Thanks to their exceptional properties, rare-earth-doped fiber lasers have established clear dominance in many technologies. Although their metrics are continuously being improved, a persistent hurdle is the heat induced by the laser’s quantum defect. In high-power fiber lasers, the resulting temperature rise can induce power fluctuations, transverse-mode instability [1], frequency instabilities, and catastrophic failure. Even at lower powers, in single-frequency fiber lasers for example, a small temperature rise will broaden the linewidth and increase frequency noise [2].

Although conventional fluid-based cooling systems are effective, they are cumbersome, bulky in high-power systems, and they introduce vibrations that can cause power and frequency instabilities. A promising alternative is anti-Stokes fluorescence (ASF) cooling [3,4]. The laser ions are pumped at a wavelength longer than the mean fluorescence wavelength. The fluorescence photons then have a greater mean energy than the pump photons (energy that they acquired from the host’s phonon bath), and when they escape the fiber, the fiber cools. This thermal management is fundamentally more effective because it eliminates the root of the problem: heat generation. Demonstrated in the past with several rare-earth ions in many exotic materials [5], it has been successfully applied to silica only recently, with the cooling of Yb-doped silica preforms in a vacuum [6,7], silica fibers [8,9], and a rod-like fiber [10] at atmospheric pressure, and the first internally cooled silica fiber amplifier [11] and laser [12]. Given the overwhelming prominence of silica fiber lasers and amplifiers, improving the efficacy of this technique in silica fibers is critically important.

Two main limitations faced by ASF cooling are concentration quenching and, to a lesser extent, residual absorption by impurities. Concentration quenching is a mechanism by which the energy of an excited electron in a rare-earth ion is transferred to another excited rare-earth ion or an impurity, which relaxes non-radiatively and releases heat [13]. The probability of energy transfer increases rapidly with increasing rare-earth concentration. As a result, this concentration must not exceed a certain limit, which puts a cap on the heat that can be extracted per unit volume. This maximum concentration depends on the host composition. Optimizing the core-glass composition to minimize quenching is therefore a critical and timely endeavor, albeit a complex task. Adding a co-dopant to the glass influences quenching, but also the numerical aperture (usually raising it and compromising single-mode operation), the cross sections (which may lower the gain), as well as thermal and nonlinear properties. So far, the silica-based glasses that have cooled are aluminosilicate [8,9], aluminofluorosilicate [6], and aluminophosphosilicate [6,7]. The presence of Al or P increases the solubility of Yb₂O₃ in silica, which reduces quenching.

An avenue well worth investigating is nanoparticle-doped fibers, in which the laser ions are encapsulated in dielectric nanoparticles of a well-chosen composition. The glass as a whole retains the excellent optical and mechanical properties of silica, but the physico-chemical environment of the laser ions is now partly controlled by the nanoparticles. The latter therefore alter the laser-ion spectroscopic properties in a manner that depends on their composition. For example, it is possible to broaden the ion’s emission spectrum [14] or increase its radiative lifetime[15].

This Letter reports ASF cooling at atmospheric pressure of a highly Yb-doped aluminosilicate fiber and three nanoparticle-doped fibers that will be denoted by the original nanoparticles: CaF₂, SrF₂, and BaF₂. The first three fibers successfully cooled below room temperature. All three have almost the same cooling efficiency as the reported silica-based fiber that cooled the best so far [9].

The Yb-doped aluminosilicate fiber was fabricated using conventional solution doping in accordance with published cooling silica fibers [8,9]. The nanoparticles were synthesized using a polyol process. CaF₂, SrF₂, and BaF₂, each doped with 20 mol.% YbF₃, were formed by first dissolving ammonium fluoride in diethylene glycol (DEG) at 90°C. Alkaline-earth (Ca, Sr, or Ba) acetate hydrate and ytterbium nitrate hydrate were dissolved into a separate DEG water solution. All precursors were reagent grade or better. The alkaline-earth/Yb solution was added to the fluorinating solution, reacted at 90°C under a nitrogen atmosphere for 2 h, and cooled to room temperature. The resultant suspension was mixed with equal parts DEG, and aluminum chloride hexahydrate was added to yield a 0.05-M Al₂O₃ concentration in the final doping suspension. X-ray diffraction confirmed the phase of the as-formed nanoparticles. These suspensions were incorporated into the porous SiO₂ soot by a conventional solution doping process on an SG Controls MCVD lathe. Cl was used during the drying stages to ensure low OH levels in the doped fibers, comparable to that of conventionally prepared fibers that cooled [8,9]. The preforms, ∼15.5 mm in diameter, were drawn to ∼125-µm fiber using a custom Heathway draw tower at ∼1925°C. All fibers were coated with UV-curable high-index polymer (DSM 3471-3-14). Fiber compositions were determined by energy-dispersive x-ray spectroscopy, and refractive-index and Yb-emission profiles with an IFA-100 refractive index profiler.

The fibers were either single moded (BaF₂) or few moded (all others), with V numbers between ∼2.25 and ∼3.5 at 1.04 µm (see Table 1). The measured Yb³⁺ lifetimes were close to 800 µs. The parameter values of the best fiber reported in Ref. [9] are listed for comparison. The OH concentration in each fiber core was inferred from cutback measurements of the loss at 1380 nm using Ref. [16]. They are very low (0.30 to 0.73 ppm), and much lower than the values of 1.5–3 ppm reported for the silica preforms that cooled in Refs. [6,7].

Table 1. Physical and Spectroscopic Parameters of the Yb-Doped Silica Fibers

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ASF cooling was tested using the same setup as in Refs. [8,9,17]. A 60-cm fiber sample in air was pumped with a continuous-wave (cw) 1040-nm laser or a cw 1030-nm Yb-doped fiber laser. The fiber was spliced to the laser’s fiber pigtail. The splice loss was small (∼0.3 dB) to minimize the power coupled into the cladding, which induces undesirable heating when it is stripped and absorbed by the fiber coating. A 20-cm length of jacket was stripped at the center of the fiber. The fiber temperature was measured in the middle of the stripped section with a slow-light fiber-Bragg-grating sensor placed in contact with it. The sensor’s principle and performance are described in Refs. [17,18].

The temperature changes observed in all fibers were expectedly small (tens of mK or less) because of the fibers’ small doped areas. To obtain accurate temperature measurements, for each fiber and pump power, three to ten measurements were taken. In each one, the temperature of the unpumped fiber was measured when the fiber was in thermal equilibrium with the air. Then the pump was turned on and the fiber temperature recorded for 20 to 30 s. Finally, the pump was turned off and the temperature recorded for 10 to 20 s, long enough for the fiber to reach thermal equilibrium again [19]. Each measurement therefore provided two readings of the temperature in the unpumped fiber: one before the cooling event and one after. These two readings should be the same, since the room temperature does not change by more than a few mK during this one-minute measurement. Due to drift in the sensor [18], however, the “before” and “after” temperature readings occasionally differed. Such sets of data were deemed questionable and discarded. Only temperature traces with a difference between the initial and final readings of 6 mK or less were retained.

Figure 1 plots the temperature change measured in the aluminosilicate fiber as a function of the pump power absorbed per unit length. At either pump wavelength, as the power was increased, the temperature first decreased below room temperature as more Yb ions were excited and more ASF power was emitted. As the power was further increased, the temperature reached a minimum, then increased. This reversal is the result of (1) saturation of the Yb population inversion (slower increase in cooling) and (2) increased pump absorption by impurities (increased heating) [20]. As observed in other Yb-doped silica fibers [8,9], cooling was stronger with 1040-nm than 1030-nm photons. The lowest temperature drop was 21.5 mK below ambient. This was achieved for an absorbed pump power at the measurement site of 54 mW/m.

 

Fig. 1. Measured temperature change of the aluminosilicate fiber pumped at 1030 nm or 1040 nm as a function of the absorbed pump power per unit length, and fits of the model of Ref. [20] to the data points.

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An important metric in optical refrigeration is energy efficiency. For an unjacketed silica fiber in still air, and for a small amount of heating, the steady-state temperature change in °C induced by a power P_abs (in W) absorbed over a length L (in m) is given by ΔT = 31.3ηP_abs/L, where η is the fraction of P_abs converted into heat (e.g., via multiphonon relaxation) [19]. The injected heat is then ΔQ = ηP_abs. By symmetry, this expression also applies when heat is extracted by ASF and the fiber cools. The heat that must be extracted per unit length to lower the fiber temperature by ΔT is then ΔQ/L = ΔT/31.3. Accordingly, for the silicate fiber to cool by −20.5 mK, the extracted heat was ΔQ/L = 0.65 mW/m. The measured value was 54 mW/m. The cooling efficiency is then the ratio of extracted pump power absorbed per unit length that produced this cooling to the absorbed power, or 1.21% (first row in Table 2). For comparison, the reported Yb-doped silica fiber that has cooled the most so far in air reached 70 mK below ambient temperature for 170 mW/m of absorbed pump power per unit length [9], or an efficiency of 1.32% (last row in Table 2). The solid curves in Fig. 1 are fits to the experimental data generated with the advanced model of Ref. [20]. For reference, this model derives a simple expression for the temperature change of a fiber cooled by ASF and placed in still air. The model accounts for the lifetime, cross-section spectra, and concentration of the Yb ions, the pump wavelength, and the doped area. Importantly, it also accounts for the two main extraneous heat sources that work against cooling, namely the absorption of pump power and amplified spontaneous emission by impurities such as OH (absorption coefficient α_ba) and concentration quenching (critical quenching concentration N_c). The two solid curves in Fig. 1 are in good agreement with the measured data. They were adjusted for best fitting using only α_ba and N_c (all other parameter values were measured). The fitted values of α_ba and N_c are listed in Table 2. As expected, the inferred values of N_c are the same for 1030-nm and 1040-nm pumping, as are the values of α_ba (the absorptive loss is expected to be essentially the same at both wavelengths). Compared to the best silica fiber of Ref. [9], this new aluminosilicate fiber exhibits a higher absorptive loss (15 dB/km versus less than 5 dB/km) and a slightly lower, but still remarkably high, critical quenching concentration.

Table 2. Cooling Performance of the Yb-Doped Silica Fibers and Inferred Parameter Values

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The temperature changes measured versus the 1040-nm pump power for the nanoparticle-doped fibers are plotted in Fig. 2. The CaF₂-doped fiber cooled the most (−26.2 mK), although it required nearly twice as much power as the conventional fiber (90 mW/m versus 54 mW/m), so its cooling efficiency was slightly lower (0.9%). The SrF₂-doped fiber exhibited the smallest temperature change (−16.7 mK). Its efficiency was a little lower (0.8%). The BaF₂-doped fiber is the only one that did not cool: it heated slightly. These cooling metrics are summarized in Table 2. The solid curves in Fig. 2 are best fits to the experimental data. Again, there is reasonable agreement. The values of N_c and α_ba inferred from the fits are listed in Table 2. The CaF₂-doped and SrF₂-doped fibers have a low α_ba (4–15 dB/km) and a high N_c value, comparable to that of the aluminosilicate fibers. The BaF₂-doped fiber did not cool because of its lower N_c (due partly to a low Al content and the as-formed nanoparticles not being pure-phase BaF₂), its low Yb concentration, and its higher loss. The as-formed CaF₂ and SrF₂ were phase pure.

 

Fig. 2. Measured temperature changes of the three nanoparticle-doped fibers pumped at 1040 nm as functions of the absorbed pump power per unit length, and dependences fitted to these data points using the model of Ref. [20].

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Figure 3 compares the cooling efficiencies of the four fibers and those of the three silica fibers reported in [9]. The maximum measured temperature change is plotted against absorbed pump power per unit length. The new aluminosilicate fiber (red-filled square) and the best-cooling silica fiber [9] (green-filled square) fall on the same dashed line: they have the same cooling efficiency. The best fiber cooled ∼3.5 times more (−70 mK versus −20.5 mK), almost entirely because its doped-core area is 4 times larger than that of the new fiber (21-µm versus 10.5-µm diameter) and because the maximum extracted heat is proportional to the doped area [20]. The conclusion is that the new silicate fiber reported here performs almost as well as the best reported Yb-doped silica fiber. The CaF₂- and SrF₂-doped fibers (stars in Fig. 3) were a little less efficient, as commented in relation to Fig. 2. On the other hand, their cooling efficiency was significantly higher than the other two aluminosilicate fibers reported in Ref. [9] (blue-filled and green-filled squares).

 

Fig. 3. Measured maximum temperature drop versus absorbed pump power per unit length at 1040 nm for the three new fibers that cooled as reported in this Letter, and the three fibers reported in Ref. [9].

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For a given critical quenching concentration N_c, there is an optimum Yb concentration N_0,opt that maximizes the extracted heat [20]. For all three fibers that cooled, the calculated ratio N_0,opt/N_c is 0.090–0.093. Since these fibers had a ratio N₀/N_c of 0.1–0.12, they were a little too heavily doped – by 8–12% (nanoparticle-doped fibers) and ∼18% (aluminosilicate fiber) – for maximum cooling. Simulations predict that with optimum doping, the maximum temperature drop will increase by ∼23% for the aluminosilicate fiber, ∼8% for the CaF₂-doped fiber, and ∼13% for the SrF₂-doped fiber.

In conclusion, the first observation of laser cooling in nanoparticle-doped fibers has been reported, as well as laser cooling in a new, heavily doped aluminosilicate fiber. For the three fibers that cooled, the cooling efficiency approached the best reported to date. This result validates, for the first time, the significant potential of nanoparticle-doped silica in the ongoing exploration of silica fibers for optical refrigeration. While the nanoparticle-doped fibers did not outperform conventional silica fibers in this study, it demonstrates unambiguously that with targeted control of the Yb-ion chemical environment and careful reduction of OH contamination, it is possible to produce nanoparticle-doped fibers that cool remarkably well. This finding opens the door to new fiber compositions with superior cooling efficiencies.