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Abstract
We report on the optical refrigeration of ytterbium doped silica glass by >40 K starting at room temperature, which represents more than a two-fold improvement over the previous state-of-the-art. A spectroscopic investigation of the steady-state and time-dependent fluorescence was carried out over the temperature range 80 K to 400 K. The calculated minimum achievable temperature for our Yb3+ doped silica sample is ≈150 K, implying the potential for utilizing ytterbium doped silica for solid-state optical refrigeration below temperatures commonly achieved by standard Peltier devices.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
To achieve solid-state laser cooling in a rare-earth doped crystal or glass, one must pump the system with a laser sufficiently far in the red-tail of the absorption spectrum and allow the (on average) blue-shifted photons to carry away heat. Optical refrigeration in the solid-state is primarily a function of the pump wavelength $\lambda _p$ and the temperature $T$ [1]. The cooling efficiency, the cooling power relative to the absorbed power, can be written as [1]
where $\lambda _f(T)$ is the mean fluorescence wavelength, $\eta _{abs}(\lambda _p,T)$ is the absorption efficiency, and $\eta _{ext}$ is the external quantum efficiency. These last two quantities, which are strongly rooted in the material purity [2,3], are the culprits as to why the early attempts at solid-state optical refrigeration were unsuccessful in achieving net cooling [4]. The absorption efficiency is given by where $\alpha _r(\lambda _p,T)$ is the resonant absorption coefficient, and $\alpha _b$ is the parasitic background absorption. The parasitic background absorption arises predominantly from impurities, including transition metals and other rare-earth elements, that possess overlapping absorption bands with ytterbium ions and therefore act as sites capable of stealing incident pump photons resulting in heating [5]. The external quantum efficiency is given by where $W_r$ and $W_{nr}$ are the radiative and non-radiative decay rates, respectively, and $\eta _e$ represents the escape efficiency of a photon generated by a radiative decay. Factors such as excited state quenching by multi-phonon relaxation, hydroxyl species, and ion-ion interaction decrease the external quantum efficiency.Here we report laser cooling of ytterbium doped silica glass by 41 K starting at room temperature (Section 3.1). This is more than a two-fold improvement of our previous efforts which saw cooling by 18.4 K from room temperature [6]. In addition, a comprehensive spectroscopic study is conducted spanning the temperature range 80 K to 400 K (Section 3.2). With this, the global minimum achievable temperature (MAT$_G$) of our sample is calculated to be 151 K (Section 3.3).
2. Background
The accidental discovery of stable, multi-component fluoride glasses by Poulain et al. led to a boom in the study of halide glass [7]. Research in the 1980s was driven by the theoretical low loss and good infrared transmission of halide glasses [8]. Subsequently, in the 1990s, the research focused heavily on the the use of halide glasses for optically active gain media following the discovery of their high rare-earth solubility [8]. With the know-how to produce ultra-pure rare-earth doped materials, solid-state laser cooling was reported for the first time in Yb:ZBLANP by Epstein and co-workers at Los Alamos National Lab [9]. These first experiments observed cooling by 0.3 K from room temperature. In the following years, ytterbium doped fluoride glasses were cooled by 16 K (1997), then by 21 K (1998) and then by an impressive 65 K (1999) (see Fig. 1) [10–12]. A few more years would pass before optical cooling of Yb:ZBLAN down to 208 K was reported [13]. Thereafter, researchers vying for a cryogenic all solid-state cooler redirected their attention to crystalline materials [14–16] which has yielded immense success [17–19].
Fig. 1. Temperatures achieved by solid-state laser cooling in Yb:ZBLAN (black squares) and Yb:SiO$_2$ (red circles) since the first observations in 1995 and 2019, respectively.
Despite its ubiquity in optics, laser cooling of silica evaded observation [22] until 2019 [23]. Before this, silica was not accepted as an appropriate material for laser cooling. In Fig. 2, the emission spectra of Yb$^{3+}$ (red lines) and the infrared absorption spectra (black lines) for SiO$_2$ and ZBLAN are shown [20,21,24]. The higher phonon energy of silica results in the requirement of roughly half the number of phonons to quench the Yb emission relative to ZBLAN. However, it was Mobini et al. [25] who pointed out that this was actually only part of the picture, and that when one takes into account the difference in the electron-phonon coupling, silica could potentially be an even better material for optical refrigeration than ZBLAN. This was welcome news and experimental observation and applications ensued [26–32]. Indeed, our latest results (Fig. 3) give strong empirical evidence in support of the theoretical proposition that silica will be a superior material for laser cooling than ZBLAN.
Fig. 2. (a) Normalized infrared absorption coefficient spectrum of SiO$_2$ (black) and normalized spontaneous emission spectrum of Yb:SiO$_2$ (red). (b) Normalized infrared absorption coefficient spectrum of ZBLAN (black) and normalized spontaneous emission spectrum of Yb:ZBLAN (red). All measurements were made at room temperature. Infrared spectra are from Ref. [20] (SiO$_2$) and Ref. [21] (ZBLAN).
Fig. 3. (a) Temperature versus time plot of an experiment with 50 W pump power at $\lambda _P=1030\,\rm {nm}$. The inset depicts the configuration of the experiment. (b) Difference spectra relative to $t=0$ for $t=30\,\rm {s}$ and $t=240\,\rm {s}$ for the experiment shown in (a). (c) The integrated area of the DLT difference spectra as a function of the integrated intensity of the measured photoluminescence spectra over the duration of the experiment. In (a) and (b) the black lines are drawn to guide the eye.
3. Results and discussion
3.1 Laser cooling of Yb:silica to 255 K
We have previously reported on our power cooling results [6] and external quantum efficiency measurements [33] of ytterbium doped silica glasses that have been manufactured by the modified chemical vapor deposition technique [34]. In this report, we focus on the more highly doped sample, which displayed indistinguishably high external quantum efficiency ($\eta _{ext}\,=\,0.99)$ and better cooling performance. The sample is cylindrical with a doped core region of diameter 900 $\mu$m surrounded by a thin passive cladding 50 $\mu$m thick [35]. The core has a Yb$^{3+}$ ion density of 6.56$\cdot$10$^{25}$ ions per cubic meter (0.15 mol$\%$ Yb$_2$O$_3$). Aluminum is present to increase the ytterbium solubility within the silicate framework [36,37], with an Al:Yb ratio of 6:1. Fluorine was also added to the core to decrease the refractive index relative to the cladding [38]. The targeted and real numerical aperture of the core-cladding is 0.06, as measured on the preform with a commercial instrument. These materials were optimized for high power fiber-laser applications [39,40]. This required fabrication of glasses with low background loss, high purity, low photodarkening, and careful attention to the doping profile. Optimization of such properties render these materials a perfect candidate for optical refrigeration.
The experimental setup is similar to that which we have used in the past [6,26,29], with some optimization and enhancement. A custom-built multi-stage fiber amplifier [41], constructed with off-the-shelf parts, provides up to 50 W of output. The seed consists of two fiber Bragg grating (FBG) lasers combined with a 2-to-1 coupler. The FBGs have center wavelengths 200 pm apart, 500 pm bandwidths, and 50% transmission at the respective center wavelengths. This resulted in laser emission at 1030 nm with a bandwidth of roughly 120 pm. A similar broadening approach was used in Ref. [40]. The seed lasers are simultaneously pumped by the split output of a single mode 978 nm diode laser. The 5 cm long sample was placed on a fiber support system in a vacuum chamber held at about 1$\cdot$10$^{-5}$ torr. These measures are taken to minimize the conductive and convective heat loads. Pump light was coupled into the sample through a 15 cm focal length anti-reflection (AR) coated plano-convex lens placed before the entrance to the chamber. The entrance and exit windows of the vacuum chamber have AR coatings to both maximize the available pump light and minimize the scattered pump in the chamber. In an additional effort to minimize the scattered pump light, another AR coated lens was placed inside the chamber at the output end of the cylinder to collimate and remove unabsorbed pump from the chamber.
Temperature measurements are made utilizing the non-contact method of differential luminescence thermometry (DLT) [42,43]. The fluorescence of the sample was monitored through a fused silica window with collection optics and a 600 $\mu$m core diameter multimode fiber feeding a CCD spectrometer. Experimental spectra were acquired once per second with a 100 ms integration time. For a high signal-to-noise ratio, we area normalize the measured fluorescence over the interval $\lambda$ $\in$ {900,1020} nm, avoiding the influence of scattered pump light. Then, the difference is taken relative to ambient temperature, or the first measurement at the start of the experiment. The relationship between the absolute area considered in the difference spectra recorded by the spectrometer and the sample temperature was determined in separate calibration experiments using a low power laser diode near the pump wavelength as the excitation source and the sample placed inside a temperature controllable liquid nitrogen cryostat. For the calibration (as well as the spectroscopy discussed below), a sample from the same preform draw was used with identical dimensions of the sample used in laser cooling experiments.
The time-temperature evolution of the sample pumped with 50 W of 1030 nm laser light is shown in Fig. 3(a). Figure 3(b) displays the difference spectra, $\Delta S(\lambda )$, relative to the measured spectrum at the start of the experiment at $t=0$ for $t=30\,\rm {s}$ and $t=240\,\rm {s}$. As the temperature drops, so does the resonant absorption at wavelengths in the vicinity of the pump wavelength. Since fluorescence power is directly proportional to absorbed power, as a sanity check of our results, we plot the integrated absolute value area of the difference spectra, $S_{DLT}$, against the integrated intensity of the as-measured photoluminescence spectra over the interval $\lambda \in$ {900,1020} nm (Fig. 3(c)). A nice linear relationship is observed. When the minimum temperature is reached in Fig. 3(a) and the sample is held at 41 K below room temperature, the measured photoluminescence intensity and extracted $S_{DLT}$ after data processing are stable.
3.2 Optical spectroscopy from 80 K to 400 K
In addition to these results, we report here an evaluation of the minimum achievable temperature (MAT) of cooling-grade ytterbium doped silica glass. To find the MAT, we need to evaluate the cooling efficiency given by Eq. (1) over a wide temperature range [44]. $\lambda _f(T)$ is calculated from steady-state fluorescence spectra (Fig. 4(a)) [33]. The spontaneous emission spectra in Fig. 4(a) were collected from the side of the previously mentioned calibration sample, using a 940 nm laser diode excitation source. The sample was mounted once again in the liquid nitrogen cryostat equipped with a heater. A 400 $\mu$m diameter fiber sent the collected light to an optical spectrum analyzer set at 1 nm resolution. As expected, the mean fluorescence wavelength increases with decreasing temperature. The mean fluorescence wavelength is fitted with a linear expression of $\lambda _f=b-mT$ where $b=1015.2\,\pm 0.2\,\rm {nm}$ and $m=0.0271\,\pm 0.0008\,\rm {nm}~\rm {K^{-1}}$. It is interesting to note that this is very close to the slope of 0.03 $\rm {nm}~\rm {K^{-1}}$ that Seletskiy et al. found for ytterbium doped yttrium lithium fluoride (YLF) [44]. As can be seen in the inset of Fig. 4(a), the position of the peak at circa 977 nm broadens and shifts to shorter wavelengths as the temperature increases. This shift is shown in Fig. 4(c) to be linear to a first-order approximation. The discretization is an artifact of the employed resolution of 1 nm of the optical spectrum analyzer, which was used to obtain measurements with good signal-to-noise ratio.
Fig. 4. (a) Measured emission spectrum shown for selected temperatures. The inset highlights the shift to higher energies and broadening of the 978 nm transition. (b) Calculated mean fluorescence wavelength as a function of temperature. (c) Measured peak wavelength as a function of temperature.
The radiative lifetime, $\tau _{r}$, is required for computation of the emission cross-section. For high quantum efficiency materials, it is acceptable to make the approximation $\tau _{r} \approx \tau _{f}$ where $\tau _{f}$ is the fluorescence lifetime. The $\tau _{f}$ values (see Fig. 5, black circles) were measured using 978 nm single mode diode laser as the excitation source chopped to provide pulses of roughly 85 $\mu$s duration at a 95 Hz repetition rate. The chopped beam was focused into the sample in the cryostat. The fluorescence was collected and passed through a 1000 nm long pass filter toward an InGaAs amplified detector connected to an oscilloscope. A microscope slide was inserted into the path of the chopped beam so that the reflection was incident on a second detector to allow recording of the pulse shape and triggering the oscilloscope to allow acquisition in averaging mode. Measurements were repeated at each temperature with coupling into the sample lightly adjusted each time with the mirrors and lenses. The measured lifetimes are fitted with an expression for a two-level system [45],
Fig. 5. Depiction of the temperature dependence of the population of the second lowest sub-level in upper state manifold of Yb$^{3+}$. The measured lifetime as a function of temperature is shown by black circles. The solid red line was obtained by a two-level model fit of the measured lifetime data (Eq. (4)). The light blue squares represent the integrated area between $\lambda \in$ {900,945} nm in the steady-state fluorescence spectra. The axes have been scaled for comparison.
Alternatively, insight into the distribution between the sub-levels in the upper manifold can also be determined from the steady-state fluorescence spectra. Equation 4 describes the distribution between the two lower levels of the upper manifold where a is the lowest level and b is the second lowest level. The lowest level is identified from the emission spectra 4(a) to be at 10230 cm$^{-1}$ (taking the mean value of the two observed components). The fit of the observed lifetimes gives $\delta E \approx 600\,\rm {cm^{-1}}$, implying level b lies 600 cm$^{-1}$ above a. This puts level b at circa 923 nm. Insight into the wavelength range characteristic of this transition is acquired by inspecting the difference spectra in the cooling experiments (Fig. 3(b)). As a reasonable approximation, the area between 900-945 nm is taken as representative of the population in b. Integrating this area of the normalized emission spectra (Fig. 4(a)) and plotting against the temperature (see Fig. 5, blue squares) produces almost the same trend as seen from the time-domain fluorescence measurements. Indeed, the integrated area and modeled $\tau (T)$ (Fig. 5, solid red line) are linearly correlated with an $R^2$ value of 0.997.
$\eta _{abs}(\lambda _p,T)$ requires knowledge of the resonant absorption spectrum as a function of temperature. To obtain this, the Füchtbauer-Ladenburg equation is applied to the measured emission spectra at different temperatures using $\tau (T)$ from the two-level model fit as the radiative lifetime at each temperature [51]. With the calculated emission cross-section, McCumber theory allows the determination of the absorption cross section [52]. This in turn allows us to obtain $\alpha _r(\lambda,T)$ by scaling with the Yb$^{3+}$ ion dopant density via $\alpha _r(\lambda,T)=\sigma _{abs}(\lambda,T)*N_T$. $\alpha _r(\lambda,T)$ is shown Fig. 6 for selected temperatures.
3.3 Minimum achievable temperature
With the results of our spectroscopic measurements and taking $\alpha _b=$10 dB$\cdot$km$^{-1}$ [26], we can fully evaluate $\eta _c(\lambda _p,T)$, which is shown in Fig. 7. We employ here the convention of a positive cooling efficiency coinciding with cooling, and so the blue region encompasses the cooling window. To determine the MAT$_G$, we graphically inspect the white contour in Fig. 7 where $\eta _c(\lambda _p,T)=0$, which represents the minimum achievable temperature spectrum, MAT($\lambda$). At a given wavelength, the temperature corresponding to $\eta _c(\lambda _p,T)=0$ gives the local MAT, and solid-state cooling is no longer possible at that wavelength at lower temperatures. MAT$_G$ is then given by the lowest temperature at which $\eta _c(\lambda _p,T)=0$. The MAT$_G$ of the sample under investigation is found to be 151 K (Fig. 7). For simplicity, we assume in this analysis that $\eta _{ext}$ and $\alpha _b$ are temperature independent [44,53]. Before solid-state cooling of Yb:silica was ever observed, a spectroscopic investigation by Mobini et al. was conducted using a commercial ytterbium doped silica single mode optical fiber [25]. Based off their measurements and assumptions, they predicted the MAT of Yb:silica to be 175 K with an assumed $\eta _{ext}=0.99$. This was already a lower MAT than determined for ZBLAN, which is about 190 K [44].
The measurements reported here are on our in-house made glasses, for which we have experimentally measured an $\eta _{ext}=0.99$ and repeatedly shown cooling [6,33], indicate the MAT is about 24 K below what was previously thought possible for ytterbium doped silica. Moreover, this direct calculation on a true cooling-grade sample shows that Yb:silica can be optically cooled below temperatures presently achieved by off-the-shelf thermo-electric coolers. While this is not as low as the MAT of some fluoride crystals [54], silica has some advantages such as being rugged, isotropic, and able to be readily formed into microspheres, planar substrates, and drawn into fibers.
Considering our decision to use the observed $\tau (T)$ relation, we compute the MAT$_G$ for values of $\tau$ that are more characteristic of the typically found intrinsic lifetime of Yb$^{3+}$ in silica. These produce lower MAT$_G$ values. For example, setting $\tau =0.85\,\rm {ms}$ gives MAT$_G=144\,\rm {K}$. As such, we are satisfied with our more conservative calculation employing the extrinsic values relevant to our experiments and sample.
4. Outlook
A recent study by Volpi et al. revealed that the background absorption decreased significantly in a Yb:YLF specimen with decreasing temperature [55]. In addition, the $\alpha _b$ of rare-earth doped silica fibers can in some cases be as small as 3-5 dB$\cdot$km$^{-1}$ [26]. Passive fibers used by the telecommunications industry routinely display $\alpha _b<1$ dB$\cdot$km$^{-1}$, but this is not attained in rare-earth doped fibers despite using modern methods. In light of this, we fix the pump wavelength at $\lambda _p=1030\,\rm {nm}$ and take $\eta _{ext}=0.99$ then consider several different values of $\alpha _b$ that might be accessible (Fig. 8(a)). The calculation indicates that lower MATs might be achievable in ytterbium doped silica, possibly below cryogenic levels. Investigations into the temperature dependence of the background absorption in our glasses are currently underway.
Fig. 8. Cooling efficiency versus temperature for (a) several background absorption values with fixed external quantum efficiency and (b) several external quantum efficiency values with fixed background absorption.
The importance of the background absorption at low temperature in Yb-doped silica is highlighted in Fig. 8(b). We’ve taken a fixed, rather standard, value for silica fabricated by CVD of 10 dB$\cdot$km$^{-1}$ and evaluated the cooling efficiency at different values of $\eta _{ext}$ and the corresponding optimal pumping wavelength. Although an improvement in the external quantum efficiency will increase the cooling efficiency around room temperature, the background absorption demands more attention for future progress. Especially since $\alpha _b$ values between $3\,\rm {and}\,5$ dB$\cdot$km$^{-1}$ have been reported, while an $\eta _{ext}=0.995$ has not been achieved yet in Yb:silica, to our knowledge.
5. Conclusion
We demonstrated laser cooling of silica glass co-doped with ytterbium and aluminum by 41 K starting at room temperature. Temperature dependent spectroscopic measurements allowed us to then calculate the minimum achievable temperature of our sample. The MAT was found to be in the vicinity of 150 K which is lower than the previously suggested MAT of 175 K, as well as below the limit of typical thermo-electric coolers. Questions about the temperature dependence of the background absorption in Yb$^{3+}$ doped silica glass remain and will be addressed in a later report.
Funding
Air Force Research Laboratory (FA9451-22-2-0016); Air Force Office of Scientific Research (FA9550-16-1-0362); Bundesministerium für Bildung und Forschung (13N15978).
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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