Open Access
Add to BibSonomy
Abstract
We report a high power transverse-mode-switchable fiber laser in a master oscillator power amplifier (MOPA) configuration. The output modes of a few-mode fiber amplifier can be actively controlled by the input polarization state of the fundamental mode seed laser using SPGD algorithm. A fast, stable and safety mode switching between LP01 and LP11 modes is achieved in the amplifier at output power of 500 W level.
© 2017 Optical Society of America
1. Introduction
High power fiber lasers are widely used in both scientific and industrial applications due to their advantages such as compact size, maintenance-free operation, and easy thermal management [1,2]. Due to the requirement of diffraction limited beam in many applications, such as coherent LIDAR system [3] and coherent beam combination [4,5], most of the research works in high power fiber lasers focus on achieving LP01 mode operation by suppressing high-order mode (HOM) [6–8]. In order to obtain good beam quality, a usually used method is increasing the loss of HOM in large mode area (LMA) fiber by coiling the fiber with a suitable diameter [9]. However, fiber lasers with HOM operation have attracted growing interest in recent years, since laser beams with specific spatial profile are desired in many applications. For example, appropriate optical field distribution can improve the speed and the quality of materials processing [10]. Dark hollow beams are often used in atomic optics, free space optical communications, optical trapping of particles, and so on [11,12].
In order to obtain specific HOMs lasers, various methods have been demonstrated. HOMs can be generated from laser oscillators by employing devices such as spatial light modulator [13,14], spatially variant wave-plate [15,16], special fiber Bragg grating [17–22], and polarization control device [23–25]. However, the output powers and efficiencies of the HOM lasers aforementioned are always relatively low. Another effective approach for HOMs generation is injecting the single mode laser into a multimode fiber and manipulating the mode transformation process [26–30]. For example, HOM laser can be obtained by coupling the laser beam into a multimode fiber with a suitable incidence angle [26,27]. For another example, dynamic modal control can be realized by employing a photonic lantern device [29,30]. In order to scaling the output power, master oscillator power amplifier (MOPA) architecture has been employed for HOMs generating, where a mode selection element was inserted between the oscillator and the fiber amplifier. By using a photonic lantern as the mode convertor, Wittek et al obtained multi-watt output power while preserving high spatial mode selectivity [31]. By applying an appropriate pressure to a mechanic long-period grating, Liu et al achieved a 100 W level fiber laser which can be switchable between LP01 mode and the LP11 mode, with an optical-to-optical efficiency of ~62% [32].
In this paper, we firstly studied the polarization dependence of the output transverse mode in the amplifier and successfully demonstrated an active way to control the output mode of high power fiber amplifier. The amplifier can be actively controlled to operate at LP01 or LP11 mode and can be easily switched while running at high power level. Stable LP11 mode fiber laser with 521W output power and ~79.0% optical-to-optical efficiency is generated, which is the highest output power for such a HOM laser to the best of our knowledge.
2. Mode operation dependence on input polarization state
In this section, an experiment is conceived to study the dependence of transverse mode properties on polarization state. A schematic of the experimental setup is shown in Fig. 1. A linearly polarized single-frequency distributed feedback fiber laser is utilized as the laser seed [33,34], with the central wavelength of 1064 nm and output power of ~80 mW. In order to suppress the stimulated Brillouin scattering (SBS), the linewidth of the seed is firstly broadened to ~45 GHz by using a phase modulator (P-M). Phase modulation technique is a preferable approach to achieve narrow linewidth laser sources for SBS suppressing. The SBS threshold enhancement factor is influenced not only by the linewidth of the modulated signal, but also by the modulation sources (such as sinusoidal source, white noise source and pseudo-random bit sequence) [35]. By using ~45 GHz laser seed based on three-stage cascaded sinusoidal phase modulation, no SBS was observed at the output power of 1.89 kW in our previous work [7]. Then the polarization states of the seed laser is controlled with a fiber-squeezer-based polarization controller, whose passive fiber is a single mode fiber. The polarization state of the laser can be controlled by varying the driven voltage of the piezoelectric actuators [36]. The laser is then amplified and collimated into free space by using a beam collimator (CO). In order to analyze the power and polarization state of the laser, the collimated laser is split with a polarization beam splitter (PBS). Two power meters (P1, P2) are employed to record the power of the p-polarized and the s-polarized light from the PBS after reflected by two mirrors (M1 and M2, reflectivity of ~99.9%), respectively. The transmitted s-polarized light from M2 is focused with a lens and arrives at an infrared camera (CCD2) for the far-field observation. The transmitted p-polarized light from M1 is split by using a sampler (S) with the reflectivity of 30%. And one part of the beam arrives at another infrared camera (CCD1) after passing through a lens. The other part of light is sent to a pinhole (diameter of ~500 μm) and detected by a photoelectric detector (PD). The pinhole is adjusted and placed at the center of the beam spot so that the voltage from the PD represents the sampling power in the central position of the laser beam. In our control system, the voltage is defined as the cost function J of the stochastic parallel gradient descent (SPGD) algorithm. Once the SPGD starts to work, small random perturbations δui (i = 1, 2, 3 and 4) are simultaneously applied to the controller, and the control signals ui are updated to keep the cost function J evolving to its extremums. That is, the power in the central position of the laser beam can be controlled to be either maximum or minimum by adjusting the input polarization state [37,38].
Fig. 1 A schematic of the experimental setup of the active polarization control system. P-M, phase modulator; CO, collimator; PBS, polarization beam splitter; M1/M2, mirror; S, sampler; PD, photo detector; CCD1/CCD2, infrared camera, P1/P2, power meter.
Firstly, a two-stage single-mode fiber amplifier was established and the laser seed was amplified to ~10 W, as shown in Fig. 1(a). A single-clad Yb-doped fiber (YDF) and a double-clad YDF with core diameters of 6 μm and 10 μm were used in the first and second stage of the amplifier, respectively. Based on the SPGD algorithm circuit, the power in the pinhole (used as the cost function J in SPGD algorithm) can be controlled to either maximum or minimum, and hence, most of the power from the amplifier pass through or reflected from the PBS, as shown in Fig. 2(a). During our experiment, the measured polarization extinction ratios (PER) was >17 dB when J was locked to its maximum or minimum. It is worth to be noted that during the polarization control process, the amplifier remains operating at nearly LP01 mode whenever the J is locked to minimum or maximum. This was confirmed from the far field intensity patterns of the laser beams detected by CCD1 and CCD2, as one of the typical patterns shown in Fig. 2(b).
Fig. 2 (a) Normalized intensity in the pinhole during the polarization control of the preamplifier. (b) Typical far field intensity pattern detected by the infrared camera.
Next step, a main amplifier was established based on a few-mode double-clad YDF and the laser was amplified to ~500W, as shown in Fig. 1(b). In the main amplifier, a length of ~15 m double-clad YDF with core/inner-cladding diameter of 20/400 μm and numerical aperture of NA = 0.064 was used as the gain fiber. The normalized frequency of the YDF (V~3.78) indicate that not only LP01 mode (consists of two vector modes: HE11 × 2) but also LP11 mode (consists of four vector modes: TM01, TE01, and HE21 × 2) can be supported in this YDF. This is different from the previous case where no high order mode is supported in the amplifier. The pump light consists of six fiber-pigtailed laser diodes with central wavelength of 976 nm and maximum output power of ~110 W. They were coupled into the YDF with a (6 + 1) × 1 signal/pump combiner. Due to the phase modulation of the laser seed, no SBS was observed during the amplification process.
When the laser operated at the power of 500 W level, the polarization state of the input laser was adjusted and the SPGD algorithm circuit was involved to lock the cost function J. Once the cost function J was locked to its maximum, most of the power passed through the PBS and the measured PER was 6.4 dB. According to the far field patterns detected by CCD1 and CCD2, both the p- and s-polarized beams from the PBS exhibited LP01 mode shown in Fig. 3(a) and 3(c). On the other hand, when cost function J was locked to its minimum, most of the power was reflected by the PBS and the measured PER was 6.1 dB. In this case, the p-polarized beam have a mode shape close to the LP11 mode shown in Fig. 3(b) and the s-polarized beam was a combination of LP01 and LP11 modes shown in Fig. 3(d).
Fig. 3 Typical far field intensity pattern detected by (a, b) CCD1 and (c, d) CCD2 during the polarization control of the main amplifier.
By active controlling the polarization of the pre-amplifier, PER of the output laser can exceed 17 dB, and LP01 mode operation can be maintained whether the cost function J was locked to its maximum or minimum. However, for the LMA fiber based main amplifier, HOM is tend to be excited and amplified because of the dislocation of the splicing joint, squeezing of the fiber and so on. This results in the PER decrease from 17 dB to ~6.1 dB because of the random superposition of different modes [39]. In this situation, when the cost function J was locked to its maximum, both the s- and p-polarized beam from the PBS were nearly LP01 mode. However, when cost function J was locked to its minimum, LP11 mode can be observed from both the s- and p-polarized beams. Noted that when cost function J was locked to its maximum, the polarization state of the major beams (beam with higher power from the PBS) were orthogonal to the case when J was locked to its minimum. In one word, the polarization state of the input laser seed can influence the output mode of the amplifier-and high PER can be obtained if and only if fundamental mode is involved in the amplifying process. We assume the reason is that the polarization of the seed laser impacts the stimulation, evolution and gain of the laser modes in the main amplifier [24,25,39]. In the next section, we will experimentally verify that the mode control can be realized by changing the polarization of the seed laser.
3. Switchable output modes based on active control
In the previous section, we demonstrate that the output mode can be influenced by the input polarization states when HOMs are supported in the amplifier. In this section, we conceive a switchable-modes operation in the high power amplifier based on active control. As shown in Fig. 4, the experimental setup is similar to the polarization control system (shown in Fig. 1). In this experiment, the collimated laser beam is split into two beams by using a mirror (M1, reflectivity of ~99.9%). The transmitted light is then sent to a pinhole with the diameter of ~500 μm and detected by a photoelectric detector (PD). The light reflected by M1 arrives at another mirror (M2, reflectivity of ~99.9%) and most of the power (reflected by M2) is received by a power meter for power measurement. The light passing through M2 is split with a sampler (S) and one part is used for beam quality measurement by using a commercial laser quality monitor (LQM). The other part arrives at an infrared camera (CCD) for far-field observation by focusing with a lens.
Fig. 4 Experimental setup of the active mode control system. P-M, phase modulator; CO, collimator; M1/M2, mirror; S, sampler; PD, photo detector; CCD, infrared camera, LQM, laser quality monitor; HPW, half-wavelength plate; PBS, polarization beam splitter; P1/P2, power meter.
Firstly, random signals were generated by the circuit and sent to the polarization controller. As shown in Fig. 5, the cost function J (normalized intensity in the pinhole) changed randomly, and the corresponding far field pattern varied gradually, as shown in Fig. 6(a)-6(d). Then, SPGD algorithm was implemented to lock the cost function J to its maximum, as shown in the second stage in Fig. 5. Nearly LP01 mode was observed from the far field pattern of the laser beam shown in Fig. 6(e). On the other hand, once the cost function J was locked to be its minimum, as shown in third stage in Fig. 5, nearly LP11 mode was obtained Fig. 6(f). In fact, laser beam profile of narrow-linewidth few-moded fiber lasers is always unstable because of the fluctuations in fiber position and thermal environment [40]. Due to the effective active control, the intensity patterns remained unchanged during the whole mode control process (with several minute) in our experiment. As we assumed in section 2, the laser modes can be switched by controlling the polarization of the seed laser. The feasibility and stability were verified in this experiment. In our experiment, the iteration rate of the SPGD algorithm was ~1 kHz, and the switching time between the modes was less than 0.3 s.
Fig. 6 Far field intensity patterns of the output laser beams with (a-d) random disturbing and (e, f) mode control.
The power and the beam quality of the locked beams were characterized in the experiment. The output power of the amplifier was measured and showed in Fig. 7(a). When random signals were sent to the controller and the pump power was kept at its maximum of 652 W, the output power gradually varied between ~500 W and ~510 W. Once the cost function J was locked to its maximum, the laser operated in LP01 mode shown in Fig. 6(e) and the output power was 486 W stably, corresponding to an optical-to-optical efficiency of ~73.6%. The beam quality was measured with a LQM and the M2X and M2Y were 1.03 and 1.06, respectively. However, when the cost function J was locked to its minimum, the output mode switched to LP11 and the output power was at the maximum of 521 W steadily with the optical-to-optical efficiency of ~79.0% and the M2X and M2Y were 1.03 and 2.18, respectively. We contribute this to the difference of the amplifier’s gain efficiency between the LP01 and LP11 modes. We can also find from Fig. 7(a) that the laser powers remained stably both in the LP01 and LP11 modes, the fluctuations were both less than 0.3%.
Fig. 7 (a) Output power and (b) degree of polarization of the laser beam from the amplifier in active mode control.
Then, as shown in Fig. 4, a half-wave plate (HWP) and a polarization beam splitter (PBS) were used to characterize the polarization state of the laser beam. Figure 7(b) shows the value of P1/(P1 + P2) when cost function J was locked to its extremums, where P1 and P2 are the powers transmitted (p-polarized) and reflected (s-polarized) by the PBS, respectively. That means the polarization state remained steadily, and the polarization extinction ratio (PER) of the LP01 and LP11 modes were ~5.0 dB and 6.5 dB respectively. It is worth to note that the major polarization directions (the polarization direction with higher power) of the LP01 and LP11 modes were perpendicular to each other. This conforms to the experimental results obtained in section 2.
In the experiment, we noticed that the location of the pinhole also affects the locked beam of the amplifier. The amplifier can be locked to operate at nearly LP01 and LP11 modes when the pinhole was in the central of the laser beam. However, when the pinhole was shifted off the center, the mode distribution exhibited a mixture of LP01 and LP11 modes.
4. Conclusions
In conclusion, we experimentally demonstrated an active way to control the output mode of fiber laser and achieved a mode-switchable high power all fiber MOPA with the output power of 500 W level. A fiber-squeezer-based polarization controller and a SPGD algorithm circuit were employed to establish an active polarization control system and polarization dependence of the output transverse mode was studied experimentally. The experimental results indicate that the output modes are affected by the polarization state of the input fundamental mode signal laser. Active mode control was realized by lock the central section of the laser beam. The fundamental mode (LP01) was obtained when the cost function J was controlled to be its maximum. The M2X and M2Y are 1.03 and 1.06 respectively, and the corresponding efficiency of the main amplifier was ~73.6%. On the other hand, when the cost function J was controlled to be its minimum, LP11 mode was obtained. The M2X and M2Y were 1.03 and 2.18 respectively, and the efficiency of the main amplifier was ~79.0%.
Funding
This research is sponsored by National Key R&D Program of China (2016YFB0402204).
Acknowledgments
The authors thank Xiaoyong Xu, Kun Zhang, Siliu Liu and Lin Chen for providing technical support in the experiments.
References and links
1. 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] [PubMed]
2. 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), 63–92 (2010). [CrossRef]
3. C. G. Carlson, P. D. Dragic, R. K. Price, J. J. Coleman, and G. R. Swenson, “A Narrow-Linewidth, Yb Fiber-Amplifier-Based Upper Atmospheric Dopper Temperature Lidar,” IEEE J. Sel. Top. Quantum Electron. 15(2), 451–461 (2009). [CrossRef]
4. R. Su, P. Zhou, X. Wang, Y. Ma, P. Ma, X. Xu, and Z. Liu, “High power narrow-linewidth nanosecond all-fiber lasers and their actively coherent beam combination [Invited],” IEEE J. Sel. Top. Quantum Electron. 20, 0903913 (2014).
5. 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(3), A7–A14 (2017). [CrossRef]
6. F. Stutzki, F. Jansen, C. Jauregui, J. Limpert, and A. Tünnermann, “2.4 mJ, 33 W Q-switched Tm-doped fiber laser with near diffraction-limited beam quality,” Opt. Lett. 38(2), 97–99 (2013). [CrossRef] [PubMed]
7. P. Ma, R. Tao, R. Su, X. Wang, P. Zhou, and Z. Liu, “1.89 kW all-fiberized and polarization-maintained amplifiers with narrow linewidth and near-diffraction-limited beam quality,” Opt. Express 24(4), 4187–4195 (2016). [CrossRef] [PubMed]
8. T. H. Loftus, A. Liu, P. R. Hoffman, A. M. Thomas, M. Norsen, R. Royse, and E. Honea, “522 W average power, spectrally beam-combined fiber laser with near-diffraction-limited beam quality,” Opt. Lett. 32(4), 349–351 (2007). [CrossRef] [PubMed]
9. M. Lei, Y. Qi, C. Liu, Y. Yang, Y. Zheng, and J. Zhou, “Mode controlling study on narrow-linewidth and high power all-fiber amplifier,” Proc. SPIE 9543, 95431L (2015). [CrossRef]
10. N. Sanner, N. Huot, E. Audouard, C. Larat, and J. P. Huignard, “Direct ultrafast laser micro-structuring of materials using programmable beam shaping,” Opt. Lasers Eng. 45(6), 737–741 (2007). [CrossRef]
11. H. Ye, C. Wan, K. Huang, T. Han, J. Teng, Y. S. Ping, and C. W. Qiu, “Creation of vectorial bottle-hollow beam using radially or azimuthally polarized light,” Opt. Lett. 39(3), 630–633 (2014). [CrossRef] [PubMed]
12. A. P. Porfirev and R. V. Skidanov, “Dark-hollow optical beams with a controllable shape for optical trapping in air,” Opt. Express 23(7), 8373–8382 (2015). [CrossRef] [PubMed]
13. S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013). [CrossRef] [PubMed]
14. A. Ishaaya, N. Davidson, and A. Friesem, “Very high-order pure Laguerre-Gaussian mode selection in a passive Q-switched Nd:YAG laser,” Opt. Express 13(13), 4952–4962 (2005). [CrossRef] [PubMed]
15. D. Lin and W. A. Clarkson, “Polarization-dependent transverse mode selection in an Yb-doped fiber laser,” Opt. Lett. 40(4), 498–501 (2015). [CrossRef] [PubMed]
16. D. Lin, J. M. O. Daniel, M. Gecevičius, M. Beresna, P. G. Kazansky, and W. A. Clarkson, “Cladding-pumped ytterbium-doped fiber laser with radially polarized output,” Opt. Lett. 39(18), 5359–5361 (2014). [CrossRef] [PubMed]
17. N. Andermahr and C. Fallnich, “Optically induced long-period fiber gratings for guided mode conversion in few-mode fibers,” Opt. Express 18(5), 4411–4416 (2010). [CrossRef] [PubMed]
18. J. M. O. Daniel and W. A. Clarkson, “Rapid, electronically controllable transverse mode selection in a multimode fiber laser,” Opt. Express 21(24), 29442–29448 (2013). [CrossRef] [PubMed]
19. J. M. O. Daniel, J. S. P. Chan, J. W. Kim, J. K. Sahu, M. Ibsen, and W. A. Clarkson, “Novel technique for mode selection in a multimode fiber laser,” Opt. Express 19(13), 12434–12439 (2011). [CrossRef] [PubMed]
20. B. Sun, A. Wang, L. Xu, C. Gu, Y. Zhou, Z. Lin, H. Ming, and Q. Zhan, “Transverse mode switchable fiber laser through wavelength tuning,” Opt. Lett. 38(5), 667–669 (2013). [CrossRef] [PubMed]
21. T. Liu, S. P. Chen, and J. Hou, “Selective transverse mode operation of an all-fiber laser with a mode-selective fiber Bragg grating pair,” Opt. Lett. 41(24), 5692–5695 (2016). [CrossRef] [PubMed]
22. L. Li, M. Wang, T. Liu, J. Leng, P. Zhou, and J. Chen, “High-power, cladding-pumped all-fiber laser with selective transverse mode generation property,” Appl. Opt. 56(17), 4967–4970 (2017). [CrossRef]
23. N. Andermahr and C. Fallnich, “Interaction of transverse modes in a single-frequency few-mode fiber amplifier caused by local gain saturation,” Opt. Express 16(12), 8678–8684 (2008). [CrossRef] [PubMed]
24. B. Sun, A. Wang, L. Xu, C. Gu, Z. Lin, H. Ming, and Q. Zhan, “Low-threshold single-wavelength all-fiber laser generating cylindrical vector beams using a few-mode fiber Bragg grating,” Opt. Lett. 37(4), 464–466 (2012). [CrossRef] [PubMed]
25. X. Du, H. Zhang, P. Ma, X. Wang, P. Zhou, and Z. Liu, “Spatial mode switchable fiber laser based on FM-FBG and random distributed feedback,” Laser Phys. 25(9), 095102 (2015). [CrossRef]
26. K. K. Bobkov, M. M. Bubnov, S. S. Aleshkina, and M. E. Likhachev, “The first experimental observation of long-term mode degradation in high peak power Yb-doped amplifiers,” Proc. SPIE 10083, 100830T (2017). [CrossRef]
27. C. Zhao, Y. Cai, F. Wang, X. Lu, and Y. Wang, “Generation of a high-quality partially coherent dark hollow beam with a multimode fiber,” Opt. Lett. 33(12), 1389–1391 (2008). [CrossRef] [PubMed]
28. L. Huang, J. Leng, P. Zhou, S. Guo, H. Lü, and X. Cheng, “Adaptive mode control of a few-mode fiber by real-time mode decomposition,” Opt. Express 23(21), 28082–28090 (2015). [CrossRef] [PubMed]
29. T. A. Birks, I. Gris-Sanchez, S. Yerolatsitis, S. G. Leon-Saval, and R. R. Thomson, “The photonic lantern,” Adv. Opt. Photonics 7(2), 107–167 (2015). [CrossRef]
30. J. Montoya, C. Aleshire, C. Hwang, N. K. Fontaine, A. Velázquez-Benítez, D. H. Martz, T. Y. Fan, and D. Ripin, “Photonic lantern adaptive spatial mode control in LMA fiber amplifiers,” Opt. Express 24(4), 3405–3413 (2016). [CrossRef] [PubMed]
31. S. Wittek, R. Bustos Ramirez, J. Alvarado Zacarias, Z. Sanjabi Eznaveh, J. Bradford, G. Lopez Galmiche, D. Zhang, W. Zhu, J. Antonio-Lopez, L. Shah, and R. Amezcua Correa, “Mode-selective amplification in a large mode area Yb-doped fiber using a photonic lantern,” Opt. Lett. 41(10), 2157–2160 (2016). [CrossRef] [PubMed]
32. T. Liu, S. Chen, X. Qi, and J. Hou, “High-power transverse-mode-switchable all-fiber picosecond MOPA,” Opt. Express 24(24), 27821–27827 (2016). [CrossRef] [PubMed]
33. S. Xu, Z. Yang, W. Zhang, X. Wei, Q. Qian, D. Chen, Q. Zhang, S. Shen, M. Peng, and J. Qiu, “400 mW ultrashort cavity low-noise single-frequency Yb3+-doped phosphate fiber laser,” Opt. Lett. 36(18), 3708–3710 (2011). [CrossRef] [PubMed]
34. C. Li, S. Xu, X. Huang, Y. Xiao, Z. Feng, C. Yang, K. Zhou, W. Lin, J. Gan, and Z. Yang, “All-optical frequency and intensity noise suppression of single-frequency fiber laser,” Opt. Lett. 40(9), 1964–1967 (2015). [CrossRef] [PubMed]
35. 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] [PubMed]
36. Z. Huang, C. Liu, J. Li, D. Zhang, H. Cheng, Y. Luo, Q. Hu, and M. Han, “Fiber polarization control based on a fast locating algorithm,” Appl. Opt. 52(27), 6663–6668 (2013). [CrossRef] [PubMed]
37. M. A. Vorontsov, G. W. Carhart, and J. C. Ricklin, “Adaptive phase-distortion correction based on parallel gradient-descent optimization,” Opt. Lett. 22(12), 907–909 (1997). [CrossRef] [PubMed]
38. P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett. 94(23), 231106 (2009). [CrossRef]
39. 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, 2760–2765 (2017).
40. J. M. O. Daniel, N. Simakov, P. C. Shardlow, and W. A. Clarkson, Effect of seed linewidth on few-moded fiber amplifiers, in 2014 Conference on Lasers and Electro, OSA Technical Digest (online) (Optical Society of America, 2014), paper STu2N.7. [CrossRef]
