1. Introduction

In recent years we have seen dramatic advances in rare-earth-doped fiber laser technology. Kilowatt, and even multi-kilowatt continuous-wave output power is now achievable from fiber lasers in various regimes [1–5]. This remarkable progress is attributed to the unique combination of highly-efficient rare-earth-doped fibers and high-brightness pump diodes.

In particular, in contrast to “bulk” solid-state lasers (i.e., without a waveguide), the geometry of fiber lasers is good for thermal management because the heat generated in the laser cycle is distributed over a long length of fiber that also provides a large surface-to-volume ratio of the laser-active core. Some rare-earth-doped fiber lasers provide very high conversion efficiency, e.g., in excess of 80% from ytterbium-doped fibers (YDFs) when pumped at 975 nm [1], >70% from thulium-doped fibers pumped at 808 nm [4], etc. Therefore, fiber lasers are relatively free from costly thermal management, which makes them very attractive for a variety of scientific and industrial applications, benefiting from the low cost of ownership. However, even with the fiber geometry, thermal management becomes demanding as the heat dissipation per unit length grows, e.g., because of a higher output power, shorter length, or lower pump-to-signal conversion efficiency. In particular, some fiber lasers of relatively low efficiency, e.g., ytterbium-sensitized erbium-doped fiber (YSEDF) lasers [5,6] or ytterbium-sensitized thulium-doped fiber lasers [7], whose conversion efficiencies are normally no more than 30–40%, are thermally challenged already at relatively low pump powers, which hampers power-scaling [6, 7].

On the other hand, the temperature rise of the gain fiber due to the heat dissipation of the absorbed pump power sometimes becomes helpful: For single-frequency master-oscillator power amplifiers, the stimulated Brillouin scattering (SBS) is, in general, a big limiting factor as the signal power increases [8]. However, when the amplifier fiber is strongly pumped there is a spontaneous, gradual temperature variation in the longitudinal direction as a result of the gradual absorption, and thus decrease, of pump power along the fiber. This reduces the peak Brillouin gain because the temperature variation along the fiber significantly changes the speed of the acoustic wave along the fiber, which broadens the gain spectrum. This effect has been very useful in suppressing SBS [8]; however, it cannot be exploited beyond temperatures which degrade fiber performance or damage the material.

There are a number of recent reports on the thermal characteristics of fiber lasers in various regimes [9–12]; however, mostly theoretical. By contrast, the experimental information has been very limited in the literature [12]. In particular, experimental investigations of the longitudinal temperature variation induced by the absorbed pump power are incomplete. Such data are very important for the thermal management of fiber lasers, normally cooled by unforced convection and conduction. Accurate information about the thermal characteristics of fiber lasers or amplifiers is also needed for the analysis of the temperature-induced spectral broadening of nonlinear scattering, e.g., SBS [8].

In this paper, we use a simple technique based on an arrayed fiber Bragg grating (FBG) sensor to measure the longitudinal temperature distribution of high-power fiber lasers and investigate the thermal characteristics of an YSEDF up to the damage point, when cooled by natural convection. While the fluorescence spectra out of a gain fiber can be another indicative of the temperature [12,14,15], this technique requires cumbersome calibration to determine the accurate temperature since the spectra and its strength can vary with the composition and condition of the gain medium. Furthermore, it is only applicable for certain dopant ions [12,14,15], and typically requires a mechanical scan to obtain longitudinal data. A thermal imaging camera can also be considered [16]; however, the fiber laser is relatively thin, making it hard to get a sufficient resolution out of the thermal imaging camera. Furthermore, the emissivity of the fiber needs to be known, and reflections must be considered, too. Though not impossible, it is not straightforward to resolve such issues. Therefore, we propose to use a simple and cost-effective arrayed FBG sensor that can be used with many types of fiber lasers, including embedded ones.

2. Experimental result and discussion

The experimental arrangement is shown in Fig. 1. We built a fiber laser based on an YSEDF [5,6]. We chose ytterbium-sensitized erbium for the gain medium because its quantum defect is relatively high when it is pumped at ~975 nm [5,6], and because the absorption per unit length is normally higher than, e.g., YDFs. Therefore, the heat dissipation per unit length can be significantly higher than in other high-power fibers, including YDFs [1]. The diameters of the core, silica inner cladding, and low-index-polymer outer cladding are 30 µm, 400 µm, and 640 µm, respectively. The small signal absorption rate was 4 dB/m at the 976-nm peak. The fiber was 2.4 m long.

 

Fig. 1. Experimental arrangement for an end-pumped YSEDF laser. HR-1.1: high reflectivity at ~1.1 µm; HR-1.5: high reflectivity at ~1.5 µm.

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Fig. 2. Fiber laser output power vs. launched pump power. Slope efficiency 36% with respect to launched pump power and 41% with respect to absorbed pump power. Lasing wavelength: 1565 nm.

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The fiber was pumped by a 975-nm diode source, launched through one end of the fiber. Both ends of the fiber were cleaved perpendicularly to the fiber axis. In the fiber end away from the pump source, high feedback was provided by a dichroic mirror with high transmission at the pump wavelength and high reflection at the signal wavelength around 1.5 µm. The laser output coupler was formed by the 4% reflecting flat perpendicular cleave at the other end of the fiber. The signal was separated from the pump beam by another dichroic mirror having the same characteristics as the feedback mirror. An additional dichroic mirror with high reflection at ~1.1 µm and high transmission at the pump wavelength was inserted between the pump and the output couple mirror, in order to protect the pump source from any possible parasitic lasing at ~1.1 µm. This often occurs when the energy transfer from ytterbium ions and to erbium ions is bottle-necked [5]. The fiber was held in free space with minimal contact with two holders at the ends and one in the middle in order to restrict the cooling mechanism to unforced convection. No additional cooling mechanisms were fitted. The output power characteristics are shown in Fig. 2. The measured slope efficiency was 36% with respect to launched pump power and 41% with respect to absorbed pump power. Up to the maximum pump power, there was no parasitic emission at ~1.1 µm, the power level of which was negligible as had been seen in Ref. [6].

To build a temperature sensor array, we fabricated FBGs using a 248 nm excimer laser. We used different phase masks to differentiate the center wavelengths of the FBGs which are at 1546.48 nm, 1549.13 nm, 1552.47 nm, 1556.42 nm, 1558.92 nm, respectively, at room temperature (20 °C). The length of an individual FBG was 25 mm, and the peak reflectivity was over 20 dB. Although we only used five FBGs, the method is readily extended to more FBGs that would enable higher longitudinal resolution. We measured that the temperature sensitivity of our sensor FBGs was 12 pm/K. All the FBGs were fusion-spliced in series to a standard single-mode fiber which enabled multi-point measurement in a single wavelengthsweep of the source or the receiver. The Bragg wavelength changes with its temperature, and thus, each FBG functions as a temperature point-sensor [13]. The outer polymer coating of the FBG section was removed and a thin film tape of 5 µm thickness was utilized to firmly attach the sensor fiber to the YSEDF (see Fig. 1). Because the FBG fiber is sufficiently thin in comparison with the YSEDF dimension and the conductivity of silica is one order of magnitude higher than that of the polymer coating of the YSEDF [9], we assume that the temperature drop in the sensor fiber is insignificant. One end of the FBG sensor array fiber was fed by a broadband light source at ~1550 nm, and the transmitted light was monitored by an optical spectrum analyzer, the resolution of which was set to 10 pm.

 

Fig. 3. Experimental data with the pump power up to 60.8 W: (a) Measured sensor spectra. (b) Longitudinal temperature distribution. The distance is measured from the pump-launch end of the fiber.

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The measured sensor spectra at pump power levels from 0 W to 60.8 W are shown in Fig. 3(a). The Bragg wavelengths of the FBGs at the different positions of the fiber laser change with the pump power but by different amounts. The individual wavelength shift indicates the temperature change of the sensing point of the YSEDF. Based on 12 pm/K we convert the quantity of the wavelength shift into the temperature change and plot the resultant longitudinal (a) (b) temperature distributions in Fig. 3(b). We can see that the point z1, closest to the pump launch end, reached the highest temperature and the temperature gradually decreased away from it. The temperature distribution followed the trend of an exponential decrease: This is due to the fact that the heat dissipation at a point in the YSEDF is roughly proportional to the locally absorbed power. The pump absorption of an YSEDF is expected to be largely independent of the pump level [17], and therefore, the propagating pump power, as well as the locally absorbed pump power, the dissipated heat, and the temperature increase, are all expected to decrease exponentially away from the pump launch end, when the fiber is end-pumped from a single end [10]. The maximum pump power was limited to 60.8 W by the failure of the low-index polymer coating of the YSEDF at the higher pump power attempt. In general, the thermal damage of the outer polymer is most critical for fiber lasers since the silica inner cladding and core have considerably higher thermal damage limits [9]. We verified that the damage temperature of the polymer coating that we used is ~200 °C, as seen in Fig. 3.

We estimate that the highest heat dissipation of the YSEDF by the quantum-defect heating [9] was 21 W/m before observing the coating failure. Therefore, the maximum thermal load that the low-index polymer coating, with its specific geometry, can sustain under natural convection (without being assisted by any additional cooling mechanisms) is around this level. It is noteworthy that such heat dissipation is typically expected when an YDF laser is pumped to produce >1 kW output power if the pump absorption rate is ~1 dB/m, because of its much smaller quantum defect [1]. While the natural convection cooling is enough for such a kilowatt YDF laser, it is only marginal, and thus, additional cooling, e.g., forced air or conductive cooling should be used for more stable operation and for further power scaling.

We next use a numerical model introduced in Ref. [10] to calculate the longitudinal temperature profile of our fiber laser, for different pump-power levels. See Fig. 4. The numerical data correspond to the experimental condition and fiber parameters. We only take into account the heating induced by the quantum defect [9].

 

Fig. 4. Numerical result: (a) The solid curves and dashed curves denote the temperature of the outer surface of the polymer cladding and the temperature of the center of the core, respectively. (b) The temperature profile in the radial direction at z=0 (the pump launch end) for a pump power of 60.8 W.

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The solid curves denote the temperature of the outer surface of the polymer cladding for the sake of comparison with Fig. 3(b), and the dashed curves denote the temperature of the center of the fiber core. The core temperature reaches approximately 236 °C at z=0 at the maximum pump power of 60.8 W. The temperature difference between the fiber ends is then 190 K. This type of temperature gradients is very useful for broadening the Brillouin gain [8]. The calculated temperatures are slightly higher than those measured through the experiment, but they are generally in good agreement. This difference can be explained, at least in part, by the temperature drop by the conduction of the sensor fiber. Figure 4(b) shows the temperature profile in the radial direction at the pump launch end (z=0) for a pump power of 60.8 W, as calculated without the sensor fiber attached. While the core temperature reaches ~236 °C, the temperature variation across the whole fiber section is below 20 K, more than a half of which is over the polymer-coating section. Note that the polymer has a thermal conductivity that is an order of magnitude lower than that of the silica [9]. Consequently, concerns for stress fracture or thermal lensing in the silica glass section are much smaller than the concern for the coating damage [9]. Good heat-sinking arrangements, e.g., forced-air cooling or water-assisted cooling, are primarily required for the protection of the low-index polymer.

Returning to the effect of the sensor fiber, this modifies the temperature distribution somewhat. We calculated this effect using the finite-element-method (FEM). We utilized a commercial software package, COMSOL Multiphysics^® to obtain the precise two-dimensional temperature distribution across the fiber assembly, in particular, at z=z₁ (0.2 m). We neglected axial heat-flow and determined the heat transfer coefficient to be 50 W·m^-2K^-1 based on the unforced convection [10] and the corresponding hydraulic diameter which takes into account the shape of the fiber assembly. Although the heat transfer coefficient at the surface can vary with many other factors, such as the surface condition (e.g., roughness) and the ambient air condition (e.g., humidity and pressure), we did not take them into account for the sake of simplicity. This leads to some uncertainties in the theoretical determination of the overall heat transfer coefficient and thus the temperature distribution. On the other hand, the effect on the experimental determination of the temperature distribution is small.

Figure 5 shows the numerically calculated transverse temperature distribution in the presence of the sensor fiber, when 60.8 W of pump power is launched into the YSEDF. The sensor fiber induces a temperature drop of ~8 K or ~9 K, in comparison with the temperature on the opposite side of the YSEDF or that obtained by ignoring the sensor fiber See Fig. 4(a). The FEM result matches better the experimental data: The difference is below 1 K. Thus, our further numerical simulation verifies that the sensor fiber can measure the surface temperature of the YSEDF without significantly disturbing it. In view of this, it is viable to measure the temperature distribution of a fiber laser in the way that we have demonstrated.

 

Fig. 5. Numerical result based on an FEM analysis at z=z₁ (0.2 m), with pump power of 60.8 W: (a) The 2-D temperature profile including the YSEDF and sensor fiber assembly. (b) The temperature profile cross-section at y=0.

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3. Conclusion

We have experimentally analyzed the thermal characteristics of a fiber laser based on an YSEDF, utilizing an arrayed FBG sensor technique. We measured the longitudinal temperature distributions along the fiber axis at various pump power levels and verified them by rigorous numerical simulations. The agreement was excellent while there remained some uncertainties in determining the overall heat transfer coefficient. Under natural convection, the maximum heat dissipation allowed in a polymer-clad fiber laser, with the given cross-sectional parameters, was found to be approximately 20 W/m. This level would also be typical for a kilowatt fiber laser based on ytterbium. The demonstrated sensing technique is very simple and cost-effective for monitoring the fiber laser temperature. We further propose that the sensor assembly could be fabricated during the drawing process, putting an individual sensor fiber inside or underneath the polymer cladding of the gain fiber. This will lead to a monolithic fiber laser system that has a separate, temperature sensor port for the gain fiber.