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Abstract
We report the first observation of laser cooling in Yb3+:KYW and validate the results by comparison with experiments in the well-studied material Yb3+:YAG. Radiation from a single-mode Ti:Al2O3 laser was used to achieve cooling of 1.5 K/W in 1% Yb:KYW at 1025 nm, comparing well with the reference material 3% Yb:YAG which cooled by 3.5 K/W at 1030 nm under open lab conditions. Experimental results for KYW crystals mounted on aerogels and doped with 1-20% Yb were in excellent agreement with the theoretical dependence of cooling power on the Yb absorption spectrum. Elimination of thermal conduction through the sample support structure was found to permit the attainment of lower temperatures and to simplify modeling of radiation balance conditions in self-cooled lasers with longitudinal thermal gradients. Contrary to the notion that more coolant ions yield higher cooling power, concentrations of Yb over 1% caused re-absorption of luminescence in KYW crystals, leading to a progressive red shift in the optimal cooling wavelength and the prevention of laser cooling altogether in a 20% sample at room temperature. The prospect of attaining radiation-balanced lasing in commercially-available tungstate crystals is evaluated.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical refrigeration was first achieved using laser-induced anti-Stokes fluorescent emission in Yb3+:ZBLANP glass in 1995 [1]. This experiment demonstrated that light could indeed cool bulk matter through changes in the mode structure of the optical field that led to entropy flow and heat transfer [1–3]. Since then, advances in experimental methods and the purification of materials have led to optical cooling of crystalline media [4], the reduction of attainable temperatures to the cryogenic range [5,6], the first optical cryocooler [7], and self-cooling or radiation-balanced lasers (RBLs) [8,9]. Despite these advances, only one active ion has been investigated for solid-state lasers with reduced heat loads, namely trivalent Ytterbium, and the host media of self-cooled lasers reported to date comprise only KGW [9], YLF [10], and YAG [10–12]. Consequently, many material systems remain to be evaluated for their suitability as self-cooled gain media. In this paper, we investigate laser cooling of crystalline Yb:KY(WO4)2 or Yb:KYW which has a high figure of merit for radiation-balanced lasing [4] but has not previously been investigated. In parallel with benchmark measurements of Yb:YAG, a well-studied RBL crystal, we report the first observations of laser cooling in Yb3+:KYW, performed at atmospheric pressure near room temperature. The prospects for achieving radiation balance and RBL laser action in KYW crystals doped with concentrations of trivalent Ytterbium ions in the range of 1-20% are evaluated.
In order to reach cryogenic temperatures with optical refrigeration, vacuum enclosures with low emissivities are typically used to reduce heat loads originating from thermal conduction through air and blackbody radiation [1]. For self-cooled lasers, however, operating in the open lab the objective is different, being to reach high output powers at atmospheric pressure while maintaining thermal equilibrium with the environment. Hence in RBL research the blackbody heat load, proportional to the difference between sample and lab temperatures to the fourth power, is vanishingly small. Similarly, when the RBL condition is met, the thermal gradient and conduction over the cross section of the gain medium is negligible. However, small temperature gradients may exist at points of support and between the ends of an RBL crystal, leading to non-optimal performance. More uniform temperature distributions call for RBL designs that reduce or eliminate thermal transport at points of contact. Sample holders that minimize thermal conduction while maintaining a practical degree of mechanical support are therefore a significant part of the design of practical RBL resonators. Laser cooling by 8.8 K was previously reported [12] in a Yb:YAG crystal supported by glass fibers inside a sealed chamber at atmospheric pressure. It was found that thermal conduction through the glass fibers had to be taken into account to model the results accurately. Here we have compared the temperature drops obtainable with glass and silica aerogel supports and found that aerogels improved thermal isolation by a factor of three while maintaining a rigid structure suitable for high power, self-cooled lasers. While the reduction of thermal loads at contact points is not essential for reaching radiation-balanced conditions in commercial RBL crystals, it improves the uniformity of temperature distributions and the predictability of the radiation balance requirements. At the same time, improved thermal isolation makes it possible to investigate laser cooling in less common host materials. This is advantageous if the test materials are less pure than ones that have undergone decades of optimization. Crystal growth of YAG, for example, has benefited from efforts to minimize impurities in controlled atmospheres, owing to its popularity as a laser host. KYW on the other hand is far less common as a laser host and could have background impurity levels high enough to prevent optical cooling altogether. With these considerations in mind, we investigated laser cooling in four commercial KYW crystals doped with concentrations of Yb between 1% and 20%.
2. Experiments and results
Thermal lens spectroscopy (TLS) was performed as a first step to characterize the external quantum efficiency (ηext) and background impurity absorption coefficient (αb) of our samples. If the absorption coefficient of the coolant ions αc(λ) is known, the parameters ηext and αb govern the theoretical cooling power [11] at a laser wavelength of λ through the formula
Fig. 1. (a) Absorption and emission cross sections for 3% Yb:YAG. (b) Absorption and emission cross sections for 1% Yb:KYW (polarization E||Nm). (c) Emission spectra for samples of Yb:KYW doped with 1, 2, 10, and 20% Yb3+ (polarization E||Nm). (d) DLT calibration plot for 1% Yb:KYW.
For the TLS measurements, a tunable Ti:Sapphire laser was used to pump the samples and a counter-propagating He-Ne laser probed the induced thermal lens at 632.8 nm. In order to increase the signal-to-noise ratio, the pump beam was chopped mechanically and the signal from the photodiode was detected synchronously using a lock-in amplifier. TLS signals were modeled by considering two separate contributions to lensing – a fast one from photo-induced population change between the ground and excited states, and a slower one from thermal diffusion. The refractive index changes due to both processes had to be included to model the complex transient TLS signal accurately [17,18] over the pump wavelength range 930-1030 nm. The normalized TLS signal and the fits accounting for population and thermal effects are shown in Fig. 2(a) for the 1% Yb3+:KYW crystal. At 942 nm, a strong population lens contribution caused a rapid initial increase of the signal. At long times, the thermal effect dominated, causing the signal to decrease. At 1025 nm, the thermal component in Fig. 2(a) reversed sign, indicative of sample cooling.
Fig. 2. (a) TLS transient signals for 1% Yb:KYW at 942 nm (heating) and 1025 nm (cooling), magnified by a factor of 7. (b) TLS measurements of cooling efficiency in the same sample as a function of wavelength. The external quantum efficiency and background absorption coefficient are obtained by the best fit of Eq. (2) to the data and are listed in Table 1.
Table 1. Sample specifications and parameters deduced from TLS and DLT analysis.
Best fits of the TLS signals provided values for the thermal lens strength, and the corresponding cooling efficiency ${\eta _c}$ derived from it, at fixed wavelengths within the pump range. This cooling efficiency was then plotted versus wavelength (see Fig. 2(b)) and a least squares best fit was found to the expression [1]
Samples were supported in either of two ways: (a) on three glass capillaries oriented transverse to the sample length to minimize the line contacts and thermal load from the supports, or (b) on a commercial aerogel disk (Classic Silica Disk, Aerogel Technologies). Pump radiation was focused to a spot diameter of 165 μm and passed once through the sample, generating infrared luminescence (Figs. 1(a)–1(c)) that was analyzed by DLT in a time short enough (20 ms) to permit real-time tracking of the temperature dynamics. One hundred measurements were averaged to reduce noise, i.e. 2 seconds per measurement. Infrared camera data obtained with a FLIR A655sc (equipped with a T198059 lens with resolution of 50 μm/pixel in the 7.5-14 μm range) also yielded good temporal and spatial resolution in quantitative agreement with the temperature curves deduced from differential luminescence thermometry, as shown in Figs. 3(a) and 3(b). In these figures, lineouts are shown for two different parts of the overall thermal image. The red curve monitored the support material immediately adjacent to the crystal. The blue curve monitored temperature versus time of the crystal itself. For comparison, temperatures deduced from differential luminescence are shown in black, closely overlapping the blue curve.
Fig. 3. (a) Data from the infrared camera, showing image lineouts of temperature versus time of the 1% Yb:KYW crystal (blue) and the glass support next to it (red). Because the camera was focused on the crystal, not the glass, only the left scale is accurately calibrated. (b) Image lineouts and DLT data on temperature versus time for the same sample on aerogel. For comparison, in each of Figs. 3(a) and 3(b), temperature versus time obtained by the DLT method is also displayed (black). (c) Longitudinal temperature distribution of the crystal on glass supports. (d) Longitudinal temperature distribution of the crystal on an aerogel disk. For Figs. 3(c) and 3(d), insets show the thermal camera image and pump beam (introduced from the left).
A small temperature drop, followed by a heating transient, was observed in samples supported on glass (Fig. 3(a)) in both the thermal camera and DLT data. This was interpreted as the result of fast initial cooling in the interaction volume followed by an influx of heat from uncooled portions of the sample itself and through contacts of the sample with its holder. Curves on glass support were not reproducible, because of the random positioning and variable contact between the crystals and the glass. Occasionally cooling even turned into heating when crystals were re-positioned. Upon replacing the glass supports with an aerogel disk, the data of Fig. 3(b) were obtained. Despite the increase in contact area incurred by placing the crystal directly on this support, the thermal isolation improved markedly due to the exceedingly low thermal conductivity of the aerogel. Three-dimensional COMSOL simulations of heat transport and cooling (as well as the infrared camera data of Figs. 3(a) and 3(b)) confirmed that localized heat transfer through the contact points of a crystal supported by glass capillaries offset most of the radiative cooling provided by the laser beam. Much larger temperature drops, indicating better thermal isolation, were noted in samples supported on aerogels. Glass supports were heated by fluorescent emission from the sample as evidenced by the red trace in Fig. 3(a) whereas the aerogels absorbed less fluorescence and cooled, as shown by the red trace in Fig. 3(b). Additionally, a small heating transient in the blue and black curves tracking sample temperature in Fig. 3(a) disappeared with the use of aerogels (Fig. 3(b)). This indicated that the heat load responsible for the observed rise of temperature following the fast initial drop was delivered through the glass supports and was negligible with aerogels. An experimental trace of the longitudinal temperature distribution in a 1% Yb:KYW crystal on glass is shown in Fig. 3(c). Two peaks in temperature were observed at contact points between the sample and glass, confirming the strong influx of heat from the support. Although the support was made of three capillaries, only two of them made contact with the crystal in this experiment. The temperature distribution on aerogel support was plotted in Fig. 3(d), where it may be noted that the location where temperature was lowest was not at the input face of the crystal where pump power was highest. Instead, because of convective heat input at the ends, the crystal was coolest near its mid-point.
Finite element computations were performed using COMSOL to determine sample temperature from a set of coupled equations. The equations specified relations for cooling power, the Stefan-Boltzmann Law, diffusion and convection following prior work [12]. Boundary conditions corresponded to actual sample sizes. Material parameters were taken from the literature or, in the case of emissivities, were determined from thermal camera data taken over a range of temperatures for calibration using the Stefan-Boltzmann Law. Mesh sizes for calculated temperature distributions were chosen to ensure very high spatial resolution (Fig. 4(a)). These simulations predicted more uniform cooling with twice the temperature drop on aerogels versus glass. Experimental data however showed a factor of three improvement on aerogel. This discrepancy arose from absorption of fluorescence by the glass capillaries, an extra source of heat which was omitted in the simulation but appears to be strong in the experiments on glass as indicated by the thermal camera image in Fig. 3(c). For simulations and experiments exclusively on aerogels, much better agreement was obtained. In 1% Yb:KYW and 3% Yb:YAG, the simulated temperature drop was within 10% of the experimental value based on either DLT or thermal camera measurements. In Figs. 4(d) and 4(e) the scale of the simulation has been magnified to permit more detailed visualization of the temperature distributions. It is evident in these figures that on aerogel the temperature distribution is more uniform and the longitudinal gradient of temperature is smaller than on glass. The points of contact on glass can also be seen to display local heating which is absent in the results on aerogel. Residual differences between measured and simulated temperatures on aerogel supports in Figs. 3 and 4, while small, were ascribed to non-optimal positioning of the pick-up fiber in relation to the point of lowest temperature along the sample axis. A further conclusion can be drawn from Fig. 4(f) where the temperature drop obtained on a fictitious substrate having zero thermal conductivity is simulated. While a non-conducting substrate provides better thermal isolation as expected, the experimental results on aerogel (Fig. 3(b)) reveal a temperature drop that is 70% of the theoretical value, showing nearly ideal performance. Thus, the combined results of Figs. 3–4 confirm that better thermal isolation and greater uniformity of temperature can be achieved with the use of aerogel supports.
Fig. 4. (a) Images of the crystal and mesh geometries used for the COMSOL simulation. The upper inset shows the 3-D mesh of the crystal end and the lower one shows the 2-D mesh grid on that surface. (b)-(e) COMSOL simulations of laser cooling with input power of 1 W at 1025 nm in a 1×1×10 mm3 sample of 1% Yb:KYW, on various platforms. (b) On glass. (c) On aerogel. (d),(e) are identical to (b) and (c) but have magnified temperature scales to highlight local heating and gradients. The calculated temperature drops are 0.87 K in (b), (d) and 1.73 K in (c), (e). (f) Simulation of laser cooling with a substrate thermal conductivity of zero. The calculated temperature drop is ΔT = 2.45 K. All simulations include thermal conduction, convection and black-body radiation. Crystal parameters were taken from Table 1.
By tuning the pump laser, it was possible to record the wavelength dependence of laser cooling. Cooling power in general has a nonlinear relationship with respect to temperature changes when convection, blackbody radiation and impurity absorption are taken into account. However, it exhibits a simple proportionality to the steady-state value of $\Delta T$ for small temperature excursions. The various sources of heating power are then collectively proportional to $\Delta T$ (see for example Ref. [1]) and the thermal balance equation [20] reduces to $C{{\partial T} \mathord{\left/ {\vphantom {{\partial T} {\partial t}}} \right.} {\partial t}} = a\Delta T - {P_{cool}}$, where C is the heat capacity of the cooling element and a is a constant. Setting the time derivative in this expression equal to zero, one finds ${P_{cool}} = a\Delta T$ which justifies the use of ΔT as an accurate gauge of steady-state cooling power. Experimental values of ΔT versus λ were therefore used to find values of ${\eta _c}$, ${\alpha _b}$, and a that yielded the best fit to Eq. (1). Fits are presented in Fig. 5 after normalization to the input power for convenient comparison. Optimum cooling in 1% Yb:KYW was at ∼1025 nm, in close accord with the wavelength of maximum cooling power expected from Eq. (1). Results for DLT temperature versus time at the optimum wavelengths for YAG and KYW are shown in Fig. 5(a). The cooling power versus wavelength in each sample is shown in Figs. 5(b)–5(f), where the solid curves are best fits to Eq. (1) using the experimental absorption spectra and a wavelength-independent level of background impurity absorption. The calculated maximum cooling efficiencies are 2.3% at 1050 nm for 3% Yb:YAG, 1.0% at 1030 nm for 1% Yb:KYW, 0.9% at 1038 nm for 2% Yb:KYW, 0.5% at 1051 nm for 10% Yb:KYW, and −0.8% at 1051 nm for 20% Yb:KYW. The external quantum efficiency ηext and background impurity absorption coefficients αb determined from the best fits are shown in Table 1. These values are in reasonable agreement with the estimates from thermal lens spectroscopy, apart from the absorption coefficient αb, which is considerably lower than the value from TLS. The TLS method is sensitive to the strength of the thermally-induced lens in the illuminated portion of the crystal. However, the unilluminated part of the crystal can also undergo small temperature changes due to fluorescence reabsorption that affects the inferred strength of the lens. In principle these small effects can alter the deduced value of αb but were ignored in TLS fits here. DLT measurements are not subject to this issue, and the best fit DLT curve in Fig. 5(b) is constrained by a larger data set, so the value of αb = 2×10−4 cm−1 for YAG measured by DLT was deemed to be more accurate than the TLS value. This small background coefficient in the YAG sample indicates higher purity than the KYW crystals, and partly accounts for its superior cooling power, which is evident from a comparison of Figs. 5(b) and 5(c).
Fig. 5. (a) Experimental measurements of sample temperature versus time in Yb-doped samples of YAG and KYW. (b-f) Temperature change versus wavelength, with a theoretical fit (solid curve) of cooling power from Eq. (1) using the best fit parameters of Table 1. Pump power was 1 W for (b) and (c), 0.8 W for (e) and 0.1 W for (f). In (d), the pump power was 1 W for wavelengths shorter than 1036 nm, and 0.8 W for the rest due to laser tuning limitations.
3. Discussion and conclusion
Conditions necessary for continuous radiation-balanced laser operation in 1% Yb:KYW and 10% Yb:KYW were considered next. The pump and laser wavelengths were taken to be 1022.5 nm and 1039.6 nm respectively and mean fluorescence wavelengths were taken from Table 1. With these parameters, together with an absorption cross section of 5.36×10−21 cm2 and a fluorescence lifetime of τ = 0.3 ms [21], Eq. (13) of Ref. [8] was used to evaluate radiation balance requirements in a pump beam volume of 1.4×10−4 cm3. A multi-pass pump beam was assumed to undergo complete absorption in the gain medium. The minimum pump and laser output intensities were then determined to be (IP)min=6.1 kW/cm2 and (IL)min=2.9 kW/cm2 in 1% Yb:KYW and (IP)min=38.8 kW/cm2 and (IL)min=16.3 kW/cm2 in 10% Yb:KYW when the cavity was assigned a quality factor of Q = 33000. From this comparison, it was evident that the pumping requirement for radiation balance in 1% Yb:KYW is lower than for 10% doping and the efficiency is higher. This is primarily due to non-uniform absorption in 10% Yb:KYW, where pump light is completely absorbed in the first third of the crystal. Re-absorption of fluorescence is also significant in the 10% sample, as one can see from the absence of the 980 nm emission line in Fig. 1(c). Contrary to the expectation that more coolant ions should improve laser cooling, the cooling power in 10% Yb:KYW was less than in 1% Yb:KYW or 2% Yb:KYW near room temperature. In the 20% sample, net heating was observed (Fig. 5(f)). Dopant densities below 10% are therefore the most favorable for RBL operation in KYW at present. Numerical simulations for 1% Yb:KYW predicted that laser output versus input intensity maximizes at an efficiency of η = 49% for an output coupling of 2.3%. Raw output power can be doubled if the output coupling is increased to ∼5.7%, resulting in an output of 5.5 kW/cm2 at a pump intensity of 34 kW/cm2. However, the efficiency then decreases to a mere 16%. For larger output couplings, there is no solution for radiation balance even in the most promising Yb:KYW candidate (1%), based on the limited cooling powers measured in this work. Hence cw operation of kilowatt-class RBLs should be feasible at low dopings in commercial crystals with efficiencies of up to 49%. However, because pump photons must fulfill the dual purpose of cooling and producing gain in an RBL, better performance than this would require much purer crystals, capable of delivering superior cooling power.
In summary laser cooling has been demonstrated under ambient conditions in KYW crystals doped with 10% or less concentrations of trivalent Yb. It was possible to sustain a steady temperature drop of 10 K using 8 W of power from a seeded fiber amplifier in a single pass through 1% Yb3+:KYW. Optimal wavelengths for cooling were determined to be 1025 nm in 1% Yb:KYW, 1030 nm in 2% Yb:KYW, and 1045 nm in 10% Yb:KYW. When samples were mounted on aerogels, cooling of 1.5 K/W was achieved in 1% Yb:KYW which compares well with 3.5 K/W in a reference crystal of 3% Yb:YAG at 1030 nm. Cooling power of this magnitude could support RBL action in commercial tungstate crystals in high Q cavities. Reduction of the thermal load from support structures using aerogels permits accurate theoretical modeling of self-cooled lasers, particularly when there are temperature gradients along the optical axis. This is due to reduction in the experiments of localized heating input through the support, induced by fluorescence absorption. This heat load is substantial when other support structures are used but has not been taken into account in prior theories, simulations, or cooling analyses. The use of aerogels not only draws theory and experiment closer together, but does so while maintaining the practical advantage of rigid support of laser components in radiation-balanced laser designs. Quantitative agreement (within 10%) was achieved between COMSOL modeling and measured temperature changes recorded by the DLT method or with a thermal camera. Consequently, we are confident that small non-uniformities in temperature distributions in the simulations, such as minor heating at the ends of the gain medium due to convection (Figs. 4(d) and 4(e)), are also accurate.
Although the cooling efficiencies and radiation-balanced laser conditions analyzed here are mainly limited by unintended impurity content, laser cooling in relatively impure Yb:KYW can nevertheless be achieved, at background impurity levels higher than in YAG. Given the impurity levels present in commercial-grade crystals, radiation-balanced lasing is expected to be achievable only in Yb:KYW with dopant densities less than 10% in high Q cavities since no laser cooling was observed at all in a 20% sample of Yb:KYW. Efficient high power RBL operation in KYW would clearly benefit from improved crystal growth to reduce parasitic absorption and to heighten cooling power for higher laser efficiency.
Funding
Air Force Office of Scientific Research (MURI FA9550-16-0383); Conselho Nacional de Desenvolvimento Científico e Tecnológico (425930/2018-1, Universal).
Acknowledgments
A preliminary version of these results was presented at SPIE Photonics West 2019.
Disclosures
The authors declare no conflicts of interest.
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