Noise-like pulse trapping in a figure-eight fiber laser Ai-Ping Luo,1,* Zhi-Chao Luo,1 Hao Liu,1 Xu-Wu Zheng,1 Qiu-Yi Ning,1 Nian Zhao,1 Wei-Cheng Chen,2 and Wen-Cheng Xu1,3 1
Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou, Guangdong 510006, China 2 Department of Photoelectric Information and Engineering, Foshan University, Foshan 528000, China 3 [email protected] * [email protected]
Abstract: We report on the trapping of noise-like pulse in a figure-eight fiber laser mode locked by nonlinear amplifier loop mirror (NALM). After achievement of noise-like vector pulse, it was found that the wavelength shift of the two resolved polarization components responsible for the pulse trapping was very sensitive to the cavity birefringence. By properly rotating the polarization controllers (PCs), the wavelength shift could be up to 4.8 nm, which is much larger than that of conventional soliton trapping. The observed results would shed some light on the fundamental physics of noise-like pulse as well as its vector features in fiber lasers. ©2015 Optical Society of America OCIS codes: (250.5530) Pulse propagation and temporal solitons; (140.3500) Lasers, erbium; (140.3510) Lasers, fiber; (140.4050) Mode-locked lasers.
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
L. F. Mollenauer, R. H. Stolen, and J. G. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45(13), 1095–1098 (1980). W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78(2), 023830 (2008). Ph. Grelu, W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonance as a guideline for high-energy pulse laser oscillators,” J. Opt. Soc. Am. B 27(11), 2336–2341 (2010). X. Wu, D. Y. Tang, H. Zhang, and L. M. Zhao, “Dissipative soliton resonance in an all-normal-dispersion erbium-doped fiber laser,” Opt. Express 17(7), 5580–5584 (2009). X. Li, X. Liu, X. Hu, L. Wang, H. Lu, Y. Wang, and W. Zhao, “Long-cavity passively mode-locked fiber ring laser with high-energy rectangular-shape pulses in anomalous dispersion regime,” Opt. Lett. 35(19), 3249–3251 (2010). Z. C. Luo, W. J. Cao, Z. B. Lin, Z. R. Cai, A. P. Luo, and W. C. Xu, “Pulse dynamics of dissipative soliton resonance with large duration-tuning range in a fiber ring laser,” Opt. Lett. 37(22), 4777–4779 (2012). B. A. Malomed, “Bound solitons in the nonlinear Schrodinger–Ginzburg–Landau equation,” Phys. Rev. A, Mol. Opt. Phys. 44, 6954–6957 (1991). 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). P. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, “Phase-locked soliton pairs in a stretched-pulse fiber laser,” Opt. Lett. 27(11), 966–968 (2002). F. Amrani, M. Salhi, P. Grelu, H. Leblond, and F. Sanchez, “Universal soliton pattern formations in passively mode-locked fiber lasers,” Opt. Lett. 36(9), 1545–1547 (2011). F. Amrani, M. Salhi, H. Leblond, A. Haboucha, and F. Sanchez, “Intricate solitons state in passively modelocked fiber lasers,” Opt. Express 19(14), 13134–13139 (2011). M. Horowitz, Y. Barad, and Y. Silberberg, “Noiselike pulses with a broadband spectrum generated from an erbium-doped fiber laser,” Opt. Lett. 22(11), 799–801 (1997). Y. Jeong, L. A. Vazquez-Zuniga, S. Lee, and Y. Kwon, “On the formation of noise-like pulses in fiber ring cavity configurations,” Opt. Fiber Technol. 20(6), 575–592 (2014). S. Kobtsev, S. Kukarin, S. Smirnov, S. Turitsyn, and A. Latkin, “Generation of double-scale femto/pico-second optical lumps in mode-locked fiber lasers,” Opt. Express 17(23), 20707–20713 (2009). C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I: Equal propagation amplitudes,” Opt. Lett. 12(8), 614–616 (1987). C. R. Menyuk, “Stability of solitons in birefringent optical fibers. II. Arbitrary amplitudes,” J. Opt. Soc. Am. B 5(2), 392–402 (1988).
#234289 - $15.00 USD © 2015 OSA
Received 11 Feb 2015; revised 30 Mar 2015; accepted 3 Apr 2015; published 14 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010421 | OPTICS EXPRESS 10421
17. S. T. Cundiff, B. C. Collings, N. N. Akhmediev, J. M. Soto-Crespo, K. Bergman, and W. H. Knox, “Observation of polarization-locked vector solitons in an optical fiber,” Phys. Rev. Lett. 82(20), 3988–3991 (1999). 18. D. Y. Tang, H. Zhang, L. M. Zhao, and X. Wu, “Observation of high-order polarization-locked vector solitons in a fiber laser,” Phys. Rev. Lett. 101(15), 153904 (2008). 19. C. Mou, S. Sergeyev, A. Rozhin, and S. Turistyn, “All-fiber polarization locked vector soliton laser using carbon nanotubes,” Opt. Lett. 36(19), 3831–3833 (2011). 20. L. M. Zhao, D. Y. Tang, X. Wu, H. Zhang, and H. Y. Tam, “Coexistence of polarization-locked and polarization-rotating vector solitons in a fiber laser with SESAM,” Opt. Lett. 34(20), 3059–3061 (2009). 21. H. Zhang, D. Y. Tang, L. M. Zhao, X. Wu, and H. Y. Tam, “Dissipative vector solitons in a dispersionmanaged cavity fiber laser with net positive cavity dispersion,” Opt. Express 17(2), 455–460 (2009). 22. Y. F. Song, H. Zhang, D. Y. Tang, and Y. Shen, “Polarization rotation vector solitons in a graphene modelocked fiber laser,” Opt. Express 20(24), 27283–27289 (2012). 23. H. Zhang, D. Y. Tang, L. M. Zhao, and N. Xiang, “Coherent energy exchange between components of a vector soliton in fiber lasers,” Opt. Express 16(17), 12618–12623 (2008). 24. L. M. Zhao, D. Y. Tang, H. Zhang, X. Wu, and N. Xiang, “Soliton trapping in fiber lasers,” Opt. Express 16(13), 9528–9533 (2008). 25. D. Mao, X. Liu, and H. Lu, “Observation of pulse trapping in a near-zero dispersion regime,” Opt. Lett. 37(13), 2619–2621 (2012). 26. Z. C. Luo, Q. Y. Ning, H. L. Mo, H. Cui, J. Liu, L. J. Wu, A. P. Luo, and W. C. Xu, “Vector dissipative soliton resonance in a fiber laser,” Opt. Express 21(8), 10199–10204 (2013). 27. Q. Y. Ning, H. Liu, X. W. Zheng, W. Yu, A. P. Luo, X. G. Huang, Z. C. Luo, W. C. Xu, S. H. Xu, and Z. M. Yang, “Vector nature of multi-soliton patterns in a passively mode-locked figure-eight fiber laser,” Opt. Express 22(10), 11900–11911 (2014). 28. B. C. Collings, S. T. Cundiff, N. N. Akhmediev, J. M. Soto-Crespo, K. Bergman, and W. H. Knox, “Polarization-locked temporal vector solitons in a fiber laser: experiment,” J. Opt. Soc. Am. B 17(3), 354–365 (2000). 29. Y. Wang, S. M. Wang, J. L. Luo, L. Li, D. Y. Tang, D. Y. Shen, S. M. Zhang, F. W. Wise, and L. M. Zhao, “Vector soliton generation in a Tm fiber laser,” IEEE Photon. Technol. Lett. 26(8), 769–772 (2014). 30. A. Zaytsev, C. H. Lin, Y. J. You, C. C. Chung, C. L. Wang, and C. L. Pan, “Supercontinuum generation by noise-like pulses transmitted through normally dispersive standard single-mode fibers,” Opt. Express 21(13), 16056–16062 (2013). 31. D. Lei, H. Yang, H. Dong, S. Wen, H. Xu, and J. Zhang, “Effect of birefringence on the bandwidth of noise-like pulse in an erbium-doped fiber laser,” J. Mod. Opt. 56(4), 572–576 (2009).
1. Introduction Since its first observation in optical fiber by Mollenauer et al. in 1980 [1], temporal solitons have become a fascinating topic over the past decades due to the importance of fundamental physics and wide range of applications. The passively mode-locked fiber lasers, which are actually nonlinear dissipative systems, have been regarded as the powerful tools for generating temporal solitons and observing nonlinear soliton dynamics. Thus, there is always a strong motivation to investigate different soliton dynamics and evolutions in fiber lasers by skillfully designing the laser cavities. Indeed, when the cavity parameters are properly set, various soliton formation and dynamics could be observed in fiber lasers, such as dissipative soliton resonance [2–6], bound soliton [7–9], soliton cluster [10,11], noise-like pulse [12–14] and so on. The discovery and investigations of different soliton types in nonlinear fiber systems greatly contribute to the understanding of fundamental physics of temporal solitons. Generally, the solitons emitted from fiber lasers are treated as scalar ones for the purpose of simple analyses. However, as the single mode fiber (SMF) used to constructed fiber laser actually supports two orthogonal polarization modes, the solitons could exhibit complex polarization dynamics due to the small amounts of random birefringence in SMF. Therefore, it would be also meaningful to consider the vector characteristics of optical soliton along the two polarization axes of SMF, namely, vector solitons [15,16]. It has been demonstrated the vector solitons could be naturally generated from a fiber laser without polarization discrimination devices, i.e., polarizer. Therefore, the polarization-insensitive real saturable absorbers (SAs), such as semiconductor saturable absorber mirror (SESAM), nanotube and graphene SA were mostly employed in fiber laser to investigate the vector solitons. With the aforementioned mode-locking techniques, so far different vector soliton dynamics have been observed in fiber lasers, for example, polarization-locked vector soliton (PLVS) [17–19], polarization-rotation vector soliton (PRVS) [20–22], coherent energy exchange [23], and soliton trapping [24,25]. Nevertheless, the operation regimes of mode-locked fiber lasers with
#234289 - $15.00 USD © 2015 OSA
Received 11 Feb 2015; revised 30 Mar 2015; accepted 3 Apr 2015; published 14 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010421 | OPTICS EXPRESS 10422
real SAs are difficult to be tuned since it is insensitive to the adjustments of polarization controllers (PCs) inside the laser cavity. Consequently, the real SAs mode-locked fiber lasers are generally suitable for observation of conventional vector solitons. Recently, we have proposed that the passively mode-locked figure-eight fiber laser could act as the excellent platforms to observe the vector nature of optical solitons [26], because there are also no polarization discrimination components in the laser cavity. In comparison to fiber laser systems using real SAs, in the figure-eight fiber laser the intracavity PC offers one more degree of freedom to adjust the laser operation regime. Therefore, the figure-eight fiber lasers are particularly suitable for investigating the vector features of special soliton states [27]. As one of the special soliton states, the noise-like pulse could be frequently observed in fiber lasers. The noise-like pulse is found to be a localized wave packet that consists of many chaotic pulses with high peak powers [12–14]. Moreover, the noise-like pulse possesses broadband and smooth mode-locked spectrum. Therefore, considering the unique characteristics of noise-like pulse both in time and spectral domains, it would be interesting to investigate the vector nature of noise-like pulse in a fiber laser. In this work, we reported on the trapping of noise-like pulse in a passively mode-locked figure-eight fiber laser. Despite of noise-like operation regime, it was found that the pulse trapping of two polarization components centered at different wavelengths was still obtained and they propagated as a group-velocity locked vector soliton (GLVS). The wavelength shift of two polarization components could be up to 4.8 nm by adjusting the cavity birefringence, which is much larger than that of conventional soliton trapping. The observed results would further reveal the fundamental physics of noise-like pulse in fiber lasers. 2. Experimental setup
Fig. 1. Schematic of the vector soliton figure-eight fiber laser.
The schematic of the proposed figure-eight fiber laser is shown in Fig. 1. The fiber laser is mode-locked by using the NALM technique. A piece of 4 m long erbium-doped fiber (EDF) is used as the gain medium. The other fibers are all standard SMFs with a length of 32.8 m. Thus, the fundamental repetition rate is 5.58 MHz. All the fibers are fastened to the optical table to prevent any change of their birefringence. A polarization-independent isolator (PIISO) ensures the unidirectional operation. Two polarization controllers (PCs), which are fiber squeezer types, are employed to adjust the polarization state of circulating light and the cavity birefringence. A 10% fiber coupler is used to output laser. For resolving the two orthogonal polarization components, a polarization beam splitter (PBS) is connected to the output coupler. Generally the birefringence between the output coupler and the PBS needs to be compensated for investigating the polarization-locked vector soliton [28]. However, for the pulse trapping in this work, the polarization state of the vector noise-like pulse evolves during propagation in the laser cavity. The fiber between the output coupler and the PBS is conventional single mode fiber with low birefringence, which is the same as the intracavity fiber. Thus, the vector characteristics of noise-like pulse measured at the PBS could be traced back to one specific point of intracavity fiber. In this case, the fiber birefringence between the output coupler and the PBS was not compensated in our experiment. The laser output was recorded by an optical spectrum analyzer (OSA, Anritsu MS9710C) and an oscilloscope (LeCroy WaveRunner 104MXi, 1 GHz) with a photodetector (Tektronix P6703B, 1.2 GHz).
#234289 - $15.00 USD © 2015 OSA
Received 11 Feb 2015; revised 30 Mar 2015; accepted 3 Apr 2015; published 14 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010421 | OPTICS EXPRESS 10423
In addition, the pulse profile was measured by a commercially available autocorrelator (Femtochrome FR-103XL). 3. Experimental results and discussions In the experiment, the mode-locking threshold of the proposed fiber laser is about 65 mW. By simply rotating the PCs, the mode-locked soliton with different operation regimes could be achieved. As mentioned above, because there was no polarizer used in the laser cavity and all fibers possessed weak birefringence, the fiber laser naturally emitted vector soliton once it operated in mode-locking regime. For the purpose of comparison, we firstly investigated the pulse trapping of conventional soliton operation under the pump power of ~100 mW. The measured results are summarized in Fig. 2. Figure 2(a) presents the mode-locked spectrum with and without passing the PBS. As can be seen here, the center wavelength of the total mode-locked spectrum is 1575.4 nm. And the 3-dB spectral bandwidth is 3.2 nm. However, when the total mode-locked spectrum was resolved by the PBS, it can be seen that the two orthogonal polarization components located at different wavelengths with a separation of 0.54 nm. Here, the central wavelength of the mode-locked spectrum is defined by the center point of the 3-dB spectral bandwidth. As a result, the fiber birefringence-induced polarization dispersion could be compensated by shifting the center wavelengths. Then the pulse trapping was achieved and the two orthogonal polarization components propagated as a stable GLVS. Note that the 0.54 nm was the largest wavelength shift we observed in our fiber laser by carefully rotating the PCs while keeping the conventional soliton regime. Therefore, we selected it for comparing the trapping effects of the conventional soliton and noise-like pulse regimes. The corresponding pulse-trains are shown in Fig. 2(b). The fundamental repetition rate is 5.58 MHz and the pulse-trains of the two polarization components have uniform profiles (blue and red curves). Figure 2(c) illustrates the autocorrelation trace of the modelocked pulse. The pulse duration is measured to be ~0.9 ps. Thus, the time-bandwidth product is 0.348, indicating the pulse is slightly chirped. It should be noted that the pulse durations of two polarization components are slightly different from each other, as shown in Fig. 2(c) with blue and red curves, which is caused by the different bandwidths of mode-locked spectra.
Fig. 2. Conventional soliton operation. (a) Polarization-resolved spectra; (b) Corresponding pulse trains; (c) Autocorrelation traces.
Fig. 3. Noise-like pulse operation. (a) Spectrum; (b) Pulse train; (c) Autocorrelation traces.
After investigating the conventional soliton mode-locking operation, the PCs were further rotated and the pump power was fixed. At the proper orientations of PCs, the mode-locked spectrum broadened suddenly and the Kelly sidebands disappeared at the same time. From the spectral characteristics, it can be deduced that the obtained pulse is operating in noise-like regime. Figure 3(a) shows the mode-locked spectrum of noise-like pulse. The corresponding
#234289 - $15.00 USD © 2015 OSA
Received 11 Feb 2015; revised 30 Mar 2015; accepted 3 Apr 2015; published 14 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010421 | OPTICS EXPRESS 10424
pulse-train is measured to be similar to those of conventional solitons due to the limited bandwidth of oscilloscope, as shown in Fig. 3(b). To further identify that the fiber laser operated in noise-like pulse regime, the autocorrelation trace of mode-locked pulse was measured. The autocorrelation traces are presented in Fig. 3(c), in which we can see that there is a narrow coherent peak with wide shoulders. The pulse characteristics in spectral and time domains are in good agreement with the intrinsic characteristics of the previously reported noise-like pulse fiber laser [12–14].
Fig. 4. Noise-like pulse trapping. (a) Polarization-resolved spectra; (b) Corresponding pulse trains; (c) Corresponding autocorrelation traces.
Then the vector nature of noise-like pulse was investigated. To this end, a PBS was employed to characterize the orthogonal polarization components in both spectral and time domains. Figure 4(a) shows the spectral components of the two orthogonal polarization states. Notably, it can be seen that the two orthogonal polarization components located at different wavelengths (1564.9 nm and 1568 nm) with a separation of 3.1 nm, which is much larger than that of conventional soliton trapping. The corresponding pulse-trains of the two orthogonal polarization states are shown in Fig. 4(b). Apart from the intensity difference of the two pulse-trains, they are similar to each other. The autocorrelation traces of the polarization resolved components are presented in Fig. 4(c), indicating that both of them operated in noise-like mode-locking states. The comparative experiments demonstrated that although the fiber laser was constructed by SMF with moderate cavity birefringence, the two polarization components of the noise-like pulse still could trap each other, which is similar to the case of conventional solitons. It should be also noted that if the cavity birefringence is too large to be compensated, the soliton trapping would not occur [29].
Fig. 5. Noise-like pulse trapping with a wavelength shift of 4.8 nm. (a) Spectrum of total pulse; (b) Total pulse train. Inset: corresponding autocorrelation trace; (c) Polarization-resolved spectra; (d) Corresponding pulse trains.
As we know, the wavelength separation of soliton trapping could be influenced by the cavity birefringence due to the compensation of the birefringence-induced polarization dispersion [29]. To investigate this issue, the PCs were further adjusted to purposely change the cavity birefringence. In the experiment, it was found that the wavelength shift of noise-
#234289 - $15.00 USD © 2015 OSA
Received 11 Feb 2015; revised 30 Mar 2015; accepted 3 Apr 2015; published 14 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010421 | OPTICS EXPRESS 10425
like pulse is sensitive to the cavity birefringence. For better showing the effect of cavity birefringence on the wavelength shift, the spectral shape of noise-like pulse including the 3dB spectral bandwidth which is similar to the case of Fig. 4 was chosen. Figure 5(a) presents the mode-locked spectrum of noise-like pulse when the PCs were further rotated. Note that the center wavelength varies slightly to be 1567.5 nm. The corresponding pulse-train is shown in Fig. 5(b), whose repetition rate is also 5.58 MHz. Moreover, the autocorrelation trace is provided in the inset of Fig. 5(b), which is a typical one of noise-like pulse. In the following, the vector characteristics of this case were analyzed. Again, the polarization resolved measurement was employed. The resolved optical spectra of the two components are shown in Fig. 5(c). As can be seen here, the center wavelengths of two polarization components are 1567.1 nm (blue curve) and 1571.9 nm (red curve), respectively. Thus, the wavelength shift of pulse trapping reached to 4.8 nm. It should be also noted that the intensity difference of two polarization components is about 8.3 dB in this case, which is much larger than that of Fig. 4(a). It is believed that the large intensity difference of two polarization components was caused by the large ellipticity of vector noise-like pulse. The resolved pulsetrains centered at two wavelengths are shown in Fig. 5(d). Both of them operated at modelocking regime at the fundamental repetition rate with uniform intensities, suggesting that the two polarization components still could trap each other despite of the variation of cavity birefringence. Obviously, in our experiments the wavelength shift of noise-like pulse trapping is much larger than that of a conventional soliton trapping. It has been shown that the tiny pulses inside the noise-like pulse packet possess high peak power, which could be used to supercontinuum generation in optical fiber laser [30]. In this case, the nonlinear birefringence induced by the noise-like pulse could be larger than that induced by the conventional solitons. Therefore, in the case of noise-like operation regime in the fiber laser, the frequency shift of the two polarized components needs to be large enough to compensate the fiber birefringence-induced polarization dispersion. Then, they could trap each other as a groupvelocity locked vector soliton. Because of the high peak power of the noise-like wave packet, it is expected that the wavelength shift would be sensitive to the cavity birefringence, which was also verified by our experimental results. However, note that the individual pulse inside the noise-like wave packet could not be resolved by the autocorrelator. Therefore, the precise peak powers of the noise-like pulses could not be calculated. Moreover, in order to better quantifiably relate the cavity birefringence to the wavelength shift of pulse trapping, the adjustment of cavity birefringence by coiling the fiber sections could be introduced in the laser cavity to control the cavity birefringence. It was demonstrated that the spectral bandwidth of noise-like pulse is related to the average cavity birefringence. Thus, it is expected that larger spectral bandwidth of noise-like pulse as well as the larger wavelength shift could be observed by properly optimizing the cavity birefringence [31]. On the other hand, regarding the vector nature of noise-like pulse, it should be noted that only the pulse trapping was observed. However, by further adjusting the cavity parameters, it is believed that other vector dynamics of noise-like pulse such as PRV and PLV noise-like pulse may be obtained. These results would be beneficial for complementing the understanding of pulse characteristics operating in noise-like regime. 4. Conclusion In conclusion, we have investigated the trapping of the noise-like pulse in a figure-eight fiber laser. To achieve the pulse trapping and propagate as a GLVS, the frequency shift of two orthogonal polarized noise-like pulses occurs. It was also found that the wavelength shift of noise-like pulse trapping was much larger than that of conventional soliton trapping, which could be up to 4.8 nm by properly rotating the PCs. The obtained results reveal the vector characteristics of noise-like pulses in fiber lasers, and further demonstrate that the figure-eight fiber laser could be indeed a good platform for investigating the vector nature of different soliton types.
#234289 - $15.00 USD © 2015 OSA
Received 11 Feb 2015; revised 30 Mar 2015; accepted 3 Apr 2015; published 14 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010421 | OPTICS EXPRESS 10426
Acknowledgments This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11304101, 61307058, 61378036, 11474108, 11204037), the PhD Start-up Fund of Natural Science Foundation of Guangdong Province, China (Grant No. S2013040016320), and the Scientific and Technological Innovation Project of Higher Education Institute, Guangdong, China (Grant No. 2013KJCX0051). Z.-C. Luo acknowledges the financial support from the Guangdong Natural Science Funds for Distinguished Young Scholar (Grant No. 2014A030306019), and the Zhujiang New-star Plan of Science & Technology in Guangzhou City (Grant No. 2014J2200008).
#234289 - $15.00 USD © 2015 OSA
Received 11 Feb 2015; revised 30 Mar 2015; accepted 3 Apr 2015; published 14 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010421 | OPTICS EXPRESS 10427
Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou, Guangdong 510006, China 2 Department of Photoelectric Information and Engineering, Foshan University, Foshan 528000, China 3 [email protected] * [email protected]
Abstract: We report on the trapping of noise-like pulse in a figure-eight fiber laser mode locked by nonlinear amplifier loop mirror (NALM). After achievement of noise-like vector pulse, it was found that the wavelength shift of the two resolved polarization components responsible for the pulse trapping was very sensitive to the cavity birefringence. By properly rotating the polarization controllers (PCs), the wavelength shift could be up to 4.8 nm, which is much larger than that of conventional soliton trapping. The observed results would shed some light on the fundamental physics of noise-like pulse as well as its vector features in fiber lasers. ©2015 Optical Society of America OCIS codes: (250.5530) Pulse propagation and temporal solitons; (140.3500) Lasers, erbium; (140.3510) Lasers, fiber; (140.4050) Mode-locked lasers.
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
L. F. Mollenauer, R. H. Stolen, and J. G. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45(13), 1095–1098 (1980). W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78(2), 023830 (2008). Ph. Grelu, W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonance as a guideline for high-energy pulse laser oscillators,” J. Opt. Soc. Am. B 27(11), 2336–2341 (2010). X. Wu, D. Y. Tang, H. Zhang, and L. M. Zhao, “Dissipative soliton resonance in an all-normal-dispersion erbium-doped fiber laser,” Opt. Express 17(7), 5580–5584 (2009). X. Li, X. Liu, X. Hu, L. Wang, H. Lu, Y. Wang, and W. Zhao, “Long-cavity passively mode-locked fiber ring laser with high-energy rectangular-shape pulses in anomalous dispersion regime,” Opt. Lett. 35(19), 3249–3251 (2010). Z. C. Luo, W. J. Cao, Z. B. Lin, Z. R. Cai, A. P. Luo, and W. C. Xu, “Pulse dynamics of dissipative soliton resonance with large duration-tuning range in a fiber ring laser,” Opt. Lett. 37(22), 4777–4779 (2012). B. A. Malomed, “Bound solitons in the nonlinear Schrodinger–Ginzburg–Landau equation,” Phys. Rev. A, Mol. Opt. Phys. 44, 6954–6957 (1991). 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). P. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, “Phase-locked soliton pairs in a stretched-pulse fiber laser,” Opt. Lett. 27(11), 966–968 (2002). F. Amrani, M. Salhi, P. Grelu, H. Leblond, and F. Sanchez, “Universal soliton pattern formations in passively mode-locked fiber lasers,” Opt. Lett. 36(9), 1545–1547 (2011). F. Amrani, M. Salhi, H. Leblond, A. Haboucha, and F. Sanchez, “Intricate solitons state in passively modelocked fiber lasers,” Opt. Express 19(14), 13134–13139 (2011). M. Horowitz, Y. Barad, and Y. Silberberg, “Noiselike pulses with a broadband spectrum generated from an erbium-doped fiber laser,” Opt. Lett. 22(11), 799–801 (1997). Y. Jeong, L. A. Vazquez-Zuniga, S. Lee, and Y. Kwon, “On the formation of noise-like pulses in fiber ring cavity configurations,” Opt. Fiber Technol. 20(6), 575–592 (2014). S. Kobtsev, S. Kukarin, S. Smirnov, S. Turitsyn, and A. Latkin, “Generation of double-scale femto/pico-second optical lumps in mode-locked fiber lasers,” Opt. Express 17(23), 20707–20713 (2009). C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I: Equal propagation amplitudes,” Opt. Lett. 12(8), 614–616 (1987). C. R. Menyuk, “Stability of solitons in birefringent optical fibers. II. Arbitrary amplitudes,” J. Opt. Soc. Am. B 5(2), 392–402 (1988).
#234289 - $15.00 USD © 2015 OSA
Received 11 Feb 2015; revised 30 Mar 2015; accepted 3 Apr 2015; published 14 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010421 | OPTICS EXPRESS 10421
17. S. T. Cundiff, B. C. Collings, N. N. Akhmediev, J. M. Soto-Crespo, K. Bergman, and W. H. Knox, “Observation of polarization-locked vector solitons in an optical fiber,” Phys. Rev. Lett. 82(20), 3988–3991 (1999). 18. D. Y. Tang, H. Zhang, L. M. Zhao, and X. Wu, “Observation of high-order polarization-locked vector solitons in a fiber laser,” Phys. Rev. Lett. 101(15), 153904 (2008). 19. C. Mou, S. Sergeyev, A. Rozhin, and S. Turistyn, “All-fiber polarization locked vector soliton laser using carbon nanotubes,” Opt. Lett. 36(19), 3831–3833 (2011). 20. L. M. Zhao, D. Y. Tang, X. Wu, H. Zhang, and H. Y. Tam, “Coexistence of polarization-locked and polarization-rotating vector solitons in a fiber laser with SESAM,” Opt. Lett. 34(20), 3059–3061 (2009). 21. H. Zhang, D. Y. Tang, L. M. Zhao, X. Wu, and H. Y. Tam, “Dissipative vector solitons in a dispersionmanaged cavity fiber laser with net positive cavity dispersion,” Opt. Express 17(2), 455–460 (2009). 22. Y. F. Song, H. Zhang, D. Y. Tang, and Y. Shen, “Polarization rotation vector solitons in a graphene modelocked fiber laser,” Opt. Express 20(24), 27283–27289 (2012). 23. H. Zhang, D. Y. Tang, L. M. Zhao, and N. Xiang, “Coherent energy exchange between components of a vector soliton in fiber lasers,” Opt. Express 16(17), 12618–12623 (2008). 24. L. M. Zhao, D. Y. Tang, H. Zhang, X. Wu, and N. Xiang, “Soliton trapping in fiber lasers,” Opt. Express 16(13), 9528–9533 (2008). 25. D. Mao, X. Liu, and H. Lu, “Observation of pulse trapping in a near-zero dispersion regime,” Opt. Lett. 37(13), 2619–2621 (2012). 26. Z. C. Luo, Q. Y. Ning, H. L. Mo, H. Cui, J. Liu, L. J. Wu, A. P. Luo, and W. C. Xu, “Vector dissipative soliton resonance in a fiber laser,” Opt. Express 21(8), 10199–10204 (2013). 27. Q. Y. Ning, H. Liu, X. W. Zheng, W. Yu, A. P. Luo, X. G. Huang, Z. C. Luo, W. C. Xu, S. H. Xu, and Z. M. Yang, “Vector nature of multi-soliton patterns in a passively mode-locked figure-eight fiber laser,” Opt. Express 22(10), 11900–11911 (2014). 28. B. C. Collings, S. T. Cundiff, N. N. Akhmediev, J. M. Soto-Crespo, K. Bergman, and W. H. Knox, “Polarization-locked temporal vector solitons in a fiber laser: experiment,” J. Opt. Soc. Am. B 17(3), 354–365 (2000). 29. Y. Wang, S. M. Wang, J. L. Luo, L. Li, D. Y. Tang, D. Y. Shen, S. M. Zhang, F. W. Wise, and L. M. Zhao, “Vector soliton generation in a Tm fiber laser,” IEEE Photon. Technol. Lett. 26(8), 769–772 (2014). 30. A. Zaytsev, C. H. Lin, Y. J. You, C. C. Chung, C. L. Wang, and C. L. Pan, “Supercontinuum generation by noise-like pulses transmitted through normally dispersive standard single-mode fibers,” Opt. Express 21(13), 16056–16062 (2013). 31. D. Lei, H. Yang, H. Dong, S. Wen, H. Xu, and J. Zhang, “Effect of birefringence on the bandwidth of noise-like pulse in an erbium-doped fiber laser,” J. Mod. Opt. 56(4), 572–576 (2009).
1. Introduction Since its first observation in optical fiber by Mollenauer et al. in 1980 [1], temporal solitons have become a fascinating topic over the past decades due to the importance of fundamental physics and wide range of applications. The passively mode-locked fiber lasers, which are actually nonlinear dissipative systems, have been regarded as the powerful tools for generating temporal solitons and observing nonlinear soliton dynamics. Thus, there is always a strong motivation to investigate different soliton dynamics and evolutions in fiber lasers by skillfully designing the laser cavities. Indeed, when the cavity parameters are properly set, various soliton formation and dynamics could be observed in fiber lasers, such as dissipative soliton resonance [2–6], bound soliton [7–9], soliton cluster [10,11], noise-like pulse [12–14] and so on. The discovery and investigations of different soliton types in nonlinear fiber systems greatly contribute to the understanding of fundamental physics of temporal solitons. Generally, the solitons emitted from fiber lasers are treated as scalar ones for the purpose of simple analyses. However, as the single mode fiber (SMF) used to constructed fiber laser actually supports two orthogonal polarization modes, the solitons could exhibit complex polarization dynamics due to the small amounts of random birefringence in SMF. Therefore, it would be also meaningful to consider the vector characteristics of optical soliton along the two polarization axes of SMF, namely, vector solitons [15,16]. It has been demonstrated the vector solitons could be naturally generated from a fiber laser without polarization discrimination devices, i.e., polarizer. Therefore, the polarization-insensitive real saturable absorbers (SAs), such as semiconductor saturable absorber mirror (SESAM), nanotube and graphene SA were mostly employed in fiber laser to investigate the vector solitons. With the aforementioned mode-locking techniques, so far different vector soliton dynamics have been observed in fiber lasers, for example, polarization-locked vector soliton (PLVS) [17–19], polarization-rotation vector soliton (PRVS) [20–22], coherent energy exchange [23], and soliton trapping [24,25]. Nevertheless, the operation regimes of mode-locked fiber lasers with
#234289 - $15.00 USD © 2015 OSA
Received 11 Feb 2015; revised 30 Mar 2015; accepted 3 Apr 2015; published 14 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010421 | OPTICS EXPRESS 10422
real SAs are difficult to be tuned since it is insensitive to the adjustments of polarization controllers (PCs) inside the laser cavity. Consequently, the real SAs mode-locked fiber lasers are generally suitable for observation of conventional vector solitons. Recently, we have proposed that the passively mode-locked figure-eight fiber laser could act as the excellent platforms to observe the vector nature of optical solitons [26], because there are also no polarization discrimination components in the laser cavity. In comparison to fiber laser systems using real SAs, in the figure-eight fiber laser the intracavity PC offers one more degree of freedom to adjust the laser operation regime. Therefore, the figure-eight fiber lasers are particularly suitable for investigating the vector features of special soliton states [27]. As one of the special soliton states, the noise-like pulse could be frequently observed in fiber lasers. The noise-like pulse is found to be a localized wave packet that consists of many chaotic pulses with high peak powers [12–14]. Moreover, the noise-like pulse possesses broadband and smooth mode-locked spectrum. Therefore, considering the unique characteristics of noise-like pulse both in time and spectral domains, it would be interesting to investigate the vector nature of noise-like pulse in a fiber laser. In this work, we reported on the trapping of noise-like pulse in a passively mode-locked figure-eight fiber laser. Despite of noise-like operation regime, it was found that the pulse trapping of two polarization components centered at different wavelengths was still obtained and they propagated as a group-velocity locked vector soliton (GLVS). The wavelength shift of two polarization components could be up to 4.8 nm by adjusting the cavity birefringence, which is much larger than that of conventional soliton trapping. The observed results would further reveal the fundamental physics of noise-like pulse in fiber lasers. 2. Experimental setup
Fig. 1. Schematic of the vector soliton figure-eight fiber laser.
The schematic of the proposed figure-eight fiber laser is shown in Fig. 1. The fiber laser is mode-locked by using the NALM technique. A piece of 4 m long erbium-doped fiber (EDF) is used as the gain medium. The other fibers are all standard SMFs with a length of 32.8 m. Thus, the fundamental repetition rate is 5.58 MHz. All the fibers are fastened to the optical table to prevent any change of their birefringence. A polarization-independent isolator (PIISO) ensures the unidirectional operation. Two polarization controllers (PCs), which are fiber squeezer types, are employed to adjust the polarization state of circulating light and the cavity birefringence. A 10% fiber coupler is used to output laser. For resolving the two orthogonal polarization components, a polarization beam splitter (PBS) is connected to the output coupler. Generally the birefringence between the output coupler and the PBS needs to be compensated for investigating the polarization-locked vector soliton [28]. However, for the pulse trapping in this work, the polarization state of the vector noise-like pulse evolves during propagation in the laser cavity. The fiber between the output coupler and the PBS is conventional single mode fiber with low birefringence, which is the same as the intracavity fiber. Thus, the vector characteristics of noise-like pulse measured at the PBS could be traced back to one specific point of intracavity fiber. In this case, the fiber birefringence between the output coupler and the PBS was not compensated in our experiment. The laser output was recorded by an optical spectrum analyzer (OSA, Anritsu MS9710C) and an oscilloscope (LeCroy WaveRunner 104MXi, 1 GHz) with a photodetector (Tektronix P6703B, 1.2 GHz).
#234289 - $15.00 USD © 2015 OSA
Received 11 Feb 2015; revised 30 Mar 2015; accepted 3 Apr 2015; published 14 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010421 | OPTICS EXPRESS 10423
In addition, the pulse profile was measured by a commercially available autocorrelator (Femtochrome FR-103XL). 3. Experimental results and discussions In the experiment, the mode-locking threshold of the proposed fiber laser is about 65 mW. By simply rotating the PCs, the mode-locked soliton with different operation regimes could be achieved. As mentioned above, because there was no polarizer used in the laser cavity and all fibers possessed weak birefringence, the fiber laser naturally emitted vector soliton once it operated in mode-locking regime. For the purpose of comparison, we firstly investigated the pulse trapping of conventional soliton operation under the pump power of ~100 mW. The measured results are summarized in Fig. 2. Figure 2(a) presents the mode-locked spectrum with and without passing the PBS. As can be seen here, the center wavelength of the total mode-locked spectrum is 1575.4 nm. And the 3-dB spectral bandwidth is 3.2 nm. However, when the total mode-locked spectrum was resolved by the PBS, it can be seen that the two orthogonal polarization components located at different wavelengths with a separation of 0.54 nm. Here, the central wavelength of the mode-locked spectrum is defined by the center point of the 3-dB spectral bandwidth. As a result, the fiber birefringence-induced polarization dispersion could be compensated by shifting the center wavelengths. Then the pulse trapping was achieved and the two orthogonal polarization components propagated as a stable GLVS. Note that the 0.54 nm was the largest wavelength shift we observed in our fiber laser by carefully rotating the PCs while keeping the conventional soliton regime. Therefore, we selected it for comparing the trapping effects of the conventional soliton and noise-like pulse regimes. The corresponding pulse-trains are shown in Fig. 2(b). The fundamental repetition rate is 5.58 MHz and the pulse-trains of the two polarization components have uniform profiles (blue and red curves). Figure 2(c) illustrates the autocorrelation trace of the modelocked pulse. The pulse duration is measured to be ~0.9 ps. Thus, the time-bandwidth product is 0.348, indicating the pulse is slightly chirped. It should be noted that the pulse durations of two polarization components are slightly different from each other, as shown in Fig. 2(c) with blue and red curves, which is caused by the different bandwidths of mode-locked spectra.
Fig. 2. Conventional soliton operation. (a) Polarization-resolved spectra; (b) Corresponding pulse trains; (c) Autocorrelation traces.
Fig. 3. Noise-like pulse operation. (a) Spectrum; (b) Pulse train; (c) Autocorrelation traces.
After investigating the conventional soliton mode-locking operation, the PCs were further rotated and the pump power was fixed. At the proper orientations of PCs, the mode-locked spectrum broadened suddenly and the Kelly sidebands disappeared at the same time. From the spectral characteristics, it can be deduced that the obtained pulse is operating in noise-like regime. Figure 3(a) shows the mode-locked spectrum of noise-like pulse. The corresponding
#234289 - $15.00 USD © 2015 OSA
Received 11 Feb 2015; revised 30 Mar 2015; accepted 3 Apr 2015; published 14 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010421 | OPTICS EXPRESS 10424
pulse-train is measured to be similar to those of conventional solitons due to the limited bandwidth of oscilloscope, as shown in Fig. 3(b). To further identify that the fiber laser operated in noise-like pulse regime, the autocorrelation trace of mode-locked pulse was measured. The autocorrelation traces are presented in Fig. 3(c), in which we can see that there is a narrow coherent peak with wide shoulders. The pulse characteristics in spectral and time domains are in good agreement with the intrinsic characteristics of the previously reported noise-like pulse fiber laser [12–14].
Fig. 4. Noise-like pulse trapping. (a) Polarization-resolved spectra; (b) Corresponding pulse trains; (c) Corresponding autocorrelation traces.
Then the vector nature of noise-like pulse was investigated. To this end, a PBS was employed to characterize the orthogonal polarization components in both spectral and time domains. Figure 4(a) shows the spectral components of the two orthogonal polarization states. Notably, it can be seen that the two orthogonal polarization components located at different wavelengths (1564.9 nm and 1568 nm) with a separation of 3.1 nm, which is much larger than that of conventional soliton trapping. The corresponding pulse-trains of the two orthogonal polarization states are shown in Fig. 4(b). Apart from the intensity difference of the two pulse-trains, they are similar to each other. The autocorrelation traces of the polarization resolved components are presented in Fig. 4(c), indicating that both of them operated in noise-like mode-locking states. The comparative experiments demonstrated that although the fiber laser was constructed by SMF with moderate cavity birefringence, the two polarization components of the noise-like pulse still could trap each other, which is similar to the case of conventional solitons. It should be also noted that if the cavity birefringence is too large to be compensated, the soliton trapping would not occur [29].
Fig. 5. Noise-like pulse trapping with a wavelength shift of 4.8 nm. (a) Spectrum of total pulse; (b) Total pulse train. Inset: corresponding autocorrelation trace; (c) Polarization-resolved spectra; (d) Corresponding pulse trains.
As we know, the wavelength separation of soliton trapping could be influenced by the cavity birefringence due to the compensation of the birefringence-induced polarization dispersion [29]. To investigate this issue, the PCs were further adjusted to purposely change the cavity birefringence. In the experiment, it was found that the wavelength shift of noise-
#234289 - $15.00 USD © 2015 OSA
Received 11 Feb 2015; revised 30 Mar 2015; accepted 3 Apr 2015; published 14 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010421 | OPTICS EXPRESS 10425
like pulse is sensitive to the cavity birefringence. For better showing the effect of cavity birefringence on the wavelength shift, the spectral shape of noise-like pulse including the 3dB spectral bandwidth which is similar to the case of Fig. 4 was chosen. Figure 5(a) presents the mode-locked spectrum of noise-like pulse when the PCs were further rotated. Note that the center wavelength varies slightly to be 1567.5 nm. The corresponding pulse-train is shown in Fig. 5(b), whose repetition rate is also 5.58 MHz. Moreover, the autocorrelation trace is provided in the inset of Fig. 5(b), which is a typical one of noise-like pulse. In the following, the vector characteristics of this case were analyzed. Again, the polarization resolved measurement was employed. The resolved optical spectra of the two components are shown in Fig. 5(c). As can be seen here, the center wavelengths of two polarization components are 1567.1 nm (blue curve) and 1571.9 nm (red curve), respectively. Thus, the wavelength shift of pulse trapping reached to 4.8 nm. It should be also noted that the intensity difference of two polarization components is about 8.3 dB in this case, which is much larger than that of Fig. 4(a). It is believed that the large intensity difference of two polarization components was caused by the large ellipticity of vector noise-like pulse. The resolved pulsetrains centered at two wavelengths are shown in Fig. 5(d). Both of them operated at modelocking regime at the fundamental repetition rate with uniform intensities, suggesting that the two polarization components still could trap each other despite of the variation of cavity birefringence. Obviously, in our experiments the wavelength shift of noise-like pulse trapping is much larger than that of a conventional soliton trapping. It has been shown that the tiny pulses inside the noise-like pulse packet possess high peak power, which could be used to supercontinuum generation in optical fiber laser [30]. In this case, the nonlinear birefringence induced by the noise-like pulse could be larger than that induced by the conventional solitons. Therefore, in the case of noise-like operation regime in the fiber laser, the frequency shift of the two polarized components needs to be large enough to compensate the fiber birefringence-induced polarization dispersion. Then, they could trap each other as a groupvelocity locked vector soliton. Because of the high peak power of the noise-like wave packet, it is expected that the wavelength shift would be sensitive to the cavity birefringence, which was also verified by our experimental results. However, note that the individual pulse inside the noise-like wave packet could not be resolved by the autocorrelator. Therefore, the precise peak powers of the noise-like pulses could not be calculated. Moreover, in order to better quantifiably relate the cavity birefringence to the wavelength shift of pulse trapping, the adjustment of cavity birefringence by coiling the fiber sections could be introduced in the laser cavity to control the cavity birefringence. It was demonstrated that the spectral bandwidth of noise-like pulse is related to the average cavity birefringence. Thus, it is expected that larger spectral bandwidth of noise-like pulse as well as the larger wavelength shift could be observed by properly optimizing the cavity birefringence [31]. On the other hand, regarding the vector nature of noise-like pulse, it should be noted that only the pulse trapping was observed. However, by further adjusting the cavity parameters, it is believed that other vector dynamics of noise-like pulse such as PRV and PLV noise-like pulse may be obtained. These results would be beneficial for complementing the understanding of pulse characteristics operating in noise-like regime. 4. Conclusion In conclusion, we have investigated the trapping of the noise-like pulse in a figure-eight fiber laser. To achieve the pulse trapping and propagate as a GLVS, the frequency shift of two orthogonal polarized noise-like pulses occurs. It was also found that the wavelength shift of noise-like pulse trapping was much larger than that of conventional soliton trapping, which could be up to 4.8 nm by properly rotating the PCs. The obtained results reveal the vector characteristics of noise-like pulses in fiber lasers, and further demonstrate that the figure-eight fiber laser could be indeed a good platform for investigating the vector nature of different soliton types.
#234289 - $15.00 USD © 2015 OSA
Received 11 Feb 2015; revised 30 Mar 2015; accepted 3 Apr 2015; published 14 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010421 | OPTICS EXPRESS 10426
Acknowledgments This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11304101, 61307058, 61378036, 11474108, 11204037), the PhD Start-up Fund of Natural Science Foundation of Guangdong Province, China (Grant No. S2013040016320), and the Scientific and Technological Innovation Project of Higher Education Institute, Guangdong, China (Grant No. 2013KJCX0051). Z.-C. Luo acknowledges the financial support from the Guangdong Natural Science Funds for Distinguished Young Scholar (Grant No. 2014A030306019), and the Zhujiang New-star Plan of Science & Technology in Guangzhou City (Grant No. 2014J2200008).
#234289 - $15.00 USD © 2015 OSA
Received 11 Feb 2015; revised 30 Mar 2015; accepted 3 Apr 2015; published 14 Apr 2015 20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010421 | OPTICS EXPRESS 10427
