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Abstract
Yb3+/P5+/Al3+ co-doped silica fiber core glasses with different P5+/Al3+ molar ratios were prepared by the sol-gel method and modified chemical vapor deposition (MCVD) method. The absorption and fluorescence spectra were measured using a temperature range from 25°C to 200°C. Results show that both the major absorption and emission peaks of the Yb3+ ions become weaker and wider with the temperature increasing. The absorption cross sections of HYPA1 (the molar compositions of 0.2Yb2O3-2P2O5-2Al2O3-95.8SiO2) preform slices made by MCVD with a composition similar to the commercial 20/400 ytterbium-doped silica fibers (YDFs) decrease by ∼31.8% (915 nm), ∼25.3% (940 nm) and ∼41.6% (975 nm), in addition, the emission cross sections decrease by ∼32.1% (1030 nm) and ∼22.7% (1080 nm), respectively, all which indicate the decline of the laser properties with the temperature increasing of Yb3+ doped glass samples. The highest absorption peak at 975 nm of HYPA1 is blue-shifted by 0.80 nm as temperature raised from 25°C to 200°C and the absorption coefficient of the peak wavelength is reduced by nearly 5%. Additionally, the results also demonstrate that the Rabs (the ratio of σabs@975 nm/σabs@915 nm) and Rem (the ratio of σem@1030 nm/σem@1080 nm) are affected not only by the P5+/Al3+ molar ratio but also by the temperature. This work is helpful for understanding the fiber laser performance variations with the increase of the fiber core temperature due to high power operation.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
It is well known, that Yb3+ ions have a simple outer electronic structure (4f146s2), and do not participate in energy up-conversion, cross-relaxation, and excited-state absorption [1]. Thus, ytterbium-doped host materials can be widely studied as excellent gain media. In recent years, the Yb3+-doped silica large-mode-area (LMA) fiber has obtained essential applications in high-power, high-energy, and high beam quality fiber lasers and amplifiers [2,3]. In 2009, IPG Photonics achieved a 10 kW single-mode fiber laser output by the LMA fiber, and the output power of the fiber laser after beam combination reached 100 kW in 2013 [4]. Since then, the development of single-mode laser power in a single fiber has entered a long-term stagnation period, due to transverse mode instability (TMI) under high power. TMI in the fiber amplifier mainly depends on the thermal effects under high power [5,6].
Additionally, the nonlinear effects (NLEs) [2,7] and photodarkening (PD) effects [8–10] should be considered in the amplifiers. To suppress NLEs, the doping concentration of Yb3+ ions in the core glass can be increased to reduce the length of the fiber [11]. However, when high-concentration Yb3+ ions are doped in the silica matrix, there is a problem of clustering which has a detrimental effect on the spectral properties. By introducing P5+ and Al3+ ions, the solubility of Yb3+ ions in the silica glass increases, and the PD effects can be suppressed at the same time [12–14]. The PD effect is one of the main contributors to heat load [15]. Thus, the introduction of P5+ and Al3+ ions can also effectively increase the TMI threshold [5,8]. It also influences the valence state change, spectral properties, and distribution of Yb3+ ions [11,16,17]. Notably, when the P5+/Al3+ molar ratio equals 1, the formation of the [AlPO4] structure can effectively decrease the refractive index of the core glass [11,18].
In the common fiber laser, the 915nm and 975 nm laser diode (LD) is generally used as the pump source. In terms of the high absorption coefficient, 975 nm is more appropriate as the operating wavelength, and a short-fiber length can significantly suppress NLEs [19,20]. However, because of the shorter length, the heat load is more severe, resulting in a lower TMI threshold than that obtained from the wavelength at 915 nm [21]. Additionally, the narrow absorption peak at 975 nm is greatly affected by the wavelength drifting of the high LD pump power. By contrast, the wider absorption peak at ∼915 nm is less affected by the wavelength drifting of the high LD pump power, but has a lower quantum efficiency [22]. Therefore, ∼940 nm LD and ∼1018 nm fiber lasers as alternatives for a tandem pump source have also been developed [23]. However, the absorption coefficients of these two wavelengths differ greatly because of the composition of the ytterbium-doped matrix and other factors, so they are rarely used in the industry. Designing fiber lasers on the basis of the properties of the ytterbium-doped matrix, such as the appropriate pump wavelength, is of great significance for the development of high-power fiber lasers.
Presently, lots of fiber laser simulation design works are published, but the basic spectral parameters of the Yb3+-doped fiber matrix are usually measured at room temperature or on the basis of the theoretical model [24–26]. However, during the operation of a high-power fiber laser, temperature rises considerably inside the Yb3+-doped fiber core. Due to the limitation of YDFs protective acrylate/fluoroacrylate coating, the operating temperature of the kW fiber laser is required to be lower than 200°C [27]. Studying the spectral properties of Yb3+-doped fiber core glass under the temperature rise condition can provide a more sufficient basis for the simulation design of fiber lasers. This paper, discusses the cross-section changes of the primary absorption and emission peaks in spectra of Yb3+/P5+/Al3+ co-doped silica fiber core glasses when the P5+/Al3+ molar ratio and temperatures (ranging from 25°C to 200°C) are changed, including the ∼915, ∼940, ∼975, ∼1030, ∼1060, and ∼1080 nm. Simultaneously, when constructing a laser system, the introduction of the values of Rabs and Rem can help in choosing the appropriate pump wavelength, laser wavelength and fiber length.
2. Experiment details
2.1 Sample preparation and spectrum tests
The chemical compositions of the Yb3+/Al3+/P5+ co-doped glasses are shown in Table 1. The samples of the L# series were prepared by the sol-gel method combined with high-temperature sintering, and the preparation details are described in the Ref. [28]. The bulk glasses of L# were polished into the glass with a thickness of 2 mm (Φ ≈15 mm). The fiber preform slices of the H# series were prepared by the modified chemical vapor deposition (MCVD) method with the solution doping [29]. The core diameter of the H# fiber preform slice is 2.8 mm and the outer diameter is about 16.2 mm. The theoretical concentrations of Yb2O3 are 0.1mol% for the L# series and 0.2 mol% for the H# series, and the molar ratio of P5+/Al3+ ranges from 0 to 2. The content of Yb2O3, P2O5, and Al2O3 in the sample was measured by an inductively coupled plasma emission spectrometer (ICP-OES; radial-view Thermo iCAP 6300). The results in Table 1 show that the ratio of P5+ to Al3+ is consistent with the theoretical value. It should be noted that the H# sample is preform slices, and the accurate element composition was obtained by calculating the proportion of the core volume of the preform. The density data of H# sample measured by the Archimedes principle is also processed in the same way.
Table 1. Mean compositions of two series of the Yb3+/Al3+/P5+ co-doped silica glass (mol%).
The Perkin-Elmer 950UV/VIS/NIR spectrophotometer was used to test the absorption spectra with a scanning step of 0.05 nm. The absorption spectra were measured at 25°C, 60°C, 100°C, 140°C and 200°C, respectively, by a heating device.
The various temperature fluorescence spectra and lifetimes were tested with the FLS920 steady-state/transient fluorescence spectrometer from the Edinburgh Instruments Ltd. A xenon lamp was used to measure the fluorescence spectra of Yb3+ ions under 896 nm excitation. The fluorescence lifetime of Yb3+ ions was measured at ∼1030 nm under the excitation of a 980 nm LD. Meanwhile, a filter (FESH900) was added, which was used to filter out signals with a wavelength less than 900 nm.
2.2 The calculation method of cross sections
The absorption cross sections curve of Yb3+ ions at 800–1200 nm can be calculated by the following formula:
N0 is the Yb3+ ion concentration (∼ions/cm3) and L is the thickness (cm) of the glass sample. Before the calculation of cross sections, the baseline of the absorption spectra must be deducted to prevent errors caused by the measurement process.Because of the low concentration of Yb3+ ions, the Fuchtbauer-Lademnurg (F-L) method is more accurate in the calculation of the cross sections of this experiment [30,31]:
3. Experiment details
3.1 Temperature dependence of spectral properties of the HYPA1
Note that the composition of the HYPH1 sample is very similar to that of commercial 20/400 µm YDFs (e.g., the nufern LMA-YDF-20/400-HP-XM). Thus, the temperature dependence of the HYPA1 sample spectrum was considered, firstly. Figure 1(a) and (b) show the change of the absorption and emission cross sections of HYPA1 with the increase in temperature and that the fluorescence lifetime decreases. As the temperature increases from 25°C to 200°C, the major absorption and emission cross sections decrease significantly. The absorption cross sections of the HYPA1 sample at 915, 940 and 975 nm decrease from 0.391 to 0.267pm2, 0.283 to 0.251 pm2, and 1.716 to 1.000 pm2, which results in decreases of 32%, 25% and 45%, respectively. However, the absorption cross section at 1018 nm increases by 16.6%.The emission cross sections at 1030 and 1080 nm decrease from 0.650 to 0.442 pm2 and 0.283 to 0.219 pm2, which results in decreases of 32.1% and 22.7%, respectively. Especially, the absorption peak at 975 nm is blue-shifted by ∼0.8 nm as the temperature increases from 25°C to 200°C. Although this change is very slight, for the wavelength-locked LD pump system using volume Bragg gratings, this shift may also have a significant impact on the laser performance [32]. For the HYPA1, the shift reduces the absorption coefficient by ∼5%.
The reduction of absorption cross sections is caused by the temperature-dependent electron-phonon interaction at the sub-level, which could be analyzed through the Stark level splitting and the Full Width at Half Maximum (FWHM) broadening [1]. In the silica matrix, under the influence of the crystal field, the ground state 2F7/2 and the excited state 2F5/2 are split into four sub-levels and three sub-levels, respectively, which broadens the absorption and emission peaks of Yb3+ ions in the spectra [33]. The number of particles in the ground state is well known conforms to the Boltzmann thermal distribution. In the following formula, b1N represents the ratio of the number of particles on the Nth Stark sub-energy level to the whole ground state 2F7/2 energy level, kb is Boltzmann constant, T is the temperature, and E1N-E11 is the energy difference relative to the lowest Stark energy level [1,34]. Similarly, b2N represents the ratio of the number of particles on the Nth Stark sub-energy level to the whole ground state 2F5/2 energy level.
Fig. 2. The absorption cross sections of the HYPA1 are separately processed by Lorentz fitting at (a) 25°C and (b) 200°C, and the dashed curve shows the decomposition peaks corresponding to different Stark transitions; (c) The normalization of the number of particles of Yb3+ ions at the sub-level of 2F7/2 is drawn by formula (3); (d) the FWHM varies with temperatures for HYPA1.
It shows that the FWHM of the absorption peaks of b12 → b21 and b12 → b22 increase in Fig. 2(a) and (b). Figure 2(c) confirms this result. As the temperature increases, the number of particles on sub-level 2F7/2 will be redistributed, and some of the particles at the b11 energy level absorb energy to b12 b13 and b14. Thus, the σabs at ∼1018 nm increases. Additionally, the position of absorption peak at 975 nm is affected by the nearby Lorentz decomposition peak. The increase in the transition probability of b12 → b22 is the main reason for the blue shift of the 975 nm absorption peak by 0.80 nm.
In Fig. 2(d), the FWHM of the 930 nm and 975 nm absorption peak, both broadened by 1.3 and 9.3 nm from 25°C to 200°C, respectively. The reason for the FWHM broadening is that the transition process accompanies a phonon’s absorption or emission, contributing to uniform broadening. Meanwhile, the FWHM can be accurately calculated by the electron-phonon interaction of the non-adiabatic system [36,37]. Generally, the broadening of FWHM and the population change of Stark sub-energy level are the main reasons for the decrease of the main absorption peak cross sections.
Additionally, the temperature dependence of the primary absorption and emission peaks should be discussed. As displayed in Fig. 3(a) and (b), the ordinate is the ratio of major σabs and σem at the corresponding temperature to cross sections at 25°C. The σabs at ∼940 nm decreases slightly when the temperature increases, especially at the beginning 60°C. This reveals that the absorption at ∼940 nm generally has a weak temperature dependence. Meanwhile, compared with the HYPA1, the absorption at ∼940 nm significantly increased and became “flat” for the sample with high P5+ ions content [16]. Thus, the Yb3+-doped silica fiber with a high P5+ content is more stable when using the pump excitation wavelength at ∼940 nm under high power. However, the absorption cross section at 975 nm is most affected by temperature. Hence, when the high-power fiber laser is pumped by a ∼975 nm LD, the temperature rise caused by the increase of power may have a greater impact on the laser characteristics such as mode instability. On the other hand, compared with a short emission wavelength 1018nm and 1028nm, the influence of temperature on the emission spectrum of the 1060 and 1080 nm is relatively small in Fig. 3(b). It can be predicted that with the increase of pump power, the laser output of the fiber with this core component is relatively stable in this band. These results correspond to the above speculation that the number of particles on sub-level b12 increases as the temperature increases.
Fig. 3. Ratio of the major (a) absorption and (b) emission peaks cross sections of HYPA1 at different temperatures to the cross sections at 25°C and the curve fitted by the data points.
3.2 Spectral properties of samples with different P5+/Al3+ molar ratios on the function of temperature
The LYPA1.5 sample prepared by the sol-gel method has a much higher content of phosphorus (∼6 mol %), resulting in poor glass quality. In the absorption spectrum, the large fluctuation of the baseline has a negative impact on the accuracy of the data at ∼915 and ∼940 nm, so we discard it. As shown in Table 2, the σabs at 915, 940 and 975 nm decrease with the increase of P5+ ions content for the L# and H# series of samples. Especially, compared with LYPA1 and HYPA1, the σabs@975nm of the LYPA1.5 and HYPA1.5 significantly decreases by 37.4% and 58.7% in 25°C, respectively. The reason for this is the decrease of crystal field strength around the Yb3+ ions [16]. When P5+/Al3+ ≤ 1, with the increase of the content of P5+ ions, the formation of the [AlPO4] structure results in a slight increase of the crystal field strength and structural asymmetry. When P5+/Al3+ > 1, the second coordination of Yb3+ ions is almost occupied by P5+ ions, and the crystal field intensity of Yb3+ ions is significantly weakened [17].
Table 2. Absorption cross sections at 915, 940 and 975 nm in Yb3+/Al3+/P5+ co-doped silica glass with the temperatures from 25–140°C
Comprehensively considered, the Rabs and Rem are introduced, which helps to select the appropriate pump and laser wavelengths. The detailed theoretical analysis has been described in the introduction section. The main purpose of this work is to provide a more sufficient basis on fiber core glass, which can facilitate the theoretical simulation and experimental design of other researchers. For the commercial YDFs (e.g., the nufern Yb SM-YDF-5/130-VIII), the Rabs (∼3.2) is generally considered unchanged in the actual operation. In this work, the fact that the Rabs could be slightly changed is observed. As shown in Fig. 4(a), the Rabs shows a decreasing trend with the increase of the temperature. For the LYPA0 without phosphorus, the temperature dependence of the Rabs value is strong, and the Rabs value is reduced by 14.8%. For phosphorus-containing samples, with the increase of phosphorus content, the temperature dependence of the Rabs value gradually decreased. For the HYPA1, from 25°C to 140°C, the Rabs changes from 4.39 to 4.06, reduced by 7.3%. The result reveals that the advantage of the high absorption coefficient at 975 nm becomes smaller. This finding has great significance for practical applications. Because of the effect of the change of the Rabs, on designing the high-power laser amplification system, the factors of excess and insufficient pump power must be considered. Figure 4(b) displays that the ∼1030 and ∼1080 nm laser output is also affected by both the temperature and P5+/Al3+ molar ratio. For the samples of the L# series with the molar P5+/Al3+ molar ratio ≤ 1, the Rem is small, and it is conducive to achieve the laser output at a longer wavelength (∼1080 nm). For the samples of H# series with the P5+/Al3+ molar ratio > 1, with the increase of the P5+/Al3+ molar ratio, the Rem becomes larger, indicating that the higher P5+/Al3+ molar ratio contributes to the short-wavelength (∼1030 nm) laser output. Especially, for the HYPA2 with a higher P5+/Al3+ molar ratio, as the temperature increases, the laser output at 1080 nm will be suppressed.
Fig. 4. For the samples of the L# and H# series, (a) the Rabs and (b) the Rem change with temperature, and the dashed curve is fitted by the data points.
4. Conclusion
In this work, Yb3+/P5+/Al3+ co-doped silica fiber core glasses with different P5+/Al3+ molar ratios were prepared by the sol-gel method and MCVD method. The spectra of two series of Yb3+/Al3+/P5+ co-doped silica fiber core glasses are comprehensively analyzed with a temperature range from 25°C to 200°C. The results demonstrate that the spectral properties are affected not only by the P5+/Al3+ molar ratio but also by the temperature.
The results show that the major absorption peaks at ∼915 and 975 nm highly depend on the temperature and P5+/Al3+ molar ratios, and the temperature dependence of 940 nm absorption is much lower than the above two wavelengths. Because of the rearrangement of the number of particles on the sub-level and the broadening of major absorption-peak FWHM, the absorption cross sections decrease significantly. With the temperature from 25°C to 200°C, and the highest absorption peak at 975 nm of HYPA1 is blue-shifted by 0.80 nm and the absorption coefficient of the peak wavelength is reduced by nearly 5%. With the increase of P5+/Al3+ molar ratio at high temperature, the ratio of σabs@975nm/σabs@915nm become smaller. When P5+/Al3+ ≤ 1, it is conducive to output the high-power laser at a longer wavelength (1080 nm). This work is helpful for understanding the fiber laser performance variations with the increase of the fiber core temperature due to high power operation, especially in improving fiber laser simulation design works.
Funding
National Natural Science Foundation of China (61775224, 61875216).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
1. Y. S. Yong, S. Aravazhi, S. A. Vazquez-Cordova, J. J. Carjaval, F. Diaz, J. L. Herek, S. M. Garcia-Blanco, and M. Pollnau, “Temperature-dependent absorption and emission of potassium double tungstates with high ytterbium content,” Opt. Express 24(23), 26825–26837 (2016). [CrossRef]
2. M. N. Zervas and C. A. Codemard, “High power fiber lasers: a review,” IEEE J. Sel. Top. Quantum Electron. 20(5), 219–241 (2014). [CrossRef]
3. C. Jauregui, J. Limpert, and A. Tunnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013). [CrossRef]
4. J. Limpert, F. Stutzki, F. Jansen, H.-J. Otto, T. Eidam, C. Jauregui, and A. Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light: Sci. Appl. 1(4), e8 (2012). [CrossRef]
5. H.-J. Otto, C. Jauregui, J. Limpert, and A. Tuennermann, “Average power limit of Ytterbium-doped fiber-laser systems with nearly diffraction-limited beam quality,” Proc. SPIE 9728, 97280E (2016). [CrossRef]
6. M. N. Zervas, “Power scaling limits in high power fiber amplifiers due to transverse mode instability, thermal lensing and fiber mechanical reliability,” Proc. SPIE 10512, 1051205 (2018). [CrossRef]
7. Q. Chu, Q. Shu, Z. Chen, F. Li, D. Yan, C. Guo, H. Lin, J. Wang, F. Jing, C. Tang, and R. Tao, “Experimental study of mode distortion induced by stimulated Raman scattering in high-power fiber amplifiers,” Photonics Res. 8(4), 595–600 (2020). [CrossRef]
8. C. Jauregui, H. J. Otto, F. Stutzki, J. Limpert, and A. Tunnermann, “Simplified modelling the mode instability threshold of high power fiber amplifiers in the presence of photodarkening,” Opt. Express 23(16), 20203–20218 (2015). [CrossRef]
9. H. J. Otto, N. Modsching, C. Jauregui, J. Limpert, and A. Tunnermann, “Impact of photodarkening on the mode instability threshold,” Opt. Express 23(12), 15265–15277 (2015). [CrossRef]
10. R. Cao, G. Chen, Y. Chen, Z. Zhang, X. Lin, B. Dai, L. Yang, and J. Li, “Effective suppression of the photodarkening effect in high-power Yb-doped fiber amplifiers by H2 loading,” Photonics Res. 8(3), 288–295 (2020). [CrossRef]
11. S. Wang, F. Lou, C. Yu, Q. Zhou, M. Wang, S. Feng, D. Chen, L. Hu, W. Chen, M. Guzik, and G. Boulon, “Influence of Al3+ and P5+ ion contents on the valence state of Yb3+ ions and the dispersion effect of Al3+ and P5+ ions on Yb3+ ions in silica glass,” J. Mater. Chem. C 2(22), 4406–4414 (2014). [CrossRef]
12. S. Unger, A. Schwuchow, S. Jetschke, V. Reichel, A. Scheffel, and J. Kirchhof, “Optical properties of Yb-doped laser fibers in dependence on codopants and preparation conditions - art. no. 689016,” Proc. SPIE 6890, 689016 (2008). [CrossRef]
13. M. Engholm and L. Norin, “Preventing photodarkening in ytterbium-doped high power fiber lasers; correlation to the UV-transparency of the core glass,” Opt. Express 16(2), 1260–1268 (2008). [CrossRef]
14. A. J. Boyland, A. S. Webb, S. Yoo, F. H. Mountfort, M. P. Kalita, R. J. Standish, J. K. Sahu, D. J. Richardson, and D. N. Payne, “Optical fiber fabrication using novel gas-phase deposition technique,” J. Lightwave Technol. 29(6), 912–915 (2011). [CrossRef]
15. C. Jauregui, F. Stutzki, A. Tunnermann, and J. Limpert, “Thermal analysis of Yb-doped high-power fiber amplifiers with Al:P co-doped cores,” Opt. Express 26(6), 7614–7624 (2018). [CrossRef]
16. W. B. Xu, J. J. Ren, C. Y. Shao, X. Wang, M. Wang, L. Y. Zhang, D. P. Chen, S. K. Wang, C. L. Yu, and L. L. Hu, “Effect of P5+ on spectroscopy and structure of Yb3+/Al3+/P5+ co-doped silica glass,” J. Lumin. 167, 8–15 (2015). [CrossRef]
17. T. Deschamps, H. Vezin, C. Gonnet, and N. Ollier, “Evidence of AlOHC responsible for the radiation-induced darkening in Yb doped fiber,” Opt. Express 21(7), 8382–8392 (2013). [CrossRef]
18. C. Shao, F. Wang, Y. Jiao, S. Wang, X. Wang, C. Yu, and L. Hu, “Relationship between glass structure and spectroscopic properties in Er3+/Yb3+/Al3+/P5+-doped silica glasses,” Opt. Mater. Express 10(5), 1169–1181 (2020). [CrossRef]
19. J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, A. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, “High-power air-clad large-mode-area photonic crystal fiber laser,” Opt. Express 11(7), 818–823 (2003). [CrossRef]
20. P. D. Dragic, M. Cavillon, and J. Ballato, “Materials for optical fiber lasers: A review,” Appl. Phys. Rev. 5(4), 041301 (2018). [CrossRef]
21. C. Jauregui, H. J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tunnermann, “Passive mitigation strategies for mode instabilities in high-power fiber laser systems,” Opt. Express 21(16), 19375–19386 (2013). [CrossRef]
22. P. Yan, Y. Huang, J. Sun, D. Li, X. Wang, M. Gong, and Q. Xiao, “3.1 kW monolithic MOPA configuration fibre laser bidirectionally pumped by non-wavelength-stabilized laser diodes,” Laser Phys. Lett. 14(8), 6 (2017). [CrossRef]
23. K. J. Lim, S. K. W. Seah, J. Y. Ye, W. W. Lim, C. P. Seah, Y. B. Tan, S. T. Tan, H. T. Lim, R. Sidharthan, A. R. Prasadh, C. J. Chang, S. Yoo, and S. L. Chua, “High absorption large-mode area step-index fiber for tandem-pumped high-brightness high-power lasers,” Photonics Res. 8(10), 1599–1604 (2020). [CrossRef]
24. S. Lee, L. A. Vazquez-Zuniga, D. Lee, H. Kim, J. K. Sahu, and Y. Jeong, “Comparative experimental analysis of thermal characteristics of ytterbium-doped phosphosilicate and aluminosilicate fibers,” J. Opt. Soc. Korea 17(2), 182–187 (2013). [CrossRef]
25. I. Tamer, S. Keppler, J. Koerner, M. Hornung, M. Hellwing, F. Schorcht, J. Hein, and M. C. Kaluza, “Modeling of the 3D spatio-temporal thermal profile of joule-class Yb3+-based laser amplifiers,” High Power Laser Sci. Eng. 7, e42 (2019). [CrossRef]
26. M. M. Tao, H. W. Chen, G. B. Feng, K. P. Luan, F. Wang, K. Huang, and X. S. Ye, “Thermal modeling of high-power Yb-doped fiber lasers with irradiated active fibers,” Opt. Express 28(7), 10104–10123 (2020). [CrossRef]
27. S. W. Moore, T. Barnett, T. A. Reichardt, and R. L. Farrow, “Optical properties of Yb3+-doped fibers and fiber lasers at high temperature,” Opt. Commun. 284(24), 5774–5780 (2011). [CrossRef]
28. F. Wang, L. L. Hu, W. B. Xu, M. Wang, S. Y. Feng, J. J. Ren, L. Zhang, D. P. Chen, N. Ollier, G. J. Gao, C. L. Yu, and S. K. Wang, “Manipulating refractive index, homogeneity and spectroscopy of Yb3+-doped silica-core glass towards high-power large mode area photonic crystal fiber lasers,” Opt. Express 25(21), 25960–25969 (2017). [CrossRef]
29. A. S. Webb, A. J. Boyland, R. J. Standish, S. Yoo, J. K. Sahu, and D. N. Payne, “MCVD in-situ solution doping process for the fabrication of complex design large core rare-earth doped fibers,” J. Non-Cryst. Solids 356(18-19), 848–851 (2010). [CrossRef]
30. S. X. Dai, J. H. Yang, L. Wen, L. L. Hu, and Z. H. Jiang, “Effect of radiative trapping on measurement of the spectroscopic properties of Yb3+: phosphate glasses,” J. Lumin. 104(1-2), 55–63 (2003). [CrossRef]
31. K. Lu and N. K. Dutta, “Spectroscopic properties of Yb-doped silica glass,” J. Appl. Phys. 91(2), 576–581 (2002). [CrossRef]
32. J. Kim and Y. Song, “Ultralow-noise mode-locked fiber lasers and frequency combs: principles, status, and applications,” Adv. Opt. Photonics 8(3), 465–540 (2016). [CrossRef]
33. B. H. Yang, X. Q. Liu, X. Wang, J. J. Zhang, L. L. Hu, and L. Y. Zhang, “Compositional dependence of room-temperature Stark splitting of Yb3+ in several popular glass systems,” Opt. Lett. 39(7), 1772–1774 (2014). [CrossRef]
34. Q. He, F. Wang, Z. Q. Lin, C. Y. Shao, M. Wang, S. K. Wang, C. L. Yu, and L. L. Hu, “Temperature dependence of spectral and laser properties of Er3+/Al3+ co-doped aluminosilicate fiber,” Chin. Opt. Lett. 17(10), 101401 (2019). [CrossRef]
35. D. A. Grukh, A. S. Kurkov, V. M. Paramonov, and E. M. Dianov, “Effect of heating on the optical properties of Yb3+-doped fibres and fibre lasers,” Quantum Electron. 34(6), 579–582 (2004). [CrossRef]
36. G. G. Demirkhanyan and R. B. Kostanyan, “Temperature dependence of spectral-line intensities in YAG : Yb3+,” Laser Phys. 18(2), 104–111 (2008). [CrossRef]
37. M. Eichhorn and M. Pollnau, “Spectroscopic foundations of lasers: spontaneous emission into a resonator mode,” IEEE J. Sel. Top. Quantum Electron. 21(1), 486–501 (2015). [CrossRef]
