Open Access
Add to BibSonomyAbstract
We report on an interesting phenomenon of the combination of Q-switched mode locked pulses (QSMLP) and rectangular noise-like pulses (RNLP) as a unit in a Tm-doped ring fiber laser which contains a Fabry-Perot (F-P) subcavity based on the nonlinear polarization evolution (NPE) technique. The RNLP and QSMLP are independently generated in the ring cavity and F-P subcavity, respectively. A notable characteristic is that the physical parameters of RNLP, e.g. repetition rate and pulse duration, are controlled by QSMLP. Thus, they form as a composite bunching, which is termed as “Q-switched mode locking controlled rectangular noise-like soliton bunching (QRNSB)”. Further investigation shows that the existence of QRNSB only occurs in high pumping conditions, while both fundamental mode-locking pulses and the coexistence of QSMLP and solitons are achieved in low pumping ones. Our work can enrich the understanding of the nonlinear dynamics in fiber lasers.
© 2016 Optical Society of America
1. Introduction
Fiber lasers are one of the most attractive optical sources for their wide applications in fields such as optics communications, material processing, medical apparatus and instruments [1–3]. Particularly, 2.0 μm Tm-doped fiber lasers have potential usage in special fields, e.g. laser radar and biomedical imaging [4–6]. The nonlinear effects caused by high pump powers can result in soliton bunching and multipulsing in the cavity due to soliton energy quantization effect. There are many interesting phenomena which have been observed, including Q-switched mode locking bunching [7,8], vector soliton bunching [9,10], noise-like pulses [11], soliton molecules [12,13], soliton rains [14], dissipative soliton resonance (DSR) [15], soliton explosion [16], and rogue waves [17]. The formation of bound solitons, such as soliton molecule, owes to the interaction among the same type of soliton pulses through direct, or continuous wave (CW) mediated, or dispersive waves mediated interactions [18,19]. Meanwhile, the unbound solitons which are composed of different types of soliton pulses usually exhibit simply superposition of different types of solitons without strong coherent interaction among them. Especially, noise-like pulses (NLP) with smooth spectral profiles can develop into rectangular bunching in a negative dispersion region and broaden with pump powers, even lasting more than a cavity round trip time in time domain [20–22]. The interaction among the pulses in the NLP is incoherent since the spectral profiles do not show the characteristic fringes.
Recently, the research interests have extended to the generation of high repetition rate pulses or multi-wavelength outputs through incorporating a subcavity into a main cavity. To the best of our knowledge, however, there are no reports about different types of solitons independently generated from subcavities and main cavities, respectively. Moreover, the interaction among different types of solitons originating from a laser with a hybrid cavity configuration has been hardly reported.
In this work, an extraordinary complex pulse structure is observed in a ring Tm-doped laser with a subcavity. Q-Switched mode locked pulses (QSMLP) and rectangular noise-like pulses (RNLP) are independently generated in the F-P and ring cavities, respectively. Different from the rectangular pulse that has been reported, the repetition rate and pulse duration of the RNLP are controlled by QSMLP. They appear as a whole unit for exhibiting an extraordinary composite bunching, which is termed as “Q-switched mode locking controlled Rectangular Noise-like Soliton Bunching (QRNSB)”. Our work will open up a new viewpoint of the nonlinear dynamics in a hybrid cavity configuration.
2. Experimental setup
The experimental setup of a Tm-doped ring fiber laser with a F-P subcavity is shown in Fig. 1. There are two polarization controllers (PC), a 1570/1950 wavelength division multiplexer (WDM), a piece of 15 cm long self-made Tm-doped germanate single mode fiber (TDF), a fiber coupler (90:10), and a polarization-dependent isolator (PD-ISO) in the ring cavity. The self-made high power pump system can provide a maximum power up to 3.3 W at 1570 nm. The core/cladding diameter and numerical aperture (NA) of TDF are 8.6/125 μm and 0.145, respectively. The thulium dosage concentration is 4.5 × 1020 cm−3, which means that TDF has a 0.63 dB/cm absorption at 1562 nm and a 2.3 dB/cm gain coefficients at 1950 nm [23–25]. The pigtails of optical devices are SM 1950 fibers with 36.29 ps/nm/km dispersion and 10 dB/km attenuation coefficients at 1950 nm. The length and net dispersion of the whole cavity are about 7.4 m and −0.495 ps2, respectively.
The self-made TDF is directly collimated to the commercial SM 1950 fibers with the plane faces, whose reflectivity can reach as high as 7% due to germanate glass having a relatively high refractive index of 1.75. Thus, a 15 cm-long F-P cavity is constructed via two plane faces of the TDF, schematically illustrated in the dashed line box of Fig. 1. The function of F-P subcavity will act as a potential filter, while the joint operation of a PD-ISO and two PCs will take a role of an artificial saturable absorber for mode locking. Thus, the fiber laser with a hybrid cavity configuration will display diverse temporal patterns of nonlinear dynamics.
An optical spectrum analyzer (Yokogawa AQ6375), a 1 GHz oscilloscope (Agilent DSO-X 3120A) with 12.5 GHz photoelectric detector (Newport 818-BB-51F), and a 3 GHz radio spectrum analyzer (Agilent N9320A) are employed to measure the spectral and temporal characteristics of the 10% laser output.
3. Experimental observation and discussions
3.1 The observation of QRNSB
The self-started mode-locking occurs at the pump power of 1 W in our experimental setup. The fundamental mode locking pulses operate at 28.3 MHz. The mode locking state is still sustained under the pump power as low as 400 mW due to pump hysteresis phenomenon. However, when the pump power increases to about 2.6 W, an interesting composite bunching, QRNSB, could be observed under appropriate polarization biases of PCs. Figures 2(a) and 2(b) are the spectral and temporal shapes of QRNSB, respectively. The spectrum of QRNSB shows a sharp peak of 1910 nm whose 3-dB bandwidth is 0.7 nm riding on a broad bell-shaped profile with 3-dB bandwidth of 45.71 nm. Irregular distribution of small dips across the spectral profile corresponds to featured water absorption [26]. It should be noted that the sharp peak is much stabilized without evident changes despite of how to adjust PCs. However, the spectral bandwidth of bell shape can broaden or narrow during squeezing the PCs.
The temporal shape of QRNSB shows a strong modulated bunching distributed on the tailing edge of a broad rectangular profile with 3 μs duration, which is approximate 85 round trip times. The zoom-in structure of the modulated bunching is shown in the right inset of Fig. 2(b). The repetition rate of pulses in the modulated bunching is 28.3 MHz, corresponding to the fundamental repetition rate of the main ring cavity. The left inset of Fig. 2(b) shows zoom-out of QRNSBs with the time span of 80 μs. There are four QRNSBs with the temporal interval of 20 μs. The repetition rate of QRNSB changes with pump powers. It decreases from 59.3 kHz to 24.1 kHz with pump powers from 2.6 W to 1.8 W. However, the repetition rate of the pulses in the modulated bunching [right inset of Fig. 2(b)] is still locked at the fundamental rate 28.3 MHz of the ring cavity despite of pump powers changing. These imply that the strong modulated bunching of QRNSB operates at the state of Q-switched mode-locking.
In general, rectangular pulses, such as DSR and RNLP, broaden with the increase of pump powers. However, our QRNSB becomes narrower with increasing pump powers, which is much different from the results of previous references [21,22]. Figure 3 shows different profiles with different pump powers. The duration of rectangular component of QRNSB shrinks from 4.09 μs to 3.35 μs in the range of pump powers from 1.8 W to 2.6 W. This notable characteristic will be explained in the following experiments.
Fig. 3 A single QRNSB profile with different pump powers. (a) 1.8 W. (b) 2.0 W. (c) 2.2 W. (d) 2.4 W. (e) 2.6W.
3.2 The structure of QRNSB
In order to further analyze the fine structure of QRNSB, a self-made Lyot birefringence fiber filter (BFF) [27] is built to analyze physical characteristics of QRNSB. Firstly, a stable QRNSB at the pumping power of 2.3 W is achieved. Its spectral and temporal profiles are shown in Figs. 4(a) and 4(b), respectively. Then a discrete sharp spectral peak of QRNSB at 1910 nm is obtained by filtering out the bell-shaped broad spectrum under an appropriate filtering function of BFF. Meanwhile, the corresponding temporal measurement is carried out. The experiment results in Figs. 4(c) and 4(d) demonstrate that the filtering out bell-shaped broad spectrum of 45.71 nm leads to that the rectangular temporal profile is remarkably suppressed. Since a rectangular temporal profile with a broad smooth spectrum is a characteristic of NLP, it can be deduced that the rectangular temporal profile corresponds to RNLP. The remainder spectral peak of 1910 nm after passing a filter corresponds to a macro modulated bunching temporal profile in the range of kHz repetition rate. The repetition rate of the whole bunching increases with pump powers. However, the modulated pulse repetition rate in the survival modulated bunching is still kept at 28.3 MHz. They are evident features of Q-switched mode-locking. It can be deduced that the temporal modulated bunching with a sharp spectral peak is linked with QSMLP. Thus, a QRSNB indeed is composed of the combination of a QSMLP and a RNLP. The aforementioned experiments in section 3.1 show that the repetition rate of QSMLP increases with pump powers. However, the temporal duration of the RNLP decreases with pump powers. It is evident that QSMLP and RNLP are not simply superposition for forming a QRSNB. The repetition rate of QSMLP increases with pump powers, which leads to both duration and interval of QSMLP decreasing. RNLP should be decreasing temporal duration with pump powers increasing in order to reach their temporal synchronization. Thus, RNLP component is controlled by QSMLP component in the QRSNB.
Fig. 4 The QRSNB before and after passing a filter. (a) spectrum before passing a filter. (b) corresponding temporal profiles of (a). (c) spectrum after passing a filter. (d) corresponding temporal profiles of (c).
4. Numerical simulation and discussions
4.1 The transmissivity function of F-P subcavity
To understand the generation of the QSMLP in a F-P subcavity, a simplified filter model is established. Since the refractive index of the TDF and the air gap between the TDF and air are 1.75 and 1, respectively, the relatively large refractive index difference at the two edges of the TDF makes it become a weak F-P filter with a low reflectance. The mode interval of the F-P filter is theoretically described as follows:
The mode interval of the F-P subcavity is about 7.2 pm in our experimental setup. In high pumping condition, the effective filter function of F-P subcavity will take effect, whose mathematical relation can be described as follows:where A, R, n and l demonstrate absorption loss, reflectance, refractive index and length of the F-P subcavity, respectively. λ is the oscillating wavelength. According to our experiment setup, the parameters are selected as following: R = 0.07, n = 1.7, l = 0.15 m, and λ = 1910 nm. Then the spectral transmission curve of the F-P filter is calculated in Fig. 5 based on Eq. (2). It is evident that the oscillating longitude modes with an interval of 7.2 pm construct a macro periodical modulated profile with an approximate bandwidth of 0.7 nm. Due to the minimum spectral resolution of 0.1 nm of our optical spectrum analyzer, we do not observe the modulation across the spectral profile. We can actually achieve a whole Q-switched spectrum of 0.7 nm bandwidth in the experiments, which coincides with the theoretical transmissivity function of the F-P subcavity. A conclusion can be drawn that the F-P subcavity leads to the generation of QSMLP component of QRSNB. It should be noted that the bandwidth of the F-P subcavity narrows with the increase of the cavity length through theoretically analyzing the Eq. (2). Thus, 3-dB bandwidth of QSMLP varies with the length of F-P subcavity.4.2 The transmissivity function of artificial saturable absorber
Reducing the pump power from 2.6 W to 2.2 W, the collapse process of QRSNB can be observed. A QRSNB state shown in Fig. 6(a) collapses into the coexistence state of QSMLP and soliton. It is evident that the bell-shaped spectral profile evolves into a conventional soliton spectrum with Kelly sidebands [28] except for the retained 1910 nm spectral peak of QSMLP. The temporal profile of a modulated bunching distributed in the tailing of a rectangular pulse disappears. When the pump power further drops down to 1.6 W, the QSMLP disappears, leaving a conventional soliton alone, as shown in Fig. 6(c). The insets of Fig. 6(c) exhibit that the radio spectrum and temporal train of a soliton. The SNR of the soliton arrives at 74 dB, exhibiting that the soliton in our hybrid cavity is much stable.
It should be noted that QSMLP neither move nor disappear during rotating or squeezing the PCs, suggesting that NPE-based transmissivity function has no effect on QSMLP. The spectral peak of QSMLP has been still locked at 1910 nm during the experiments. On the other hand, it can be inferred that the ring cavity takes an important role for shaping RNLP and solitons based on the physical phenomenon of the soliton suddenly switching at between 1933.62 nm and 1937.98 nm during adjusting PCs. As to NPE technique, the ring cavity is quite polarization sensitive. The transmissivity function T of the ring cavity without considering the F-P subcavity can be described as following [29]:
where Δφl ( = 2πLΔn/λ) and Δφnl ( = γPLcos2α1) illustrate that linear and nonlinear phases. α1 and α2 are the angles between polarization directions and the extraordinary axis of the fiber, respectively. Δn represents the birefringence of the fiber. L, P and γ are the cavity length, pulse peak power and nonlinear coefficient, respectively. Altering the PCs means that α1, α2, and Δn relatively change. As a result, T changes with them. Owing to the linear phase shift, the transmissivity function is wavelength-dependent. According to our experiment conditions, the parameters are selected as follows in the calculation: L = 7.4 m, γ = 3 (W·km)−1, Δn = 7.09 × 10−5, and P = 1000 W. Thus, the periodical maximum transmissivity curve from 1930 nm to 1940 nm is shown in Fig. 7. The NPE-based transmissivity function presents that the soliton will appear at the maximum transmissivity wavelengths, or that obtained soliton will suddenly switch between neighboring wavelengths with a maximum transmissivity. The neighboring spectral interval between maximum transmissivity wavelengths is 4.36 nm, which fully matches with the experimental phenomenon of the inset of Fig. 6(b). Furthermore, the aforementioned experiments show that the adjustment of PCs can affect the spectral bandwidth of RNLP. It can be concluded that the generation of both RNLP and solitons originates from the ring cavity.Fig. 7 The calculated spectral transmissivity with wavelengths from 1930 nm to 1940 nm (red curve: α1 = 0.223π, α2 = 0.75π; blue curve: α1 = 0.2π,α2 = 0.25π).
5. Conclusion
In summary, a Tm-doped ring fiber laser with a F-P subcavity is constructed. The ring cavity is 7.4 m and the F-P subcavity is 15 cm. A composite bunching, QRSNB, is observed in high pump power conditions. The filtering experiments illustrate that the QRSNB is composed of the combination of QSMLP and RNLP. The spectral peak of QSMLP is still locking at 1910 nm while the spectral of RNLP can stretch or shrink during altering the PCs. Both experimental and theoretical analyses show that the QSMLP and RNLP independently generate from the F-P subcavity and ring cavity, respectively. Moreover, RNLP is controlled by the QSMLP to reach temporal synchronization, i.e. repetition rate and pulse duration of RNLP are controlled by QSMLP. Our work enhances the understanding of the nonlinear dynamics of fiber lasers.
Funding
China National Funds for Distinguished Young Scientists (61325024); Fundamental Research Funds for Central Universities (2015ZP019); Scientific Research Project of Guangdong Province (2013A061401004, 20150903, 2015B090926010); Special Support Program for High-quality Professionals in Guangdong Province (2014TX01C087); National Natural Science Foundation of China (NSFC) (11204037).
References and Links
1. W. Chen, W. Lin, T. Qiao, and Z. Yang, “Additive mode-locked resembling pulses in a Tm-doped fiber laser with a hybrid cavity configuration,” Opt. Express 23(21), 28012–28021 (2015). [CrossRef] [PubMed]
2. A. G. Demir and B. Previtali, “Dross-free submerged laser cutting of AZ31 Mg alloy for biodegradable stents,” J. Laser Appl. 28(3), 032001 (2016). [CrossRef]
3. V. P. Minaev, “Laser apparatus for surgery and force therapy based on high-power semiconductor and fibre lasers,” Quantum Electron. 35(11), 976–983 (2005). [CrossRef]
4. C. W. Rudy, M. J. F. Digonnet, and R. L. Byer, “Advances in 2-μm Tm-doped mode-locked fiber lasers,” Opt. Fiber Technol. 20(6), 642–649 (2014). [CrossRef]
5. W. Zhou and D. Shen, “Above 100 nJ solitons from a passively mode-locked thulium-doped fiber oscillator,” Laser Phys. Lett. 12(7), 075103 (2015). [CrossRef]
6. K. Yin, B. Zhang, W. Yang, H. Chen, S. Chen, and J. Hou, “Flexible picosecond thulium-doped fiber laser using the active mode-locking technique,” Opt. Lett. 39(14), 4259–4262 (2014). [CrossRef] [PubMed]
7. X. He, A. Luo, W. Lin, Q. Yang, T. Yang, X. Yuan, S. Xu, W. Xu, Z. Luo, and Z. Yang, “A stable 2 μm passively Q-switched fiber laser based on nonlinear polarization evolution,” Laser Phys. 24(8), 085102 (2014). [CrossRef]
8. S. Kivistö, R. Koskinen, J. Paajaste, S. D. Jackson, M. Guina, and O. G. Okhotnikov, “Passively Q-switched Tm3+, Ho3+-doped silica fiber laser using a highly nonlinear saturable absorber and dynamic gain pulse compression,” Opt. Express 16(26), 22058–22063 (2008). [CrossRef] [PubMed]
9. Y. F. Song, L. Li, H. Zhang, Y. Shen, D. Y. Tang, and K. P. Loh, “Vector multi-soliton operation and interaction in a graphene mode-locked fiber laser,” Opt. Express 21(8), 10010–10018 (2013). [CrossRef] [PubMed]
10. W. C. Chen, G. J. Chen, D. A. Han, and B. Li, “Different temporal patterns of vector soliton bunching induced by polarization-dependent saturable absorber,” Opt. Fiber Technol. 20(3), 199–207 (2014). [CrossRef]
11. A. P. Luo, Z. C. Luo, H. Liu, X. W. Zheng, Q. Y. Ning, N. Zhao, W. C. Chen, and W. C. Xu, “Noise-like pulse trapping in a figure-eight fiber laser,” Opt. Express 23(8), 10421–10427 (2015). [CrossRef] [PubMed]
12. N. Zhao, Z. C. Luo, H. Liu, M. Liu, X. W. Zheng, L. Liu, J.-H. Liao, X.-D. Wang, A.-P. Luo, and W.-C. Xu, “Trapping of soliton molecule in a graphene-based mode-locked ytterbium-doped fiber laser,” IEEE Photonics Technol. Lett. 26(24), 2450–2453 (2014). [CrossRef]
13. M. Liu, A. P. Luo, X. W. Zheng, N. Zhao, H. Liu, Z. C. Luo, W. C. Xu, Y. Chen, C. J. Zhao, and H. Zhang, “Microfiber-based highly nonlinear topological insulator photonic device for the formation of versatile multi-soliton patterns in a fiber laser,” J. Lightwave Technol. 33(10), 2056–2061 (2015). [CrossRef]
14. C. Bao, X. Xiao, and C. Yang, “Soliton rains in a normal dispersion fiber laser with dual-filter,” Opt. Lett. 38(11), 1875–1877 (2013). [CrossRef] [PubMed]
15. H. Zhang, D. Y. Tang, X. Wu, and L. M. Zhao, “Multi-wavelength dissipative soliton operation of an erbium-doped fiber laser,” Opt. Express 17(15), 12692–12697 (2009). [CrossRef] [PubMed]
16. A. F. J. Runge, N. G. R. Broderick, and M. Erkintalo, “Observation of soliton explosions in a passively mode-locked fiber laser,” Optica 2(1), 36–39 (2015). [CrossRef]
17. M. Liu, Z. R. Cai, S. Hu, A. P. Luo, C. J. Zhao, H. Zhang, W. C. Xu, and Z. C. Luo, “Dissipative rogue waves induced by long-range chaotic multi-pulse interactions in a fiber laser with a topological insulator-deposited microfiber photonic device,” Opt. Lett. 40(20), 4767–4770 (2015). [CrossRef] [PubMed]
18. D. Y. Tang, B. Zhao, D. Y. Shen, C. Lu, W. S. Man, and H. Y. Tam, “Bound-soliton fiber laser,” Phys. Rev. A 66(3), 033806 (2002). [CrossRef]
19. D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, “Observation of bound states of solitons in a passively mode-locked fiber laser,” Phys. Rev. A 64(3), 033814 (2001). [CrossRef]
20. T. Liu, D. Jia, Y. Liu, Z. Wang, and T. Yang, “Generation of microseconds-duration square pulses in a passively mode-locked fiber laser,” Opt. Commun. 356, 416–420 (2015). [CrossRef]
21. F. Z. Wang, H. Liu, Y. Q. Huang, M. Liu, A. P. Luo, Z. C. Luo, and W. C. Xu, “Flexible generation of coherent rectangular pulse from an ultrafast fiber laser based on dispersive Fourier transformation technique,” Opt. Express 23(21), 27315–27321 (2015). [CrossRef] [PubMed]
22. H. Liu, X. Zheng, N. Zhao, Q. Ning, M. Liu, Z. Luo, A. Luo, and W. Xu, “Generation of multiwavelength noiselike square-pulses in a fiber laser,” IEEE Photonics Technol. Lett. 26(19), 1990–1993 (2014). [CrossRef]
23. X. Wen, G. Tang, J. Wang, X. Chen, Q. Qian, and Z. Yang, “Tm3+ doped barium gallo-germanate glass single-mode fibers for 2.0 μm laser,” Opt. Express 23(6), 7722–7731 (2015). [CrossRef] [PubMed]
24. X. He, A. Luo, Q. Yang, T. Yang, X. Yuan, S. Xu, Q. Qian, D. Chen, Z. Luo, W. Xu, and Z. Yang, “60 nm bandwidth, 17 nJ noiselike pulse generation from a thulium-doped fiber ring laser,” Appl. Phys. Express 6(11), 112702 (2013). [CrossRef]
25. X. He, S. Xu, C. Li, C. Yang, Q. Yang, S. Mo, D. Chen, and Z. Yang, “1.95 μm kHz-linewidth single-frequency fiber laser using self-developed heavily Tm3+-doped germanate glass fiber,” Opt. Express 21(18), 20800–20805 (2013). [CrossRef] [PubMed]
26. G. Sobon, J. Sotor, I. Pasternak, A. Krajewska, W. Strupinski, and K. M. Abramski, “Thulium-doped all-fiber laser mode-locked by CVD-graphene/PMMA saturable absorber,” Opt. Express 21(10), 12797–12802 (2013). [CrossRef] [PubMed]
27. P. S. Liang, Z. X. Zhang, Q. Q. Kuang, and M. H. Sang, “All-fiber birefringent filter with fine tunability and changeable spacing,” Laser Phys. 19(11), 2124–2128 (2009). [CrossRef]
28. J. Li, Z. Zhang, Z. Sun, H. Luo, Y. Liu, Z. Yan, C. Mou, L. Zhang, and S. K. Turitsyn, “All-fiber passively mode-locked Tm-doped NOLM-based oscillator operating at 2-μm in both soliton and noisy-pulse regimes,” Opt. Express 22(7), 7875–7882 (2014). [CrossRef] [PubMed]
29. Z. Yan, X. Li, Y. Tang, P. P. Shum, X. Yu, Y. Zhang, and Q. J. Wang, “Tunable and switchable dual-wavelength Tm-doped mode-locked fiber laser by nonlinear polarization evolution,” Opt. Express 23(4), 4369–4376 (2015). [CrossRef] [PubMed]
