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Abstract
The pulsed 1.7 µm vortex beams (VBs) has significant research prospects in the fields of imaging and material processing. We experimentally demonstrate the generation of sub-200 fs pulsed VBs at 1.7 µm based on a home-made mode-selective coupler (MSC). Through dispersion management technology in a thulium-doped fiber laser, the stable linearly polarized VBs pulse directly emitting from the cavity is measured to be 186 fs with central wavelength of 1721.2 nm. By controlling the linear superposition of LP11 modes, cylindrical vector beams (CVBs) can also be obtained. In addition, a variety of bound states pulsed VBs at 1.7 µm can also be observed. Our finding provides an effective way to generate ultrashort pulsed VBs and CVBs at 1.7 µm waveband.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent years, the 1.7 µm laser has received extensive attention due to its unique spectral characteristics. Compared with lasers in other waveband, the laser operating at the 1.7 µm waveband have important application in biological imaging due to their lower energy loss in biological tissues [1–6]. For the photoacoustic imaging and material processing, they also exhibit great potential arising from the strong absorption of the covalent bonds such as C-H, O-H and C-O at the 1.7 µm waveband [7–9]. In addition, due to the unique spiral phase characteristics, vortex beams (VBs) have drowned widespread attention in the fields of imaging and material processing [10–14]. Specially, the pulsed VBs further increase the peak power of the laser and have enormous application potential in many cutting-edge fields [15–17]. Therefore, ultra-fast pulsed VBs at 1.7 µm may greatly promote the special application of lasers at 1.7 µm in imaging and material processing.
Naturally, the pulse duration becomes the key parameter of pulsed lasers, especially the femtosecond pulse laser for application in the fields of ultrafast imaging and fine processing [18,19]. Currently, the dispersion management technique has been used to reduce the pulse duration to 1.2 ps, after compressed outside the cavity with an external 70 m single-mode fiber [20]. By taking full advantage of external grating pairs outside the cavity, the pulse was compressed to 348 fs [21]. Recently, it has been compressed to 174 fs using a piece of single-mode fiber outside the cavity in a W-type thulium-doped fiber laser [22]. However, they all needed external excessively long single-mode fibers or non-fiber devices outside the laser cavity for pulse compression, which enlarges the system complexity and damages the integration. And the pulses directly emitting from the cavity at 1.7 µm waveband are almost kept at picosecond level [23]. Therefore, a simple and effective way to obtain femtosecond pulses directly emitting from the cavity is still needed at the 1.7 µm waveband.
Considering the requirement of integration, an all-fiber based method of VBs generation is also necessary. Compared with the offset splicing technology, acoustic induction fiber grating, long-period fiber grating and other methods [24–27], the mode-selective coupler (MSC) is known as lower loss, lower cost and wider operating bandwidth, which has been used as a high-efficient device for VBs in all fiber system [28,29]. Up to now, the generation of VBs based on MSC has been successfully demonstrated in many mode-locked fiber lasers at the waveband of 1 and 1.5 µm [29,30]. In particular, in our previous work, the application of MSC in some special wavelengths like 1.65 µm has been successfully realized to achieve pulsed VBs in a mode-locking Raman fiber laser [31,32]. However, the generation of VBs at 1.7 µm has never been reported, let alone an ultra-fast pulsed VB.
Here, we propose a scheme to generate sub-200 fs pulsed VBs at 1.7 µm. A piece of thulium-doped fiber and a filter are incorporated into the ring cavity for the generation of 1.7 µm laser. The intracavity dispersion is controlled within the near-zero dispersion regime by adjusting the length of ultra-high numerical aperture fiber (normal dispersion). The linearly polarized pulsed VBs with a pulse width of 186 fs is achieved by using nonlinear polarization rotation (NPR) mechanism and home-made MSC, which is the shortest pulse directly emitting from the cavity at 1.7 µm to date. Through finely adjusting the PCs in the cavity, the cylindrical vector beams (CVBs) can also be obtained in the experiment. In addition, different multi-solitons bound state at 1.7 µm are also investigated, including adjustable bound spacing two-soliton bound state, and three-soliton to five-soliton bound state. The proposed thulium-doped fiber laser has potential applications in material processing and optical imaging.
2. Experimental setup
2.1 Fabrication of MSC
The MSC used in our experiment is fabricated by the fused biconical taper method with a single-mode fiber (SMF) and four-mode fiber (FMF), as shown in Fig. 1(a). Based on the coupled-mode theory, when the propagation constant of the LP01 mode in SMF is equal to the propagation constant of the LP11 mode in FMF (the phase matching condition), the mode conversion from the LP01 mode to LP11 mode can be achieved almost completely [33,34]. The propagation constant β is proportional to the mode effective refractive index neff, which has been calculated for LP01 and LP11 at 1720nm with different fiber core radiuses by the finite element method [35], as shown in Fig. 1(b). When the mode effective index is less than 1.433 and the fiber core radius of SMF and FMF is less than 3.1 µm and 5.3 µm respectively, the slope of the mode effective refractive index curve is approximately equal, which indicates that the optimal fiber core radius ratio is 3.1/5.3 = 0.585, achieving the phase matching condition. Then we connect the FMF with the SMF carefully and taper them together. After obtaining the optimal fiber core radius ratio, we stop tapering and then package the MSC. The output coupling ratio of the home-made MSC is measured about 40% with total insertion loss of 0.65 dB at 1720nm. The intensity distribution from the FMF end is detected by a CCD (Spiricon, SP90404, USA).
Fig. 1. (a)The schematic of the MSC; (b)The mode effective index versus different fiber core radius for the LP01 in the SMF and LP11 in the FMF at the wavelength of 1720nm.
2.2 Setup of thulium-doped fiber laser
Figure 2 schematically shows our 1.7 µm mode-locking thulium-doped fiber laser. A piece of thulium-doped fiber (SM-TSF-9/125, Nufern) is used as the gain medium with length of 1.8 m, which is backward pumped by a 1570 nm commercial single-mode laser with maximum output power of 2 W. Although thulium-doped fiber exhibits a broad emission waveband ranging from 1.65 to 2.1 µm [36], the 1.7 µm waveband is at the edge of the emission band. Therefore, for 1.7 µm, a wavelength selecting device must be introduced to suppress amplified spontaneous emission at longer wavelength [20,37,38]. Then, a filter with a central wavelength of 1716nm is introduced with a bandwidth of 26 nm, which is the key device for generating 1.7 µm lasing. A polarization-dependent isolator (PDI) and two polarization controllers (PCs) act as an artificial saturable absorber to realize mode-locking operation. To compensate the dispersion of cavity, a segment of ultra-high numerical aperture fiber (UHNA4, Coherent) with length of 1.9 m is incorporated, which have a dispersion parameter of 0.0813 ps2/m at 1720nm. The total cavity length is about 5.5 m, the total net cavity dispersion at 1720nm is estimated to be 0.0014 ps2, indicating that the laser operates in the near-zero dispersion regime. The 40% port of the home-made MSC is used as the output terminal, which is measured by an optical spectrum analyzer (Yokogawa, AQ6375B), an oscilloscope (Tektronix, MDO4104C) with a bandwidth of 1 GHz, a radio frequency (RF) spectrum analyzer (Keysight, N9010B), a 12.5 GHz photoelectric detector (E-O Tech. Inc., ET-5000F) and an autocorrelator (APE, PulseCheck 150 USB).
Fig. 2. The schematic diagram of 1.7 µm mode-locked fiber laser. WDM: Wavelength division multiplexer; PC: Polarization controller; PDI: Polarization dependent isolator; TDF: Thulium-doped fiber; BPF: Band-pass filter.
3. Results and discussion
When the pump power is increased to 1.36 W, stable mode-locking pulse with LP11 mode can be obtained by properly adjusting PCs. Figure 3 summarizes the mode-locking performance of single-soliton operation with the pump power of 1.6 W. The mode-locking optical spectrum centered at 1721.2 nm is shown in Fig. 3(a) with 0.3 m pigtail (FMF). It shows a broadband spectrum with 3 dB bandwidth of 21.1 nm. Compared with the smooth spectrum of general soliton [39], it exhibits some fringes riding, which are caused by the interference between the degenerated vector modes of LP11 mode [40]. When the length of the pigtail increases (1.5 m), the spectral fringes are more obvious, as shown in the inset of Fig. 3(a). The mode-locking pulse train with a time span of 210 ns is presented in Fig. 3(b). The pulse interval is 28.93 ns, satisfying the fundamental repetition rate of 34.57 MHz, which corresponds to the cavity length of 5.5 m. The average output power is measured as 16.65 mW, indicating that the pulse energy is 0.48 nJ. The inset of Fig. 3(b) shows the pulse train within 6 µs scanning range, and the consistency of pulse intensity indicates the high stability of our fiber laser. Figure 3(c) shows the corresponding radio frequency (RF) spectrum at the fundamental repetition frequency with a resolution bandwidth of 1 Hz and scanning range of 30 MHz. It can be seen that the signal-to-noise (SNR) ratio is about 65.3 dB, which indicates the highly stable mode-locking performance. The corresponding autocorrelation trace is presented in Fig. 3(d). The duration of the output pulse is measured as 186 fs with the assumption of Sech2 pulse shape, which is the shortest pulse duration obtained directly from the cavity at 1.7 µm to the best of our knowledge. Therefore, the time-bandwidth product (TBP) is calculated as 0.397, which is slightly larger than the Fourier transform limit of 0.315 of Sech2 pulse.
Fig. 3. (a) Mode-locking optical spectrum. Insert: optical spectrum of FMF at 1.5 m; (b) Pulse train. Insert: pulse train in the range of 6 µs; (c) RF spectrum at the fundamental frequency; (d)Autocorrelation trace of the pulse.
LP01 and LP11 are supported for transmission in FMF, where LP01 consists of two degenerated vector modes ($\textrm{HE}_{\textrm{11}}^{\textrm{x/y}}$) and LP11 consists of four vector modes ($\textrm{HE}_{\textrm{21}}^{\textrm{even/odd}}$, TE01, TM01). The LP11 mode generated in FMF is linearly polarized mode, which supports four scalar polarization modes, including $\textrm{LP}_{\textrm{11a}}^\textrm{x}$, $\textrm{LP}_{\textrm{11b}}^\textrm{x}$, $\textrm{LP}_{\textrm{11a}}^\textrm{y}$, and $\textrm{LP}_{\textrm{11b}}^\textrm{y}$ modes, where x/y represents polarization direction and a/b represents intensity direction [41]. Due to the wide spectrum of our femtosecond pulses, $\textrm{HE}_{\textrm{11}}^\textrm{x}{\; }({\textrm{HE}_{\textrm{11}}^\textrm{y}} )$ can only be converted into TM01 (TE01) and $\textrm{HE}_{\textrm{21}}^{\textrm{even}}{\; }({\textrm{HE}_{\textrm{21}}^{\textrm{odd}}} )$ simultaneously, so circular polarization VBs cannot be obtained like continuous laser [42,43]. In our experiment, linearly polarized VBs can be obtained by linear superposition of two related LP11 modes with a ±π/2 phase difference [32,43]. Here, Eq. (1) and Eq. (2) shows how VBs is achieved:
Fig. 4. Near-field intensity distributions of VBs. (a) VBs with topological charge of -1; (b) VBs with topological charge of +1; (c) Phase image of cylindrical lens with focal length of 300 mm; (d) Examination of polarization state of the VBs.
To demonstrate the stability of the mode locked state and VBs, we recorded the optical spectrum analyzer and CCD every 15 minutes, shown in Fig. 5. The optical spectra and intensity distributions all keep almost unchanged.
Moreover, it worth noting that, CVBs can also be obtained by linear superposition of two related LP11 modes in our laser:
Fig. 6. Near-field intensity distributions of CVBs. (a) Radially polarized beams; (b) Azimuthally polarized beams; White arrow: Polarization axis of Glan polarization prism.
In addition to single pulsed VBs, bound state pulsed VBs at 1.7 um can also be obtained by finely adjusting the PCs in the cavity. The optical spectrum exhibits periodically modulating fringes, as shown in Fig. 7(a), which is the typical periodically of bound state soliton [46]. Figure 7(b) shows the optical spectrum in the range of 20 nm, and the modulation period is 1.21 nm. The autocorrelation trace shown in Fig. 7(c) further confirms the bound state. The pulse interval of two solitons bound state is 8.04 ps, which corresponds correctly to the modulation period. In addition, the autocorrelation trace shows a typical peak-to-peak ratio of 1:2:1, indicating that the bound state pulsed VBs is composed by two pulses with the same intensity [47]. In our experiment, by slightly tuning PC, two solitons bound state pulsed VBs with other pulse interval can be generated, as shown in Figs. 7(d)-(f). The modulation period of 0.46 nm corresponds to the pulse interval of 21.26 ps.
Fig. 7. Characterization of two-solitons bound state. (a) Optical spectrum. Inset: VBs; (b) Optical spectrum in the range of 20 nm; (c) Autocorrelation trace. (d) Optical spectrum. Inset: VBs; (e) Optical spectrum in the range of 20 nm; (f) Autocorrelation trace.
Apart from the two-solitons bound state pulsed VBs, the multi-solitons bound state can also be observed. Figure 8 characterizes the optical spectrum and autocorrelation trace of three-solitons to five-solitons bound state. Compared with the two-solitons bound state, the optical spectrum of the multi-solitons bound state is more complex with multiple modulation peaks. For each additional bound solitons, the optical spectrum will have an additional set of modulation peaks, corresponding to an additional pair of peaks in the autocorrelation trace [48]. The modulation period of each group in the optical spectrum of three-solitons bound state is 0.94 nm as presented in Fig. 8(b), corresponding to the time delay of 10.41 ps in the autocorrelation trace. The peak-to-peak ratio shown in Fig. 8(c) is 1:2:3:2:1, which indicates the bound state is composed by three almost identical solitons. Furthermore, the modulation periods of the four-solitons bound state and the five-solitons bound state are 0.94 nm and 0.96 nm respectively, which corresponds well to the time delay in the autocorrelation trace. But the peak-to-peak ratio of the four-solitons bound state and the five-solitons bound state do not match well with 1:2:3:4:3:2:1 and 1:2:3:4:5:4:3:2:1 respectively, as shown in Fig. 8(f) and Fig. 8(i), indicating that the strength of the multiple solitons is not exactly the same [49].
Fig. 8. Characterization of multi-solitons bound state. Three-solitons bound state: (a) Optical spectrum. Inset: VBs; (b) Optical spectrum in the range of 20 nm; (c) Autocorrelation trace. Four-solitons bound state: (d) Optical spectrum. Inset: VBs; (e) Optical spectrum in the range of 20 nm; (f) Autocorrelation trace. Five-solitons bound state: (g) Optical spectrum. Inset: VBs; (h) Optical spectrum in the range of 20 nm; (i) Autocorrelation trace.
4. Conclusion
In conclusion, we have experimentally demonstrated the generation of sub-200 fs pulsed VBs at 1.7 µm based on a home-made MSC. The thulium-doped fiber laser operates in the near-zero dispersion regime by utilizing normal dispersion fiber (UHNA4). We have realized the pulsed VBs with a central wavelength of 1721.2 nm by controlling the superposition of LP11 modes with a certain phase difference and verified its linear polarization characteristics experimentally. The pulse duration emitting from the cavity is measured as 186 fs, which is the shortest pulse duration obtained directly from the cavity to date. CVBs can also be obtained in the same way, including radially polarized pulsed CVB and azimuthally polarized pulsed CVB. The mode purity of VBs and CVBs obtained in the experiment are both higher than 90%. Furthermore, various bound states of VBs at 1.7 µm can be observed in our experiment by finely adjusting the PCs in the cavity. Finally, we concluded that our experimental results could provide the way for investigation of ultra-fast pulsed VBs at 1.7 µm, which is useful for the application of imaging and material processing.
Funding
National Natural Science Foundation of China (11604095, 62271332, 62275162); Basic and Applied Basic Research Foundation of Guangdong Province (2023A1515030152); Shenzhen Government’s Plan of Science and Technology (JCYJ20190808150205481).
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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