool the crystal and avoid thermal fracture, the crystal was wrapped with indium foil and mounted on water-cooled copper heat-sink whose temperature was maintained at 13 °C during the whole experiment process. The host medium was placed near the input mirror and tilted slightly to avoid on-axis reflections which generate a coupled cavity that can narrow the gain bandwidth and hinder the mode locking . The SESAM (BATOP GmbH) was employed to sustain the mode-locking. The pulse temporal behavior was recorded by a digital oscilloscope (1 GHz bandwidth and 20 G samples/s sampling rate, Tektronix DPO7102 Inc., USA) and a fast pin photodiode detector with a rise time of 0.4 ns. A laser power meter (MAX 500AD, Coherent, USA) was used to measure the average output power.
Experimental results and discussions
Owing to the negative thermal dependence of refractive index, the estimated focal length of the gain medium  was negative as displayed in the right ordinate of Fig. 2. Using the ABCD matrix and considering the thermal lens effect of the gain medium, we simulated the radii of the TEM00 mode as described in the left ordinate of Fig. 2. With the increase of incident pump power, the TEM00 mode radii in the gain medium and on the SESAM were 100-83 μm and 24–47 μm, respectively. As shown in Fig. 2, the mode radius on the SESAM increases with the increase of the incident pump power, thus could protect the SESAM from damage with high incident pump power.
The relation between output power and incident pump power was shown in Fig. 3. The cavity was first characterized in CW-regime, with an HR mirror instead of the SESAM. At an incident pump power of 12.6 W, a maximum output power of 1.35 W was achieved with a slope efficiency of 11.8%. Meanwhile, the threshold pump power was 0.95 W. Then in the subsequent passive mode-locking regime, OC with the same transmission of T = 4% was employed.
When the average output power exceeded 0.25 W, a stable mode-locking laser was observed, corresponding to a threshold pump power of 3.9 W. At this pump power, the TEM00 mode radii in the gain medium and on the SESAM were 95 μm and 28 μm in Fig. 2, respectively. So the theoretical estimated critical average output power obtained from Eq. (1) was 0.12 W which was lower than the experimental result of 0.25 W. The maximal average output power of 1.21 W was achieved with an incident pump power of 12.6 W, corresponding to a slope efficiency of 10.8% and an optical efficiency of 9.6%. The average output power was larger than those gotten by Nd:YLF lasers [1,18], but the value of the optical efficiency was lower than the data given in Refs . and . When compared with passive mode-locking lasers using SESAM as saturable absorber, the average output power and the optical efficiency were higher than those obtained by Nd:GGG  or Nd:LGGG  crystal, but smaller than those achieved by Nd:Gd0.5Y0.5VO4 crystal . The output powers shown in Fig. 3 were the total of two beams through OC. Though no power saturated was shown in Fig. 3, we did not add incident pump power further to protect the gain host and the SESAM from damaging.
The typical pulse train in 50 ns and 2 ms per division time scales are shown in the inset of Fig. 4 and Fig. 4, respectively, which were measured under an incident pump power of 12.6 W. One can see that the pulse train had a good pulse shape in short time span and a good stability in long time span. And the pulse repetition rate was 40 MHz, which was corresponding to the cavity length of 3.75 m. The corresponding single pulse energy and peak power were 30.25 nJ and 5.93 kW, respectively.
The pulse duration was measured by a commercial Pulse Check noncollinear autocorrelator (APE Inc.). Figure 5 shows the autocorrelation trace of the output pulse and the corresponding spectrum recorded by a laser spectrometer (APE Wavescan APE Inc.) with a resolution bandwidth of 0.05 nm at the maximal average output power of 1.21 W. The pulse was an autocorrelation signal with a FWHM of 7.8 ps. Taking a hyperbolic secant (sech2), the estimated pulse duration is about 5.1 ps. The emission spectral bandwidthof 0.45 nm (FWHM) was measured at the central wavelength of 1046.4 nm, corresponding to = 123.3 GHz. Thus, the time-bandwidth product of the pulses is about 0.628, which is 1.99 times of the theoretical transform-limited value (0.315) for sech2 soliton mode-locking pulses. By inserting negative dispersion elements, the intra-cavity dispersion can be appropriately compensated and the pulse duration can be reduced further. By employing 10.0/90.0 knife-edge method, the beam quality of the passive mode-locking laser was measured to be 1.11 in tangential plane and 1.21 in sagittal plane under an average output power of 1.21 W, which was near diffraction limited, see Fig. 6.
In conclusion, we have successfully investigated the passively mode-locked Nd:LLF laser performance with a SESAM for the first time. 40-MHz CW mode-locking pulse trains with an average output power of 1.21 W and a pulse duration of ~5.1 ps were generated at an incident pump power of 12.6 W, corresponding to a single pulse energy and a peak power of 30.25 nJ and 5.93 kW, respectively.
The research leading to these results were supported by the Natural Science Foundation of Shandong Province, China (ZR2013FM027), the National Science Foundation for Distinguished Young Scholars of China (No. 61308020), and Independent Innovation Foundation of Shandong University, IIFSDU (2082014TB011).
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