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High energy switchable pulsed High-order Mode beams in a mode-locking Raman all-fiber laser with high efficiency
1. Introduction . The high-order mode (HOM) beams with unique spatial intensity and polarization distribution have attracted widespread attention [ 1 , 2 ]. Two kinds of HOM beams including cylindrical vector beams (CVBs) and optical vortex beams (OVBs) have been widely studied, which have potential applications in many advancing frontiers, such as nanoparticle manipulation [ 3 ], material processing [ 4 ], optical tweezers [ 5 ], high-capacity communication [ 6 ] and data storage [ 7 ]. Initially, a number of effective methods have been applied to generate HOM beams, including birefringent components [ 8 ], q-plate [ 9 ], helical phase plate [ 10 ], sub-wavelength gratings [ 11 ], spatial light modulators (SLMs) [ 12 ], and so on. However, considering the integration requirements of an all-fiber system for better flexibility, stability and compactness, fiber-based methods have furtherly come forth. Firstly, the few-mode fiber-based Bragg grating (FBG) and offset splicing technique were proposed to generate HOM beams but with large loss and poor beam quality [ 13 ]. Subsequently, the acoustically induced fiber grating (AIFG) and long-period fiber grating (LPFG) were adopted to further reduce the loss. But the intrinsic property of narrow-band operation limits its further application [ 14 , 15 ]. Recently, due to its low loss and wide operating bandwidth, the mode-selective coupler (MSC) has gradually been valued and widely utilized in mode-locking all-fiber lasers [ 16 – 19 ]. Comparing with bulk solid-state lasers, high energy pulses in mode-locking all-fiber lasers with great compact, high stability, and low cost have attracted more and more attention recently in laser material processing, biology, telecommunication, medical equipment, and laser range finding [ 20 – 23 ]. Especially, with unique spatial intensity, phase, and polarization distribution, high energy pulsed HOM beams have shown important applications in materials processing [ 24 , 25 ] and particle acceleration [ 26 , 27 ]. However, high energy pulses are generally achieved by a cascade of delicate amplifiers after a pulsed seed source [ 28 ], which much enhances the complexity. Hence, high-energy pulses directly emitting from an all-fiber laser cavity are always an attractive scientific issue. In view of soliton area theorem [ 29 ] salient in an all-anomalous-dispersion cavity, for high energy pulse, the major solution is dispersion management that neutralizes the nonlinear effects for preventing pulse splitting, including stretched-pulse [ 30 ], parabolic pulse [ 31 ], and dissipative soliton pulse [ 32 ]. An effective way to generate high energy pulses (also for pulsed HOM beams) is still a challenge in mode-locking all-fiber lasers. Noting that a compact continuous wave (CW) Raman all-fiber laser with HOM beams has been demonstrated [ 33 ]. As for pulsed laser, Raman all-fiber laser is an instantaneous pump-to-signal conversion without energy storage in the long gain fiber. So that, the pulse splitting can be reasonably suppressed, which can greatly enhance the pulse energy [ 34 ]. Besides, thanking to the low quantum defect and absence of photon darkening, Raman all-fiber laser possesses outstanding features of high efficiency, good for further improving pulse energy [ 35 ]. Moreover, without the particular gain wavelength limitation in rare-earth-doped fibers, Raman all-fiber lasers can operate at arbitrary wavelength with an appropriate pump source. Therefore, Raman all-fiber laser would be a better choice to achieve high energy pulsed HOM beams even at some special wavelengths. In this paper, combined with MSC and stimulated Raman scattering, we experimentally demonstrate a high energy mode-locking Raman all-fiber laser with switchable HOM state and high efficiency. Benefited from broad conversion bandwidth of MSC and intrinsic characteristic of mode-locking Raman laser, 1.1 μJ pulsed HOM beams with high efficiency of 20.3% are achieved. Through controlling the category and phase delay of vector modal superposition, switchable HOM beams including CVBs and OVBs can be generated both in mode-locking and continuous wave operations. In addition, the mode purity of switchable HOM beams is all over 95% in such broad mode-locking Raman spectrum. The proposed mode-locking Raman all-fiber laser with MSC provide an elastic way to generate high energy pulsed HOM beams directly emitting from the cavity. 2. Experimental setup . 2.1 MSC simulation and fabrication . Here, the central conversion wavelength of our MSC is set to 1583 nm, which is propriate for our Raman all-fiber laser with 1480 nm pump source. Based on the coupled-mode theory, once the propagation constant β1 of fundamental mode in single-mode fiber (SMF) equals to β2 of HOM in four-mode fiber (FMF) [ 36 ], mode conversion will occur. The propagation constant β can be calculated by k 0 n eff , where k 0 is the propagation constant in vacuum, n eff is the mode effective index. In order to meet the phase-matching condition, we calculate the mode effective index with different fiber core radius at 1583?nm for SMF and FMF by finite element method [ 37 ], as shown in Fig.? 1 (a). Two points with the same mode effective index (the horizontal dotted line) are choose to meet phase-matching condition for LP 11 , indicating that the SMF should be pre-tapered until the ratio of 0.58. Then, according to the above results, we experimentally manufacture an appropriate MSC, schematic structure is shown in Fig.? 1 (b), comprising a SMF and a FMF (OFS). To achieve high energy pulsed HOM beams, we choose 40% as output. According to our simulations, for 40% output with LP 11 mode, the diameter of the SMF should be pre-tapered to 73 μm and then carefully coupled to FMF with modified flame brushing technique [ 17 ]. Noting that a Raman mode-locking all-fiber laser is usually accompanied by a broad spectrum, we then test the wavelength tolerance of our MSC device. The clear and distortionless two-lobe-shaped intensity patterns of output LP 11 mode at different wavelengths are shown in Fig.? 1 (c), captured by a CCD (Spiricon, BGS-USB-SP928-OSI, USA). It affirms the broadband operating wavelength of our MSC with 60 nm. Using tight bend method [ 38 ], we further investigate the mode purity of LP 11 mode output from our MSC. During the overall Raman operating wavelength (1540 to 1600 nm), the mode purity is all over 90% with insertion loss around 0.8 dB. Especially, at the central wavelength (1583 nm) of our Raman fiber laser, the mode purity is about 95% with a low total insertion loss of 0.55 dB. ? Fig. 1. (a) Mode effective index with different fiber core radius at 1583 nm for SMF and FMF (b)Schematic of the MSC; (c) CCD images of LP 11 at different wavelengths. Download Full Size PPT Slide PDF 2.2 Raman all-fiber laser setup . Figure? 2 schematically shows our mode-locking Raman all-fiber laser. The Raman gain medium is provided by a piece of 600 m high nonlinear fiber (HNLF) (OFS, Furukawa) with a nonlinear coefficient of 11.3/(W·km). The HNLF is backward pumped by a 1480 nm commercial high-power single-mode Raman laser with maximum output power of 10 W through a 1480/1583 nm wavelength division multiplexer (WDM). To protect intra-cavity fiber components, a second WDM is used to export unconverted pump. A polarization-dependent isolator (PDI) at ?1583 nm together with two polarization controllers (PCs) act as a mode-locker. The main purpose of extra PC3 is further increasing the tuning accuracy and extending tuning range of polarization states. The total ring-cavity length is about 615 m. The 40% port of our home-made MSC is engaged as the output. Meanwhile, the output from the FMF is directly measured by an optical spectrum analyzer (OSA, Yokogawa, AQ6375B, Japan), a 12.5 GHz high-speed oscilloscope (Tekrtonix, DPO71254C, USA) together with a 12.5 GHz photodetector (E-O Tech. Inc., ET-5000F), a radio frequency (RF) spectrum analyzer (Keysight, N9322C, USA). ? Fig. 2. Schematic of mode-locking Raman all-fiber laser. WDM: wavelength division multiplexer, PDI: polarization-dependent isolator, PC: polarization controller, HNLF: high nonlinear fiber, MSC: mode-selective coupler, SMF: single-mode fiber, FMF: four-mode fiber. Download Full Size PPT Slide PDF 3. Results and discussion . 3.1 Mode-locking operation . By increasing pump power to 1185 mW and adjusting PCs, stable fundamental mode-locking pulses with HOM state could be achieved. The output spectrum centered at 1587.93 nm with a 3-dB linewidth of 14.59 nm is illustrated in Fig.? 3 (a) under the pump power of 1250 mW. The obvious spectrum fringes are caused by the interference between the degenerated vector modes of LP 11 [ 39 ]. The corresponding oscilloscope trace is shown in Fig.? 3 (b) with a span of 150 μs, which possessing a highly uniform amplitude. We further capture a single pulse with smaller sampling interval and larger storage depth, shown in Fig.? 3 (c), indicating a width of 374.6 ns. Also, corresponding autocorrelation trace is measured, there is no any coherent peak in a span of 150 ps. The homologous radio frequency (RF) spectrum is shown in Fig.? 3 (d) with a high signal-to-noise ratio (SNR) of 64.6 dB at the fundamental frequency of 319.3 kHz. The insert represents a wider RF spectrum span of 3.5 MHz, in which, there is no other redundant frequency components except mode locking. All these confirm the high stability of pulsed HOM beams. Figure? 3 (e) demonstrates the evolution of output power and pulse energy versus pump power when fundamental mode-locking state can be maintained. The average output power can reach 342 mW at the maximal pump power of 2635 mW with slope efficiency of 20.3%. Correspondingly the highest pulse energy of pulsed HOM beams is up to 1.1 μJ. The spectrum at pump power of 2635 mW is shown in Fig.? 3 (f). The 3-dB bandwidth gradually enlarges as pump power increasing due to the self-phase modulation, finally stays around 25.59 nm. The profile and transverse field distribution of corresponding pulsed HOM beams are also shown in the inset of Fig.? 3 (f). The pulse width broadens to 760.4 ns still with stable and unchanged two-lobe-shaped pattern. ? Fig. 3. Output characteristics of pulsed HOM beams in stable fundamental mode-locking operation. (a) Spectrum; (b) pulse train; (c) temporal characteristics of single pulse; (d) RF spectrum with RBW of 10 Hz. Insert: 1KHz; (e) Output power and pulse energy versus pump power; (f) Spectrum and temporal characteristics of 1.1 μJ pulsed HOM beams at pump power of 2635 mW. Download Full Size PPT Slide PDF The expected intensity distribution of HOM (LP 11 ) shown in the insert of Fig.? 3 (f) is a typical scalar mode distribution in the fiber. After carefully adjusting the polarization, LP 11 modes in fiber will degenerate into vector modes (TE 01 , TM 01 and $\textrm{HE}_{21}^{\textrm{even}/\textrm{odd}}$ modes) due to different phase velocities [ 18 ]. Thus, we keep pump power at 2635 mW and then carefully adjusting the PC4 on the FMF. Once only TE 01 and TM 01 modes survive, an annularly-distributed beam with a hollow core will generate [ 40 ], as shown in Fig.? 4 (a) and Fig.? 4 (b). After inserting a polarizer for testing the polarization states, it splits to two-lobe-like profile, which is a typical property of CVBs. As shown in Fig.? 4 (a 1 -a 4 ), after gradually rotating a polarizer, the two-lobe-like profiles always orient perpendicular to the transmission axis of Glan prism (the white arrows), which is a typical polarization evolution of azimuthally polarized CVBs. While in the Fig.? 4 (b 1 -b 4 ), it is always parallel, indicating its radially polarized state. Through tight bend method, the mode purity of azimuthally polarized and radially polarized CVBs are measured as 95.5% and 95.6%, respectively. In addition, once the HOM in the FMF form superposition of $\textrm{HE}_{21}^{\textrm{even}} \pm \textrm{iHE}_{21}^{\textrm{odd}}$ modes with a π/2 phase shift, the OAMs will be obtained [ 18 ], shown in Fig.? 4 (d) and Fig.? 4 (e). It also presents a doughnut-shaped intensity profile. Then for distinguishing the topological charge, we load a phase image (shown in Fig.? 4 (c)) of cylindrical lens into the SLMs (Hamamatsu, X13138-SPL, Japan). As seen in Fig.? 4 (d 1 ) and Fig.? 4 (e 1 ), it presents only one tilted dark stripe with opposite direction, corresponding to l?=?±1 [ 41 ]. The corresponding mode purity are calculated to be 96.5% and 97.5%, respectively. ? Fig. 4. Near-field intensity distributions of switchable pulsed HOM beams in mode-locking operation. (a) Azimuthally polarized beams; (b)Radially polarized beams; (c) A phase image of cylindrical lens; (d-e) OAMs±1. Download Full Size PPT Slide PDF For demonstrating the long-term stability of our pulsed HOM Raman all-fiber laser, we capture the mode-locking spectra and intensity distribution of CVBs every 15 minutes at pump power of 2435?mW, shown in the Fig.? 5 . As seen, during an hour, the spectra and intensity distribution of CVBs can always keep unchanged, confirming the high long-term stability of our pulsed HOM Raman all-fiber laser. ? Fig. 5. Long term stability of spectra in our Raman laser at pump power of 2435?mW. Insert: CVBs. Download Full Size PPT Slide PDF Moreover, we summarize pulsed HOM all-fiber lasers as shown in Table? 1 . It can be observed that the pulse energy achieved in our all-fiber laser is the highest one directly emitting from the laser cavity. A matter of course, higher energy pulsed HOM beams can be achieved by multi-stage amplification [ 42 ], but with higher cost, more complicated structure, lower compactness. Such a low-cost, compact and high efficiency Raman mode-locking all-fiber laser maybe a more effective way to generate high energy pulsed HOM beams directly. Table 1. Summary of Pulsed HOM All-fiber Lasers View Table 3.2 Continuous Wave (CW) operation . For comparison, we also demonstrate the characteristics of HOM beams in CW operation. the threshold of CW state is about 980?mW. Figure? 6 (a) shows the spectrum of CW operation at a pump power of 1005?mW with obvious spectrum fringes. The center wavelength locates at 1587.41?nm with a 3-dB bandwidth of 3.8?nm. Figure? 6 (b) shows the evolution of output power versus pump power with slope efficiency up to 31.8%. Also, we further investigate the generation of different HOM beams in CW operation. Through carefully adjusting the PC4, switchable HOM beams (CVBs and OVBs) can be obtained, as shown in Fig.? 6 (c-d). Similarly, the typical characteristic of CVBs and OVBs are confirmed by a polarizer and cylindrical lens. It is worth mentioning that the highest output power of HOM beams in CW operation is as much as 514 mW. Higher output power is limited by the second-order Raman scattering. ? Fig. 6. Output characteristics of HOM beams in CW operation (a) Spectrum of CW operation; (b) Output power versus pump power in CW operation; (c) Azimuthally polarized and radially polarized beams; (d) OAMs±1. Download Full Size PPT Slide PDF 4. Conclusion . In conclusion, we reported the generating of high energy pulsed HOM beams in a mode-locking all-fiber laser, based on stimulated Raman scattering and MSC. A MSC is fabricated with modified flame brushing technique and then placed in the cavity as a mode converter with broadband bandwidth (60 nm) and low insertion loss (0.55 dB). Thanks to the advantage of Raman mode-locking laser and MSC, high energy pulsed HOM beams with high efficiency (20.3%) are achieved. The maximum average output power directly emitting from the laser cavity is as much as 342 mW, correspondingly the single pulse energy is up to 1.1 μJ. In addition, different HOM beams (CVBs and OVBs) can be achieved with high mode purity (all over 95%) by appropriately adjusting the polarization state. Furtherly, the characteristics of HOM beams in CW operation are also demonstrated for comparison. The present work provides an effective method to obtain high energy pulsed HOM beams, even at some special wavelength. Funding . National Natural Science Foundation of China (Grant No.11604095); Science and Technology Planning Project of Guangdong Province (Grant No. 2016B050501005); Shenzhen Government's Plan of Science and Technology (Grant No. JCYJ20180305124927623, Grant No. JCYJ20190808150205481). Disclosures . The authors declare no conflicts of interest. Data availability . 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