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Abstract
Random fiber lasers are of tremendous interest to diverse applications for optical fiber sensing, speckle-free imaging. To date, random fiber lasers with fundamental mode oscillation have been well developed. However, controllable oscillating spatial mode in random fiber lasers have not been reported yet. Here, we propose and demonstrate a few-mode random fiber laser with a switchable oscillating spatial mode based on mode injection locking. An external signal light is injected to realize the locking of transverse mode in this random fiber laser and the direct oscillations of the fundamental mode, hybrid mode, and high order mode can be realized, respectively. This random fiber laser operates in the high-order LP11 mode stably with a threshold of as low as 88 mW. High efficiency and high purity cylindrical vector beams can be obtained by removing the degeneracy of the LP11 mode. This work may pave a path towards random fiber lasers with controllable spatial modes for specific applications in mode division multiplexing, imaging, and laser material processing.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Random fiber lasers (RFLs) based on random distributed feedback have attracted considerable attention since the first report by Turitsyn et al. in 2010 [1]. Compared to the traditional fiber laser, RFLs are on the feedback provided by extremely weak distributed Rayleigh scattering along a long single-mode fiber and the gain is provided by stimulated Raman scattering [2], stimulated Brilliouin scattering [3], active fibers [4]. Owing to the unique intriguing properties such as simple structure, low cost, modeless behavior, low spatial coherence, and robust operation, RFLs have many excellent potential applications in free-space communication [5,6], optical fiber sensing [7], speckle-free imaging [8,9]. In recent years, a great deal of studies on RFLs have been reported in various aspects such as multi-wavelength emission [10,11], wavelength tuning [12,13], narrow linewidth [14], high power [15], linear polarization output [16,17], pulse operation [18,19] and super-continuous spectrum generation [20].
However, almost all of the previously reported RFLs oscillate at fundamental mode because single-mode fiber (SMF) is adopted, which restricts the application of RFLs. To switch oscillating mode from fundamental mode to high-order mode (HOM), few-mode or multimode fiber have to be used to support HOM propagating along the fiber, which will dramatically increase the threshold of RFLs. Recently, there are several methods to generate HOM in RFLs, such as the lateral offset splicing [21], long-period fiber gratings [22], mode selective couplers [23]. Nevertheless, the above RFLs substantially oscillate at fundamental mode rather than the desired HOM directly and lack the flexibility of switching transverse modes. Meanwhile, practical applications are also limited by high lasing threshold, poor mode purity as well as low slope efficiency. To the best of our knowledge, a few-mode random fiber laser with switchable oscillating spatial mode has not yet been reported. RFLs with different spatial mode are very useful in many practical applications, such as mode division multiplexing (MDM) [24–26], reducing laser speckle [23,27] lowering turbulence-induced scintillation in free-space optical communication [28,29], ghost imaging technique that is not affected by meteorological conditions [30], dental caries lesions diagnosis [31], and laser material processing [32,33]. Therefore, there are strong motivations to develop RFLs with different spatial modes.
In this letter, we propose and demonstrate a few-mode random fiber laser with switchable spatial mode based on mode injection locking. A home-made narrow-linewidth fiber laser is used as signal light and injected into the cavity to control the oscillating mode. The oscillating mode can be easily switched among LP01 mode, hybrid mode, and LP11 mode by adjusting the signal light power. Besides, cylindrical vector beams with high efficiency and high purity can be obtained by removing the degeneracy of LP11 mode. The proposed random fiber laser has the characteristics of low cost, low coherence, low threshold, switchable spatial mode operation, and adjustable beam profiles, which can be used as a versatile laser in a variety of fields, such as mode division multiplexing systems, speckle-free imaging, and ghost imaging, dental diagnosis, free-space optical communication, laser material processing.
2. Experimental principle and setup
The schematic of the proposed few-mode random fiber laser with switchable oscillating spatial mode is illustrated in Fig. 1. A length of 55 cm annular doping Yb-doped fiber (ADYDF) (doping concentration of 5000 ppm) is served as gain fiber and pumped by a 974 nm laser diode via a 980/1064 nm wavelength division multiplexer (WDM). The cavity of this random fiber laser is comprised of a few-mode fiber Bragg grating (FMFBG) and a 3 km long SMF-28e (core diameter of 8.2 um and numerical aperture of 0.14, support LP01 and LP11 mode at 1060 nm). The FMFBG written on the few-mode photosensitive fiber (core diameter of 9.1um and NA of 0.12) serves as a highly reflective mirror with a reflectivity of 94% and wavelength selector, the reflection spectrum is shown in Fig. 2(a). It is obvious that three peaks appear in the reflection spectrum, which corresponds to the reflection from LP11 to LP11 (1055.0 nm), LP01 to LP11 (1056.0 nm), and LP01 to LP01 (1057.0 nm), respectively. A 3 km long few-mode fiber (FMF) is used as another laser mirror to provide random distributed feedback due to Rayleigh scattering. A circulator with FMF pigtails is inserted behind 3 km long fiber, which has three functions: a) introducing signal light into the cavity to realize mode injection locking; b) serving as an isolator to eliminate unwanted Fresnel reflection at the output end facets of the fiber and ensure that the feedback is provided only by random distributed Rayleigh scattering; c) working as an output coupler. The insertion loss of the circulator is measured to be 2.5 dB for LP11 and 4 dB for LP01 at 1055 nm, respectively. To avoid the parasitic oscillation, an optical isolator is placed before WDM in this random fiber laser. A home-made single wavelength fiber laser centered at 1055.03 nm with a 3-dB bandwidth of 0.02 nm is utilized as a signal light to realize the mode injection locking. When signal light is injected into the laser cavity, the gain profile is controlled by signal light power. The light with the same wavelength as the signal light (1055.03 nm) will extract more population inversion, and get sufficient gain above the threshold, the resonant wavelength of the laser is locked at about 1055.03 nm. Owing to the particular transverse mode-wavelength association characteristics of FMFBG [34], only LP11 mode at 1055 nm is reflected back into the cavity and amplified by active fiber. The transverse mode of the laser can be locked by wavelength locking. Moreover, the mode gain profile can be flexibly changed by controlling signal light power. Consequently, oscillating spatial mode can be easily switched by adjusting signal light power. The spectrum of the signal light is shown in Fig. 2(b). A polarization controller (PC) is placed at the output end to lift the degeneracy and purify the polarization state of the output high-order mode. In this experiment, an optical spectrum analyzer (Yokogawa AQ6373B), a 2 GHz radio-frequency (RF) spectrum analyzer, a power meter (Thorlab PM100D), and CCD camera are used to measure the laser spectra, RF spectrum, output power, and beam profiles, respectively.
Fig. 1. The schematic of the proposed few-mode random fiber laser with switchable oscillating spatial mode. ISO, isolator; LD, laser diode; WDM, wavelength division multiplexer; FMFBG, few-mode fiber Bragg grating; PC, polarization controller; ADYDF, annular doping Yb-doped fiber; CIR, circulator.
3. Results and discussion
In our experiment, oscillating spatial mode can be easily switched by adjusting signal light power. Three different spatial modes can directly oscillate in this few-mode RFL, namely the fundamental mode (LP01), high-order mode (LP11), and hybrid mode (LP01 and LP11 coexistence). Figure 3 shows the spectrum of laser output without signal light injection, RFL oscillates at 1057.01 nm corresponding to the right reflection peak of the FMFBG, and the output intensity distribution is shown in the inset. These results indicate that the fundamental mode oscillates in the cavity. The 3 dB linewidth is 0.23 nm limited by the reflection bandwidth of the FMFBG. The ratio between the signal peak and maximum non-resonant peak is as high as 40 dB. In comparison to traditional RFL, this fiber laser has a low threshold that attributes to half-open cavity structure and active fiber used as the gain medium. Figure 4(a) presents lasing with a threshold pump power of 160 mW and good linear growth of the generated output power with a slope efficiency of 13.4% exceed the threshold. The maximum output power is 18.03 mW at the pump power of 291.8 mW, which is limited by the available pump laser. Besides, the stability of RFL for LP01 mode operation is investigated, as shown in Fig. 4(b). The output spectra are recorded with 3 minutes interval in 30 minutes, the fluctuation of the intensity is inconspicuous and the center wavelength nearly keeps at 1057.01 nm. Moreover, no transverse mode hopping is observed. These results reveal that this RFL has a good performance on stability when oscillating at LP01 mode.
Fig. 3. Spectrum of laser output when oscillating at LP01 mode. The inset shows intensity distribution of output mode.
Fig. 4. (a) Laser output power versus pump power for LP01 mode operation. (b) The stability measurements when oscillating at LP01 mode.
RFL can be easily switched in the dual-wavelength hybrid mode oscillation state when the pump power is maintained at 291.8 mW and 0.57 mW signal light are injected into the cavity through Port 1 of the circulator. As shown in Fig. 5, the oscillation wavelengths are 1055.04 nm and 1057.01 nm, corresponding to the left and the right reflection peaks of FMFBG, respectively. The inset shows the intensity distribution of the output beam, half-moon shape profile is the typical feature of hybrid mode. The 3 dB linewidths of a dual-wavelength are 0.07 nm and 0.22 nm, respectively. The ratio between the signal peak and maximum non-resonant peak of two wavelengths are over 37 dB, indicating that high stability of the laser output. Figure 6(a) presents output power versus pump power at the signal light power of 0.57 mW. It can be seen that an inflection point appears at the pump power of 224 mW. It can be explained as the following: A small amount of signal light enhances the competition of the mode that is in resonance with signal light wavelength due to injection locking by modulating gain in the cavity [35,36]. When pump power is below 224 mW, the output power increases with a slope efficiency of 4.2% once the pump power is over the lasing threshold of 100.3 mW, the RFL operates at 1055.04 nm as denoted by red line in Fig. 6(a). When the pump power exceeds 224 mW, output power of the laser at 1055.04 nm decrease from 5.42 mW to 4.26 mW temporarily, which results from the single wavelength output change into dual-wavelength output. Meanwhile, the 1057.01 nm RFL also begins lasing due to the gain of the wavelength at 1057.01 nm overcomes total loss in the cavity. The output power of the laser at 1057.01 nm increases with a slope efficiency of 12.2% as denoted by the blue line in Fig. 6(a). As a result, dual-wavelength output can be obtained. The total output power is 15.13 mW at the maximum pump power of 291.8 mW. The unsmooth spectrum of the right resonance wavelength at 1057.01 nm can be clearly observed due to random distributed feedback. The output dual-wavelength spectra are repeatedly scanned every 3 minutes in 30 minutes, as shown in Fig. 6(b). The fluctuation of intensity is not obvious, and the variation of the central wavelength of different channels are maintained within 0.02 nm in 30 minutes, which implies the good stability of the hybrid mode operation state.
Fig. 5. The spectrum of laser output for hybrid mode operation. The inset shows intensity distribution of output mode.
Fig. 6. (a) Laser output power versus pump power when signal light power is fixed at 0.57 mW. (b) The stability measurements of dual-wavelength hybrid mode operation.
The experiment above has shown that a small amount of signal light can enhance the competition of LP11 mode. However, LP01 mode can not be completely eliminated with the increasement of pump power. Thus, the power of signal light injected into the cavity is crucial to realize LP11 mode oscillating. In our experiment, LP01 mode at 1057.01 nm is completely suppressed, and this RFL oscillates only at LP11 mode when keeping the pump power at 291.8 mW and increasing the signal light power to 4.23 mW, as shown in Fig. 7. The detailed process can be described as following: when the signal light (1055.03 nm) with appropriate power is injected into the cavity, the light near 1055 nm can extract more population inversion than the light at 1056 nm or 1057 nm. The light near 1055 nm gets sufficient gains and oscillates in the cavity when the threshold condition is satisfied. In contrast, other wavelengths cannot extract population inversion effectively. Consequently, they can not oscillate due to mode competition. Moreover, owing to the transverse mode selectivity of FMFBG [34], only LP11 mode at 1055 nm is reflected back into the cavity and amplified by active fiber. As a result, RFL directly oscillates at LP11 mode. The output spectrum is shown in Fig. 7. The RFL oscillates at 1055.04 nm, which is consistent with the LP11-LP11 reflection peak of the FMFBG, its 3 dB linewidth is 0.08 nm and the ratio between the signal peak and maximum non-resonant peak is 48 dB. The inset shows the intensity distribution of laser output, the doughnut-shaped intensity profile is the typical characteristic of second-order mode. These results indicate that this RFL oscillates at LP11 mode. Figure 8(a) shows output power versus pump power for LP11 mode output when signal light power is fixed at 4.23 mW. The laser threshold is 88 mW lower than LP01 mode operation due to the gain modulation of injected signal light as well as the special designs of few-mode active fiber benefiting for LP11 mode competition [37]. In addition, it’s worth noting that LP11 mode directly oscillates in the cavity, which significantly promotes the efficiency of fiber laser [38,39]. In our experiment, the slope efficiency of laser is measured to be 7.2%, which is higher than that of reported RFLs with LP11 mode output using mode converter [21–23]. Output power of 17.17 mW is obtained at the maximum pump power of 291.8 mW. The threshold, slope efficiency and output power for LP11 mode operation are mainly limited by the relatively high cavity loss, including propagation loss (1.86 dB/km) in SMF-28e, high insert loss of the circulator (2.5 dB) at 1055 nm, available pump laser, non-optimized active fiber, and cavity structure. Thus, low threshold, high-efficiency, and high power RFL with LP11 mode oscillating may be feasible by optimizing the length of the active fiber and SMF-28e [4,40]. To testify the stability of this RFL oscillating at LP11 mode, we continuously monitored output spectra with 3 minutes interval in 30 minutes, as shown in Fig. 8(b). There is almost no significant variation in the intensity and central wavelength over the observed period. More importantly, transverse mode hopping resulting from mode competition is not observed. These experimental results indicate that this RFL has remarkable stability when oscillating at LP11 mode.
Fig. 7. Spectrum of laser output when oscillating at LP11 mode. The inset shows intensity distribution of output mode.
Fig. 8. (a) Laser output power versus pump power for LP11 mode operation. (b) The stability measurements when oscillating at LP11 mode.
By adjusting the PC outside the laser cavity when RFL oscillates in LP11 mode, azimuthally and radially polarized beams can be obtained, their intensity distributions are shown in Fig. 9(a) and Fig. 9(f), respectively. The doughnut-shaped intensity profile is the typical characteristic of CVB, a linear polarizer is placed after the fiber collimator, the polarization properties of output beams can be confirmed by rotating the polarizer. The intensity distributions of TE01 mode and TM01 mode after passing through the linear polarizer at different orientations are shown in Figs. 9(b)–(e), Figs. 9(g)–(j), respectively. Using the method proposed in Ref. [41], when the output mode is TE01 mode, the fiber of the output end is bent to a circle with a radius of 1.2 cm, which results in the output power dropping from 17.17 mW to 0.45 mW. It gives a 97.4% loss. To remove the contribution of the LP01 mode, we measure the power change from 16.8 mW to 15.8 mW when the LP01 mode propagates in the same conditions, which gives a 6% loss. Thus, the purity of TE01 mode is measured to be 97.2%. Similarly, the purity of TM01 mode is measured to be 96.5%.
Fig. 9. (a) Intensity distribution of TE01 mode without a linear polarizer and (b)–(e) corresponding intensity distribution of TE01 mode after a linear polarizer. (f) Intensity distribution of TM01 mode without a linear polarizer and (g)–(j) after a linear polarizer. The axis of linear polarizer are denoted by the white arrows.
Finally, RF spectra were analyzed to further verify that this configuration was operating in a random state. A conventional fiber laser has a fixed cavity length, and the cavity modes are spaced equally with a separation $\Delta \nu \textrm{ = }c\textrm{/}2nL$, where c is the speed of light, n is the effective refractive index of the fiber, L is the length of cavity, mode beating signal can be always observed in RF spectra. However, random fiber lasers have no well-defined cavity modes due to the random distributed feedback, which causes uncertain cavity length [12]. In our experiment, random distributed feedback is provided via Rayleigh scattering resulting from randomly distributed refractive index inhomogeneities of 3 km long fiber. Although Rayleigh scattering in the fiber is extremely weak, the effect can be accumulated in a 3 km long fiber. Only a fraction of the Rayleigh scattered light can be recaptured and amplified, which gives rise to the necessary feedback process for lasing action. Figure 10(a)–(c) show RF spectra within 1 MHz span range with a resolution of 100 Hz when the laser oscillates at LP01 mode, hybrid mode, LP11 mode, respectively. It can be seen that there is no obvious longitudinal mode beating signal corresponding to the fiber length ($\Delta \nu \textrm{ = }c\textrm{/}2nL \approx 34.5$ kHz), which verifies the laser operates as RFL.
Fig. 10. RF spectra of the RFL at different operation states. (a) LP01 mode operation. (b) Hybrid mode operation. (c) LP11 mode operation.
4. Conclusion
In summary, we experimentally demonstrate a few-mode random fiber laser whose operation states of spatial mode can be easily switched through mode injection locking technology. By changing the injected power of signal light, the oscillating mode is switchable among fundamental mode, hybrid mode, and high order mode. Meanwhile, CVB output with high purity of 97.2% and high efficiency of 7.2% is obtained by removing the degeneracy of LP11 mode. The proposed RFL shows good stability in 30 minutes for all three different mode operation states. Moreover, RF spectra measurements were made verifying the random lasing action. This random fiber laser with low cost, simple structure, low threshold, switchable oscillating mode can satisfy diverse requirements in mode division multiplexing systems, speckle-free imaging and ghost imaging, dental diagnosis, free-space optical communication, laser material processing. Moreover, we believe that our work may give a strong impetus to the applications of random fiber lasers.
Funding
National Natural Science Foundation of China (61675188); National Key Research and Development Program of China (2016YFB0401901).
Disclosures
The authors declare no conflicts of interest.
References
1. S. K. Turitsyn, S. A. Babin, A. E. El-Taher, P. Harper, D. V. Churkin, S. I. Kablukov, J. D. Ania-Castañón, V. Karalekas, and E. V. Podivilov, “Random distributed feedback fibre laser,” Nat. Photonics 4(4), 231–235 (2010). [CrossRef]
2. S. K. Turitsyn, S. A. Babin, D. V. Churkin, I. D. Vatnik, M. Nikulin, and E. V. Podivilov, “Random distributed feedback fibre lasers,” Phys. Rep. 542(2), 133–193 (2014). [CrossRef]
3. M. Pang, S. Xie, X. Bao, D. P. Zhou, Y. Lu, and L. Chen, “Rayleigh scattering-assisted narrow linewidth Brillouin lasing in cascaded fiber,” Opt. Lett. 37(15), 3129–3131 (2012). [CrossRef]
4. M. Fan, Z. Zon, X. Tian, D. Xu, D. Zhou, R. Zhang, N. Zhu, L. Xie, H. Li, J. Su, and Q. Zhu, “Comprehensive Investigations on 1053 nm Random Distributed Feedback Fiber Laser,” IEEE Photonics J. 9(2), 1–9 (2017). [CrossRef]
5. J. C. Ricklin and F. M. Davidson, “Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication,” J. Opt. Soc. Am. A 19(9), 1794–1802 (2002). [CrossRef]
6. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013). [CrossRef]
7. Z. N. Wang, Y. J. Rao, H. Wu, P. Y. Li, Y. Jiang, X. H. Jia, and W. L. Zhang, “Long-distance fiber-optic point-sensing systems based on random fiber lasers,” Opt. Express 20(16), 17695–17700 (2012). [CrossRef]
8. B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6(6), 355–359 (2012). [CrossRef]
9. R. Ma, Y. J. Rao, W. L. Zhang, and B. Hu, “Multimode Random Fiber Laser for Speckle-Free Imaging,” IEEE J. Select. Topics Quantum Electron. 25(1), 1–6 (2019). [CrossRef]
10. S. Sugavanam, Z. Yan, V. Kamynin, A. S. Kurkov, L. Zhang, and D. V. Churkin, “Multiwavelength generation in a random distributed feedback fiber laser using an all fiber Lyot filter,” Opt. Express 22(3), 2839–2844 (2014). [CrossRef]
11. S. Sugavanam, M. Z. Zulkifli, and D. V. Churkin, “Multi-wavelength erbium/Raman gain based random distributed feedback fiber laser,” Laser Phys. 26(1), 015101 (2016). [CrossRef]
12. S. A. Babin, A. E. El-Taher, P. Harper, E. V. Podivilov, and S. K. Turitsyn, “Tunable random fiber laser,” Phys. Rev. A 84(2), 021805 (2011). [CrossRef]
13. Y. J. Song, L. Zhan, S. Hu, Q. H. Ye, and Y. X. Xia, “Tunable Multiwavelength Brillouin–Erbium Fiber Laser With a Polarization-Maintaining Fiber Sagnac Loop Filter,” IEEE Photonics Technol. Lett. 16(9), 2015–2017 (2004). [CrossRef]
14. M. Pang, X. Bao, and L. Chen, “Observation of narrow linewidth spikes in the coherent Brillouin random fiber laser,” Opt. Lett. 38(11), 1866–1868 (2013). [CrossRef]
15. J. Ye, J. Xu, J. Song, Y. Zhang, H. Zhang, H. Xiao, J. Leng, and P. Zhou, “Pump scheme optimization of an incoherently pumped high-power random fiber laser,” Photonics Res. 7(9), 977–983 (2019). [CrossRef]
16. J. Xu, L. Huang, M. Jiang, J. Ye, P. Ma, J. Leng, J. Wu, H. Zhang, and P. Zhou, “Near-diffraction-limited linearly polarized narrow-linewidth random fiber laser with record kilowatt output,” Photonics Res. 5(4), 350–354 (2017). [CrossRef]
17. X. Du, H. Zhang, X. Wang, P. Zhou, and Z. Liu, “Investigation on random distributed feedback Raman fiber laser with linear polarized output,” Photonics Res. 3(2), 28–31 (2015). [CrossRef]
18. Y. Tang and J. Xu, “A random Q-switched fiber laser,” Sci. Rep. 5(1), 9338 (2015). [CrossRef]
19. R. Ma, W. L. Zhang, X. P. Zeng, Z. J. Yang, Y. J. Rao, B. C. Yao, C. B. Yu, Y. Wu, and S. F. Yu, “Quasi mode-locking of coherent feedback random fiber laser,” Sci. Rep. 6(1), 39703 (2016). [CrossRef]
20. L. Chen, R. Song, C. Lei, W. Yang, and J. Hou, “Random fiber laser directly generates visible to near-infrared supercontinuum,” Opt. Express 27(21), 29781–29788 (2019). [CrossRef]
21. X. Y. Du, H. W. Zhang, P. F. Ma, X. L. Wang, P. Zhou, and Z. J. Liu, “Spatial mode switchable fiber laser based on FM-FBG and random distributed feedback,” Laser Phys. 25(9), 095102 (2015). [CrossRef]
22. M. Z. Zulkifli, K. Y. Lau, F. D. Muhammad, and M. Yasin, “Dual-mode output in half open cavity random fibre laser,” Opt. Commun. 430, 273–277 (2019). [CrossRef]
23. J. Wang, R. Chen, J. Yao, H. Ming, A. Wang, and Q. Zhan, “Random Distributed Feedback Fiber Laser Generating Cylindrical Vector Beams,” Phys. Rev. Appl. 11(4), 044051 (2019). [CrossRef]
24. G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics 6(4), 413–487 (2014). [CrossRef]
25. G. Milione, M. P. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 ( 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015). [CrossRef]
26. L. Li, R. Zhang, P. Liao, Y. Cao, H. Song, Y. Zhao, J. Du, Z. Zhao, C. Liu, K. Pang, H. Song, A. Almaiman, D. Starodubov, B. Lynn, R. Bock, M. Tur, A. F. Molisch, and A. E. Willner, “Mitigation for turbulence effects in a 40-Gbit/s orbital-angular-momentum-multiplexed free-space optical link between a ground station and a retro-reflecting UAV using MIMO equalization,” Opt. Lett. 44(21), 5181–5184 (2019). [CrossRef]
27. R. Ma, J. Q. Li, J. Y. Guo, H. Wu, H. H. Zhang, B. Hu, Y. J. Rao, and W. L. Zhang, “High-power low spatial coherence random fiber laser,” Opt. Express 27(6), 8738–8744 (2019). [CrossRef]
28. F. Wang, X. Liu, L. Liu, Y. Yuan, and Y. Cai, “Experimental study of the scintillation index of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 103(9), 091102 (2013). [CrossRef]
29. W. Cheng, J. W. Haus, and Q. W. Zhan, “Propagation of vector vortex beams through a turbulent atmosphere,” Opt. Express 17(20), 17829–17836 (2009). [CrossRef]
30. H. Wu, B. Han, Z. Wang, G. Genty, G. Feng, and H. Liang, “Temporal ghost imaging with random fiber lasers,” Opt. Express 28(7), 9957–9964 (2020). [CrossRef]
31. J. Y. Guo, W. L. Zhang, Y. J. Rao, H. H. Zhang, R. Ma, D. S. Lopes, I. C. X. Lins, and A. S. L. Gomes, “High contrast dental imaging using a random fiber laser in backscattering configuration,” OSA Continuum 3(4), 759–766 (2020). [CrossRef]
32. C. Hnatovsky, V. G. Shvedov, W. Krolikowski, and A. V. Rode, “Materials processing with a tightly focused femtosecond laser vortex pulse,” Opt. Lett. 35(20), 3417–3419 (2010). [CrossRef]
33. S. Matsusaka, Y. Kozawa, and S. Sato, “Micro-hole drilling by tightly focused vector beams,” Opt. Lett. 43(7), 1542–1545 (2018). [CrossRef]
34. B. A. Sun, A. T. Wang, L. X. Xu, C. Gu, Y. Zhou, Z. X. Lin, H. Ming, and Q. W. Zhan, “Transverse mode switchable fiber laser through wavelength tuning,” Opt. Lett. 38(5), 667–669 (2013). [CrossRef]
35. B. Hu, W. Zhang, R. Ma, J. Guo, A. Ludwig, and Y. Rao, “Wavelength locking of Er-doped random fiber laser,” Laser Phys. Lett. 16(5), 055102 (2019). [CrossRef]
36. W. L. Zhang, R. Ma, C. H. Tang, Y. J. Rao, X. P. Zeng, Z. J. Yang, Z. N. Wang, Y. Gong, and Y. S. Wang, “All optical mode controllable Er-doped random fiber laser with distributed Bragg gratings,” Opt. Lett. 40(13), 3181–3184 (2015). [CrossRef]
37. H. Li, K. Yan, Y. Zhang, C. Gu, P. Yao, L. Xu, R. Zhang, J. Su, W. Chen, Y. Zhu, and Q. Zhan, “Low-threshold high-efficiency all-fiber laser generating cylindrical vector beams operated in LP11 mode throughout the entire cavity,” Appl. Phys. Express 11(12), 122502 (2018). [CrossRef]
38. W. T. Fang, R. X. Tao, Y. M. Zhang, H. X. Li, P. J. Yao, and L. X. Xu, “Adaptive modal gain controlling for a high-efficiency cylindrical vector beam fiber laser,” Opt. Express 27(22), 32649–32658 (2019). [CrossRef]
39. H. Li, Y. Zhang, Z. Dong, J. Lv, C. Gu, P. Yao, L. Xu, R. Zhang, J. Su, W. Chen, Y. Zhu, and Q. Zhan, “A High-Efficiency All-Fiber Laser Operated in High-Order Mode using Ring-Core Yb-Doped Fiber,” Ann. Phys. 531(10), 1900079 (2019). [CrossRef]
40. W. Zinan, W. Han, F. Mengqiu, Z. Li, R. Yunjiang, Z. Weili, and J. Xinhong, “High Power Random Fiber Laser With Short Cavity Length: Theoretical and Experimental Investigations,” IEEE J. Select. Topics Quantum Electron. 21(1), 10–15 (2015). [CrossRef]
41. B. A. Sun, A. T. Wang, L. X. Xu, C. Gu, Z. X. Lin, H. Ming, and Q. W. 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]
