Efficient, diode-pumped, high-power (>300W) cryogenic Yb:YLF laser with broad-tunability (995-1020.5 nm): investigation of E//a-axis for lasing.

We present, what is to our knowledge, the first detailed lasing investigation of cryogenic Yb:YLF gain media in the E//a-axis. Compared to the usually employed E//c-axis, the a-axis of Yb:YLF provides a much broader and smooth gain profile, but this comes at the expense of reduced gain product. We have shown that, despite the lower gain, which (i) increases susceptibility to cavity losses, (ii) raises lasing threshold, and (iii) inflates thermal load, efficient and high-power lasing could be achieved in the E//a axis as well. A record continuous-wave (cw) powers above 300 W, cw slope efficiencies of 73%, and a tuning range covering the 995-1020.5 nm region were demonstrated. In quasi-cw lasing experiments, via minimization of thermal effects, slope efficiencies can be scaled up to 85%. In gain-switched operation, sub-50-µs long pulses with a peak power exceeding 2.5 kW at multi-kHz repetition rate were attained. We measured a beam quality factor below 1.5 for laser average powers up to 100 W and below 3 for laser average powers up to 300 W. Power scaling limits due to thermal effects, laser dynamics in pulsed pumping, and multicolor lasing operation potential were also investigated. The detailed results presented in this manuscript will pave the way towards development of high-power and high-energy Yb:YLF oscillators and amplifiers with sub-500-fs pulse duration.

One of the main drawbacks of Yb:YAG media is its relatively narrow and steep gain profile. The gain bandwidth of Yb:YAG at room temperature has a full-width-half-maximum (FWHM) of 8 nm ( Fig. 1(b), calculated for an inversion level of 25%), and this enables generation of down to 35 fs long pulses in RT mode-locking [26]. On the other hand, as it can be seen from Fig. 1(b), the gain profile has an almost triangular shape around the gain peak; and hence, in regenerative or multipass amplifiers based on RT Yb:YAG, where orders of magnitude amplification is required, strong gain narrowing effect is present and the achievable pulsewidth upon amplification is usually limited around 1 ps (requires a great effort on the seed source side to reach shorter pulses: as in [27], where 615 fs long 17 mJ pulses was reported). Once cooled to liquid nitrogen temperatures, the bandwidth of Yb:YAG reduces to just around 1.5 nm, limiting the obtainable pulsewidths to few picoseconds upon amplification. Hence, research for alternative laser/amplifier materials with strong thermo-opto-mechanical parameters and broad emission bandwidth is ongoing. (b) Comparison of effective gain cross section of Yb:YLF (E//a, 80 K) with room temperature (RT:300 K) and cryogenic (80 K) Yb:YAG. An inversion level of 25% is assumed for Yb:YAG, and all curves are shown in normalized units. The Yb:YLF gain profile is broader (10 nm), and smoother compared to Yb:YAG (8 nm). The flatter gain profile enables smoother tuning in lasing operation, and minimizes gain narrowing effect in amplifier applications.
As a promising alternative material, Yb:YLF gain medium is known to possess a broader emission band centered around 1015 nm even at cryogenic temperatures [28][29][30][31]. As can be seen from Fig. 1(b), for the E//a axis, the Yb:YLF has a gain bandwidth of 10 nm, which is even broader than that of RT Yb:YAG. Moreover, the gain profile has a much smooth/flat shape, that could potentially minimize the effect of gain narrowing upon amplification. In terms of emission cross section, as usual, the price one pays for broader bandwidth is a lower emission cross section (σ em : 0.7 × 10 −20 cm 2 ). The longer fluorescence lifetime of Yb:YLF (τ:1990 µs [22]), partly balances for the gain, resulting in a gain product (σ em τ) of 1.4 x10 −23 cm 2 s, but this is still lower than the value of RT Yb:YAG (2 x10 −23 cm 2 s). Note that for the E//c axis, the gain product of Yb:YLF is as high as 8.95 x10 −23 cm 2 s around 995 nm, and 2.5 x10 −23 cm 2 s around 1020 nm, but these transitions are quite narrow ( Fig. 1(a)), and are not really suitable for ultrashort (sub-ps level) pulse amplification. For the broadband E//a axis, besides the low gain product, one also suffers due to the relatively high saturation fluence (14.1 J/cm 2 ), that create challenges in optimizing extraction efficiency. In addition, cavities based on Yb:YLF are more sensitive to losses and care should be taken in minimizing the loss level of Yb:YLF based systems. On the positive side, parameters such as thermal conductivity, thermal expansion coefficient, thermo-optic coefficient (dn/dT) are better compared to room temperature Yb:YAG. Moreover, Yb:YLF thermo-optic coefficient has a negative value, which provides a knob for a laser engineer in designing laser systems with minimal thermal lens. Furthermore, unlike Yb:YAG, efficient lasing could also be obtained in heavily doped Yb:YLF samples [32,33] (i.e. 60% doping is used in [28]), that is potentially an advantage in TD geometry.
In spite of the aforementioned advantages, research interest towards Yb:YLF was rather weak so far. Table 2 [21,23,28,32,[34][35][36][37][38][39][40][41] which presents a detailed summary of lasing results obtained with Yb:YLF shows that earlier high-power (>10 W) lasing studies mostly explored E//c axis of Yb:YLF at cryogenic temperatures [21,29,37]. On the other hand, the main advantage of Yb:YLF is its broad/smooth emission band in the E//a axis, where the gain is 6.4 fold lower (compared to the 995 nm line of the E//c axis). Despite lacking high-power lasing results, the broad emission band of the E//a axis was heavily explored in Yb:YLF amplifiers [42][43][44][45], and average powers up to 100 W was already demonstrated [44]. Hence, we believe that, there is a further need to investigate lasing potential in the E//a axis of Yb:YLF at cryogenic temperatures, in terms of power scaling prospects and tunability to understand the usability of Yb:YLF in high average power sub-500-fs lasers/amplifiers. In this study we have thoroughly investigated power scaling potential of cryogenic Yb:YLF lasers for the E//a axis, in continuous-wave, quasi continuous-wave and gain-switched modes of operation. A state-of-the-art 2 kW pump module at 960 nm was used to pump a 2 cm long 0.5% Yb-doped Yb:YLF crystal. In cw lasing experiments, using a simple & compact flat-flat laser cavity, record cw output powers as high as 310 W was obtained around 1018 nm and laser slope efficiencies of 73% were demonstrated. Tuning of the laser wavelength in the 995-1020.5 nm region was further achieved, and tendency of the laser system for multicolor laser operation was shown. Effect of pump spot diameter on laser performance was analyzed. In quasi-cw and gain-switched lasing experiments, variation of laser average and peak power with output coupling, pump pulsewidth duration, repetition rate, duty cycle, and pump spot diameter were investigated. In quasi-cw experiments, with the minimization of thermal effects, a record slope efficiency of 85% was realized. Gain-switched operation resulted in generation of sub-50-µs long pulses with peak powers exceeding 2.5 kW at multi-kHz repetition rates. The laser output beam was quite symmetric and had a measured beam quality below 1.5 and 3 for laser powers up to 100 W and 300 W, respectively. To our knowledge, in this paper, we are presenting: (i) a first detailed study focusing on high-power lasing investigation of cryogenic Yb:YLF in E//a axis, (ii) record output power levels in cw operation, (iii) record slope efficiencies in quasi-cw operation, (iv) an investigation of effect of pump spot size in laser performance and (v) first comprehensive tuning results and first report of multi-color lasing with Yb:YLF.
The paper is organized as follows. Section 2 provides details on the experimental setup, and discuses effectiveness/limits of boiling liquid-nitrogen cooling. In section 3 we present the experimental results on quasi-cw lasing, cw lasing, gain-switched lasing and finally on tunable lasing. We finalize the paper with a brief conclusion in Section 4. Figure 2 shows a schematic of the cryogenic Yb:YLF laser that is used in cw, quasi-cw and gain-switched lasing experiments. The state-of-the-art fiber coupled diode module provided up to 2 kW of output power at a central wavelength of 960 nm. A 600 µm core diameter fiber with a numerical aperture (NA) of 0.22 was used to transfer the pump beam. The fiber coupled pump beam had a specified beam parameter product of 0.66 mm mrad, a full divergence angle of 25.2°, and an estimated M 2 of 220. Note that a smaller core fiber or a lower numerical aperture was not possible at this 2 kW pump power level due to the limited brightness of single-emitter multimode diodes. Hence, in this study, compared to earlier work, we had higher pump powers at the expense of reduced brightness due to the requirement to use the large core fiber. The pump output from the fiber tip is first collimated with a 72 mm focal length 2-inch lens (f1). Later, a focusing lens with a focal length of 250 mm was used to obtain a pump diameter of 2.08 mm inside the gain element. The pump beam at focus had a flattop profile [46], and Fig. 3 shows detailed information on pump caustic. Note that, in one set of experiments, to investigate the effect of pump spot size on laser performance, we have used alternative focusing lenses (f2) of 200 mm and 300 mm to obtain pump spot sizes of 1.67 mm and 2.5 mm. All the laser experiments except what will be presented in Fig. 7, were performed using the 2.08 mm (∼2.1 mm) beam. With the 72-mm (f1) collimating and 250-mm (f2) focusing lens, the pump beam is focused at a distance about 225 mm away from the focusing lens. The laser was built at this focus directly, without re-imaging, resulting in a relatively compact laser setup. First, a flat dichroic mirror (DM) was used at a small angle to pick a few percent of the pump to diagnose incident pump power via power meter 1 (PM1). The remaining pump light is focused inside the Yb:YLF crystal, where the focal point was around the center of the gain element. The laser cavity consisted of a flat dichroic mirror and a flat output coupler. In most of the laser experiments, a cavity length of 18 cm were employed (smaller cavities were not possible due to the size of the dewar at hand). In the experiments output couplers with transmissions of 10%, 20%, 40% and 60% were investigated. The dichroic mirrors had a reflectivity higher than 99.9% in the 990-1040 nm range, and had a transmission > 99% around 960 nm. The laser gain element was a 0.5% Yb-doped 20 mm long Yb:YLF crystal (10 mm x 15 mm cross section), and contained 3-mm-long un-doped end cap diffusion bonded sections on both ends to minimize surface deformations under thermal load. The surfaces contained antireflection coatings that were effective both at the pump and laser wavelengths. The Yb:YLF crystal was a c-cut sample; and hence, the E//a axis was available for lasing experiments. On the other hand, the c-axis was oriented 10°away from the direction of propagation to create some natural birefringence to minimize depolarization losses that could be activated by stress-induced birefringence (see Fig. 1(b) in [44] for a sketch of crystal orientation). Moreover, the two surfaces of the crystal were wedged with respect to each other to minimize parasitic effects. The crystal was indium bonded from the top side to a cold head, which was cooled by boiling liquid nitrogen. Antireflection coated windows on each side of the crystal enabled the entrance and exit of the pump and laser beams to the dewar. The remaining non-absorbed pump beam passing through the output coupler is separated from the laser beam via another flat DM. The transmitted pump power and the output laser power were measured using PM2 and PM3, respectively. For tuning experiments, the cavity length is extended to around 25 cm, and a 2 mm thick crystal quartz birefringent filter, and a thin-film polarizer were inserted at Brewster's angle for wavelength control. The laser wavelength was monitored using a 3648 pixel CCD array (Toshiba TCD1304AP) based spectrometer with a resolution of 0.1 nm.

Experimental setup
As a side information, as it is done in this study, liquid nitrogen is mostly used in cooling cryogenic laser/amplifier systems to low temperatures due to ease of use and lower cost of operation. In a typical system, a thermal cold head in contact with liquid nitrogen (LN 2 ) extracts the heat load from the laser material. This enables a boundary temperature of 77 K on the cold side of the cold head, and with that in well-designed systems crystal temperatures could be ideally kept below 100-120 K (even under heavy thermal load). The main disadvantage of this cooling system is the appearance of insulating nitrogen gas between the liquid nitrogen and the cold head due to the boiling process of LN 2 (Leidenfrost effect) [47][48][49]. As a result, the cooling efficiency is rather limited, and typical heat extraction coefficients that could be reached is around 10 kW/Km 2 at the LN 2 boundary [47][48][49], and with heat spreading engineering cooling efficiency could be improved to 20-30 kW/K m 2 level at the crystal boundary. Hence, despite all the aforementioned advantages, there are limits in power scaling imposed by the restrictions of boiling liquid nitrogen boundary conditions, which has not been studied thoroughly for Yb:YLF systems yet (due to limited pump power levels in earlier studies).

Quasi-continuous-wave (long-pulse) lasing results
We would like to start the presentation of lasing results with Fig. 4, which shows the measured performance of the cryogenic Yb:YLF laser in long pulse or quasi-cw operation, using several different output couplers with transmission values ranging from 10% to 60%. The specific data in Fig. 4 is taken while pumping the Yb:YLF laser with 10 ms long pump pulses at 10 Hz, with a corresponding duty cycle of 10%. Measured laser efficiency curves are presented in Fig. 4(a), and variation of pump absorption with incident pump powers at different output coupling are presented in Fig. 4(b). Note that, for the 10% OC, we have not used the full available pump power, to prevent possible damages to the optics due to the high intracavity laser power levels. Among the output couplers we have tried, the best laser performance was obtained with the 20% OC. With this OC, the laser had a lasing threshold of about 8 W (average power), and a slope efficiency of 77% with respect to absorbed pump power could be observed. Average output powers as high as 102 W was obtained at incident and absorbed pump power levels of 192 W and 146 W, respectively. The corresponding peak powers were as high 1020 W. Optical-to-optical conversion efficiency of the system was above 53%. Note from Fig. 4(b) that, at low incident pump powers, pump absorption is only around 40%, but as the incident powers increase, with the stabilization of diode temperature, better matching of the diode wavelength to the 960 nm absorption peak improves absorption amount, and at higher pump powers the pump absorption exceeds 75%.
The highest slope efficiency was obtained with the 40% OC, where we have achieved a slope efficiency of 85% with respect to the absorbed pump power. For the 960 nm pumped cryogenic Yb:YLF laser operating at 1016 nm, the quantum limited slope efficiency is 94.5%. The slope efficiency obtained in this study (85%) is very close to the quantum limited efficiency for the system. This is good indication of good mode matching between the pump and the laser modes, which was an open question due to the low beam quality of the pump module (M 2 ∼220 as discussed earlier). This also shows that the total cavity losses were low compared to the output coupling used (40%) in obtaining this efficiency. To confirm this, we have also measured the losses of the cavity using a Yb-fiber laser operating at 1020 nm [50], and found a round-trip loss value of around 6%, which could be further reduced via minimizing the loses in the cryogenically cooled crystal setup. As another note, to our knowledge, this is the highest slope efficiency reported from any cryogenic Yb:YLF lasers to date ( Table 2). A close slope efficiency of 82% was reported in [21], but this was with a higher brightness diode array, and for a 960 nm pumped 995 nm Yb:YLF laser, where the quantum defect limited slope efficiency is higher (96.5%). The laser output beam profile were measured at selected representative power levels for the 20% and 40% OCs, and the results are shown in Figs. 4(c) and (d). At low laser average powers, the laser output beam profile was very close to a Gaussian TEM 00 mode, and the M 2 of the beam was measured to be below 1.1. As the laser power levels were increased further, the laser output beam turned into a flattened Gaussian profile [46]. This is expected since the mode-matching between the pump and laser modes were good, and the pump had a flattop beam profile. On the other hand, at all average power levels, we have measured the M 2 of the output beam to be below 3. Later, while presenting the pure cw lasing results, this issue will be discussed in more detail.
In Fig. 5(a) lasing performance of cryogenic Yb:YLF laser is shown at again 10 Hz, but this time using different pump pulsewidths in the range from 5 ms to 100 ms. All the data is taken at an output coupling of 20%, which we have shown to be the optimum coupling in the current setup. Note that the corresponding duty cycle is between 5% to 100%, where 100 ms 10 Hz operation corresponds to true cw pumping/lasing, which will be discussed in more detail in the next section. As a side note, while performing this experiment in the lab, we have realized that, at the low duty cycles (5-10%) the laser was very stable (in terms of output power fluctuations and pointing), thermal effects were minimal, and the obtainable output powers were limited by the available pump power level. At moderate duty cycles (25-50%), due to the increased role of thermal effects, the laser become less stable. At even higher duty cycles, the cavity stability improved again (e.g. performance at 75% duty cycle was better compared to 25% duty cycle). This we believe is due to the stabilization of thermal lens and the cavity mode generated by the thermal lens at higher duty cycles. However, for all cases, for absorbed pump powers roughly above 500 W, it was not possible to increase the obtainable output powers further, even with careful cavity realignment. We believe this point is imposed by the heat extraction capability of the boiling liquid nitrogen boundary (as discussed in the experimental section), which puts a hard barrier to laser performance independent of the pumping conditions. Note that, we have still reached record output powers above 300 W in cw operation, which will be discussed in the upcoming sub-section.
In another experiment, we have fixed the pump pulsewidth to 5 ms level, and varied the repetition rate between 10 Hz and 200 Hz (Fig. 5(b)). Here a 5 ms long pump pulsewidth is chosen in purpose, since in our earlier multipass with Yb:YLF amplifiers, we have seen that this pump pulsewidth is a reasonable value for pumping the Yb:YLF gain media (2.5 times longer than the 2 ms fluorescence lifetime of Yb:YLF) [51]. So, one can see this experiment as the investigation of repetition rate scaling potential of cryogenic Yb:YLF multipass amplifiers, but of course the lasing physics observed here is quite different than the mechanism that will be observed in a seeded amplifier with limited number of passes through the gain media. So the results in Fig. 5(b) should be considered as an upper limit for multi-pass amplifier performance in terms of obtainable average power levels.

Continuous wave lasing results
In this subsection, we would like to present cw lasing results we have obtained with the cryogenic Yb:YLF laser. For that purpose, Fig. 6(a) shows the measured variation of laser output power with the absorbed pump power amount, using the 20% and 40% transmitting output couplers. Besides the laser output power, measured absorption of the crystal during cw lasing ( Fig. 6(b)), typical near-filed (NF) and far-field (FF) beam profiles at selected output power levels (Figs. 6(c) and 6(d)), and measured M 2 value at different power levels (Fig. 6(e)) are also shown. Note that, we have not taken cw data with the 10% OC due to the risk of damage to the dewar windows, which we believe to have some growth issues that resulted it relatively low laser induced damage thresholds. Also, no data could be taken with the 60% OC, because of thermal effects (lasing threshold was too high to obtain useful laser output powers).
In the cw laser experiments with the 20% transmitting OC, we have achieved cw powers up to 305 W at an incident pump power of 656 W. Effective absorption of the system was around 78%, and hence the corresponding absorbed pump power was around 513 W. The optical-to-optical conversion efficiency of the system was 46.5%. The lasing threshold of the system was 63 W, and the slope efficiency with respect to pump power was around 66%. To our knowledge, the cw output powers obtained in this study is the highest output powers ever obtained from any Yb:YLF laser system to date ( Table 2). The measured near and far file beam profiles as well as the measured M 2 of the laser output beam at different output power levels show that: (i) for laser powers up to around 100 W, the output beam is quite symmetric and has an almost TEM 00 beam profile, and a beam quality better than 1.5 (ii) as the output power increases the output beam profile starts to resemble the flat-top beam profile of the pump, (iii) above 200 W power level the output beam gets slightly asymmetric due to the one sided cooling geometry applied in this work, and finally (iv) despite all of this, the beam quality of the laser stays below 3 in all cases.
For the 40% transmitting OC, the lasing threshold increased to 155 W, and the slope efficiency of the system improved to 73%. Note that, the increase in lasing threshold from 63 W to 155 W is more than what is expected (∼110 W: total loss of the cavity increased from around 26% to 46%, where 6% is the measured round-trip passive losses of the cavity, and 20 and 40% are the losses due to output coupling). We believe this unexpected increase observed in lasing threshold is mostly due to the increased role of thermal effects, creating issue on the generation of a stable cavity mode that could mode-match to the pump mode effectively. On the other side, we have estimated the small-signal self-absorption losses of the 0.5%-doped 2 cm long Yb:YLF crystal that at 1018 nm as 0.04%, 0.23% and 0.71% at temperatures of 80 K, 100 K and 120 K, respectively. Hence, a small increase of self-absorption losses is also expected with increasing temperature, which should be also contributing to the observed increase in lasing threshold.
To investigate the effect of pump spot diameter on laser performance, we have also taken cw data with the 20% output coupler using pump spot sizes of 1.67 mm and 2.5 mm (Fig. 7). As expected, with the increasing gain, the laser threshold decreased from 63 W to 25 W level, when the pump spot diameter decreased from 2.08 mm to 1.67 mm. Inversely, the lasing threshold increased to 85 W level for the spot size of 2.5 mm. Using the 1.67 mm beam, we have achieved cw output powers as high as 310 W, and a slope efficiency of 67% frrom the system. Note that, compared to the 2.1 mm pump beam, the observed improvement in laser performance for the 1.67 mm is minimal, and the system again did not allow usage of pump powers above 500 W level. On the other hand, with the larger 2.5 mm spot size, the thermal effects get worse, and we could only reach an output power level of around 220 W. These findings also indicate that, the 2.1 mm spot size is about the optimum value for this geometry.
In closing this sub-section, we would like to underline the important difference in fractional thermal load caused by the absorbed pump power in lasing and non-lasing conditions. Note that, when the system is lasing and the extraction efficiency is high (60-80%), most of the absorbed pump power applied to the system (above the lasing threshold) is extracted out with the laser beam. Hence, the fractional thermal load on the crystal is expected to be slightly above the quantum defect limit (5.5%) [52]. On the other hand, when there is no lasing (such as the threshold pump power we use to just attain lasing), all the energy stored in the system is extracted via the spontaneous emission process [52]. In this case, ideally, one should also encounter a similar fractional thermal load since there is not any known nonradiative transition process in Yb:YLF that could result in additional heat load. However, in our setup, we have realized that, possibly due to effects such as radiation trapping and undesired re-entry of the fluorescence emission back into the crystal, or via the absorption of the spontaneously emitted light by the cold head, the observed fractional thermal load was higher. Hence, the 500 W absorbed pump power limit we have discussed above as a hard barrier to laser performance due to liquid nitrogen boundary is only valid for efficiently operating systems with low lasing threshold. As we see in the cw experiments with the 40% OC, once the lasing threshold is high, the increased fractional thermal load of the system reduces the maximum applicable power level on the system. We expect that, the maximum average power applicable to the system under non-lasing conditions is limited to around 350 W level. Of course, usage of longer crystal, pumping from both sides rather than one side, improving the liquid nitrogen contact via using liquid nitrogen jets rather than a boiling liquid nitrogen contact, usage of a better heat spreading geometry, or using more than one crystal could all improve the performance of the Yb:YLF lasers in the future.

Gain-switched (short-pulse) operation
In Section 3.1, we have already discussed long-pump pulsed (quasi-cw) operation of cryogenic Yb:YLF laser, and presented lasing data with ≥ 5 ms pump pulses. In this sub-section, we would like to extend pulse pumping discussion towards shorter pulses and higher repetition rates. We will name this section as "gain-switched" operation, since in most of the cases that will be discussed, the pump pulses that are applied are shorter than the upper state lifetime of the Yb:YLF gain medium.
As a starting point, Fig. 8 shows the measured laser performance of the cryogenic Yb:YLF laser using the 20% output coupler at repetition rates between 10 Hz and 2.56 kHz. While taking the data in Fig. 8, the pump peak power was kept at 2 kW, and pump pulsewidth is varied to change the amount of average power on the crystal. Note that the horizontal scale in the graphs is in logarithmic units. Moreover, in the graph both the (a) average and (b) peak power of the laser pulses are presented. Here, the peak power values in Fig. 8(b) are calculated by dividing the average laser power with pump duty cycle. Hence, the calculation of laser peak power assumes a square laser pulse with a width same as the pump pulse. As we will discuss later, this assumption is not valid for short pump pulsewidths, but is a good starting point for a rough estimation. Note from Fig. 8 that, except the data taken at 10 Hz and 20 Hz, within experimental errors, the laser provided about the same average (∼250-300 W) and peak power (∼kW) levels. While operating at 10 Hz, relatively long pump pulsewidths is required to apply reasonably large average powers on the crystal. For example, a 10 ms pulse at 10 Hz only provides around 190 W of incident power on the crystal (10% duty cycle), where as a 1 ms pulse at 100 Hz is sufficient enough to provide a similar incident pump power level. If the thermal effects at similar average powers were to be same, one would expect similar laser performance at different repetition rates. However, as we see the laser performance at 10 Hz was considerably lower than those at higher repetition rates due to the earlier onset of thermal effects. This clearly shows that, thermal effects do not only depend on average power (average thermal load), but also on the distribution of the thermal load in time. Therefore, we can say that the Yb:YLF system was not in favor of pulsed pumping for pump pulses longer than around 10 ms at 2 kW incident pump power level. On the positive side, we have seen that, the laser performance is quite good in gain-switched operation at higher repetition rates. However, similar to the results presented in earlier sections, once the absorbed pump powers exceeded ∼500 W level, it was not possible to improve the laser performance further, and this limited the average powers to 250-300 W regime. Fig. 8. Variation of cryogenic Yb:YLF laser's (a) average power, and (b) peak power with pump pulse-width duration for repetition rates ranging from 10 Hz to 2.56 kHz. The data is taken using a 20% transmitting output coupler, at a constant pump peak power of 2 kW. As mentioned earlier, the peak powers shown in Fig. 8(b) are rough estimates, and the actual values were higher. To elaborate on this issue, Fig. 9 shows the measured time dynamics of the Yb:YLF laser (a) at 1 kHz with 100 µs long pump pulses, and (b) at 100 Hz with 1 ms long pump pulses. In the traces, we have shown time dynamics of the incident pump, transmitted pump, inversion and laser output. The curve for inversion is measured by monitoring the amount of instantaneous spontaneous emission using a detector positioned perpendicular to the optic axis of laser light. Note that the inversion curve is only a best effort measurement, since it contains some small portion of scattered laser light as it is evident from the rapid oscillations coinciding with the oscillations in laser output. Looking at Fig. 9, we see that, at higher repetition rates, as one decreases the pump pulsewidth, and as the operation regimes moves from quasi-cw towards gain-switching, the laser pulse starts to become considerably shorter than the pump pulse. As an example, as we can see in Fig. 9(b), at the repetition rate of 100 Hz, when the system is excited with a 1 ms pulse, due to the delay in lasing, the laser pulse had a width of only around 750 µs. One can also notice that, the laser pulse actually consists of many shorter pulses, and the initial relaxation oscillation process creates pulses with quite high peak power. Self-pulsing is quite often observed in laser materials with long fluorescence lifetime such as Cr:LiCAF [53] and Alexandrite [54], and considering its relatively long lifetime, it is not a surprise to see rich laser dynamic in the Yb:YLF crystal as well. Fig. 9. Measured variation of the Yb:YLF laser output in the time domain for gain-switched mode of operation, while pumping with: (a) 100 microsecond long pump pulses at 1 kHz repetition rate, (b) 1 ms long pulses at 100 Hz repetition rate. The data is taken with the 20% transmitting output coupler at a pump peak power of 2 kW.
As another example, Fig. 9(a) shows the laser dynamics at 1 kHz repetition rate with 100 µs long pump pulses. We already see from the figure that the diode laser module is having difficulty in creating these short pulsewidths, and the pump pulse had a width of around 150 µs (rather than the desired 100 µs length), where as the laser pulses had a width of around 60 µs. We can see that, in a similar manner, multiple pulsing phenomena creates shorter and higher peak power spikes within the main laser pulse envelope. Note also that, at these high repetition rates, the time interval between each pulse gets comparable and even shorter then Yb:YLF lifetime (2 ms), and hence, the created inversion is efficiently shared by the pulse train. In the experiments, pulses as short as 30-40 µs was observed at repetition rate of 2.56 kHz, and the estimated peak power of the pulses exceeded 2.5 kW level. Note that the corresponding pulse energy of the system is around 107 mJ at 2.56 kHz, 235 mJ at 1.28 kHz, 390 mJ at 640 Hz, and up to 6 J at 40 Hz. Shorter pulses from the Yb:YLF laser is of course possible via optimizing the cavity round-trip time and output coupling in gain switched operation or by using active or passive Q-switching methods, but there one needs to sacrifice from the pulse energy to prevent laser induced damage to the optics, since laser peak powers will be higher. As an example, 60 ns pulses at 10 kHz with 5 mJ pulse energy (80 kW peak power) and 8-ns long pulses at 500 Hz with 13 mJ pulse energy (1.6 MW peak power) were demonstrated in an actively Q-switched Yb:YLF laser [21].

Investigation of wavelength tuning
As discussed in the introduction section, to our knowledge, tuning behavior of cryogenic Yb:YLF lasers has not been studied in detail yet [28], and earlier tuning results are mostly limited to low-power room-temperature Yb:YLF systems [23,32,34]. In this work, we have used a 2 mm thick crystal quartz birefringent filter (BRF) for wavelength selection. A regular on-surface optic axis BRF with an optic axis that lies on the surface of the plate was used in the experiments [55][56][57][58]. For the insertion of the BRF plate, the laser cavity is extended to a length of around 25 cm and the BRF plate was inserted at Brewster's angle inside the cavity. Furthermore, to increase the modulation depth of the filter, we have inserted a thin-film polarizer (TFP), with a highly transmittive coating for TM (p) polarized light, and a highly reflective coating for the TE (s) polarized light. The laser power only dropped 5-10% with the insertion of the BRF and the polarizer, and the laser could be tuned both in cw and pulsed regimes. Note that, as a disadvantage, the increasing modulation depth with the insertion of the TFP also widens the FWHM of the birefringent filter (without the TFP: modulation depth is only around 30%, but filter FWHM is around 2.5 nm; with the TFP: modulation depth could be scaled up to 100%, but FWHM is 15 nm) [58]. Figure 10 summarizes the tuning results obtained from the E//a axis of the cryogenic Yb:YLF laser. First of all, the dashed black curve with a central wavelength around 1018 nm is a typical free running laser spectrum. Free running spectra was usually structured, and had a FWHM of around 1 nm. Also, besides what is shown here, we have also observed free-running lasing at other wavelengths within the 1013-1019 nm range, since the laser gain profile is quite flat in this region. Note that, with the insertion of tuning elements, the laser spectrum FWHM narrowed down to around 0.2 nm, which is close to the resolution limit of the spectrometer used. The orange solid spectrum centered around 1013 nm shows a sample spectrum obtained by the insertion of the BRF. By adjusting the rotation angle of the BRF, the laser could be tuned smoothly in the 1003.6-1020.5 nm and 1006.3-1019.4 nm range using 10% and 20% transmitting output couplers, respectively. Besides this range, lasing could also be achieved around the emission peaks at 995 and 1000 nm. Due to the rather large effective FWHM of our intracavity filter, as well as the small emission cross section values, we could not get lasing in the 1000-1003.6 nm and 995-1000 nm regions. Furthermore, we could not achieve lasing at the 993 nm emission peak of Yb:YLF, probably due to the higher amount of self-absorption losses and limited selectivity and free-spectral range of our tuning elements. The estimated small-signal self-absorption losses of the 0.5%-doped 2 cm long Yb:YLF around 993 nm is 2.8%, 6.1% and 9.8% at temperatures of 80 K, 100 K and 120 K, respectively. It should be borne in mind that, the self-absorption losses are much stronger at shorter wavelengths due to the quasi-3 level laser structure, explaining the difficulties observed in achieving lasing around 993 nm. It is also worth noting that, due the flat gain profile in the region, laser powers obtained in the 1013.5-1019 nm range were almost constant, demonstrating the amplification potential of femtosecond pulses in this spectral range. We believe that, in future studies, using tuning elements with better wavelength selectivity, the Yb:YLF laser should be tunable smoothly in the whole spectral gain bandwidth (993-1021 nm). As another interesting point, the measured emission spectra and the obtained tuning curve clearly shows that, the E//a polarization of Yb:YLF has the potential to produce sub-100-fs long pulses upon mode-locking. To our knowledge, mode-locking of Yb:YLF has not been demonstrated yet at cryogenic temperatures, and this is an interesting open question in the literature.
We finish our experimental results with Fig. 11, which shows sample multicolor optical spectra that was obtained during laser tuning experiments. With almost flat and broadband gain profile centered around 1015 nm, accompanied with additional strong emission peaks, Yb:YLF provides a suitable environment for multicolor laser operation. In our tuning studies with the BRF element, using different filter orders, we could easily access two-color, and three-color laser operation. Moreover, output powers exceeding 100 W was obtained in dual-wavelength operation, which is, to our knowledge, is one of the highest output powers obtained in this regime [59]. It is clear that, with properly designed birefringent tuning elements optimized for multicolor laser operation, cryogenic Yb:YLF gain media could also be used in generating high power multicolor lasing in both cw [59,60] and cw mode-locked [61][62][63] operation regimes.

Conclusions
In conclusion, to our knowledge, we have presented the first detailed high power lasing investigation of cryogenic Yb:YLF gain media in the E//a-axis. Lasing in quasi-cw, cw and gain-switched modes have been presented. Record power levels and slope efficiencies have been reported. Broadband tuning results confirmed the earlier emission cross section measurements. Our future work will focus on development of high power and high energy femtosecond Yb:YLF oscillators and amplifiers, for applications such as ultrafast X-ray generation [64,65], pumping of high energy and average power optical parametric amplifiers and spectral broadening and compression of high energy pulses.