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We analyzed the output power characteristics of a cryogenically cooled Yb:YAG total-reflection active-mirror (TRAM) laser oscillator including the temperature dependence of the emission cross section and the reabsorption loss of the Yb:YAG TRAM. A CW multi-transverse mode oscillation of a 9.8 at.% doped 0.6 mm thick Yb:YAG ceramic TRAM was investigated for various pump spot sizes and compared with theoretical results. The Yb:YAG temperatures were inferred from the ratio between fluorescence intensities at 1022 nm and 1027 nm which varied significantly with temperature below 200 K. Output power calculations using evaluated temperatures were in good agreement with the experimental data measured between 77 and 200 K, and the output power suppression due to the temperature rise observed above ~140 K. To the best of our knowledge, this is the first evaluation of output power for a cryogenically cooled Yb:YAG TRAM laser.
©2012 Optical Society of America
1. Introduction
In recent years, 10 kW-class high power solid-state-laser systems have been developed and widely used in scientific and industrial applications [1]. In the future, however, laser systems possessing not only higher output power but also optical efficiency and good beam quality will be required for many new applications. For developing such higher performance sources, thermal effects, in particular thermal lensing and birefringence loss induced by the temperature gradient inside the laser medium, are among the most significant issues to be addressed. To satisfy both, low temperature gradient in the laser gain medium and high performance operation, the choice of the laser material and the design of the amplification configuration are important.
Our early research focused on a cryogenic Yb:YAG laser in thin disk active-mirror configuration [2]. Nowadays, cryogenically-cooled Yb:YAG has attracted considerable attention as one of the perspective laser materials for high power laser systems because of its leading material properties [3–5]. Yb:YAG has low thermal loading due to its high Stokes efficiency of over 90%, and the quasi-three-level nature of the Yb3+ ion at room temperature becomes a four-level system below 100 K, therefore, eliminating the re-absorption of the laser radiation from the ground level. The peak emission-cross section of Yb:YAG increases almost fivefold at liquid nitrogen (LN2) temperature [6]. In addition to these advantages, thermal properties such as thermal conductivity, thermo-optical effects, and thermal expansion are significantly improved at low temperatures, preferred especially in high-average-power laser systems. From these benefits, below 1 W output power range, efficient operation with over 90% slope efficiency with respect to absorbed pump power has been demonstrated [7,8]. For higher power operation, slope efficiency and output power of 80% and 75 W with a sapphire conductive-cooled Yb:YAG disk [9], 85% and 165 W with a Yb:YAG rod [10], 66% and 264 W, and 59% and 550 W with Yb:YAG disks [11,12] have been reported, respectively.
In terms of amplification configuration, we believe that the thin-disk concept is one of the most efficient designs [13]. It minimizes the temperature gradient in the laser gain medium due to the large cooling area and the thin active layer. One disadvantage of this approach is the low absorption of pump power due to its thin layer (approximately 200 μm) configuration. It requires a complicated multi-pass pumping system to achieve total absorption of the available pump power. Additionally, it requires a high-reflection coating on its bottom surface, which has a quite low thermal conductivity. The temperature rise within the coating layer cannot be ignored in high intensity pumping systems.
Recently, we proposed a new total-reflection active-mirror configuration to increase the absorption and to exclude the high-reflection coating from the laser gain medium [14]. Since both pump and laser beams pass through the gain medium at an angle of 60 degrees satisfying the total-reflection condition, the optical length becomes longer and the absorption increases. Additionally, if sufficient cooling is used such as an LN2 recirculating system, the thermal resistance between laser gain medium and the coolant will be low, reducing the average temperature of the medium. We performed multi-transverse oscillation experiments to test the performance of a 9.8 at.% doped, 0.4-mm thick Yb:YAG TRAM laser and demonstrated an output power of 273 W with a high optical efficiency of 65% and slope efficiency of 72% vs. absorbed pump power.
One viable solution for power scaling over 10 kW would be increasing the number of TRAMs within laser systems like a ZigZag Active-Mirror (ZiZa-AM) laser [15]. Actually, for developing over 10 kW-class high-average power laser systems, designs using several laser elements have been already utilized [16,17]. Thus, a power potential estimation method for a single laser gain element is required to assess the possibilities for power scaling to a desired level. Comparisons between numerical models and experiments for a Yb:YAG thin disk laser oscillator at around room temperature have been reported [18,19]. To our best knowledge, however, this has not been demonstrated for temperatures below 200 K.
In this paper, we report on a simple output power estimation method for a TRAM laser oscillator at cryogenic temperatures with comparison of the output characteristics with experimental data. To increase the absorbed pump power and to achieve higher optical efficiency, we used a 9.8 at.% doped 0.6 mm-thick Yb:YAG TRAM sample whose absorption at one bounce was 95%. We used various pump spot sizes to investigate the output power and Yb:YAG temperature characteristics. In the experiments presented here, the maximum pump intensity reached up to 10 kW/cm2. At even higher pump intensities the output power was thermally suppressed. To infer the Yb:YAG temperature at each pump condition, we measured the fluorescence spectra and evaluated the Yb:YAG temperatures from the emission spectral shapes. Using estimated Yb:YAG temperature, we calculated the output power taking into consideration the temperature dependence of Yb:YAG emission cross section and reabsorption loss. The calculations were in good agreement with experimental data at temperatures below 200 K.
2. Multi-transverse mode CW oscillation and Yb:YAG temperature estimation
2.1. Experimental method
Figure 1 shows the experimental setup of our multi-transverse mode laser oscillator. A detailed discussion of the sample configuration and setup can be found in Ref [14]. Briefly, the TRAM sample, fabricated by Konoshima Chemical Co., Ltd., consists of a YAG trapezoidal prism and a 9.8 at.% doped Yb:YAG layer with 40 x 40 mm2 dimensions. In our previous work, the thickness of the Yb:YAG ceramic layer was 0.18 mm or 0.4 mm. In this work, we have used a specially designed TRAM which has a 0.6 mm-thickness of the Yb:YAG ceramic layer. This sample was put into an LN2 dewar inside a cryostat which has AR-coated windows for optical access and for measuring the fluorescence spectra form the Yb:YAG layer. A 500 W, 940 nm fiber coupled laser diode (LD) was used as a pump laser. The flat-top pump beam was focused onto the Yb:YAG layer with a spot size of 2.4 mm, 4 mm, or 6 mm, respectively. The laser cavity design was V-shaped consisting of a flat dichroic mirror (DM), a flat output coupler (OC), and a lens of f = 1000 mm. The laser output characteristics were measured by varying the reflectivity of the output coupler to estimate the resonator loss δ using the Findlay and Clay method [20].
Fig. 1 Experimental setup of the multi-transverse mode oscillator. DM, dichroic mirror, OC, output coupler, LN2, liquid nitrogen, LD, laser diode.
The temperature of the Yb:YAG layer of the TRAM is greatly influenced by LN2 boiling and resulting bubble sizes, occurring due to insufficient cooling in the non-flow geometry. The boiling effect itself strongly depends on both pump intensity and pump spot size, thus making accurate measurements at constant temperatures and understanding the output power characteristics of the TRAM laser difficult. To overcome this problem, we carried out time-resolved measurements of the output power, using a photo-diode and an oscilloscope during switch on of the LD. In these measurements, at time “zero”, just after switch-on, the sample temperature can be considered equal to the LN2 temperature. For time-resolved measurements, the LD signal was used as a trigger.
We also measured the Yb:YAG fluorescence spectra after longer pump durations (t > 10 s) to estimate the temperature dependence with respect to the pump intensity in quasi steady-state equilibrium [9]. The temperatures were evaluated by comparing the observed fluorescence spectra with temperature controlled reference spectra which were measured independently prior to the test [21]. Figure 2(a) and 2(b) show the reference spectra and the temperature dependence of fluorescence intensities at 1022 nm and 1027 nm, respectively. We used the ratio between fluorescence intensities at 1022 nm and 1027 nm, because it significantly varied with temperature below 200 K, as also shown in Fig. 2(b).
Fig. 2 (a) Fluorescence intensity of Yb:YAG at low temperatures [21]. (b) Fluorescence intensities and their ratio at 1022 nm and 1027 nm as a function of temperature.
2.2. Experimental results
Figure 3 shows the output power in steady-state as a function of pump power and pump intensity for pump spot diameters; (a) 6 mm, (b) 4 mm and (c) 2.4 mm, respectively. Note that for simplification the pump intensities were calculated by considering circular- instead of elliptical beam profiles [14,15]. When the pump spot diameter was 6 mm, the output power increased linearly and we achieved the maximum output power of 267 W. In this case, optical and slope efficiencies vs. pump power were calculated as 56% and 62%, respectively. For the cases of 4 mm and 2.4 mm pump spot sizes, output power showed saturation behavior above ~3 kW/cm2 and ~5 kW/cm2 pump intensities, respectively. The maximum slope- and optical efficiencies were 71% and 62%, respectively, in case of pumping below ~5 kW/cm2 (63.5% output coupler reflectivity), shown in Fig. 3(c). As the absorption of this sample was 95%, the slope efficiency with respect to absorbed pump power can be evaluated to be 75%. From these experiments, the average cavity loss of the TRAM laser was calculated to be 3.4%.
Fig. 3 Output powers of the 0.6 mm-thick TRAM laser as a function of launched pump power for pump spot sizes of (a) 6 mm, (b) 4 mm, and (c) 2.4 mm, respectively. Solid and dashed lines show corresponding fitting curves below output saturation intensity.
Figure 4(a) shows the time-dependent output signal measured using a photo diode for various pump powers. The pump spot size and reflectivity of the output coupler were 2.4 mm and 63.5%, respectively. As can be seen in Fig. 4(a), the output signal reduced with time due to the temperature rise of the Yb:YAG, and became almost constant within 10 seconds after LD switch-on. The output power at t = 0 was evaluated by using the output power at t = 10 seconds and the ratio of the transient signal intensities at t = 0 and 10 seconds. Figure 4(b) shows the evaluated peak power together with the results at steady-state corresponding to the results shown in Fig. 3(c). The output power at t = 0 increased linearly with pump power, and the maximum power was evaluated to be 322 W corresponding to an output intensity of 7.1 kW/cm2.
Fig. 4 (a) Time-resolved output intensity for a 2.4 mm pump spot diameter. The output coupler of 63% reflectivity was used. (b) Output power as a function of pump power at t = 0 sec and t = 10 sec after switch-on of the pump, respectively. The output power at t = 10 sec corresponds to the results shown in Fig. 2(c). The dashed line in (b) shows the fitting result.
Figure 5(a) shows inferred temperatures of the Yb:YAG layer with a 63.5% output coupler for each pump spot size as a function of the pump intensity. The measured fluorescence spectrum was a sum of spectra originating from different parts of pumped volume, therefore, the inferred temperatures represent the average temperatures. For the 2.4 mm pump spot size, we evaluated that the temperature of Yb:YAG will be over 200 K if the pump intensity exceeds 7.5 kW/cm2. As shown in Fig. 5(a), under the same pump intensity conditions, the Yb:YAG temperature rise is smaller for the smaller pump spot size. For this reason, we believe that with enlarging the excitation spot the heat transfer gradient would behave like in one dimensional case and the heat flux would be closer to a constant. Thus, the cooling ability for smaller pump spot sizes is higher due to the omnidirectional cooling. From Fig. 5(a) one can also see that the output saturation occurred around 140 K for both 2.4 mm and 4 mm pump spot sizes corresponding to pump intensities of 3 kW/cm2 and 5 kW/cm2, respectively. For 6 mm pump spot size, the temperature of Yb:YAG was 122 K at the maximum pump intensity of 1.5 kW/cm2 in this experimental region, therefore, saturation was not observed. In Fig. 5(b), an example of fluorescence spectra under high pump intensity ( = 5.7 kW/cm2) with- and without lasing is shown together with a reference spectrum for 150 K which can be found also in Fig. 2(a). There is a discrepancy between spectra at 1029.5 nm due to the lasing and amplified spontaneous emission, however, fluorescence intensities at 1022 nm and 1027 nm are invariant.
Fig. 5 (a) Temperature rise of 0.6 mm-thick TRAM sample as a function of pump intensity. (b) Example of fluorescence spectra for high pumping case with- and without lasing together with a low pumping reference spectrum at 150 K.
3. Numerical Calculations of the TRAM laser output power and discussion
In this section, we compare calculated and experimental data of the TRAM laser oscillator output power at different conditions. Figure 6 represents the schematic of the TRAM amplifier configuration. In the following, we assume that the pumped volume V is an elliptical column made by the pump diameter D as seen in Fig. 6. In the TRAM laser oscillator, the laser beam bounces within the gain medium at an angle of θ with the output power expressed by the well know equation [22]:
where Is(T) is the saturation fluence, S is the cross section of the pump beam, R is the reflectivity of the output coupler, g0(T) is the small signal gain coefficient, l is the optical length of the gain medium for one bounce, which can be expressed by using the thickness of Yb:YAG layer d, l = 2d/cosθ, δ is the cavity loss, and α’(T) is the reabsorption coefficient, which is dependent on the temperature. The temperature dependence of the Yb:YAG emission cross section σemi(T), given in Ref [6], can be used for evaluating the saturation fluence and the small signal gain coefficient for the four-level system as follows: where fl and fu are the fractional populations in the lower and upper laser levels of Yb:YAG for a given temperature, τf is the lifetime of the upper manifold, ηt is the pump radiation transfer efficiency to the gain medium, ηQ is the quantum efficiency, ηS is the Stokes efficiency, ηa is the absorption efficiency of the pump power for one bounce, ηB is the beam overlap efficiency, hν is the photon energy of the laser, and P is the pump power. The reabsorption coefficient α’(T) can be expressed by [22]Here I is the laser fluence in the cavity and α0(T) is the reabsorption coefficient in the unpumped medium given bywhere N0 is the total dopant concentration. In the calculations, we used the following parameters: τf = 1.0 ms, ηt = 0.96, ηQ = 1.0, ηS = 0.91, ηa = 0.95, ηB = 0.91, hν = 1.93 x 10−19 J, N0 = 9.8 at.% x (1.38 x 1020 cm−3), θ = 60 degrees, R = 63.5%, and δ = 3.4%, respectively. The beam overlap efficiency ηB was determined to fit the experimental data.Figure 7 shows the calculated and experimental results for output power for different pump spot diameters. In the calculations, evaluated Yb:YAG temperatures, shown in Fig. 5, were used. Calculated results were in good agreement with the experiments except at the highest pump intensity in the case of 2.4 mm excitation spot size. The small discrepancy at that point may be caused by a larger error in Yb:YAG temperature estimation above 200 K. To investigate correlations between Yb:YAG temperature and laser output, we calculated the output power as a function of temperature at the highest pump intensity (D = 2.4 mm, P = 403 W, and R = 63.5%). Figure 8 shows the calculated results, and it is seen that the output power is practically unchanged below ~140 K. The decreasing slope of the output power can be attributed to the decrease of emission cross section and increase of the reabsorption loss.
Fig. 7 Experimental and numerical results of output power characteristics at thermal equilibrium with respect to pump power for pump spot diameter of (a) 6 mm, (b) 4 mm and (c) 2.4 mm, respectively.
Fig. 8 Calculated results of output power as a function of temperature for the 2.4 mm pump spot diameter, pump power of 403 W and the output coupler reflectivity of 63.5%. The black circle shows the experimental data point for the same pump and output coupler conditions, whose temperature and output power can be found in Fig. 5(a) and Fig. 7(c).
As discussed above, in the case of large pump spots one would expect reduced cooling efficiency due to the one dimensional heat flow mechanism. In that case, the maximum temperature of the Yb:YAG layer can be expressed by
where IQ is the generated heat flux, h is the heat transfer coefficient, K(T) is the thermal conductivity, and TLN is the LN2 temperature. Based on our numerical results we believe that the pump power can be increased if the average Yb:YAG temperature of TRAM is kept below ~140 K. To calculate the pump power corresponding to maximum achievable output power, the heat transfer coefficient needs to be known. However, it is difficult to evaluate this parameter in the present TRAM system since the thermal resistance, due to the LN2 boiling, would change depending on the pump condition. In our future works, finite-element model calculations will be carried out to understand the thermal resistance and the temperature distribution in detail. Also, we will introduce an LN2 re-circulation system in our experiments as in Ref [12]. to avoid the decline of the heat transfer coefficient between Yb:YAG layer and LN2.4. Conclusions
In conclusion, we have performed multi-transverse mode power oscillation experiments using a 9.8 at.% doped, 0.6 mm-thick Yb:YAG TRAM sample to determine its output power characteristics. We obtained 135 W output power at thermal equilibrium with high optical and slope efficiencies of 61% and 71% with respect to pump power, respectively. By enlarging the pump spot diameter, we obtained a maximum output power of 267 W. We also investigated the Yb:YAG temperature from the ratio between fluorescence intensities at 1022 nm and 1027 nm. We applied a simple output power calculation method for the Yb:YAG TRAM laser oscillator demonstrating very good agreement with the experimental data at cryogenic temperatures. From these results, we believe that in output power calculation the inferred average temperatures could be used for multi-transverse mode oscillator in present pump conditions. Present experimental results and output power calculations including the temperature dependent emission cross section and reabsorption loss of Yb:YAG, indicate that the laser will not operate efficiently if the Yb:YAG temperature is above ~140 K. By introducing an LN2 re-circulation system, the temperature rise can be reduced, hence increasing the pump- and output powers, and efficiency of the system. To investigate the output power in the absence of a temperature rise, time-resolved output power measurements have also been performed. It was revealed that the power output at time “zero” pump, where the TRAM temperature can be considered to be equal to 77 K, was not suppressed below 10 kW/cm2 pump intensity, and a maximum peak output intensity of 7.1 kW/cm2 was demonstrated.
The temperature retrieval method using steady-state fluorescence intensity ratio at different wavelengths revealed to be useful for determining the Yb:YAG temperature rise for thin layers for temperatures below 200 K. From the inferred temperatures, we found that the smallest pump spot size yields the best cooling efficiency due to the omni-directional heat flux. In our future works, however, the whole cooling area will be pumped for multi-kW output power and MOPA system using TRAM elements will be configured to obtain a good beam quality. In order to understand the power potential and beam profile, thermal conditions should be studied both experimentally and theoretically. To obtain the detailed temperature distribution in the Yb:YAG layer and thermal resistance, finite element model calculations will be performed. Additionally, the gain distribution due to the temperature gradient in the Yb:YAG layer will be considered for power scaling of the MOPA system. The amplification characteristics of the TRAM laser such as the small signal gain, wave-front distortion, beam profile, and birefringence loss are also under investigation. From the wave-front distortion measurement results we expect that for the pump intensities of up to 1 kW/cm2 the transmitted wave-front, ignoring defocus component which can be compensated by lenses, will be almost aberration free. The amplification characteristics and detailed discussions will be reported in the future.
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