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Abstract
Optical cooling of a YLF:Yb single crystal to 87 K, well below the minimum achievable temperature predicted from existing theory, has been observed. This discrepancy between theory and data has motivated us to revisit the current model of optical refrigeration, in particular the critical role of parasitic background absorption. Challenging experiments that measured the cooling efficiency as a function of temperature reveal that the background absorption coefficient decreases with temperature, resulting in a significant enhancement of the cooling efficiency at cryogenic temperatures. These discoveries emphasize the high sensitivity of optical cooling to impurity-mediated processes and show the necessity of formulating a cooling model that includes the temperature dependence of the background absorption. To properly characterize the cooling properties of any sample, it is necessary to measure its low-temperature performance.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Originally suggested by Pringsheim in 1929 [1], anti-Stokes cooling was first attained in gaseous systems [2] but not experimentally observed in solids until materials with sufficiently high purity could be synthesized. Net laser cooling of a solid was first observed in 1995 in a high-purity Yb-doped ZBLANP glass [3]. Notable advances have since been made, particularly by exploiting the high-purity Yb3+-doped fluoride single-crystal host LiYF4 (YLF). This has enabled the breakthroughs to the cryogenic and sub-100 K regimes [4–7]. A recent major advance has been the demonstration of an YLF:Yb single crystal optical cryocooler cooling a HgCdTe infrared sensor to 135 K [8,9], the first practical demonstration of an all-solid-state cryocooler device capable of cooling an optical sensor to cryogenic temperatures without moving parts and the associated mechanical vibrations and microphonic noise.
In anti-Stokes cooling of rare-earth doped crystals, the solid is excited by laser light tuned below the average fluorescence energy. The subsequent spontaneous emission of photons with a higher average energy annihilates lattice phonons producing cooling of the bulk material. There are several specific material conditions that must be met in order to achieve net cooling. Most importantly, a variety of competing non-radiative and impurity-mediated processes must be minimized as they can degrade or limit laser-induced cooling. The intrinsic optical cooling efficiency ${\eta _c}$ of a given material, defined as the heat lift per absorbed photon, can be expressed as [10,11]:
Undesired impurities are currently believed to be the main source of parasitic background absorption. They introduce additional energy levels that can cause absorption of pump photons which is typically followed by non-radiative decay, i.e. heat generation. Such impurities can also act as traps by accepting energy from excited Yb3+ ions via non-radiative energy transfer, thereby lowering ${\eta _{ext}}$. The nature of parasitic absorption is not yet completely understood and may arise from a variety of contaminants which vary from sample to sample. Of particular concern for Yb-doped materials are 3d transition metals. Divalent ions such as Cu2+, Fe2+, and Co2+ have strong and spectrally broad absorption bands around 1 µm in fluoride materials that overlap with Yb3+ pump wavelengths [13]. In particular, in some YLF:Yb single crystals a strong correlation has been found between the background absorption and the iron contamination at concentrations on the order of ppm (parts per million) [14]. Traces of transition metals, especially iron, can lower or completely offset the cooling process [15]. Besides 3d transition-metal ions, impurities such as OH- ions or other rare earths may introduce exothermic multi-phonon relaxation, act as traps in non-radiative energy-transfer processes, and contribute to ${\alpha _b}$ by ground or excited-state absorption. The low threshold concentration for these impurities to become detrimental and their unknown origin makes accurate quantification and purification procedures challenging [16]. This high sensitivity to material purity necessitates tightly controlled purification and growth procedures.
The cooling efficiency ${\eta _c}(\lambda ,T)$ decreases with decreasing temperature. As a result of the Boltzmann distribution governing the thermal population of electronic states, the resonant absorption in the anti-Stokes region decreases exponentially with temperature and the mean emission wavelength redshifts. In rare-earth doped materials, a Boltzmann quasi-equilibrium establishes in each multiplet prior to spontaneous emission, and the following functional dependencies can thus be estimated from a simple 4-level model [11]: ${\alpha _r}(\lambda ,T) \propto {({1 + {e^{\delta {E_{es}}/{k_B}T}}} )^{ - 1}}$ and $h{\nu _f}(T) \sim h{\nu _f}(0) + \delta {E_{es}}/(1 + {e^{\delta {E_{es}}/kT}})$, where $\delta {E_{gs}}$ and $\delta {E_{es}}$ denote the width of the ground- and excited-state multiplet, respectively, i.e. 2F7/2 and 2F5/2 multiplets in the case of Yb3+, respectively. These temperature dependencies of ${\alpha _r}$ and ${\lambda _f}$ are the inherent causes for ${\eta _c}(\lambda ,T)$ decreasing with temperature. A minimum achievable temperature (MAT) can therefore be defined as the lowest temperature for which ${\eta _c}(\lambda ,T) \to 0$ . It is important to note that for a given material, the MAT critically depends on ${\alpha _b}$ since the cooling efficiency is limited by the ratio ${\alpha _b}/{\alpha _r}$ (Eq. (1)). The external quantum efficiency ${\eta _{ext}}$ also shifts the position of this minimum. The MAT is thus highly sensitive to the growth quality and purity of the material. Models for solid-state optical refrigeration to date have assumed ${\alpha _b}$ to be both temperature and wavelength independent. The rationale has been that 3d transition-metal ions are likely the primary source of parasitic absorption, and the respective absorption bands are spectrally much broader than the resonant Yb3+ absorption. A weak temperature dependence for ${\eta _{ext}}$ was also expected in Yb-doped fluorides.
In this paper, we describe how recent experiments led us to revisit these approximations. We performed power cooling experiments that excited a YLF:5%Yb,Tm crystal with ∼50 W of laser power at 1020 nm in an astigmatic Herriot-cell [7] and achieved a record optical cooling to 87 K starting at room temperature [17]. Figure 1(a) shows the temperature of the YLF:5%Yb,Tm sample as a function of time after turning on the 1020 nm excitation. The lowest observed temperature of 87 K, however, was much lower than the MAT of 110–120 K that was predicted from a model in which ${\alpha _b}$ and ${\eta _{ext}}$ were held constant at their measured room-temperature value (Fig. 1(b)). This paper presents measurements of ${\alpha _b}$ and ${\eta _{ext}}$ as a function of temperature for the first time, providing new insights in the role of ${\alpha _b}$.
Fig. 1. (a) Temperature of the YLF:5%Yb,Tm sample as a function of time after turning on the multi-pass 1020 nm (∼50 W) excitation in astigmatic Herriot-cell [7,17]. The copper clamshell structure [8] surrounding the crystal was kept at 6 °C. (b) 2D plot of cooling efficiency vs. wavelength and temperature calculated in the approximation of constant ${\alpha _b}$ and ${\eta _{ext}}$ . The dashed lines indicate the predicted MAT of 110–120 K for a pump wavelength of 1020 nm
2. Results
2.1 Room-temperature LITMoS tests
The measurements reported in this paper were performed on a YLF:Yb,Tm crystal that was grown at Pisa University by the Czochralski process from high-purity (99.999%) raw materials of LiF, YF3, YbF3, and TmF3 under controlled Ar and CF4 atmosphere [18,19]. The crystal was doped with 5 mol% Yb3+ and very lightly co-doped (∼16 ppm) with Tm3+. The pulling rate was 0.5 mm/h with the crystal rotating at 5 rpm. A 3.4 × 4.5 × 10.4 mm3 Brewster-cut sample of high optical quality was prepared from the crystal boule and used for the laser cooling experiments.
Measuring ${\eta _{ext}}$ and ${\alpha _b}$ at room temperature by the so-called LITMoS (Laser Induced Thermal Modulation Spectroscopy) test evaluates the cooling grade of a given material [15]. In this method, ${\eta _c}$ is determined by measuring temperature changes as a function of excitation wavelength, $\lambda $, which is varied from below to above ${\lambda _f}$. Under steady-state conditions and for small temperature changes, the measured (experimental) cooling efficiency is given by
Where ${P_{abs}}(\lambda )$ denotes the total absorbed power (at wavelength $\lambda $) that causes the temperature change $\Delta T$, and $K$ is a constant parameter that is proportional to the heat exchange (such as conductive and radiative load) with the environment in the given configuration. In order to achieve accurate measurements of the pump-induced $\Delta T$, an experimental setup has to be designed that minimizes external heat loads onto the sample and avoids changes of the heat capacity. Fitting of the normalized $K \cdot \Delta T/{P_{abs}}(\lambda )$ data to the model curve of Eq. (1) then yields estimates of ${\eta _{ext}}$ and ${\alpha _b}$. From the spectral dependence of ${\eta _c}$ in Eq. (1) it follows that the shorter wavelength range is primarily determined by ${\eta _{ext}}$ while the longer wavelength range is determined by ${\alpha _b}$. Measurement of the latter becomes increasingly difficult as the resonant absorption decreases with increasing $\lambda $, and therefore $\Delta T$ becomes very small.2.2 Estimation of ${\eta _c}(T)$ in the approximation of constant ${\alpha _b}$ and ${\eta _{ext}}$.
When ${\alpha _b}$ and ${\eta _{ext}}$ are constant, the temperature dependence of ${\eta _c}$ is a result of the thermal occupancy of the crystal-field levels of the ground and excited state. A spectroscopic investigation of ${\alpha _r}(\lambda )$ and ${\lambda _f}$ as a function of temperature, combined with RT ${\alpha _b}$ and ${\eta _{ext}}$ data, can therefore be used to evaluate ${\eta _c}$ and the MAT. The temperature-dependent resonant absorption coefficients and mean emission wavelength were measured by placing the YLF:Yb,Tm sample in a closed-cycle helium cryostat that allowed the sample temperature to be controlled from 300 K to below 50 K [15]. The resonant absorption ${\alpha _r}(\lambda )$ in the low-energy region was obtained with a high signal-to-noise ratio from polarized fluorescence spectra using the reciprocity theory and the McCumber relationship [20,21], which gives ${\alpha _r}(\lambda ) \propto {\lambda ^5}S(\lambda ,T){e^{hc/\lambda {k_B}T}}$, where $S(\lambda ,T)$ denotes the polarized emission spectrum at temperature T. Proportional spectra calculated from this relationship were calibrated by direct temperature dependent absorption measurements at some fixed wavelength in order to obtain absolute absorption values. The mean fluorescence wavelength ${\lambda _f}$ was directly calculated from ${\lambda _f}(T) = \int {\lambda S(\lambda ,T)d\lambda /\int {S(\lambda ,T)d\lambda } } $. In the case of an optically anisotropic crystal such as YLF, the weighted average of the two polarized emission spectra was taken. The absorption and emission properties of Yb3+, measured at room and cryogenic temperatures and compared to pure Yb doped YLF, were found to be independent of the relatively low Tm3+ co-doping in the present sample. Also, ground state absorption of Tm3+ in YLF at 1 µm is found negligible.
Figure 1(b) shows the cooling efficiency of the YLF:Yb,Tm sample as a function of $T$ and $\lambda $, calculated by using ${\alpha _r}(\lambda ,T)$ and ${\lambda _f}(T)$ spectroscopic data as well as the room-temperature values of ${\alpha _b} = 2 \cdot {10^{ - 4}}c{m^{ - 1}}$ and ${\eta _{ext}} = (99.4 \pm 0.2)\%$. The white transition line separating cooling (blue) and heating (red) regions corresponds to ${\eta _c} = 0$ and represents the spectrum of the MAT. Under the aforementioned approximations, the global (lowest) MAT reachable for zero heat-load is found to be 110–120 K for this sample, for excitation around 1020 nm. This wavelength corresponds to the energy difference between the top of the ground state to the bottom of the excited state in YLF:Yb, i.e. the lowest-energy 2F7/2→2F5/2 crystal-field transition. However, the actual laser-cooling experiments performed on this crystal and shown in Fig. 1(a) surprisingly indicated that the sample reached a much lower temperature of 87 K. Note that this material is very lightly co-doped with Tm (0.0016%). Therefore one potential argument for this experimental result outperforming the theoretical prediction was the possibility of resonant absorption enhancements at low temperatures and endothermic Yb-Tm energy-transfer processes [18,22]. High-resolution absorption measurements however did not reveal any enhancement of ${\alpha _r}$ at low temperatures. The role of Yb-Tm energy-transfer is still under investigation at Pisa University through the growth of different co-doping concentration. However, as the cooling efficiency is limited at low-temperatures by the ratio ${\alpha _b}/{\alpha _r}$, our leading hypothesis is the temperature dependence of the background absorption; a sufficient reduction in ${\alpha _b}$ with decreasing temperature would lower the MAT.
One way to investigate if and how ${\alpha _b}$ changes with temperature is to perform LITMoS tests at different temperatures down to the cryogenic regime. The temperature dependencies of ${\eta _{ext}}$ and ${\alpha _b}$ could then be obtained by fitting experimental data of cooling efficiency with the model curve of Eq. (1) using ${\alpha _r}(\lambda ,T)$ and ${\lambda _f}(T)$ spectroscopic data at each temperature. The following two sections presents such measurements and their results for the first time.
2.3 Low-temperature LITMoS test experiment
Carrying out highly sensitive LITMoS tests at low temperatures presents a variety of experimental challenges. A first challenge is the need to accurately control heat loads and thermal conductance in the experimental sample configuration. Rewriting Eq. (2) as $\Delta T = {\eta _c}(\lambda ) \cdot {P_{abs}}(\lambda )/K$ shows that larger intrinsic pump-induced temperature change, $\Delta T$, can be achieved under conditions of smaller heat conductance, $K$. However, sufficiently large thermal contact between the sample and the cooling source (cryostat) is required to control the sample temperature within a reasonably short period of time. One therefore requires a means to fine-tune thermal conductance in order to measure relative $\Delta T$ at different sample temperatures. A special sample mounting was designed for this purpose, as schematically shown in Fig. 2(a). This setup allowed for a tunable thermal conductance by using high-purity glass (Suprasil, Heraeus) slides between the sample and the cold-finger structure to which the sample was held by aluminum clamps. The glass thickness determined the time constant of the system. It was optimized with respect to (1) the time constant for the pump-induced temperature change to reach equilibrium and (2) the time constant for heat transfer from the cold finger to the sample. The cold finger, which was part of the closed-cycle helium cryostat, was connected to a heater in order to balance the cooling power and maintain a stable sample temperature using a PID control loop. As shown in Fig. 2(a), a silicon diode sensor (TS 1) was attached to the cold finger to control its temperature, and a second sensor (TS 2) was used to monitor the temperature of the aluminum clamp with a stability better than 50 mK.
Fig. 2. (a) Sample mounting (schematic: top, and picture: bottom) for the temperature-dependent LITMoS tests. (b) Schematic of the complete setup (top), and the timing of the probe-pump excitation for the time-gated DLT (bottom).
A second challenge is the need for an accurate non-contact measurement of the induced $\Delta T$ in the crystal sample down to cryogenic temperatures. A special pump-probe version of Differential Luminescence Thermometry (DLT) [4] was developed for this purpose. This type of DLT was similar to what was developed earlier for investigating laser cooling in semiconductors [11] and allows for temperature measurements over a wide range with high resolution [23]. DLT [4] is a non-contact method that is based on temperature-dependent variations in the spectral shape of the normalized fluorescence spectrum relative to a spectrum recorded at a reference temperature. The DLT signal ${s_{DLT}}(T,{T_0}) = \int {\left|{{\textstyle{{S(\lambda ,T)} \over {\int {S(\lambda ,T)d\lambda } }}} - {\textstyle{{S(\lambda ,{T_0})} \over {\int {S(\lambda ,{T_0})d\lambda } }}}} \right|} d\lambda $, where $S(\lambda ,T)$ denotes the emission spectrum at temperature $T$ and ${T_0}$ a reference temperature, is converted to an absolute temperature $T$ through a calibration. For the present experiments, we implemented a time-gated DLT in which a continuous-wave low-power probe laser produced the luminescence spectrum (DLT signal) from which the sample temperature was obtained. A superimposed high-power tunable pump laser was then turned on for a period of time determined by the heat-load time scale. The thermal conductance between the sample and the cold-finger of the cryostat was tuned by adjusting the thickness of total glass inserted in order to achieve a long enough thermal time constant to allow a sufficient accumulation of $\Delta T$ induced by the pump laser at a given wavelength and temperature. The pump was subsequently turned off, and the resulting temperature change was derived from the difference in the fluorescence spectra immediately before and after pump excitation. Efficient collection of the sample fluorescence and high stability of the sample temperature were essential to reduce the DLT uncertainty to $\le 0.1\; $K and to obtain a sufficiently high signal-to-noise ratio, especially at low temperatures.
The resonant absorption rapidly decreases as the temperature approaches the cryogenic regime. This decrease is particularly pronounced in the long wavelength range, which is the region of most interest for measuring ${\alpha _b}$. This would lead to a rapid reduction of the magnitude of pump-induced $\Delta T$ if the power of the pump lasers were not increased to achieve sufficiently accurate measurements. A variety of pump lasers were used to obtain adequate coverage of the spectral region of interest. These included a tunable (930-1080 nm) Ti:Sapphire laser with ∼1 W maximum output power, a VECSEL tunable between 1010 and 1030 nm with ∼5 W maximum output power [24], a YLF:Nd laser delivering up to ∼10 W at 1047 nm, an YAG:Yb laser delivering up to ∼10 W at 1064 nm, and a 1070-nm fiber laser providing up to 20 W. All these pump lasers were configured to excite the sample in the $\vec{{\boldsymbol E}}\parallel \vec{{\boldsymbol c}}$ configuration that afforded the greatest absorption in YLF:Yb sample [18]. A 1020-nm fiber laser, set to low power ($\sim $3 W) and configured in a $\vec{{\boldsymbol E}} \bot \vec{{\boldsymbol c}}$ pumping configuration, was used as the probe laser for the DLT temperature measurements. A schematic of the complete setup is shown in Fig. 2(b).
2.4 Low-temperature LITMoS test results
Temperatures from RT to ∼100 K were explored, and the results provide the first experimental evidence of a temperature dependence of the parasitic background absorption in a laser-cooling crystal. For presenting and analyzing the data, we find it useful to redefine the cooling efficiency as the ratio of the cooling power to the resonantly absorbed power, $P_{abs}^r = {P_{in}}(1 - {e^{ - {\alpha _r}L}})$, rather than the total absorbed power, ${P_{abs}} = {P_{in}}(1 - {e^{ - ({\alpha _b} + {\alpha _r})L}})$, as was the case leading to Eq. (1). Here $L$ denotes the sample length in a single pass, and ${P_{in}}(\lambda )$ is the incident pump power. This redefinition helps the analysis since ${\alpha _b}$ is a critical fitting parameter and could potentially become comparable or even exceed ${\alpha _r}$ in the relevant long-wavelength tail of the absorption spectrum. The revised cooling efficiency can be expressed as:
Fig. 3. Low-temperature LITMoS results showing experimental data (symbols) and fits to Eq. (3) (solid lines) of the cooling efficiencies measured at 300, 170, and 110 K for the YLF:5%Yb,Tm sample. The dotted lines show a prediction of the cooling efficiency at 170 and 110 K in the original model that assumed a temperature independent ${\alpha _b}$.
Figure 4(a) summarizes the measured ${\alpha _b}$, derived from fitting the cooling efficiency Eq. (3) to experimental data, at different temperatures. A decrease of ${\alpha _b}$ of nearly one order of magnitude is observed as the temperature is lowered from 300 K to ∼100 K. ${\eta _{ext}}$, also fitted as independent parameter, only increased by ∼0.5% over this temperature range. The measured ${\alpha _b}(T)$ can be fitted well using a Boltzmann-type function, suggesting that ${\alpha _b}$ is dominated by an impurity absorption transition that originates from a thermally excited state. The respective function ${\alpha _b}(T) \approx 7.5 \cdot {e^{ - 387.6/T}}{10^{ - 4}}c{m^{ - 1}}$ yielded the best fit to the data and was used to obtain an extrapolation of ${\alpha _b}$ to below 100 K, as shown by the black curve in Fig. 4(a). With this extrapolation, a global MAT of $\sim \;\ $70 K is predicted for this YLF:5%Yb,Tm sample, consistent with the results of the power cooling experiments (Fig. 1a). Figure 4(b) shows the revised 2D plot of ${\eta _c}$ vs $\lambda $ and $T$ that uses the measured ${\alpha _b}(T)$ of Fig. 4(a) instead of a temperature-independent room-temperature value for ${\alpha _b}$ (Fig. 1(b)). Previous results, shown in Fig. 1(b), have been re-evaluated with the revised definition of cooling efficiency (Eq. (3)) and no change in the global-MAT is found.
Fig. 4. (a) Experimental data of background absorption vs sample temperature (red dots) with Boltzmann fit (black line). (b) Revised 2D plot of cooling efficiency vs $\lambda $ and T using the measured ${\alpha _b}(T )$ from Fig. 4a. A global MAT of $\sim 7$0 K is predicted. Previous results, shown in Fig. 1(b), have been re-evaluated with the new definition of cooling efficiency and no change in the value of the global-MAT, under the assumption of temperature-independent ${\alpha _b}$, is found.
3. Discussion
We suggest the primary source of background absorption in Yb-doped laser-cooling materials, are 3d transition metals impurities. A temperature dependence in the respective ${\alpha _b}$ is not unexpected for these impurities. Assume a 3d ion having an electronic ground state and an electronic excited state that couples to the vibrational modes of the first coordination sphere. The resulting absorption spectrum is then given (1) by the Franck-Condon factors, which are determined by the ground and excited state vibrational energies, the reduced mass of the relevant vibration, and the material-dependent electron-phonon coupling strength given by the Huang-Rhys parameter, (2) by the thermal population of the vibrational levels of the electronic ground state, and (3) by homogeneous and material-specific inhomogeneous broadening of the involved vibronic transitions [25]. The change in thermal population of the initial vibrational states generally causes the absorption coefficient to decrease with decreasing temperature in the long-wavelength region of the 3d absorption spectrum. Examples are KCoF3, CoCl2, and CoBr2 in which the absorption coefficient of the various Co2+ transitions decreases by more than an order of magnitude in some regions of the spectrum as the temperature is lowered from room temperature to 20 K [26]. This is not a general trend, as transitions originating from the vibrational ground state of the electronic ground state may show the opposite trend and will gain intensity as the temperature is lowered. We therefore consider our observation of a decreasing ${\alpha _b}$ with decreasing temperature in YLF:Yb,Tm being the result of an impurity or set of impurities that are specific to this sample. Unfortunately, spectroscopic data of various transition metals in YLF are not readily available in literature, which prevents us from assigning the observed behavior to a specific impurity. We are currently working on growing transition-metal doped crystals such as YLF and LuLiF4 (LLF) in order to gain a better understanding of their temperature-dependent absorption spectra.
4. Conclusion
We have developed a highly sensitive experimental method for measuring the key solid-state laser-cooling parameters ${\eta _{ext}}$ and ${\alpha _b}$ over a wide range of temperatures. These temperature-dependent LITMoS measurements were performed on a YLF:Yb,Tm crystal and have revealed, for the first time, a nearly one order of magnitude decrease in the background absorption coefficient, ${\alpha _b}$, as the sample temperature was lowered from 300 to ∼100 K. We conclude that the observed temperature dependence of ${\alpha _b}$ is the primary explanation for the much lower (87 K) measured minimum achievable temperature (MAT) than was predicted previously from a traditional laser-cooling model that treated ${\alpha _b}$ as temperature independent. This result shows that the cryogenic performance of a laser-cooling sample may be significantly better than predicted from room-temperature LITMoS tests alone and that temperature-dependent LITMoS tests are required to obtain a quantitative picture of sample performance. Temperature-dependent LITMoS tests however are laborious and rather unsuited as a routine characterization technique. A graded approach for characterizing laser-cooling samples is therefore still most effective, involving the sequential steps of (1) exciting the sample at a desirable pump wavelength at room temperature to assess if net cooling is produced, (2) performing a room-temperature LITMoS test to quantify ${\eta _{ext}}$ and ${\alpha _b}$ as initial quality metrics and to obtain an initial estimate of the MAT, (3) measuring the actual MAT in a power-cooling experiment, and (4) performing temperature-dependent LITMoS tests if the actual MAT substantially deviates significantly from the MAT predicted from room-temperature values of ${\eta _{ext}}$ and ${\alpha _b}$. A beneficial effect from endothermic Yb-Tm energy-transfer [18,22] cannot be excluded and is still under investigation for different co-doping concentrations.
Funding
Air Force Office of Scientific Research (FA9550-15-1-0241, FA9550-16-1-0362 (MURI)).
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