Open Access
Add to BibSonomy
Abstract
In this work, we conduct a detailed experimental study on the impact of signal bandwidth on the TMI threshold of fiber amplifiers. Both the filtered superfluorescent fiber sources and the phase-modulated single-frequency lasers are employed to construct seed lasers with different 3 dB spectral linewidths ranging from 0.19 nm to 7.97 nm. The TMI threshold of the fiber amplifier employing those seed lasers are estimated through the intensity evolution of the signal laser, and different criteria have been utilized to characterize the spectral linewidth of the seed lasers. Notably, the experimental results reveal that the TMI threshold of fiber amplifiers grows, keeps constant, and further grows as a function of spectral linewidth of seed lasers. Our experimental results could provide a well reference to understand the mechanism of the TMI effect and optimize the TMI effect in high-power fiber amplifiers.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High-power fiber lasers have been highly required in many industrial and scientific applications, such as laser material processing, remote sensing, and laser-induced nuclear fusion [1–3]. Thereinto, ytterbium-doped fiber lasers, including ytterbium-doped fiber oscillators [4–6] and ytterbium-doped fiber amplifiers (YDFAs) [7–11], provide one of the most effective solutions to achieve multi-kilowatt fiber lasers with near-diffraction-limited beam quality. However, power scaling of fiber lasers is currently restricted by the sudden onset of thermally induced transverse mode instability (TMI) effect [12–14]. The TMI effect describes an intense and dynamic modal degeneration phenomenon after a certain threshold has been reached, which sets the practical upper brightness limit for high-power fiber laser systems [12,15].
In the past decade, a series of theoretical models have been proposed to investigate the mechanism of the TMI effect in high-power fiber amplifiers [13–21], which have also clarified the basic principles and strategies to suppress the TMI effect. The basic principles to suppress the TMI effect mainly involve two aspects, i.e., reducing the strength of the thermally induced refractive index grating and decreasing the net gain coefficient of higher-order modes [14]. The common strategies to suppress the TMI effect could be fulfilled through optimizing the structure and parameters of the amplifier stage, such as pump wavelength [22,23], pump structure [24], coiling active fiber [25], and special design of active fiber [26–29].
Despite of those advances, it should be noted that the set of signal bandwidth in most reported theoretical models is restricted to a few tens of kHz, which means that the impact of signal bandwidth is completely neglected. Furthermore, theoretical prediction for the TMI threshold of a fiber amplifier with broad signal bandwidth is difficult due to the large difference between the time scales for the signal modulation and the thermal response of the fiber [30]. Accordingly, it is unclear so far how the signal bandwidth would impact the TMI threshold of high-power fiber amplifiers, which is significant in the design of high-power fiber amplifiers.
The aim of this work is to unveil the potential impact of the signal bandwidth on the TMI threshold of high-power fiber amplifiers experimentally. Through constructing seed lasers with different spectral linewidths and measuring the corresponding TMI threshold of fiber amplifiers employing those seed lasers, the relationship between the TMI threshold of fiber amplifiers and the spectral linewidth of seed lasers is demonstrated in detail.
2. Experimental setup
The signal bandwidth of a fiber amplifier is mainly determined by the different spectral of the seed laser. Thus, a primary issue in the experimental setup is to construct seed lasers with different spectral linewidths. For common seed lasers applied in high-power fiber amplifiers, including multi-longitudinal fiber oscillators [9], superfluorescent fiber sources (SFSs), random distributed feedback fiber lasers [11], and phase-modulated single-frequency lasers (SFLs) [31–34], their spectral linewidths could be effectively controlled through laser design or spectral filtering [35–37]. It is superior to choose seed lasers which could suppress or weaken the spectral broadening phenomenon in fiber amplifiers. Thus, the filtered SFSs and phase-modulated SFLs are chosen as the seed laser in the experiments. As for a filtered SFS, its spectral linewidth could be simply controlled through adjusting the bandwidth of the filter. Nevertheless, a filtered SFS with narrower spectral linewidth might suffer from more serious issue of the spectral broadening phenomenon during power amplification [38]. As for a phase-modulated SFL, it has the advantage of spectral preservation during power amplification, and its spectral linewidth could be easily controlled through adjusting the phase-modulation signal. Nevertheless, limited by the power handling and bandwidth of the phase modulator, the maximum 3 dB spectral linewidth of a phase-modulated SFL is around 1 nm. Accordingly, both the filtered SFSs and the phase-modulated SFLs are employed in our experiments to cover a wide range for the spectral linewidths of seed lasers.
Figure 1 illustrates the experimental setup of the polarization-maintained (PM) YDFA which employs two types of seed lasers separately. In Seed 1, a broadband PM SFS with an output power of about 150 mW is spectrally filtered through a tunable filter, and the central wavelength of the filter is 1064 nm. In Seed 2, a commercial PM SFL at 1064 nm with an output power of about 50 mW is externally modulated through a LiNbO3 electro-optic modulator (EOM). A white noise source (WNS) signal is amplified by a ratio-frequency amplifier and then drives the modulator. In the amplifier stage, the seed laser (Seed 1 or Seed 2) is first power amplified by three stages of PM pre-amplifiers. A PM circulator with the central wavelength of 1064 nm is used to monitor the backward propagating light from the main amplifier. The output power of the seed laser is adjusted to about 20 W after the circulator. The seed laser is then launched into the main amplifier via a PM mode field adaptor (MFA) and a PM combiner, together with the pump laser provided by high-power laser diodes (LDs) at 976 nm. The core/cladding diameters of the input and output fibers of the PM mode field adaptor are 10/125 µm and 20/400 µm, respectively. The active fiber in the main amplifier is a commercial double clad PM Yb-doped fiber (YDF), which has the core and cladding diameters of 20 µm and 400 µm, respectively. The numerical aperture (NA) of the PM Yb-doped fiber is about 0.06. The cladding absorption coefficient of the PM Yb-doped fiber is about 1.5 dB/m at 976 nm, and about 10 m YDF is used in the main amplifier. The amplifier output end is spliced with a cladding power stripper (CPS) and a quartz block holder (QBH) to mitigate the residual cladding light and deliver the laser power into space.
When a filtered SFS is applied as the seed laser, the minimum 3 dB spectral linewidth of the inserted filtered SFS (after the pre-amplifiers) is about 1.47 nm in the experiment to avoid serious spectral broadening phenomenon. In addition, the maximum 3 dB spectral linewidth of the inserted filtered SFS is about 7.97 nm. When a phase-modulated SFL is applied as the seed laser, enough enhancement of the stimulated Brillouin scattering (SBS) threshold is required to avoid the possible impact of the SBS effect on the output properties of the fiber amplifier. Thus, the minimum and maximum 3 dB spectral linewidth of the inserted phase-modulated SFL (after the pre-amplifiers) is about 0.19 nm and 1.21 nm in the experiment, respectively. Therefore, the 3 dB spectral linewidth of the seed laser could be adjusted from 0.19 nm to 7.97 nm.
3. Experimental results
3.1 Properties of the fiber amplifier employing filtered SFSs as a seed laser
Figures 2(a) and 2(b) illustrate the output powers and spectra of the signal laser in the fiber amplifier, when the 3 dB spectral linewidth of the inserted filtered SFS is about 1.47 nm. As shown in Fig. 2(a), the output power grows almost linearly as a function of the pump power, and the corresponding slope efficiency is about 75%. As shown in Fig. 2(b), the overall output spectrum of the signal laser broadens with the increasing output power, while the change of the 3 dB spectral linewidth is irregular. Specifically, the 3 dB spectral linewidths of the signal laser are about 1.24 nm, 1.93 nm, and 1.53 nm when the output powers are 362 W, 744 W, and 988 W, respectively.
Fig. 2. Basic output properties of the fiber amplifier when the 3 dB spectral linewidth of the inserted filtered SFS is about 1.47 nm: (a) power curve; (b) output spectrum.
The TMI threshold of a fiber amplifier is commonly defined as the output power when sudden onset of beam fluctuations occurs, which could also be characterized through employing the sudden increase of the normalized standard deviation (NSD) for the intensity evolution of the signal laser [39]. Accordingly, both the beam quality and the NSD for the intensity evolution of the signal laser are utilized to estimate the TMI threshold of the fiber amplifier in the experiments. Specifically, the beam quality is measured by a laser quality monitor and the intensity evolution is measured by a photodetector of 100 MHz bandwidth with an oscilloscope of 10 GHz bandwidth. Figure 3(a) and 3(b) illustrate the M2 beam quality and the NSD for the intensity evolution of the signal laser as a function of output power when the 3 dB spectral linewidth of the inserted filtered SFS is about 1.47 nm. As shown in Fig. 3(a), the M2 beam quality of the signal laser grows quickly after an output power of about 900 W. As shown in Fig. 3(b), the NSD for the intensity evolution of the signal laser also grows quickly after an output power of about 900 W. Accordingly, both the measured M2 beam quality and NSD indicate that the TMI threshold of the fiber amplifier is around 900 W when the 3 dB spectral linewidth of the inserted filtered SFS is about 1.47 nm.
Fig. 3. Properties of the signal laser as a function of output power when the 3 dB spectral linewidth of the inserted filtered SFS is about 1.47 nm: (a) M2 beam quality; (b) NSD.
Compared to the M2 beam quality, the NSD could provide a more quantitative estimation for the TMI threshold of the fiber amplifier through curve fitting with the expression of ${y_{fit}} = a \cdot \textrm{exp} ({b \cdot x} )+ c$. For better comparisons among the TMI threshold of the fiber amplifier in different cases, we set b = 0.04 and define the TMI threshold of the fiber amplifier as the output power when the slope of the fitting curve reaches 0.01‰/W here. Figure 4 illustrates the TMI threshold of the fiber amplifier as a function of 3 dB spectral linewidth of the inserted filtered SFS. As shown in Fig. 4, the overall TMI threshold of the fiber amplifier keeps around 0.93 kW when the 3 dB spectral linewidth of the inserted filtered SFS is less than 5.79 nm, and increases quickly to about 1.26 kW when the 3 dB spectral linewidth of the inserted filtered SFS is 7.97 nm.
Fig. 4. TMI threshold of the fiber amplifier as a function of 3 dB spectral linewidth of the inserted filtered SFS.
3.2 Properties of the fiber amplifier employing phase-modulated SFLs as a seed laser
Figures 5(a) and 5(b) illustrate the output powers and spectra of the signal laser in the fiber amplifier, when the 3 dB spectral linewidth of the inserted phase-modulated SFL is about 0.19 nm. As shown in Fig. 5(a), the output power grows almost linearly as a function of the pump power and there is no sign of nonlinear increase in the backward propagating power, thus the fiber amplifier works well below the SBS threshold. As shown in Fig. 5(b), the spectrum of the output signal laser at an output power of 569 W is nearly identical to the seed laser, and the 3 dB spectral linewidth of the output signal laser is about 0.18 nm. Similarly, the fiber amplifier also works well below the SBS threshold and the spectrum of the output signal laser is also close to the spectrum of the inserted phase-modulated SFL, when the 3 dB spectral linewidth of the inserted phase-modulated SFL ranges from 0.19 nm to 1.21 nm.
Fig. 5. Basic output properties of the fiber amplifier when the 3 dB spectral linewidth of the inserted phase-modulated SFL is about 0.19 nm: (a) power curve; (b) output spectrum.
Similar to the treatment of the results shown in Fig. 4, we obtain the TMI threshold of the fiber amplifier when the 3 dB spectral linewidth of the inserted phase-modulated SFL is different, which is shown in Fig. 6. As shown in Fig. 6, the TMI threshold of the fiber amplifier grows with the increasing 3 dB spectral linewidth of the inserted phase-modulated SFL. Specifically, the TMI threshold of the fiber amplifier is about 483 W when the 3 dB spectral linewidth of the inserted phase-modulated SFL is about 0.19 nm, and increases to about 767 W when the 3 dB spectral linewidth of the inserted phase-modulated SFL is about 1.21 nm.
Fig. 6. TMI threshold of the fiber amplifier as a function of 3 dB spectral linewidth of the inserted phase-modulated SFL.
3.3 Impact of the signal bandwidth on the TMI threshold of the fiber amplifier
Combing the results shown in Fig. 4 and Fig. 6, the impact of the signal bandwidth on TMI threshold of the fiber amplifier could be demonstrated. To give a more comprehensive description of the spectral linewidth for both the phase-modulated SFL and filtered SFS, another two criteria, i.e., the root-mean-square (RMS) linewidth and the power-ratio linewidth, are utilized to characterize the linewidth of the seed laser. The RMS linewidth is defined by the secondary moment of the spectrum and the power-ratio linewidth is defined as the minimum spectral linewidth within which the power ratio of the signal laser is over a certain proportion.
Figures 7(a)–7(c) illustrate the TMI thresholds of the fiber amplifier as a function of spectral linewidth of the seed laser. The blue square and the green round in Figs. 7(a)–7(c) correspond to the phase-modulated SFL and filtered SFS, respectively. As shown in Figs. 7(a)–7(c), the overall trends of the TMI thresholds are similar to each other when different criteria are utilized to characterize the spectral linewidth of the seed laser. Specifically, there are three regions for the evolution of the TMI threshold as a function of spectral linewidth of the seed laser: (A) growth region; (B) smooth region; (C) growth region. Take the 95% power-ratio linewidth as an example, the TMI threshold grows with the spectral linewidth when the linewidth is below 2 nm, keeps almost constant when the linewidth ranges from 2 nm to 6 nm, and further grows with the spectral linewidth when the linewidth is over 6 nm.
Fig. 7. TMI threshold of the fiber amplifier as a function of spectral linewidth of the seed laser: (a) 3 dB linewidth; (b) RMS linewidth; (c) 95% power-ratio linewidth.
It should be noted that the strength of the intensity fluctuation for the signal laser near the TMI threshold are also different when the 3 dB spectral linewidth of the seed laser is different. Figure 8 illustrates the maximum NSD for the intensity evolution of the signal laser at the corresponding TMI threshold as a function of the 3 dB spectral linewidth of the seed laser. The blue square and the green round in Figs. 8 correspond to the phase-modulated SFL and filtered SFS, respectively. As shown in Fig. 8, the overall maximum NSD decreases along with the increasing spectral linewidth of the seed laser. Specifically, the maximum NSD is about 2.2% when the 3 dB spectral linewidth of the seed laser is 0.22 nm, and the maximum NSD is about 0.2% when the 3 dB spectral linewidth of the seed laser is 7.97 nm.
Fig. 8. Maximum NSD for the intensity evolution of the signal laser at the corresponding TMI threshold as a function of the 3 dB spectral linewidth of the seed laser.
4. Discussion and conclusion
Previous studies have pointed out that the TMI threshold of fiber amplifiers is closely related to two issues, i.e., the strength of the thermally induced refractive index grating and the phase shift between the modal interference pattern and the thermally induced refractive index grating [14,16,40]. Accordingly, the impact of the signal bandwidth on TMI threshold of fiber amplifiers could be possibly understood through the two issues. On the one hand, the strength of thermally induced refractive index grating could be reduced if the coherence time of the signal laser is less than the group-velocity-induced walk off between the two interacting modes [30]. In this case, the TMI threshold of a fiber amplifier would grow with the increasing signal bandwidth. On the other hand, the phase shift is provided by a small frequency shift between laser in the two interacting modes, and the small frequency shift further contributes to the intensity fluctuation of the signal laser after the TMI threshold. Accordingly, the decreasing maximum NSD indicates that the phase shift might be weakened with the increasing signal bandwidth. Overall, the mechanism for the signal bandwidth on TMI threshold of fiber amplifiers still requires further experimental and theoretical investigations.
In conclusion, we demonstrate a detailed experimental study on the impact of signal bandwidth on TMI threshold of fiber amplifiers through constructing seed lasers with different spectral linewidths and measuring the corresponding TMI threshold of fiber amplifiers. Specifically, both the filtered SFSs and the phase-modulated SFLs are employed as the seed lasers, and 3 dB spectral linewidth of the seed lasers could range from 0.19 nm to 7.97 nm. Meanwhile, the TMI threshold of the fiber amplifier employing those seed lasers are estimated through the intensity evolution of the signal laser. Notably, the experimental results reveal that the TMI threshold of fiber amplifiers grows, keeps constant, and further grows as a function of spectral linewidth of seed lasers when different criteria are utilized to characterize the spectral linewidth of the seed lasers. In addition, the experimental results also reveal that the overall maximum NSD of the signal laser decreases as a function of the spectral linewidth of the seed laser. Our experimental results could provide a well reference to understand the mechanism of the TMI effect and optimize the TMI effect in high-power fiber amplifiers.
Funding
National Natural Science Foundation of China (62005313, 62061136013); Innovative Research Team in Natural Science Foundation of Hunan Province (2019JJ10005).
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.
References
1. D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives [Invited],” J. Opt. Soc. Am. B 27(11), B63–B92 (2010). [CrossRef]
2. W. Shi, Q. Fang, X. Zhu, R. A. Norwood, and N. Peyghambarian, “Fiber lasers and their applications [Invited],” Appl. Opt. 53(28), 6554–6568 (2014). [CrossRef]
3. 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]
4. K. Shima, S. Ikoma, K. Uchiyama, Y. Takubo, M. Kashiwagi, and D. Tanaka, “5-kW single stage all-fiber Yb-doped single-mode fiber laser for materials processing,” Proc. SPIE 10512, 11 (2018). [CrossRef]
5. M. Friedrich, G. K. Ria, M. Christian, S. Maximilian, P. Marco, S. Fabian, W. Till, S. Thomas, E. Ramona, N. Stefan, and T. Andreas, “Multi-kW performance analysis of Yb-doped monolithic single-mode amplifier and oscillator setup,” Proc. SPIE 10897, 12 (2019). [CrossRef]
6. R. G. Kramer, F. Moller, C. Matzdorf, T. A. Goebel, M. Strecker, M. Heck, D. Richter, M. Plotner, T. Schreiber, A. Tunnermann, and S. Nolte, “Extremely robust femtosecond written fiber Bragg gratings for an ytterbium-doped fiber oscillator with 5 kW output power,” Opt. Lett. 45(6), 1447–1450 (2020). [CrossRef]
7. V. Khitrov, J. D. Minelly, R. Tumminelli, V. Petit, and E. S. Pooler, “3 kW single-mode direct diode-pumped fiber laser,” Proc. SPIE 8961, 89610V (2014). [CrossRef]
8. J. Wang, D. Yan, S. Xiong, B. Huang, and C. Li, “High power all-fiber amplifier with different seed power injection,” Opt. Express 24(13), 14463–14469 (2016). [CrossRef]
9. Q. Fang, J. Li, W. Shi, Y. Qin, Y. Xu, X. Meng, R. A. Norwood, and N. Peyghambarian, “5 kW near-diffraction-limited and 8 kW high-brightness monolithic continuous wave fiber lasers directly pumped by laser diodes,” IEEE Photonics J. 9(5), 1–7 (2017). [CrossRef]
10. P. Nikolai, Y. Roman, C. Joel De La, Y. Alexander, and G. Valentin, “Up to 2.5-kW on non-PM fiber and 2.0-kW linear polarized on PM fiber narrow linewidth CW diffraction-limited fiber amplifiers in all-fiber format,” Proc. SPIE 10512, 13 (2018). [CrossRef]
11. Z. Wang, P. Yan, Y. Huang, J. Tian, C. Cai, D. Li, Y. Yi, Q. Xiao, and M. Gong, “An efficient 4-kW level random fiber laser based on a tandem-pumping scheme,” IEEE Photonics Technol. Lett. 31(11), 817–820 (2019). [CrossRef]
12. C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013). [CrossRef]
13. R. Tao, X. Wang, and P. Zhou, “Comprehensive theoretical study of mode instability in high-power fiber lasers by employing a universal model and its implications,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–19 (2018). [CrossRef]
14. C. Jauregui, C. Stihler, and J. Limpert, “Transverse mode instability,” Adv. Opt. Photonics 12(2), 429–484 (2020). [CrossRef]
15. M. N. Zervas, “Transverse mode instability, thermal lensing and power scaling in Yb3+-doped high-power fiber amplifiers,” Opt. Express 27(13), 19019–19041 (2019). [CrossRef]
16. A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19(11), 10180–10192 (2011). [CrossRef]
17. B. Ward, C. Robin, and I. Dajani, “Origin of thermal modal instabilities in large mode area fiber amplifiers,” Opt. Express 20(10), 11407–11422 (2012). [CrossRef]
18. C. Jauregui, T. Eidam, H. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Physical origin of mode instabilities in high-power fiber laser systems,” Opt. Express 20(12), 12912–12925 (2012). [CrossRef]
19. K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Laegsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express 21(2), 1944–1971 (2013). [CrossRef]
20. M. N. Zervas, “Transverse-modal-instability gain in high power fiber amplifiers: Effect of the perturbation relative phase,” APL Photonics 4(2), 022802 (2019). [CrossRef]
21. N. Xia and S. Yoo, “Investigation of thermal loads for transverse mode instability in Ytterbium-Doped large mode area fibers,” J. Lightwave Technol. 38(16), 4478–4489 (2020). [CrossRef]
22. C. Jauregui, H.-J. Otto, S. Breitkopf, J. Limpert, and A. Tünnermann, “Optimizing high-power Yb-doped fiber amplifier systems in the presence of transverse mode instabilities,” Opt. Express 24(8), 7879–7892 (2016). [CrossRef]
23. P. Ma, H. Xiao, D. Meng, W. Liu, R. Tao, J. Leng, Y. Ma, R. Su, P. Zhou, and Z. Liu, “High power all-fiberized and narrow-bandwidth MOPA system by tandem pumping strategy for thermally induced mode instability suppression,” High Pow Laser Sci Eng 6(4), e57 (2018). [CrossRef]
24. Z. Li, Z. Huang, X. Xiang, X. Liang, H. Lin, S. Xu, Z. Yang, J. Wang, and F. Jing, “Experimental demonstration of transverse mode instability enhancement by a counter-pumped scheme in a 2 kW all-fiberized laser,” Photonics Res. 5(2), 77–81 (2017). [CrossRef]
25. R. Tao, R. Su, P. Ma, X. Wang, and P. Zhou, “Suppressing mode instabilities by optimizing the fiber coiling methods,” Laser Phys. Lett. 14(2), 025101 (2017). [CrossRef]
26. F. Stutzki, F. Jansen, H.-J. Otto, C. Jauregui, J. Limpert, and A. Tünnermann, “Designing advanced very-large-mode-area fibers for power scaling of fiber-laser systems,” Optica 1(4), 233–242 (2014). [CrossRef]
27. C. Robin, I. Dajani, and B. Pulford, “Modal instability-suppressing, single-frequency photonic crystal fiber amplifier with 811 W output power,” Opt. Lett. 39(3), 666–669 (2014). [CrossRef]
28. Y. Wang, G. Chen, and J. Li, “Development and prospect of high-power Yb3+ doped fibers,” High Power Laser Sci. Eng. 6(3), 03000e40 (2018). [CrossRef]
29. H. Otto, A. Klenke, C. Jauregui, J. Limpert, and A. Tünnermann, “Four-fold increase of the mode instability threshold with a multi-core photonic crystal fiber,” in Frontiers in Optics (2013), paper FW6A.5.
30. J. J. Smith and A. V. Smith, “Influence of signal bandwidth on mode instability thresholds of fiber amplifiers,” Proc. SPIE 9344, 93440L (2015). [CrossRef]
31. C. X. Yu, O. Shatrovoy, T. Y. Fan, and T. F. Taunay, “Diode-pumped narrow linewidth multi-kilowatt metalized Yb fiber amplifier,” Opt. Lett. 41(22), 5202–5205 (2016). [CrossRef]
32. F. Beier, C. Hupel, S. Kuhn, S. Hein, J. Nold, F. Proske, B. Sattler, A. Liem, C. Jauregui, J. Limpert, N. Haarlammert, T. Schreiber, R. Eberhardt, and A. Tunnermann, “Single mode 4.3 kW output power from a diode-pumped Yb-doped fiber amplifier,” Opt. Express 25(13), 14892–14899 (2017). [CrossRef]
33. Z. Huang, Q. Shu, R. Tao, Q. Chu, Y. Luo, D. Yan, X. Feng, Y. Liu, W. Wu, H. Y. Zhang, H. Lin, J. Wang, and F. Jing, “5 kW record high power narrow linewidth laser from traditional step-index monolithic fiber amplifier,” IEEE Photonics Technol. Lett. 33(21), 1181–1184 (2021). [CrossRef]
34. P. Ma, H. Xiao, W. Liu, H. Zhang, X. Wang, J. Leng, and P. Zhou, “All-fiberized and narrow-linewidth 5 kW power-level fiber amplifier based on a bidirectional pumping configuration,” High Power Laser Sci. Eng. 9(3), e45 (2021). [CrossRef]
35. W. Liu, P. Ma, and P. Zhou, “Unified model for spectral and temporal properties of quasi-CW fiber lasers,” J. Opt. Soc. Am. B 38(12), 3663–3682 (2021). [CrossRef]
36. J. Ye, X. Ma, Y. Zhang, J. Xu, H. Zhang, T. Yao, J. Leng, and P. Zhou, “From spectral broadening to recompression: dynamics of incoherent optical waves propagating in the fiber,” PhotoniX 2(1), 15 (2021). [CrossRef]
37. J. Ye, C. Fan, J. Xu, H. Xiao, J. Leng, and P. Zhou, “2-kW-level superfluorescent fiber source with flexible wavelength and linewidth tunable characteristics,” High Power Laser Sci. Eng. 9(4), e55 (2021). [CrossRef]
38. W. Liu, P. Ma, P. Zhou, and Z. Jiang, “Spectral property optimization for a narrow-band-filtered superfluorescent fiber source,” Laser Phys. Lett. 15(2), 025103 (2018). [CrossRef]
39. H.-J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnermann, “Temporal dynamics of mode instabilities in high-power fiber lasers and amplifiers,” Opt. Express 20(14), 15710–15722 (2012). [CrossRef]
40. C. Stihler, C. Jauregui, S. E. Kholaif, and J. Limpert, “Intensity noise as a driver for transverse mode instability in fiber amplifiers,” PhotoniX 1(1), 8 (2020). [CrossRef]
