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Abstract
The prospect for developing a passively Q-switched Yb:YAG/Cr:YAG monolithic microchip laser that operates at cryogenic temperature is theoretically analyzed. It is concluded that such a system has the potential to deliver laser pulses with improved energy and increased peak power in comparison with composite Yb:YAG/Cr:YAG or Nd:YAG/Cr:YAG devices that are operated at room temperature. Consequently, a cryogenically cooled Yb:YAG/Cr:YAG system is built and the emission performances are investigated. Laser pulses with 3.2 mJ energy, 6.1 MW peak power and high beam quality of M2 = 1.8 are achieved. By increasing the pump beam diameter, laser pulses with higher energy 32 mJ are obtained at 25 MW peak power with M2 = 5.4. To our knowledge, these are the best results obtained from passively Q-switched composite Yb:YAG/Cr:YAG monolithic microchip lasers.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Passively Q-switched (PQS) lasers are well known and have been extensively studied [1]. Among them, PQS microchip lasers have the advantages of having a simple structure, being almost alignment free, and providing high peak power with nanosecond to sub-nanosecond pulse duration [2,3]. Thus, they are promising devices for applications such as laser ignition [4–6], laser processing [7], laser spectroscopy [8,9], and nonlinear frequency conversion [10–12].
Though many microchip lasers with discrete elements can output multi-MW peak power pulses [13–16], here we focus on only monolithic microchip lasers, which are simpler and more compact. In 2007, Dong et al. [17] reported a composite Yb:YAG/Cr:YAG monolithic microchip laser with 0.172 mJ energy, 0.72 MW peak power and an M2 factor of 1.09. This was the first MW level monolithic microchip laser. In 2008, Sakai et al. [18] optically contacted Nd:YAG and Cr:YAG components to realize a quasi-monolithic laser with 0.67 mJ energy and 1.7 MW peak power. However, the beam quality was not high in the optical contact cavity since fine alignment of the cavity was impossible, and parallelism of the crystals needed to be improved. In 2011, Pavel et al. [19] developed a Nd:YAG/Cr:YAG monolithic microchip laser with 2.4 mJ energy and 2.8 MW peak power. But the beam quality was as low as M2 = 3.7. Similarly in 2012, Sandu et al. [20] presented a Nd:YAG/Cr:YAG monolithic microchip laser with 2.5 mJ energy, 1.9 MW peak power and low beam quality with M2 factor of 3.15. Some other papers [21,22] have reported over 5 MW peak power Nd:YAG/Cr:YAG monolithic microchip lasers, but the beam quality was not indicated. All the above monolithic microchip lasers are operated at room temperature (RT) and the performances are summarized in Table 3. We can conclude that boosting the microchip lasers’ energy, peak power and keeping a high beam quality is a challenge.
For microchip lasers, with thermal lens’s (induced by the thermal loading) focal length and laser material thickness (cavity length), one can obtain the cavity mode. A longer focal length can lead to a larger cavity mode and thus support higher output energy and peak power. The thermal lens’s focal length is proportional to the thermal conductivity and inversely proportional to the thermal-optic coefficient dn/dT (the derivative of the refractive index with respect to temperature) of the laser material [23–25]. Thus, a laser material with high thermal conductivity and small dn/dT will be beneficial for achieving high energy, high peak power, and high beam quality in microchip lasers.
Fortunately, the properties of the YAG medium’s thermal conductivity will be much improved and dn/dT will be much smaller at cryogenic temperatures [CT, typically liquid nitrogen (LN) temperature 77 K] than at RT. In addition, Yb:YAG at CT will be a 4-level laser system and the emission cross section will increase substantially, which will reduce the pump intensity, increase efficiency, and avoid damage problems. Furthermore, Yb:YAG has a long storage lifetime, large absorption bandwidth, and high doping concentration. Thus, Yb:YAG/Cr:YAG monolithic microchip lasers at CT are promising devices for high energy, high peak power, high repetition rate, low threshold, and high efficiency operation. We have already reported cryogenically cooled Yb:YAG/Cr:YAG monolithic microchip lasers with energy, duration, and beam quality at 0.6 mJ/1.8 ns/M2 = 1.1 [26] and 6.3 μJ/160 ps/M2 = 1.01 [27].
In this paper, we propose a simple theoretical model to predict a microchip laser’s highest energy and peak power with good beam quality. With this model, we show the potential of Yb:YAG/Cr:YAG monolithic microchip lasers at CT. Then, we describe a cryogenically cooled Yb:YAG/Cr:YAG monolithic microchip laser experiment that we carried out. This experiment achieved 3.2 mJ energy, 526 ps duration (full width at half maximum, FWHM), and 6.1 MW peak power with an M2 factor of 1.8 at a 200 Hz repetition rate. To our knowledge, this is the highest energy and peak power for monolithic microchip lasers with good beam quality (M2 < 2).
2. Theoretical model
In this section, we will conclude a theoretical model to simulate a microchip laser’s highest energy and peak power with good beam quality.
The focal length of the thermal lens can be simply estimated as [23–25]
where Ip is the incident pump intensity, ηabs is the absorption efficiency, ηs is the ratio between the pump wavelength and the laser wavelength (i.e., the Stokes ratio), κ is the thermal conductivity, and dn/dT is the thermal-optic coefficient. Figure 1(a) shows the calculated thermal lens focal length as a function of dn/dT for different thermal conductivities with Ip = 6 kW/cm2, ηabs = 90%, and ηs = 91%. We can see that the calculated focal length is in the range of meters to tens of meters and that it dramatically increases for small values of the thermal-optic coefficient, especially those below 2 × 10−6/K.
Fig. 1 (a) Calculated curves of thermal lens focal length as a function of thermal optic coefficient dn/dT for different thermal conductivities with Ip = 6 kW/cm2, ηabs = 90%, and ηs = 91%. (b) Calculated cavity (two flat mirror cavity with an internal lens) mode diameter as a function of internal lens focal length for different cavity lengths.
The cavity mode radius from a two flat mirror resonator with an internal lens can be calculated as [28]
where λ is the laser center wavelength, Lcav is the cavity length, and f is the lens focal length. Figure 1(b) shows the cavity mode diameter as a function of lens focal length for different cavity lengths. It is obvious that a longer focal length and a longer cavity will result in a larger cavity mode. If the focal length is much larger than the cavity length, then Eq. (2) can be further simplified toNeglecting the cavity round trip loss, the saturable absorber excited state absorption effect, and so on, the microchip laser’s threshold pump intensity (Ith), output energy (E), pulse duration (τ), peak power (Ppeak), and intensity (I) can be estimated as follows [25,29,30]
where Isat, Jsat, and Esat are the laser gain material saturation intensity, saturation fluence, and saturation energy, respectively. R is the output coupler reflectivity, T0 is the initial transmission of the saturable absorber, r0 is the laser beam radius, τT is the photon cavity round trip time, and τf is the laser material fluorescence lifetime.We further assume that (1) the total thickness of the microchip laser material is the cavity length L = Lcav, (2) the thermal lens focal length fth is the focal length [Eqs. (2,3)] of the flat-flat cavity’s inserted lens fth = f, (3) the pump and laser beam radius is the same as cavity mode radius r0 = ω0, and (4) the pump intensity is the threshold pump intensity Ip = Ith.
Combining Eqs. (1) and (4), we obtain the equivalent inserted lens focal length,
Combining Eqs. (3) and (10), we obtain the maximum laser beam radius,
Finally, combining Eqs. (5) and (11), we obtain the maximum laser energy,
Equation (12) clearly shows the relationship between the microchip laser’s maximum energy and the gain material’s properties. A higher saturation fluence, longer fluorescence lifetime, a larger Stokes efficiency, a higher thermal conductivity, and smaller dn/dT will all lead to a higher laser energy. Note that this is the maximum energy with good beam quality, i.e. the laser beam radius equals to the cavity mode radius. If we do not care about the beam quality, the energy is calculated from Eq. (5) i.e. the laser beam radius maybe larger than the cavity mode radius, and we can increase energy by simply enlarging the pump beam diameter (we assume the pump beam and laser beam overlap efficiency is 1). The maximum peak power can be easily calculated from Eqs. (6), (7), and (12). To obtain the laser performances, the detailed spectroscopic and thermo-optic properties are required. Table 1 summarizes these parameters of Nd:YAG, Yb:YAG at RT, and Yb:YAG at CT.
Table 1. Summary of the spectroscopic and thermo-optic properties of Nd:YAG and Yb:YAG at room temperature (RT) and Yb:YAG at cryogenic temperature (CT)
Within the parameters from Table 1, given the same saturable absorber initial transmission T0, microchip laser material thickness L, and output coupler reflectivity R, we can compare laser performances, as summarized in Table 2. In Table 2, performance is normalized by that of RT Nd:YAG/Cr:YAG.
Table 2. Comparisons of the RT Nd:YAG/Cr:YAG, RT Yb:YAG/Cr:YAG, and CT Yb:YAG/Cr:YAG microchip laser (normalized by RT Nd:YAG/Cr:YAG values)
The calculated maximum energy for CT Yb:YAG/Cr:YAG is 34 times that of RT Nd:YAG/Cr:YAG, which is a dramatic improvement. The calculated maximum energy for CT Yb:YAG/Cr:YAG is also 2.4 times that of RT Yb:YAG/Cr:YAG. In fact, taking into account the damage limitation of RT Yb:YAG/Cr:YAG microchip lasers, the real improvement is by a factor of ~15. From Eqs. (6) and (9), we can see that, given the saturable absorber’s initial transmission T0, the pulse duration is determined by the crystal thickness, and a thinner crystal will result in a shorter pulse. From Table 1, we can see that for the same absorption, the required thickness of Nd:YAG at RT is similar to that for Yb:YAG at RT and almost 2 times that for Yb:YAG at CT. So, the CT Yb:YAG/Cr:YAG pulse is shorter than that of RT Nd:YAG/Cr:YAG and RT Yb:YAG/Cr:YAG. Therefore, the peak power for CT Yb:YAG/Cr:YAG is over 34 times that for RT Nd:YAG/Cr:YAG. In summary, a CT Yb:YAG/Cr:YAG microchip laser has the potential to deliver much higher energy and much higher peak power pulses. Of course, this is calculated using a simple model with many assumptions, and the parameters used may not be completely accurate. In practice, results may not be as good as these calculations, but we believe the trend is correct.
Using Eq. (4) and the parameters from Table 1, we can see that the CT Yb:YAG/Cr:YAG threshold pump intensity is half that of RT Nd:YAG/Cr:YAG and less than 1/6 that of RT Yb:YAG/Cr:YAG. Hence, the pump to laser efficiency will be correspondingly higher. In addition, due to the higher thermal conductivity and smaller dn/dT, the average power for CT Yb:YAG/Cr:YAG will be higher than that of RT Nd:YAG/Cr:YAG and of Yb:YAG/Cr:YAG. Using a thick (~4 mm) CT Yb:YAG active mirror amplifier, 1 J / 500 Hz / 500 W laser pulses have been achieved [34]. We believe that CT Yb:YAG/Cr:YAG microchip lasers could also support 100 W level average power in the future.
Furthermore, compared with Nd:YAG, Yb:YAG has a much longer fluorescence lifetime. In quasi-continuous wave (QCW) operation, if we assume the pump LD’s duration equals the fluorescence lifetime, then, for the same storage energy, the required pump peak power of Yb:YAG is only one fifth that of Nd:YAG. In addition, Yb:YAG’s absorption bandwidth is much broader, which reduces the requirement for the LD’s bandwidth. All of these make Yb:YAG’s pump LD cheaper than that of Nd:YAG.
3. Experimental setup
We constructed an Yb:YAG/Cr:YAG monolithic microchip laser and investigated its properties experimentally. Figure 2 is a schematic diagram of the microchip laser. A YAG/Yb:YAG/Cr:YAG composite monolithic crystal made by thermal diffusion bonding technology (Cryslaser Inc.) was used in the experiment. The undoped 3.1 mm YAG layer was used to relieve thermal loading and support high average power. The Yb:YAG and Cr:YAG layers were 2.3 mm and 0.9 mm thick, respectively. The total thickness of the monolithic crystal was thus 6.3 mm. The crystal was square with 5 mm sides. The cut orientations of the undoped YAG, Yb:YAG, and Cr:YAG were [111], [111], and [110], respectively. The doping concentration of Yb ions was 10 at. % and the initial transmission of the Cr:YAG was 50%. The undoped YAG surface was coated with a film that is highly reflective (HR, R > 99.8%) at 1030 nm and a film that is high transmission (HT, R < 5%) at 940 nm, which worked as an input cavity mirror. The Cr:YAG surface was coated with a partially reflective (PR) film with reflectivity R = 40% at 1030 nm, which worked as an output coupler. The surface flatness of the coated cavity surfaces was λ/10 (λ = 633 nm). The composite crystal was mounted on thermally conductive copper plates and thin indium foils were used between the crystal and copper. The copper heat sink was cooled in vacuum with LN to 77 K.
A fiber coupled water cooled 938 nm laser diode (LD, BWT Inc.) was used as the pump source. The LD maximum output power was 200 W. The fiber’s numerical aperture was 0.22 with a core diameter of 135 μm. The pump light from the fiber was delivered to the microchip crystal by a pair of lenses. The laser diode worked in QCW mode with a pulse duration of 1 ms. When the coupled pump beam diameter on the laser crystal was 0.67 mm, the laser diode repetition was set at 200 Hz.
The laser output energy was measured with an energy meter (QE8SP-B-MT, Gentec-EO). The laser pulse waveform was detected with a fast (<25 ps rise time) photodiode (ET-3500, Electro-optics Technology) and recorded with a 12 GHz bandwidth oscilloscope (Infiniium DSO81204B, Agilent). The beam profile was measured using a charge coupled device (DMK51BU02.WG, The Imaging Source, GmbH). The emission spectrum of the laser was measured with a spectrometer (resolution ~0.1 nm; HR4000, Ocean Optics).
4. Experimental results
Figures 3 shows the laser output parameters. In the experiment, we kept one laser pulse during one pump pulse. Figures 3(a) shows the laser pulse energy as the function of pump beam diameter. It is clear that the pulse energy is directly increased by increasing the pump beam diameter. At a pump beam diameter of 2 mm, the laser output energy reached 32 mJ. The threshold pump energy reached 190 W near the limit of the LD’s maximum power, and we stopped increasing the pump beam diameter. The calculated data [using Eq. (5)] agree well with the experimental data. Figures 3(b) shows the laser beam quality M2 as the function of pump beam diameter. We can see that once the pump beam diameter exceeds 0.67 mm (i.e., the laser pulse energy over 3.2 mJ), the beam quality dramatically decreases. As a comparison, using Eq. (12), we calculate that this microchip laser can support a maximum of 3.5 mJ energy with a good beam quality, which agrees well with our experiment.
Fig. 3 (a) Laser pulse energy, solid circles are experimental data and the solid line is the calculated data using Eq. (5); (b) laser pulse M2 factor; (c) laser pulse duration; (d) laser pulse peak power; (e) laser pulse waveform; (f) laser pulse spectrum; (g) laser pulse energy stability; (h) threshold pump intensity; and (i) pump to laser efficiency.
In theory, the pulse duration is insensitive to the beam diameter. However, once the pump beam diameter becomes much larger than the supported maximum cavity mode (as theoretically analyzed in Section 2), the beam quality will degrade and multimode oscillations will broaden the pulse, as shown in Figs. 3(c). With the pulse energy and duration, we can calculate the peak power as shown in Figs. 3(d). The maximum peak power reached 25 MW, but at this peak power the beam quality was low, at M2 = 5.4. At a pump beam diameter of 0.67 mm, we achieved 3.2 mJ energy, 526 ps duration [the pulse shape is shown in Figs. 3(e)], and 6.1 MW peak power with an M2 factor of 1.8. The pulse fluence and intensity were estimated to be 0.9 J/cm2 and 1.7 GW/cm2, respectively. This is below the damage threshold, and the pulse energy and peak power can be further increased by using a Cr:YAG with lower initial transmission. Figures 3 (f) shows the laser pulse spectrum. The bandwidth is as narrow as 0.1 nm.
Figures 3(g) shows the pulse energy variation for a pump beam diameter of 0.67 mm at a 200 Hz repetition rate. The average energy is 3.2 mJ (average power is 0.64 W) with a root mean square (RMS) variation of 1.6%. In the experiment, the LN volume was only ~0.4 liter. In the future, by using a larger volume of LN, we believe the laser repetition rate can be improved. Figures 3(h)-3(i) show the threshold incident pump intensity and incident pump to laser efficiency as a function of pump beam diameter. The threshold incident pump intensity was ~6 kW/cm2, and the incident pump to laser efficiency was ~15%. The threshold is low, and the efficiency is high.
Figures 4(a)-4(f) show the laser near field beam pattern for different output energies (with different pump beam diameters). When the laser pulse energy was 0.64 mJ, the beam was nearly diffraction limited, symmetric, and clean. Once the energy reached 2 mJ, it became elliptical and rings appeared. Once the laser pulse energy reached 4.6 mJ, the rings were as strong as 15% of the center part. Once the laser pulse energy reached 8.2 mJ, the rings were as strong as the center part. We focused 3.2 mJ/6.1 MW laser pulses in the air using a 10 mm focal length lens, as shown in Figs. 4(g). Stable and clear air breakdown occurred, which demonstrates the high intensity of this laser.
Fig. 4 Output laser near field beam pattern with energy of (a) 0.64 mJ; (b) 2 mJ; (c) 3.2 mJ; (d) 4.6 mJ; (e) 8.2 mJ; and (f) 32 mJ with cuts across the center (white lines are measured; red lines are fitted with a Gaussian function); (f) air breakdown with 6.1 MW pulse.
Finally, Table 3 summarizes the performance of MW level monolithic microchip lasers including the one described in this work. It is clear that the results in this work improve a lot compared with the previous work.
Table 3. Summary of the performance of MW level monolithic microchip lasers
5. Conclusion
In conclusion, we theoretically analyzed a cryogenically cooled Yb:YAG/Cr:YAG microchip laser, finding that it could support higher energy and peak power than RT Nd:YAG/Cr:YAG and Yb:YAG/Cr:YAG monolithic microchip lasers. A CT Yb:YAG/Cr:YAG monolithic microchip laser was developed, which achieved 6.1 MW peak power at a 200 Hz repetition rate. With a lower initial transmission Cr:YAG layer and a larger volume of LN, it is expected that higher energy, higher peak power and higher average power pulses would be achieved.
Funding
Japan Society for the Promotion of Science (JSPS) KAKENHI (JP26287145); Photon Frontier Network of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.
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