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Abstract
In the perspective of building a solid state cryocooler based on optical refrigeration, it is strategic to develop high purity crystals and to have a full understanding of the mechanisms that can reduce cooling efficiency. In this paper we highlight two loss mechanisms that can hinder the optical refrigeration performance of a Yb:YLF monocrystal: the presence of impurities and fluorescence reabsorption. We show how the presence of impurities can be inferred by measuring the mean lifetime of the Yb optical transition. We measure how a few ppms of other rare earth ions can be detrimental for optical refrigeration by exciting a cooling Yb:YLF sample with two laser sources. We also report the first practical demonstration of the negative effect of fluorescence reabsorption on the cooling performance.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Ever since optical refrigeration by anti-Stokes fluorescence [1] was first demonstrated in solids back in 1995 [2], over the years great advances have been made. From the first focus on fluoride glasses doped with rare earth elements, researchers switched to fluoride single crystals, which offer more suitable hosts, allowing for higher optical refrigeration efficiency [3]. Also, among the various ions of rare earth elements, Ytterbium was chosen because of its simple energy levels structure, composed by only two multiplets. The combination of Yb3+ ions and LiYF4 (YLF) as a host has led to amazing results: over the years, samples have been cooled first to 119 K [4], then to 91 K [5], both from room temperature. These results were obtained by refining the growth techniques and the dopant concentration.
The discovery that trivalent Thulium (Tm3+) can have beneficial effects on the cooling efficiency when it is present in very small amounts inside a Yb:YLF crystal [6,7] brought to a new record temperature of 87 K [8]. These promising results prompted the creation of a first optical solid state cryo-cooler device [9], which was used to cool to 135 K the HgCdTe sensor of a Fourier Transform Infrared (FTIR) spectrometer. These results open up the possibility of developing devices with innovative aspects such as compactness, lightness and absence of vibrations. These characteristics can have interesting spin-offs in different application fields such as biomedical (PET), metrology, and space, the latter in particular for the development of micro and nanosatellites.
In this paper we present a series of experiments addressed to measure the impact that impurities can have on the cooling efficiency of a system, via their effect on the external quantum efficiency, $\eta _{ext}$, and on the background absorption coefficient $\alpha _{b}$, the two parameters usually considered to evaluate the efficiency of the cooling process of a sample.
In this paper we also highlight the correlation between the presence of impurities, such as transition metals, and the mean lifetime of the excited Yb3+ manifold.
2. Theoretical background
Factors such as material purity and quantum efficiency of the optical transition are fundamental, because we can express the efficiency of the cooling process as [10]:
The background absorption coefficient $\alpha _{b}$ is a particularly interesting parameter, because its value encompasses a multitude of aspects that may be present in the samples, such as photon absorption due to impurities, light scattering due to microbubbles and the presence of dislocations. Their total contribution is not trivial to quantify and the value of $\alpha _{b}$ is still under investigation, but - in order to have a better performance - this term needs to be as low as possible.
The external quantum efficiency $\eta _{ext}$ is defined as:
It depicts the probability that a photon absorbed by the dopant ions will be, first of all, re-emitted as a fluorescence photon, and that such photon will then be able to escape from the system, as quantified by the extraction efficiency $\eta _{e}$. $\eta _{ext}$ must be as high as possible, and it is influenced by the quantum efficiency of the electronic transition (radiative/non-radiative decay ratio $W_{r}/W_{nr}$), fluorescence reabsorption, and radiation trapping inside the sample.
In the development of solid state optical coolers, the most important parameter is its cooling efficiency $\eta _{c}$. Consequently, it is strategic to study the two quantities $\eta _{abs}$ and $\eta _{ext}$, which are closely related to the cooling efficiency. This analysis is particularly difficult because these parameters are related to the purity of the analyzed material, and impurity values of a few ppms are sufficient to alter these values and change the cooling efficiency.
3. Crystal growth and sample preparation
In our experiments we used many different samples, obtained from seven separate boules of YLF grown using the Czochralski technique in the crystal growth facility at the Physics Department of the University of Pisa. Four boules were doped with 10% Yb, while the other three were doped with 5%Yb. We focused on these two Yb concentrations since they are the most suitable ones for optical refrigeration applications.
The growth process is very delicate, and all steps between the raw powders and the final mono-crystal samples are carefully controlled to minimize contamination or defects.
The high purity powder components (5N or 6N) were weighted and mixed in a controlled environment to minimize exposure to humidity, which can be detrimental since OH- molecules can absorb in the IR region, and their presence inside the crystal matrix can cause background absorption or quench the optical transition responsible for the cooling process. After that, the crucible containing the powders was placed inside the furnace. All the successive operations were conducted in a high purity (5N) Argon-CF4 atmosphere, with the CF4 being added to prevent the reduction of Yb3+ ions into Yb2+ ones. Under these conditions, the boules were grown at a pulling rate of 1 mm/h and a rotation speed of 5 rpm. The melt temperature was adjusted (with a stability of 10−4) to ensure accurate control of the diameter of the growing crystal. The typical dimensions obtained were a diameter of $\sim$12 mm and a length that could vary from 60 to 150 mm.
After the growth, an accurate analysis of the defects of the boule was performed: by employing two different lasers (respectively at 680 nm and 473 nm) and an optical microscope we looked for micro bubbles inside the crystal. Once the best optical part (defect-free) of the grown boules was localized, this part was cut into a series of samples, all free of defects greater than a few $\mu$m in size. The typical dimensions was 3x3x10 mm3, with the sides aligned along the crystallographic axes, and with the c-axis along one of the smaller sides. All data reported in this paper was collected using an E $\parallel$ c pump polarization.
For the experiments reported in this paper we used 9 different samples: 6 of them were cut from boules with 10% Yb, while the other 3 came from 5% Yb boules.
4. Effect of impurities on Yb3+2F5/2 manifold lifetime
The external quantum efficiency $\eta _{ext}$ depends strongly from the non-radiative decay rate $W_{nr}$; the measurements presented here correlate the presence of transition metal impurities to the $\eta _{ext}$ value, and to the cooling efficiency of a sample. The cooling process is very sensitive, and it can be influenced by a few ppms of transition metal impurities. Roughly, an Yb3+ doping of 10% corresponds to 1021 ions/cm3, and for a unitary value of the segregation coefficient of transition metal ions, a concentration of 1015 ions/cm3 can be estimated for a metal ions concentration of 1 ppm. We focused our attention on Fe2+ and Cu2+, both of which are resonant with the Yb3+ ion emission band [11]. Table 1 shows the magnitude of these impurities obtained by a Q-ICP-MS analysis of samples taken from four of our boules. For each boule, all of the mentioned samples were cut from the same section, so that they were all adjacent to each other. Sample 1 and 2 came from the same boule, just as sample 5 and sample 6 did, and this is why the values reported for these two pairs of samples are the same.
Table 1. Q-ICP-MS analysis on the samples for copper and iron. To evaluate the heating performance, we used the same setup described in Section 5, but we pumped the samples with only the IR laser at 1024 nm
To highlight the variation of Wnr, the radiative lifetime of the Yb3+ 2F5/2 level of all the six samples has been measured. Notice that the cooling behavior (heat up or cool down) for each sample is obtained in the same conditions, when pumped by a VECSEL tuned at 1024 nm (which is an ideal wavelength to obtain the cooling effect [12]). To measure the lifetimes of the 2F5/2 →2F7/2 transition, the samples were excited with a Titanium-Sapphire pulsed laser tuned to a wavelength of 930 nm, with pulses 30 ns wide, and a repetition rate of 10 Hz. We maintained the same experimental conditions (to compare the lifetime value among the samples) by using a dedicated sample holder with two pinholes (1 mm in diameter), that allows us to excite and collect orthogonally the emission from the same volume (about 1 mm3), which is very close to the sample surface. The fluorescence emitted by the sample was collected with a lens and sent to a Jobin-Yvon Triax 320 monochromator. The signal obtained from the detector was averaged and processed with a digital oscilloscope and analyzed with a computer. Each of the averaged signals is fitted with a single exponential model (see Fig. 1), in order to determine the mean lifetime value T. Table 2 shows the mean value for each sample, obtained from three separate measurements. Figure 2 graphically reports the same results, highlighting that the values of the cooling samples are systematically higher than the values of the heating ones. All these values are higher than the radiative lifetime at room temperature reported in literature [13] (2.20 ms) because of reabsorption inside the samples, which is the same in all of our samples since we ensured the same experimental conditions for each one of them.
Table 2. Mean lifetime values obtained for each of the samples
This systematic difference could be attributed to the presence of transition metal impurities, as shown by the Q-ICP-MS measurements. These impurities could cause a quenching of the 2F5/2→2F7/2 transition of the Yb ion, which then leads to a decrease in $\eta _{ext}$ that may be responsible for the heating of these samples.
5. Effect of impurities ($\alpha _{b}$) on the optical refrigeration cycle
We investigated the effect of impurities of rare earth ions within a sample, in particular Er3+, Ho3+, and Tm3+, that are present in quantities of 1 ppm or less inside sample 7 (YLF:5% Yb, 3x3x10 mm3), as detected by LA-ICP-MS analysis during previous studies [6]. The absorption from these impurities changes $\alpha _{b}$ , affecting the cooling process. Figure 3 shows the experimental setup used to measure the effect of background absorption on the cooling efficiency. The sample was placed inside a steel vacuum chamber designed to minimize any heat load [14]: the sample was placed on top of two quartz fibers (diameter of 120 $\mu$m) and then the air was removed from the chamber. The sample was irradiated with two counter propagating laser sources, accurately superimposed inside the crystal in a volume with a minimum diameter of about 100 $\mu$m. This value was due to the good spatial mode (near TEM00) of both sources, focused on the sample with lenses of 100 mm focal length placed at a distance of about 100 mm from the sample. The first source was a home-made VECSEL laser [14] tuned to 1024 nm, a wavelength longer than the mean emission wavelength ($\lambda _{f}=999\pm 1$ nm for the doping level of 5% [12]) and thus ideal to activate the cooling effect. The second source was a DPSSL at a wavelength of 473 nm, which was the most suitable source for pumping the Ho3+ and Er3+ impurities among the lasers already at our disposal. The powers incident on the sample were $\sim$ 200 mW (IR) and $\sim$ 100 mW (blue). For both lasers the polarization was parallel to the c-axis of the sample. The temperature of the sample was monitored with a bolometer (Raytheon 2500AS Thermal Camera) with a precision of $\pm$0.2 K. The fluorescence emitted by the sample was recorded with an Ocean Optics QEpro spectrometer.
The effect of the two counter propagating lasers is shown in Fig. 4. In all measurements the sample started at ambient temperature, specifically 295 K. The blue circles show how the sample cooled down when excited with only the 1024 nm laser, until it stabilized at 1.4 K below the initial temperature. The two graphs with black squares and red crosses correspond to the case when both beams were used: for the first twenty minutes the sample was excited only with the laser at 473 nm, then at the 20th minute it was also excited with the laser at 1024 nm. Both measurements showed, during the same time period, a decrease of 1 K from the initial temperature. The effect of the blue laser alone is a heating of 0.2 K: this temperature increase can be ascribed to impurities absorption or other phenomena such as Rayleigh scattering at the surfaces. The temperature increase when both lasers are used is 0.4 K, confirming that in this case there are additional losses which we can assume come from both heating and radiation scattering.
Fig. 4. Temperature variations (from room temperature) measured for the sample when using only the infrared laser (185 mW, 1024 nm) is depicted in blue circles. The red crosses and the black squares represent the temperature variation when using both the blue laser (80 mW, 473 nm) and the infrared one
The fluorescence spectra (corrected with a calibrated blackbody source at 3000K) shown in Fig. 5 allow us to understand the origin of these losses. The blue laser was resonant with the 5I8 →5F3 transition of the Ho3+ ion, and 5F3 rapidly decays on the 5S2 level, which in turn decays to the fundamental level, giving rise to the 5S2 →5I7 transition at $\sim$ 750 nm. The fluorescence at 750 nm was strongly enhanced when both lasers excited the sample: the effect was very high, taking into account that impurities excited by the blue laser at 473 nm are $\sim$ 1 ppm, about 1015 ions/cm3, compared to 1021 ions/cm3 of Yb3+ ions.
Fig. 5. Comparison of the fluorescence spectra emitted by the sample when pumped with only the infrared (1024 nm) laser and when pumped with both the infrared and blue (473 nm) lasers. We represent the entire recorded spectra (a) and the detail of the 750 nm peak (b)
Fig. 6 shows the presumed energy transfer mechanisms, absorption and emission processes that cause the fluorescence shown in Fig. 5. When the sample was excited with both lasers, an increase in the emission at 750 nm led to a cross-relaxation in the Ho3+ ion between the 5S2 →5I7 and 5I8 →5F4 levels. The Ho3+ ions transferred energy from the 5I4 manifold (populated by the aforementioned cross-relaxation) to the 4I9/2 manifold of the Er3+ ion, process that involves the creation of heating phonons. These heating phonons hindered the cooling of the sample. These processes depend non-linearly on the infrared pump power density: when it is increased, as in the case of multi-pass pumping [5], the decrease of the cooling efficiency becomes important. This result shows that the background absorption due to even a minimal presence of rare earth impurities can decrease the overall efficiency of the device.
Fig. 6. Transitions involved when the specimen is excited with both lasers (IR+blue). It has to be compared with [6], where Di Lieto et al. reported the transitions that occur when the specimen is excited by the infrared laser only.
6. Effect of fluorescence reabsorption on $\eta _{e}$
Another crucial parameter in optical refrigeration is $\eta _{e}$, which accounts for both fluorescence reabsorption and radiation trapping: if the fluorescence emitted by the sample is reflected or re-emitted on the sample itself by the surrounding environment, the cooling performance will be negatively affected. This has been evaluated theoretically [15,16] (see Eq. (3)) but, to our knowledge, never shown experimentally.
We studied the cooling performance of a sample while another sample was placed near it to act as a fluorescence emitter. Samples 8 and 9 (YLF doped with 5%Yb, both characterized by a good cooling performance [6,7]), were placed inside the same vacuum cell, 4 mm apart, over two quartz fibers with a diameter of 120 $\mu$m. The dimensions of the samples are: 2.28 mm x 2.14 mm x 11.68 mm (Sample 8 [6]) , 3.09 mm x 2.9 mm x 12.09 mm (Sample 9 [7]).
Fig. 7(a) shows the experimental setup we used: the beam from the VECSEL was split in two and each beam was focused on one sample. The laser was tuned at 1024 nm, a value greater than the mean fluorescence wavelength; the power incident on Sample 8 was 200 mW, while the one on Sample 9 was 400 mW. The laser beams were both polarized parallel to the c axis of the two samples.
Fig. 7. a) Setup used for the analysis of the effect of fluorescence reabsorption; b) Geometrical approximation of fluorescence reabsoprtion
The thermal camera acquired the temperature of sample 8 in two different conditions, as shown in Fig. 8: the blue circles show how it cooled down when it was pumped on its own, the red crosses track its temperature when both samples were excited by the laser. It is evident that the steady state temperature of sample 8 was strongly affected (0.4 K less than its cooling value of 1.4K) by the fluorescence emitted from sample 9.
Fig. 8. Temperature variations of sample 8 when it was pumped on its own (blue circles), and when both samples were pumped (red crosses)
As a further check, the temperature of sample 8 was recorded while only sample 9 was pumped (still with 400 mW). The result was a temperature decrease of 0.7 K which indicated that sample 8 cooled down indirectly due to the cooling of sample 9. This fact allowed us to exclude the influence of the quartz fibers on which the two samples were laid in the temperature change shown in Fig. 7. The sketch of the geometrical setup shown in Fig. 7(b) allowed us to roughly estimate at 8 mW the amount of fluorescence that sample 8 absorbed when sample 9 was pumped at 400 mW; this small value led to a decrease of about 30% of the temperature limit reached by sample 8, highlighting how fluorescence reabsorption affects the external quantum efficiency and consequently the cooling efficiency.
7. Conclusions
In this work we investigated the role of impurities in a few aspects of optical refrigeration in Yb:YLF single crystals. Firstly, we correlated the change in the average lifetime of the Yb3+ 2F5/2 manifold (and the cooling performances) to the presence of a few ppms of transition metals inside the samples, demonstrating that the measurement of average lifetime is an independent method to verify the cooling potential of a sample.
We then studied the influence of rare earth ion impurities on the cooling performance of another sample by directly pumping certain transitions of the unwanted ions with a blue laser (473 nm) while we cooled the sample with an infrared laser at 1024 nm. We noticed that the blue laser decreased the cooling efficiency of the sample and, by monitoring the fluorescence emitted by the sample, we proposed a scheme for energy transfer between Ho3+ and Er3+ ions that might create heating phonons and thus explain the reduction of the cooling efficiency.
Finally, for the first time (to our knowledge) it has been experimentally demonstrated the effect of fluorescence reabsorption on the cooling efficiency.
The results presented here highlight the role of impurities in affecting the external quantum efficiency $\eta _{ext}$ and the background absorption coefficient $\alpha _{b}$ , and in definitive the cooling efficiency of a sample.
Thanks to the experiments discussed in this paper we can now better understand how the presence of impurities can affect the cooling performance of a sample. We also proposed a method for discerning the cooling capabilities of different samples by studying their mean lifetimes.
Acknowledgements
The authors would like to acknowledge I. Grassini for her competence and care in preparing all the samples.
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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