- Email: [email protected]
Diode-side-pumped, passively Q-switched Yb:LuAG laser
Optics & Laser Technology 73 (2015) 101–104
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Diode-side-pumped, passively Q-switched Yb:LuAG laser Mateusz Kaskow a,n, Lukasz Galecki a, Jan K. Jabczynski a, Marek Skorczakowski a, Waldemar Zendzian a, Jan Sulc b, Michal Nemec b, Helena Jelinkova b a b
Institute of Optoelectronics, Military University of Technology, str. gen. Sylwestra Kaliskiego 2, 00-908 Warsaw, Poland Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Brehova 7, 115 19 Prague, Czech Republic
art ic l e i nf o
a b s t r a c t
Article history: Received 5 February 2015 Received in revised form 24 March 2015 Accepted 7 April 2015 Available online 14 May 2015
A high-gain, diode-side-pumped Yb:LuAG slab laser was designed and investigated for use at room temperature. Pumping occurred from a fast-axis collimated 2D laser diode stack emitting at a wavelength of 970 nm, with 0.8 J over a duration of 0.8 ms. The pump scheme, which enabled efficient mode matching and high gain, was analysed and experimentally verified for different dopant levels. An energy of 100 mJ with 23% slope efficiency in a near fundamental mode was achieved in the free-running regime. A peak power of 2.5 MW and a pulse energy of 10.1 mJ were demonstrated in passive Q-switching by means of a Cr:YAG saturable absorber with 39% initial transmission. The study defined the indications for optimizing such a system. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Side-pumped Q-switched Ytterbium
1. Introduction Ytterbium-doped laser media have attracted much interest for the last two decades, because of their significant advantages (low quantum defects, long fluorescence lifetimes, negligible up-conversion losses, possibility of a high-doping level, etc.) in comparison to Nd laser media [1–16]. Their main deficiencies, resulting from a quasi-three-level scheme, can be overcome via cryogenic operation [4,5,8,10] or by applying special architectures such as thin disks [6,13,16], slabs [7–11] or fibers [12]. Excluding a few cases [9,10], the end-pumping scheme has dominated high-power Yb laser systems because of the specific requirements of quasi-III-level media and the relative simplicity and compactness of beam-shaping optics currently available for high-power laser diode stacks. Our particular aim in this work is to show the feasibility of the side-pumped scheme for Yb oscillators operating at room temperature. These have to deliver energies of several dozens of mJ in the Q-switching regime. It is well known that efficient, high-energy operation in the Q-switching mode requires high gain and results in high fluencies inside the cavity [17–21]. In the Q-switching regime, efficient extraction in the case of Yb oscillators (72% of energy in the free-running regime as demonstrated in [11]) is possible despite the limitation imposed by a quasiIII-level scheme. However, compared to Nd gain media, the saturation fluency in Yb-doped media is significantly larger (for instance, it is as high as 10 J/cm2 for Yb:YAG); this poses a risk of damage to the laser elements inside the cavity. Therefore, we have chosen as a gain medium the relatively novel Yb:LuAG crystal [13–16], which has n
Corresponding author. E-mail address: [email protected] (M. Kaskow). URL: http://www.ioe.wat.edu.pl (M. Kaskow).
http://dx.doi.org/10.1016/j.optlastec.2015.04.003 0030-3992/& 2015 Elsevier Ltd. All rights reserved.
comparable thermo-optical and mechanical parameters as Yb:YAG but about 25% higher gain cross-section,sem ¼ 2.5 10 20 cm2. We present an analysis that aims to decrease the gain in such a laser system concurrently with efficient energy extraction. Moreover, we focus here on exploring the potential offered by novel, fast-axiscollimated, low-duty-factor, 2D laser diode stacks with up to 200 W per 1 cm bar. For pump units consisting of 8 bars, power densities above 50 kW/cm2 are feasible if used in an elongated rectangle format, as this seems to be better matched to the side-pumped slab than to end-pumping architecture. Section 2 describes the laser scheme, an analysis of the pump unit and gain distribution, and the results of the characterization with free running for different doping levels. We have shown that, with the proper choice of laser mode size and pumping channel shape, efficient generation with reduced internal laser power density is possible. The third section presents the analysis and experiments on passive Q-switching. In the final section we provide concluding results and formulate the directions for optimization of these types of oscillators.
2. Design and analysis of a laser oscillator The analysed laser oscillator (see Fig. 1) consists of a slabshaped gain medium, which was side-pumped by a 2D laser diode stack (DILAS C3Y-976.3-2400Q-V051.1). We examined three 3 3 13 mm3 Yb:LuAG media with 6 at%, 9.35 at% and 15 at% doping concentrations. The active medium was located inside a half-symmetrical cavity with a concave rear mirror (r ¼150 mm) and a flat output coupler. The output transmission Toc was optimized to get the highest energy at the output. The parameters of applied Cr:YAG modulators are described in Section 3. In order to
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omit thermal effects pump duration was tpump ¼0.8 ms and pulse repetition rate was PRF ¼2 Hz. The excited volume cross-section was 11.7 0.1 mm2. The size of the gain channel can be controlled by the choice of cylindrical lens (HCL) and the effective absorption coefficient of the gain medium at the pump wavelength. Assuming a quasi-stationary pumping condition (see details in [22]), a qualitative model for estimation of the inversion, gain profiles, internal fluency and stored energy was elaborated. A typical 2D image of a gain profile (cross-section of the side-pumped active medium) truncated to laser mode is shown in Fig. 2. The model was applied to analyse and optimise the pumping scheme in order to maximize the stored energy, assuming fundamental mode of the cavity. The exemplary results of the stored energy and gain for different mode radii (wmode) inside a gain medium are presented in Figs. 3 and 4, relatively. As shown in Fig. 3, the wider the fundamental mode, the higher the output energy can be obtained – in contrast, the higher the gain is obtained for the smaller mode area (Fig. 4). This is caused
Fig. 1. Scheme of the laser oscillator: HCL – cylindrical lens, RM – concave rear mirror, OC – flat out-coupling mirror, Cr:YAG – passive Q-switch, Yb:LuAG – slab shape gain medium, and 2D LD Stack – 2D, fast-axis-collimated laser diode array.
Fig. 2. 2D plot of gain distribution truncated to the fundamental mode area: radius – 0.25 mm, distance from the edge – 0.35 mm, pump power – 300 W, vertical width of pump – 0.25 mm, and frame size – 1 1 mm2.
Fig. 3. Stored energy in the fundamental mode vs. pump energy: wmode ¼0.1 mm – red continuous curve, wmode ¼ 0.2 mm – blue dashed curve, wmode ¼ 0.3 mm – black dashed-dot curve, pump width – 0.2 mm, and slab length – 12 mm. (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this paper.)
Fig. 4. Small signal gain coefficient vs. pump energy: wmode ¼ 0.1 mm – red continuous curve, wmode ¼ 0.2 mm – blue dashed curve, wmode ¼ 0.3 mm - black dasheddot curve, pump width – 0.2 mm, and slab length – 12 mm. (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this paper.)
Fig. 5. Output energy vs. incident pump energy experiments: blue triangles – 15% Yb:LuAG, Toc ¼ 60%, wmode ¼ 0.202 mm; red circles – 9.35% Yb:LuAG, Toc ¼ 10%, wmode ¼0.256 mm; black squares – 6% Yb:LuAG, Toc ¼ 10%, wmode ¼ 0.324 mm; pump width – 0.2 mm, and slab length – 12 mm. (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this paper.)
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Table 1 Results of passive Q-switching experiments: Tini, exp – initial transmission of Q-switch, Toc – transmission of output coupler, Epulse, exp – output energy from experiments, τpulse – pulse duration, Ppeak – peak power, Fint , exp – internal energy density, experimental, 2g0 lcalc – estimated round trip gain, Fint , calc – internal energy density, calculation. Case
Tini
Toc
2g0l
Epulse, exp (mJ)
τpulse (ns)
Ppeak (MW)
Fint , exp (J/cm2)
Fint , calc (J/cm2)
1 2 3 4
0.83 0.83 0.62 0.39
0.4 0.6 0.8 0.96
1.1 1.5 2.8 5.2
1.7 2.3 5.3 10.1
12.5 13.2 3.5 4
0.14 0.18 1.51 2.53
2.6 2.4 4.0 6.4
3.5 2.8 5.6 9.6
by the high inhomogeneity of local gain (see Fig. 2), which has an asymmetric profile narrower in the y-direction (vertical) than the fundamental mode. The slightly non-linear dependences shown in both Figs. 3 and 4 are caused by a certain decrease of the modematching efficiency with pump power. The effective gain inside the mode can be controlled via changing of the pump caustic and by varying the laser mode size and its location. The model was confirmed in the experiments carried out first in the free-running regime (see Fig. 5). The highest gain corresponding to the highest out-coupling transmission was obtained for the 15% Yb:LuAG with the smallest mode radius of 0.2 mm. The best slope efficiency (η ¼22.9%) and output energy (Eout ¼ 101 mJ) were obtained for 9.35% Yb:LuAG and a 0.26 mm mode radius. These experimental results basically confirm the model and constitute the starting point for the design and examination of the Q-switching regime.
Toc, exp = 0.96, we achieved single pulse output with energy of Eout , exp = 10.1 mJ and pulse duration of τpulse (see Table 1, case 4). The corresponding peak power was 2.5 MW. Further increase of the pump energy caused volumetric damage of the gain medium. We achieved high spatial quality of the output beam with neardiffraction-limited divergence (M2 < 2). According to the optimization model of passive Q-switching [18,19], for the highest roundtrip gain, 2g0 lcalc = 5.2, the optimal initial transmission of saturable absorber should be Tini,opt ¼0.27 and the out-coupling transmission Toc,opt ¼0.72. In this case, the output pulse energy Eout,opt and the internal fluency Fint,opt would be equal to 17.3 mJ and 10.2 J/cm2, respectively. Assuming the uniform gain, the maximum available energy (in case of ideal, lossless Q-switch) would be Eout,max ¼ 21.4 mJ and the internal fluency Fint,max ¼12.6 J/cm2 – this is an unacceptable case due to high risk of damaging the laser elements. Thus, to extract all of the stored, available energy from the gain medium, a much wider laser mode is required.
3. Experiments in passive Q-switching regime The proper choices of mode size (defined mainly by resonator parameters) and pump caustic shape are crucial to the design of an efficient laser operating in a Q-switching mode, taking into account the specific requirements posed by the risk of damage to the laser elements by intracavity fluency. Analysis and experiments in the Q-switching regime were performed for the 9.35% Yb:LuAG. In preliminary estimations, we determined the potential parameters which could be achieved in such a system. The estimated roundtrip quasistationary gain was 2g0 l = 8.4 for maximum pump power, and the laser mode radius was wmode ¼0.42 mm. According to Q-switching theory [18], for 2g0 l = 8.4 and assuming passive losses L¼0.2 (which include aperture reabsorption effects), the optimal out-coupling transmission Toc, ideal = 0.86. In such a case, the expected output energy Eout , ideal = 73.2 mJ and the internal fluency Fint ¼30.6 J/cm2, which are far above the damage threshold for the laser elements. We decided to perform step-by-step analysis and experiments in the passive Q-switching regime by applying several saturable absorbers made of Cr:YAG. The results of the experiments and calculations are summarized in Table 1. We used here the generalized model of passive Q-switching taking into account the excited state absorption effect in a saturable absorber [19–21]. We assumed for Cr:YAG a crystal ground-state absorption cross section sGSA ¼8.7 10 19 cm2 and an excited-state absorption cross section sESA ¼2.2 10 19 cm2 [19]. The quality of passive Q-switching depends on the ratio α ¼ sGSA/(σem ·γlas), which is 33 in case of Cr:YAG/Yb:LuAG pair (for Yb:LuAG, γlas ¼1.05 at room temperature). The passive losses L, which should take into account aperture reabsorption and other parasitic effects, and the effective mode radius wmode were not well-defined parameters in the analysis. We assumed the values L ¼0.2 and wmode ¼ 0.33 mm in the calculations. The estimated round-trip gain and the calculated internal energy density are presented in the fourth and the last column in Table 1, respectively. In the best case, for the incident pump energy of 436 mJ, initial transmission of the Cr:YAG modulator equal to Tini, exp = 0.39 and outcoupling transmission of
4. Conclusion We proposed an analytical–experimental approach to designing an efficient laser operating in the Q-switching mode, based on a Yb:LuAG gain element side pumped by a high power 2D laser diode stack. We showed that the model agreed well with the experiments, despite the lack of well-defined parameters such as passive losses and laser mode diameter. We demonstrated an output energy of 10.1 mJ and peak power of 2.5 MW in a diodeside-pumped Yb:LuAG oscillator operating at room temperature. The available stored energy was not fully exploited mainly due to limitations posed by too high fluency in the cavity. To get the most out of this pumping unit/gain medium configuration, a proper choice of laser mode-size and pumping channel shape must be done, taking into account the risk of damage to the laser elements.
Acknowledgements This work was supported by the Polish National Science Center under the projects NCN2012/06/M/ST/00425 and NCN2012/05/B/ ST7/00088, European Union resources under the National Strategic Reference Framework (Innovative Economy Programme no. WNDPOIG.01.01.00-14-095/09) and the Czech Ministry of Education, Youth and Sport under Project no. RVO 6840770. The Yb:LuAG samples were manufactured by CRYTUR, spol. r.o., Czech Republic.
References [1] DeLoach LD, Payne SA, Chase LL, Smith LK, Kway WL, Krupke WF. Evaluation of absorption and emission properties of Yb3 þ -doped crystals for laser applications. IEEE J Quantum Electron 1993;29:1179–91. [2] Fan TY. Optimizing the efficiency and stored energy in quasi-three-level lasers. IEEE J Quantum Electron 1992;28(12):2692–7.
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[3] Krupke WF. Ytterbium solid-state laser—the first decade. IEEE J Sel Top Quantum Electron 2000;6(6):1287–96. [4] Fan TY, Ripin DJ, Aggarwal RL, Ochoa JR, Chann B, Tilleman M, et al. Cryogenic Yb3 þ -doped solid-state lasers. IEEE J Sel Top Quantum Electron 2007; 13(3):448–59. [5] Rand D, Miller D, Ripin DJ, Fan TY. Cryogenic Yb3 þ -doped materials for pulsed laser applications [Invited]. Opt Mater Express 2011;1(3):434–50. [6] Giesen A, Speiser J. Fifteen years of work on thin-disk lasers: results and scaling laws. IEEE J Sel Top Quantum Electron 2007;13(3):598–609. [7] Russbueldt P, Mans T, Weitenberg J, Hoffmann HD, Poprawe R. Compact diode-pumped 1.1 kW Yb:YAG Innoslab femtosecond amplifier. Opt Lett 2010;35(24):4169–71. [8] Tokita S, Divoky M, Furuse H, Matsumoto K, Nakamura Y, Yoshida M, et al. Generation Of 500-mJ nanosecond pulses from diode-pumped Yb:YAG. Opt Mater Express 2014;4(10):2122–6. [9] Filgas D, Clatterbuck T, Cashen M, Daniele A, Hughes S, Mordaunt D. Recent results for the Raytheon RELI Program. In: Proceedings of SPIE, vol. 8381; 2012. p. 838110. [10] Banerjee S, Ertel K, Mason PD, Phillips PJ, Siebold M, Loeser M, et al. Highefficiency 10 J diode pumped cryogenic gas cooled Yb:YAG multislab amplifier. Opt Lett 2012;37(12):2175–7. [11] Wu H, Gong M, Yan P, Liu Q, Chen G, Wang Q. Quasi-continuous-wave diode array side-pumped Q-switched Yb:YAG slab laser. Opt Eng 2004;43(4):986–90. [12] Dawson JW, Messerly MJ, Beach RJ, Shverdin MY, Stappaerts EA, Sridharan AK, et al. Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power. Opt Express 2008;16(17):13240–66.
[13] Beil K, Fredrich-Thorton ST, Tellkamp F, Peters R, Krankel C, Petermann K, et al. Thermal and laser properties of Yb:LuAG for kW thin disk lasers. Opt Express 2010;18(20):20712–22. [14] Pirri A, Vannini M, Babin V, Nikl M, Toci G. CW and quasi-CW laser performance of 10 at. Yb3 þ :LuAG ceramic. Laser Phys 2013;23:1–7. [15] Xu CW, Luo DW, Zhang J, Yang H, Qin XP, Tan WD, et al. Diode pumped highly efficient Yb:Lu3A5O12 ceramic laser. Laser Phys Lett 2012;9:30–4. [16] Nakao H, Inagaki T, Shirakawa A, Ueda K-I, Yagi H, Yanagitani T, et al. Yb3 þ -doped ceramic thin-disk lasers of Lu-based oxides. Opt Mater Express 2014;4(10):2122–6. [17] Siegman A. Lasers, University science books, 6th revised and updated edn.; 1986. [18] Degnan JJ. Optimization of passively Q-switched lasers. IEEE J Quantum Electron 1995;31:1890–901. [19] Xiao G, Bass M. A generalized model for passively q-switched lasers including excited state absorption in the saturable absorber. IEEE J Quantum Electron 1997;33:41–4. [20] Kalisky Y. Cr4 þ -doped crystals: their use as lasers and passive Q-switches. Prog Quantum Electron 2004;28:249–303. [21] Mlynczak J, Kopczynski K. Comparison of parameters of q-switching saturable absorbers estimated by different models and the impact of accuracy of input data. Opt Mater 2014;36:867–72. [22] Jabczynski JK, Gorajek L, Kwiatkowski J, Kaskow M, Zendzian W. Optimization of end-pumped, actively Q-switched quasi-III-level lasers. Opt Express 2011;19(17):15652–64.
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Diode-side-pumped, passively Q-switched Yb:LuAG laser Mateusz Kaskow a,n, Lukasz Galecki a, Jan K. Jabczynski a, Marek Skorczakowski a, Waldemar Zendzian a, Jan Sulc b, Michal Nemec b, Helena Jelinkova b a b
Institute of Optoelectronics, Military University of Technology, str. gen. Sylwestra Kaliskiego 2, 00-908 Warsaw, Poland Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Brehova 7, 115 19 Prague, Czech Republic
art ic l e i nf o
a b s t r a c t
Article history: Received 5 February 2015 Received in revised form 24 March 2015 Accepted 7 April 2015 Available online 14 May 2015
A high-gain, diode-side-pumped Yb:LuAG slab laser was designed and investigated for use at room temperature. Pumping occurred from a fast-axis collimated 2D laser diode stack emitting at a wavelength of 970 nm, with 0.8 J over a duration of 0.8 ms. The pump scheme, which enabled efficient mode matching and high gain, was analysed and experimentally verified for different dopant levels. An energy of 100 mJ with 23% slope efficiency in a near fundamental mode was achieved in the free-running regime. A peak power of 2.5 MW and a pulse energy of 10.1 mJ were demonstrated in passive Q-switching by means of a Cr:YAG saturable absorber with 39% initial transmission. The study defined the indications for optimizing such a system. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Side-pumped Q-switched Ytterbium
1. Introduction Ytterbium-doped laser media have attracted much interest for the last two decades, because of their significant advantages (low quantum defects, long fluorescence lifetimes, negligible up-conversion losses, possibility of a high-doping level, etc.) in comparison to Nd laser media [1–16]. Their main deficiencies, resulting from a quasi-three-level scheme, can be overcome via cryogenic operation [4,5,8,10] or by applying special architectures such as thin disks [6,13,16], slabs [7–11] or fibers [12]. Excluding a few cases [9,10], the end-pumping scheme has dominated high-power Yb laser systems because of the specific requirements of quasi-III-level media and the relative simplicity and compactness of beam-shaping optics currently available for high-power laser diode stacks. Our particular aim in this work is to show the feasibility of the side-pumped scheme for Yb oscillators operating at room temperature. These have to deliver energies of several dozens of mJ in the Q-switching regime. It is well known that efficient, high-energy operation in the Q-switching mode requires high gain and results in high fluencies inside the cavity [17–21]. In the Q-switching regime, efficient extraction in the case of Yb oscillators (72% of energy in the free-running regime as demonstrated in [11]) is possible despite the limitation imposed by a quasiIII-level scheme. However, compared to Nd gain media, the saturation fluency in Yb-doped media is significantly larger (for instance, it is as high as 10 J/cm2 for Yb:YAG); this poses a risk of damage to the laser elements inside the cavity. Therefore, we have chosen as a gain medium the relatively novel Yb:LuAG crystal [13–16], which has n
Corresponding author. E-mail address: [email protected] (M. Kaskow). URL: http://www.ioe.wat.edu.pl (M. Kaskow).
http://dx.doi.org/10.1016/j.optlastec.2015.04.003 0030-3992/& 2015 Elsevier Ltd. All rights reserved.
comparable thermo-optical and mechanical parameters as Yb:YAG but about 25% higher gain cross-section,sem ¼ 2.5 10 20 cm2. We present an analysis that aims to decrease the gain in such a laser system concurrently with efficient energy extraction. Moreover, we focus here on exploring the potential offered by novel, fast-axiscollimated, low-duty-factor, 2D laser diode stacks with up to 200 W per 1 cm bar. For pump units consisting of 8 bars, power densities above 50 kW/cm2 are feasible if used in an elongated rectangle format, as this seems to be better matched to the side-pumped slab than to end-pumping architecture. Section 2 describes the laser scheme, an analysis of the pump unit and gain distribution, and the results of the characterization with free running for different doping levels. We have shown that, with the proper choice of laser mode size and pumping channel shape, efficient generation with reduced internal laser power density is possible. The third section presents the analysis and experiments on passive Q-switching. In the final section we provide concluding results and formulate the directions for optimization of these types of oscillators.
2. Design and analysis of a laser oscillator The analysed laser oscillator (see Fig. 1) consists of a slabshaped gain medium, which was side-pumped by a 2D laser diode stack (DILAS C3Y-976.3-2400Q-V051.1). We examined three 3 3 13 mm3 Yb:LuAG media with 6 at%, 9.35 at% and 15 at% doping concentrations. The active medium was located inside a half-symmetrical cavity with a concave rear mirror (r ¼150 mm) and a flat output coupler. The output transmission Toc was optimized to get the highest energy at the output. The parameters of applied Cr:YAG modulators are described in Section 3. In order to
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M. Kaskow et al. / Optics & Laser Technology 73 (2015) 101–104
omit thermal effects pump duration was tpump ¼0.8 ms and pulse repetition rate was PRF ¼2 Hz. The excited volume cross-section was 11.7 0.1 mm2. The size of the gain channel can be controlled by the choice of cylindrical lens (HCL) and the effective absorption coefficient of the gain medium at the pump wavelength. Assuming a quasi-stationary pumping condition (see details in [22]), a qualitative model for estimation of the inversion, gain profiles, internal fluency and stored energy was elaborated. A typical 2D image of a gain profile (cross-section of the side-pumped active medium) truncated to laser mode is shown in Fig. 2. The model was applied to analyse and optimise the pumping scheme in order to maximize the stored energy, assuming fundamental mode of the cavity. The exemplary results of the stored energy and gain for different mode radii (wmode) inside a gain medium are presented in Figs. 3 and 4, relatively. As shown in Fig. 3, the wider the fundamental mode, the higher the output energy can be obtained – in contrast, the higher the gain is obtained for the smaller mode area (Fig. 4). This is caused
Fig. 1. Scheme of the laser oscillator: HCL – cylindrical lens, RM – concave rear mirror, OC – flat out-coupling mirror, Cr:YAG – passive Q-switch, Yb:LuAG – slab shape gain medium, and 2D LD Stack – 2D, fast-axis-collimated laser diode array.
Fig. 2. 2D plot of gain distribution truncated to the fundamental mode area: radius – 0.25 mm, distance from the edge – 0.35 mm, pump power – 300 W, vertical width of pump – 0.25 mm, and frame size – 1 1 mm2.
Fig. 3. Stored energy in the fundamental mode vs. pump energy: wmode ¼0.1 mm – red continuous curve, wmode ¼ 0.2 mm – blue dashed curve, wmode ¼ 0.3 mm – black dashed-dot curve, pump width – 0.2 mm, and slab length – 12 mm. (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this paper.)
Fig. 4. Small signal gain coefficient vs. pump energy: wmode ¼ 0.1 mm – red continuous curve, wmode ¼ 0.2 mm – blue dashed curve, wmode ¼ 0.3 mm - black dasheddot curve, pump width – 0.2 mm, and slab length – 12 mm. (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this paper.)
Fig. 5. Output energy vs. incident pump energy experiments: blue triangles – 15% Yb:LuAG, Toc ¼ 60%, wmode ¼ 0.202 mm; red circles – 9.35% Yb:LuAG, Toc ¼ 10%, wmode ¼0.256 mm; black squares – 6% Yb:LuAG, Toc ¼ 10%, wmode ¼ 0.324 mm; pump width – 0.2 mm, and slab length – 12 mm. (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this paper.)
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Table 1 Results of passive Q-switching experiments: Tini, exp – initial transmission of Q-switch, Toc – transmission of output coupler, Epulse, exp – output energy from experiments, τpulse – pulse duration, Ppeak – peak power, Fint , exp – internal energy density, experimental, 2g0 lcalc – estimated round trip gain, Fint , calc – internal energy density, calculation. Case
Tini
Toc
2g0l
Epulse, exp (mJ)
τpulse (ns)
Ppeak (MW)
Fint , exp (J/cm2)
Fint , calc (J/cm2)
1 2 3 4
0.83 0.83 0.62 0.39
0.4 0.6 0.8 0.96
1.1 1.5 2.8 5.2
1.7 2.3 5.3 10.1
12.5 13.2 3.5 4
0.14 0.18 1.51 2.53
2.6 2.4 4.0 6.4
3.5 2.8 5.6 9.6
by the high inhomogeneity of local gain (see Fig. 2), which has an asymmetric profile narrower in the y-direction (vertical) than the fundamental mode. The slightly non-linear dependences shown in both Figs. 3 and 4 are caused by a certain decrease of the modematching efficiency with pump power. The effective gain inside the mode can be controlled via changing of the pump caustic and by varying the laser mode size and its location. The model was confirmed in the experiments carried out first in the free-running regime (see Fig. 5). The highest gain corresponding to the highest out-coupling transmission was obtained for the 15% Yb:LuAG with the smallest mode radius of 0.2 mm. The best slope efficiency (η ¼22.9%) and output energy (Eout ¼ 101 mJ) were obtained for 9.35% Yb:LuAG and a 0.26 mm mode radius. These experimental results basically confirm the model and constitute the starting point for the design and examination of the Q-switching regime.
Toc, exp = 0.96, we achieved single pulse output with energy of Eout , exp = 10.1 mJ and pulse duration of τpulse (see Table 1, case 4). The corresponding peak power was 2.5 MW. Further increase of the pump energy caused volumetric damage of the gain medium. We achieved high spatial quality of the output beam with neardiffraction-limited divergence (M2 < 2). According to the optimization model of passive Q-switching [18,19], for the highest roundtrip gain, 2g0 lcalc = 5.2, the optimal initial transmission of saturable absorber should be Tini,opt ¼0.27 and the out-coupling transmission Toc,opt ¼0.72. In this case, the output pulse energy Eout,opt and the internal fluency Fint,opt would be equal to 17.3 mJ and 10.2 J/cm2, respectively. Assuming the uniform gain, the maximum available energy (in case of ideal, lossless Q-switch) would be Eout,max ¼ 21.4 mJ and the internal fluency Fint,max ¼12.6 J/cm2 – this is an unacceptable case due to high risk of damaging the laser elements. Thus, to extract all of the stored, available energy from the gain medium, a much wider laser mode is required.
3. Experiments in passive Q-switching regime The proper choices of mode size (defined mainly by resonator parameters) and pump caustic shape are crucial to the design of an efficient laser operating in a Q-switching mode, taking into account the specific requirements posed by the risk of damage to the laser elements by intracavity fluency. Analysis and experiments in the Q-switching regime were performed for the 9.35% Yb:LuAG. In preliminary estimations, we determined the potential parameters which could be achieved in such a system. The estimated roundtrip quasistationary gain was 2g0 l = 8.4 for maximum pump power, and the laser mode radius was wmode ¼0.42 mm. According to Q-switching theory [18], for 2g0 l = 8.4 and assuming passive losses L¼0.2 (which include aperture reabsorption effects), the optimal out-coupling transmission Toc, ideal = 0.86. In such a case, the expected output energy Eout , ideal = 73.2 mJ and the internal fluency Fint ¼30.6 J/cm2, which are far above the damage threshold for the laser elements. We decided to perform step-by-step analysis and experiments in the passive Q-switching regime by applying several saturable absorbers made of Cr:YAG. The results of the experiments and calculations are summarized in Table 1. We used here the generalized model of passive Q-switching taking into account the excited state absorption effect in a saturable absorber [19–21]. We assumed for Cr:YAG a crystal ground-state absorption cross section sGSA ¼8.7 10 19 cm2 and an excited-state absorption cross section sESA ¼2.2 10 19 cm2 [19]. The quality of passive Q-switching depends on the ratio α ¼ sGSA/(σem ·γlas), which is 33 in case of Cr:YAG/Yb:LuAG pair (for Yb:LuAG, γlas ¼1.05 at room temperature). The passive losses L, which should take into account aperture reabsorption and other parasitic effects, and the effective mode radius wmode were not well-defined parameters in the analysis. We assumed the values L ¼0.2 and wmode ¼ 0.33 mm in the calculations. The estimated round-trip gain and the calculated internal energy density are presented in the fourth and the last column in Table 1, respectively. In the best case, for the incident pump energy of 436 mJ, initial transmission of the Cr:YAG modulator equal to Tini, exp = 0.39 and outcoupling transmission of
4. Conclusion We proposed an analytical–experimental approach to designing an efficient laser operating in the Q-switching mode, based on a Yb:LuAG gain element side pumped by a high power 2D laser diode stack. We showed that the model agreed well with the experiments, despite the lack of well-defined parameters such as passive losses and laser mode diameter. We demonstrated an output energy of 10.1 mJ and peak power of 2.5 MW in a diodeside-pumped Yb:LuAG oscillator operating at room temperature. The available stored energy was not fully exploited mainly due to limitations posed by too high fluency in the cavity. To get the most out of this pumping unit/gain medium configuration, a proper choice of laser mode-size and pumping channel shape must be done, taking into account the risk of damage to the laser elements.
Acknowledgements This work was supported by the Polish National Science Center under the projects NCN2012/06/M/ST/00425 and NCN2012/05/B/ ST7/00088, European Union resources under the National Strategic Reference Framework (Innovative Economy Programme no. WNDPOIG.01.01.00-14-095/09) and the Czech Ministry of Education, Youth and Sport under Project no. RVO 6840770. The Yb:LuAG samples were manufactured by CRYTUR, spol. r.o., Czech Republic.
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