Accurate Characterization of the Properties of the Rare-Earth-Doped Crystal for Laser Cooling

Abstract

We present a method for calibrating a commercial thermal camera adopted to accurately measure the temperature change of the sample in a laser-induced temperature modulation spectrum (LITMoS) test, which is adopted for measuring two crucial parameters of the external quantum efficiency ${\eta }_{ext}$ and the background absorption coefficient ${\alpha }_b$ for assessing the laser cooling grade of the rare-earth-doped materials. After calibration, the temperature resolution of the calibrated thermal camera is better than 0.1 K. For the cooling grade Czochralski-grown 5% Yb³⁺:LuLiF₄ crystal, the corresponding values of ${\eta }_{ext}$ and ${\alpha }_b$ are LITMoS = measured to be ${\eta }_{ext}=99.4 \left(\pm 0.1\right)\%$ and ${\alpha }_b=1.5 \left(\pm 0.1\right)\times {10}^{-4} {\mathrm{cm}}^{-1}$, respectively.

1. Introduction

Optical cooling of solids is based on the anti-Stokes fluorescence principle, in which the average wavelength of fluorescence (${\lambda }_f$) emitted by a transparent solid is shorter than the wavelength of the coherent light ($\lambda$) for excitation [1,2]. The extra energy of the fluorescence over the excitation light comes from the kinetic energy of the lattice vibrations in the substrate [3]. The kinetic energy of the lattice vibrations is continuously pumped away, causing a temperature drop of the substrate until the cooling effect is balanced by the heating effect [4,5,6,7]. Optical cooling of solids is effective for developing both the cryogenic optical refrigerator of free vibration with high reliability and radiation-balanced lasers (RBLs) of no gain medium heating from quantum defects and non-radiative attenuation [8,9,10,11,12,13,14].

R. Epstein and co-workers first demonstrated the anti-Stokes fluorescence cooling concept on the 1 wt.% Yb³⁺-doped ZBLANP fluoride glass in 1995 [1]. Since then, researchers have focused on exploring new promising potential materials for cryogenic optical cooling. So far, net cooling by laser has been demonstrated not only in a variety of rare-earth-doped (Yb³⁺-, Tm³⁺-, Er³⁺- and Ho³⁺-) bulk and nano crystals [2,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31], but also in glassy materials [32,33,34] and semiconductors of nano structure [35,36,37]. Among all the crystals tested, fluoride crystals have exhibited the best cooling performances [38,39,40]. The Yb³⁺/Tm³⁺ co-doped LiYF₄ crystal has been cooled to a record temperature of 87 K [41] and the Yb³⁺ doped LuLiF₄ crystal has the potential to be cooled to 89 K [29]. Recently, the Yb³⁺ doped fibers (such as ZBLAN and silica fibers) have been attracting researchers as the platform for RBLs. Especially, the fibers can be further improved in purity and doped with modifiers to increase the Yb ion solubility [42,43]. Demonstration of RBLs and radiation-balanced amplifiers based on the fiber platform has also been reported [14,44,45].

M. Sheik-Bahae and R. Epstein developed a four-level model in theory to describe the laser-cooling processes of rare-earth-doped hosts with four parameters: the external quantum efficiency ${\eta }_{ext}$, the resonant absorption coefficient ${\alpha }_r\left(\lambda ,T\right)$, the background absorption coefficient ${\alpha }_b$ and the mean fluorescence wavelengths ${\lambda }_f\left(T\right)$ being derived for characterizing their cooling performances [7]. Accurate characterization of the laser cooling properties in both theory and experiment is very important for determining high-cooling-grade materials [46,47,48]. The external quantum efficiency ${\eta }_{ext}$ and the background absorption coefficient ${\alpha }_b$ are two crucial parameters for assessing the laser cooling grade of a material. The laser-induced temperature modulation spectrum (LITMoS) method has been developed to accurately measure these two parameters [48]. The laser-cooling limits of both rare-earth doped fluoride glass of ZBLAN(P) and fluoride crystal of LiYF₄ were accurately predicted from their corresponding “cooling windows” obtained with the help of the LITMoS method [41,42,48,49,50]. For instance, the minimum achievable temperature (MAT) of the Yb³⁺-doped LiYF₄ crystal was predicted to be as low as 60 K, which is lower than the temperature of liquid nitrogen [41,51,52]. However, the MAT of the Yb³⁺-doped ZBLAN glass was estimated to be only about 200 K [33]. Recently, a Yb³⁺/Tm³⁺ co-doped LiYF₄ crystal picked up by LITMoS test was used to cool a Fourier Transform Infrared detector (HgCdTe) down to 135 K [53,54].

Here we adopt the LITMoS method at room temperature to accurately characterize a sample material in its external quantum efficiency ${\eta }_{ext}$ and background absorption coefficient ${\alpha }_b$, two crucial laser-cooling parameters for assessing its corresponding cooling grade. The accuracy of the characterization depends on the precise measurement in situ of the laser-induced temperature change of the sample. A well-calibrated thermal camera is adopted to contactlessly measure the temperature of the sample in the LITMoS test. The calibration of the thermal camera is described in detail with a temperature resolution better than 0.1 K. The cooling window of a Czochralski-grown 5% Yb³⁺:LuLiF₄ crystal of size 2 $\times$ 2 $\times$ 5 mm³ is deduced from the LITMoS-measured cooling parameters. Corresponding results indicate that this crystal sample can be potentially cooled to about 110 K.

2. LITMoS Test Theory

The cooling efficiency ${\eta }_c\left(\lambda ,T\right)$ is used to deduce the cooling grade of the material and expresses as [36]:

$${\eta }_c\left(\lambda ,T\right)=1-{\eta }_{ext}\frac{{\alpha }_r\left(\lambda ,T\right)}{{\alpha }_r\left(\lambda ,T\right)+{\alpha }_b}\frac{\lambda }{{\lambda }_f\left(T\right)}$$

(1)

where ${\eta }_{ext}$ is the external quantum efficiency, and ${\alpha }_r\left(\lambda ,T\right)$ and ${\alpha }_b$ are the resonance absorption coefficient and the background absorption coefficient, respectively. The four parameters ${\eta }_{ext},{\alpha }_b,{\lambda }_f\left(T\right)$ and ${\alpha }_r\left(\lambda ,T\right)$ in Equation (1) describe the optical cooling grade of the sample. It is necessary to precisely measure the four parameters above to calculate the wavelength- and temperature-dependent cooling efficiency contour map (cooling window).

The effect of various thermal loads on the sample can be expressed as:

$$C_v\frac{dT}{dt}=-{\eta }_c{P}_{abs}+\frac{{\epsilon }_s{A}_s\sigma }{1+\chi }\left(T_a{}^4-T_s{}^4\right)+A_S{k}_h\left(T_a-T_s\right)+\frac{N{k}_l{A}_l}{d_l}\left(T_a-T_s\right)$$

(2)

In the right side of the equation, the first term represents the heat extracted from the anti-Stokes cooling. The second term represents the radiative heat load from the ambience. The third and fourth terms represent the convective and conductive heat loads on the sample, respectively. $\sigma$ = $5.67\times {10}^{-8} \mathrm{W}/{\mathrm{mm}}^2{\mathrm{K}}^4$ is the Stefan-Boltzmann constant and $\chi =\left(1-{\epsilon }_a\right){\epsilon }_s{A}_S/{\epsilon }_a{A}_a$. Here $T_{a,s}$, $A_{a,s}$ and ${\epsilon }_{a,s}$ are the temperature, the surface area and the thermal emissivity, respectively. Subscripts a and s denote the ambience and the sample. N is the number of contacting points with the length $d_l$ of support, the area $A_l$ of the contact points and the conductivity $k_l$ of support. $k_h$ is the convective heat transfer coefficient of the surrounding. $C_v=c_v\rho V$ is the heat capacity, where $\rho$, $c_v$ and V are specifically the heat, density and volume of the sample, respectively.

The last two terms in Equation (2) represent the convective heat load and the conductive heat load on the samples, respectively. Their contributions can be neglected for a sample supported by two optical fibers of 100 μm diameters inside the high vacuum cavity. Since the cavity surface area A_a is much larger than the sample surface area A_s, the influence of $\chi$ can be neglected. For the case of the small temperature change $\Delta T\left(│T_a-T_s│\le 5 \mathrm{K}\right)$, Equation (2) is simplified as [46].

$$C_v\frac{dT}{dt}\approx -{\eta }_c{P}_{abs}-4{\epsilon }_s{A}_s\sigma T_a{}^3\left(T_s-T_a\right)$$

(3)

The experimentally measured cooling efficiency ${\eta }_c{\left(\lambda \right)}^{exp}$ under steady-state (dT/dt = 0) condition can be expressed as Equation (4).

$${\eta }_c{\left(\lambda \right)}^{exp}=K_{rad}·\Delta T/P_{abs}\left(\lambda \right)$$

(4)

where $K_{rad}=4{\epsilon }_s{A}_s\sigma T_a{}^3$ and $P_{abs}\left(\lambda \right)\propto k{\displaystyle \int }S\left(\lambda \right)d\lambda$. Here, k and $S\left(\lambda \right)$ are the scaling factor and the fluorescence spectrum, respectively. The cooling efficiency of the sample ${\eta }_c{\left(\lambda \right)}^{exp}$ can be obtained by precisely measuring the sample temperature change ΔT as a function of the pump wavelength $\lambda$ and the absorption power. To accurately measure the laser-induced temperature change ΔT, a special experimental set-up has been designed to minimize the sample’s external thermal load and a calibrated thermal imaging camera is used to precisely monitor the sample temperature in real time.

With the measured values of the average fluorescence wavelength of the sample ${\lambda }_f\left(T\right)$ and the resonance absorption coefficient ${\alpha }_r\left(\lambda ,T\right)$, the external quantum efficiency ${\eta }_{ext}$ and the background absorption coefficient ${\alpha }_b$ can be obtained by fitting the cooling efficiency ${\eta }_c{\left(\lambda \right)}^{exp}$ measured in the experiment utilizing Equation (1). Two zero-crossing wavelengths can be observed throughout the crystal temperature change. The external quantum efficiency ${\eta }_{ext}$ is determined by the ratio of the average fluorescence wavelength ${\lambda }_f$ to the first zero-crossing wavelength ${\lambda }_{cross1}$ [46]. The second crossing wavelength ${\lambda }_{cross2}$ helps solve the background absorption coefficient ${\alpha }_b$ on the basis of Equation (1) with the measured parameters of ${\eta }_{ext}$, ${\lambda }_f\left(T\right)$ and ${\alpha }_r\left(\lambda , T\right)$.

3. Experimental Set-Up

A schematic diagram of the experimental set-up for LITMoS testing is shown in Figure 1. A tunable fiber laser with a wavelength range of 1010–1080 nm is used to pump the 5% Yb³⁺-doped LuLiF₄ crystal with size of 2 $\times$ 2 $\times$ 5 ${\mathrm{mm}}^3$. The sample is placed in the vacuum chamber of 10⁻⁵ Pa. The pump laser beam is collected by beam dump after passing through the sample. A calibrated thermal camera (FLIR A300) equipped with 100 μm macro lens is used to measure the temperature change ΔT of the sample in real time. A spectrometer (Ocean Optics Maya 2000Pro-NIR, Dunedin, FL, USA) is used to measure the fluorescence spectra and the absorption power $P_{abs}\left(\lambda \right)$ of the sample. The cooling efficiency ${\eta }_c{\left(\lambda \right)}^{exp}$ of the sample at the different pump wavelength λ can be acquired by precisely measuring ΔT and $P_{abs}\left(\lambda \right)$.

Figure 2 shows the picture of devices for the LITMoS test and the thermal camera calibration. The picture of the thermal camera and the cooling grade testing chamber (CGTC) is shown in Figure 2a. The infrared camera is used for non-contact temperature measurement in the LITMoS test. The camera’s detector contains a focal plane array of uncooled micro-radiometric thermometers (320 × 240 pixels) and a spectral response range of 7.5–13 μm. The BK7 glass windows (25 mm diameter) for pump laser are AR coated at a wavelength of 1 μm. The other pair of BaF₂ windows (25 mm diameter) is used for the sample temperature measurement with the thermal camera. The temperature of the CGTC can be adjusted in the range of 276–308 K with an accuracy of ±0.05 K by the chiller. The interior of the CGTC is shown in Figure 2b. There are two copper blocks with a slit in the middle for accommodating a reference sample identical in size to the cooling one. A TEC is contact-fixed to the copper clamp for varying the sample temperature. A K-type thermocouple with very thin strings is connected to the copper clamp for temperature measurement. A low-evaporation silicone grease is used on all contact surfaces for good thermal conductivity. These electronic devices are wired to the outside of the CGTC through connectors on the sealed cap. The temperature of the reference sample, which is embedded in the sample holder, can be controlled by adjusting the current of the TEC and measured by the thermal camera at the same time. Figure 2c shows the side view of the CGTC.

It is difficult to directly measure the temperature change of the sample in the CGTC using thermal camera imaging because the sample has low thermal emissivity and is transparent at thermal wavelengths. In order to identify the proportional relationship between pixel brightness and temperature change of the sample, it is necessary to vary the temperature of the sample inside the CGTC and acquire its thermal images accordingly. The micro-radiometer technology is based on the principle that the change in pixel resistivity is proportional to the energy of the infrared radiation absorbed by the detector. After calibration, one can deduce the temperature of the emitting source from the pixel intensity variation of the output images. The thermal camera outputs an 8-bit depth grayscale image with intensity values between 0 (black) and 255 (white) for each pixel in the photo. By calibrating the proportional relationship between pixel intensity and temperature, the change of the target temperature within the thermal image region can be inferred from the change of the pixel intensity. To measure the change in the sample temperature in real time, the thermal image of the sample is recorded for a sufficiently long time (30–50 min) while the ambient temperature is kept constant.

In order to minimize the fluctuations, the pixel intensity values of the specified area, as shown by the red dash line box in the thermal image in Figure 3a, are summed and averaged. It is important to specify the temperature scale range of the thermal image, such as 288–302 K for our case here, and establish the mapping relationship between temperature and pixel intensity. The pixel intensity at the lowest temperature of 288 K is 0, and the pixel intensity at the highest temperature of 302 K is 255. The dependence relationship of the reference sample temperature in the copper clamp on the TEC current is affected by both the background pressure of the vacuum and the temperature of the CGTC, as shown in Figure 3b. To minimize the effect of background pressure, the CGTC is maintained in a high vacuum of ~10⁻⁵ Pa during the whole process of the experiment.

The pixel intensities of the thermal image of the reference sample (LuLiF₄ crystal) are measured with the temperature of the surrounding CGTC being 295 K and 293 K, respectively. The temperature scale range of the thermal image is chosen from 288 K to 302 K, as shown in Figure 3c. The black and red dots correspond to results for the cases of the CGTC temperature being 295 K and 293 K, respectively. Although the slopes of the two fitting lines are almost the same, the absolute pixel intensities of the reference sample are different for the same sample temperature. Therefore, the temperature of the surrounding CGTC should be kept constant during the whole process of the LITMoS test.

Figure 3d shows the relationship between the measured pixel intensity variation $\Delta \mathrm{p}$ixel ($\Delta \mathrm{p}$ixel = P − P_R) of the thermal image and the temperature variation $\Delta T\left(\Delta T = T-T_R\right)$ of the sample. Here, P_R indicates the pixel intensity of the thermal image at the reference temperature of T_R, which is the same as the surrounding CGTC temperature (295 K). The red dots correspond to the case with the temperature scale range of the thermal images being 288–302 K. The red solid line is a linear fit of the measured results. For |ΔT| ≤ 5 K, the relationship between $\Delta \mathrm{p}$ixel and $\Delta T$ is rather linear. As the value of |ΔT| grows, the relationship deviates more from being linear. Therefore, the variation of the sample temperature |ΔT| is kept at no more than 5 K in our LITMoS test. The slope of the linear fit, $\Delta T/\Delta \mathrm{p}$ixel, defines the calibration factor, which is 0.07736 for the case here and used for later determination of the sample temperature variation from the pixel intensity of the thermal image.

4. Results and Discussions

Under the irradiation of the 1015 nm pump laser, the 5% Yb³⁺-doped LuLiF₄ crystal is optically cooled. With the decrease in the sample temperature the pixel intensities of thermal images are reduced, as shown in Figure 4a. The sample temperature reaches a steady state after 20 min of irradiation. The averaged pixel intensities decrease from 158 to 102.1, corresponding to a pixel intensity drop of 55.9 and a sample temperature drop of about 4.3 K. When the pump wavelength is changed to 1080 nm, the 5% Yb³⁺-doped LuLiF₄ crystal is optically heated. The sample reaches a steady state in temperature after 20 min of irradiation. With the increase in the sample temperature, the pixel intensities of thermal images are enhanced, as shown in Figure 4b. The averaged pixel intensities increase from 161.8 to 206, corresponding to a pixel intensity rise of 44.2 and a sample temperature rise of about 3.4 K.

Similar experimental studies were also performed in other pump wavelengths in the range of 1010 nm and 1080 nm. The temperature changes of the crystal at each pump wavelength were extracted from thermal images following the above-mentioned image-processing procedure, which involves both spatial and temporal averaging. The CGTC temperature was kept at a constant value of 22 °C during the experiment. The absorbed power $P_{abs}\left(\lambda \right)\propto k{\displaystyle \int }S\left(\lambda \right)d\lambda$ at each pump wavelength λ was calculated from the photo-luminescence excitation spectroscopy measurement technique. The measured cooling efficiency ${\eta }_c{\left(\lambda \right)}^{exp}$ for each pump wavelength was fitted with Equation (1). The corresponding results are shown in Figure 4c. The external quantum efficiency ${\eta }_{ext}=99.4\left(\pm 0.1\right)\%$ and the background absorption coefficient ${\alpha }_b=1.5\left(\pm 0.1\right)\times {10}^{-4} {\mathrm{cm}}^{-1}$ are acquired accordingly. The net cooling of the sample is observed between the first zero-crossing wavelength ${\lambda }_{cross1}$ = 1005 nm and the second crossing wavelength ${\lambda }_{cross2}$ = 1065 nm. The filled blue region between ${\lambda }_{cross1}$ and ${\lambda }_{cross2}$ represents the cooling area.

A “cooling window” capable of predicting the optical cooling potential of the sample can be calculated according to the cooling parameters of the crystal, such as ${\eta }_{ext}$, ${\alpha }_b$, ${\alpha }_r$ and ${\lambda }_f$ measured in experiment. Figure 4d shows the “cooling window” of the 5% Yb³⁺:LuLiF₄ crystal under our study. The dash line separating the blue area of cooling and red area of heating indicates the points where the cooling efficiency is equal to zero. From Figure 4d one can see that the global MAT of the crystal can reach ~110 K at 1020 nm by maximizing the power absorption of the pump laser (astigmatic Herriot cavity [55,56]) and minimizing heat loads from the environment [46,49,50].

The cooling performance of a sample strongly depends on its cooling parameters, such as ${\eta }_{ext}$ and ${\alpha }_b$ etc. In a previous work, a temperature drop of ~2.2 K was reported in a Czochralski-grown bulk 5% Yb³⁺-doped LuLiF₄ under 1025 nm pump laser of 220 mW with the corresponding parameters ${\eta }_{ext}=99.0 \left(\pm 0.1\right)$, ${\alpha }_b=1.3 \left(\pm 0.2\right)\times {10}^{-3 }{\mathrm{cm}}^{-1}$ [57]. Later, a Czochralski-grown bulk 5% Yb³⁺-doped LuLiF₄ of better purity was cooled to 117.3 K under 1020 nm pump laser of 33 W with estimated cooling parameters being ${\eta }_{ext}=99.4\%$ and ${\alpha }_b=4.5\times {10}^{-4} {\mathrm{cm}}^{-1}$ [29] Recently, a Bridgman-grown 5% Yb³⁺-doped LuLiF₄ was cooled to ~195 K under 1020 nm pump laser of 45 W with ${\eta }_{ext}=98.9 \left(\pm 0.1\right)\%$ and ${\alpha }_b=3.3 \left(\pm 0.2\right)\times {10}^{-4} {\mathrm{cm}}^{-1}$ [58]. Based on the cooling window from the LITMoS test, the crystal sample under current study can be potentially cooled to ~110 K under 1020 nm pump laser with its measured parameters ${\eta }_{ext}=99.4 \left(\pm 0.1\right)\%$ and ${\alpha }_b=1.5 \left(\pm 0.1\right)\times {10}^{-4} {\mathrm{cm}}^{-1}$. In a recent report working with 5% Yb, Tm co-doped LiYF₄ crystal, A. Volpi et al. found that when the sample temperature decreased from 300 K to 100 K, the corresponding background absorption ${\alpha }_b$ dropped more than an order of magnitude [41]. This study indicated that the background absorption ${\alpha }_b$ does not remain constant but changes dramatically during the cooling process. As an isomorph of the LiYF₄ crystal, the LuLiF₄ crystal displays similar optical behavior [57,58,59,60]. Considering the reduction in ${\alpha }_b$ with decreasing temperature [41], one can expect that the 5% Yb³⁺:LuLiF₄ crystal under our study can be potentially cooled to even lower temperatures than 110 K.

5. Conclusions

The LITMoS test has been adopted here to measure the laser-cooling properties of the 5% Yb³⁺:LuLiF₄ crystal placed inside a special cooling-grade test chamber at room temperature. With a carefully calibrated thermal camera (temperature resolution < 0.1 K), the external quantum efficiency ${\mathsf{\eta }}_{\mathrm{ext}}$ and the background absorption coefficient ${\alpha }_b$ of the sample were accurately measured to be ${\eta }_{ext}=99.4 \left(\pm 0.1\right)\%$ and ${\mathsf{\alpha }}_{\mathrm{b}}=1.5 \left(\pm 0.1\right)\times {10}^{-4}{ \mathrm{cm}}^{-1}$, respectively. The cooling window of the sample was deduced from the LITMoS measured parameters and indicates a global MAT of ~110 K. Our study shows that the 5% Yb³⁺:LuLiF₄ crystal is of excellent laser-cooling grade for applications in cryogenic optical coolers and RBLs.