Open Access
Add to BibSonomy
Abstract
In this paper, an oscillating transverse mode switchable mode-locked fiber laser with a few-mode fiber linear cavity is proposed and demonstrated. An artificial filter is used to realize the mode gain modulation of the laser. The stable mode-locked pulsed operation with switchable wavelength is easily achieved and the oscillating transverse mode can be flexibly switched between the fundamental mode and high-order mode by adjusting the polarization controller. The mode-locked fiber laser directly oscillates in the high-order mode stably with a slope efficiency of as high as 12%, and the corresponding operating wavelength, repetition rate as well as pulse duration are 1054.07 nm, 22.662 MHz, 31.5 ps, respectively. Besides, a cylindrical vector beam with a high mode purity of 98.6% is obtained by removing the degeneracy of the LP11 mode. This compact and high-efficiency mode-locked fiber laser operating in switchable transverse mode has the potential application for laser processing, particle trapping, bioimaging, and mode division multiplexing system.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Mode-locked fiber lasers with short pulse and high peak power are widely used in fundamental science and industrial laser processing applications due to the advantages of high compactness, low cost, and efficient heat dissipation [1]. However, the mode-locked fiber laser based on single-mode fibers only can operate in fundamental mode and have a small mode area, which restrains the development of optical fiber communications, laser processing, and high power fiber laser system. In recent years, mode-locked lasers based on few-mode or multimode fiber operating in controllable spatial transverse modes have attracted intensive attention since specific high-order mode (HOM) with unique polarization distributions and spatial profiles are desired in many applications. For example, the degenerate linear polarization mode is made up of different vector eigenmodes, which can excite cylindrical vector beams (CVBs) [2]. Doughnut-shape vector beams are widely used in material processing [3,4], particle trapping [5], and surface surface-enhanced Raman spectroscopy [6,7], and super-resolution imaging [8]. To obtain HOMs output in a mode-locked pulsed fiber laser, various methods have been proposed and demonstrated, such as laterally offset splicing [9,10], few-mode fiber Bragg grating (FMFBG) [11,12], long-period fiber grating (LPFG) [13,14], acoustically induced fiber grating (AIFG) [15], and mode selective coupler (MSC) [16,17], where the mode purity of generated HOMs is limited by the mode conversion efficiency. Besides, there are several reports on pulsed mode-locked fiber lasers that realize switchable transverse modes output by using offset splicing [18,19] and acousto-optic mode converter [20], but the efficiency is limited by high offset splicing loss and insertion loss of mode converter. Recently, a multimode oscillation Q-switched erbium-doped fiber laser with a few-mode fiber (FMF) cavity is demonstrated [21,22]. All-FMF Q-switched laser was proposed to realize single HOM direct oscillation inside the cavity based on HOM pump through a self-made wavelength-division-multiplexing mode selective coupler (WDM-MSC) [23]. And then, mode-locked pulsed lasers with HOM oscillation were also realized [24–26].
However, the aforementioned pulsed fiber lasers have low efficiency, only oscillate in single transverse mode, and lack the flexibility of oscillating transverse mode switching, which restricts their scope of practical applications. To the best of our knowledge, a high-efficiency FMF pulsed fiber laser that enables desired transverse modes to be oscillating and switchable has not yet been reported. Mode-locked pulsed fiber laser operating in switchable transverse modes is of great value due to their great flexibility and versatility, which has excellent practical applications in mode division multiplexing systems (enlarging the capacity of optical communications) [27–29], laser processing (improving processing speeds and cut quality due to dynamically controllable beam profiles) [30–32], optical manipulation [33,34], and stimulated emission depletion (STED) microscopy [35]. Therefore, there are strong motivations to develop high-efficiency pulsed fiber lasers with switchable oscillating transverse modes.
In this letter, we propose and demonstrate an FMF linear-cavity mode-locked fiber laser with switchable oscillating transverse mode. A specially designed ring-core Yb-doped fiber (RC-YDF) is used to enhance the efficiency of HOM oscillation. A commercial semiconductor-saturable absorber mirror (SESAM) provides a saturable absorption effect as a reliable mode-locking device. The mode gain of the laser can be modulated using an artificial filter. The switchable operating wavelength can be realized and the oscillating transverse mode of the mode-locked pulsed fiber laser can be easily and flexibly switched between LP01 mode and LP11 mode by adjusting the PC. Besides, high efficiency and high mode purity are obtained with LP11 mode direct oscillation in the FMF cavity.
2. Experimental setup and principle
The schematic of the proposed FMF linear-cavity mode-locked fiber laser with the switchable oscillating mode is depicted in Fig. 1. A segment of 1.5 m ring-core Yb-doped fiber is used as a gain medium and to promote the competitiveness of HOM, which is pumped by a 976 nm laser diode via a 980/1064 nm wavelength division multiplexer (WDM). The RC-YDF is spliced to FMF with splicing loss of 0.8 dB for LP01 mode and 1 dB for LP11 mode at 1055 nm, respectively. The linear cavity consists of an FMFBG and a commercial SESAM (BATOP, SAM-1064-28-15ps-1.3b-0). The FMFBG with a reflectivity of 94% is written in the few-mode photosensitive fiber (core diameter of 9.1 µm and numerical aperture (NA) of 0.12) and works as a wavelength selector. The SESAM with FMF pigtail (core diameter of 8.2 µm and NA of 0.14, supporting LP01 and LP11 mode at 1060 nm) is used as the reflector with a reflectivity of 70% at another end. In addition, the SESAM provides a saturable absorption effect as a mode-locking device, which has a modulation depth of 18%, saturation fluence of 30µJ/cm2, non-saturable loss of 10%, the damage threshold of 1.5 mJ/cm2. A polarization beam splitter (PBS) with few-mode polarization-maintaining fiber (PMF) pigtails (supporting LP01 and LP11 mode at 1064 nm) is used as a polarizer and an output coupler. The insertion loss of the PBS is measured to be 2 dB for LP11 mode and 0.8 dB for LP01 mode at 1055 nm, respectively. An artificial Lyot filter is used to realize the selection of the operating wavelength, which is composed of a PBS, a 30-cm-long PM1550 fiber (core diameter of 8.5 µm and NA of 0.125, supporting LP01 mode and LP11 mode at 1060 nm), and two polarization controllers (PCs). PC1 is used to adjust the polarization state before entering the PBS. PC2 placed behind a piece of PM1550 fiber is used to create a stress-induced birefringence in the FMF. The transmission spectrum of this filter can be tuned precisely by adjusting PCs. Besides, the splicing loss of FMF and PM1550-XP fiber is measured to be 0.03 dB for LP01 mode and 0.25 dB for LP11 mode at 1055 nm, respectively. The output properties of this fiber laser are directly measured by an optical spectrum analyzer (Yokogawa AQ6373B), an oscilloscope (LeCroy Wave Runner 640Zi, 4 GHz) with a 4 GHz photodetector, a radio-frequency (RF) spectrum analyzer (AV4021), and an autocorrelator (APE PulseCheck), and a power meter (Thorlabs PM100D). Besides, the intensity profiles of the output mode are monitored by a CCD camera.
Fig. 1. The schematic of the proposed mode-locked fiber laser with switchable oscillating mode. LD, laser diode; WDM, wavelength division multiplexer; FMFBG, few-mode fiber Bragg grating; RC-YDF, ring-core doping Yb-doped fiber; PC1, polarization controller 1; PC2, polarization controller 2; PBS, polarization beam splitter; SESAM, semiconductor-saturable absorber mirror; FMF, few-mode fiber.
According to Jones Matrix function, the transmission characteristics of the Lyot filter can be written as [36]:
Where Δn is the birefringence of PMF, λ is the wavelength, LPMF is the length of the PMF fiber, θ is the angle between the polarization direction of the input light and the fast axis of the PMF. The free spectral range (FSR) can be expressed as:In our experiment, the length of PMF is tailored at 30 cm (marked in Fig. 1). Since the laser passes through the PBS and PM1550 fiber twice per round, the FSR of the filter can be calculated to be 4 nm. Based on Eq. (1), the simulated transmission spectra of the filter with individually spliced angles of 30°, 45°, 70°and 80° are shown in Fig. 2(a). It can be seen that the different splicing angle has a different contrast ratio, a splicing angle of 45° presents the highest modulation depth. Besides, the FMFBG serves as a wavelength selector and transverse mode selector, simultaneously. The reflection wavelengths of the FMFBG can be expressed as:
where λ01(11) is the reflection wavelength of LP01 (LP11) mode, Λ is the grating period, neff-01(11) is the effective reflective index of LP01 (LP11) modes. Owing to the different effective reflective indexes for LP01 mode and LP11 mode, the corresponding reflection wavelengths are also different. The measured reflection spectrum is shown in Fig. 2(b) (red solid line). It is clear that the three peaks appear in the reflection spectrum (red solid line), which corresponds to the reflection from LP01 to LP01 mode (1056 nm), LP01 to LP11 mode (1055 nm), and LP11 to LP11 mode (1054 nm), respectively. That is to say, only LP01 mode at 1056 nm can be reflected by the FMFBG and only LP11 mode at 1054 nm can be reflected. It is worth noting that the wavelength spacing between reflection peaks of LP01 to LP01 mode and LP11 to LP11 mode of the FMFBG is about 2 nm, which is equal to the wavelength spacing of the adjacent peak-valley of the Lyot filter. The position of peak or valley can be shifted by adjusting the PC due to the change in stress-induced birefringence, and the simulated transmission spectrum of the designed filter in two different states are shown (dashed line) in Fig. 2(b). For state 1, the peak (1056 nm) and the valley (1054 nm) of the filtering spectrum locate at the right and left reflection peak of the FMFBG, respectively, which means that LP01 mode can get the highest gain, and LP11 mode can be well suppressed. Thus, this laser can directly oscillate in LP01 mode. Similarly, when the filtering spectrum is switched to state 2, the peak (1054 nm) locates at the left reflection peak of the FMFBG, which indicates that LP11 mode can get the highest gain to directly oscillate in the cavity and LP01 mode can be well suppressed. Consequently, the switchable oscillating spatial mode can be readily realized by controlling the filtering spectrum of the Lyot filter.Fig. 2. (a) The simulated transmission spectra of the Lyot filter with spliced angles of 30°, 45°, 70°, and 80°. (b) The measured reflection spectrum of the FMFBG (red solid line) and the simulated transmission spectrum of the filter (dashed line) in two different states.
3. Results and discussion
In our experiment, the fiber laser operates in the continuous-wave (CW) state when the pump power is 80 mW below the threshold of mode-locking. As increasing the pump power to 95 mW of mode-locked threshold and carefully adjusting the PCs simultaneously, a stable single-wavelength mode-locked operation is achieved, which attributes to the reliable saturable absorption effect of SESAM. Figure 3 shows the output characteristics of the stable mode-locked operation with the output power of 6.5 mW at a pump power of 110 mW. The mode-locked fiber laser operates at 1056.06 nm with the 3 dB bandwidth of 0.14 nm, as shown in Fig. 3(a). It is worth noting that the operating wavelength corresponds to the LP01 to LP01 mode reflection peaks of the FMFBG (the red line in Fig. 2(b)), and the output beam profile is shown in the inset of Fig. 3(a), which is the typical characteristic of the fundamental mode (LP01 mode). These results indicate that LP01 mode directly oscillates in this mode-locked fiber laser. The mode-locked pulse train with a pulse interval of 44.17 ns is captured by an oscilloscope, as shown in Fig. 3(b), which is consistent with the total cavity length of about 4.5 m. Figure 3(c) presents the measured RF spectrum within a 3 MHz range with a resolution of 30 Hz. The fundamental repetition rate of the mode-locked pulse is 22.638 MHz, and the signal-to-noise ratio (SNR) is 70 dB, which confirms the stability of the mode-locking operation. The autocorrelation trace of a single pulse is detected by an autocorrelator, as shown in Fig. 3(d). The pulse duration is measured to be 21.1 ps with the Gaussian profile assumed. In addition, as pump power increases from 95 mW to 136 mW, the mode-locked operation is maintained and no mode hopping is observed. The relationship between output power and pump power is in Fig. 4. It presents a mode-locking operation with a threshold pump power of 95 mW and good linear growth of the generated output power with a slope efficiency of 19%. It is worth mentioning that once the mode-locked state is obtained, this laser can self-start and operate in a stable mode-locked regime when the pump power reaches the threshold value of 95 mW.
Fig. 3. Output results of mode-locked fiber laser when oscillating in LP01 mode at the pump power of 110 mW. (a) The spectrum of laser output (blue line) and measured reflection spectrum of the FMFBG (red line). The inset shows the intensity distribution of the output mode. (b) Pulse train with an interval of 44.17 ns. (c) RF spectrum at a fundamental frequency of 22.638 MHz. (d) Autocorrelation trace of the mode-locked pulse.
Fig. 4. Output power versus pump power when mode-locked fiber laser directly oscillates in the LP01 mode regime.
The filtering spectrum of the Lyot filter can be precisely tuned by carefully rotating the PCs, that is to say, wavelengths at 1054 nm or 1056 nm will experience different gains and losses in the cavity. Thus, by properly adjusting the PCs, the operating wavelength of the mode-locked fiber laser can be easily switched from 1056.06 nm to 1054.07 nm when the pump power is maintained at 110 mW, which indicates that the oscillation transverse mode is switched from LP01 mode to LP11 mode due to the particular transverse mode-wavelength association characteristics of the FMFBG [37]. In this case, the output characteristics of the mode-locked pulsed operation are shown in Fig. 5. The mode-locked fiber laser operates at 1054.07 nm corresponding to the left reflection peaks of the FMFBG, and its 3dB bandwidth is 0.1 nm, as displayed in Fig. 5(a). The wavelength at 1056 nm is well suppressed and the ratio between the signal peak and maximum non-resonant peak is over 40 dB. Such weak nonresonant CW backgrounds (located at 1054nm/1055nm (Fig. 3(a)) and 1055nm/1056nm (Fig. 5(a))) are always observed due to the reflection of the FMFBG, however, which do not affect the mode-locking of LP01 and LP11 mode. The beam profile of two lobes is the typical feature of LP11 mode in the inset, which indicates that mode-locked fiber laser directly oscillates in the LP11 mode regime. The mode-locking pulse train is shown in Fig. 5(b), where the pulse interval is about 44.13 ns corresponding to the repetition rate of 22.662 MHz. The difference in repetition rate is mainly caused by the modal dispersion. The corresponding RF spectrum is measured within a 3 MHz range with a resolution of 30 Hz. The SNR of as high as 67 dB demonstrates the stability of the mode-locking state as shown in Fig. 5(c). The output pulse duration is measured to be 31.5 ps, as shown in Fig. 5(d). Similarly, once the mode-locked state is obtained, the laser can self-start and directly oscillate in LP11 mode when keeping the states of the PCs unchanged. As the pump power increases from 107 mW to 136 mW, fiber laser with LP11 mode direct oscillation keeps in a stable mode-locking state, and output power versus pump power is shown in Fig. 6. The threshold of mode-locked fiber laser with LP11 mode oscillation is 107 mW, which is higher than that of LP01 mode oscillation due to the higher cavity loss of LP11 mode. The slope efficiency of as high as 12% is obtained. Besides, to verify that 12% for LP11 mode is high efficiency, we summarize pulsed HOM fiber laser using different methods, as shown in Table 1. It can be seen that high order mode direction with the slope efficiency of 12% in our work is highest compared to LPG [13], MSC [16], offset splicing [19], AIFG [20]. This result can attribute to HOM direct oscillation and specially designed RC-YDF having a larger overlap integral between the intensity within the doping region [38]. Consequently, the HOM signal beam can extract the population inversion more effectively. In this FMF laser, splicing loss has a slight effect on the efficiency of the laser, and it is inevitable during the splicing of different optical fibers. However, the higher slope efficiency may be obtained by optimizing the length of the active fiber and using a SESAM with a higher reflectivity (SESAM with a reflectivity of 70% at 1055 nm is used in our experiment, which results in a waste of 30% of LP11 mode output power). Moreover, by properly adjusting the PCs, the operating wavelength can be easily switched to 1056.06 nm again, which corresponds to the LP01 mode oscillation. Then, we continue adjusting the PCs, the operating wavelength is switched to 1054.07 nm again corresponding to LP11 mode oscillation. These results indicate that mode switching is accessible and repeatable.
Fig. 5. Output results of mode-locked fiber laser when oscillating in LP11 mode at the pump power of 110 mW. (a) The spectrum of laser output (blue line) and the intensity distribution of output mode (inset). (b) Pulse train with an interval of 44.19 ns. (c) RF spectrum at a fundamental frequency of 22.662 MHz. (d) Autocorrelation trace of the mode-locked pulse.
Fig. 6. Output power versus pump power when mode-locked fiber laser directly oscillates in the LP11 mode regime.
Table 1. Summary of Pulsed HOM fiber Lasers
When mode-locked fiber laser operates at 1054.07 nm, LP11 linear polarization mode can be obtained from the output end of the PBS with a few-mode polarization-maintaining fiber pigtail. To obtain cylindrical vector beams (CVB) output, a piece of FMF is directly spliced to the output end of the PBS and the degeneracy of the LP11 mode is removed by a PC mounted on FMF, which is not shown in Fig. 1. By adjusting the PC, radially polarized beams can be obtained, corresponding intensity distribution is imaged by the CCD camera giving a doughnut-shaped pattern, which is the typical characteristic of CVB, as shown in Fig. 7(a). The intensity profiles of TM01 mode through a linear polarizer at different orientations are shown in Figs. 7(b)-(e). The purity of TM01 mode is measured to be 98.6% using the bend method proposed in [39].
Fig. 7. (a) Intensity profile of TM01 mode and (b)-(e) corresponding intensity distribution of TM01 mode after a linear polarizer. The white arrows represent the axis orientations of a linear polarizer.
4. Conclusion
In summary, we propose and experimentally demonstrate an FMF linear cavity mode-locked fiber laser with switchable oscillating transverse modes. The stable mode-locked pulsed operation is easily achieved based on a commercial SESAM providing a reliable saturable absorption effect. The mode gain profile of the laser can be flexibly controlled by an artificial filter. By simply adjusting the PC, the operating wavelength can be switched from 1056.06 nm to 1054.07 nm, and the oscillating transverse mode can be flexibly switched between LP01 mode and LP11 mode when the mode-locked pulsed operation is maintained. The stable mode-locked fiber laser with HOM direct oscillation operates at 1054.07 nm with a 3 dB bandwidth of 0.1 nm and a slope efficiency of as high as 12%. The repetition rate of the pulse is 22.662 MHz and the pulse duration is measured to be 31.5 ps. Besides, a radially polarized beam (TM01 mode) with a high purity of 98.6% is obtained by removing the degeneracy of the LP11 mode. This compact and high-efficiency mode-locked fiber laser with switchable wavelength and transverse modes can be used as alternative laser sources for many applications such as laser processing, particle trapping, optical bioimaging, wavelength/mode division multiplexing system.
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.
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. K. C. Phillips, H. H. Gandhi, E. Mazur, and S. K. Sundaram, “Ultrafast laser processing of materials: a review,” Adv. Opt. Photonics 7(4), 684–712 (2015). [CrossRef]
2. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009). [CrossRef]
3. S. G. Matsusaka, Y. C. Kozawa, and S. C. Sato, “Micro-hole drilling by tightly focused vector beams,” Opt. Lett. 43(7), 1542–1545 (2018). [CrossRef]
4. Y. Kozawa, M. Sato, Y. Uesugi, and S. Sato, “Laser microprocessing of metal surfaces using a tightly focused radially polarized beam,” Opt. Lett. 45(22), 6234–6237 (2020). [CrossRef]
5. L. Huang, H. Guo, J. Li, L. Ling, B. Feng, and Z. Y. Li, “Optical trapping of gold nanoparticles by cylindrical vector beam,” Opt. Lett. 37(10), 1694–1696 (2012). [CrossRef]
6. M. Liu, W. D. Zhang, F. F. Lu, T. Y. Xue, X. Li, L. Zhang, D. Mao, L. G. Huang, F. Gao, T. Mei, and J. L. Zhao, “Plasmonic tip internally excited via an azimuthal vector beam for surface enhanced Raman spectroscopy,” Photonics Res. 7(5), 526–531 (2019). [CrossRef]
7. L. Zhang, W. D. Zhang, F. F. Lu, Z. Q. Yang, T. Y. Xue, M. Liu, C. Meng, L. Peng, D. Mao, T. Mei, and J. L. Zhao, “Azimuthal vector beam exciting silver triangular nanoprisms for increasing the performance of surface-enhanced Raman spectroscopy,” Photonics Res. 7(12), 1447–1453 (2019). [CrossRef]
8. Y. Kozawa, D. Matsunaga, and S. Sato, “Superresolution imaging via superoscillation focusing of a radially polarized beam,” Optica 5(2), 86–92 (2018). [CrossRef]
9. B. Sun, A. Wang, C. Gu, G. Chen, L. Xu, D. Chung, and Q. Zhan, “Mode-locked all-fiber laser producing radially polarized rectangular pulses,” Opt. Lett. 40(8), 1691–1694 (2015). [CrossRef]
10. Y. Zhou, J. Lin, X. Zhang, L. Xu, C. Gu, B. Sun, A. Wang, and Q. Zhan, “Self-starting passively mode-locked all fiber laser based on carbon nanotubes with radially polarized emission,” Photonics Res. 4(6), 327–330 (2016). [CrossRef]
11. H. Li, K. Yan, Y. Zhang, Z. Dong, C. Gu, P. Yao, L. Xu, R. Zhang, J. Su, W. Chen, Y. Zhu, and Q. Zhan, “Passively Q-switching cylindrical vector beam fiber laser operating in high-order mode,” J. Opt. 21(9), 095502 (2019). [CrossRef]
12. 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]
13. R. X. Tao, H. X. Li, Y. M. Zhang, P. J. Yao, L. X. Xu, C. Gu, and Q. W. Zhan, “All-fiber mode-locked laser emitting broadband-spectrum cylindrical vector mode,” Opt. Laser Technol. 123, 105945 (2020). [CrossRef]
14. L. Teng, J. Lu, Y. He, L. Wang, and X. Zeng, “Vortex soliton oscillation in a mode-locked laser based on broadband long-period fiber grating,” Opt. Lett. 46(11), 2710–2713 (2021). [CrossRef]
15. Y. Li, L. Huang, H. Han, L. Gao, Y. Cao, Y. Gong, W. Zhang, F. Gao, I. P. Ikechukwu, and T. Zhu, “Acousto-optic tunable ultrafast laser with vector-mode-coupling-induced polarization conversion,” Photonics Res. 7(7), 798–805 (2019). [CrossRef]
16. H. Wan, J. Wang, Z. Zhang, Y. Cai, B. Sun, and L. Zhang, “High efficiency mode-locked, cylindrical vector beam fiber laser based on a mode selective coupler,” Opt. Express 25(10), 11444–11451 (2017). [CrossRef]
17. T. Wang, F. Wang, F. Shi, F. Pang, S. Huang, T. Wang, and X. Zeng, “Generation of Femtosecond Optical Vortex Beams in All-Fiber Mode-Locked Fiber Laser Using Mode Selective Coupler,” J. Lightwave Technol. 35(11), 2161–2166 (2017). [CrossRef]
18. Y. Cai, Z. Wang, H. Wan, Z. Zhang, and L. Zhang, “Mode and Wavelength-Switchable Pulsed Fiber Laser With Few-Mode Fiber Grating,” IEEE Photonics Technol. Lett. 31(14), 1155–1158 (2019). [CrossRef]
19. Y. Xu, Y. Cai, H. D. Wan, and Z. X. Zhang, “Linear-cavity mode-locked fibre laser with cylindrical vector beam generation,” IET Optoelectron. 13(5), 232–234 (2019). [CrossRef]
20. J. Lu, F. Shi, L. Meng, L. Zhang, L. Teng, Z. Luo, P. Yan, F. Pang, and X. Zeng, “Real-time observation of vortex mode switching in a narrow-linewidth mode-locked fiber laser,” Photonics Res. 8(7), 1203–1212 (2020). [CrossRef]
21. J. Wei, P. Zhang, Z. X. He, S. He, X. Y. Gong, Y. L. Fan, and S. F. Tong, “Multimode oscillation Q-switched mode-locking fiber laser based on gain equalized few-mode Er-doped fiber,” Opt. Eng. 60(5), 056108 (2021). [CrossRef]
22. S. M. Han, K. Yang, Z. H. Wang, Y. G. Liu, and Z. Wang, “Multimode oscillation Q-switched erbium-doped fiber laser with a few-mode fiber cavity,” Optoelectron. Lett. 14(6), 417–420 (2018). [CrossRef]
23. T. Wang, A. Yang, F. Shi, Y. Huang, J. Wen, and X. Zeng, “High-order mode lasing in all-FMF laser cavities,” Photonics Res. 7(1), 42–49 (2019). [CrossRef]
24. T. Wang, F. Shi, Y. Huang, J. Wen, Z. Luo, F. Pang, T. Wang, and X. Zeng, “High-order mode direct oscillation of few-mode fiber laser for high-quality cylindrical vector beams,” Opt. Express 26(9), 11850–11858 (2018). [CrossRef]
25. Y. Xu, D. Wang, Z. Wang, S. Chen, and Z. Zhang, “All Few-Mode Fiber Passively Mode-Locked Figure-8 Cavity Laser,” IEEE Photonics Technol. Lett. 31(21), 1729–1732 (2019). [CrossRef]
26. S. Chen, W. X. Hu, Y. Xu, Y. Cai, Z. Q. Wang, and Z. X. Zhang, “Mode-locked pulse generation from an all-FMF ring laser cavity,” Chin. Opt. Lett. 17(12), 121405 (2019). [CrossRef]
27. N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545 (2013). [CrossRef]
28. T. Mori, T. Sakamoto, M. Wada, T. Yamamoto, and K. Nakajima, “Few-mode fiber technology for mode division multiplexing,” Opt. Fiber Technol. 35, 37–45 (2017). [CrossRef]
29. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-Division Multiplexing Over 96 km of Few-Mode Fiber Using Coherent 6×6 MIMO processing,” J. Lightwave Technol. 30(4), 521–531 (2012). [CrossRef]
30. V. Niziev and A. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D: Appl. Phys. 32(13), 1455–1461 (1999). [CrossRef]
31. M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A 86(3), 329–334 (2007). [CrossRef]
32. O. J. Allegre, W. Perrie, S. P. Edwardson, G. Dearden, and K. G. Watkins, “Laser microprocessing of steel with radially and azimuthally polarized femtosecond vortex pulses,” J. Opt. 14(8), 085601 (2012). [CrossRef]
33. X. Wang, Y. Zhang, Y. Dai, C. Min, and X. Yuan, “Enhancing plasmonic trapping with a perfect radially polarized beam,” Photonics Res. 6(9), 847–852 (2018). [CrossRef]
34. Y. Zhang, J. Shen, C. Min, Y. Jin, Y. Jiang, J. Liu, S. Zhu, Y. Sheng, A. V. Zayats, and X. Yuan, “Nonlinearity-Induced Multiplexed Optical Trapping and Manipulation with Femtosecond Vector Beams,” Nano Lett. 18(9), 5538–5543 (2018). [CrossRef]
35. W. Yu, Z. Ji, D. Dong, X. Yang, Y. Xiao, Q. Gong, P. Xi, and K. Shi, “Super-resolution deep imaging with hollow Bessel beam STED microscopy,” Laser Photonics Rev. 10(1), 147–152 (2016). [CrossRef]
36. S. Liu, F. P. Yan, F. Ting, L. N. Zhang, Z. Y. Bai, W. G. Han, and H. Zhou, “Multi-Wavelength Thulium-Doped Fiber Laser Using a Fiber-Based Lyot Filter,” IEEE Photonics Technol. Lett. 28(8), 864–867 (2016). [CrossRef]
37. 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]
38. H. X. Li, Y. M. Zhang, Z. P. Dong, J. L. Lv, C. Gu, P. J. Yao, L. X. Xu, R. Zhang, J. Q. Su, W. Chen, Y. G. Zhu, and Q. W. 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]
39. B. 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]
