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Abstract
In this paper, a linear cavity mode-locked pulsed fiber laser generating cylindrical vector beams (CVBs) is proposed and demonstrated based on a nonlinear multimode interference. A homemade long-period fiber grating with a broad bandwidth of 121 nm is used as a mode converter inside the cavity. The saturable absorber was formed by single-mode fiber-graded index multimode fiber-single mode fiber (SMF-GIMF-SMF) structure. By controlling the pump power, the operation states are switchable among continuous-wave, Q-switched mode-locked (QML), and mode-locked regimes. The repetition rate of the QML CVB pulse envelope varies from 57.4 kHz to 102.7 kHz at the pump range of 118 to 285 mW. When increasing pump power to 380 mW, mode-locked CVB pulse repetition rate of 3.592 MHz, and pulse duration of 4.62 ns are achieved. In addition, the maximum single-pulse envelope energy can reach 510 nJ, and 142 mW average-power CVBs with a slope efficiency of as high as 20.2% can be obtained. Moreover, azimuthally and radially polarized beams can be obtained with mode purity over 95% in different operating regimes. The proposed fiber laser has a simple structure, and the operation is controllable in both temporal and spatial domains, which presents a flexible pulsed CVB source for application of laser processing, time or mode division multiplexing system, and spatiotemporal nonlinear optics.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Cylindrical vector beams (CVBs) with unique polarization and amplitude symmetry properties have attracted considerable attention, which has potential applications in optical tweezers [1,2], surface-enhanced Raman spectroscopy [3,4], and super-resolution imaging [5], mode division multiplexing [6], and STED microscopy [7,8]. In terms of generating CVBs, all-fiber systems have the advantages of compactness, stability, and flexibility compared to solid-state laser systems containing volume optical elements, such as sub-wavelength gratings [9], q-plate [10], spatial light modulators (SLMs) [11]. In recent years, various methods for the generation of CVBs based on fiber laser have been proposed and demonstrated, such as using laterally offset splicing and few-mode fiber Bragg grating (FMFBG) [12,13], long-period fiber grating (LPFG) [14], acoustically induced fiber grating (AIFG) [15], and mode selective coupler (MSC) [16,17], a pair of few-mode fiber Bragg gratings [18,19], metal-clad transverse mode filter [20], and mode superposition [21,22]. Compared to continuous-wave (CW) CVB fiber lasers, pulsed CVBs with high peak power and high pulse energy have shown important applications in materials processing [23,24], electronic acceleration [25,26], and optical trapping and manipulation [27]. To obtain pulsed CVB output, various saturable absorbers (SAs) materials have been employed to realize Q-switching or mode-locked pulses based on semiconductor saturable absorption mirror (SESAM) [28–30], carbon nanotube [31,32], tungsten disulphide (WS2) [33], Bi2Te3 [34]. However, these materials often require complicated fabrication processes, and their applicability is limited by their relatively low damage threshold [35–37]. The alternative methods to address the issues are to use artificial SA, such as nonlinear polarization rotation (NPR) [38], nonlinear amplifying loop mirror (NALM) [39], and nonlinear optical loop mirrors (NOLM) [40]. These devices have a relatively high damage threshold, while they are easily affected by environmental perturbations and have a relatively complicated laser cavity.
Recently, a novel all-fiber SA based on nonlinear multimode interference effect (NL-MMI) in graded-index multimode fiber (GIMF) has been studied extensively due to the advantages of high damage threshold, simple fabrication procedure, low cost, and long term reliability. When the light in SMF is coupled to GIMF, a number of high order modes are excited, which leads to the periodic interference pattern in the GIMF due to the self-imaging effect. In the nonlinear regime, the additional phase shifts introduced by self-phase modulation (SPM) and cross-phase modulation (XPM) effects will change the self-imaging beat length in GIMF and the self-imaging length at high peak power is different from that at the low peak power, which has an effective influence on the power coupling efficiency of the light from GIMF to SMF and presents the characteristics of high-power transmission and low-power attenuating. Thus, this SMF-GIMF-SMF structure could act as an effective SA with distinct intensity-dependent transmission for mode-locking. In 2013, single mode-graded index multimode-single mode fiber (SMF-GIMF-SMF) structures as a SA based on NL-MMI were theoretically proposed by Elham and Mafi for the first time [41]. Subsequently, various NL-MMI structures were experimentally demonstrated to realize a Q-switching or mode-locked pulse output in a ring or linear fiber laser cavity [42–45]. However, pulsed CVB fiber laser based on NL-MMI has not been reported yet.
In this letter, we propose and demonstrate a pulsed CVB linear-cavity fiber laser mode-locked by GIMF-SA. An SMF-GIMF-SMF structure is employed as SA based on nonlinear multimode interference effect to realize stable pulse operation. The operation state of this fiber laser can be flexibly controlled between Q-switched mode-locked and mode-locked states by adjusting pump power. A broadband long-period fiber grating is used as a mode converter to realize the conversion from LP01 mode to LP11 mode. A tailored fiber coupler with a few-mode fiber pigtail serves as a laser mirror and supports LP11 mode output. CVBs with mode purity over 95% are easily obtained by adjusting the polarization controller at the output end. Besides, the maximum single-pulse envelop energy can reach 510 nJ, and the maximum average power can reach 142 mW with a slope efficiency of as high as 20.2% can be obtained.
2. Experimental setup and principle
The schematic of the proposed pulsed CVB linear cavity Yb-doped fiber laser mode-locked based on GIMF-SA is presented in Fig. 1. A segment of 50 cm single-mode ytterbium-doped fiber (Liekki Yb1200) is used as a gain medium and pumped by a 974 nm laser diode via a 980/1060 nm wavelength division multiplexer (WDM). The linear cavity configuration is constructed by using an optical fiber mirror (OFM) with a single-mode fiber (SMF) pigtail (Corning HI1060) and an optical loop mirror. The loop mirror is formed with a fiber coupler composed of few-mode fiber (FMF) (core diameter of 8.2 µm and NA of 0.14, supporting LP01 and LP11 mode at 1060 nm) whose coupling ratio is 10:90, which not only provides a 64% laser output but also supports LP11 mode transmission. The insertion loss of this fiber coupler is measured to be 0.6 dB for LP11 mode at 1064 nm. It is worth noting that laser output from an optical loop mirror consisting of a fiber coupler has a higher damage threshold than that of a flat-end connector deposited with gold. The SMF-GIMF-SMF structure works as a saturable absorber (SA), which guarantees the mode-locking pulse operation. A broadband long-period fiber grating (LPFG) served as a mode converter is inserted into the linear cavity to realize the oscillation of LP11 modes. This laser cavity is a hybrid cavity, which is divided into two fiber sections propagating LP01 and LP11 modes. The left section (pink line) composed of few-mode fiber propagates LP11 mode and the right section (blue line) composed of single-mode fiber propagates LP01 mode. PC1 is used to control the intracavity polarization states. PC2 placed at the output end is employed to remove the degeneracy of the output high-order mode. The output beam profiles are captured by a CCD camera through a fiber collimator. The optical spectrum, pulse train, frequency spectrum, and output power are monitored 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 a power meter (Thorlabs PM100D), respectively.
Fig. 1. The schematic of the proposed pulsed CVB fiber laser based on GIMF SA. LPFG, long-period fiber grating; LD, laser diode; WDM, wavelength division multiplexer; YDF, Yb-doped fiber; SA, saturable absorber; PC1, polarization controller 1; PC2, polarization controller 2; OFM, optical fiber mirror; GIMF, graded-index multimode fiber; SMF, single-mode fiber; FMF, few-mode fiber.
In our experiment, the LPFG is a key element that is used as an LP01-LP11 mode converter to achieve CVB output, which is written in two-mode fiber by using a CO2 laser. The wavelength response of the conversion efficiency for the LPFG is measured by using the method in Ref. [46]. The corresponding result is shown in Fig. 2(a), which has a broad bandwidth with mode conversion efficiency higher than 95% in the range of 943-1064 nm. The mode conversion efficiency and bandwidth of LPFG are significant for the generation of high mode purity and wideband-spectrum CVB. To obtain pulsed CVB, the GIMF-based SA is used to realize stable mode-locking. The SA consists of two sections of 10 cm-long SMF and a section of GIMF (Corning) with core/cladding diameters of 62.5/125 µm. In consideration of the gain profile of Yb-doped fiber and the conversion spectral range of the LPG, the GIMF length of 32cm is chosen so as to obtain high power and high purity output of pulsed CVB. To acquire further insight into the proposed SA device, the nonlinear optical properties of the SMF-GIMF-SMF device is measured by using a homemade 1064 nm mode-locked fiber laser with a repetition rate of 10.6 MHz and a pulse width of 6.7 ps, as shown in Fig. 2(b). The obtained experimental datas are fitted with the below transmission function of the SA model [47]:
where T is the transmittance, α is the modulation depth, I is the input light intensity, Isat is the saturation intensity, and αns is the non-saturable loss. The transmission curve dependence on the pulse intensity exhibits typical characteristics of saturable absorption. The modulation depth is measured to be 10.6%. The result indicates that the proposed SMF-GIMF-SMF structure is capable of using as SA for pulse output.Fig. 2. (a) The wavelength response of the conversion efficiency for the LPFG. (b) The nonlinear transmission curve of the SMF-GIMF-SMF device. Black dots correspond to experimental data, and the red line is their fitting curve;
3. Results and discussion
3.1. Q-switched mode-locked operation
The fiber laser operates in the continuous-wave (CW) state when the pump power is over the laser threshold of 30 mW. With the pump power increasing to 118 mW and appropriately adjusting the PC1 simultaneously, a stable Q-switched mode-locked operation is achieved, which attributes to the saturable absorption effect of nonlinear multimode interference. Figure 3(a) shows output characteristics of the stable Q-switched mode-locked operation (QML). The oscilloscope traces of the pulse trains at different pump powers are shown in Fig. 3(a). It can be seen that as the pump power rises, the repetition rate of the pulse envelope gradually increases while the pulse envelope width decreases, which can be explained as the nonlinear dynamics of GIMF-based SA and the gain medium. With the increasement of the pump power, more gains are supplied to saturate the SA, and the cavity energy accumulates and release became faster, which results in the increase of the repetition rate and the decrease of pulse duration. The zoom-in detail image of a single pulse envelope at the pump power of 187 mW is presented in Fig. 3(b). It can be observed that the amplitude of the pulses with the fundamental repetition rate of 3.592 MHz corresponding to the pulse interval of 278.4 ns is modulated, and single pulse envelope duration is measured to be 4.2 µs. To further investigate QML operation, the corresponding RF spectrum is also measured within a 2 MHz range with a resolution of 30 Hz, as shown in Fig. 3(c). The RF spectrum locates at the fundamental mode-locked frequency of 3.592 MHz, which matches well with the cavity length of 28.4 m. The signal-to-noise ratio (SNR) of the center peak is about 61 dB. It is worth noting that multiple frequency sidebands with a 74.8 kHz interval around the center frequency of the mode-locked pulse can be clearly observed, which further confirms that the amplitude of the 3.592 MHz mode-locked pulse train is modulated at a frequency of 74.8 kHz and consistent with the experimental results presented in Fig. 3(a). These results confirm the typical characteristic of Q-switched mode-locked operation. Figure 3(d) shows the output spectrum of Q-switched mode-locked operation at a pump power of 187 mW, which contains two peaks at 1036.46 nm and 1040.44 nm. This result may be attributed to the filtering effect of the SMF-GIMF-SMF structure. The most intense peak is centered at 1036.46 nm with a 3 dB bandwidth of 1.66 nm.
Fig. 3. Output results of Q-switched mode-locked operation (a) The pulse trains under different pump powers. (b) Details of a single Q-switched mode-locked pulse envelope at a pump power 187 mW. (c) RF spectrum in a 2 MHz range with a resolution of 30 Hz. (d) The spectrum of laser output at a pump power 187 mW.
The variation of the Q-switched mode-locked pulses is investigated in detail as the pump power increases from 118 mW to 285 mW. The width of the pulse envelope and the pulse repetition rate versus pump power are shown in Fig. 4(a), where the pulse envelope width decreases from 4.8 µs to 3.5 µs, and the repetition rate increases from 57.4 kHz to 102.7 kHz. The output power and the calculated single pulse envelope energy as a function of the pump power are shown in Fig. 4(b). It can be seen that both output power and pulse envelope energy increase with the pump power. The average output power presents a good linear growth with a slope efficiency of 20.2%. The output power of 52.4 mW and maximum single-pulse envelope energy of 510 nJ are obtained at the pump power of 285 mW, respectively.
Fig. 4. The variation of the Q-switched mode-locked pulses as the pump power increases from 118 mW to 285 mW. (a) Pulse width and repetition rate versus pump power. (b) Output power and pulse envelope energy as a function of pump power.
Finally, high purity CVBs can be obtained by adjusting PC2 when the laser operates in a Q-switched mode-locked regime. The beam profiles of the azimuthally polarized modes (TE01) and radially polarized modes (TM01) are captured using a CCD camera, as shown in Fig. 5(a) and 5(f), respectively. The polarization properties are characterized by rotating a linear polarizer before the CCD camera. The intensity profiles of TM01 mode and TE01 mode after the linear polarizer at different orientations are shown in Figs. 5(b)-(e) and Figs. 5(g)-(j). By using the bend method [12], the purity of TM01 mode and TE01 mode are measured to be 97.1% and 95.1%, respectively.
Fig. 5. (a) Intensity profile of TM01 mode and (b)-(e) corresponding intensity distribution of TM01 mode after a linear polarizer. (f) Intensity profile of TE01 mode and (g)-(j) corresponding intensity distribution of TE01 mode after a linear polarizer. The white arrows represent the axis orientations of a linear polarizer.
3.2. Mode-locked operation
The operation state of this fiber laser can be easily switched from the Q-switched mode-locked operation to stable mode-locked (ML) pulse operation just by increasing the pump power and keeping the state of PC1 unchanged. As the pump power exceeds 316 mW, the Q-switched mode-locked operation automatically evolves into a mode-locking state. Figure 6 shows the output characteristics of the mode-locked pulsed operation at a pump power of 380 mW. The output spectrum is significantly broadened due to the nonlinear effect. The mode-locked fiber laser operates at 1038.34 nm with a 3dB bandwidth of 5.22 nm, as displayed in Fig. 6(a). The oscilloscope trace of the mode-locking pulse train is shown in Fig. 6(b), where the pulse interval is about 278.4 ns corresponding to the round trip time of the cavity. The corresponding temporal profile of a single pulse is shown in Fig. 6(c), which has a full width at half maximum (FWHM) of 4.62 ns. The inset of Fig. 6(c) shows the autocorrelation trace with a span of 150 ps. There is a narrow coherent spike on the top of a wide pedestal, which is consistent with the typical characteristic of the noise-like pulse (NLP) [48,49]. Figure 6(d) gives the RF spectrum measured within a 2.5 MHz range with a resolution of 30 Hz. The SNR of the RF spectrum is more than 55 dB as the fundamental frequency peak is located at 3.592 MHz, which matches well with the cavity length of 28.4 m. It is worth noting that there are two symmetrical RF spectral sidelobes around the fundamental cavity repetition frequency, which results from random peak modulation of the mode-locked pulses [48,49]. Here, we only get nanosecond pulse duration in the mode-locking regime, which is mainly limited by the parameters of the laser cavity. To verify the operation of the high-order mode inside the cavity, the mode field distribution of the laser output is monitored by a CCD camera. The donut-shaped mode patterns can be obtained by adjusting PC2 to eliminate the degeneracy of the LP11 mode. The TE01 and TM01 modes could be discriminated after passing through a linear polarizer at different orientations, as shown in Fig. 7(a)–7(j). Similarly, the purity of TM01 mode and TE01 mode are estimated to be 97.6% and 96.2% by adopting a fiber bending method, respectively. The purity of CVB in the mode-locked state is slightly higher than that in Q-switched mode-locked operation, which is mainly attributed to different operation wavelengths corresponding to the different mode conversion efficiency of the LPG.
Fig. 6. Output results of the mode-locked pulsed fiber laser at the pump power of 380 mW. (a) The spectrum of laser output (b) Oscilloscope traces of output mode-locked pulse train (c) The single-pulse profile. Inset: autocorrelation trace with a span of 150 ps (d) RF spectrum at a fundamental frequency of 3.592 MHz. Inset: RF spectrum in a span of 200 MHz.
Fig. 7. (a) Intensity profile of TM01 mode and (b)-(e) corresponding intensity distribution of TM01 mode after a linear polarizer. (f) Intensity profile of TE01 mode and (g)-(j) corresponding intensity distribution of TE01 mode after a linear polarizer. The white arrows represent the axis orientations of a linear polarizer.
Finally, to intuitively understand the behavior of the proposed fiber laser concerning pump power, the evolution of the operation state with the pump power increasing from 0 to the maximum available pump power of 724 mW is depicted, as shown in Fig. 8. The output power increases steadily and linearly with the pump power, which gives a slope efficiency of 20.2%. The operation regimes of the laser comprise three lasing states, including CW, QML, and ML, corresponding to the pump power ranges of 30-118 mW, 118-316 mW, and 316-724 mW, respectively. This result indicates that the operation states of the proposed CVB fiber laser can be flexibly switched just by controlling the pump power. The maximum output power of 141 mW is obtained at the pump power of 724 mW, where the laser operates in a stable mode-locked regime.
4. Conclusion
In summary, we propose and experimentally demonstrate a pulsed CVB linear cavity fiber laser with switchable operation states based on GIMF-SA. A broadband long-period fiber grating inserted into the half-SMF and half-FMF laser cavities is used as a mode converter to realize CVB output, and the output mode can be switchable from TM01 mode to TE01 mode by properly adjusting PC2. The stable pulse operation can be obtained by employing an SMF-GIMF-SMF structure served as SA based on the nonlinear multimode interference. The operation state of the proposed fiber laser can be flexibly controlled among continuous-wave, Q-switched mode-locked, and mode-locked states by changing the pump power. The QML CVB pulse envelope with the repetition rate changing from 57.4 kHz to 102.7 kHz, the corresponding pulse duration reducing from 4.8 µs to 3.5 µs are realized. Mode-locked CVB pulse with the repetition rate of 3.592 MHz and pulse duration of 4.62 ns is obtained when the pump power is 380 mW. Besides, the maximum single-pulse envelope energy can reach 510 nJ, and 142 mW pulsed CVBs with a slope efficiency of 20.2% can be achieved. This compact and high-efficiency pulsed CVB fiber laser with controllable temporal-spatial properties can find potential applications in laser processing, particle trapping, time/mode division multiplexing system. Moreover, our work may provide an effective method to achieve high power and high energy all-fiber pulsed CVB laser.
Funding
National Key Research and Development Program of China (2021YFF0307804); Open Project of Advanced Laser Tenchnology Laboratory of Anhui Province (AHL2021ZR02).
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.
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