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Abstract
We proposed and demonstrated a bidirectional mode-locked fiber laser to generate cylindrical vector beam (CVB) asynchronous pulses based on a graded index multimode fiber. A homemade fused taper two-mode fiber optical coupler (TMF-OC) is employed as a mode converter. The central wavelength for clockwise (CW) pulses can be tuned from 1030.32 nm to 1041.04 nm due to the filtering effect based on multimode interference, that of counterclockwise (CCW) pulses is from 1030.81 nm to 1039.28 nm. When the central wavelengths are 1033.22 nm and 1032.71 nm for CW direction and CCW direction respectively, CVB asynchronous noise-like pulses with a repetition rate difference of ∼436.9 Hz can be obtained. The purity of CVB in CW direction and CCW direction is 95.7% and 93.4% respectively. This bidirectional mode-locked fiber laser with CVB output can be better applied to laser gyroscopes, asynchronous sampling, and dual-comb technique, and impel the interdisciplinary studies in the future.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Asynchronous pulses have good applications in rotation sensing [1], asynchronous sampling [2], and dual-comb technique [3]. And there are usually three methods to generate asynchronous pulses, including wavelength multiplexing [4], polarization multiplexing [5], and bidirectional mode-locking. As for the bidirectional mode-locking, the lasers in different directions are mutually coherent. It has attracted more attention due to system compactness and environmental robustness. Bidirectional mode-locked fiber lasers based on different saturable absorbers (SAs) have been proposed such as carbon nanotubes [6–8], transmitted semiconductor SA [9], and thulium-doped fiber [10]. Unfortunately, SAs usually have low damage threshold. To avoid this problem, Li et al. designed a bidirectional mode-locked laser based on the nonlinear polarization rotation (NPR) effect [11]. It is worth noting that these bidirectional mode-locked lasers can only output fundamental mode.
On the other hand, as a kind of high-order mode, cylindrical vector beams (CVBs) have many unique characteristics, and thus have been used in material processing [12], optical tweezers [13,14], fiber communication [15], sensor [16], and so on. CVB mode-locked ring fiber lasers based on lateral offset splicing [17], long-period fiber gratings [18], and mode selective couplers [19] have been demonstrated. By all kinds of methods, the purity of CVBs and the slope efficiency of mode-locked CVB fiber lasers have been improved continuously. Besides, different kinds of CVB pulses have been reported such as dissipative soliton resonance and dissipative soliton [20,21]. However, the isolators in these CVB fiber lasers result in less compact design and only unidirectional pulse trains can be obtained [22].
In this work, a bidirectional mode-locked CVB laser with an all-fiber structure was proposed. The mode-locking mechanism is based on the nonlinear multimode interference effect. CVB noise-like pulse trains with a period of 138.5 ns can be obtained. The fundamental repetition rate difference of the CVB asynchronous pulse trains is measured to be ∼436.9 Hz. Due to the filtering effect of the fused taper TMF-OC and single mode fiber-graded index multimode fiber-single mode fiber (SMF-GIMF-SMF) structure, its central wavelength can be tuned in a span of more than 8 nm.
2. Experiment principle and setup
Figure 1 shows the schematic of our proposed bidirectional mode-locked laser with CVBs generation. A 974 nm laser diode (LD) pumps a 42 cm single-mode ytterbium-doped fiber (YDF, Nufern, Yb1200) via a 980/1064 nm wavelength-division multiplexer (WDM). A homemade fused taper TMF-OC fabricated using TMF (Corning, SMF 28e) is employed to convert LP01 mode to LP11 mode. An SMF-GIMF-SMF structure shown in Fig. 2(a) consists of two sections of SMF (Corning, HI-1060) and a 23 cm GIMF (Corning, 50/125 µm), which is used to guarantee mode-locked operation based on the mode-locking mechanism of nonlinear multimode interference effect [23]. The loss of the SMF-GIMF-SMF structure is measured to be ∼3.89 dB. The nonlinear optical properties of the SMF-GIMF-SMF device are measured by a 1064 nm mode-locked fiber laser with a repetition rate of 102.32 MHz and pulse duration of ∼20 ps, which is shown in Fig. 2(b). The measured datas are fitted with the transmission function mentioned in Ref. [24], and the modulation depth is measured to be 20.29%. A polarization controller (PC1) is employed to adjust the polarization state of the light inside the laser cavity. PC2 and PC3 are used to eliminate the degeneracy of LP11 mode from the two directions. A linear polarizer (LP) is placed after the fiber collimator (COL) to confirm the polarization distribution characteristics of the output beam. The output spectra are measured by an optical spectrum analyzer (OSA, YOKOGAWA, AQ6373B). The time-domain waveforms are recorded by a 4 GHz oscilloscope (LeCroy, Waverunner 640Zi) together with a 3 GHz photoelectric detector. The pulse duration is measured by a commercial autocorrelator (A.P.E, pulseCheck 600). A radio-frequency (RF) spectrum analyzer and a charge-coupled device (CCD, @1.0 µm) are employed to record RF spectra and the beam profiles. Blue lines and green lines in Fig. 1 represent SMF and TMF respectively.
Fig. 2. (a) Schematic diagram of the SMF-GIMF-SMF structure; (b) nonlinear saturable absorption curve of the SMF-GIMF-SMF structure.
The fused taper TMF-OC can excite and split higher-order mode, which is fabricated by stretching and fusing two identical TMFs together to form a common taper waist [25]. The principle is as follows: On the one hand, LP11 mode will be excited when LP01 mode passes through tapered TMF [26]. On the other hand, the effective indices of the LP01 and LP11 modes will reduce while the fiber diameter decreases. When the effective indices of the LP01 and LP11 modes are less than the refractive index of the fiber cladding, they will break away from the bond of the core because of not satisfying the total reflection principle of geometrical optics. Noticeably, the mode effective index of the LP11 mode decreases faster than LP01 mode with the decrease of the fiber diameter. Therefore, when the tapered fiber diameter is suitable, LP11 mode can diffuse into the cladding and be coupled to the second fiber while LP01 mode still satisfies the total reflection principle of geometrical optics. Thus we can obtain high-purity LP11 mode in the second fiber while hybrid spatial modes (LP01 and LP11 modes) exist in the input fiber. Figure 3(a) shows the schematic of the fused taper TMF-OC. When LP01 mode is launched into input port 4, LP11 mode can be obtained at output port 1 and hybrid spatial modes will be obtained at port 3. Similarly, when port 3 acts as input port, we can obtain LP11 mode at output port 2. Figure 3(b) and Fig. 3(c) illustrate mode field distributions at output port 1 and output port 2 respectively at different wavelengths, which shows the typical two-lobed shape of LP11 mode.
Fig. 3. (a) Schematic diagram of the fused taper TMF-OC; CCD images of the output LP11 mode at (b) port 1 and (c) port 2 at different wavelengths.
3. Result and discussion
Under the pump power of 570 mW, we adjust PC1 carefully to achieve bidirectional mode-locking operation of the laser. The output spectra of CW and CCW are shown in Fig. 4(a) and Fig. 4(b) respectively, which indicate the central wavelengths are 1033.22 nm and 1032.71 nm respectively. The spectrum shapes of the two directions are different, which may be due to the asymmetry of the cavity and the different strengths of the nonlinear effect. The 3 dB linewidths are 8.08 nm and 6.24 nm respectively. The pulse trains of CW and CCW illustrated in Fig. 4(c) and Fig. 4(d) indicate the pulse periods are 138.5 ns, which matches with the cavity length of 27.7 m. Figure 5(a) and Fig. 5(b) show the RF spectra of the CW and CCW pulses respectively with a 1 MHz span, which indicate signal-to-noise ratios (SNRs) are > 62 dB. The RF spectra show the fundamental frequency rates are ∼7.22 MHz. The insets of Fig. 5(a) and Fig. 5(b) exhibit wider RF spectra with a 500 MHz span. Autocorrelation traces with 51 ps time window illustrated in Fig. 5(c) and Fig. 5(d) show there is a narrow peak located on the top of a wide pedestal, which is the typical characteristic of noise-like pulses [27].
Fig. 4. Output spectra of (a) CW pulses and (b) CCW pulses; oscilloscope traces of (c) CW pulses and (d) CCW pulses.
Fig. 5. RF spectra of (a) CW pulses and (b) CCW pulses; autocorrelation traces of (c) CW pulses and (d) CCW pulses.
To test the stability of the laser, we record the output spectra of the two directions every 15 minutes in 1.5 hours with the pump power of 570 mW, which are shown in Fig. 6(a) and Fig. 6(b). The spectral profile does not change obviously, which indicates the bidirectional mode-locking operating states are stable. Actually, the bidirectional mode-locking operation can last for at least six hours. The output spectra under different pump power are illustrated in Fig. 6(c) and Fig. 6(d), which indicates the spectral widths are broadened with the increase of pump power. This is due to the enhancement of the nonlinear effect with higher pump power. Furthermore, the central wavelength has a blue shift trend when the pump power increases. This is because higher pump power attenuates the reabsorption effect of the YDF, which makes shorter wavelength have larger gains compared with lower pump power [28]. As depicted in Fig. 7, the output power in CW direction and CCW direction will increase with the pump power. However, the output powers of the two directions are unequal because CW and CCW gains are usually different in practice. Limited to the pump power, the maximum output powers in CW direction and CCW direction are 1.520 mW and 0.308 mW respectively, corresponding to the single pulse energy of 0.21 nJ and 0.04 nJ.
Fig. 6. Measured output spectra of (a) CW pulses and (b) CCW pulses every 15 minutes in 1.5 hours; measured output spectra of (c) CW pulses and (d) CCW pulses under different pump power.
Fig. 7. Output power of CW pulses (black square) and CCW pulses (red circle) as functions of the pump power.
To measure the repetition rate difference between CW pulses and CCW pulses, we use a 1 ${\times} $ 2 70:30 diaphragm TMF-OC to achieve beam combination of the two directions as shown in Fig. 8. The 30% and 70% ports of the diaphragm TMF-OC are connected to output port 1 and output port 2 of the laser respectively by fiber connectors. The oscilloscope traces of the combined pulses at different times are shown in Fig. 9(a)–9(c), where the pulses with higher and lower amplitude represent CW and CCW pules respectively. The interval of the two sets of pulse trains varies with time, which indicate CW pulse trains and CCW pulse trains are asynchronous. Figure 9(d) shows the interferogram of CW pulses and CCW pulses with the range of 10 ms, which indicates the period of the beat note signal is ∼2.289 ms corresponding to the fundamental repetition rate difference of ∼436.9 Hz [29]. The inset of Fig. 9 shows the RF spectrum of the combined pulses. And there are two peaks with an interval of 437.5 Hz, which is consistent with the repetition rate difference calculated by the period of the beat note signal. The small discrepancy may originate from the insufficient measuring accuracy of the RF spectrum analyzer and photoelectric detector.
Fig. 9. (a)-(c) Oscilloscope traces of the combined pulses at different times; (d) oscilloscope traces of the combined pulses with the range of 10 ms.
When the pump power is 570 mW, bidirectional mode-locking operation can be obtained with different central wavelengths by adjusting PC1. The spectra at different central wavelengths are illustrated in Fig. 10, where the blue lines and red lines represent the spectra of CW pulses and CCW pulses respectively. As we can see, the central wavelength of CW can be tuned from 1030.32 nm to 1041.04 nm, and that of CCW is from 1030.81 nm to 1039.28 nm. This is due to the filtering effect based on multimode interference brought by the SMF-GIMF-SMF structure [30] and the fused taper TMF-OC [26]. As the single-mode light is launched into GIMF or the taperd TMF, high-order modes will be exited. Only the light from the GIMF or taperd TMF with the wavelength which meets reimaging distance can be coupled to SMF again with low loss [31].
When the laser operates at bidirectional mode-locking operating state, adjusting PC2 and PC3 carefully to remove the degeneracy of the LP11 mode, we can obtain radially and azimuthally polarized beams from port 1 and port 2 of the laser. Figure 11(a) and Fig. 11(f) show the intensity distributions of the radially and azimuthally polarized beams respectively recorded by CCD camera. To test the polarization characteristics of them, an LP is inserted between the COL and CCD and then the intensity distributions are observed. As depicted in Fig. 11(b) to 11(e) and Fig. 11(g) to 11(j), the beam profiles show a two-lobed shape with different orientations of LP, which is the typical characteristics of CV modes. The measured mode purity of CVB using bending-loss method [32] in CW direction is 95.7%, and that of CCW is 93.4%. The purity of the two directions has a difference, which may be due to the asymmetry of the fused taper TMF-OC.
Fig. 11. The intensity distributions of (a) radially polarized beam and (f) azimuthally polarized beam; intensity distributions of (b)-(e) radially polarized beam and (h)-(j) azimuthally polarized beam after an LP; white arrows represent the axis of the LP.
4. Conclusion
In conclusion, an all-fiber bidirectional mode-locked CVB laser was proposed and demonstrated. CVB asynchronous noise-like pulses with a repetition rate difference of ∼436.9 Hz can be obtained. As far as we know, this is the first time to generate CVB asynchronous pulse and CVB noise-like pulse in an all-fiber structure. The purity of CVBs is over 93%. This CVB laser with simple structure, tunable wavelength, and asynchronous noise-like pulses has good application prospects in many areas such as asynchronous sampling, laser gyroscopes, material processing, and fiber communication. It is also helpful to impel the interdisciplinary studies.
Funding
Open Project of Advanced Laser Tenchnology Laboratory of Anhui Province (AHL2021ZR02).
Acknowledgements
Y. Lu thanks the Open Project of Advanced Laser Tenchnology Laboratory of Anhui Province for helping to identify collaborators for this work.
Disclosures
The authors declare no conflicts of interest.
Data availability
The 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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