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Curr. Opt. Photon. 2022; 6(6): 521-549

Published online December 25, 2022 https://doi.org/10.3807/COPP.2022.6.6.521

## Optically Managing Thermal Energy in High-power Yb-doped Fiber Lasers and Amplifiers: A Brief Review

Nanjie Yu1, John Ballato2, Michel J. F. Digonnet3, Peter D. Dragic1

1Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
2Department of Materials Science and Engineering, Clemson University, Clemson, South Carolina 29634, USA
3Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA

Corresponding author: *p-dragic@illinois.edu, ORCID 0000-0002-4413-9130
Current affiliation: Cepton Inc., San Jose, California 95131, USA

Received: May 22, 2022; Revised: September 13, 2022; Accepted: September 19, 2022

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Fiber lasers have made remarkable progress over the past three decades, and they now serve farreaching applications and have even become indispensable in many technology sectors. As there is an insatiable appetite for improved performance, whether relating to enhanced spatio-temporal stability, spectral and noise characteristics, or ever-higher power and brightness, thermal management in these systems becomes increasingly critical. Active convective cooling, such as through flowing water, while highly effective, has its own set of drawbacks and limitations. To overcome them, other synergistic approaches are being adopted that mitigate the sources of heating at their roots, including the quantum defect, concentration quenching, and impurity absorption. Here, these optical methods for thermal management are briefly reviewed and discussed. Their main philosophy is to carefully select both the lasing and pumping wavelengths to moderate, and sometimes reverse, the amount of heat that is generated inside the laser gain medium. First, the sources of heating in fiber lasers are discussed and placed in the context of modern fiber fabrication methods. Next, common methods to measure the temperature of active fibers during laser operation are outlined. Approaches to reduce the quantum defect, including tandem-pumped and short-wavelength lasers, are then reviewed. Finally, newer approaches that annihilate phonons and actually cool the fiber laser below ambient, including radiation-balanced and excitation-balanced fiber lasers, are examined. These solutions, and others yet undetermined, especially the latter, may prove to be a driving force behind a next generation of ultra-high-power and/or ultra-stable laser systems.

Keywords: Anti-stokes fluorescence cooling, Fiber lasers, Tandem-pumped lasers, Thermal management, Radiation-balanced lasers

OCIS codes: (000.6850) Thermodynamics; (060.2320) Fiber optics amplifiers and oscillators; (060.3510) Lasers, fiber; (140.3615) Lasers, ytterbium; (140.6810) Thermal effects

Despite the commercial availability of fiber laser systems exceeding 100 kW [1], the demand for higher brightness and power fiber laser sources continues to grow. A wide range of very good reviews have been written in the preceding decades, serving as an archive of the remarkable progress these lasers have made [29]. The evolution from just a few watts about 30 years ago [1012] required multiple parallel developments, including active fibers [1317], optical fiber components [1820], and pump lasers [2124]. Regarding fibers, a key issue that was and continues to be an obstacle is photodarkening [2528], which, over time, may result in excess absorption at the pump and signal [29] wavelengths, and consequently degradation of the output power. Another persistent issue is heating due to the quantum defect (QD), which manifests itself in many ways. First, it is responsible for transverse-mode instability (TMI): above a certain threshold power, the fundamental-mode output of a fiber becomes distorted and fluctuates, an issue that has been explained by the formation of a thermally-induced long-period index grating [3032]. Fiber heating can also lead to catastrophic damage via coating failure [33] or thermal lensing [34], the latter being driven by the thermo-optic effect. Additionally, fiber heating generally leads to a reduction in both the emission and absorption cross-sections of the active ions. This may adversely affect the gain, particularly if the change in temperature approaches 200 K [3537].

At the forefront of these heat-related issues is the quantum defect. In the quantum limit, the maximum slope efficiency a fiber laser can achieve is equal to the ratio of pump wavelength λp to signal wavelength λs, ηQ = λp / λs. The QD represents the fraction of power QD = 1 − ηQ that is lost in generating a signal photon of energy hc / λs from a pump photon of energy hc / λp. It is, therefore, intuitive to bring the pump and signal wavelengths closer to each other to decrease this source of thermal energy.

Another fundamental source of internal heat related to the laser ion’s spectroscopy is non-radiative relaxation associated with concentration quenching [3841]. When the concentration of the rare-earth ion exceeds a certain (host-dependent) limit, excited ions interact with each other, through up-conversion processes for example, leading to non-radiative relaxation of excited electrons, and therefore heating. Because the rate of concentration quenching increases rapidly with laser-ion concentration, this mechanism also limits the maximum concentration that can be doped into the fiber, in all materials, imposing the use of longer fibers, in turn exacerbating nonlinear effects. On the other hand, distributing a given total thermal energy over a longer fiber has the obvious advantage of lowering the maximum change in fiber temperature.

Similarly, as mentioned above, photodarkening can lead to increased background absorption by color centers, leading to excess heating. Again, optimization [25, 27, 28], especially with respect to the fiber material [42], has given rise to fibers with high immunity to photodarkening. Moreover, non-radiative (multi-phonon) relaxation within the laser ions [43, 44] is another path to heating. Non-radiative relaxation can be mitigated by a combination of selection of the proper laser ion, glass host, and pump wavelength. In the work reviewed here, the focus is on Yb3+, an ion that exhibits negligible non-radiative relaxation in most hosts, so that this is not an issue. Finally, non-radiating impurity absorption is another undesirable source of heat in an active fiber [45]. As discussed in the next section, modern fiber processing methods have largely eliminated these impurities as a primary concern, although they can still have a noticeable impact in radiation-balanced lasers (RBL) and amplifiers.

Owing to the large surface area-to-volume ratio of a fiber, it is not usually necessary to manage the fiber temperature when operated up to several tens of watts. At higher powers, however, active cooling methods, such as forced air and liquids, are required [46]. At the multi-kW level, it is common practice to insert the active fiber in a groove that is etched or scribed into a metal substrate across which a liquid is flowed [4749]. Such cooling systems perform very well, but they are bulky, frustrating the portability in high-power applications, and they are subject to leaks. In this context, optical cooling is classified as those methods where temperature is moderated without thermomechanical intervention (i.e., forced flow of a fluid) and includes techniques where optical quantities (such as the pump wavelength) are selected by the user to mitigate heating. While not discussed here, there also are fiber design-based approaches to improved thermal management. For example, a glass-coated or metal-coated fiber has a much higher damage threshold than a polymer-coated fiber [50]. One can then let the fiber laser operate at a higher temperature. Appropriately shaping the cladding can also give rise to a larger outer surface diameter and more efficient convective cooling [51].

The goal of this review is to highlight the main optical cooling approaches that can lower the operating temperatures of an active fiber. Since the highest power systems currently available utilize Yb-doped fibers, and Yb3+ has been so far the rare-earth ion that has produced the most efficient cooling (as relates to anti-Stokes fluorescence, ASF), this paper is limited to Yb3+, although many discussions and principles can be extended to other rare earths. The paper begins with a brief overview of optical fiber fabrication. That is followed by an exemplary set of thermal calculations for two fiber lasers: 1) a low-power laser and 2) a laser operating in the multi-kW regime. Following that, conventional low-QD fibers systems, including tandem-pumped and short-wavelength lasers, are briefly reviewed. The paper then transitions to alternative, multi-wavelength approaches to thermal management in fiber lasers, namely methods that utilize ASF, including RBLs [52]. The paper concludes with a short discussion of a new type of laser that utilizes anti-Stokes pumping (ASP).

A materials approach to mitigating parasitic effects in high-power lasers and amplifiers, ranging from thermal management to optical nonlinearities, is arguably the better of the two approaches (namely mechanical versus optical) because such detrimental effects inevitably originate from light-matter interactions. Hence, management and mitigation based on materials is a more fundamental and potentially effective method [53]. However, while the periodic table offers bountiful compositional permutations, fabrication methods for high-power laser and amplifier fibers do not because of the strict low-loss requirement imposed on gain fibers to maximize fiber-laser efficiency. This requirement necessitates the use of chemical vapor deposition (CVD) methods, which, courtesy of 50 years of telecom fiber development, produce fibers of exceptional quality in terms of homogeneity, purity, and loss. However, CVD processes are fundamentally limited in the range of compositions that can be achieved due to both the availability of precursors and glass forming ranges given the time / temperature profiles involved. See, for example, Tables I and V in [42] for compositional comparisons from selected fiber fabrication methods.

Choosing and optimizing core compositions is a complex multi-variable task, especially for high-efficiency high-power fiber lasers. Each co-dopant added to the core has multiple effects, not always beneficial. The composition influences not only the optical profile of the fiber (e.g., numerical aperture), hence the mode characteristics, but also the spectroscopic, thermal, and nonlinear properties of the fiber, which are not independent of one another. For example, the spectroscopy of Yb3+ in a given composition influences the efficiency and QD of the ion, both contributing to heat generation, which then impact thermal behaviors such as thermo-optic-induced mode instabilities and thermal expansion-induced core/cladding stress and changes to the linear and nonlinear properties through the strain-optic coefficient. Accordingly, glass is not just glass, and careful selection and concentration of a co-dopant are as important as the fiber design itself. Based on these limitations and considerations, the most studied and commercially available fiber lasers are based on Yb-doped aluminosilicate and aluminophosphosilicate core compositions. In this context, the aluminum, as aluminum oxide (Al2O3), increases the refractive index relative to silica, lowers the stimulated Brillouin scattering (SBS) gain coefficient, and promotes greater solubility of the active ion (Yb3+) in the silica glass, thereby lessening concentration quenching. This latter point is especially important for optical thermal management since concentration quenching generates heat. The phosphorus, as phosphorus pentoxide (P2O5), also increases the refractive index, reduces glass viscosity (as does Al2O3 to some extent) during fabrication, and enhances the glass resistance to photodarkening [54]. Of course, there is also the additional complexity introduced through the AlPO4 join [55]. Though beyond the scope of this paper, the materials development of advanced optical fibers is a very powerful approach that offers considerable opportunities for effective and novel approaches to all-optical thermal management [56].

As is well known, the Yb3+ ion, possessing one unpaired spin in the 4f manifold [57], is a simple two-level system. Due to the lanthanum contraction [5860], the 4f shells in the rare earths are effectively shielded from their environments by the 5s and 5p shells [61,62]. This results in an energy-level diagram that appears to be much like a free-ion and therefore relatively insensitive to the host. However, the triple and quadruple degeneracies of the upper and (2F5/2) lower states (2F7/2), respectively, are still broken by the Stark splitting effect [63], giving rise to upper and lower manifolds with energetic widths that are comparable to the phonon energies found in typical laser glasses [38] (see Fig. 1). It implies that at room temperature, most sub-levels in each manifold are populated. Furthermore, the amorphous nature of the glass host broadens and can ambiguate identifying the Stark levels in these hosts [64] relative to those in crystals [65]. As discussed below, despite this shielding effect, the relative positions of these Stark components can still be significantly impacted by the host. Importantly, this means that the host can play some role in shaping both the emission and absorption spectra [66, 67], and affecting the radiative lifetime, which can have a significant influence on laser operation [68, 69] and the thermal management approaches described herein.

Figure 1.Stark energy levels for two common laser glasses: (a) Al2O3-doped and (b) P2O5-doped silica. The zero-phonon lines are roughly at the same energies in both systems [70].

The Stark manifolds of the Yb3+ ion for two relatively common laser glasses, aluminosilicates and phosphosilicates, are shown in Fig. 1 (adapted from data found in [70]). The corresponding absorption and emission cross-sections are shown in Fig. 2 [71], as well as the spectra for a fluorosilicate glass taken from [72] for comparison. Due to the nephelauxetic effect [73], the more covalent environment (aluminosilicates) produces a broader spectrum whose emission extends somewhat more deeply into the infrared. The effect of degree of covalency on an emission spectrum can be quantified through the average fluorescence wavelength λem, which are 1,007.4 nm, 998.9 nm, and 999.5 nm for the aluminosilicate, phosphosilicate, and fluorosilicate fibers, respectively. The latter two have lower emission cross-section values and therefore concomitantly longer radiative lifetimes (typically in the range of 1.3 ms to 1.5 ms [68, 70] compared with the aluminosilicates, in which the radiative lifetime is around 0.8 ms [68]).

Figure 2.Cross-section data for various Yb3+ doped glasses. (a) Measured emission and (b) absorption cross-sections of three Yb-doped glass fibers. The spectroscopic properties of the fluorosilicate and phosphosilicate glasses are quite similar and are influenced by the less covalent environment they promote to the Yb3+ ions.

Regardless of the pumping wavelength, for a given temperature the rare-earth ion’s upper state will rapidly come to the same thermal equilibrium distribution. Therefore, phonons must either be produced or annihilated in support of this process. The former is a natural result of the positive QD associated with lasing, while the latter gives rise to a negative QD and cooling of the host. This process is very fast due to the width of the manifold compared with the maximum phonon energy, as described above [38]. The optical processes relevant for the remainder of this paper are identified in Fig. 3. In Fig. 3(a), the more common process is shown wherein a pump photon drives either spontaneous or stimulated emission at a lower energy. This configuration is referred to as Stokes pumping (SP) and generates heat through a positive QD. When the pumping wavelength is longer than λem, as illustrated in Fig. 3(b), the resulting fluorescence carries thermal energy away from the gain material, giving rise to cooling. This process, referred to as ASF, therefore has a negative QD [74]. It is a form of ASP. A radiation-balanced laser (RBL) [Fig. 3(c)] makes use of ASF to offset the positive QD stemming from the lasing wavelength. These processes are discussed in more detail later. The final configuration [Fig. 3(d)] makes use of both SP and ASP to drive a single lasing process. ASP in this case is not used to generate fluorescence but rather contributes to stimulated emission.

Figure 3.Illustrations of the various inter- and intra-manifold transitions relevant to the generation and management of heat in rare earth doped fiber lasers and amplifiers. Dashed and solid arrows represent absorption and stimulated emission, respectively. The green, vertical wiggly lines represent fluorescence. The red wiggly lines correspond to phonon generation and heating, and the blue wiggly lines to phonon annihilation and cooling. Heating or cooling requires the intra-manifold movement to lower (red) and higher (blue) energies, respectively. (a) Pumping at an energy higher than the mean emission energy leads to quantum defect (QD) heating. (b) Pumping at a wavelength longer than λem leads to phonon annihilation and cooling. (c) radiation-balanced lasers (RBLs) incorporate anti-Stokes fluorescence (ASF) to offset the QD heating. (d) Excitation-balanced lasers (EBLs) make use of both Stokes pumping (SP) and anti-Stokes pumping (ASP) to drive stimulated emission. Note that signal re-absorption, where relevant, was intentionally left off these diagrams.

The three-dimensional temperature distribution in a fiber laser is critical to understanding laser operation and the cooling required to manage the fiber temperature in fiber lasers. This knowledge can be gained by modeling. It is important to model the longitudinal temperature distribution, which provides the location of the hottest spot(s) along the fiber and their temperature. It is also important in some applications to have access to the radial distribution, for example to understand the impact of fiber heating on its guiding properties [75]. This effect becomes more significant with increasing thermal loading, particularly when combined with active convective cooling. To calculate the fiber core temperature, one first needs to identify the optical power distributions along the fiber, the thermal processes within the fiber that drive the increase in temperature, and the mechanisms that dissipate heat away from the fiber. In this section, SP is assumed, such that the dominant source of heating is assumed to be the QD. The gain fibers are assumed to be pumped with a continuous-wave laser and convectively cooled with flowing water. Two exemplary systems are modeled to illustrate the thermal management problem from two very different perspectives, namely a low-power DBR laser, in which even small fluctuations in the temperature can result in instability in the wavelength and increased frequency noise, and a high-power double-clad fiber laser. It will be shown that in the former case, the radial temperature distribution is nearly uniform and that a determination of the core temperature alone is sufficient to model the system. A final sub-section provides very simple expression to calculate the temperature of a doped fiber pumped by Stokes or anti-Stokes in the limit of small temperature changes.

### 4.1. Three-dimensional Fiber Temperature Model

The temperature is calculated in the three regions of interest of the fiber, namely the core of radius r1, the cladding of radius r2, and the coating of radius r3. Each region has a thermal conductivity ki, where i = 1 for the core, i = 2 for the cladding, and i = 3 for the coating. In [76] it was shown that after solving the thermal conduction equation subject to the appropriate boundary conditions between the four regions (the fourth being the medium surrounding the coating), the radial temperature distribution of the core T1(r), cladding T2(r), and coating T3(r) are given by:

T1r=T0q1r24k10<r<r1

T2r=T0q1r124k1q1r122k2ln(rr1)r1<r<r2

T3r=T0q1r124k1q1r122k2ln r2 r1q1r122k3ln(rr2)r2<r<r3

where q1 is the heat power density (heat generated per unit volume) in the core. T0 is the temperature at the core center, expressed as

T0=Ta+q1r122hr3+q1r124k1+q1r122k2lnr2r1+q1r122k3ln(r3r2)

where h is the heat transfer coefficient and Ta is the temperature of the fluid surrounding the coating. The heat transfer coefficient quantifies the rate at which heat is extracted from the outer surface of the fiber, via natural convection of air or water surrounding the fiber, or a forced flow of air or water around the fiber. In the case of natural convection, this coefficient depends on the temperature difference between the fiber outer surface and the surrounding medium T3(r3) – Ta [77]. When this temperature difference is small, h is a constant; but when this difference is large, h increases with increasing temperature difference. In this last case, calculating the temperatures in (1)–(4) requires applying for example an iterative process, as done for example to generate Fig. 4 in [77].

Figure 4.Thermal analysis of the distributed-Bragg-reflector (DBR) laser. (a) Simulated radial temperature distribution of the Yb-doped fiber in the single-frequency DBR fiber laser of [82]. (b) With varying temperature of the fiber, the corresponding wavelength shift (absolute value) of the DBR fiber laser. A mode hop is observed at a temperature change near 9 K as the red-shifted mode m is replaced by m + 1 entering on the blue side of the FBG spectrum.

### 4.2. DBR Lasers

Single-frequency fiber lasers serve a wide range of applications [7880]. Among the various configurations that are routinely used, which include distributed-feedback (DFB) lasers, distributed-Bragg-reflector (DBR) lasers, and ring-cavity lasers, DBR lasers are a common choice [81]. In this section, a simulation of a low-power DBR laser is presented. The objective is to calculate the temperature profile in the gain fiber, and from this profile determine the temperature and pump-power dependences of the lasing wavelength. The specific laser that is modeled is the DBR fiber laser reported in [82]. It utilized a phosphate fiber doped with 15.2 wt.% of Yb3+ pumped at 976 nm, and it produced a maximum output power of 408 mW at 1,063.9 nm. The active fiber length was L1 = 0.8 cm and the cavity length L2 = 1.3 cm. The fiber is short enough that the pump absorption can be assumed uniform along the fiber. The dominant sources of heating are assumed to be the QD and nonradiative processes, which lead to a less-than-unity quantum conversion efficiency ηQCE. ηQCE specifies the fraction of absorbed pump photons that contribute to the desired optical process, namely laser emission. Other sources of heating, such as poor splice quality, are not considered here. In [82] pump coupling efficiency was estimated to be 85%, and an approximate ηQCE, was provided as 93% [82]. Given the output power Pout, the heat power density in the fiber core q1 can be estimated as

q1=Ppabs,th1 λp λem +Ppabs1ηQCE+PoutλsλpQDπr12L1

where λs is the laser wavelength and λp the pump wavelength. Equation (5) has three distinct terms in the numerator. The first term accounts for the QD heating associated with the absorbed pump power needed to reach threshold. As discussed above, there is a thermal equilibrium population in the upper state manifold, which is indicated by the average emission wavelength, λem. This term can be neglected when the threshold power is small compared to the pump power, as it is in the present case. The second term reflects the fact that ηQCE is less than unity; (100% − 93% = 7%) of the absorbed pump power is directly converted to heat, likely driven by quenching mechanisms. In the subsequent calculations, Ppabs is assumed to be the total pump power (as provided in [82]), multiplied by the pump coupling efficiency. The third term in the numerator is linked to the output power curves (Fig. 2(c) in [82]) and states that the useful pump power absorbed by the gain fiber is λs / λp times the output power, and of this the fraction QD is converted into heat. Dividing by the fiber core volume πr2L1 gives the heat density.

Assuming Ta = 300 K, k1 = k2 = 0.84 W/m-K for a phosphate fiber [83], k3 = 0.2 W/m-K, and h = 1,000 W/m2-K (a typical value for the flowing water cooling conditions used in [76]), the temperature distribution in the radial direction at the maximum output power is shown in Fig. 4(a). The temperature decreases radially from the center of the core to the cladding and coating, as expected. The predicted increase in the core temperature is ~23 K, whereas the temperature difference between the core center and the cladding’s outer edge is around 6.5 K. Due to the moderate numerical aperture (NA = 0.14) of the fiber, any temperature related changes to the NA will have a negligible impact on the transverse mode characteristics in comparison to the temperature-dependent phase shift.

One of the most important characteristics of a single-frequency DBR laser is the stability of its output wavelength λs. If no thermal energy is generated, the output wavelength can be expressed as

λs=cm×FSR

where m is the longitudinal mode selected by the laser that brings this value closest to the central wavelength of the laser’s fiber Bragg grating (FBG) (here 1,063.9 nm). The free spectral range (FSR) is related to the cavity length and the effective index neff of the core mode by FSR = c/(2neffL2). After thermal energy is generated and the laser fiber heats, two effects take place. First, the refractive index decreases due to the negative thermo-optic coefficient of the phosphate glass (−2.1 × 10−6 K−1) [84]. Second, the fiber expands (coefficient of thermal expansion is 4.0 × 10−6 K−1 [85]) physically lengthening the cavity. These two effects modify the laser wavelength in opposing directions. In the present example, a thermally induced wavelength shift of 7.7 pm is expected when operating at the maximum output power. More generally, the sensitivity of the wavelength to changes in temperature is simulated and shown in Fig. 4(b). With increasing output power and the resulting increase in fiber temperature, the output wavelength can shift up to ±13.93 pm and experiences a mode hop every 18 K in temperature change, which is undesirable in applications requiring high wavelength stability.

### 4.3. High-power Fiber Lasers

The high-power system is assumed to be cladding end pumped. Here, the pump absorption is no longer assumed to be uniform, and the pump power distribution along the fiber is taken into consideration, leading to a prediction of a three-dimensional temperature distribution. More specifically, as the pump power is depleted along the axial dimension, the thermal load and therefore the temperature both decrease along the length. The core glass is assumed to be aluminosilicate, and the active fiber geometry is chosen to be a common commercial Yb-doped fiber with the parameter values summarized in Table 1. The emission and absorption cross-sections are shown in Fig. 2 above. An idealized fiber is assumed, in which the QD is taken to be the only source of heating.

TABLE 1 Basic optical parameters of Yb-doped aluminosilicate

Core Diameter (µm)Cladding Diameter (µm)Buffer Diameter (µm)Numerical ApertureUpper-state Lifetime (µs)Yb3+ Concentration (wt.%)
254005000.077431

A master oscillator power amplifier (MOPA)-based fiber laser setup is considered, using a 10-m length of the Yb-doped fiber mentioned above as the active medium in its final amplifying stage. Pump powers of 2 kW at 975 nm and a signal input power of 20 W at 1,030 nm (where amplified spontaneous emission (ASE) would be produced) are assumed. First, using a model based on the laser rate equations [86], the evolution along the fiber length of the pump and signals (including ASE) powers are calculated. The results are shown in Fig. 5(a). The thermal model described in Section 2.1 is then used to simulate the temperature distribution, assuming Ta = 300 K, k1 = k2 = 1.38 W/m-K, k3 = 0.2 W/m-K, and h = 100 W/m2-K (a typical value under the condition of a fan blowing air) [76]. The temperature of the core center, core-cladding boundary, cladding-coating boundary, and coating surface are plotted versus position along the fiber in Fig 5(b). The inset at the top right corner displays the radial temperature distribution at 0.25 m, where the highest temperature is experienced. The highest temperatures at the core center and the coating surface are 694.8 K and 663.2 K, respectively, which is sufficiently high to cause failure of both acrylate [87] and polyimide [88] coatings. Several obvious approaches can relieve this problem to some extent, including utilizing a larger cladding and coating, reducing the Yb concentration (to distribute the thermal energy over a longer fiber), and adopting water cooling.

Figure 5.1,030 nm master oscillator power amplifier (MOPA) simulations. (a) Calculated pump and signal power distribution of the MOPA; (b) calculated temperature distribution along the fiber length for core center, core edge, cladding edge, and coating edge.

To illustrate the efficacy of these solutions, Fig. 6 plots the predictions of similar temperature simulations performed under different conditions. Obviously, all the approaches effectively reduce the fiber temperature. However, both increasing the cladding size and lowering the Yb concentration lead to the need for a longer Yb-doped fiber. As a result, the system may become more likely to suffer from nonlinear effects. Water cooling, on the other hand, although bulky, allows the active fiber to remain relatively shorter. Power scaling, especially for a real fiber (in which ηQCE is less than unity), therefore clearly requires either far more aggressive water cooling or alternative means to lower the QD. The latter is the main focus of this review.

Figure 6.Temperature distribution along the fiber length for core center, core-cladding boundary, cladding-coating boundary, and coating surface calculated under the same simulation conditions as in Fig. 5 except that (a) the cladding and coating radii are increased to 350 µm and 500 µm, respectively, (b) the Yb concentration is decreased to 0.2 wt.%, and (c) the fiber is water cooled (h = 1,000 W/m2-K). In all cases, the maximum temperature is reduced to below 400 K.

### 4.4. Low-power Fiber Lasers

The same heat conduction equation and boundary conditions that were used to derive the fiber radial temperature profile (1)–(4) at steady state can also be solved to predict the temporal evolution of this profile from the time the pump is turned on [77]. This evolution is useful for example to predict the temperature profile (and hence index profile of the core region) in fiber lasers and amplifiers that are pumped by short pulses. This model can also be used to calculate simply the thermal time constant of a fiber and its dependence on the fiber transverse dimensions, heat conductivity, and specific density, which can be useful to predict for example the time it takes for the temperature of a fiber to reach steady state, or to cool down to room temperature after the pump has been turned off. For example, as a useful rule of thumb, the thermal time constant of a bare silica fiber with a core diameter of 4 μm and a cladding diameter of 125 μm that is core pumped is 1.2 s. This is the time it takes for the center of the core and the cladding surface to reach 95% of their respective steady-state temperature (see Fig. 5 in [77]) after the pump has been turned on.

At low to moderate pump powers, (1)–(4) show that the radial temperature distribution of the fiber is essentially uniform, as also demonstrated in [77]. In this case, and for a silica fiber, the first two conductivity-related terms in (4) can then be neglected. The steady-state temperature at the center of the fiber, assumed to be stripped of its coating (and therefore the temperature of the surface of the cladding, since the profile is uniform) can be expressed in the simple form [77]

T0T2(r2)=q1r122hr2q1r122klnr1 r2

where k is the thermal conductivity of the fiber, assumed to be the same in the core and the cladding. For a silica fiber, the first term in (7) strongly dominates and provides an accurate estimate of the overall temperature change of the fiber. (7) shows that the temperature rise of the fiber is inversely proportional to the heat transfer coefficient. Since q1 is the heat injected in the core per unit volume by the pump, following (5) it can be expressed in the general form q1 = hPabs/(pr12L), where Pabs is the pump power absorbed over a length of fiber L, and h is the percentage of this power that is converted into heat (by the processes modeled in (7)). (If the pump absorption is not uniform, Pabs/L can be calculated at each point along the fiber from the knowledge of the pump power distribution along the fiber). Therefore in (7) the temperature rise is independent of the radius r1 of the doped core. Also, for small temperature differences the product hr2 is independent of r2 (see Fig. 8 in [77]). As a result, the steady-state fiber temperature rise is given by the very simple expression [77]

Figure 8.Block diagram for a representative tandem pumped fiber laser. LD, laser diode; FBG, fiber Bragg gratings; CMS, cladding mode stripper. In this example, six FBG-based fiber lasers are pumped individually by semiconductor lasers. Their outputs are combined to serve as the pump for the power amplifier stage.

ΔTss=ηPabs2πLhr2

where again hr2 is a constant. For a fiber cooled by natural air convection, this expression gives a temperature rise of 3.13 °C for every mW of heat that is generated in the fiber core per unit length. For example, in a 1-cm fiber pumped with 1 W of pump power, of which only 5% is absorbed (50 mW), and assuming the QD is the sole mechanism that generates heat, for a QD of 4% (2 mW of heat in 1 cm) the fiber temperature rise is predicted to be 6.2 °C. Note again that these expressions are valid only for small temperature rises. They provide a convenient rule of thumb to quickly estimate the temperature of a fiber pumped at low pump powers. They are also useful in the context of optical cooling to calculate the temperature drop induced by ASF pumping in a fiber, since the fiber temperature changes are then typically quite small (a few degrees or less).

There are several ways to measure a fiber temperature. The magnitude of the anticipated temperature change of a fiber is a key factor towards the selection of the most appropriate method to measure it. The dominant form of heat transfer, such as radiative in a properly configured vacuum chamber, or convective in a water-cooled system, ultimately drives the change in fiber temperature, and therefore the required sensitivity of the temperature sensor. Suitable sensors can further be classified into external or in-situ. External sensors are physically brought into the vicinity of or in contact with the fiber, such as FBGs or thermal cameras. In-situ sensors, on the other hand, rely on a change in a physical characteristic of the laser, such as a fluorescence spectrum. This short section briefly outlines a few methods used to measure fiber temperature, including their operating principle and their accuracies.

When placed in air or water, a fiber may experience one or more of convective, conductive, and radiative heat-transfer mechanisms with its surroundings. Depending on the temperature of both the fiber and its surroundings, one of these may dominate. For example, in the case of ASF cooling, the amount of heat removed per unit volume is almost always small. When the cooled fiber is in air, convection continuously brings heat into it, which prevents the fiber temperature from decreasing far below the air temperature. The temperature difference between the fiber and the air is then small (millidegrees) [89], making its measurement more difficult. For the same reason, achieving cryogenic temperatures under such conditions is also difficult. A common solution is to place the fiber in a vacuum chamber to eliminate convective heating, as well as holding the fiber on a carefully designed low-contact mount to minimize conductive heat intake from the mount. When this is done properly, the only heat that is transferred from the fiber surroundings into the fiber is radiative heat from the walls of the chamber [90]. A recent demonstration of cooling of an optical fiber preform benefitted significantly from such a system [91]. Although the use of a vacuum is clearly not beneficial for the thermal management of high-power fiber lasers, it can still serve as part of a measurement platform that can help elucidate the sources of parasitic heating such as concentration quenching or background absorption.

### 5.1. Absorption or Emission Spectrum Measurements

The thermal population in the ground-state manifold of laser ions obeys Boltzmann distribution. As such, an increase in fiber temperature gives rise in each manifold to increased populations in sub-levels of higher energy, as illustrated in Fig. 7. This results in increased absorption at longer wavelengths, and decreased absorption at shorter wavelengths [35]. In aluminosilicates, “longer” and “shorter” are relative to ~950 nm [35]. This change in absorption results in a distortion of the absorption spectrum, distortion that can be measured to infer the temperature of the gain medium. Absorption, however, is not a practical means of monitoring fiber temperature at high power because it requires the introduction of an additional light source to carry out the measurement. Instead, the shape of either the fluorescence spectrum [3537] or the ASE spectrum [92] can be used as a gauge. In the case of fluorescence, the most prominent change with an increase in temperature is a spectral broadening due to the increased absorption at the long wavelength side of the S band. In the case of ASE, this same effect leads to a redshift of the peak wavelength. Such measurements require system calibration since the dependence of the spectrum on temperature must be known a priori. This methodology has been successfully applied to the study of ASF cooling of solids [9395]. From a practical perspective, however, the method works for relatively large changes in temperature (tens of Kelvin), but it is not sufficiently sensitive for temperature changes of less than a few Kelvin.

Figure 7.The population in the lower manifold obeys the Boltzmann distribution. When the temperature of the Yb3+ host is increased (red), there is increased population at higher energy, and a concomitant increase in the absorption cross-section at longer wavelengths. When cooled (blue), the Yb3+ acts like a four-level system across a wider range of wavelengths, including in the S-band. Upon fiber heating, the fluorescence spectrum around the zero-phonon line (shown as the green arrow) is broadened.

### 5.2. Brillouin-scattering and Rayleigh-scattering Temperature Measurements

This class of in-situ measurements utilizes either Brillouin [96] or Rayleigh [97, 98] scattering. They are, in their principle, identical to temperature measurements in distributed fiber-optic sensing systems [99]. Brillouin scattering is an acousto-optic interaction whereby an incident lightwave scatters from a Bragg-matched hypersonic acoustic wave (spontaneous scattering). The scattered and incident light waves may interfere and further drive the acoustic wave through electrostriction. The latter then induces a grating in the fiber, which efficiently reflects the incident wave (SBS). Because the grating is moving at the velocity of the acoustic wave in the fiber, the reflected wave is Doppler shifted (~10–20 GHz depending on the host glass and signal wavelength). This Brillouin shift is temperature-dependent and can be measured to obtain the temperature of the fiber core. The signal used to measure the Brillouin-scattering characteristics of the fiber must obviously not overlap with the lasing wavelength (~1 μm for Yb3+). As such, the 1.5-µm telecommunication band serves as a convenient spectral range for this ion. This signal must be injected into the gain fiber through additional components such as wavelength-division multiplexers and circulators. The first report of such a measurement was made in 2009 [100]. It has recently been used to quantify the quantum conversion efficiency in a lightly Yb-doped fiber by pumping at the zero-phonon wavelength and measuring the subsequent QD heating [101, 102]. In that case, the fiber was held in a vacuum to enhance the temperature change relative to atmospheric pressure and improve the signal amplitude, as discussed above.

Unfortunately, Brillouin-based systems can be complicated and expensive, and therefore more recently Rayleigh-based approaches have been established. This method utilizes optical frequency domain reflectometry (OFDR) technologies [103, 104]. It is the temperature-dependent Rayleigh scattering fingerprint that is now probed via the OFDR method. The probe signal is incorporated in the fiber under test using the same approach as for Brillouin-scattering temperature measurements. The main complication in making either Brillouin-scattering or Rayleigh measurements at high power is, indeed, the high power itself. Attempting to internally probe the temperature with multiple kW of power present not only endangers the requisite additional equipment and optical components, but also the user.

### 5.3. Thermal Cameras

Thermal cameras have been used to make high-spatial-resolution measurements on relatively larger samples [91, 105]. These commercial devices can have a noise equivalent temperature (or temperature resolution) on the order of tens of mK [106]. However, depending on the fiber diameter, expensive infrared magnification schemes may be required to be able to discern the temperature of the fiber from that of its surroundings [107]. Calibration of the temperature change can also be a tedious and not always reproducible process.

### 5.4. FBG Temperature Sensors

FBGs are a well-known temperature-sensing platform. Through the thermo-optic effect, slightly offset by thermal expansion, the Bragg wavelength of an FBG (i.e., the wavelength at which the grating reflectivity is maximum) increases with increasing fiber temperature. In a silica fiber for example, this wavelength shift is 13 pm/°C near 1,550 nm [108]. The FBG temperature can then be inferred with a simple measurement of the Bragg wavelength. This measurement can be carried out with an optical spectrum analyzer (OSA). A typical OSA with a resolution of 0.01 nm will then provide a relatively poor temperature resolution of 1.3 °C. Alternatively, the FBG can be interrogated with a laser tuned to the steepest portion of the FBG’s transmission spectrum; a small temperature-induced shift will then result in a large change in transmission, and a greater temperature resolution. However, most FBGs still can resolve only 0.1 °C at best [109]. The temperature-sensing FBG may be placed at a fixed location inside a fiber laser cavity to measure its temperature locally [110], although when the temperature change is small, the heat generated by the weak absorption of the intracavity laser power by the grating can increase the temperature reading and yield an erroneous measurement. Alternatively, an external FBG can be conveniently placed in physical contact with the laser fiber at any position along its length [111, 112].

The temperature resolution can be significantly improved by using a slow-light FBG. In a slow-light FBG, the index modulation is significantly higher than in a conventional FBG. As a result, the field reflectivity per unit length is much stronger, and the grating behaves like a Fabry-Perot resonator, like in a DFB laser. A slow-light FBG then exhibits sharp resonances in transmission and reflection within its bandgap, on the short-wavelength edge. These resonances can be as narrow as 50 fm [113]. When the temperature of a slow-light FBG is changed, the entire spectrum of the FBG, including resonances, shifts at the same rate as a conventional grating. But thanks to the much greater steepness of the resonance slope, the ability to resolve a small temperature change is much greater [113] than in a conventional FBG. A temperature sensor utilizing a slow-light FBG with a noise of ~0.5 mK and a drift of only ~2 mK/minute has been demonstrated [114]. Such a sensor can therefore discriminate between a fiber laser that is running slightly above room temperature from one that is running slightly below, even by a few mK. This is critical to determine whether a fiber laser operating near the zero-phonon line is actually cooled. This sensor was instrumental to the first demonstration of ASF cooling of a silica fiber [89].

A key approach to reducing the heat load on the active fiber in a fiber laser is to reduce the QD. For a conventional system, it involves bringing the pump and signal wavelengths closer together. To this end, in Yb-doped silica there is great flexibility in selecting a pump source with a wavelength that covers most of the broad pump band, namely either longer wavelength pumping (above 1 µm) or short-wavelength laser operation. Regarding long-wavelength pump sources, there is considerable on-going work targeting InGaAs materials [115], but the technology has not yet matured sufficiently to enter the commercial mainstream. Therefore, long-wavelength pumps currently come in the form of fiber lasers, thereby defining a class of lasers referred to as “tandem-pumped fiber lasers” [116, 117]. Regarding short-wavelength pumps, efficient, high-power and high-brightness commercial diode lasers are available in the 915-nm to 980-nm range [118, 119]. Short-wavelength pump light can also be obtained from Yb-doped fiber lasers pumped near 975 nm, although they require careful optimization [120] because these lasers tend to be less efficient owing to the higher absorption at short laser wavelengths. This section briefly outlines approaches using either semiconductor lasers or fiber lasers as the pump source.

### 6.1. Tandem-pumped Lasers

In a high-power, low-QD application, laser diodes, usually at 976 nm, pump relatively shorter wavelength fiber lasers, typically in the range of 1,015 nm to 1,020 nm. These lasers, in turn, pump another fiber laser that produces a longer wavelengths, typically above 1,030 nm. Since the pump and signal wavelengths differ by only 10–20 nm, the QD of this final stage of the laser is very small. Figure 8 shows a block diagram for a representative tandem-pumped fiber laser. In this case, six fiber lasers are pumped by wavelength-stabilized semiconductor lasers at 976 nm. These six lasers pump the last amplifier stage, which produces a multi-kW, and often single mode [1], or diffraction-limited [121], output. The first stage (976 nm to 1,015 nm) represents a QD of 4% (with aggregate thermal energy distributed across all six pump lasers), while the second stage (1,015 nm to 1,030+ nm) can have QD values under 2%. In this scheme, the thermal energy is distributed relatively evenly across several laser and (or) amplifier subassemblies [4, 121].

The semiconductor lasers that drive the fiber laser-based pumps possess the lowest brightness in the system. Therefore, the active fiber’s pump-cladding diameter and its numerical aperture limit how much power can be obtained from them, since this sets the maximum pump power that can be coupled into the fiber. Fiber lasers can enhance the pump brightness by several orders of magnitude as pump power is converted to signal in the core. As a result, there is far more flexibility in the cladding geometry when pumped with sources having much greater brightness than semiconductor lasers. In principle, nonlinearities and fiber damage aside, power scaling is then limited only by the number of fiber laser pumps and stages one is willing to construct, although the entire laser system can then become somewhat daunting as its complexity increases.

There have been a wide range of developments in tandem-pumped Yb-doped fiber lasers in the past decade, focusing on several different aspects of the system. Much of the work has targeted short-wavelength lasers as pump sources [122129]. Since the absorption cross-section of Yb3+ in the range of 1,015 nm to 1,020 nm depends on the host, and since it is roughly 25 to 50 times lower than around 976 nm, longer active fiber lengths are required, and nonlinearities such as stimulated Raman scattering (SRS) [130] can become problematic. Power scaling may also lead to catastrophic damage, for example from thermal lensing [131]. As a result of these investigations, significant progress has been made toward understanding and mitigating SRS [132, 133] through fiber designs that enhance mode size and balance absorption in cladding-pumped lasers [134136]. Another approach to suppressing SRS includes adding wavelength-selective filters such as FBGs to attenuate the Raman signal [137139]. Tandem-pumped laser configurations have been shown, thanks to reduced QD heating, to have less susceptibility to TMI [140] and reduced photodarkening relative to diode-pumped lasers [126, 141, 142]. Therefore, low-QD tandem-pumped configurations offer several practical operational advantages. While few 10-kW, diffraction-limited systems have been described [1, 143], several multi-kW demonstrations have been reported [133, 144]. Pulsed operation has also been investigated, but not nearly as thoroughly as continuous-wave systems [145147].

### 6.2. Short-wavelength Lasers

Analogous to the gain spectrum of Er-doped fiber amplifiers, the Yb3+ gain spectrum can be divided into a short (S, less than 1,060 nm), a center (C, 1,060 nm to 1,130 nm), and a long (L, greater than 1,130 nm) wave bands [148]. As discussed above, S-band lasers can serve as pumps in tandem-pumped fiber lasers. Lasing at wavelengths less than 980 nm usually is achieved by pumping at 915 nm [149151], corresponding to a QD in the range of 6 to 7%. As a result, longer wavelength pumping is of greater interest in reducing the QD. From a spectroscopic standpoint, both phosphosilicate [152] and fluorosilicate [72] fibers have relatively flat absorption spectra on the short-wavelength side of the zero-phonon line (see Fig. 2). This feature enables longer wavelength pumping (~960–970 nm versus 915 nm as is typical in aluminosilicate fibers) to achieve lasing below around 980 nm, thereby illuminating one path to reducing the QD. Such short-wavelength lasing, however, is challenging due to strong competition from ASE at longer wavelengths (~1,030 nm), which tends to deplete the gain.

Utilizing wavelength-stabilized pumps [153] near 976 nm, on the other hand, and lasing at 1000 nm, gives rise to a QD of 2.5%. Capitalizing on this concept, a core-pumped Yb-doped laser with a very low QD (≤0.5 %) was demonstrated, but it exhibited a rather low slope efficiency [154]. Recently, a demonstration of a high-efficiency, less-than-1%-QD core-pumped fiber laser based on a fluorosilicate glass was reported [155]. In that work, two sets of pump and signal wavelengths were selected (976.6 nm/985.7 nm and 981.0 nm/989.8 nm). Scaling this result to a cladding-pumped geometry can be challenging, again mainly due to ASE at longer wavelengths. This requires careful fiber design and selecting the appropriate fiber length to prevent both ASE buildup and signal re-absorption [120, 156, 157]. That said, a systematic study of lasing throughout the entirety of the S-band, and below 1,000 nm in particular, is still lacking.

A simulation of such a high-power S-band laser is performed as an example. The Yb-doped fiber (in the final amplifying stage) is assumed to have a length of 10 m and the same parameters as in Table 1, except that the lifetime and cross-section values are assumed to be those of the phosphosilicate fiber found in [71]. A pump power of 2 kW at 975 nm and a signal input power of 20 W at 1,000 nm are assumed. The effect of ASE on the gain is also taken into consideration in the laser rate equations. First, the evolution along the fiber length of the pump, signal, and ASE powers are calculated and shown in Fig. 9(a). From the result, it can be observed that the signal power is maximum at a position of approximately 4 m. Further along the fiber, there is strong competition from ASE, becoming the dominant process at positions greater than about 5 m since in that region the signal is mostly re-absorbed. This trend observed here agrees with the one reported in [155].

Figure 9.Short wavelength master oscillator power amplifier (MOPA) simulations. (a) Pump and signal power distribution of the MOPA, and (b) temperature distribution along the fiber length for core center, core edge, cladding edge, and buffer edge. The sharp increase in temperature at around 5 m results from the large quantum defect (QD) associated with signal reabsorption and the buildup of amplified spontaneous emission (ASE).

Then, using the model described in section 2.1, with the assumption of Ta = 300 K, k1 = k2 = 1.38 W/m-K, k3 = 0.2 W/m-K, and h = 100 W/m2-K (forced air cooling), the predicted temperatures of the core center, core-cladding boundary, cladding-coating boundary, and coating surface are plotted in Fig. 9(b) as a function of position along the fiber. Along the first few meters of fiber, the trend is similar to that in Fig. 5(b), a rapid increase in temperature near the fiber input and a steady decline further along the fiber as the pump is absorbed. However, under the same cooling condition (h = 100 W/m2-K), the peak temperature at the coating surface drops from 663.2 K in Fig. 5(b) to 347 K in this S-band laser, a significant decrease that is beneficial to reducing thermal-related problems.

### 7.1. ASF Cooling and Radiation-balanced Lasers

As pointed out earlier, ASF cooling extracts relatively small amounts of power per unit volume [74]. Therefore, in addition to the heat generated by the QD, any number of other undesirable exothermic effects can incidentally inject heat into the sample and either partially negate or overwhelm the heat extracted by ASF. The two dominant exothermic mechanisms in Yb3+ are absorption of pump and/or fluorescence photons by impurities [45], and concentration quenching [158].

Impurity absorption is minimized by using high-purity precursors to fabricate the sample [159, 160]. The CVD methods employed to fabricate silica-based optical fibers is ideal in this regard because they afford near-intrinsic levels of purity and, hence, very low levels of impurities and low absorptive losses. However, even with low extrinsic (impurity) losses, heat can be generated in a rare-earth-doped glass through energy transfer, followed by non-radiative relaxation.

Concentration quenching is a well-known mechanism in which the energy of an electron in the excited state of an active rare-earth ion is transferred to another ion, which relaxes non-radiatively and releases heat. This energy transfer can occur to either an impurity present in the glass, such as OH- or a heavy-metal ion, or another Yb ion in its excited state. In the case of transfer to an impurity, for all common impurities the level that is excited by this energy transfer is strongly non-radiatively coupled to the ground state, so that the excited electron quickly relaxes non-radiatively to the ground state, thereby exciting phonons and heat [158]. Regarding the second mechanism, when two Yb3+ ions in the excited state are close by, one ion will donate its energy to the other, thereby exciting it to a virtual level, from which it will relax back to its excited state non-radiatively, again exciting phonons in the process. For both processes, the probability of energy transfer increases rapidly with the ion concentration, which limits the number of heat engines that can be doped into a given volume, and by the same token the amount of heat that can be extracted per unit time from this volume via ASF.

The susceptibility of a particular host to quenching is quantified by its critical quenching concentration Nc, the concentration for which the average distance between laser ions is such that the probability of non-radiative energy transfer is the same as the probability of spontaneous emission [158]. The critical quenching concentration for Yb3+ is typically one order of magnitude lower in silica than in crystals or in fluoride hosts [41, 161]. This is due to a combination of factors, including the comparatively low solubility of Yb2O3 in silica, which results in the formation of Yb clusters [162]. In a Yb cluster, the mean distance between Yb ions is small, which increases the rate of energy transfer between excited ions.

ASF cooling was first proposed in 1929 [163] yet not demonstrated until 1995, in a bulk sample of Yb:ZBLANP [164]. Since then, many hosts and trivalent rare-earth ions have been successfully cooled by this technique [89, 165173]. The most efficient and popular ion has been Yb3+ [168, 174, 175] for its simpler electronic structure generally devoid of non-radiative relaxation processes, followed by Tm3+ [171, 176178], Er3+ [170, 179], and Ho3+ [180]. The most common hosts are crystals, which are generally free of impurities and therefore of extraneous heating due to absorption of the pump by impurities, as well as fluorides, which can generally be more heavily doped than oxides and therefore offer greater cooling per unit volume. Most experiments were performed in bulk samples [169, 171174, 181], because a greater volume can be optically pumped and more energy extracted by ASF, leading to lower absolute temperatures. Most demonstrations were also performed in a vacuum chamber to minimize convective heat transfer between the sample and the surrounding air and maximize the sample temperature reduction. In 2015, cryogenic temperatures were achieved using highly purified YLiF4 crystals highly doped with Yb3+ [159]. In addition, cooling was also observed in optical fibers, which is generally more difficult due to the greater surface to volume ratio (greater convective heating from the surrounding air) and smaller doped volume (smaller total number of heat engines performing the cooling). Temperature changes of −65 K were reported in short sections of Yb-doped ZBLANP fibers [93], and −30 K in Tm-doped tellurite fibers [177], both in a vacuum. All fibers were multimode [93, 167, 175, 177, 182184] which makes it easier to achieve lower absolute temperatures compared to single-mode fibers, which have an even smaller volume of doped material.

Two RBLs have also been reported, both in a highly doped Yb:YAG crystal [185, 186]. In the earliest demonstration (2010), the gain medium was a highly doped Yb:YAG rod end-pumped with an array of high-power Yb-doped silica fiber lasers at 1,030 nm [186] that induced both gain at 1,050 nm and ASF cooling. The gain medium had a large dimension (3 × 120 mm) and the pump beam a large transverse size to maximize the extracted heat [186]. This laser produced 80-W of output power while maintaining radiation-balanced operation (zero average temperature change along the crystal). More recently (2019), a second radiation-balanced laser was demonstrated using a Yb:YAG disk [185]. The disk was pumped at 1,030 nm to produce 1 W of output power at 1,050 nm.

### 7.2. Recent Demonstrations of Radiation-balanced Silica Fiber Lasers and Amplifiers

The first internally cooled fiber amplifier, reported in 2021 [187], capitalized on this major innovation. The gain medium was the best performing silica fiber reported in [188]. The fiber had a core with a 21-µm diameter and a numerical aperture (NA) of 0.13, so that it was slightly multimoded at the signal (1,064-nm) and pump (1,040 nm) wavelengths. The core was doped with 2.0 wt.% Al to reduce concentration quenching, and with 2.52 wt.% Yb, or 1.93 × 1026 Yb ions/m3. From the measured emission spectrum of the fiber, the mean fluorescence wavelength, measured from the fluorescence-emission spectrum of the fiber, was 1,003.9 nm. This fiber exhibited significant cooling thanks in part to the sizeable energy difference between the fluorescence and the pump photons, in part to the relatively short upper-state lifetime of the Yb ions (765 µs), and in part to its high concentration and high Nc, inferred to be 1.20 × 1027 Yb ions/m3. Yb from cooling measurements [89, 189].

Turning to the amplifier configuration, the 1,040-nm pump (a commercial cw fiber-pigtailed laser) was combined to the 1,064-nm seed (a semiconductor laser) through a 90/10 fiber splitter. The splitter output that carried 90% of the pump power and 10% of the seed power was spliced to the input of the Yb-doped silica fiber. The other splitter output was used as a calibration tap to measure the power launched into the fiber amplifier. At the amplifier output, the unabsorbed pump power was eliminated with a long-pass filter, and the signal was sent to a power meter.

The temperature of the Yb-doped fiber was measured at seven locations using a slow-light FBG sensor (see Section 5.4). At each measurement location, a ~10-cm length of the Yb-doped fiber was stripped of its jacket to prevent re-absorption of the radially escaping ASF. The stripped section was placed in contact with the FBG sensor. 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 (a few seconds) reach thermal equilibrium [77].

Figure 10 plots the measured longitudinal temperature profile of the amplifier fiber when it was seeded with 3 mW at 1,064 nm for increasing pump power. When the amplifier fiber length was 2.74-m [Figs. 10(a)10(c)], the temperature remained below room temperature at all seven locations along the fiber and at all three pump powers. With 1.12 W of pump power [Fig. 10 (a)], the measured small-signal gain was 5.7 dB. At low pump powers (below saturation), the Yb ions are insufficiently excited, resulting in low ASF and low extracted heat. At large pump powers (well above saturation), excitation of the Yb ions is saturated (maximum) and the cooling rate is maximum. While the pump power in excess of the saturation power contributes very little to cooling, it is still absorbed by impurities. This process is essentially unsaturable and increases heating in proportion to this additional pump power. As a result of these two opposing effects, there is an optimum pump power that maximizes the extracted heat per unit length. Simulations using a model of ASF cooling in a fiber [190] predict that the optimum pump power for this fiber is 510 mW. When the input pump power was 1.12 W, the residual pump power at the output of the amplifier fiber was only 80.2 mW. Consequently, the negative temperature change is smaller near the input end, where the pump power is above 510 mW. It is also smaller near the output end, where it is below this optimum value. The lowest temperature is observed in the middle of the fiber where the pump power is near the optimum value.

Figure 10.Measured temperature change versus position along the fiber amplifier, and simulated dependencies using the model based on [191] for (a)–(c) a 2.74-m, and (d) a 4.35-m amplifier fiber.

When the launched pump power was increased to 1.38 W, the gain increased to 9.1 dB. As expected, the negative temperature change [see Fig. 10(b)] at the fiber input was now smaller than with 1.12 W because the input pump power was further above the 510-mW optimum value. On the other hand, the pump power at the output end of the fiber was now higher (154 mW). This value being closer to the optimum, that end of the fiber experienced a larger negative temperature change than with 1.12 W of pump. The trend continued when the pump power was increased to 1.64 W [Fig. 10(c)]: cooling decreased near the input end and increased near the output end, where the residual pump power was now 247 mW. The gain in this case increased 11.4 dB.

To further increase the gain, the pump power was increased to 2.62 W and the length of the amplifier was increased to 4.35 m, the calculated value that maximizes the gain for this power. This resulted in 16.9 dB of gain, while the average temperature change remained negative [see Fig. 10(d)]. The higher pump power resulted in a positive temperature change at the input end, but past the first ~100 cm the pump power was sufficiently attenuated, and the fiber temperature was below room temperature.

Figure 10 also plots as solid curves the fiber temperature predicted by the model of a radiation-balanced fiber laser described in [191], but with the cavity removed to simulate this fiber amplifier. All the fiber parameter values needed for these simulations were either measured or inferred from fits to independent cooling and absorption measurements. Thanks to this comprehensive characterization, no fitting parameters were needed to generate the solid curves in Fig. 10. For each pump power and length, the measured temperatures agree well with simulations. From the model curves, the average temperature change is −107 mK for 1.12 W of input pump power, −105 mK for 1.38 W, −93 mK for 1.64 W, and −24.4 mK for 2.62 W.

This work demonstrated that the seemingly small amount of cooling exhibited in fibers is sufficient to negate the heating induced by significant amplification of a seed signal. The obvious next step, now that a significant gain had been observed, was to attempt demonstrating a cooled fiber laser, which was accomplished shortly after [192]. The maximum gain of the cooled fiber was certainly high enough (~19 dB) to reach threshold, but it remained to be seen whether the signal intensity circulating in the laser resonator was not too high to cause substantial heating of the fiber and negate the cooling effect of ASF. The model of [191] showed, among other important trends, that in order to maximize cooling the transmission of the resonator’s output coupler must be as low as possible, which maximizes the resonator loss, and therefore the gain at and above threshold, and hence the population inversion, to which the amount of heat extracted by ASF is proportional. The other benefit of using a low output coupler transmission is that it also reduces the signal intensity circulating in the resonator, and hence reduces also the extraneous heat generated by absorption of this intensity by impurities.

The fiber laser diagram is depicted in Fig. 11. The gain fiber was the same Yb-doped silica fiber used in the fiber amplifier. The 1,065-nm resonator was formed by two FBGs, a high reflector (100% power reflection) and an output coupler with an 8% power reflection. Rather than splicing them directly to the gain fiber, they were each spliced to a short length of SMF-28 fiber, and each length of SMF-28 fiber was spliced to the ends of the Yb-doped fiber. Because the gain fiber has a larger core (21-µm diameter) than the HI-1060 fiber in which the FBGs were written (6-µm diameter), the splice loss between these two dissimilar fibers would have been fairly high. The role of these two intermediary lengths of SMF-28 fiber (9-µm core diameter) was to provide a more gradual match between the mode size of the FBG and gain fibers and reduce the splice loss. 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. The length of the gain fiber (2.64 m) was chosen so that at least 85% of the launched pump power was absorbed. The fiber laser was core-pumped at 1,040 nm through the high-reflection grating (see Fig. 11). A 10% fiber tap coupler was spliced between the pump and the high-reflectivity FBG to monitor the spectrum of the pump laser and ensure that it did not lase at 1,065 nm due the high-reflectivity FBG. At the laser output, a long-pass filter removed the residual pump power and passed the signal to a power meter.

Figure 11.Simplified diagram of a Yb-doped fiber laser internally cooled by anti-Stokes fluorescence. Upper portion of the diagram (in purple and green, enclosed in the solid box) is the fiber laser. Lower portion (in blue, enclosed on the dashed box) is the closed-loop temperature sensor utilizing a slow-light fiber Bragg grating (FBG) that was used to measure the temperature of the Yb-doped fiber at various points along its length.

The measured output power of the fiber laser is plotted as a function of launched pump power in Fig. 12. The threshold was ~1.07 W, which is high because of the high transmission of the output coupler and the relatively high loss at the four intra-cavity splices. As expected, above threshold the output power increased linearly with pump power. The laser output was in the TEM00 mode, since the higher order modes were filtered out by the SMF-28 and HI-1060 fibers spliced to the output end. This filtering caused only slight fluctuations in the output power (~5%) due to variations in the amount of power coupled to the higher order modes along the Yb-doped fiber.

Figure 12.The laser output power measured as a function of the launched pump power, along with a linear fit to the data. The color gradient is a pictorial representation of the average temperature change along the length of the gain fiber.

The temperature of the gain fiber was measured at eight approximately evenly spaced locations along its length, and at four different pump powers. For a given pump power, the fiber was found to be warmest at the pump input end and cooled monotonically more toward the pump output end. For the lowest pump power (1.22 W), the transition to a temperature below ambient took place ~1 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 optimum power that produces maximum cooling discussed in the previous section, calculated to be ~420 mW for this fiber. Second, the higher pump power corresponds to greater gain, and the generation of more Stokes phonons (more heating). Third, this region 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, the pump is attenuated and the gain saturates, which lessens these heating effects and ASF cooling dominates. The average temperature of the fiber calculated from these measurements for each pump power was used to calibrate the vertical scale on the right of Fig. 12. It shows that below threshold and up to an output of 114 mW, the gain fiber’s average temperature remained below room temperature. Above 114 mW, the fiber gradually warmed up above room temperature.

The data was fit to a model of a radiation-balanced fiber laser [191]. Here too, all 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 [161]. This fit gave a round-trip loss for the cavity of 20.6 dB, including of 11 dB from the transmission of the output coupler. The rest of the loss was assigned to 2.4 dB per pair of splices per pass, in good agreement with the value calculated from the modal overlap between the two pairs of fibers (2.2 dB). Using these values of the loss in the model gave the solid curve plotted in Fig. 12, which shows great agreement with the measured data. The slope efficiency was 41%, about half as much as typical commercial silica fiber lasers. In future iterations, the slope efficiency and the threshold can be significantly improved by essentially eliminating the splice losses by fabricating the FBGs directly in the gain fiber.

To complete this section, a few comments on power scaling are provided. First, fiber lasers and amplifiers operating in the deeply saturated regime are naturally very efficient. Indeed, this is one of the more attractive benefits of waveguide lasers. Therefore, it is challenging to configure the system to produce enough spontaneous emission to balance heating. A promising approach to solving this problem in double-clad fibers is to decouple the laser from the cooler, for example, by adding active dopants to both the core and inner (pump) cladding [191, 193]. Excited ions in the core contribute to stimulated emission and light amplification/lasing, while fluorescence from the pump cladding cools the whole structure. Recent modeling results [191] indicate that greater than 100 W, with full radiation-balancing, can be generated from such a laser using Yb in both the core and the cladding, and bidirectional pumping. Aside from background loss, drawbacks to this approach, included in the recent modeling, are the fluorescence capture coefficient of the pump cladding, leading to the reabsorption of fluorescence and subsequent heating, and ASE. It is important to point out that full radiation balancing may not be necessary in a real system; just a small amount of cooling can go a very long way, even if there is net heating in the active fiber. For example, consider the tandem pumped systems described above. When pumped at 1,017 nm, they too produce ASF. If the relative abundance of fluorescence can be increased even slightly, this could offset some heating in multi-kW systems.

### 7.3. Excitation-balanced Laser

In the RBL discussed above, one pump drives two simultaneous processes: lasing (at a longer wavelength) and ASF, wherein cooling through the latter offsets, or balances, the heat generated through the former. However, to achieve significant cooling, a large fraction of the absorbed pump power must contribute to fluorescence, and therefore does not contribute to gain—the useful “product” of a fiber laser or amplifier. Very recently, an alternate approach to balanced thermal management in Yb-doped fiber lasers has been demonstrated, in which the AS pump contributes to laser emission rather than to ASF [194]. The schematic for the EBL can be found in Fig. 3(d). Two pumps, one an anti-Stokes pump and the other a Stokes pump, both drive lasing. The representative experimental setup described in [194] is shown in Fig. 13(a). The AS pump is launched first and populates the upper state, but it does not achieve inversion (gain) for the signal, since it has a shorter wavelength. The Stokes pump is launched second, and its role is to complete the pumping process and bring the upper state population to threshold. The cooling is produced by the AS pump, according to the same principle as ASF cooling. The main difference, and the beauty of this technique, is that ASF is considerably weaker—most of the thermal energy is now extracted by the signal (a useful output) instead of by ASF (a wasted output).

Figure 13.Basic excitation-balanced lasers (EBL) configuration. (a) Schematic of the experimental setup in [194]. The Stokes pump (SP) and anti-Stokes pump (ASP) are pulsed and combined into the laser cavity via a coupler. (b) Representation of the relative timing of the two pumps. The pulse width is tp and the two pulses overlap for a time equal to tpdt.

In the experimental laser based on this principle reported in [194] and depicted in Fig. 13(a), the S and AS pumps provided output wavelengths of λSP = 976.6 nm and λASP = 989.6 nm, respectively. The Stokes pump was a commercial fiber-pigtailed laser diode, while the anti-Stokes pump was an FBG-based fiber laser described in [195]. Both pumps’ amplitudes were pulsed and combined into the laser cavity (purple dashed box) via a 3-dB coupler. The core-pumped laser cavity was defined by a pair of FBGs at λL = 985.7 nm and a segment of Yb-doped fluorosilicate fiber (see Section III). The timing between the two pumps was controlled by a multi-channel digital delay/pulse generator. An illustration of the time sequence is shown in Fig. 13(b). The pulse width for both pumps is tp, the time difference between the rising edges of the two pump pulses is dt, and the repetition rate is frep. The peak powers for Stokes and anti-Stokes pumps are noted as PSP and PASP, respectively. The set of parameter values presented in [194] was tp = 1 ms, dt = 0.8 ms, and frep = 400 Hz. The laser will behave differently as tp, dt, and/or frep are modified, and some optimization of these parameters will be needed in practice. However, to summarize it was shown that for long pump pulse durations (comparable to the upper state lifetime), a short temporal overlap, namely where tpdt ≠ 0 is beneficial.

The pump power was measured at the pump check point [see Fig. 13(a)], and the output power was measured at the laser output. The results are presented as the average laser output power PL versus the average launched anti-Stokes pump power PASP for different average launched Stokes pump power PSP [Fig. 14(a)]. Positive slopes were observed for all the cases, meaning that for the same PSP increasing PASP produced more laser output power, giving direct evidence that the anti-Stokes pump had contributed to stimulated emission. Linear fits to each data set disclosed a maximum slope efficiency of 38.3%. Furthermore, the fact that the anti-Stokes pump contributed to laser emission indicated that phonons had been extracted from the fiber, therefore reducing the overall QD of the system. To quantify this, an effective quantum defect (EQD) was defined to be

Figure 14.Results obtained with the first fiber laser-based excitation-balanced lasers (EBL). (a) Average laser output power (PL), (b) effective quantum defect (EQD), and (c) powers required from the SP to reach threshold (PSPth) measured as a function of PASP, for different values of PSP.

EQD=QDSP×P¯SPabsP¯SPabs+P¯ASPabs+QDASP×P¯ASPabsP¯SPabs+P¯ASPabs

where QDSP = 1 − λSP / λL, QDASP = 1 − λASP / λL, and PSPabs and PASPabs are the absorbed pump powers from the Stokes and anti-Stokes pump, respectively. Using Eq. (8), the EQD values for all the data points in Fig. 14(a) were calculated and shown here in Fig. 14(b). As a starting reference point, when PASP was set to zero, EQD = QDSP = 0.91% for the presented case. With increasing PASPabs, the EQD was found to gradually decrease. For the maximum available powers from the two pumps, the EQD decreased by 13.2% from QDSP. Modeling results indicates that if greater anti-Stokes pump power was available, the EQD could be much further reduced.

The role of both pumps in exciting the Yb3+ ions was further examined by measuring the required PASP for the laser to reach threshold. Threshold is defined as the SP power needed for lasing to occur, and it is labeled PSPth. The results are summarized in Fig. 14(c). It shows that PSPth decreases with increasing PASP. A maximum reduction of 13.8% was observed experimentally. The phenomenon can be explained as stated above; the anti-Stokes pump partly populates the upper state prior to the arrival of the Stokes pump. To corroborate the experimental results, a finite difference-method time-domain (FDTD) model was constructed and showed excellent agreement with the experimental results, details of which can also be found in [194].

The demonstration in [194] clearly shows that ASP can contribute to stimulated emission at a higher photon energy (although it cannot produce gain at a higher photon energy on its own; a Stokes pump must be added for this to happen). It is therefore meaningful to discuss applications. Since the system operated in a pulsed regime, it was suggested in [194] that a low-QD, high-power, excitation-balanced pulse amplifier is worthwhile investigating, which is discussed briefly here as an example. A modified FDTD model based on [194] was developed to simulate such a system. Specifically, PSP, PASP, the power of the signal pulse PSIG, and the upper state Yb3+ population N1 are simulated as a function of axial position z and time t. The resulting equations are:

N1z,t+Δt=N1z,t+ΔtN1z,tt+λSP σa SP+σe SPπreff 2hcPSPz,tN1z,t+λSP σa SPρπreff 2hcPSPz,t+λASP σa ASP+σe ASPπreff 2hcPASPz,tN1z,t+λASP σa ASPρπreff 2hcPASPz,t+λSIG σa SIG+σe SIGπreff 2hcPASPz,tN1z,t+λSIG σa SIGρπreff 2hcPSIGz,t

PSP/ASP/SIGz+Δz,t=PSP/ASP/SIGz,texpΓΔzN1 z,tσe SPASPSIGρN1 z,tσa SPASPSIG

where τ is the upper state lifetime, λSP, λASP, λSIG are the wavelengths for the Stokes pump, the anti-Stokes pump, and the signal, respectively, σaSP, σaASP, and σaSIG are the absorption cross-sections at the corresponding wavelengths, and, σeSP, σeASP, and σeSIG the emission cross-sections. reff is the effective fiber mode radius, h is Planck’s constant, c is the speed of light, ρ is the Yb3+ number density, and Γ is the active ion-light intensity spatial overlap integral. Table 2 summaries the values for these parameters. In the examples below, both the anti-Stokes and Stokes pump pulses are rectangular, with widths of 40 µs (tpASP) and 20 µs (tpSP), respectively, with the Stokes pump immediately following the anti-Stokes pump with no overlap, since the pulse widths are much shorter than the upper state lifetime. The signal pulse is set to come in right after the SP pulse ends and the system runs at frep = 1 kHz.

TABLE 2 Fiber constants used in simulations

τ (ms)σaSP (pm2)σaASP (pm2)σaSIG (pm2)σeSP (pm2)σeASP (pm2)σeSIG (pm2)ρ (m−3)reff(µm)Γ
1.31.7220.1810.2431.6600.3360.3641.65 × 1026100.8

First, simulations were performed to show the contribution of the anti-Stokes pump. The input signal pulse is assumed Gaussian with a full width at half maximum tSIG = 0.5 µs and a peak power PSIGmax = 20 W. The peak Stokes pump power is PSP = 20 W, and the peak anti-Stokes pump power PASP is a variable. Using Eqs. (10) and (11), N1 (z,t), PSP (z,t), PASP (z,t), and PSIG (z,t) are calculated and the active fiber length is optimized to maximize the output-signal pulse energy. The position where the output pulse energy is maximum is defined as z’. Finally, the corresponding PASP (z’,t) and PSP (z’,t) are shown in Fig. 15(a), and the corresponding PSIG (z’,t) in Fig. 15(b). For comparison, PSP (0,t), PASP (0,t), PSIG (0,t) are also shown. Several observations can be made. First, with increasing PASP, the output PSIG (and therefore the pulse energy) increases. In particular, the input pulse energy is 11.3 µJ and without ASP, the output pulse energy is 35.3 µJ, whereas with 20 W of PASP the output pulse energy increases to 75.2 µJ. Second, from Fig. 15(b), it can be observed that the output signals undergo some shaping. Specifically, with increasing PASP the peak of the output pulse occurs earlier in time compared to that of the original pulse. This can be explained by the increasing signal energy depleting the upper state more rapidly. Finally, as PASP increases, the anti-Stokes pump leakage also increases due to incomplete absorption. In a physical arrangement, this pump light could potentially be recycled. In terms of EQD, Eq. (9) can be modified by dividing both the numerator and denominator by frep, giving rise to

Figure 15.Under the conditions tpASP = 40 µs, tpSP = 20 µs, frep = 1 kHz, PSP = 20 W, PSIGmax = 20 W, tSIG = 0.5 µs (Gaussian pulse), and varying PASP: (a) the input and output pump powers versus time, (b) the input and output signal powers versus time, and (c) the Yb3+ upper state population at the input and output ends of the fiber.

EQD=QDSP×ESPabsESPabs+EASPabs+QDASP×EASPabsESPabs+EASPabs

in which ESPabs and EASPabs represent the absorbed energies. For the four values of PASP (0, 5, 10, and 15 W), the corresponding EQD is 0.909%, 0.567%, 0.413%, and 0.354%, respectively. Similar to the results in Fig. 2(b), a greater PASP helps reduce the EQD of the system.

The simulated temporal evolution of N1 (z,t) is plotted at z = 0 and z = z’ in Fig. 15(c). First, from 0 to 40 µs, it is obvious that increasing PASP is more helpful in populating the upper state. Second, at the same time setting, the input end of the fiber has a higher Yb3+ upper state population compared to the output end of the fiber. The reason is that greater pump power is available at the beginning of the fiber, which is beneficial for pumping more Yb3+ ions into the upper state. Finally, starting from 60 µs, there is a rapid decrease due to signal amplification, after which the population gradually decreases via spontaneous emission, until the next anti-Stokes pump pulse comes in. Note that the abscissa in Fig. 15(c) only extends to 75 µs, while the next ASP pulse comes in at t = 1,000 µs.

Simulations were also performed with a fixed PSP of 20 W and PASP of 15 W. The signal pulse was again assumed to be Gaussian with a width of 0.5 µs. However, PSIGmax is now variable and takes on values of 1 W, 5 W, 10 W, and 20 W. The simulated pump power, signal power, and upper state population are shown in Figs. 16(a), 16(b), and 16(c), respectively. From Fig. 16(a), it can be observed that with higher input signal power (and hence energy), the anti-Stokes pump leakage decreases. The reason is that when the signal power is higher, the upper state is more depleted, which can be seen in Fig. 16(c) starting from 60 µs. As a result, when the next anti-Stokes pump pulse arrives, more energy is needed to excite the ground-state ions, resulting in reduced leakage (in other words, greater absorption). To understand the process another way, greater signal power facilitates efficient energy transfer from the anti-Stokes pump to stimulated emission, which is the preferred process since according to Eq. (12) a larger ESAPabs results in a smaller EQD. In these four situations, the EQD is 0.380%, 0.373%, 0.364%, and 0.354% respectively, which agrees with the analysis above. For the signal, a similar pulse reshaping is observed as in Fig. 15(b). In terms of pulse energy amplification, the calculated energy gain for the four cases are 9.62 dB, 9.26 dB, 8.87 dB, and 8.24 dB. The decrease in gain with increasing input pulse energy comes from the fact that greater input pulse energy brings the system closer to saturation.

Figure 16.Under the conditions tpASP = 40 µs, tpSP = 20 µs, frep = 1 kHz, PSP = 20 W, PASP = 15 W, tSIG = 0.5 µs (Gaussian pulse), and varying PSIGmax: (a) the input and output pump powers versus time, (b) the input and output signal powers versus time, and (c) the Yb3+ upper state populations at the input and output ends of the fiber.

To conclude this section, the EBL is placed into the context of high-energy lasers. As it has been shown above, the EBL is most appropriate for pulsed lasers or amplifiers. From the perspective of power scaling, multi-mJ systems appear to be feasible. Most of the value in this laser configuration likely will be found in the reduced heat generation during the pulse amplification process. Although not yet representing a practical ceiling to power scaling, thermal lensing [54, 131] can effectively be eliminated. These results apply not only to fiber lasers, but also to bulk solid-state systems.

In conclusion, this review highlighted some of the relevant optical-based approaches that can lead to lower fiber operating temperatures. While the focus here was on Yb3+, the discussion can readily be extended to other active ions, including Tm3+ and Er3+. Fiber heating typically arises from a combination of the QD and deleterious non-radiative processes such as quenching or energy transfer to impurities. The latter processes could potentially be alleviated through careful compositional design and fiber purification. The former, representing a more fundamental limit, requires that the pump and signal wavelengths be closer together. In an example presented above, even with hefty convective water cooling, a 2 kW-pumped conventional active fiber’s temperature may rise by well over 50 °C when operating with a QD of 5.6% (and no non-radiative heating). Tenfold or more power scaling, therefore, necessitates the use of tandem pumping to drive down the total heat generated. A summary of some of the more recent work on tandem pumped lasers, which were also conceptually outlined here, was therefore provided. Another approach to reducing the QD is to retain diode pumping (such as at 976 nm) while operating the laser at shorter wavelengths. This, too, was briefly summarized here, with a key requirement being appropriate fiber design. For completeness, basic strategies for measuring active fiber temperatures were also identified.

After that, two newer approaches to optical thermal management, namely those that can annihilate phonons, were presented. Specifically, these were radiation and excitation balanced fiber lasers. With respect to the former, following the very first demonstration of ASF cooling in a silica fiber in 2020 [89], the very first radiation balanced fiber laser was demonstrated in 2021 [192]. In the radiation balanced fiber laser, one pump drives two processes. The first is ASF, which carries thermal energy away from the gain medium (since the average emission wavelength is less than that of the pump). This ASF cooling, in turn, balances the QD heating resulting from the second process: lasing at a wavelength longer than the pump. The excitation-balanced fiber laser, first demonstrated in 2021 [194], on the other hand, operates with two pumps; one above (ASP) and one below (SP) the lasing wavelength and does not make use of ASF. In this configuration, the ASP serves to populate the upper state in a way that benefits stimulated emission at a shorter wavelength. Finally, an application worthy of exploration, an excitation balanced pulse amplifier, was discussed by way of an example, demonstrating the feasibility of such a system. The RBL and EBL, and other yet undetermined approaches, specifically those that can remove phonons from the host glass, may prove to be a driving force behind a next-generation of ultra-high-power systems.

Authors are grateful for the continued support from our colleagues, collaborators, and friends, especially (in alphabetical order) Martin Bernier, Magnus Engholm, Thomas Hawkins, Jennifer Knall, Pierre-Baptiste Vigneron, and Mingye Xiong.

The authors declare no conflicts of interest.

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.

U.S. Department of Defense Directed Energy Joint Transition Office (DE JTO) (N00014-17-1-2546); Air Force Office of Scientific Research (FA9550-16-1-0383).

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### Article

#### Article

Curr. Opt. Photon. 2022; 6(6): 521-549

Published online December 25, 2022 https://doi.org/10.3807/COPP.2022.6.6.521

## Optically Managing Thermal Energy in High-power Yb-doped Fiber Lasers and Amplifiers: A Brief Review

Nanjie Yu1, John Ballato2, Michel J. F. Digonnet3, Peter D. Dragic1

1Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
2Department of Materials Science and Engineering, Clemson University, Clemson, South Carolina 29634, USA
3Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA

Correspondence to:*p-dragic@illinois.edu, ORCID 0000-0002-4413-9130
Current affiliation: Cepton Inc., San Jose, California 95131, USA

Received: May 22, 2022; Revised: September 13, 2022; Accepted: September 19, 2022

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

### Abstract

Fiber lasers have made remarkable progress over the past three decades, and they now serve farreaching applications and have even become indispensable in many technology sectors. As there is an insatiable appetite for improved performance, whether relating to enhanced spatio-temporal stability, spectral and noise characteristics, or ever-higher power and brightness, thermal management in these systems becomes increasingly critical. Active convective cooling, such as through flowing water, while highly effective, has its own set of drawbacks and limitations. To overcome them, other synergistic approaches are being adopted that mitigate the sources of heating at their roots, including the quantum defect, concentration quenching, and impurity absorption. Here, these optical methods for thermal management are briefly reviewed and discussed. Their main philosophy is to carefully select both the lasing and pumping wavelengths to moderate, and sometimes reverse, the amount of heat that is generated inside the laser gain medium. First, the sources of heating in fiber lasers are discussed and placed in the context of modern fiber fabrication methods. Next, common methods to measure the temperature of active fibers during laser operation are outlined. Approaches to reduce the quantum defect, including tandem-pumped and short-wavelength lasers, are then reviewed. Finally, newer approaches that annihilate phonons and actually cool the fiber laser below ambient, including radiation-balanced and excitation-balanced fiber lasers, are examined. These solutions, and others yet undetermined, especially the latter, may prove to be a driving force behind a next generation of ultra-high-power and/or ultra-stable laser systems.

Keywords: Anti-stokes fluorescence cooling, Fiber lasers, Tandem-pumped lasers, Thermal management, Radiation-balanced lasers

### I. INTRODUCTION

Despite the commercial availability of fiber laser systems exceeding 100 kW [1], the demand for higher brightness and power fiber laser sources continues to grow. A wide range of very good reviews have been written in the preceding decades, serving as an archive of the remarkable progress these lasers have made [29]. The evolution from just a few watts about 30 years ago [1012] required multiple parallel developments, including active fibers [1317], optical fiber components [1820], and pump lasers [2124]. Regarding fibers, a key issue that was and continues to be an obstacle is photodarkening [2528], which, over time, may result in excess absorption at the pump and signal [29] wavelengths, and consequently degradation of the output power. Another persistent issue is heating due to the quantum defect (QD), which manifests itself in many ways. First, it is responsible for transverse-mode instability (TMI): above a certain threshold power, the fundamental-mode output of a fiber becomes distorted and fluctuates, an issue that has been explained by the formation of a thermally-induced long-period index grating [3032]. Fiber heating can also lead to catastrophic damage via coating failure [33] or thermal lensing [34], the latter being driven by the thermo-optic effect. Additionally, fiber heating generally leads to a reduction in both the emission and absorption cross-sections of the active ions. This may adversely affect the gain, particularly if the change in temperature approaches 200 K [3537].

At the forefront of these heat-related issues is the quantum defect. In the quantum limit, the maximum slope efficiency a fiber laser can achieve is equal to the ratio of pump wavelength λp to signal wavelength λs, ηQ = λp / λs. The QD represents the fraction of power QD = 1 − ηQ that is lost in generating a signal photon of energy hc / λs from a pump photon of energy hc / λp. It is, therefore, intuitive to bring the pump and signal wavelengths closer to each other to decrease this source of thermal energy.

Another fundamental source of internal heat related to the laser ion’s spectroscopy is non-radiative relaxation associated with concentration quenching [3841]. When the concentration of the rare-earth ion exceeds a certain (host-dependent) limit, excited ions interact with each other, through up-conversion processes for example, leading to non-radiative relaxation of excited electrons, and therefore heating. Because the rate of concentration quenching increases rapidly with laser-ion concentration, this mechanism also limits the maximum concentration that can be doped into the fiber, in all materials, imposing the use of longer fibers, in turn exacerbating nonlinear effects. On the other hand, distributing a given total thermal energy over a longer fiber has the obvious advantage of lowering the maximum change in fiber temperature.

Similarly, as mentioned above, photodarkening can lead to increased background absorption by color centers, leading to excess heating. Again, optimization [25, 27, 28], especially with respect to the fiber material [42], has given rise to fibers with high immunity to photodarkening. Moreover, non-radiative (multi-phonon) relaxation within the laser ions [43, 44] is another path to heating. Non-radiative relaxation can be mitigated by a combination of selection of the proper laser ion, glass host, and pump wavelength. In the work reviewed here, the focus is on Yb3+, an ion that exhibits negligible non-radiative relaxation in most hosts, so that this is not an issue. Finally, non-radiating impurity absorption is another undesirable source of heat in an active fiber [45]. As discussed in the next section, modern fiber processing methods have largely eliminated these impurities as a primary concern, although they can still have a noticeable impact in radiation-balanced lasers (RBL) and amplifiers.

Owing to the large surface area-to-volume ratio of a fiber, it is not usually necessary to manage the fiber temperature when operated up to several tens of watts. At higher powers, however, active cooling methods, such as forced air and liquids, are required [46]. At the multi-kW level, it is common practice to insert the active fiber in a groove that is etched or scribed into a metal substrate across which a liquid is flowed [4749]. Such cooling systems perform very well, but they are bulky, frustrating the portability in high-power applications, and they are subject to leaks. In this context, optical cooling is classified as those methods where temperature is moderated without thermomechanical intervention (i.e., forced flow of a fluid) and includes techniques where optical quantities (such as the pump wavelength) are selected by the user to mitigate heating. While not discussed here, there also are fiber design-based approaches to improved thermal management. For example, a glass-coated or metal-coated fiber has a much higher damage threshold than a polymer-coated fiber [50]. One can then let the fiber laser operate at a higher temperature. Appropriately shaping the cladding can also give rise to a larger outer surface diameter and more efficient convective cooling [51].

The goal of this review is to highlight the main optical cooling approaches that can lower the operating temperatures of an active fiber. Since the highest power systems currently available utilize Yb-doped fibers, and Yb3+ has been so far the rare-earth ion that has produced the most efficient cooling (as relates to anti-Stokes fluorescence, ASF), this paper is limited to Yb3+, although many discussions and principles can be extended to other rare earths. The paper begins with a brief overview of optical fiber fabrication. That is followed by an exemplary set of thermal calculations for two fiber lasers: 1) a low-power laser and 2) a laser operating in the multi-kW regime. Following that, conventional low-QD fibers systems, including tandem-pumped and short-wavelength lasers, are briefly reviewed. The paper then transitions to alternative, multi-wavelength approaches to thermal management in fiber lasers, namely methods that utilize ASF, including RBLs [52]. The paper concludes with a short discussion of a new type of laser that utilizes anti-Stokes pumping (ASP).

### II. Improving Cooling with Fiber Materials

A materials approach to mitigating parasitic effects in high-power lasers and amplifiers, ranging from thermal management to optical nonlinearities, is arguably the better of the two approaches (namely mechanical versus optical) because such detrimental effects inevitably originate from light-matter interactions. Hence, management and mitigation based on materials is a more fundamental and potentially effective method [53]. However, while the periodic table offers bountiful compositional permutations, fabrication methods for high-power laser and amplifier fibers do not because of the strict low-loss requirement imposed on gain fibers to maximize fiber-laser efficiency. This requirement necessitates the use of chemical vapor deposition (CVD) methods, which, courtesy of 50 years of telecom fiber development, produce fibers of exceptional quality in terms of homogeneity, purity, and loss. However, CVD processes are fundamentally limited in the range of compositions that can be achieved due to both the availability of precursors and glass forming ranges given the time / temperature profiles involved. See, for example, Tables I and V in [42] for compositional comparisons from selected fiber fabrication methods.

Choosing and optimizing core compositions is a complex multi-variable task, especially for high-efficiency high-power fiber lasers. Each co-dopant added to the core has multiple effects, not always beneficial. The composition influences not only the optical profile of the fiber (e.g., numerical aperture), hence the mode characteristics, but also the spectroscopic, thermal, and nonlinear properties of the fiber, which are not independent of one another. For example, the spectroscopy of Yb3+ in a given composition influences the efficiency and QD of the ion, both contributing to heat generation, which then impact thermal behaviors such as thermo-optic-induced mode instabilities and thermal expansion-induced core/cladding stress and changes to the linear and nonlinear properties through the strain-optic coefficient. Accordingly, glass is not just glass, and careful selection and concentration of a co-dopant are as important as the fiber design itself. Based on these limitations and considerations, the most studied and commercially available fiber lasers are based on Yb-doped aluminosilicate and aluminophosphosilicate core compositions. In this context, the aluminum, as aluminum oxide (Al2O3), increases the refractive index relative to silica, lowers the stimulated Brillouin scattering (SBS) gain coefficient, and promotes greater solubility of the active ion (Yb3+) in the silica glass, thereby lessening concentration quenching. This latter point is especially important for optical thermal management since concentration quenching generates heat. The phosphorus, as phosphorus pentoxide (P2O5), also increases the refractive index, reduces glass viscosity (as does Al2O3 to some extent) during fabrication, and enhances the glass resistance to photodarkening [54]. Of course, there is also the additional complexity introduced through the AlPO4 join [55]. Though beyond the scope of this paper, the materials development of advanced optical fibers is a very powerful approach that offers considerable opportunities for effective and novel approaches to all-optical thermal management [56].

### III. HEAT-MANAGEMENT AND COOLING SCHEMES IN Yb3+

As is well known, the Yb3+ ion, possessing one unpaired spin in the 4f manifold [57], is a simple two-level system. Due to the lanthanum contraction [5860], the 4f shells in the rare earths are effectively shielded from their environments by the 5s and 5p shells [61,62]. This results in an energy-level diagram that appears to be much like a free-ion and therefore relatively insensitive to the host. However, the triple and quadruple degeneracies of the upper and (2F5/2) lower states (2F7/2), respectively, are still broken by the Stark splitting effect [63], giving rise to upper and lower manifolds with energetic widths that are comparable to the phonon energies found in typical laser glasses [38] (see Fig. 1). It implies that at room temperature, most sub-levels in each manifold are populated. Furthermore, the amorphous nature of the glass host broadens and can ambiguate identifying the Stark levels in these hosts [64] relative to those in crystals [65]. As discussed below, despite this shielding effect, the relative positions of these Stark components can still be significantly impacted by the host. Importantly, this means that the host can play some role in shaping both the emission and absorption spectra [66, 67], and affecting the radiative lifetime, which can have a significant influence on laser operation [68, 69] and the thermal management approaches described herein.

Figure 1. Stark energy levels for two common laser glasses: (a) Al2O3-doped and (b) P2O5-doped silica. The zero-phonon lines are roughly at the same energies in both systems [70].

The Stark manifolds of the Yb3+ ion for two relatively common laser glasses, aluminosilicates and phosphosilicates, are shown in Fig. 1 (adapted from data found in [70]). The corresponding absorption and emission cross-sections are shown in Fig. 2 [71], as well as the spectra for a fluorosilicate glass taken from [72] for comparison. Due to the nephelauxetic effect [73], the more covalent environment (aluminosilicates) produces a broader spectrum whose emission extends somewhat more deeply into the infrared. The effect of degree of covalency on an emission spectrum can be quantified through the average fluorescence wavelength λem, which are 1,007.4 nm, 998.9 nm, and 999.5 nm for the aluminosilicate, phosphosilicate, and fluorosilicate fibers, respectively. The latter two have lower emission cross-section values and therefore concomitantly longer radiative lifetimes (typically in the range of 1.3 ms to 1.5 ms [68, 70] compared with the aluminosilicates, in which the radiative lifetime is around 0.8 ms [68]).

Figure 2. Cross-section data for various Yb3+ doped glasses. (a) Measured emission and (b) absorption cross-sections of three Yb-doped glass fibers. The spectroscopic properties of the fluorosilicate and phosphosilicate glasses are quite similar and are influenced by the less covalent environment they promote to the Yb3+ ions.

Regardless of the pumping wavelength, for a given temperature the rare-earth ion’s upper state will rapidly come to the same thermal equilibrium distribution. Therefore, phonons must either be produced or annihilated in support of this process. The former is a natural result of the positive QD associated with lasing, while the latter gives rise to a negative QD and cooling of the host. This process is very fast due to the width of the manifold compared with the maximum phonon energy, as described above [38]. The optical processes relevant for the remainder of this paper are identified in Fig. 3. In Fig. 3(a), the more common process is shown wherein a pump photon drives either spontaneous or stimulated emission at a lower energy. This configuration is referred to as Stokes pumping (SP) and generates heat through a positive QD. When the pumping wavelength is longer than λem, as illustrated in Fig. 3(b), the resulting fluorescence carries thermal energy away from the gain material, giving rise to cooling. This process, referred to as ASF, therefore has a negative QD [74]. It is a form of ASP. A radiation-balanced laser (RBL) [Fig. 3(c)] makes use of ASF to offset the positive QD stemming from the lasing wavelength. These processes are discussed in more detail later. The final configuration [Fig. 3(d)] makes use of both SP and ASP to drive a single lasing process. ASP in this case is not used to generate fluorescence but rather contributes to stimulated emission.

Figure 3. Illustrations of the various inter- and intra-manifold transitions relevant to the generation and management of heat in rare earth doped fiber lasers and amplifiers. Dashed and solid arrows represent absorption and stimulated emission, respectively. The green, vertical wiggly lines represent fluorescence. The red wiggly lines correspond to phonon generation and heating, and the blue wiggly lines to phonon annihilation and cooling. Heating or cooling requires the intra-manifold movement to lower (red) and higher (blue) energies, respectively. (a) Pumping at an energy higher than the mean emission energy leads to quantum defect (QD) heating. (b) Pumping at a wavelength longer than λem leads to phonon annihilation and cooling. (c) radiation-balanced lasers (RBLs) incorporate anti-Stokes fluorescence (ASF) to offset the QD heating. (d) Excitation-balanced lasers (EBLs) make use of both Stokes pumping (SP) and anti-Stokes pumping (ASP) to drive stimulated emission. Note that signal re-absorption, where relevant, was intentionally left off these diagrams.

### IV. Modeling of Heating in Fiber Lasers

The three-dimensional temperature distribution in a fiber laser is critical to understanding laser operation and the cooling required to manage the fiber temperature in fiber lasers. This knowledge can be gained by modeling. It is important to model the longitudinal temperature distribution, which provides the location of the hottest spot(s) along the fiber and their temperature. It is also important in some applications to have access to the radial distribution, for example to understand the impact of fiber heating on its guiding properties [75]. This effect becomes more significant with increasing thermal loading, particularly when combined with active convective cooling. To calculate the fiber core temperature, one first needs to identify the optical power distributions along the fiber, the thermal processes within the fiber that drive the increase in temperature, and the mechanisms that dissipate heat away from the fiber. In this section, SP is assumed, such that the dominant source of heating is assumed to be the QD. The gain fibers are assumed to be pumped with a continuous-wave laser and convectively cooled with flowing water. Two exemplary systems are modeled to illustrate the thermal management problem from two very different perspectives, namely a low-power DBR laser, in which even small fluctuations in the temperature can result in instability in the wavelength and increased frequency noise, and a high-power double-clad fiber laser. It will be shown that in the former case, the radial temperature distribution is nearly uniform and that a determination of the core temperature alone is sufficient to model the system. A final sub-section provides very simple expression to calculate the temperature of a doped fiber pumped by Stokes or anti-Stokes in the limit of small temperature changes.

### 4.1. Three-dimensional Fiber Temperature Model

The temperature is calculated in the three regions of interest of the fiber, namely the core of radius r1, the cladding of radius r2, and the coating of radius r3. Each region has a thermal conductivity ki, where i = 1 for the core, i = 2 for the cladding, and i = 3 for the coating. In [76] it was shown that after solving the thermal conduction equation subject to the appropriate boundary conditions between the four regions (the fourth being the medium surrounding the coating), the radial temperature distribution of the core T1(r), cladding T2(r), and coating T3(r) are given by:

$T1r=T0−q1r24k1……0

$T2r=T0−q1r124k1−q1r122k2ln(rr1)……r1

$T3r=T0−q1r124k1−q1r122k2ln r2 r1−q1r122k3ln(rr2)……r2

where q1 is the heat power density (heat generated per unit volume) in the core. T0 is the temperature at the core center, expressed as

$T0=Ta+q1r122hr3+q1r124k1+q1r122k2lnr2r1+q1r122k3ln(r3r2)$

where h is the heat transfer coefficient and Ta is the temperature of the fluid surrounding the coating. The heat transfer coefficient quantifies the rate at which heat is extracted from the outer surface of the fiber, via natural convection of air or water surrounding the fiber, or a forced flow of air or water around the fiber. In the case of natural convection, this coefficient depends on the temperature difference between the fiber outer surface and the surrounding medium T3(r3) – Ta [77]. When this temperature difference is small, h is a constant; but when this difference is large, h increases with increasing temperature difference. In this last case, calculating the temperatures in (1)–(4) requires applying for example an iterative process, as done for example to generate Fig. 4 in [77].

Figure 4. Thermal analysis of the distributed-Bragg-reflector (DBR) laser. (a) Simulated radial temperature distribution of the Yb-doped fiber in the single-frequency DBR fiber laser of [82]. (b) With varying temperature of the fiber, the corresponding wavelength shift (absolute value) of the DBR fiber laser. A mode hop is observed at a temperature change near 9 K as the red-shifted mode m is replaced by m + 1 entering on the blue side of the FBG spectrum.

### 4.2. DBR Lasers

Single-frequency fiber lasers serve a wide range of applications [7880]. Among the various configurations that are routinely used, which include distributed-feedback (DFB) lasers, distributed-Bragg-reflector (DBR) lasers, and ring-cavity lasers, DBR lasers are a common choice [81]. In this section, a simulation of a low-power DBR laser is presented. The objective is to calculate the temperature profile in the gain fiber, and from this profile determine the temperature and pump-power dependences of the lasing wavelength. The specific laser that is modeled is the DBR fiber laser reported in [82]. It utilized a phosphate fiber doped with 15.2 wt.% of Yb3+ pumped at 976 nm, and it produced a maximum output power of 408 mW at 1,063.9 nm. The active fiber length was L1 = 0.8 cm and the cavity length L2 = 1.3 cm. The fiber is short enough that the pump absorption can be assumed uniform along the fiber. The dominant sources of heating are assumed to be the QD and nonradiative processes, which lead to a less-than-unity quantum conversion efficiency ηQCE. ηQCE specifies the fraction of absorbed pump photons that contribute to the desired optical process, namely laser emission. Other sources of heating, such as poor splice quality, are not considered here. In [82] pump coupling efficiency was estimated to be 85%, and an approximate ηQCE, was provided as 93% [82]. Given the output power Pout, the heat power density in the fiber core q1 can be estimated as

$q1=Ppabs​, th1− λp λem +Ppabs1−ηQCE+PoutλsλpQDπr12L1$

where λs is the laser wavelength and λp the pump wavelength. Equation (5) has three distinct terms in the numerator. The first term accounts for the QD heating associated with the absorbed pump power needed to reach threshold. As discussed above, there is a thermal equilibrium population in the upper state manifold, which is indicated by the average emission wavelength, λem. This term can be neglected when the threshold power is small compared to the pump power, as it is in the present case. The second term reflects the fact that ηQCE is less than unity; (100% − 93% = 7%) of the absorbed pump power is directly converted to heat, likely driven by quenching mechanisms. In the subsequent calculations, Ppabs is assumed to be the total pump power (as provided in [82]), multiplied by the pump coupling efficiency. The third term in the numerator is linked to the output power curves (Fig. 2(c) in [82]) and states that the useful pump power absorbed by the gain fiber is λs / λp times the output power, and of this the fraction QD is converted into heat. Dividing by the fiber core volume πr2L1 gives the heat density.

Assuming Ta = 300 K, k1 = k2 = 0.84 W/m-K for a phosphate fiber [83], k3 = 0.2 W/m-K, and h = 1,000 W/m2-K (a typical value for the flowing water cooling conditions used in [76]), the temperature distribution in the radial direction at the maximum output power is shown in Fig. 4(a). The temperature decreases radially from the center of the core to the cladding and coating, as expected. The predicted increase in the core temperature is ~23 K, whereas the temperature difference between the core center and the cladding’s outer edge is around 6.5 K. Due to the moderate numerical aperture (NA = 0.14) of the fiber, any temperature related changes to the NA will have a negligible impact on the transverse mode characteristics in comparison to the temperature-dependent phase shift.

One of the most important characteristics of a single-frequency DBR laser is the stability of its output wavelength λs. If no thermal energy is generated, the output wavelength can be expressed as

$λs=cm×FSR$

where m is the longitudinal mode selected by the laser that brings this value closest to the central wavelength of the laser’s fiber Bragg grating (FBG) (here 1,063.9 nm). The free spectral range (FSR) is related to the cavity length and the effective index neff of the core mode by FSR = c/(2neffL2). After thermal energy is generated and the laser fiber heats, two effects take place. First, the refractive index decreases due to the negative thermo-optic coefficient of the phosphate glass (−2.1 × 10−6 K−1) [84]. Second, the fiber expands (coefficient of thermal expansion is 4.0 × 10−6 K−1 [85]) physically lengthening the cavity. These two effects modify the laser wavelength in opposing directions. In the present example, a thermally induced wavelength shift of 7.7 pm is expected when operating at the maximum output power. More generally, the sensitivity of the wavelength to changes in temperature is simulated and shown in Fig. 4(b). With increasing output power and the resulting increase in fiber temperature, the output wavelength can shift up to ±13.93 pm and experiences a mode hop every 18 K in temperature change, which is undesirable in applications requiring high wavelength stability.

### 4.3. High-power Fiber Lasers

The high-power system is assumed to be cladding end pumped. Here, the pump absorption is no longer assumed to be uniform, and the pump power distribution along the fiber is taken into consideration, leading to a prediction of a three-dimensional temperature distribution. More specifically, as the pump power is depleted along the axial dimension, the thermal load and therefore the temperature both decrease along the length. The core glass is assumed to be aluminosilicate, and the active fiber geometry is chosen to be a common commercial Yb-doped fiber with the parameter values summarized in Table 1. The emission and absorption cross-sections are shown in Fig. 2 above. An idealized fiber is assumed, in which the QD is taken to be the only source of heating.

TABLE 1. Basic optical parameters of Yb-doped aluminosilicate.

Core Diameter (µm)Cladding Diameter (µm)Buffer Diameter (µm)Numerical ApertureUpper-state Lifetime (µs)Yb3+ Concentration (wt.%)
254005000.077431

A master oscillator power amplifier (MOPA)-based fiber laser setup is considered, using a 10-m length of the Yb-doped fiber mentioned above as the active medium in its final amplifying stage. Pump powers of 2 kW at 975 nm and a signal input power of 20 W at 1,030 nm (where amplified spontaneous emission (ASE) would be produced) are assumed. First, using a model based on the laser rate equations [86], the evolution along the fiber length of the pump and signals (including ASE) powers are calculated. The results are shown in Fig. 5(a). The thermal model described in Section 2.1 is then used to simulate the temperature distribution, assuming Ta = 300 K, k1 = k2 = 1.38 W/m-K, k3 = 0.2 W/m-K, and h = 100 W/m2-K (a typical value under the condition of a fan blowing air) [76]. The temperature of the core center, core-cladding boundary, cladding-coating boundary, and coating surface are plotted versus position along the fiber in Fig 5(b). The inset at the top right corner displays the radial temperature distribution at 0.25 m, where the highest temperature is experienced. The highest temperatures at the core center and the coating surface are 694.8 K and 663.2 K, respectively, which is sufficiently high to cause failure of both acrylate [87] and polyimide [88] coatings. Several obvious approaches can relieve this problem to some extent, including utilizing a larger cladding and coating, reducing the Yb concentration (to distribute the thermal energy over a longer fiber), and adopting water cooling.

Figure 5. 1,030 nm master oscillator power amplifier (MOPA) simulations. (a) Calculated pump and signal power distribution of the MOPA; (b) calculated temperature distribution along the fiber length for core center, core edge, cladding edge, and coating edge.

To illustrate the efficacy of these solutions, Fig. 6 plots the predictions of similar temperature simulations performed under different conditions. Obviously, all the approaches effectively reduce the fiber temperature. However, both increasing the cladding size and lowering the Yb concentration lead to the need for a longer Yb-doped fiber. As a result, the system may become more likely to suffer from nonlinear effects. Water cooling, on the other hand, although bulky, allows the active fiber to remain relatively shorter. Power scaling, especially for a real fiber (in which ηQCE is less than unity), therefore clearly requires either far more aggressive water cooling or alternative means to lower the QD. The latter is the main focus of this review.

Figure 6. Temperature distribution along the fiber length for core center, core-cladding boundary, cladding-coating boundary, and coating surface calculated under the same simulation conditions as in Fig. 5 except that (a) the cladding and coating radii are increased to 350 µm and 500 µm, respectively, (b) the Yb concentration is decreased to 0.2 wt.%, and (c) the fiber is water cooled (h = 1,000 W/m2-K). In all cases, the maximum temperature is reduced to below 400 K.

### 4.4. Low-power Fiber Lasers

The same heat conduction equation and boundary conditions that were used to derive the fiber radial temperature profile (1)–(4) at steady state can also be solved to predict the temporal evolution of this profile from the time the pump is turned on [77]. This evolution is useful for example to predict the temperature profile (and hence index profile of the core region) in fiber lasers and amplifiers that are pumped by short pulses. This model can also be used to calculate simply the thermal time constant of a fiber and its dependence on the fiber transverse dimensions, heat conductivity, and specific density, which can be useful to predict for example the time it takes for the temperature of a fiber to reach steady state, or to cool down to room temperature after the pump has been turned off. For example, as a useful rule of thumb, the thermal time constant of a bare silica fiber with a core diameter of 4 μm and a cladding diameter of 125 μm that is core pumped is 1.2 s. This is the time it takes for the center of the core and the cladding surface to reach 95% of their respective steady-state temperature (see Fig. 5 in [77]) after the pump has been turned on.

At low to moderate pump powers, (1)–(4) show that the radial temperature distribution of the fiber is essentially uniform, as also demonstrated in [77]. In this case, and for a silica fiber, the first two conductivity-related terms in (4) can then be neglected. The steady-state temperature at the center of the fiber, assumed to be stripped of its coating (and therefore the temperature of the surface of the cladding, since the profile is uniform) can be expressed in the simple form [77]

$T0≈T2(r2)=q1r122hr2−q1r122klnr1 r2$

where k is the thermal conductivity of the fiber, assumed to be the same in the core and the cladding. For a silica fiber, the first term in (7) strongly dominates and provides an accurate estimate of the overall temperature change of the fiber. (7) shows that the temperature rise of the fiber is inversely proportional to the heat transfer coefficient. Since q1 is the heat injected in the core per unit volume by the pump, following (5) it can be expressed in the general form q1 = hPabs/(pr12L), where Pabs is the pump power absorbed over a length of fiber L, and h is the percentage of this power that is converted into heat (by the processes modeled in (7)). (If the pump absorption is not uniform, Pabs/L can be calculated at each point along the fiber from the knowledge of the pump power distribution along the fiber). Therefore in (7) the temperature rise is independent of the radius r1 of the doped core. Also, for small temperature differences the product hr2 is independent of r2 (see Fig. 8 in [77]). As a result, the steady-state fiber temperature rise is given by the very simple expression [77]

Figure 8. Block diagram for a representative tandem pumped fiber laser. LD, laser diode; FBG, fiber Bragg gratings; CMS, cladding mode stripper. In this example, six FBG-based fiber lasers are pumped individually by semiconductor lasers. Their outputs are combined to serve as the pump for the power amplifier stage.

$ΔTss=ηPabs2πLhr2$

where again hr2 is a constant. For a fiber cooled by natural air convection, this expression gives a temperature rise of 3.13 °C for every mW of heat that is generated in the fiber core per unit length. For example, in a 1-cm fiber pumped with 1 W of pump power, of which only 5% is absorbed (50 mW), and assuming the QD is the sole mechanism that generates heat, for a QD of 4% (2 mW of heat in 1 cm) the fiber temperature rise is predicted to be 6.2 °C. Note again that these expressions are valid only for small temperature rises. They provide a convenient rule of thumb to quickly estimate the temperature of a fiber pumped at low pump powers. They are also useful in the context of optical cooling to calculate the temperature drop induced by ASF pumping in a fiber, since the fiber temperature changes are then typically quite small (a few degrees or less).

### V. Fiber Temperature Measurement Techniques

There are several ways to measure a fiber temperature. The magnitude of the anticipated temperature change of a fiber is a key factor towards the selection of the most appropriate method to measure it. The dominant form of heat transfer, such as radiative in a properly configured vacuum chamber, or convective in a water-cooled system, ultimately drives the change in fiber temperature, and therefore the required sensitivity of the temperature sensor. Suitable sensors can further be classified into external or in-situ. External sensors are physically brought into the vicinity of or in contact with the fiber, such as FBGs or thermal cameras. In-situ sensors, on the other hand, rely on a change in a physical characteristic of the laser, such as a fluorescence spectrum. This short section briefly outlines a few methods used to measure fiber temperature, including their operating principle and their accuracies.

When placed in air or water, a fiber may experience one or more of convective, conductive, and radiative heat-transfer mechanisms with its surroundings. Depending on the temperature of both the fiber and its surroundings, one of these may dominate. For example, in the case of ASF cooling, the amount of heat removed per unit volume is almost always small. When the cooled fiber is in air, convection continuously brings heat into it, which prevents the fiber temperature from decreasing far below the air temperature. The temperature difference between the fiber and the air is then small (millidegrees) [89], making its measurement more difficult. For the same reason, achieving cryogenic temperatures under such conditions is also difficult. A common solution is to place the fiber in a vacuum chamber to eliminate convective heating, as well as holding the fiber on a carefully designed low-contact mount to minimize conductive heat intake from the mount. When this is done properly, the only heat that is transferred from the fiber surroundings into the fiber is radiative heat from the walls of the chamber [90]. A recent demonstration of cooling of an optical fiber preform benefitted significantly from such a system [91]. Although the use of a vacuum is clearly not beneficial for the thermal management of high-power fiber lasers, it can still serve as part of a measurement platform that can help elucidate the sources of parasitic heating such as concentration quenching or background absorption.

### 5.1. Absorption or Emission Spectrum Measurements

The thermal population in the ground-state manifold of laser ions obeys Boltzmann distribution. As such, an increase in fiber temperature gives rise in each manifold to increased populations in sub-levels of higher energy, as illustrated in Fig. 7. This results in increased absorption at longer wavelengths, and decreased absorption at shorter wavelengths [35]. In aluminosilicates, “longer” and “shorter” are relative to ~950 nm [35]. This change in absorption results in a distortion of the absorption spectrum, distortion that can be measured to infer the temperature of the gain medium. Absorption, however, is not a practical means of monitoring fiber temperature at high power because it requires the introduction of an additional light source to carry out the measurement. Instead, the shape of either the fluorescence spectrum [3537] or the ASE spectrum [92] can be used as a gauge. In the case of fluorescence, the most prominent change with an increase in temperature is a spectral broadening due to the increased absorption at the long wavelength side of the S band. In the case of ASE, this same effect leads to a redshift of the peak wavelength. Such measurements require system calibration since the dependence of the spectrum on temperature must be known a priori. This methodology has been successfully applied to the study of ASF cooling of solids [9395]. From a practical perspective, however, the method works for relatively large changes in temperature (tens of Kelvin), but it is not sufficiently sensitive for temperature changes of less than a few Kelvin.

Figure 7. The population in the lower manifold obeys the Boltzmann distribution. When the temperature of the Yb3+ host is increased (red), there is increased population at higher energy, and a concomitant increase in the absorption cross-section at longer wavelengths. When cooled (blue), the Yb3+ acts like a four-level system across a wider range of wavelengths, including in the S-band. Upon fiber heating, the fluorescence spectrum around the zero-phonon line (shown as the green arrow) is broadened.

### 5.2. Brillouin-scattering and Rayleigh-scattering Temperature Measurements

This class of in-situ measurements utilizes either Brillouin [96] or Rayleigh [97, 98] scattering. They are, in their principle, identical to temperature measurements in distributed fiber-optic sensing systems [99]. Brillouin scattering is an acousto-optic interaction whereby an incident lightwave scatters from a Bragg-matched hypersonic acoustic wave (spontaneous scattering). The scattered and incident light waves may interfere and further drive the acoustic wave through electrostriction. The latter then induces a grating in the fiber, which efficiently reflects the incident wave (SBS). Because the grating is moving at the velocity of the acoustic wave in the fiber, the reflected wave is Doppler shifted (~10–20 GHz depending on the host glass and signal wavelength). This Brillouin shift is temperature-dependent and can be measured to obtain the temperature of the fiber core. The signal used to measure the Brillouin-scattering characteristics of the fiber must obviously not overlap with the lasing wavelength (~1 μm for Yb3+). As such, the 1.5-µm telecommunication band serves as a convenient spectral range for this ion. This signal must be injected into the gain fiber through additional components such as wavelength-division multiplexers and circulators. The first report of such a measurement was made in 2009 [100]. It has recently been used to quantify the quantum conversion efficiency in a lightly Yb-doped fiber by pumping at the zero-phonon wavelength and measuring the subsequent QD heating [101, 102]. In that case, the fiber was held in a vacuum to enhance the temperature change relative to atmospheric pressure and improve the signal amplitude, as discussed above.

Unfortunately, Brillouin-based systems can be complicated and expensive, and therefore more recently Rayleigh-based approaches have been established. This method utilizes optical frequency domain reflectometry (OFDR) technologies [103, 104]. It is the temperature-dependent Rayleigh scattering fingerprint that is now probed via the OFDR method. The probe signal is incorporated in the fiber under test using the same approach as for Brillouin-scattering temperature measurements. The main complication in making either Brillouin-scattering or Rayleigh measurements at high power is, indeed, the high power itself. Attempting to internally probe the temperature with multiple kW of power present not only endangers the requisite additional equipment and optical components, but also the user.

### 5.3. Thermal Cameras

Thermal cameras have been used to make high-spatial-resolution measurements on relatively larger samples [91, 105]. These commercial devices can have a noise equivalent temperature (or temperature resolution) on the order of tens of mK [106]. However, depending on the fiber diameter, expensive infrared magnification schemes may be required to be able to discern the temperature of the fiber from that of its surroundings [107]. Calibration of the temperature change can also be a tedious and not always reproducible process.

### 5.4. FBG Temperature Sensors

FBGs are a well-known temperature-sensing platform. Through the thermo-optic effect, slightly offset by thermal expansion, the Bragg wavelength of an FBG (i.e., the wavelength at which the grating reflectivity is maximum) increases with increasing fiber temperature. In a silica fiber for example, this wavelength shift is 13 pm/°C near 1,550 nm [108]. The FBG temperature can then be inferred with a simple measurement of the Bragg wavelength. This measurement can be carried out with an optical spectrum analyzer (OSA). A typical OSA with a resolution of 0.01 nm will then provide a relatively poor temperature resolution of 1.3 °C. Alternatively, the FBG can be interrogated with a laser tuned to the steepest portion of the FBG’s transmission spectrum; a small temperature-induced shift will then result in a large change in transmission, and a greater temperature resolution. However, most FBGs still can resolve only 0.1 °C at best [109]. The temperature-sensing FBG may be placed at a fixed location inside a fiber laser cavity to measure its temperature locally [110], although when the temperature change is small, the heat generated by the weak absorption of the intracavity laser power by the grating can increase the temperature reading and yield an erroneous measurement. Alternatively, an external FBG can be conveniently placed in physical contact with the laser fiber at any position along its length [111, 112].

The temperature resolution can be significantly improved by using a slow-light FBG. In a slow-light FBG, the index modulation is significantly higher than in a conventional FBG. As a result, the field reflectivity per unit length is much stronger, and the grating behaves like a Fabry-Perot resonator, like in a DFB laser. A slow-light FBG then exhibits sharp resonances in transmission and reflection within its bandgap, on the short-wavelength edge. These resonances can be as narrow as 50 fm [113]. When the temperature of a slow-light FBG is changed, the entire spectrum of the FBG, including resonances, shifts at the same rate as a conventional grating. But thanks to the much greater steepness of the resonance slope, the ability to resolve a small temperature change is much greater [113] than in a conventional FBG. A temperature sensor utilizing a slow-light FBG with a noise of ~0.5 mK and a drift of only ~2 mK/minute has been demonstrated [114]. Such a sensor can therefore discriminate between a fiber laser that is running slightly above room temperature from one that is running slightly below, even by a few mK. This is critical to determine whether a fiber laser operating near the zero-phonon line is actually cooled. This sensor was instrumental to the first demonstration of ASF cooling of a silica fiber [89].

### VI. Low QD via Judicious Pump and Signal Wavelength Selection

A key approach to reducing the heat load on the active fiber in a fiber laser is to reduce the QD. For a conventional system, it involves bringing the pump and signal wavelengths closer together. To this end, in Yb-doped silica there is great flexibility in selecting a pump source with a wavelength that covers most of the broad pump band, namely either longer wavelength pumping (above 1 µm) or short-wavelength laser operation. Regarding long-wavelength pump sources, there is considerable on-going work targeting InGaAs materials [115], but the technology has not yet matured sufficiently to enter the commercial mainstream. Therefore, long-wavelength pumps currently come in the form of fiber lasers, thereby defining a class of lasers referred to as “tandem-pumped fiber lasers” [116, 117]. Regarding short-wavelength pumps, efficient, high-power and high-brightness commercial diode lasers are available in the 915-nm to 980-nm range [118, 119]. Short-wavelength pump light can also be obtained from Yb-doped fiber lasers pumped near 975 nm, although they require careful optimization [120] because these lasers tend to be less efficient owing to the higher absorption at short laser wavelengths. This section briefly outlines approaches using either semiconductor lasers or fiber lasers as the pump source.

### 6.1. Tandem-pumped Lasers

In a high-power, low-QD application, laser diodes, usually at 976 nm, pump relatively shorter wavelength fiber lasers, typically in the range of 1,015 nm to 1,020 nm. These lasers, in turn, pump another fiber laser that produces a longer wavelengths, typically above 1,030 nm. Since the pump and signal wavelengths differ by only 10–20 nm, the QD of this final stage of the laser is very small. Figure 8 shows a block diagram for a representative tandem-pumped fiber laser. In this case, six fiber lasers are pumped by wavelength-stabilized semiconductor lasers at 976 nm. These six lasers pump the last amplifier stage, which produces a multi-kW, and often single mode [1], or diffraction-limited [121], output. The first stage (976 nm to 1,015 nm) represents a QD of 4% (with aggregate thermal energy distributed across all six pump lasers), while the second stage (1,015 nm to 1,030+ nm) can have QD values under 2%. In this scheme, the thermal energy is distributed relatively evenly across several laser and (or) amplifier subassemblies [4, 121].

The semiconductor lasers that drive the fiber laser-based pumps possess the lowest brightness in the system. Therefore, the active fiber’s pump-cladding diameter and its numerical aperture limit how much power can be obtained from them, since this sets the maximum pump power that can be coupled into the fiber. Fiber lasers can enhance the pump brightness by several orders of magnitude as pump power is converted to signal in the core. As a result, there is far more flexibility in the cladding geometry when pumped with sources having much greater brightness than semiconductor lasers. In principle, nonlinearities and fiber damage aside, power scaling is then limited only by the number of fiber laser pumps and stages one is willing to construct, although the entire laser system can then become somewhat daunting as its complexity increases.

There have been a wide range of developments in tandem-pumped Yb-doped fiber lasers in the past decade, focusing on several different aspects of the system. Much of the work has targeted short-wavelength lasers as pump sources [122129]. Since the absorption cross-section of Yb3+ in the range of 1,015 nm to 1,020 nm depends on the host, and since it is roughly 25 to 50 times lower than around 976 nm, longer active fiber lengths are required, and nonlinearities such as stimulated Raman scattering (SRS) [130] can become problematic. Power scaling may also lead to catastrophic damage, for example from thermal lensing [131]. As a result of these investigations, significant progress has been made toward understanding and mitigating SRS [132, 133] through fiber designs that enhance mode size and balance absorption in cladding-pumped lasers [134136]. Another approach to suppressing SRS includes adding wavelength-selective filters such as FBGs to attenuate the Raman signal [137139]. Tandem-pumped laser configurations have been shown, thanks to reduced QD heating, to have less susceptibility to TMI [140] and reduced photodarkening relative to diode-pumped lasers [126, 141, 142]. Therefore, low-QD tandem-pumped configurations offer several practical operational advantages. While few 10-kW, diffraction-limited systems have been described [1, 143], several multi-kW demonstrations have been reported [133, 144]. Pulsed operation has also been investigated, but not nearly as thoroughly as continuous-wave systems [145147].

### 6.2. Short-wavelength Lasers

Analogous to the gain spectrum of Er-doped fiber amplifiers, the Yb3+ gain spectrum can be divided into a short (S, less than 1,060 nm), a center (C, 1,060 nm to 1,130 nm), and a long (L, greater than 1,130 nm) wave bands [148]. As discussed above, S-band lasers can serve as pumps in tandem-pumped fiber lasers. Lasing at wavelengths less than 980 nm usually is achieved by pumping at 915 nm [149151], corresponding to a QD in the range of 6 to 7%. As a result, longer wavelength pumping is of greater interest in reducing the QD. From a spectroscopic standpoint, both phosphosilicate [152] and fluorosilicate [72] fibers have relatively flat absorption spectra on the short-wavelength side of the zero-phonon line (see Fig. 2). This feature enables longer wavelength pumping (~960–970 nm versus 915 nm as is typical in aluminosilicate fibers) to achieve lasing below around 980 nm, thereby illuminating one path to reducing the QD. Such short-wavelength lasing, however, is challenging due to strong competition from ASE at longer wavelengths (~1,030 nm), which tends to deplete the gain.

Utilizing wavelength-stabilized pumps [153] near 976 nm, on the other hand, and lasing at 1000 nm, gives rise to a QD of 2.5%. Capitalizing on this concept, a core-pumped Yb-doped laser with a very low QD (≤0.5 %) was demonstrated, but it exhibited a rather low slope efficiency [154]. Recently, a demonstration of a high-efficiency, less-than-1%-QD core-pumped fiber laser based on a fluorosilicate glass was reported [155]. In that work, two sets of pump and signal wavelengths were selected (976.6 nm/985.7 nm and 981.0 nm/989.8 nm). Scaling this result to a cladding-pumped geometry can be challenging, again mainly due to ASE at longer wavelengths. This requires careful fiber design and selecting the appropriate fiber length to prevent both ASE buildup and signal re-absorption [120, 156, 157]. That said, a systematic study of lasing throughout the entirety of the S-band, and below 1,000 nm in particular, is still lacking.

A simulation of such a high-power S-band laser is performed as an example. The Yb-doped fiber (in the final amplifying stage) is assumed to have a length of 10 m and the same parameters as in Table 1, except that the lifetime and cross-section values are assumed to be those of the phosphosilicate fiber found in [71]. A pump power of 2 kW at 975 nm and a signal input power of 20 W at 1,000 nm are assumed. The effect of ASE on the gain is also taken into consideration in the laser rate equations. First, the evolution along the fiber length of the pump, signal, and ASE powers are calculated and shown in Fig. 9(a). From the result, it can be observed that the signal power is maximum at a position of approximately 4 m. Further along the fiber, there is strong competition from ASE, becoming the dominant process at positions greater than about 5 m since in that region the signal is mostly re-absorbed. This trend observed here agrees with the one reported in [155].

Figure 9. Short wavelength master oscillator power amplifier (MOPA) simulations. (a) Pump and signal power distribution of the MOPA, and (b) temperature distribution along the fiber length for core center, core edge, cladding edge, and buffer edge. The sharp increase in temperature at around 5 m results from the large quantum defect (QD) associated with signal reabsorption and the buildup of amplified spontaneous emission (ASE).

Then, using the model described in section 2.1, with the assumption of Ta = 300 K, k1 = k2 = 1.38 W/m-K, k3 = 0.2 W/m-K, and h = 100 W/m2-K (forced air cooling), the predicted temperatures of the core center, core-cladding boundary, cladding-coating boundary, and coating surface are plotted in Fig. 9(b) as a function of position along the fiber. Along the first few meters of fiber, the trend is similar to that in Fig. 5(b), a rapid increase in temperature near the fiber input and a steady decline further along the fiber as the pump is absorbed. However, under the same cooling condition (h = 100 W/m2-K), the peak temperature at the coating surface drops from 663.2 K in Fig. 5(b) to 347 K in this S-band laser, a significant decrease that is beneficial to reducing thermal-related problems.

### 7.1. ASF Cooling and Radiation-balanced Lasers

As pointed out earlier, ASF cooling extracts relatively small amounts of power per unit volume [74]. Therefore, in addition to the heat generated by the QD, any number of other undesirable exothermic effects can incidentally inject heat into the sample and either partially negate or overwhelm the heat extracted by ASF. The two dominant exothermic mechanisms in Yb3+ are absorption of pump and/or fluorescence photons by impurities [45], and concentration quenching [158].

Impurity absorption is minimized by using high-purity precursors to fabricate the sample [159, 160]. The CVD methods employed to fabricate silica-based optical fibers is ideal in this regard because they afford near-intrinsic levels of purity and, hence, very low levels of impurities and low absorptive losses. However, even with low extrinsic (impurity) losses, heat can be generated in a rare-earth-doped glass through energy transfer, followed by non-radiative relaxation.

Concentration quenching is a well-known mechanism in which the energy of an electron in the excited state of an active rare-earth ion is transferred to another ion, which relaxes non-radiatively and releases heat. This energy transfer can occur to either an impurity present in the glass, such as OH- or a heavy-metal ion, or another Yb ion in its excited state. In the case of transfer to an impurity, for all common impurities the level that is excited by this energy transfer is strongly non-radiatively coupled to the ground state, so that the excited electron quickly relaxes non-radiatively to the ground state, thereby exciting phonons and heat [158]. Regarding the second mechanism, when two Yb3+ ions in the excited state are close by, one ion will donate its energy to the other, thereby exciting it to a virtual level, from which it will relax back to its excited state non-radiatively, again exciting phonons in the process. For both processes, the probability of energy transfer increases rapidly with the ion concentration, which limits the number of heat engines that can be doped into a given volume, and by the same token the amount of heat that can be extracted per unit time from this volume via ASF.

The susceptibility of a particular host to quenching is quantified by its critical quenching concentration Nc, the concentration for which the average distance between laser ions is such that the probability of non-radiative energy transfer is the same as the probability of spontaneous emission [158]. The critical quenching concentration for Yb3+ is typically one order of magnitude lower in silica than in crystals or in fluoride hosts [41, 161]. This is due to a combination of factors, including the comparatively low solubility of Yb2O3 in silica, which results in the formation of Yb clusters [162]. In a Yb cluster, the mean distance between Yb ions is small, which increases the rate of energy transfer between excited ions.

ASF cooling was first proposed in 1929 [163] yet not demonstrated until 1995, in a bulk sample of Yb:ZBLANP [164]. Since then, many hosts and trivalent rare-earth ions have been successfully cooled by this technique [89, 165173]. The most efficient and popular ion has been Yb3+ [168, 174, 175] for its simpler electronic structure generally devoid of non-radiative relaxation processes, followed by Tm3+ [171, 176178], Er3+ [170, 179], and Ho3+ [180]. The most common hosts are crystals, which are generally free of impurities and therefore of extraneous heating due to absorption of the pump by impurities, as well as fluorides, which can generally be more heavily doped than oxides and therefore offer greater cooling per unit volume. Most experiments were performed in bulk samples [169, 171174, 181], because a greater volume can be optically pumped and more energy extracted by ASF, leading to lower absolute temperatures. Most demonstrations were also performed in a vacuum chamber to minimize convective heat transfer between the sample and the surrounding air and maximize the sample temperature reduction. In 2015, cryogenic temperatures were achieved using highly purified YLiF4 crystals highly doped with Yb3+ [159]. In addition, cooling was also observed in optical fibers, which is generally more difficult due to the greater surface to volume ratio (greater convective heating from the surrounding air) and smaller doped volume (smaller total number of heat engines performing the cooling). Temperature changes of −65 K were reported in short sections of Yb-doped ZBLANP fibers [93], and −30 K in Tm-doped tellurite fibers [177], both in a vacuum. All fibers were multimode [93, 167, 175, 177, 182184] which makes it easier to achieve lower absolute temperatures compared to single-mode fibers, which have an even smaller volume of doped material.

Two RBLs have also been reported, both in a highly doped Yb:YAG crystal [185, 186]. In the earliest demonstration (2010), the gain medium was a highly doped Yb:YAG rod end-pumped with an array of high-power Yb-doped silica fiber lasers at 1,030 nm [186] that induced both gain at 1,050 nm and ASF cooling. The gain medium had a large dimension (3 × 120 mm) and the pump beam a large transverse size to maximize the extracted heat [186]. This laser produced 80-W of output power while maintaining radiation-balanced operation (zero average temperature change along the crystal). More recently (2019), a second radiation-balanced laser was demonstrated using a Yb:YAG disk [185]. The disk was pumped at 1,030 nm to produce 1 W of output power at 1,050 nm.

### 7.2. Recent Demonstrations of Radiation-balanced Silica Fiber Lasers and Amplifiers

The first internally cooled fiber amplifier, reported in 2021 [187], capitalized on this major innovation. The gain medium was the best performing silica fiber reported in [188]. The fiber had a core with a 21-µm diameter and a numerical aperture (NA) of 0.13, so that it was slightly multimoded at the signal (1,064-nm) and pump (1,040 nm) wavelengths. The core was doped with 2.0 wt.% Al to reduce concentration quenching, and with 2.52 wt.% Yb, or 1.93 × 1026 Yb ions/m3. From the measured emission spectrum of the fiber, the mean fluorescence wavelength, measured from the fluorescence-emission spectrum of the fiber, was 1,003.9 nm. This fiber exhibited significant cooling thanks in part to the sizeable energy difference between the fluorescence and the pump photons, in part to the relatively short upper-state lifetime of the Yb ions (765 µs), and in part to its high concentration and high Nc, inferred to be 1.20 × 1027 Yb ions/m3. Yb from cooling measurements [89, 189].

Turning to the amplifier configuration, the 1,040-nm pump (a commercial cw fiber-pigtailed laser) was combined to the 1,064-nm seed (a semiconductor laser) through a 90/10 fiber splitter. The splitter output that carried 90% of the pump power and 10% of the seed power was spliced to the input of the Yb-doped silica fiber. The other splitter output was used as a calibration tap to measure the power launched into the fiber amplifier. At the amplifier output, the unabsorbed pump power was eliminated with a long-pass filter, and the signal was sent to a power meter.

The temperature of the Yb-doped fiber was measured at seven locations using a slow-light FBG sensor (see Section 5.4). At each measurement location, a ~10-cm length of the Yb-doped fiber was stripped of its jacket to prevent re-absorption of the radially escaping ASF. The stripped section was placed in contact with the FBG sensor. 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 (a few seconds) reach thermal equilibrium [77].

Figure 10 plots the measured longitudinal temperature profile of the amplifier fiber when it was seeded with 3 mW at 1,064 nm for increasing pump power. When the amplifier fiber length was 2.74-m [Figs. 10(a)10(c)], the temperature remained below room temperature at all seven locations along the fiber and at all three pump powers. With 1.12 W of pump power [Fig. 10 (a)], the measured small-signal gain was 5.7 dB. At low pump powers (below saturation), the Yb ions are insufficiently excited, resulting in low ASF and low extracted heat. At large pump powers (well above saturation), excitation of the Yb ions is saturated (maximum) and the cooling rate is maximum. While the pump power in excess of the saturation power contributes very little to cooling, it is still absorbed by impurities. This process is essentially unsaturable and increases heating in proportion to this additional pump power. As a result of these two opposing effects, there is an optimum pump power that maximizes the extracted heat per unit length. Simulations using a model of ASF cooling in a fiber [190] predict that the optimum pump power for this fiber is 510 mW. When the input pump power was 1.12 W, the residual pump power at the output of the amplifier fiber was only 80.2 mW. Consequently, the negative temperature change is smaller near the input end, where the pump power is above 510 mW. It is also smaller near the output end, where it is below this optimum value. The lowest temperature is observed in the middle of the fiber where the pump power is near the optimum value.

Figure 10. Measured temperature change versus position along the fiber amplifier, and simulated dependencies using the model based on [191] for (a)–(c) a 2.74-m, and (d) a 4.35-m amplifier fiber.

When the launched pump power was increased to 1.38 W, the gain increased to 9.1 dB. As expected, the negative temperature change [see Fig. 10(b)] at the fiber input was now smaller than with 1.12 W because the input pump power was further above the 510-mW optimum value. On the other hand, the pump power at the output end of the fiber was now higher (154 mW). This value being closer to the optimum, that end of the fiber experienced a larger negative temperature change than with 1.12 W of pump. The trend continued when the pump power was increased to 1.64 W [Fig. 10(c)]: cooling decreased near the input end and increased near the output end, where the residual pump power was now 247 mW. The gain in this case increased 11.4 dB.

To further increase the gain, the pump power was increased to 2.62 W and the length of the amplifier was increased to 4.35 m, the calculated value that maximizes the gain for this power. This resulted in 16.9 dB of gain, while the average temperature change remained negative [see Fig. 10(d)]. The higher pump power resulted in a positive temperature change at the input end, but past the first ~100 cm the pump power was sufficiently attenuated, and the fiber temperature was below room temperature.

Figure 10 also plots as solid curves the fiber temperature predicted by the model of a radiation-balanced fiber laser described in [191], but with the cavity removed to simulate this fiber amplifier. All the fiber parameter values needed for these simulations were either measured or inferred from fits to independent cooling and absorption measurements. Thanks to this comprehensive characterization, no fitting parameters were needed to generate the solid curves in Fig. 10. For each pump power and length, the measured temperatures agree well with simulations. From the model curves, the average temperature change is −107 mK for 1.12 W of input pump power, −105 mK for 1.38 W, −93 mK for 1.64 W, and −24.4 mK for 2.62 W.

This work demonstrated that the seemingly small amount of cooling exhibited in fibers is sufficient to negate the heating induced by significant amplification of a seed signal. The obvious next step, now that a significant gain had been observed, was to attempt demonstrating a cooled fiber laser, which was accomplished shortly after [192]. The maximum gain of the cooled fiber was certainly high enough (~19 dB) to reach threshold, but it remained to be seen whether the signal intensity circulating in the laser resonator was not too high to cause substantial heating of the fiber and negate the cooling effect of ASF. The model of [191] showed, among other important trends, that in order to maximize cooling the transmission of the resonator’s output coupler must be as low as possible, which maximizes the resonator loss, and therefore the gain at and above threshold, and hence the population inversion, to which the amount of heat extracted by ASF is proportional. The other benefit of using a low output coupler transmission is that it also reduces the signal intensity circulating in the resonator, and hence reduces also the extraneous heat generated by absorption of this intensity by impurities.

The fiber laser diagram is depicted in Fig. 11. The gain fiber was the same Yb-doped silica fiber used in the fiber amplifier. The 1,065-nm resonator was formed by two FBGs, a high reflector (100% power reflection) and an output coupler with an 8% power reflection. Rather than splicing them directly to the gain fiber, they were each spliced to a short length of SMF-28 fiber, and each length of SMF-28 fiber was spliced to the ends of the Yb-doped fiber. Because the gain fiber has a larger core (21-µm diameter) than the HI-1060 fiber in which the FBGs were written (6-µm diameter), the splice loss between these two dissimilar fibers would have been fairly high. The role of these two intermediary lengths of SMF-28 fiber (9-µm core diameter) was to provide a more gradual match between the mode size of the FBG and gain fibers and reduce the splice loss. 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. The length of the gain fiber (2.64 m) was chosen so that at least 85% of the launched pump power was absorbed. The fiber laser was core-pumped at 1,040 nm through the high-reflection grating (see Fig. 11). A 10% fiber tap coupler was spliced between the pump and the high-reflectivity FBG to monitor the spectrum of the pump laser and ensure that it did not lase at 1,065 nm due the high-reflectivity FBG. At the laser output, a long-pass filter removed the residual pump power and passed the signal to a power meter.

Figure 11. Simplified diagram of a Yb-doped fiber laser internally cooled by anti-Stokes fluorescence. Upper portion of the diagram (in purple and green, enclosed in the solid box) is the fiber laser. Lower portion (in blue, enclosed on the dashed box) is the closed-loop temperature sensor utilizing a slow-light fiber Bragg grating (FBG) that was used to measure the temperature of the Yb-doped fiber at various points along its length.

The measured output power of the fiber laser is plotted as a function of launched pump power in Fig. 12. The threshold was ~1.07 W, which is high because of the high transmission of the output coupler and the relatively high loss at the four intra-cavity splices. As expected, above threshold the output power increased linearly with pump power. The laser output was in the TEM00 mode, since the higher order modes were filtered out by the SMF-28 and HI-1060 fibers spliced to the output end. This filtering caused only slight fluctuations in the output power (~5%) due to variations in the amount of power coupled to the higher order modes along the Yb-doped fiber.

Figure 12. The laser output power measured as a function of the launched pump power, along with a linear fit to the data. The color gradient is a pictorial representation of the average temperature change along the length of the gain fiber.

The temperature of the gain fiber was measured at eight approximately evenly spaced locations along its length, and at four different pump powers. For a given pump power, the fiber was found to be warmest at the pump input end and cooled monotonically more toward the pump output end. For the lowest pump power (1.22 W), the transition to a temperature below ambient took place ~1 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 optimum power that produces maximum cooling discussed in the previous section, calculated to be ~420 mW for this fiber. Second, the higher pump power corresponds to greater gain, and the generation of more Stokes phonons (more heating). Third, this region 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, the pump is attenuated and the gain saturates, which lessens these heating effects and ASF cooling dominates. The average temperature of the fiber calculated from these measurements for each pump power was used to calibrate the vertical scale on the right of Fig. 12. It shows that below threshold and up to an output of 114 mW, the gain fiber’s average temperature remained below room temperature. Above 114 mW, the fiber gradually warmed up above room temperature.

The data was fit to a model of a radiation-balanced fiber laser [191]. Here too, all 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 [161]. This fit gave a round-trip loss for the cavity of 20.6 dB, including of 11 dB from the transmission of the output coupler. The rest of the loss was assigned to 2.4 dB per pair of splices per pass, in good agreement with the value calculated from the modal overlap between the two pairs of fibers (2.2 dB). Using these values of the loss in the model gave the solid curve plotted in Fig. 12, which shows great agreement with the measured data. The slope efficiency was 41%, about half as much as typical commercial silica fiber lasers. In future iterations, the slope efficiency and the threshold can be significantly improved by essentially eliminating the splice losses by fabricating the FBGs directly in the gain fiber.

To complete this section, a few comments on power scaling are provided. First, fiber lasers and amplifiers operating in the deeply saturated regime are naturally very efficient. Indeed, this is one of the more attractive benefits of waveguide lasers. Therefore, it is challenging to configure the system to produce enough spontaneous emission to balance heating. A promising approach to solving this problem in double-clad fibers is to decouple the laser from the cooler, for example, by adding active dopants to both the core and inner (pump) cladding [191, 193]. Excited ions in the core contribute to stimulated emission and light amplification/lasing, while fluorescence from the pump cladding cools the whole structure. Recent modeling results [191] indicate that greater than 100 W, with full radiation-balancing, can be generated from such a laser using Yb in both the core and the cladding, and bidirectional pumping. Aside from background loss, drawbacks to this approach, included in the recent modeling, are the fluorescence capture coefficient of the pump cladding, leading to the reabsorption of fluorescence and subsequent heating, and ASE. It is important to point out that full radiation balancing may not be necessary in a real system; just a small amount of cooling can go a very long way, even if there is net heating in the active fiber. For example, consider the tandem pumped systems described above. When pumped at 1,017 nm, they too produce ASF. If the relative abundance of fluorescence can be increased even slightly, this could offset some heating in multi-kW systems.

### 7.3. Excitation-balanced Laser

In the RBL discussed above, one pump drives two simultaneous processes: lasing (at a longer wavelength) and ASF, wherein cooling through the latter offsets, or balances, the heat generated through the former. However, to achieve significant cooling, a large fraction of the absorbed pump power must contribute to fluorescence, and therefore does not contribute to gain—the useful “product” of a fiber laser or amplifier. Very recently, an alternate approach to balanced thermal management in Yb-doped fiber lasers has been demonstrated, in which the AS pump contributes to laser emission rather than to ASF [194]. The schematic for the EBL can be found in Fig. 3(d). Two pumps, one an anti-Stokes pump and the other a Stokes pump, both drive lasing. The representative experimental setup described in [194] is shown in Fig. 13(a). The AS pump is launched first and populates the upper state, but it does not achieve inversion (gain) for the signal, since it has a shorter wavelength. The Stokes pump is launched second, and its role is to complete the pumping process and bring the upper state population to threshold. The cooling is produced by the AS pump, according to the same principle as ASF cooling. The main difference, and the beauty of this technique, is that ASF is considerably weaker—most of the thermal energy is now extracted by the signal (a useful output) instead of by ASF (a wasted output).

Figure 13. Basic excitation-balanced lasers (EBL) configuration. (a) Schematic of the experimental setup in [194]. The Stokes pump (SP) and anti-Stokes pump (ASP) are pulsed and combined into the laser cavity via a coupler. (b) Representation of the relative timing of the two pumps. The pulse width is tp and the two pulses overlap for a time equal to tpdt.

In the experimental laser based on this principle reported in [194] and depicted in Fig. 13(a), the S and AS pumps provided output wavelengths of λSP = 976.6 nm and λASP = 989.6 nm, respectively. The Stokes pump was a commercial fiber-pigtailed laser diode, while the anti-Stokes pump was an FBG-based fiber laser described in [195]. Both pumps’ amplitudes were pulsed and combined into the laser cavity (purple dashed box) via a 3-dB coupler. The core-pumped laser cavity was defined by a pair of FBGs at λL = 985.7 nm and a segment of Yb-doped fluorosilicate fiber (see Section III). The timing between the two pumps was controlled by a multi-channel digital delay/pulse generator. An illustration of the time sequence is shown in Fig. 13(b). The pulse width for both pumps is tp, the time difference between the rising edges of the two pump pulses is dt, and the repetition rate is frep. The peak powers for Stokes and anti-Stokes pumps are noted as PSP and PASP, respectively. The set of parameter values presented in [194] was tp = 1 ms, dt = 0.8 ms, and frep = 400 Hz. The laser will behave differently as tp, dt, and/or frep are modified, and some optimization of these parameters will be needed in practice. However, to summarize it was shown that for long pump pulse durations (comparable to the upper state lifetime), a short temporal overlap, namely where tpdt ≠ 0 is beneficial.

The pump power was measured at the pump check point [see Fig. 13(a)], and the output power was measured at the laser output. The results are presented as the average laser output power PL versus the average launched anti-Stokes pump power PASP for different average launched Stokes pump power PSP [Fig. 14(a)]. Positive slopes were observed for all the cases, meaning that for the same PSP increasing PASP produced more laser output power, giving direct evidence that the anti-Stokes pump had contributed to stimulated emission. Linear fits to each data set disclosed a maximum slope efficiency of 38.3%. Furthermore, the fact that the anti-Stokes pump contributed to laser emission indicated that phonons had been extracted from the fiber, therefore reducing the overall QD of the system. To quantify this, an effective quantum defect (EQD) was defined to be

Figure 14. Results obtained with the first fiber laser-based excitation-balanced lasers (EBL). (a) Average laser output power (PL), (b) effective quantum defect (EQD), and (c) powers required from the SP to reach threshold (PSPth) measured as a function of PASP, for different values of PSP.

$EQD=QDSP×P¯SPabsP¯SPabs+P¯ASPabs+QDASP×P¯ASPabsP¯SPabs+P¯ASPabs$

where QDSP = 1 − λSP / λL, QDASP = 1 − λASP / λL, and PSPabs and PASPabs are the absorbed pump powers from the Stokes and anti-Stokes pump, respectively. Using Eq. (8), the EQD values for all the data points in Fig. 14(a) were calculated and shown here in Fig. 14(b). As a starting reference point, when PASP was set to zero, EQD = QDSP = 0.91% for the presented case. With increasing PASPabs, the EQD was found to gradually decrease. For the maximum available powers from the two pumps, the EQD decreased by 13.2% from QDSP. Modeling results indicates that if greater anti-Stokes pump power was available, the EQD could be much further reduced.

The role of both pumps in exciting the Yb3+ ions was further examined by measuring the required PASP for the laser to reach threshold. Threshold is defined as the SP power needed for lasing to occur, and it is labeled PSPth. The results are summarized in Fig. 14(c). It shows that PSPth decreases with increasing PASP. A maximum reduction of 13.8% was observed experimentally. The phenomenon can be explained as stated above; the anti-Stokes pump partly populates the upper state prior to the arrival of the Stokes pump. To corroborate the experimental results, a finite difference-method time-domain (FDTD) model was constructed and showed excellent agreement with the experimental results, details of which can also be found in [194].

The demonstration in [194] clearly shows that ASP can contribute to stimulated emission at a higher photon energy (although it cannot produce gain at a higher photon energy on its own; a Stokes pump must be added for this to happen). It is therefore meaningful to discuss applications. Since the system operated in a pulsed regime, it was suggested in [194] that a low-QD, high-power, excitation-balanced pulse amplifier is worthwhile investigating, which is discussed briefly here as an example. A modified FDTD model based on [194] was developed to simulate such a system. Specifically, PSP, PASP, the power of the signal pulse PSIG, and the upper state Yb3+ population N1 are simulated as a function of axial position z and time t. The resulting equations are:

$N1z,t+Δt=N1z,t+Δt−N1z,tt+−λSP σa SP+σe SPπreff 2hcPSPz,tN1z,t+λSP σa SPρπreff 2hcPSPz,t+−λASP σa ASP+σe ASPπreff 2hcPASPz,tN1z,t+λASP σa ASPρπreff 2hcPASPz,t+−λSIG σa SIG+σe SIGπreff 2hcPASPz,tN1z,t+λSIG σa SIGρπreff 2hcPSIGz,t$

$PSP/ASP/SIGz+Δz,t=PSP/ASP/SIGz,texpΓΔzN1 z,tσe SPASPSIG−ρ−N1 z,tσa SPASPSIG$

where τ is the upper state lifetime, λSP, λASP, λSIG are the wavelengths for the Stokes pump, the anti-Stokes pump, and the signal, respectively, σaSP, σaASP, and σaSIG are the absorption cross-sections at the corresponding wavelengths, and, σeSP, σeASP, and σeSIG the emission cross-sections. reff is the effective fiber mode radius, h is Planck’s constant, c is the speed of light, ρ is the Yb3+ number density, and Γ is the active ion-light intensity spatial overlap integral. Table 2 summaries the values for these parameters. In the examples below, both the anti-Stokes and Stokes pump pulses are rectangular, with widths of 40 µs (tpASP) and 20 µs (tpSP), respectively, with the Stokes pump immediately following the anti-Stokes pump with no overlap, since the pulse widths are much shorter than the upper state lifetime. The signal pulse is set to come in right after the SP pulse ends and the system runs at frep = 1 kHz.

TABLE 2. Fiber constants used in simulations.

τ (ms)σaSP (pm2)σaASP (pm2)σaSIG (pm2)σeSP (pm2)σeASP (pm2)σeSIG (pm2)ρ (m−3)reff(µm)Γ
1.31.7220.1810.2431.6600.3360.3641.65 × 1026100.8

First, simulations were performed to show the contribution of the anti-Stokes pump. The input signal pulse is assumed Gaussian with a full width at half maximum tSIG = 0.5 µs and a peak power PSIGmax = 20 W. The peak Stokes pump power is PSP = 20 W, and the peak anti-Stokes pump power PASP is a variable. Using Eqs. (10) and (11), N1 (z,t), PSP (z,t), PASP (z,t), and PSIG (z,t) are calculated and the active fiber length is optimized to maximize the output-signal pulse energy. The position where the output pulse energy is maximum is defined as z’. Finally, the corresponding PASP (z’,t) and PSP (z’,t) are shown in Fig. 15(a), and the corresponding PSIG (z’,t) in Fig. 15(b). For comparison, PSP (0,t), PASP (0,t), PSIG (0,t) are also shown. Several observations can be made. First, with increasing PASP, the output PSIG (and therefore the pulse energy) increases. In particular, the input pulse energy is 11.3 µJ and without ASP, the output pulse energy is 35.3 µJ, whereas with 20 W of PASP the output pulse energy increases to 75.2 µJ. Second, from Fig. 15(b), it can be observed that the output signals undergo some shaping. Specifically, with increasing PASP the peak of the output pulse occurs earlier in time compared to that of the original pulse. This can be explained by the increasing signal energy depleting the upper state more rapidly. Finally, as PASP increases, the anti-Stokes pump leakage also increases due to incomplete absorption. In a physical arrangement, this pump light could potentially be recycled. In terms of EQD, Eq. (9) can be modified by dividing both the numerator and denominator by frep, giving rise to

Figure 15. Under the conditions tpASP = 40 µs, tpSP = 20 µs, frep = 1 kHz, PSP = 20 W, PSIGmax = 20 W, tSIG = 0.5 µs (Gaussian pulse), and varying PASP: (a) the input and output pump powers versus time, (b) the input and output signal powers versus time, and (c) the Yb3+ upper state population at the input and output ends of the fiber.

$EQD=QDSP×ESPabsESPabs+EASPabs+QDASP×EASPabsESPabs+EASPabs$

in which ESPabs and EASPabs represent the absorbed energies. For the four values of PASP (0, 5, 10, and 15 W), the corresponding EQD is 0.909%, 0.567%, 0.413%, and 0.354%, respectively. Similar to the results in Fig. 2(b), a greater PASP helps reduce the EQD of the system.

The simulated temporal evolution of N1 (z,t) is plotted at z = 0 and z = z’ in Fig. 15(c). First, from 0 to 40 µs, it is obvious that increasing PASP is more helpful in populating the upper state. Second, at the same time setting, the input end of the fiber has a higher Yb3+ upper state population compared to the output end of the fiber. The reason is that greater pump power is available at the beginning of the fiber, which is beneficial for pumping more Yb3+ ions into the upper state. Finally, starting from 60 µs, there is a rapid decrease due to signal amplification, after which the population gradually decreases via spontaneous emission, until the next anti-Stokes pump pulse comes in. Note that the abscissa in Fig. 15(c) only extends to 75 µs, while the next ASP pulse comes in at t = 1,000 µs.

Simulations were also performed with a fixed PSP of 20 W and PASP of 15 W. The signal pulse was again assumed to be Gaussian with a width of 0.5 µs. However, PSIGmax is now variable and takes on values of 1 W, 5 W, 10 W, and 20 W. The simulated pump power, signal power, and upper state population are shown in Figs. 16(a), 16(b), and 16(c), respectively. From Fig. 16(a), it can be observed that with higher input signal power (and hence energy), the anti-Stokes pump leakage decreases. The reason is that when the signal power is higher, the upper state is more depleted, which can be seen in Fig. 16(c) starting from 60 µs. As a result, when the next anti-Stokes pump pulse arrives, more energy is needed to excite the ground-state ions, resulting in reduced leakage (in other words, greater absorption). To understand the process another way, greater signal power facilitates efficient energy transfer from the anti-Stokes pump to stimulated emission, which is the preferred process since according to Eq. (12) a larger ESAPabs results in a smaller EQD. In these four situations, the EQD is 0.380%, 0.373%, 0.364%, and 0.354% respectively, which agrees with the analysis above. For the signal, a similar pulse reshaping is observed as in Fig. 15(b). In terms of pulse energy amplification, the calculated energy gain for the four cases are 9.62 dB, 9.26 dB, 8.87 dB, and 8.24 dB. The decrease in gain with increasing input pulse energy comes from the fact that greater input pulse energy brings the system closer to saturation.

Figure 16. Under the conditions tpASP = 40 µs, tpSP = 20 µs, frep = 1 kHz, PSP = 20 W, PASP = 15 W, tSIG = 0.5 µs (Gaussian pulse), and varying PSIGmax: (a) the input and output pump powers versus time, (b) the input and output signal powers versus time, and (c) the Yb3+ upper state populations at the input and output ends of the fiber.

To conclude this section, the EBL is placed into the context of high-energy lasers. As it has been shown above, the EBL is most appropriate for pulsed lasers or amplifiers. From the perspective of power scaling, multi-mJ systems appear to be feasible. Most of the value in this laser configuration likely will be found in the reduced heat generation during the pulse amplification process. Although not yet representing a practical ceiling to power scaling, thermal lensing [54, 131] can effectively be eliminated. These results apply not only to fiber lasers, but also to bulk solid-state systems.

### VIII. Conclusion

In conclusion, this review highlighted some of the relevant optical-based approaches that can lead to lower fiber operating temperatures. While the focus here was on Yb3+, the discussion can readily be extended to other active ions, including Tm3+ and Er3+. Fiber heating typically arises from a combination of the QD and deleterious non-radiative processes such as quenching or energy transfer to impurities. The latter processes could potentially be alleviated through careful compositional design and fiber purification. The former, representing a more fundamental limit, requires that the pump and signal wavelengths be closer together. In an example presented above, even with hefty convective water cooling, a 2 kW-pumped conventional active fiber’s temperature may rise by well over 50 °C when operating with a QD of 5.6% (and no non-radiative heating). Tenfold or more power scaling, therefore, necessitates the use of tandem pumping to drive down the total heat generated. A summary of some of the more recent work on tandem pumped lasers, which were also conceptually outlined here, was therefore provided. Another approach to reducing the QD is to retain diode pumping (such as at 976 nm) while operating the laser at shorter wavelengths. This, too, was briefly summarized here, with a key requirement being appropriate fiber design. For completeness, basic strategies for measuring active fiber temperatures were also identified.

After that, two newer approaches to optical thermal management, namely those that can annihilate phonons, were presented. Specifically, these were radiation and excitation balanced fiber lasers. With respect to the former, following the very first demonstration of ASF cooling in a silica fiber in 2020 [89], the very first radiation balanced fiber laser was demonstrated in 2021 [192]. In the radiation balanced fiber laser, one pump drives two processes. The first is ASF, which carries thermal energy away from the gain medium (since the average emission wavelength is less than that of the pump). This ASF cooling, in turn, balances the QD heating resulting from the second process: lasing at a wavelength longer than the pump. The excitation-balanced fiber laser, first demonstrated in 2021 [194], on the other hand, operates with two pumps; one above (ASP) and one below (SP) the lasing wavelength and does not make use of ASF. In this configuration, the ASP serves to populate the upper state in a way that benefits stimulated emission at a shorter wavelength. Finally, an application worthy of exploration, an excitation balanced pulse amplifier, was discussed by way of an example, demonstrating the feasibility of such a system. The RBL and EBL, and other yet undetermined approaches, specifically those that can remove phonons from the host glass, may prove to be a driving force behind a next-generation of ultra-high-power systems.

### ACKNOWLEDGEMENTS

Authors are grateful for the continued support from our colleagues, collaborators, and friends, especially (in alphabetical order) Martin Bernier, Magnus Engholm, Thomas Hawkins, Jennifer Knall, Pierre-Baptiste Vigneron, and Mingye Xiong.

### 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.

### FUNDING

U.S. Department of Defense Directed Energy Joint Transition Office (DE JTO) (N00014-17-1-2546); Air Force Office of Scientific Research (FA9550-16-1-0383).

### Fig 1.

Figure 1.Stark energy levels for two common laser glasses: (a) Al2O3-doped and (b) P2O5-doped silica. The zero-phonon lines are roughly at the same energies in both systems [70].
Current Optics and Photonics 2022; 6: 521-549https://doi.org/10.3807/COPP.2022.6.6.521

### Fig 2.

Figure 2.Cross-section data for various Yb3+ doped glasses. (a) Measured emission and (b) absorption cross-sections of three Yb-doped glass fibers. The spectroscopic properties of the fluorosilicate and phosphosilicate glasses are quite similar and are influenced by the less covalent environment they promote to the Yb3+ ions.
Current Optics and Photonics 2022; 6: 521-549https://doi.org/10.3807/COPP.2022.6.6.521

### Fig 3.

Figure 3.Illustrations of the various inter- and intra-manifold transitions relevant to the generation and management of heat in rare earth doped fiber lasers and amplifiers. Dashed and solid arrows represent absorption and stimulated emission, respectively. The green, vertical wiggly lines represent fluorescence. The red wiggly lines correspond to phonon generation and heating, and the blue wiggly lines to phonon annihilation and cooling. Heating or cooling requires the intra-manifold movement to lower (red) and higher (blue) energies, respectively. (a) Pumping at an energy higher than the mean emission energy leads to quantum defect (QD) heating. (b) Pumping at a wavelength longer than λem leads to phonon annihilation and cooling. (c) radiation-balanced lasers (RBLs) incorporate anti-Stokes fluorescence (ASF) to offset the QD heating. (d) Excitation-balanced lasers (EBLs) make use of both Stokes pumping (SP) and anti-Stokes pumping (ASP) to drive stimulated emission. Note that signal re-absorption, where relevant, was intentionally left off these diagrams.
Current Optics and Photonics 2022; 6: 521-549https://doi.org/10.3807/COPP.2022.6.6.521

### Fig 4.

Figure 4.Thermal analysis of the distributed-Bragg-reflector (DBR) laser. (a) Simulated radial temperature distribution of the Yb-doped fiber in the single-frequency DBR fiber laser of [82]. (b) With varying temperature of the fiber, the corresponding wavelength shift (absolute value) of the DBR fiber laser. A mode hop is observed at a temperature change near 9 K as the red-shifted mode m is replaced by m + 1 entering on the blue side of the FBG spectrum.
Current Optics and Photonics 2022; 6: 521-549https://doi.org/10.3807/COPP.2022.6.6.521

### Fig 5.

Figure 5.1,030 nm master oscillator power amplifier (MOPA) simulations. (a) Calculated pump and signal power distribution of the MOPA; (b) calculated temperature distribution along the fiber length for core center, core edge, cladding edge, and coating edge.
Current Optics and Photonics 2022; 6: 521-549https://doi.org/10.3807/COPP.2022.6.6.521

### Fig 6.

Figure 6.Temperature distribution along the fiber length for core center, core-cladding boundary, cladding-coating boundary, and coating surface calculated under the same simulation conditions as in Fig. 5 except that (a) the cladding and coating radii are increased to 350 µm and 500 µm, respectively, (b) the Yb concentration is decreased to 0.2 wt.%, and (c) the fiber is water cooled (h = 1,000 W/m2-K). In all cases, the maximum temperature is reduced to below 400 K.
Current Optics and Photonics 2022; 6: 521-549https://doi.org/10.3807/COPP.2022.6.6.521

### Fig 7.

Figure 7.The population in the lower manifold obeys the Boltzmann distribution. When the temperature of the Yb3+ host is increased (red), there is increased population at higher energy, and a concomitant increase in the absorption cross-section at longer wavelengths. When cooled (blue), the Yb3+ acts like a four-level system across a wider range of wavelengths, including in the S-band. Upon fiber heating, the fluorescence spectrum around the zero-phonon line (shown as the green arrow) is broadened.
Current Optics and Photonics 2022; 6: 521-549https://doi.org/10.3807/COPP.2022.6.6.521

### Fig 8.

Figure 8.Block diagram for a representative tandem pumped fiber laser. LD, laser diode; FBG, fiber Bragg gratings; CMS, cladding mode stripper. In this example, six FBG-based fiber lasers are pumped individually by semiconductor lasers. Their outputs are combined to serve as the pump for the power amplifier stage.
Current Optics and Photonics 2022; 6: 521-549https://doi.org/10.3807/COPP.2022.6.6.521

### Fig 9.

Figure 9.Short wavelength master oscillator power amplifier (MOPA) simulations. (a) Pump and signal power distribution of the MOPA, and (b) temperature distribution along the fiber length for core center, core edge, cladding edge, and buffer edge. The sharp increase in temperature at around 5 m results from the large quantum defect (QD) associated with signal reabsorption and the buildup of amplified spontaneous emission (ASE).
Current Optics and Photonics 2022; 6: 521-549https://doi.org/10.3807/COPP.2022.6.6.521

### Fig 10.

Figure 10.Measured temperature change versus position along the fiber amplifier, and simulated dependencies using the model based on [191] for (a)–(c) a 2.74-m, and (d) a 4.35-m amplifier fiber.
Current Optics and Photonics 2022; 6: 521-549https://doi.org/10.3807/COPP.2022.6.6.521

### Fig 11.

Figure 11.Simplified diagram of a Yb-doped fiber laser internally cooled by anti-Stokes fluorescence. Upper portion of the diagram (in purple and green, enclosed in the solid box) is the fiber laser. Lower portion (in blue, enclosed on the dashed box) is the closed-loop temperature sensor utilizing a slow-light fiber Bragg grating (FBG) that was used to measure the temperature of the Yb-doped fiber at various points along its length.
Current Optics and Photonics 2022; 6: 521-549https://doi.org/10.3807/COPP.2022.6.6.521

### Fig 12.

Figure 12.The laser output power measured as a function of the launched pump power, along with a linear fit to the data. The color gradient is a pictorial representation of the average temperature change along the length of the gain fiber.
Current Optics and Photonics 2022; 6: 521-549https://doi.org/10.3807/COPP.2022.6.6.521

### Fig 13.

Figure 13.Basic excitation-balanced lasers (EBL) configuration. (a) Schematic of the experimental setup in [194]. The Stokes pump (SP) and anti-Stokes pump (ASP) are pulsed and combined into the laser cavity via a coupler. (b) Representation of the relative timing of the two pumps. The pulse width is tp and the two pulses overlap for a time equal to tpdt.
Current Optics and Photonics 2022; 6: 521-549https://doi.org/10.3807/COPP.2022.6.6.521

### Fig 14.

Figure 14.Results obtained with the first fiber laser-based excitation-balanced lasers (EBL). (a) Average laser output power (PL), (b) effective quantum defect (EQD), and (c) powers required from the SP to reach threshold (PSPth) measured as a function of PASP, for different values of PSP.
Current Optics and Photonics 2022; 6: 521-549https://doi.org/10.3807/COPP.2022.6.6.521

### Fig 15.

Figure 15.Under the conditions tpASP = 40 µs, tpSP = 20 µs, frep = 1 kHz, PSP = 20 W, PSIGmax = 20 W, tSIG = 0.5 µs (Gaussian pulse), and varying PASP: (a) the input and output pump powers versus time, (b) the input and output signal powers versus time, and (c) the Yb3+ upper state population at the input and output ends of the fiber.
Current Optics and Photonics 2022; 6: 521-549https://doi.org/10.3807/COPP.2022.6.6.521

### Fig 16.

Figure 16.Under the conditions tpASP = 40 µs, tpSP = 20 µs, frep = 1 kHz, PSP = 20 W, PASP = 15 W, tSIG = 0.5 µs (Gaussian pulse), and varying PSIGmax: (a) the input and output pump powers versus time, (b) the input and output signal powers versus time, and (c) the Yb3+ upper state populations at the input and output ends of the fiber.
Current Optics and Photonics 2022; 6: 521-549https://doi.org/10.3807/COPP.2022.6.6.521

TABLE 1 Basic optical parameters of Yb-doped aluminosilicate

Core Diameter (µm)Cladding Diameter (µm)Buffer Diameter (µm)Numerical ApertureUpper-state Lifetime (µs)Yb3+ Concentration (wt.%)
254005000.077431

TABLE 2 Fiber constants used in simulations

τ (ms)σaSP (pm2)σaASP (pm2)σaSIG (pm2)σeSP (pm2)σeASP (pm2)σeSIG (pm2)ρ (m−3)reff(µm)Γ
1.31.7220.1810.2431.6600.3360.3641.65 × 1026100.8

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Wonshik Choi,
Editor-in-chief