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Abstract
Laser cooling of a 5 cm long, 1 mm diameter ytterbium doped (6.56×1025 ions/m3) silica rod by 67 K from room temperature was achieved. For the pump source, a 100 W level ytterbium fiber amplifier was constructed along with a 1032 nm fiber Bragg grating seed laser. Experiments were done in vacuum and monitored with the non-contact differential luminescence thermometry method. Direct measurements of the absorption spectrum as a function of temperature were made, to avoid any possible ambiguities from site-selectivity and deviations from McCumber theory at low temperature. This allowed direct computation of the cooling efficiency versus temperature at the pump wavelength, permitting an estimated heat lift of 1.42 W/m as the sample cooled from ambient temperature to an absolute temperature of 229 K.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
1.1 Brief history
Peter Pringsheim’s postulation that the anti-Stokes fluorescence (ASF) may be used to decrease the temperature of a material became experimentally verifiable following the invention of the laser [1,2]. In 1968, Kushida and Geusic carried out solid-state ASF pumping experiments using an undoped and a Nd$^{3+}$ doped yttrium aluminum garnet (YAG) crystal [3]. Reduced heating was observed in the doped crystal, attributed to ASF cooling, but no net cooling was observed.
Before this work, Weinstein described a "technical efficiency", $\eta$, of a lamp converting heat into light as the ratio of the power leaving the lamp in the form of luminescence radiation to the power supplied to the lamp in the form of work [4]. In Kushida and Geusic’s experiment, this could be defined as a cooling efficiency, $\eta _c$,
where $P_{out}$ is the fluorescence (luminescence radiation) leaving the crystal (lamp) and $P_{in}$ is the laser light pumping the crystal (power supplied). Kushida and Geusic elaborate on the actual realization of such a solid-state "lamp", "In order to observe net cooling, the possible heating mechanisms of Stokes fluorescence, nonradiative transitions, and the absorption of laser radiation by impurity ions in the refrigerator crystal are required to be weak compared with the cooling by anti-Stokes fluorescence". The first element of this statement alluding to "the possible heating mechanisms of Stokes fluorescence" is addressed by choosing $\lambda _p$, the wavelength of the pump source providing $P_{in}$, to be longer than the mean wavelength of the fluorescence emission lineshape, $\lambda _f$, so that $\lambda _p > \lambda _f$. $\lambda _f$ is simply the mean value of the experimentally measured emission lineshape, $S(\lambda )$ [5,6].Ignoring, for now, the nonradiative transitions and purity issues raised by Kushida and Geusic, an ideal form of the cooling efficiency can be written in more accessible terms as
Equation (2) states that as $\lambda _p$ is increasingly detuned further away from $\lambda _f$ in the red-tail of the absorption spectrum, $\alpha _r(\lambda )$, the cooling efficiency will increase. However, physically realizable materials will always have some impurities giving rise to a background absorption, $\alpha _b$. Absorption by impurities not only decreases the available energy for the ASF process, but can serve as a source of internal heat generation. The relative magnitude of the useful absorption to the background absorption can be characterized by the absorption efficiency, $\eta _{abs}(\lambda )$,
This tells us that we actually want to keep $\lambda _p$ close to $\lambda _f$, so as to keep $\eta _{abs}(\lambda )$ near 1. The last condition for net cooling given by Kushida and Geusic is that the nonradiative transitions must be few. Only radiative decays, i.e. emitted photons, that escape the bulk solid have any hope of contributing to net optical refrigeration. Nonradiative decays arising from multi-phonon relaxation, clustering, and quenching of the excited state by impurities (hydroxyl species, rare-earth ions, transition metal ions) will all hinder the ASF cooling process. The term encompassing these processes is dubbed the external quantum efficiency, $\eta _{ext}$,
where $W_r$ and $W_{nr}$ represent the radiative and nonradiative decay rates, respectively, and $\eta _e$ is the escape efficiency. The escape efficiency is dependent on the reabsorption coefficient and the sample geometry (see Refs [7] and [8] for more on $\eta _e$). Accounting for the photon conversion factors, the cooling efficiency can be written more completely asNear $\lambda _f$, $\eta _{abs} \approx 1$ for high purity materials and so $\eta _{ext}$ sets the lower limit on the choice of $\lambda _p$ to induce net cooling - the "cross-over wavelength" [9]. Together, $\eta _{ext}$ and $\eta _{abs}(\lambda )$ set the short wavelength and long wavelength bounds, respectively, for net cooling. This is the essence of the "LITMoS" test (Laser Induced Thermal Modulation Spectroscopy) developed by Sheik-Bahae and co-workers allowing determination of both $\alpha _b$ and $\eta _{ext}$ [10–12]. For a more detailed derivation of Eq. (5), see Refs. [13,14].
1.2 Net cooling
In 1995, Epstein and co-workers at Los Alamos National Labs successfully achieved net cooling by about 0.3 K in a Yb doped ZBLANP glass [15]. Foreseen applications of this new era of ’net cooling’ included mainly the cryogenic cooling of infrared detectors and other devices. The potential for an all solid-state, vibration-free, liquid-free cooling device led to the suggestion that the technology would be useful for space-based applications, which is indeed still a focus of research efforts and advancing closer to implementation [16,17].
Efforts into cooling fluoride glasses continued [18,19] and by 1999, cooling by 65 K was reported by Gosnell with a 1 wt% Yb$^{3+}$ doped multimode fiber with 170/250 $\mu$m core/clad diameter [20]. The coldest temperature achieved with Yb:ZBLAN is 208 K, achieved 6 years after Gosnell’s experiments [21]. The Yb$^{3+}$ concentration was increased by a factor of 2 relative to the 65 K cooling Yb:ZBLAN sample. Pump power was also increased to 11 W and best results were obtained at $\lambda _p$=1026 nm. To date, this remains the record in optical cooling of a vitreous material.
After ZBLAN glass was cooled to 208 K, the focus switched from glasses to crystals [22–25]. The lack of inhomogeneous broadening in crystalline materials permits more resonant absorption at a given pump power and wavelength. Additionally, fluoride crystals containing an optically inactive lanthanide, such as yttrium in YLiF$_4$, allow direct substitution of the active refrigerator ion. This allows high dopant densities before the onset of clustering. High dopant densities yield high pump absorption, which in turn allows a larger degree of cooling. To date, the coldest temperature achieved by solid state optical refrigeration is in crystalline Yb:YLiF$_4$ down to 87 K [11,26]. Infrared detectors have been cooled down to cryogenic temperatures [27]. Payloads have, as of this writing, been cooled down to 124.7 K [28] and researchers are closing in on their goal of optically refrigerating a payload to 124 K which they hope to apply to vibration-free cooling of silicon reference cavities at NIST [29].
1.3 Laser cooling silica
Recent years have also seen concentrated efforts to use laser cooling for radiation balanced lasers (RBL) and radiation balanced amplifiers (RBA) [30–32]. In the radiation balancing regime, the ASF offsets the heat generated during lasing operation [33] and was first succesful in Yb:YAG platforms [9,30]. The renewed interest in passive thermal management of fiber laser systems has brought glasses back into the spotlight for laser cooling. Some modern efforts with fluoride glasses have seen promising results [34–36]. However, the demonstration of laser cooling silica in 2019 was a significant breakthrough [14,37]. Silica remains the choice material for high power fiber laser systems. At kilowatt output levels, even bulky active cooling cannot fully mitigate the onset of thermal nonlinearities, mainly transverse mode instability [38–40]. Clever approaches to alleviate thermal issues have included cooling via ASF in accordance with Bowman’s proposition [31,32,41,42]. In addition, Yu and Dragic have developed the ’excitation balancing’ scheme for rare-earth doped fiber laser where a two-color pump scheme is utilized to decrease overall heating in pulsed fiber lasers [43–45].
Towards the goal of using ASF cooling in a fiber laser/amplifier platform, the collaboration between the authors’ institutes has led the way in terms of power cooling experiments. The first report of cooling with Yb-doped silica preforms saw cooling by about 700 mK [14]. Shortly after, the optimization of $\lambda _p$, an increase in pump power, and the partial removal of the undoped cladding resulted in cooling silica by 6 K [46]. Experiments then shifted to cane with 900/1000 micron core/cladding geometry [47]. A higher Yb concentration was used and cooling by 18 K from room temperature was achieved [47]. A later effort saw two-fold improvement reporting cooling by 41 K [48]. These results were all achieved in the absence of a convective heat load by being carried out in vacuum. At atmospheric pressure, cooling by 6.3 K remains the best effort for silica as reported in Ref [47].
This work represents the culmination of our joint efforts in power cooling ytterbium doped silica. Here, cooling to an absolute temperature of 229 K is reported. These results truly cement the viability of ASF cooling of silica as genuine route to heat mitigation in fiber lasers and amplifiers.
2. Experimental
A detailed schematic of the fiber amplifier constructed is shown in Fig. 1. A single mode pump diode simultaneously pumps two linear fiber Bragg grating (FBG) cavities. The cavities used 50 cm of single mode 4/125 $\mu$m ytterbium doped gain fibers (nLight Yb1200 4/125) and 50% reflectivity FBGs. The bandwidth of both FBGs was 500 pm and the separation of their center wavelengths was 200 pm (1032.0 and 1032.2 nm). It is noted that although it was initially thought that narrowband excitation was required for ASF cooling, the relaxation in spatial coherence requirements of the pump light in ASF cooling is well embodied experimentally by cooling of Yb:YLF to 130 K using a several nm broad multimode pump diode [49].
Fig. 1. Schematic of 100 W 1032 nm amplifier. See text for details. Abbreviations in schematic - Laser diode drive (LDD), temperature controller (TC), isolator (ISO), polarization controller (PC), wavelength division multiplexer (WDM), partial reflector (PR), high reflector (HR), power meter (PM), pre-amplifier (pre-amp), narrow bandpass filter (NBF), optical spectrum analyzer (OSA), mode field adapter (MFA), high index cladding mode stripper (HI-CMS), acid etched CMS (AE-CMS), long pass filter (LPF), dichroic mirror (DM), neutral density filter (NDF), spectrometer (SPEC).
The two parallel laser cavities were combined and the forward propagating signal was passed through an isolator and followed by a 20 dB 2x2 tap coupler to monitor the forward and backward power. Two identical pre-amplifier stages were employed, both using wavelength stabilized 976 nm multimode pump diodes and 1.5 m length of 10/125 Yb doped gain fiber (nLight Yb1200-10/125DC). Residual pump light in the cladding was removed by a high index epoxy coating on a roughly 2 cm length of fiber on either end of the splice to the following component. The first pre-amplifier was only operated at a pump level required to have on the order of 1 W signal output. This kept back-reflection toward the seed low. The signal spectrum was cleaned up with a narrowband pass filter (NBF) and isolated. The forward propagating signal was boosted by the second pre-amp so that the power entering the main amplification stage is approximately 2.5 W.
Before the main amplifier stage, a 20 dB 2x2 coupler monitors the forward and backward propagating power. The backward tap is split once more with a 3 dB splitter to monitor on one channel the back reflected power and on the other channel the spectral content with an optical spectrum analyzer (OSA). The primary forward signal goes through a mode field adapter (MFA) that takes the single mode beam from a 10/125 fiber to a 25/250 fiber architecture. The larger core size was chosen because the SBS threshold power is directly proportional to the effective area [50]. 1.8 m of Nufern LMA-YDF-25/250 was used as the gain fiber in a reverse pumping configuration using a 130 W nLight 976 nm wavelength stabilized pump diode. The combiner to gain fiber splice was recoated manually with a low index epoxy (Coherent) in a copper V-groove in good contact with the aluminum breadboard underneath. The recoated splice was positioned below a cooling fan. The gain fiber to signal input splice was acid-etched (AE) using Armor Etch with 3 applications of 6 minute exposures and rinsing with deionized water in between [51]. About 4 cm of fiber was etched in this way to function as a cladding mode stripper (CMS). This AE-CMS was suspended in air over a copper V-groove with a fan blowing on it. Because some low numerical aperture pump light may not be fully removed by the AE-CMS, some of the low index polymer coating was removed and a low-power splice protector was heat shrunk over the outer cladding of the fiber. The splice protector acts as a high-index CMS. The splice protector was bent to have about a 5 cm radius of curvature to encourage the low NA pump light to escape [52]. Lastly, a short segment of coreless 250 $\mu$m diameter fiber was spliced to the output end of the amplifier and cleaved at an angle of 7 degrees.
The output of the amplifier was collimated and steered with dielectric mirrors while passing through two long pass filters before being injected into the sample in the vacuum chamber held at 10$^{-6}$ mbar. The focusing lenses and chamber windows were all anti-reflection coated fused silica to minimize loss of pump light from Fresnel reflections. It is worth noting that in between previous cooling experiments in Ref [48] and these experiments, the sample was not removed from the chamber and had been under high vacuum for a total of over one month during that span of time, suggesting any possible off-gassing by the sample had already taken place. The vacuum obtained in these experiments was about 1 order better than previous experiments, after using a flowing He and mass spectrometer leak detection routine to identify poor seals in the vacuum chamber. In this work, cooling experiments were repeated at comparatively low pump powers (30 W) until an optimal coupling was found that yielded good cooling performance, at which point the power was scaled.
The sample’s fluorescence was used for temperature measurements, as we have done before [47,48]. Following our work in Ref [6], it is underlined here that the experiments and calibration were both carried out using 1032 nm excitation. The fluorescence was collimated and attenuated with a continuous neutral density filter (NDF) wheel. For a given experiment, the NDF was adjusted for each pump power level so that the fluorescence power reaching the spectrometer was maximized without saturating the detector. The fluorescence was coupled into the 600 $\mu$m core step-index multimode fiber feeding a CCD spectrometer. The spectra were acquired on a computer every 500 ms with a 100 ms integration time.
Cooling experiments were conducted using a 5 cm long silica rod fabricated by the modified chemical vapor deposition technique [39,53]. The doped region of the rod had a diameter of 900 $\mu$m surrounded by a 50 $\mu$m thick undoped cladding. The rare-earth ion density was 6.56$\cdot$10$^{25}$ Yb$^{3+}$ ions per m$^3$. In-depth characterization and descriptions of these materials can be found in Ref [6,12,47,48,53].
For analysis of the cooling results, temperature-dependent spectroscopic measurements were made with a liquid nitrogen cryostat equipped with an electrical heater. A piece from the same preform was used. Absorption coefficient spectrum, $\alpha (\lambda,T)$, measurements were made on a cleaved 24 mm long piece clamped in a copper V-groove mounted on the cold finger using a stabilized tungsten halogen light source and an imaging method. The absorption coefficients were obtained directly with the Beer-Lambert law following a baseline correction to the lamp source [54,55]. The absorption cross-section was found by scaling with the dopant density. Static and lifetime fluorescence measurements were made in a similiar manner as before [6,48]. Fluorescence measurements were taken on a 4 mm long cleaved section etched and coated in high index epoxy to reduce total internal reflection and reabsorption. The excitation source was a multimode 915 nm attenuated to about 50 mW of power. Lifetime measurements used a mechanical chopper for roughly 30 $\mu$s pulses at a 100 Hz repetition rate with InGaAs detectors for triggering and luminescence decay recording with the latter using 1030 nm bandpass filter (FWHM 10 nm). Emission cross-section were calculated using the Füchtbauer-Ladenburg equation [56].
3. Results and discussion
The performance of the amplifier is displayed in Fig. 2(a). The optical to optical conversion with respect to the launched pump power is linear with a slope of 78%. No significant broadening of the signal took place at the powers used in these experiments. Additionally, the power was stable, with no SBS detected in the back-reflected power or spectrum. The measurements in Fig. 2(a) were taken between the second mirror and the focusing lens just before the vacuum chamber in Fig. 1. The power for each trial was measured before and after the cooling process, observing an average drift of less than 500 mW.
Fig. 2. (a) Measured 1032 nm output power versus launched 976 nm pump power. The red line represents a linear fit of the data. (b) Maximum change in temperature achieved at different pump powers. The broken red line is drawn to guide the eye.
The maximum change in cooling sample temperature for different 1032 nm pump powers is shown in Fig. 2(b). The cooling increases with increasing pump power. A slight decrease in the magnitude of cooling per additional watt of pump occurs at the highest powers. There are several explanations for this. First, as the temperature drops, so does the cooling efficiency. This is driven, in the context of Eq. (5), by a red shift of $\lambda _f$ and even more so by the drop in the $\alpha _r(\lambda _p)$ [6]. Another contribution could come from an increase in the chamber temperature, and therefore the blackbody load, due to the radiated fluorescence [21]. At room temperature, $\alpha _r(1032\,\rm {nm})\approx 2.3\,\rm {m}^{-1}$ and so for the 5 cm long sample, roughly 10% of the pump light is absorbed. Since $\eta _{ext}\approx 0.99$ for this glass [12], practically all of this absorbed power is subsequently radiated into the chamber.
The best result in Fig. 2(b) is cooling by 67 K with 97 W of pump power. Spectral measurements acquired over the full recording spectrometer range are shown in Fig. 3(a). For reference, the background is plotted in black. The red lineshape, being the first recorded spectrum, is taken as the room temperature spectrum. A small amount of cooperative upconversion luminescence is seen at around 518 nm, which is slightly decreased in the blue spectrum which was acquired at the end of the experiment.
Fig. 3. Spectral measurements before, at the start, and at the end of the experiments using 97 W of pump power over (a) full measured range and (b) the Yb$^{3+}$ emission region only. (c) Measured temperature change with time (black circles) for trial using 97 W of pump power and a mono-exponential fit of the data (red line).
The near-infrared fluorescence of the measurement at 220 s (blue line) is significantly reduced due to the decrease in the resonant absorption with decreasing temperature, which naturally results in a lower fluorescence power. The near-infrared emission region is emphasized in Fig. 3(b). As the absorption decreases, the scattered pump light reaching the spectrometer increases. This is highlighted by the inset where it can be seen that linewidth of the pump did not undergo significant broadening and still has a linewidth well below 1 nm.
The temporal cooling curve for the new record of ASF cooling in ytterbium doped silica is shown in Fig. 3(c). The black circles represent experimentally measured data points. The red line represents an exponential fit of the data via $\Delta T(t)=\Delta T_{max} \left [ \rm {exp}(-t/\tau )-1 \right ]$. In this instance, $\Delta T_{max}$ and $\tau$ are fitting parameters and found to be 69 K and 50 s, respectively.
Next, spectroscopic measurements are analyzed to estimate the actual heat lifted from our sample via ASF. The steady-state will be reached when the cooling power and the thermal load are equivalent [29]. The thermal load in the steady-state can be expressed as $\eta _c(T_f)\,P_{abs}(T_f)$ where $T_f$ is the final temperature reached. In this work, $T_f$, is taken as the mean value of the last 20 data points (10 seconds) for each trial (see Fig. 3(c)). The thermal load, $P_{load}$, is solely from the blackbody radiation of the chamber due to the elimination of the conductive and convective loads via the experimental setup. The Beer-Lambert law and the temperature-dependent form of Eq. (5) thus need to be evaluated,
For all cases, $\lambda _p=$1032 nm. Data from Ref. [6] is used for $\lambda _f(T)$. Considering the site-selective fluorescence behavior of these glasses, values from Ref. [6] using an excitation wavelength of 1028 nm are used, as these are assumed to be a reasonable approximation of the case of $\lambda _p=$1032 nm. Our previous work showed the ambiguity in using the emission spectrum and reciprocity to calculate the absorption coefficient spectrum for use in $\eta _{abs}$ due to site-selective fluorescence behavior [6]. To remedy this, direct measurements of the absorption coefficient spectrum were made (Fig. 4(a)). A line representing $\lambda _f(T)$ is drawn as the broken grey line in Fig. 4(a). Using the directly measured spectra in Fig. 4(a), values for $\alpha (\lambda =1032\,\rm {nm})$ are shown in Fig. 4(b) and fit with a Boltzmann function, which follows the data well. $\alpha _b$ is set at 10 dB km$^{-1}$ [12,14,53] and $\eta _{ext}$ has previously been measured to be 99% [12]. $\eta _c(1032\,\rm {nm},T)$ is plotted in Fig. 4(c) showing a minimum achievable temperature (MAT) of about 145 K, slightly lower than these previous estimates (between 150-165 K) [6,48]. This is likely due to the use here of direct measurement of the absorption spectrum, as opposed to calculation of $\alpha (\lambda )$ via the fluorescence spectrum. Martin and Quimby discussed deviations from McCumber theory at low temperature, and showed for Nd-silicate, the absorption on the long wavelength side of the zero-phonon line calculated via McCumber theory was lower than directly measured values [57,58]. The results here are consistent with their work, where slightly higher values for $\alpha (\lambda )$ at a given temperature below $\approx$200 K yield a lower calculated MAT.
Fig. 4. (a) Long wavelength regime of the measured absorption coefficient spectrum (b) absorption coefficient at 1032 nm versus temperature (c) calculated cooling efficiency versus temperature and (d) calculated product of cooling efficiency and absorbed power for 97 W of 1032 nm pump
For the Beer-Lambert equation on the right side of Eq. (6), $P_{in}$=97 W, $z$=0.05 m is the sample length, and $T_{tot}$=0.956 accounting for losses due to optical elements and Fresnel reflections at the input facet of the sample. For the trial depicted in Fig. 3(c), the calculated product of $\eta _c\,P_{abs}$ is plotted Fig. 4(d).
At ambient temperature (296 K), $\eta _c$=1.19% and for 97 W of 1032 nm pump power an $\alpha _r$=2.25 $\rm {m}^{-1}$ gives $P_{abs}$=9.85 W. For the same constant pump, at $T_f$=229 K, $\eta _c$ drops to 0.88%, $\alpha _r$ drops to 1.17 $\rm {m}^{-1}$, and $P_{abs}$ falls to 5.28 W. The product of $\eta _c(T_f)\,P_{abs}(T_f)$ yields a balanced thermal load of 46 mW. At room temperature, the product of $\eta _c P_{abs}$=117 mW, which indicates as a much as 71 mW was lifted from the 5 cm long sample, or 1.42 W/m.
Alternatively, the thermal load may be estimated via [59]
where $\sigma$ is the Stefan-Boltzmann constant, $T_{c(s)}$ is the chamber (sample) temperature, $\epsilon _s$=0.85 is the sample emissivity, and $A_s$ is the sample surface area. The prefactor $\chi$ is related to the sample and chamber areas and their respective emissivities (see Ref. [59]) and is calculated for this experiment to be 0.028. Assuming the temperature of the chamber is fixed at 296 K and a sample temperature of 229 K, Eq. (7) gives a value for the thermal load of 37 mW. In this work, no steps were taken to actively cooling the chamber as the significantly larger mass relative to the sample would carry with it a much larger time scale for temperature changes. In experiments by Thiede et al., the measured chamber temperature rose to 306 K within the first few minutes of the experiment [21]. Although the setup here is not lined with absorptive foil like in Ref. [21], the pump power used here is about 9 times larger (97 W versus 11 W). Some sudden rise in the temperature of the chamber is conceivable with the roughly 10 W of incoherent fluorescence power filling the chamber. Considering this, as a thought experiment, taking $T_c$=307 K with $T_s$=229 K in Eq. (7) yields thermal load of 46 mW, and so monitoring of the internal chamber temperature should be done in future experiments.Lastly, to assess what is the maximum amount of heat that could potentially be extracted using this composition, the cooling power density, $Q$, is determined with $\eta _c$, $\alpha _r$, and the saturation intensity, $I_{sat}$,
$I_{sat}$ is given by
Fig. 5. (a) Measured and modeled lifetime decay (b) absorption and emission cross-sections at 1032 nm (c) calculated cooling power density (d) maximum linear cooling power density as a function of doping radius for a cylinder.
The cross-sections at 1032 nm were obtained as described in the Experimental section and shown in Fig. 5(b). As the temperature drops, the absorption cross-section goes to zero while the emission cross-section grows, as anticipated by the temperature-dependence of the fractional occupancy of the Yb$^{3+}$ manifolds [61,62]. Combining all this, Eq. (8) can be evaluated and is plotted for measured points along with a Boltzmann fit in Fig. 5(c). Two points from the plot of $Q(T)$ at $\lambda$=1032 nm are considered for contrived scenarios of a cylindrical sample (such as a fiber) with varying cross-sectional area (Fig. 5(d)). For the composition used in these experiments, the maximum heat load able to be extracted is fairly small for a standard 20 $\mu$m core diameter active fiber - less than 50 mW/m. However, as has been discussed [41,42,63], if the cladding is doped, W/m level heat extraction is accessible since the ASF cooling scales quadratically with the radius of the doped region for a cylinder (i.e. a fiber). This can be seen in Fig. 5(d). Imagining a scenario of a 400 micron cladding diameter fiber with doped cladding, 1.1 and 1.9 W/m could be extracted at $T$=300 and $T=360$ K, respectively. Now, if somehow the Yb ion concentration can be increased to 3$\cdot$10$^{26}$ Yb$^{3+}$ ions / m$^3$ - a nearly 5-fold increase - while keeping $\eta _{ext}$ and $\alpha _b$ fixed, then these numbers would increase to 5.3 and 9.3 W/m. Other groups have used higher doping concentrations of Yb in silicates and report cooling [64–67], and this hypothetical concentration of 3$\cdot$10$^{26}$ Yb$^{3+}$ ions / m$^3$ falls roughly in the middle of these reports.
Strictly in the context of power cooling experiments, improved cooling performance may be anticipated with taking a few additional steps. One, incorporating a clamshell around the sample would lessen the blackbody load [23,68]. Two, a multi-pass geometry would allow an increase in the absorbed power as more of the doped region will be filled by pump light [28,68]. A Herriot cell may be difficult to implement with the sample geometry, but deposition of dielectric mirrors on the facets, ideally with spectral selectivity, is a viable alternative [28]. Lastly, the approach by Gosnell can be adapted to better fill the volume of the sample while avoiding saturation intensity [20]. The numerical aperture (NA) of the core/clad glass is low and while this is desirable for mitigating transverse mode instability [69,70], if the goal is to cool the composition further, a higher NA might permit better cooling experimentally. An NA between the core/clad on the order of 0.22 could allow coupling multi-mode pump and filling the majority of the sample with pump light in a single pass, avoiding possible issues with impurities in deposited mirrors causing heating.
4. Conclusions
A 100 W multi-stage fiber amplifier was constructed and was used to pump a Yb doped silica rod in vacuum with 97 W of 1032 nm light resulting in the sample cooling to an absolute temperature of 229 K. The heat lift in this experiment is estimated to be 71 mW (1.42 W/m). The minimum achievable temperature is assessed to be approximately 145 K, and several actions that can be taken towards this goal have been discussed.
Funding
German Federal Ministry of Education and Research BMBF (13N15978); Air Force Research Laboratory Cooperative Agreement (FA9451-22-2-0016); Air Force Office of Scientific Research (FA9550-16-1-0362).
Acknowledgments
This work is dedicated to Mansoor Sheik-Bahae, who passed away in July 2023. The authors are extremely grateful and indebted to the guidance of Mansoor. Mansoor was a Fellow of Optica, SPIE, and a distinguished professor of physics at the University of New Mexico. He made significant contributions to nonlinear optics, laser science, and optical refrigeration. Mansoor began working on solid-state laser cooling at UNM more than two decades ago. The rapid progress our efforts have achieved with ytterbium doped silica in recent years stands on the shoulders of Mansoor’s pioneering work, his keen intellect, and his kind heart. More details about his life and work can be found in Ref. [71]. Portions of this work were presented at the Nonlinear Optics Topical Meeting in 2023, Optical refrigeration of ytterbium doped silica by 67 K starting at room temperature. BT gratefully acknowledges support in the form of a Postdoctoral Appointment under the supervision of Ganesh Balakrishnan.
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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