Anti-Stokes fluorescence (ASF) cooling is a fully optical form of cooling, in which the host is pumped at a photon energy that is lower than the average photon energy of the spontaneous emission [1]. The fluorescence extracts energy from the system in an amount proportional to the average energy difference between the pump and fluorescence photons. ASF cooling is a broadly accepted concept that was first proposed, to the best of our knowledge, in 1929 [2] and demonstrated for the first time, to the best of our knowledge, in 1995 using a bulk sample of Yb:ZBLAN [3]. One of its primary applications is radiation-balanced lasers, a device in which the waste heat generated by the lasing process is negated by cooling induced by ASF [4]. This technique would eliminate the need for conventional heat-removal solutions such as forced-air, water, or thermoelectric cooling, which induce vibrations and/or temperature gradients within the laser—deleterious affects that result in modal and frequency fluctuations in the laser output. For fiber lasers, it is difficult to achieve perfectly radiation-balanced operation at every point along the gain fiber. Nevertheless, using ASF cooling to achieve zero average temperature change along the length will significantly reduce the temperature deviation at each point and go a long way toward improving the output beam quality. Furthermore, the fiber can be strategically coiled to homogenize the temperature along its length [5].

In the past 25 years, there have been numerous demonstrations of ASF cooling in rare-earth-doped crystals and exotic hosts like fluorides [6]. Cryogenic temperatures have even been achieved in Yb-doped crystals placed in a vacuum to reduce the heat load due to air convection [6]. Bulk radiation-balanced lasers have also been reported in highly doped Yb:YAG [4,7]. However, until recently, cooling in silica remained elusive, precluding the application of ASF cooling from the most ubiquitous of all fiber materials.

The primary obstacle that prevented cooling in communication-grade silica was concentration quenching, a mechanism in which energy is transferred from an active rare-earth ion to an impurity, then relaxes to the ground state non-radiatively and generates heat [8]. The probability of quenching increases with ion concentration, thereby limiting the number of heat engines that can be doped into a given volume. The susceptibility of a particular host to quenching can be quantified by its critical quenching concentration, the concentration for which the mean distance between ions is such that the probability of quenching equals the probability of spontaneous emission. The critical concentration for ${{\rm Yb}^{3 +}}$ is typically one order of magnitude lower in silica than in crystals or fluoride hosts [9,10]. This is due to a combination of factors, including the comparatively low solubility of ${{\rm Yb}_2}{{\rm O}_3}$ in silica, which results in the formation of Yb clusters [11]. To achieve cooling in silica, it was critical to develop a glass composition and a fabrication protocol that addressed these issues.

This bottleneck was finally solved a year ago with reports of cooling in Yb-doped silica fiber [12] and fiber preform [13]. In both cases, the glass compositions were designed to support high concentrations of Yb with little quenching. For the silica fiber, this resulted in a critical quenching concentration 16 times larger than the highest value reported for Yb-doped silica, and comparable to values reported for Yb-doped ZBLAN, enabling the fiber to be doped with 2.06 wt. % Yb. This was achieved by co-doping the core with alumina to shift the immiscibility region to higher sesquioxide concentrations. This reduced the tendency for Yb clustering and, hence, quenching. The fiber was also co-doped with fluorine to dehydrate the glass and reduce ${{\rm OH}^{-}}$ impurities, which not only decreased the probability of quenching but also minimized heating due to direct absorption of the pump power. Care was also taken during the preform fabrication [11] to ensure that all Yb ions were in their trivalent state, since divalent Yb can have a deleterious impact on cooling performance [14]. This fiber composition and fabrication protocol enabled ${-}{50}\;{\rm mK}$ of cooling to be measured at atmospheric pressure [12]. The cooled fiber preform of [13] was also co-doped with alumina and fluorine to reduce quenching. Cooling by 0.7 K was reported in a sample doped with 0.57 wt. % Yb and placed in a vacuum to reduce the heat load [13].

Since this cooling barrier was surmounted, a few other experimental demonstrations of ASF cooling in silica have been reported. Cooling by 6 K was measured in the previously reported Yb-doped silica preform by pumping at a more optimal wavelength and removing the undoped cladding to further reduce the heat load [15]. Two more Yb-doped silica fibers have exhibited cooling, the best one cooling by ${-}{70}\;{\rm mK}$ [16]. Importantly, a radiation-balanced silica fiber amplifier with 17 dB of gain was very recently demonstrated [17]. Less than two years after the first demonstration, to the best of our knowledge, of cooling in a silica host, in this Letter, we demonstrate that although these temperature changes are small, they are sufficient for practical radiation-balanced fiber lasers (RBFL). Specifically, we report a Yb-doped silica fiber laser operated at atmospheric pressure with 105 mW of single-mode output power and no net heating.

The Yb-doped silica fiber was drawn from the same preform as the fiber presented in [12]. From the gain and cooling scale with the number of active ions [18], the fiber was highly doped with 2.06 wt. % Yb (${1.58} \times {{10}^{26}}\;{\rm Yb}/{{\rm m}^3}$). At this concentration, the level of quenching among ${{\rm Yb}^{3 +}}$ ions was found to have a negligible impact on cooling. This high concentration was enabled by co-doping the core with 0.88 wt. % ${\rm F}$ and 0.86 wt. % Al to increase the critical quenching concentration to 15.1 wt. % Yb. As discussed above, measures were taken to ensure that all Yb ions were in their trivalent state, as Yb-doped fibers with mixed valence states (i.e., ${{\rm Yb}^{2 +}}$ and ${{\rm Yb}^{3 +}}$) are known to exhibit a higher background loss and lower quantum efficiency [14]. The fiber was fabricated using conventional modified chemical vapor deposition, followed by fiber drawing at about 2000°C. Since the heat extracted by ASF is proportional to the doped area [18], the fiber core was designed to have a relatively large diameter (21 µm). Despite the large area, the numerical aperture was low enough (0.070) that the fiber was few-moded ($V = {4.5}$ at 1065 nm). The fiber also had a low background absorptive loss (11 dB/km, inferred from cooling measurements [12]), a short radiative lifetime (860 µs), and a low mean fluorescence wavelength (1006 nm), fiber characteristics that are all beneficial for ASF cooling [18]. The fiber parameters are summarized in Table 1.

Table 1. Yb-Doped Fiber Parameters

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The fiber was core-pumped at 1040 nm to create both cooling and gain at 1065 nm (Fig. 1). The output pigtail of the pump laser was spliced to a 10% fiber splitter. The 90% output was spliced to a fiber Bragg grating (FBG) with a ${\sim}{100}\%$ reflectivity at 1065 nm photo-inscribed in a Lucent HI-1060 fiber. The output of this fiber was then spliced to a Corning SMF-28 fiber, which was spliced to the input of a 2.64 m section of the Yb-doped silica fiber. This length was chosen to ensure that at least 85% of the launched pump power was absorbed. The SMF-28 fiber increased the optical transmission from the HI-1060 fiber (6-µm-diameter core) to the gain fiber (21 µm diameter), since its intermediate core size (9 µm diameter) allowed for a more gradual evolution of the propagating mode’s size. This arrangement also reduced the amount of pump and laser power that was coupled into the cladding of the Yb-doped fiber, thereby minimizing the heat generated by impurity absorption in the cladding and jacket. For the same reason, a second SMF-28 fiber was spliced between the output of the Yb-doped fiber and the output coupler (8% reflectively at 1065 nm), an FBG also inscribed in an HI-1060 fiber to ensure a single-mode output. The reflectivity of the output coupler was chosen to be low to (1) reduce the circulating laser power in the cavity, since heating due to impurity absorption is proportion to power, and to (2) increase the laser threshold power. A higher threshold results in a higher population inversion during lasing and, therefore, more heat extracted by ASF cooling, since it is proportional to the population inversion. At the laser output, a long-pass filter removed the residual pump power and passed the signal to a power meter. The 10% splitter output was used to monitor the spectrum of the pump laser and ensure that lasing did not occur at 1065 nm due the high-reflectivity FBG.

 

Fig. 1. Cooled Yb-doped silica fiber laser and the experimental setup used to measure temperature changes along the fiber.

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To characterize the laser fiber’s temperature change dependence on output power, the laser was pumped at four different powers. For each power, the induced temperature change was measured at eight locations along the Yb-doped fiber using a high-resolution slow-light FBG sensor described in [19]. At each location, an ${\sim}{10}\;{\rm cm}$ length of the Yb-doped fiber was stripped of its jacket to prevent reabsorption of the radially escaping ASF. The stripped section was placed in contact with the FBG sensor (see Fig. 1). A small amount of isopropanol was applied between the fibers to hold them together through capillary forces. When the Yb-doped fiber is pumped, its temperature changes, and the two fibers quickly (within seconds) reach thermal equilibrium [20].

Figure 2 shows an exemplary temperature measurement of the laser fiber, recorded 19 cm from the output end of the Yb-doped fiber. Before the measurement started, the pump was turned on to the lowest power of interest (1.22 W launched into the Yb-doped fiber), and the output of the laser was monitored with a power meter. The measurement started ($t = {0}\;{\rm s}$) once the output power stabilized (${\sim}{2}\;{\rm min}$ after the pump was turned on). At this time, the fiber temperature was $-104\,\,{\rm mK}$ below room temperature. The pump was left at 1.22 W for ${\sim}{25}\;{\rm s}$, then slowly turned up to the next power (1.36 W). This induced a slight heating of the fiber to a new steady-state value. This procedure was repeated for the remaining two pump powers (1.54 W and 1.73 W). After the fiber temperature reached a steady state for the highest power, the pump was abruptly turned off, and the fiber equalized to room temperature. The temperature change induced by each pump power was defined as the average difference between the last 5 s when the pump was turned off and the 5 s prior to changing the pump power. Each measurement was repeated three times and averaged.

 

Fig. 2. Temporal trace of the temperature change recorded 19 cm from the output end of the Yb-doped silica fiber, core-pumped at four powers of 1040 nm light, represented pictorially by the red curve.

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The fiber laser output power at 1065 nm was measured as a function of launched pump power (blue crosses in Fig. 3), which was measured upon completion of the experiments using a cut-back method. The laser output was in the fundamental (${{\rm TEM}_{00}}$) mode, since the higher-order modes were filtered out by the SMF-28 and HI-1060 fibers spliced to the output of the gain fiber. This filtering caused only slight fluctuations in the output power (${\sim} 5\%$) due to variations in the amount of power coupled to the higher-order modes along the Yb-doped fiber. As expected, the output power increased linearly once the threshold pump power was reached (${\sim} 1.07\,\,{\rm W}$).

 

Fig. 3. Laser output power measured as a function of the launched pump power, along with a linear fit. The color gradient is a pictorial representation of the average temperature change along the length of the gain fiber.

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The data was fit to a model of the RBFL described in [21]. All of the fiber parameter values needed for these simulations were either measured directly or inferred from fits to independent cooling and absorption measurements, as described in [10]. The FBG reflectivities were also measured. The only fitting parameters were the losses of the four splices to the SMF-28 fibers. The total round-trip loss [in decibels (dB)] of the two splices at the input of the Yb-doped fiber is defined as ${\alpha _{{\rm in}}}$; the corresponding quantity at the output end is ${\alpha _{{\rm out}}}$. The output loss is further broken down into a forward propagating loss ${\alpha _{\rm out,fw}}$ and a backward propagating loss ${\alpha _{\rm out,bw}}$, so that ${\alpha _{\rm out,fw}} + {\alpha _{\rm out,bw}} = \;{\alpha _{{\rm out}}}$. ${\alpha _{\rm out,fw}}$ directly affects the laser output power as well as the residual pump power and needs to be fitted independently from ${\alpha _{\rm out,bw}}$. Since the splices at both ends of the Yb-doped fiber are nominally identical, ${\alpha _{{\rm in}}}$ and ${\alpha _{{\rm out}}}$ were assumed to be equal. Completing the fit resulted in fitted values of ${\alpha _{{\rm in}}} = {\alpha _{{\rm out}}} = {4.8}\;{\rm dB}$ and ${\alpha _{\rm out,fw}} = {2.4}\;{\rm dB}$. These relatively high losses are in agreement with expectations. The calculated spatial overlap integral between the fundamental modes of the HI-1060 fiber and the SMF-28 fiber gives 0.27 dB of single-pass loss. Between the SMF-28 fiber and the Yb-doped fiber, this calculation gives 1.9 dB of loss. In total, the calculated round-trip loss for the two splices is 4.4 dB (compared to the fitted value of 4.8 dB). The extra 0.4 dB of loss can be reasonably attributed to (1) coupling to higher-order modes in the Yb-doped fiber, which results in an additional loss when these modes are filtered out at the splice to the SMF-28 fiber (but not in the other direction), and/or (2) core misalignment at the splices. From this fit, the threshold pump power was calculated to be 1.07 W. The slope efficiency was 41%, about half as much as typical commercial silica fiber lasers. The threshold and slope are in excellent agreement with the experimental data (see Fig. 3). In future iterations, the slope efficiency and the threshold can be significantly improved by eliminating the splice losses associated with ${\alpha _{\rm out,fw}}$.

 

Fig. 4. Average measured temperature change at eight locations along a 2.64 m silica fiber laser for four different output powers at 1065 nm.

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The temperature change along the 2.64 m fiber laser was measured for four different pump powers (Fig. 4). This resulted in the same general trend for all four powers. The fiber was the warmest at the input end and cooled monotonically along its length. For the lowest pump power (1.22 W), this resulted in a transition to negative temperature changes ${\sim}{1}\;{\rm m}$ from the input end. Increasing the pump power caused this transition to occur further along the fiber, ultimately never occurring for the highest pump power (1.73 W). Three mechanisms contribute to heating at the input end. First, the pump power in this region exceeds the power that produces maximum cooling, which is calculated to be ${\sim}{420}\;{\rm mW}$ for this fiber (see [17] for a physical explanation). Second, the higher pump power corresponds to greater signal amplification, which results in the generation of more Stokes phonons (more heating). Third, this is also where the intra-cavity signal power is the greatest and, therefore, where the depletion of the excited-state population is the highest (less cooling). Further along the fiber, as the pump power is attenuated, and the signal amplification saturates, these heating effects are lessened, and ASF cooling dominates. The dashed segments in Fig. 4 are interpolations of the eight temperature measurements taken for each output power. Integrating under each curve and dividing by the length of the fiber (2.64 m) gives an approximation for the average temperature change along the length of the fiber laser. For the 72 mW laser, this calculation yields an average temperature change of ${-}{24.4}\;{\rm mK}$, indicating that more output power needs to be extracted to achieve radiation-balanced operation. The latter was very nearly achieved with the 114 mW laser, whose average temperature was calculated to be only 2.5 mK above room temperature (which is within the error of the sensor).

As expected, the average temperature change continued to increase linearly with output power, resulting in 58.8 mK for 181 mW and 113.8 mK for 264 mW. The blue crosses in Fig. 5 show these averages plotted as a function of laser output power, along with a linear fit (solid blue curve). Figure 5 also shows the optical-to-optical efficiency of the laser, calculated from the data in Fig. 3 by dividing the laser output power by the launched pump power (red asterisks and curve). From the curves, the laser output power associated with zero average temperature change is calculated to be 105 mW, and the associated optical-to-optical efficiency is 8.0%.

 

Fig. 5. Average temperature change along the fiber laser and the optical-to-optical laser efficiency, both measured as a function of laser output power, along with their associated fits.

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For the first time, to the best of our knowledge, a RBFL is demonstrated. The gain medium was a highly doped Yb silica fiber materially tailored to significantly reduce sources of non-radiative relaxation, including concentration quenching and the parasitic effects of ${{\rm OH}^{-}}$ and ${{\rm Yb}^{2 +}}$ species. Pumped at 1040 nm to strike a near-optimum compromise between cooling and gain, the 1065 nm fiber laser had a threshold power of 1.07 W and a slope of efficiency of 41%, which was limited in part by avoidable splice losses. At an output power of 114 mW, the 2.64 m Yb-doped fiber laser had an average temperature within 3 mK of room temperature. This work launches a new class of fiber lasers with improved stability.