Open Access
Add to BibSonomy
Abstract
An approach to develop laser amplifiers is proposed based on the use of standard rod active elements with end diode pumping, the beam size of which is significantly smaller than the element cross section, and the beam center is shifted maximally close to the element cooled side surface. This approach allows effective gain and good thermal management, and offers technological simplicity. On the basis of this approach, an ultrafast Yb:YAG amplifier with ${\gt}{{100}}\;{\rm{W}}$ average power, reasonable depolarization, and good beam quality is developed.
© 2022 Optica Publishing Group
1. INTRODUCTION
Today, ultrafast lasers are widely used in various areas including industry, medicine, and science. Different applications require different pulse widths and peak power, but most benefit from an increase in the average power. In the field of low pulse energies (${\sim}{{1}}\;\unicode{x00B5}{\rm J}$), fiber lasers proved to be the best choice by virtue of their compactness, stability, and reliability. However, their peak power is limited by nonlinear effects in the fiber. Its increase requires the application of such approaches as large-mode-area fibers, chirped pulse amplification, divided pulse amplification, and coherent combining [1–4] that nullifies the advantages of fiber lasers, which makes the system much more complicated. That is why a hybrid architecture with a fiber oscillator and a bulk solid-state amplifier is becoming more and more popular. One of the most promising solutions in this area is diode end-pumped Yb:YAG amplifiers that possess a high gain coefficient, high extraction efficiency, a simple and compact one- or two-pass optical scheme, and pushing the output pulse energy up to the mJ level. However, when operating at high average power, the solid-state amplifiers are exposed to thermal effects that lead to beam quality degradation. To decrease its influence, thin-rod or single-crystal-fiber active elements (AEs) that allow efficient heat removal from the gain medium are applied [5]. The following results can be listed as the most striking during the last years from the point of average power. In [6], an average power of 116 W with a beam quality factor ${{\rm{M}}^2}$ of ${2.1} \times {1.85}$ and 17% depolarization ratio was achieved in the square rod AE with a 4 mm transverse size. The specially designed spatially variable wave plate was used for depolarization compensation. In [7], an average power of 100 W with ${{\rm{M}}^2}$ of 4 was obtained in the rod AE with a 2 mm diameter. A record average power was achieved with single-crystal-fiber AE geometry. An average power of 160 W with an ${{\rm{M}}^2}$ of 1.9 was obtained in [8] and an average power of 110 W with an ${{\rm{M}}^2}$ of 1.9 was obtained in [9].
The application of the thin-rod or single-crystal-fiber AE geometry is associated with serious technological problems that include manufacturing submillimeter AEs and, most importantly, installing them into a cooling system. It makes this technology much more expensive than the standard rods. Moreover, the application of exclusive or fragile gain media is almost impracticable.
In this paper, we propose what we believe, to the best of our knowledge, is a new approach for the development of high-average-power amplifiers. It is based on the following aspects: (i) using standard rod AEs with a transverse dimension of several mm; (ii) using end diode pumping with a beam size much smaller than the AE transverse size, which provides efficient amplification; and (iii) positioning the pump area maximum close to the AE side surface to increase its cooling efficiency.
Variants of pump geometries along the AE side surface (i.e., parallel and maximum close to it), including along the face and along the edge of an AE of rectangular cross section, as well as along the cylindrical side surface for a circular rod, are presented in Fig. 1.
Fig. 1. Variants of end-pumping schemes along the side surface of standard rod AEs with square and circular cross section: (a) pumping along the face, (b) pumping along the edge, and (c) pumping along the cylindrical side surface.
The thermal processes in such AEs including temperature distribution and thermal-induced phase distortions are investigated theoretically and experimentally considering the effects associated with the asymmetry of the thermal distribution. A comparison to the thin-rod or single-crystal-fiber geometry is theoretically carried out. Ultrafast laser signal amplification up to high average power is successfully demonstrated. The beam quality degradation at different power levels is analyzed.
2. LASER HEADS DEVELOPMENT
Laser heads based on the AE of the rectangular cross section with along-the-side and along-the-edge pump geometries were manufactured. The 1.5 at. % doped Yb:YAG crystals of ${{3}} \times {{3}} \times {{20}}\;{\rm{mm}}$ size were used. AEs were glued on the SiC heatsinks by the side surface using ultraviolet epoxy resin. In the case of along-the-face pumping, the AE was glued on one side to the heatsink plate of 1 mm thickness. For the along-the-edge pumping, the AE was glued by two adjacent sides to the 1-mm and 2-mm thick heatsinks. Both designs were soldered to the water-cooled copper block on the side of a 1 mm heatsink. Photos of the laser heads under pumping are shown in Fig. 2.
Two diode pump sources were used in different experiments. The first one is a high-brightness source with a fiber output of 105 µm core diameter and 0.22 numerical aperture with a wavelength of 940 nm and a power of 100 W. The second one is a high-power source with a fiber output with a core diameter of 200 µm and a numerical aperture of 0.22 with a stabilized wavelength of 969 nm and a power of 350 W. Telescopes were used to transfer the image from the fiber output inside the crystal. The pump beam waist diameter for both pump sources equaled 0.4 mm. Pump absorption efficiency was equal to $\sim 80\%$ for both sources. Dichroic mirrors reflecting 1030 nm and transmitting 940 nm and 969 nm were used to separate the signal and pump radiation.
3. THEORETICAL MODEL
For the theoretical analysis of the thermal and laser processes, we used a model based on the joint solution of a system of rate equations and a nonlinear heat equation that takes into account the temperature dependence of the Yb:YAG heat conductivity. The model is very similar to the one described in [10], but modified to consider a 3D thermal problem. Rate equations were still solved in 2D because of the axially symmetric pump and signal distribution. The pump distribution in the AE was calculated using the 3D ray-tracing method to consider non-coplanar rays and then transferred to 2D by averaging along the axial axis. The temperature distribution in Yb:YAG crystals as well as in SiC plates was considered. The obtained temperature distribution was used to calculate the profile of thermally induced phase distortions of radiation as, for example, in [11]. The key contribution to the phase distortions was made by the component associated with the temperature change of the refractive index dn/dT. According to the estimates, the components associated with the thermal expansion of the sample and with the population lens can be considered negligible. The following parameters were used in the calculations. The Yb:YAG thermal conductivity was considered to be temperature-dependent and taken from [12]. The Yb:YAG quantum defect equaled 6.8% [13], lifetime ${-}\;{0.95}\;{\rm{ms}}$ [14], and dn/dT - 12.1e-6 1/K [15]. The SiC thermal conductivity was equal to ${{400}}\;{\rm{W/m/K}}$ [16]. The heat transfer coefficient between the Yb:YAG crystal and SiC heatsink as well as on the cooled boundary of SiC heatsink (between the SiC and water-cooled copper plate) was considered to be ${{12}}\;{\rm{W/c}}{{\rm{m}}^2}/{\rm{K}}$ [11]. For the comparison, the calculation was also carried out for the thin-rod Yb:YAG AE of 1 mm diameter with a similar length, doping, pump parameters, and boundary conditions (${{12}}\;{\rm{W/c}}{{\rm{m}}^2}/{\rm{K}}$ heat transfer coefficient on the side boundary).
4. THERMAL EFFECTS INVESTIGATION
A thermal effects investigation was carried out with the high-brightness pump source of 100 W power. The temperature distribution on the input end of the crystal was calculated and measured by the IR camera. The distance between the center of the pump beam and the AE side faces was varied from 0.5 to 1.5 mm. The temperature relative to the cooling liquid temperature was considered. The calculated temperature distributions for a 0.5 mm distance are shown in Fig. 3(a). Experimental and theoretical values of maximal temperature as a function of the distance between the pump area center and crystal faces, and the theoretical value of temperature for a thin-rod AE are shown in Fig. 3(b).
Fig. 3. (a) Theoretical temperature distribution relative to the temperature of the cooling liquid at the input end of the AEs for along-the-face and along-the-edge pump geometries for a 0.5 mm distance between the center of the pump area and the crystal faces. (b) Experimental and theoretical values of maximal temperature as a function of the distance between the pump area center and crystal faces, and the theoretical value of temperature for a thin-rod AE.
Fig. 4. (a) Experimental profiles of thermally induced distortions in along-the-side and along-the edge pump geometries for a 0.5 mm distance between the center of the pump area and the crystal faces. (b) Theoretical and experimental curves for the thermal lens optical power plotted versus distance between the pump area center and the crystal face calculated along x and y axis for the along-the side pump geometry and along x $+$ 45° and y $+$ 45° axes for the along-the-edge pump geometry.
In the along-the-face pump geometry, the temperature is 20–30% higher than in the along-the-edge one and the crystal volume has been heated entirely. The temperature of the crystals decreases linearly with a decreasing distance between the center of the pump area and the crystal faces. According to the calculations, the difference between the along-the-edge pump geometry and the thin-rod AE is ${\sim}{{25}}\%$ under similar boundary conditions. However, the cooling for a flat surface can be organized much more efficiently than for a cylindrical surface of a small diameter. Thus, the thin-rod AE considered here is an idealized case, and is practically unfeasible. The slight difference between the theory and the experiment may be attributed to the difference in the thermal conductivity of the crystal from the one used in the calculation, but this does not interfere with the analysis of the results.
One of the features of phase distortions appearing in systems with asymmetric cooling is the beam displacement on the switching of the pump. Our measurements have shown that, in the along-the-face pump geometry, the amplified beam is deflected only by 0.15°, which is not a problem from the point of view of the amplifier operation, since, due to the large value of the thermal lens, it is usually adjusted and operates at a fixed pump power.
Fig. 5. (a) Experimental dependence of the output power on the pump power and (b) result of measuring ${\rm M}^2$ for the along-the-edge pump geometry with 0.5 mm distance to the faces when using the high-brightness pump source of 100 W power.
Thermal-induced phase distortions were measured using phase-shifting interferometry in the Mach–Zehnder interferometer. The experimental profiles of thermally induced phase distortions of the beam for two pump geometries are shown in Fig. 4(a). The profile of the distortions follows the temperature distribution in the crystal. For quantitative analysis, the distortions were divided into the parabolic (thermal lens) and the nonparabolic (aberration) components. The optical power of the thermal lens was calculated for the parabolic component. To estimate the astigmatism strength, it was calculated along the principal axes, which are horizontal and vertical for the along-the-face pump geometry (x and y axes), and rotated 45 degrees for the along-the-edge pump geometry (x $+$ 45° and y $+$ 45° axes), as shown in Fig. 4(a). The theoretical and experimental dependences of the thermal lens optical power on the distance between the center of the pump area and the crystal face are shown in Fig. 4(b).
The results of calculations and experiments agree with good accuracy. The slight difference, as in the case of temperature, may be due to the different real and theoretical thermal conductivities of the crystal. The thermal lens astigmatism was less than 10% in both pump geometries, and that is acceptable. In the calculation for both geometries, the lens strength along one principal axis coincided with the calculation for a thin-rod AE, and along the second principal axis it was slightly less. In addition, it was almost independent of the position of the pump area, which means that the temperature gradients inside the pump area are unaffected by the crystal geometry.
To analyze the magnitude of phase aberrations, we calculated the parameter ${\rm M^2}$ for an aberrated Gaussian beam of 0.2 mm radius at ${{1/}}{{\rm{e}}^2}$ level by finding its profiles along the caustic using an integral equation, similarly to [13]. For both geometries and both principal axes, it was ${\lt}{1.1}$.
All the presented results are valid in full measure for a circular rod pumped along the cylindrical side surface, as shown in Fig. 1(c), which, in fact, is similar to the geometry of pumping along the face for a sufficiently large crystal diameter.
5. ULTRAFAST SIGNAL AMPLIFICATION
Amplification of the ultrafast signal was carried out for along-the-edge pump geometry for a 0.5 mm distance between the center of the pump area and the crystal faces with two different pump sources. One-pass amplifier and pumping schemes with copropagating signal and pump beams were used. As a seed, an ultrafast laser system was used that consisted of a fiber oscillator with 1 W average power, a 3 MHz repetition rate, and 350 fs spectrally limited pulse duration stretched up to 50 ps, and two-pass Yb:YAG thin-rod amplifier amplifying signal up to 30 W average power. The amplifier output power as a function of the pump power when using the high-brightness pump source of 100 W power is shown in Fig. 5(a). The ${\rm M}^2$ factor of the amplified beam was determined by measuring the profiles along the caustic, as shown in Fig. 5(b). High amplification efficiency ($\sim 30 \%$) and excellent beam quality is demonstrated in this experiment. The beam quality is similar along both principal axes (x $+$ 45° and y $+$ 45°). The thermal lens astigmatism is almost invisible in the plot.
The integral depolarization ratio of the signal beam was measured by the crossed polarizers and equaled less than 0.5%.
Then the amplifier was tested with a high-power pump source of a 350 W average power. The dependency of the output power on the pump power is shown in Fig. 6(a).
Fig. 6. (a) Dependency of the output power on the pump power, and (b) dependency of integral depolarization on the pump power, and depolarized beam profile, for the amplifier with along-the-edge pump geometry when using the high-power pump source of 350 W power.
The 115 W output power at a 350 W pump power was achieved, which corresponds to ${\sim}{{24}}\%$ amplification efficiency. Decreasing the efficiency in comparison to the previous experiment is concerned with a higher beam divergence of the pump beam. The dependency on the pump power is linear except for a slight power reduction at a 350 W pump power. It can be associated with decreasing the beam size inside the crystal due to the thermal lensing effect. Thermal lens precompensation will solve this problem. The linear temperature gradient in the crystal associated with its asymmetric cooling leads to the appearance of stresses and, as a consequence, to a strong depolarization effect that is homogeneous over the whole beam aperture. This effect can be compensated by successive half-wave and quarter-wave plates. The residual depolarization beam profile and dependency of integral depolarization on the pump power are shown in Fig. 6(b). It did not exceed 6.5% and can be reduced when using a two-pass amplifier scheme with depolarization compensation.
The ${{\rm{M}}^2}$ parameter of the output beam was measured at different pump power levels, as shown in Fig. 7(a). The beam quality smoothly degrades when the pump power increases. The beam quality remains good (${{\rm{M}}^2} \lt {1.4}$) up to a 250 W pump power that corresponds to a 100 W output power. At higher power, it increases further and becomes different along the principal axis. The beam ellipticity equals to 0.85 in this case. The results of the measurements at maximum pump power are shown in Fig. 7(b).
Fig. 7. (a) Dependency of the ${{\rm{M}}^2}$ factor on the pump power and (b) the result of its measurement for 350 W pump power.
The beam takes on the shape of a donut beyond the waist, which is presumably concerned with the gain saturation effect described in [17]. This effect does not depend on the AE geometry and also appears in the thin rods. The FWHM spectrum bandwidth of the amplified signal was about 2 nm, which corresponds to the previously published results on Yb:YAG amplifiers with similar output parameters [6,8]. Pulse compression at this average power level can be performed using CVBG and will be done in the near future.
6. DISCUSSIONS AND CONCLUSION
We have proposed what we believe, to the best of our knowledge, a new approach to the development of high-average-power laser amplifiers with the along-the-side pump geometry that is based on three main features: first, using standard rod AEs with a large transverse size; second, using end diode pumping with a beam size much smaller than the transverse size of the AE; and third, shifting of the pump area maximum close to the AE side surface to enhance the efficiency of its cooling and reduce parasitic thermal effects.
Laser heads based on Yb:YAG AEs with along-the-face and along-the-edge pump geometries are investigated from the point of thermal effects. A theoretical comparison with a thin-rod AE of 1 mm diameter with a similar length, doping, pump parameters, and boundary conditions is carried out. The investigation showed that the proposed geometries possess a slightly higher temperature in the pump area than the thin rod ($\sim 25\%$ for along-the-edge geometry). It should be noted that the cooling for a flat surface can be organized much more efficiently than for a cylindrical surface of a small diameter. Thus, the thin-rod AE considered here is an idealized case, and is practically unfeasible. The phase distortions investigation showed that the proposed geometries possess very similar thermal lens optical power as the thin-rod AE with weak astigmatism (${\lt}{{10}}\%$). One specific feature of the proposed geometries is an insignificant beam deflection (less than 0.15°) on switching the pump, which may be compensated for by adjusting the optical scheme.
The high efficient ultrafast signal amplification is experimentally demonstrated with two different pump sources. More than 60 W average power with negligible depolarization and excellent beam quality was achieved when using the high-brightness source with a fiber output of 105 µm core diameter, a wavelength of 940 nm, and a power of 100 W. An average power of 115 W was obtained when using a high-power source with a fiber output of a 200 µm core diameter, a stabilized wavelength of 969 nm, and a power of 350 W. The amplification efficiency with a high-power pump source was sufficiently lower, which is attributed to the higher beam divergence of the pump beam. The depolarization at 350 W pump power did not exceed 6.5%. The beam quality smoothly degraded when the pump power increased. Up to a 100 W output power, the beam quality remained reasonable (${{\rm{M}}^2}\; \lt \;{1.4})$. At higher power, it increases further and becomes different along the principal axes. However, the significant and perhaps dominant factor limiting the beam quality was the gain saturation effect taking place in all end-pumped Yb:YAG amplifiers [17].
The obtained results demonstrate that the proposed geometries are in no way inferior to the thin-rod or the single-crystal-fiber AEs. The achieved output parameters outperform or compete with those obtained with other end-pumped Yb:YAG amplifiers [6–9]. However, the proposed geometries possess a number of technological advantages, including easy manufacturing of the AEs; easy mounting of the AEs in a cooling system; and the possibility of using both standard rod AEs with round and square cross sections and elements of arbitrary size and arbitrary shape of the lateral surface. In fact, to implement the pumping along the face, it is sufficient to process one flat face of the crystal and organize its cooling. Analogously, for pumping along the edge, only two adjacent faces of the AE must be processed. This degree of freedom makes the proposed approach ideal for the development of the amplifiers on fragile, hard-processed, or rare and unique gain media.
On the basis of this approach, other promising options for amplifier geometries can be proposed. For scaling the power and energy of the output radiation pulses, an oval or rectangular pump beam can be used in the along-the-face pump geometry, with the wide face being parallel to the cooled face. This geometry will be analogous to the thin-slab geometry. Another attractive solution is the application of the considered geometries in a four-channel amplifier, where four parallel beams are amplified in one AE, passing along its four side faces or four edges. Such a solution will substantially simplify the scheme of a multichannel system and provide the maximum identity of the amplifying channels.
Funding
Russian Science Foundation (18-12-00416).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
REFERENCES
1. H. Stark, J. Buldt, M. Müller, A. Klenke, and J. Limpert, “1 kW, 10 mJ, 120 fs coherently combined fiber CPA laser system,” Opt. Lett. 46, 969–972 (2021). [CrossRef]
2. F. Stutzki, F. Jansen, H.-J. Otto, C. Jauregui, J. Limpert, and A. Tünnermann, “Designing advanced very-large-mode-area fibers for power scaling of fiber-laser systems,” Optica 1, 233–242 (2014). [CrossRef]
3. M. Kienel, A. Klenke, T. Eidam, S. Hädrich, J. Limpert, and A. Tünnermann, “Energy scaling of femtosecond amplifiers using actively controlled divided-pulse amplification,” Opt. Lett. 39, 1049–1052 (2014). [CrossRef]
4. W. Zhao, X. Hu, and Y. Wang, “Femtosecond-pulse fiber based amplification techniques and their applications,” IEEE J. Sel. Top. Quantum Electron. 20, 3100513 (2014). [CrossRef]
5. X. Délen, Y. Zaouter, I. Martial, N. Aubry, J. Didierjean, C. Hönninger, E. Mottay, F. Balembois, and P. Georges, “Yb:YAG single crystal fiber power amplifier for femtosecond sources,” Opt. Lett. 38, 109–111 (2013). [CrossRef]
6. L. Veselis, R. Burokas, O. Ulcinas, T. Gertus, K. Michailovas, and A. Michailovas, “Depolarization compensation with a spatially variable wave plate in a 116 W, 441 fs, 1 MHz Yb:YAG double-pass laser amplifier,” Appl. Opt. 60, 7164–7171 (2021). [CrossRef]
7. X. Bu, Y. Xu, Z. Peng, H. Li, and P. Wang, “100 W, 7 ps hybrid Yb-fiber and Yb:YAG thin-rod MOPA laser,” Proc. SPIE 11455, 114553T (2020). [CrossRef]
8. V. Markovic, A. Rohrbacher, P. Hofmann, W. Pallmann, S. Pierrot, and B. Resan, “160 W 800 fs Yb:YAG single crystal fiber amplifier without CPA,” Opt. Express 23, 25883–25888 (2015). [CrossRef]
9. J. Yang, B. Lee, J. W. Kim, B. Jeong, E. G. Sall, S. A. Chizhov, D. Heo, V. E. Yashin, and G. H. Kim, “Femtosecond laser system based on thin rod Yb:YAG active elements with an output power of 110 W,” Quantum Electron. 49, 1168–1171 (2019). [CrossRef]
10. I. Kuznetsov, I. Mukhin, O. Palashov, and K.-I. Ueda, “Thin-tapered-rod Yb:YAG laser amplifier,” Opt. Lett. 41, 5361–5364 (2016). [CrossRef]
11. I. I. Kuznetsov, I. B. Mukhin, D. E. Silin, A. G. Vyatkin, O. L. Vadimova, and O. V. Palashov, “Thermal effects in end-pumped Yb:YAG thin-disk and Yb:YAG/YAG composite active element,” IEEE J. Quantum Electron. 50, 133–140 (2014). [CrossRef]
12. Y. Sato, J. Akiyama, and T. Taira, “Effects of rare-earth doping on thermal conductivity in Y3Al5O12 crystals,” Opt. Mater. 31, 720–724 (2009). [CrossRef]
13. I. Kuznetsov, A. Pestov, I. Mukhin, M. Volkov, M. Zorina, N. Chkhalo, and O. Palashov, “Composite Yb:YAG/sapphire thin-disk active elements for high-energy high-average power lasers,” Opt. Lett. 45, 387–390 (2020). [CrossRef]
14. D. S. Sumida and T. Y. Fan, “Emission spectra and fluorescence lifetime measurements of Yb:YAG as a function of temperature,” in Advanced Solid-State Lasers, T. Fan and B. Chai, eds., Vol. 20 of OSA Proceedings Series (Optica Publishing Group, 1994), paper YL4.
15. Y. Sato and T. Taira, “Highly accurate interferometric evaluation of thermal expansion and dn/dT of optical materials,” Opt. Mater. Express 4, 876–888 (2014). [CrossRef]
16. M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).
17. P. Albrodt, X. Delen, M. Besbes, F. Lesparre, and P. Georges, “Simulation and experimental investigation of beam distortions in end-pumped laser rod amplifiers,” J. Opt. Soc. Am. B 35, 3004–3013 (2018). [CrossRef]
