Open Access
Add to BibSonomy
Abstract
The comprehensive suppression of the stimulated Brillouin scattering (SBS) and transverse mode instability (TMI) is a critical issue for the power scaling of fiber laser with sub-GHz spectral linewidth. In this manuscript, a narrow linewidth and polarization-maintained (PM) fiber amplifier based on tapered Yb-doped fiber (T-YDF) is established, and the effects of spectral linewidth, spectral shape and pump wavelength on the SBS and/or TMI thresholds are investigated. Up to 694 W polarization-maintained fiber laser with just ∼790 MHz linewidth is obtained by combining the advantages of tapered Yb-doped fiber, near-rectangular spectral injection and 915 nm pump manner. This work could provide a well reference solution for the realization of high-power ultra-narrow linewidth fiber lasers.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High power narrow-linewidth and linear-polarized fiber lasers have attracted much attention in recent years for numerous applications, such as coherent/spectral beam combining [1–4], coherent lidar [5,6] and nonlinear frequency conversion [7]. However, the power scaling of which is primarily limited by the nonlinear stimulated Brillouin scattering (SBS), stimulated Raman scattering (SRS), and transverse mode instability (TMI) [8–10]. Besides, the effect of background spectral noise will also influence the power scaling and spectral purity [11]. With the development of high brightness pump source, the applying of bi-direction pumping technique, and the overall optimizing to suppress the detrimental effects mentioned above, the output power of narrow-linewidth fiber laser has developed rapidly in recent years. For those fiber lasers with tens of GHz or broader spectral linewidth, 5 kW power-level stochastic polarized fiber lasers have been achieved [12,13] and this power-level has been improved as high as 6 kW quite recently [14]. For the linear-polarized ones, > 2 kW output power have been reported [15–18] and the maximum power scaling has been scaled to 4 kW [14].
Except for power scaling, spectral linewidth narrowing has been always a focused point in the above-mentioned applications to ensure efficient system operation [19–24]. However, when the spectral linewidth is narrowed to within 10 GHz, the balancing of SBS and TMI effects becomes more challenging for the system design, mainly attributed to the inter-contradiction in the selection of core/cladding ratio of active fiber, pump absorption, et. al in conventional fiber laser system [25,26]. In the stochastic polarized all-fiber amplifiers, by using pseudo-random bit sequence (PRBS) phase modulation format, a 1 kW output laser with linewidth of 3.5 GHz is reported in 2016 [27]. Further incorporating thermal gradient or laser gain competition technology, the linewidth could be compressed to 2-3 GHz while the output power is still maintaining at kilowatt-level [28–30]. As for the all-fiber linear-polarized fiber lasers, the typical results are listed in Table 1 [31–38]. In the early of 2008, a kilowatt-level PM fiber amplifier with full width at half maximum (FWHM) linewidth of 8 GHz was achieved [31]. Further narrowing the linewidth to 1.8 GHz, a PM fiber amplifier with output power and PER of 827 W and 12 dB was realized by applying laser gain competition technology [35]. Moreover, by utilizing multi-phase coded signal (MPCS) modulation, W. Lai et. al reported a 737 W fiber amplifier with a linewidth of 4.6 GHz. And further importing laser gain competition technology, the output power could be improved to 1023 W [37].
Table 1. Recent progress of all-fiber high-power narrow linewidth PM fiber lasers
Despite some impressiveness has been achieved, the investigations of all-fiber linear-polarized fiber lasers with linewidth <1 GHz are seldom reported, which are strongly demanded to ensure temporal coherence and combining efficiency in high-power CBC system while propagating for a long distance [39]. Nevertheless, when the linewidth is controlled within 1 GHz, to suppress SBS, active fiber with high absorption coefficient (high dopant concentration and high core-to-cladding ratio) is required to shorten the fiber length, which will further decrease the TMI threshold [40,41]. Therefore, the SBS threshold may be comparable to the TMI threshold in the linear-polarized fiber lasers with <1 GHz linewidth, which makes it quite difficult to increase the power level.
In this paper, a PM tapered active fiber is selected to build the amplifier due to its high gain coefficient, large mode area and mode selection feature, which facilitate the mitigation of SBS effect and the maintenance of good beam quality. Based on this T-YDF constructed amplifier, we investigate the power scaling of PM fiber laser with <1 GHz linewidth by comprehensively suppressing the SBS and TMI effects. The effects of linewidth, spectral shape and pump wavelength on the SBS threshold and/or TMI threshold are studied, respectively. As a result, a linear-polarized fiber laser with the output power of 694 W and the linewidth of ∼790 MHz is obtained by employing the PM T-YDF, a seed laser with near-rectangular spectrum and 915 nm pump scheme.
2. Experimental setup
The experimental setup of the high-power narrow-linewidth fiber amplifier is based on the master oscillator power amplifier (MOPA) configuration, as shown schematically in Fig. 1. The initial seed is a linearly polarized single-frequency fiber laser operating at 1064 nm with the output power of 53 mW and the 3 dB linewidth of 20 kHz [42]. The seed is externally modulated through a LiNbO3 electro-optic modulator (EOM) driven by a white noise source (WNS) signal or a sinusoidal signal to broaden its spectral linewidth. The EOM has a half-wave voltage of 1.5 V and a bandwidth of 150 MHz. After the EOM, the phase modulated seed is injected into a pre-amplifier (Pre-1) and the output power is amplified to 500 mW. A PM isolator (ISO) is employed after Pre-1 to protect the front system. Moreover, a band-pass filter (BPF-1) with a bandwidth of 2 nm at the central wavelength of 1064 nm is used to filter out the sideband noise, which is beneficial to the suppression of amplified spontaneous emission (ASE) in the subsequent amplification system. To further scale the seed power, the second pre-amplifier (Pre-2) is utilized to improve the seed power to ∼8 W. A high-power PM circulator with 50 W maximal operating power is inserted after Pre-2. The backward power from the main amplifier is exported by the circulator and monitored by a power meter. Then, a high-power PM band-pass filter (BPF-2) with 2 nm bandwidth around 1064 nm is employed before the main amplifier to remove the sideband noise and suppress the ASE in the main amplifier.
As for the main amplifier, a forward pumped configuration is employed. LDs are combined to pump a PM T-YDF via a (6 + 1)×1 PM combiner, which has a 15/130 µm (core/cladding diameter) signal input port and 25/250 µm output port. The pump delivery fibers of the LDs and the combiner are all 105/125 µm fibers with numerical aperture (NA) of 0.22. The core and cladding diameters of the T-YDF versus the fiber length are shown in Fig. 2. The T-YDF could be divided into three sections according to the variation of core and cladding diameters, including the small-core section, tapered section and large-core section. The small-core section has the core/cladding diameter of 35.0/250.0 µm and a length of ∼1.6 m, while the large-core section has the core/cladding diameter of 56.2/400.0 µm and a length of ∼1.5 m. As for the tapered section, the core/cladding diameter shows an approximately linear trend and the length is ∼0.7 m. The total length of the T-YDF is controlled at only ∼3.8 m to better suppress the SBS effect. The core-to-cladding ratio keeps almost unchanged along the T-YDF. The seed laser and pump light inject from the small-core end to ensure good beam quality and output through the large-core end to improve the SBS threshold. In addition, the core NA of the T-YDF is ∼0.07 and the cladding pump absorption coefficients of the T-YDF are 2.0 dB/m at 915 nm and 8.0 dB/m at 975 nm. The T-YDF was coiled on the surface of a water-cooling plate with a diameter of ∼18 cm for the small-core section, a diameter of ∼38 cm for the large-core section and varying dimeter from 18 cm to 38 cm for the tapered section. An endcap is spliced at the end to avoid facet damage and possible parasitic lasing. Finally, the output beam is collimated by a free-space collimator and the residual pump light is removed by a dichroic mirror before all the measurements.
3. Experimental results and discussion
3.1 Effect of seed linewidth on SBS threshold
In our experiment, the FWHM linewidth of the seed is firstly broadened to 280 MHz, 660 MHz and 790 MHz via the EOM driven by WNS signal. The main amplifier is pumped by LDs at 915 nm. Figure 3(a) illustrates the output power and backward power versus the pump power. When the seed linewidth is adjusted to 280 MHz, there is a significant nonlinear increase in backward power when the output power exceeds 300 W, indicating the onset of SBS effect. Here, the SBS threshold is defined as the output power when the proportion of the backward power to the output power reaches 0.03% in this paper. Therefore, the SBS threshold of the amplifier is 327 W when the seed linewidth is adjusted at 280 MHz. Then, the seed linewidth is further broadened to 660 MHz and 790 MHz, and the SBS thresholds are correspondingly improved to 587 W and 639 W. Consequently, the seed linewidth is broadened by a factor of 2.4 and 2.8, and the SBS threshold increases by a factor of 1.8 and 2.0, respectively. The fitted slope efficiencies are almost the same, around 63% for the amplifier with three different linewidths. The spectral linewidths of the output laser are measured by a Fabry-Perot interferometer (FPI) with a free spectral range (FSR) of 10 GHz. Figure 3(b) shows the scanning spectra of the FPI at the maximum output power for the amplifier with three different linewidths. During the amplification process, the spectral linewidth keeps almost unchanged, and the spectral shape remains near-Gaussian. The results show that the SBS threshold can be effectively improved by broadening the seed linewidth, but the improvement factor of SBS threshold may be smaller than the broadening factor of the seed linewidth.
Fig. 3. (a) Output power and backward power versus the pump power for the amplifier with the linewidth of 280 MHz, 660 MHz and 790 MH; (b) scanning spectra for the output laser.
At the onset of SBS effect, multiple spikes would appear in the temporal trace and spectrum of the backward light [29,43]. Actually, a similar phenomenon would occur in the output laser. Figures 4(a)-(b) show the temporal trace and spectrum (measured by an optical spectrum analyzer (OSA)) of the output laser recorded at the SBS threshold, when the linewidth of laser is controlled at 790 MHz. Obvious pulses are observed in the normalized temporal trace, shown in Fig. 4(a). As shown in the output spectrum in Fig. 4(b), spikes around 1130 nm are observed, possibly Raman light excited by the SBS pulses.
Fig. 4. Temporal and spectral properties of the output laser at the SBS threshold. (a) Temporal trace normalized by the mean value; (b) spectrum measured by an OSA.
3.2 Effect of the spectral shape on SBS threshold
The previous studies have proved that the SBS threshold is tightly related to the modulated spectral shapes produced by different modulating signals [44–49]. In our experiment, when WNS signal is applied to drive the EOM, obvious pulses could be observed on the time domain at the threshold power indicating an unstable SBS effect, which may lead to the damage of front components. Comparing with other kinds of spectral shapes, rectangular spectrum performs optimizing mitigation of SBS effect [45]. Therefore, a seed laser with near-rectangular spectrum is generated through the EOM driven by a sinusoidal signal when the drive frequency and voltage was set at 40 MHz and 6.1 V. The scanning spectrum of the FPI for the seed laser is shown in Fig. 5(a), and the FWHM linewidth of the seed laser is ∼790 MHz, equal to the maximum linewidth of the near-Gaussian spectrum generated via the EOM driven by the WNS signal. Based on the seed laser with near-rectangular spectrum, further power scaling is explored. Figure 5(b) illustrates the output power and backward power versus the pump power. The output power is further improved to 694 W at the pump power of 1058 W, corresponding to the optical-to-optical efficiency of ∼65.3%. Meanwhile, the backward power shows a linear growth trend during the amplification process, indicating no SBS effect occurs. Namely, the SBS threshold of the amplifier is above 694 W when the seed laser with near-rectangular spectrum is employed.
Fig. 5. (a) The scanning spectrum for the seed laser with near-rectangular spectrum; (b) the output power and backward power versus the pump power.
Further power scaling of the amplifier based on the seed laser with near-rectangular spectrum is limited by the TMI effect. Figures 6(a)-(d) show the temporal traces and corresponding Fourier spectra around the TMI threshold. The temporal stability is evaluated by the normalized standard deviation (NSTD) of the temporal trace, i.e., the standard deviation divided by the mean value. When the output power grows from 668 W to 694 W, there are obvious fluctuations in the temporal trace (see Figs. 6(a) and 6(b)) and the NSTD increases significantly from 0.033 to 0.098. Meanwhile, characteristic peaks below 5 kHz appear on the Fourier spectrum, as shown in Fig. 6(d). The results verify the onset of TMI effect at the output power of 694 W, which restricts further power scaling of the amplifier.
Fig. 6. The temporal properties around the TMI threshold. (a) The temporal trace and (c) corresponding Fourier spectrum at the output power of 668 W; (b) the temporal trace and (d) corresponding Fourier spectrum at the output power of 694 W.
Other properties of the output laser are also measured and demonstrated in Fig. 7. Figure 7(a) is the scanning spectrum of the FPI. The picture shows that the output spectrum still has a near-rectangular shape, and the FWHM linewidth of the output laser measured at the maximum output power is still maintained at ∼790 MHz. Figure 7(b) shows the output spectrum measured by an OSA. The signal-to-noise ratio of the output laser is around 60 dB, and no spikes are observed in the spectrum. The spectral results also prove that the SBS effect is effectively suppressed. Meanwhile, the polarization extinction ratio (PER) of the output power is recorded at different pump power, which has been shown in Fig. 7(c). From this figure, we can see that the PER performs a slight decrease through the power amplification process. And the PER is measured to be 11.4 dB at the maximum output power. Besides, the typical beam quality is measured at 226 W, 521 W and 694 W and the beam profile at the focus point is shown inserted in Fig. 7(c). The M2 value of the output laser increases a little with the increase of output power, indicating a slight degradation of beam quality. At the maximum output power, the M2 value is measured to be Mx2 = 1.333, My2 = 1.111.
Fig. 7. (a) The scanning spectrum of the FPI; (b) the spectrum measured by the OSA; (c) the PER of the output laser through the amplification process. (Insert: the beam profile and corresponding beam quality M2)
The spectral linewidth of the near-Gaussian spectrum (in Fig. 3(b)) and the near-rectangular spectrum (in Fig. 7(a)) obtained in this work, are almost the same both ∼790 MHz. In addition to spectral linewidth, spectral shape of the fiber laser is also critical for some practical applications like coherent beam combining. Here, we use complex degree of coherence (CDC) to describe the spectral characteristics of the output laser with different spectral shapes, the expression of which could be described as
Figure 8 shows the CDC of the near-Gaussian spectrum (k1) and near-rectangular spectrum (k2) at the maximum output power. The CDC of the near-rectangular spectrum keeps higher than that of the near-Gaussian spectrum throughout the increase of delay time, indicating a higher combining efficiency of CBC system.
3.3 Effect of pump wavelength on TMI threshold
For those SBS limited narrow linewidth fiber lasers, LDs at ∼976 nm (one absorption peak of YDF) are often employed as the pump source owing to relatively higher absorption coefficient. Shorter active fiber is required when the pump wavelength is ∼976 nm, resulting in higher SBS threshold. However, the selection of pump wavelength would have an influence on the gain saturation effect, which greatly affects the TMI threshold of the fiber laser. And the extent to which the TMI threshold varies with pump wavelength would be weakened with the increase of the core-to-cladding ratio of the active fiber [51–53].
In this work, we investigate the effect of pump wavelength on TMI threshold in the fiber amplifier based on tapered fiber with relatively large core-to-cladding ratio. LDs at 915 nm (another absorption peak of YDF with lower absorption coefficient), 976 nm and 981 nm (with lower absorption coefficient due to deviation from 976 nm) are employed for comparison. The seed laser is modulated with the linewidth of 790 MHz and near-rectangular spectrum. Figure 9(a) illustrates the output power as a function of pump power for the amplifier with different pump wavelengths. The fitted slope efficiencies for the amplifier pumped at 915 nm, 976 nm and 981 nm are 63.9%, 81.4% and 70.0%, respectively. The amplifier pumped at 915 nm has the lowest slope efficiency, which is ∼78% of the slope efficiency of the amplifier pumped at 976 nm. Limited by the TMI effect, the maximum output powers for the amplifier pumped at 915 nm, 976 nm and 981 nm are 694 W, 490 W and 674 W, respectively. The temporal properties, including the temporal traces and their Fourier transform spectra, at the TMI thresholds of the amplifier pumped at 976 nm and 981 nm are shown in Figs. 9(b)-(c). The strong fluctuations in the temporal traces (NSTD = 0.149 for 976 nm pump; NSTD= 0.060 for 981 nm pump) and characteristics peaks around several kHz both indicate the onset of TMI effect. Compared with the TMI threshold of the amplifier pumped at 976 nm, the TMI thresholds of the amplifier pumped at 915 nm and 981 nm increase by 41.6% and 37.6%, respectively. The results show that the 915 nm and 981 nm pump schemes would sacrifice the optical-to-optical conversion efficiency but enhance the TMI threshold, compared to the 976 nm pump scheme. Although the improvement of the TMI threshold here is much smaller than the situation in fiber amplifiers based on larger core-to-cladding ratio fiber (e.g., ∼2 times for a 21/400 µm fiber [51]), it is still of great significance for the power scaling of narrow-linewidth fiber lasers.
Fig. 9. (a) Output power versus the pump power for the amplifier pumped at 915 nm, 976 nm and 981 nm; the temporal traces and their Fourier transform spectra at the TMI thresholds of the amplifier pumped at (b) 976 nm and (c) 981 nm.
4. Conclusion
In this paper, the power scaling of PM fiber laser with <1 GHz linewidth is investigated by comprehensively suppressing the SBS and TMI effects. A PM T-YDF with the core/cladding diameter varying from 35.0/250.0 µm to 56.2/400.0 µm is employed to suppress the SBS effect while maintaining good beam quality. With this T-YDF constructed amplifier, we study the effects of linewidth and spectral shape on the SBS threshold and effect of pump wavelength on the TMI threshold, respectively. The results show that the improvement factor of SBS threshold may be smaller than the broadening factor of the seed linewidth; further suppression of SBS could be realized by employing seed laser with near-rectangular spectrum instead of near-Gaussian spectrum, and the SBS threshold is improved from 639 W to >694 W (TMI limited) when the linewidth keeps ∼790 MHz; adopting LDs at 915 nm as the pump source has advantages in raising TMI threshold compared to adopting 976 nm or 981 nm LDs. Consequently, up to 694 W PM fiber laser is realized with the linewidth of ∼790 MHz and the PER of 11.4 dB by combining a PM T-YDF, a seed laser with near-rectangular spectrum and 915 nm pump scheme. We believe that employing the T-YDF and changing the pump wavelength may be an effective solution for the power scaling of narrow linewidth fiber lasers.
Funding
National Natural Science Foundation of China (62005313, 62061136013); Natural Science Foundation of Hunan Province (2019JJ10005); Special Project for Research and Development in Key areas of Guangdong Province (2018B090904001); Hunan Provincial Innovation Foundation for Postgraduate (CX20200018).
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. Angel Flores, Thomas Ehrehreich, Roger Holten, Brian Anderson, Dajani, and Iyad, “Multi-kW coherent combining of fiber lasers seeded with pseudo random phase modulated light,” in Fiber Lasers XIII: Technology, Systems, and Applications, (2016).
2. P. Ma, H. Chang, Y. Ma, R. Su, Y. Qi, J. Wu, C. Li, J. Long, W. Lai, Q. Chang, T. Hou, P. Zhou, and J. Zhou, “7.1 kW coherent beam combining system based on a seven-channel fiber amplifier array,” Opt. Laser Technol. 140, 107016 (2021). [CrossRef]
3. Y. Zheng, Y. Yang, J. Wang, M. Hu, G. Liu, X. Zhao, X. Chen, K. Liu, C. Zhao, B. He, and J. Zhou, “10.8 kW spectral beam combination of eight all-fiber superfluorescent sources and their dispersion compensation,” Opt. Express 24(11), 12063–12071 (2016). [CrossRef]
4. F. Chen, J. Ma, C. Wei, R. Zhu, W. Zhou, Q. Yuan, S. Pan, J. Zhang, Y. Wen, and J. Dou, “10 kW-level spectral beam combination of two high power broad-linewidth fiber lasers by means of edge filters,” Opt. Express 25(26), 32783–32791 (2017). [CrossRef]
5. F. Yang, Q. Ye, Z. Pan, D. Chen, H. Cai, R. Qu, Z. Yang, and Q. Zhang, “100-mW linear polarization single-frequency all-fiber seed laser for coherent Doppler lidar application,” Opt. Commun. 285(2), 149–152 (2012). [CrossRef]
6. R. Diaz, S.-C. Chan, and J.-M. Liu, “Lidar detection using a dual-frequency source,” Opt. Lett. 31(24), 3600–3602 (2006). [CrossRef]
7. A. Henderson and R. Stafford, “Low threshold, singly-resonant CW OPO pumped by an all-fiber pump source,” Opt. Express 14(2), 767–772 (2006). [CrossRef]
8. H.-J. Otto, C. Jauregui, J. Limpert, and A. A. Tünnermann, “Average power limit of fiber-laser systems with nearly diffraction-limited beam quality,” in Fiber Lasers XIII: Technology, Systems, and Applications, (2016).
9. 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]
10. J. W. Dawson, M. J. Messerly, R. J. Beach, M. Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. P. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Express 16(17), 13240–13266 (2008). [CrossRef]
11. W. Liu, J. Song, P. Ma, H. Xiao, and P. Zhou, “Effects of background spectral noise in the phase-modulated single-frequency seed laser on high-power narrow-linewidth fiber amplifiers,” Photonics Res. 9(4), 424–430 (2021). [CrossRef]
12. Z. Huang, Q. Shu, R. Tao, Q. Chu, Y. Luo, D. Yan, X. Feng, Y. Liu, W. Wu, H. Zhang, H.-H. Lin, J.-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]
13. 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 Pow. Laser Sci. Eng. 9, e45 (2021). [CrossRef]
14. P. Zhou, P. Ma, W. Liu, H. Xiao, S. Ren, J. Song, J. Xu, Y. Chen, and W. Lai, High power, narrow linewidth all-fiber amplifiers, SPIE LASE, Vol. 11981 (2022).
15. N. Platonov, R. Yagodkin, J. De La Cruz, A. Yusim, and V. Gapontsev, “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,” in Fiber Lasers XV: Technology and Systems, (International Society for Optics and Photonics, 105120E (2018).
16. Y. Wang, Y. Sun, W. Peng, Y. Feng, J. Wang, Y. Ma, Q. Gao, R. Zhu, and C. Tang, “3.25 kW all-fiberized and polarization-maintained Yb-doped amplifier with a 20 GHz linewidth and near-diffraction-limited beam quality,” Appl. Opt. 60(21), 6331–6336 (2021). [CrossRef]
17. Y. Wang, Y. Feng, Y. Ma, Z. Chang, W. Peng, Y. Sun, Q. Gao, R. Zhu, and C. Tang, “2.5 kW Narrow Linewidth Linearly Polarized All-Fiber MOPA With Cascaded Phase-Modulation to Suppress SBS Induced Self-Pulsing,” IEEE Photonics J. 12, 1–15 (2020). [CrossRef]
18. 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]
19. Z. Liu, P. Ma, R. Su, R. Tao, Y. Ma, X. Wang, and P. Zhou, “High-power coherent beam polarization combination of fiber lasers: progress and prospect [Invited],” J. Opt. Soc. Am. B 34, 1 (2016). [CrossRef]
20. S. C. Kumar, G. K. Samanta, and M. Ebrahim-Zadeh, “High-power, single-frequency, continuous-wave second-harmonic-generation of ytterbium fiber laser in PPKTP and MgO:sPPLT,” Opt. Express 17(16), 13711–13726 (2009). [CrossRef]
21. J.-P. Cariou, B. Augere, and M. Valla, “Laser source requirements for coherent lidars based on fiber technology,” C. R. Phys. 7(2), 213–223 (2006). [CrossRef]
22. Brian Anderson, Joel Solomon, Flores, and Angel, “1.1 kW, beam-combinable thulium doped all-fiber amplifier,” Proc. SPIE 11665, 116650B (2021). [CrossRef]
23. M. Shi, Z. Wu, J. Li, Y. Wu, M. Yu, Y. Sun, W. Hu, and L. Yi, “High-power narrow-linewidth fiber lasers using optical spectrum broadening based on high-order phase modulation of inversion probability-tuning sequence,” Opt. Express 30(6), 8448–8460 (2022). [CrossRef]
24. G. D. Goodno, “Linewidth Narrowing of a High Power Polarization Maintaining Fiber Amplifier using Nonlinear Phase Demodulation,” in Conference on Lasers and Electro-Optics (2021).
25. S. Ren, W. Lai, G. Wang, W. li, J. Song, Y. Chen, P. Ma, W. Liu, and P. Zhou, “Experimental study on the impact of signal bandwidth on transverse mode instability threshold of fiber amplifiers,” Opt. Express30(5), 7845–7853 (2022). [CrossRef]
26. G. P. Agrawal, Nonlinear Fiber Optics, Fourth ed. Academic Press, Singapore, (2007).
27. N. A. Naderi, A. Flores, B. M. Anderson, K. J. Rowland, and I. Dajani, “Kilowatt high-efficiency narrow-linewidth monolithic fiber amplifier operating at 1034 nm,” in Fiber Lasers XIII: Technology, Systems, and Applications, (2016).
28. N. A. Naderi, A. Flores, B. M. Anderson, and I. Dajani, “Beam combinable, kilowatt, all-fiber amplifier based on phase-modulated laser gain competition,” Opt. Lett. 41(17), 3964–3967 (2016). [CrossRef]
29. A. Flores, C. Robin, A. Lanari, and I. Dajani, “Pseudo-random binary sequence phase modulation for narrow linewidth, kilowatt, monolithic fiber amplifiers,” Opt. Express 22(15), 17735–17744 (2014). [CrossRef]
30. I. Dajani, A. Flores, R. Holten, B. Anderson, B. Pulford, and T. Ehrenreich, “Multi-kilowatt power scaling and coherent beam combining of narrow-linewidth fiber lasers,” in Fiber Lasers XIII: Technology, Systems, and Applications, (2016).
31. J. Edgecumbe, D. Björk, J. Galipeau, G. Boivin, S. Christensen, B. Samson, and K. Tankala, “Kilowatt-Level PM Amplifiers for Beam Combining,” in Frontiers in Optics 2008/Laser Science XXIV/Plasmonics and Metamaterials/Optical Fabrication and Testing (2008).
32. Y. Ran, R. Tao, P. Ma, X. Wang, R. Su, P. Zhou, and L. Si, “560 W all fiber and polarization-maintaining amplifier with narrow linewidth and near-diffraction-limited beam quality,” Appl. Opt. 54(24), 7258–7263 (2015). [CrossRef]
33. X. Zhao, Y. Yang, H. Shen, X. Chen, G. Bai, J. Zhang, Y. Qi, B. He, and J. Zhou, “302 W triple-frequency, single-mode, linearly polarized Yb-doped all-fiber amplifier,” High Power Laser Sci. Eng. 5, e31 (2017). [CrossRef]
34. Y. Wang, Y. Feng, X. Wang, H. Yan, J. Peng, W. Peng, Y. Sun, Y. Ma, and C. Tang, “6.5 GHz linearly polarized kilowatt fiber amplifier based on active polarization control,” Appl. Opt. 56(10), 2760–2765 (2017). [CrossRef]
35. D. Meng, W. Lai, X. He, P. Ma, R. Su, P. Zhou, and L. Yang, “Kilowatt-level, mode-instability-free, all-fiber and polarization-maintained amplifier with spectral linewidth of 1.8 GHz,” Laser Phys. 29(3), 035103 (2019). [CrossRef]
36. C. Jun, M. Jung, W. Shin, B.-A. Yu, Y. S. Yoon, Y. Park, and K. Choi, “818 W Yb-doped amplifier with <7 GHz linewidth based on pseudo-random phase modulation in polarization-maintained all-fiber configuration,” Laser Phys. Lett. 16, 015102 (2019). [CrossRef]
37. W. Lai, P. Ma, J. Song, S. Ren, W. Liu, and P. Zhou, “Kilowatt-level, narrow linewidth, polarization-maintained all-fiber amplifiers based on multi-phase coded signal modulation and laser gain competition,” Results Phys. 31, 105050 (2021). [CrossRef]
38. R. Prakash, B. S. Vikram, and V. R. Supradeepa, “Enhancing the Efficacy of Noise Modulation for SBS Suppression in High Power, Narrow Linewidth Fiber Lasers by the Incorporation of Sinusoidal Modulation,” IEEE Photonics J. 13(5), 1–6 (2021). [CrossRef]
39. P. Sprangle, B. Hafizi, A. Ting, and R. Fischer, “High-power lasers for directed-energy applications,” Appl. Opt. 54(31), F201–209 (2015). [CrossRef]
40. C. Jauregui, C. Stihler, and J. Limpert, “Transverse mode instability,” Adv. Opt. Photonics 12(2), 429–484 (2020). [CrossRef]
41. A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photonics 2(1), 1–59 (2010). [CrossRef]
42. Q. Zhao, S. Xu, K. Zhou, C. Yang, C. Li, Z. Feng, M. Peng, H. Deng, and Z. Yang, “Broad-bandwidth near-shot-noise-limited intensity noise suppression of a single-frequency fiber laser,” Opt. Lett. 41(7), 1333–1335 (2016). [CrossRef]
43. Y. Panbhiharwala, A. V. Harish, D. Venkitesh, J. Nilsson, and B. Srinivasan, “Investigation of temporal dynamics due to stimulated Brillouin scattering using statistical correlation in a narrow-linewidth cw high power fiber amplifier,” Opt. Express 26(25), 33409–33417 (2018). [CrossRef]
44. C. Zeringue, I. Dajani, S. Naderi, G. T. Moore, and C. Robin, “A theoretical study of transient stimulated Brillouin scattering in optical fibers seeded with phase-modulated light,” Opt. Express 20(19), 21196–21213 (2012). [CrossRef]
45. Y. Panbiharwala, A. V. Harish, Y. Feng, D. Venkitesh, J. Nilsson, and B. Srinivasan, “Stimulated Brillouin scattering mitigation using optimized phase modulation waveforms in high power narrow linewidth Yb-doped fiber amplifiers,” Opt. Express 29(11), 17183–17200 (2021). [CrossRef]
46. W. Lai, P. Ma, W. Liu, C. Li, R. Su, Y. Ma, J. Wu, M. Jiang, and P. Zhou, “Seeding High Brightness Fiber Amplifiers With Multi-Phase Coded Signal Modulation for SBS Effect Management,” IEEE Access 8, 127682–127689 (2020). [CrossRef]
47. B. Anderson, A. Flores, R. Holten, and I. Dajani, “Comparison of phase modulation schemes for coherently combined fiber amplifiers,” Opt. Express 23(21), 27046–27060 (2015). [CrossRef]
48. A. V. Harish and J. Nilsson, “Optimization of Phase Modulation Formats for Suppression of Stimulated Brillouin Scattering in Optical Fibers,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–10 (2018). [CrossRef]
49. B. S. Vikram, R. Prakash, V. Balaswamy, and V. R. Supradeepa, “Determination and Analysis of Line-Shape Induced Enhancement of Stimulated Brillouin Scattering in Noise Broadened, Narrow Linewidth, High Power Fiber Lasers,” IEEE Photonics J. 13(2), 1–12 (2021). [CrossRef]
50. W. Lai, P. Ma, W. Liu, R. Su, Y. Ma, C. Li, J. Wu, M. Jiang, and P. Zhou, “Evaluating spectral characteristics of narrow-linewidth fiber lasers in coherent beam combining system via using CDC metric,” Opt. Lasers Eng. 149, 106826 (2022). [CrossRef]
51. R. Tao, P. Ma, X. Wang, Z. Pu, and Z. Liu, “Mitigating of modal instabilities in linearly-polarized fiber amplifiers by shifting pump wavelength,” J. Opt. 17(4), 045504 (2015). [CrossRef]
52. 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]
53. S. Naderi, I. Dajani, J. Grosek, T. Madden, and T.-N. Dinh, “Theoretical analysis of effect of pump and signal wavelengths on modal instabilities in Yb-doped fiber amplifiers,” Proc. SPIE 8964, 89641W (2014). [CrossRef]
