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Observation of dissipative soliton bound states in a nonlinear multimodal interference based all-fiber all-normal-dispersion mode-locking laser
Optics and Laser Technology 119 (2019) 105626
Contents lists available at ScienceDirect
Optics and Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Full length article
Observation of dissipative soliton bound states in a nonlinear multimodal interference based all-fiber all-normal-dispersion mode-locking laser
T
⁎
Zhiguo Lv , Zhi Yang, DongDong Song, Feng Li, Yang Yang, Xiaojun Yang, Yishan Wang, Qianglong Li, Wei Zhao State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China
H I GH L IG H T S
soliton states are demonstrated in NL-MMI all-normal-dispersion fiber laser. • Bound to the third harmonic mode-locked bound soliton states can be generated. • Up • The temporal distribution characteristics of bound soliton states have been revealed.
A R T I C LE I N FO
A B S T R A C T
Keywords: Nonlinear multimodal interference Mode-locking Bound soliton states Rotating phase
This work, for the first time, demonstrates the generation of the bound soliton states in a nonlinear multimodal interference (NL-MMI) based ytterbium-doped all-normal-dispersion dissipative soliton mode-locking laser. Further, up to the third harmonic mode-locked bound soliton states with rotating phase difference can be generated under the appropriate optimization of the laser cavity parameters. Furthermore, the evolution dynamics and compressibility of the harmonic mode-locked bound soliton states have also been respectively investigated in order to reveal the temporal distribution characteristics of the highly chirped bound soliton states and inter-pulse separation after dispersion compensation.
1. Introduction Benefiting from the advantages of the integrated and maintenancefree physical design, stable and reliable laser operation, and broad application space, passively mode-locked all-fiber ultrashort pulse lasers have been one of the most popular research subjects for the laser community [1]. In addition to the practicability, passively mode-locked fiber lasers can also be used as the effective measures to investigate and explore the soliton nonlinear dynamics [2]. Under the framework of the complex Ginzburg-Landau equation, by reasonably managing and regulating the resonator cavity parameters (laser gain, losses, nonlinear, dispersion, cavity feedback and so on), various existence forms of soliton solutions can be numerically obtained [3–8]. However, among them, bound soliton states are of great interest due to their contributions to the exploration of the basic physical phenomena and potential applications in optical communications [9]. Since proposed by B. Malomed and Akhmediev et al. [10,11], bound soliton states with different phase differences (such as 0, π, ± π/2 or variable) have been widely demonstrated from anomalous to normal dispersion regimes
⁎
[12,13]. For instance, bound soliton states with locked phase and strongly spectra modulation [14], with independently evolving phase and incomplete spectra modulation [15], with rotating phase difference [16], and with vibrating phase [17] have been respectively realized in 1 μm, 1.5 μm and 2 μm mode-locked ultrashort pulse fiber lasers [18–20]. It is commonly believed that as one of the special multi-pulse states, bound soliton states are originated from the interactions between adjacent solitons [21–23], and are relevant with the dispersion and nonlinear effects under stronger pumping [24,25]. Therefore, in most cases, the investigations of the bound soliton states are performed in both anomalous dispersion and dispersion managed mode-locking regimes. In contrast, in all-normal-dispersion domain, due to the removal of the anomalous dispersion segment and solely spectral filtering based pulse shaping mechanism, this kind of mode-locked fiber laser has great tolerance of the nonlinear phase shift and is relatively difficult to realize high-order pulse splitting to generate bound soliton states. Very recently, graded-index multimode fibers (GIMFs) have received much attention in nonlinear optics regime and become very
Corresponding author. E-mail address: [email protected] (Z. Lv).
https://doi.org/10.1016/j.optlastec.2019.105626 Received 8 March 2019; Received in revised form 6 May 2019; Accepted 9 June 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
Optics and Laser Technology 119 (2019) 105626
Z. Lv, et al.
active nonlinear media of research [26]. Especially, the nonlinear multimodal interference (NL-MMI) in GIMF, which was theoretically proposed by Arash Mafi et al. in 2013 [27], has been widely investigated for the generation of the ultrashort pulse mode-locked fiber lasers [28–30]. In experiment, the NL-MMI based saturable absorber (SA) can be easily fabricated by respectively splicing a segment of single mode fiber (SMF) to both ends of the GIMF and constituting an only fiber format SMF-GIMF-SMF structure. More importantly, in addition to act as a SA in the temporal regime, the hybrid fiber structure can also be simultaneously used as a bandpass filter to shape the pulse in the spectrum regime [31,32]. Therefore, compared with the emerging materials (such as carbon nanotubes, few-layer graphene and two-dimensional materials) based all-fiber mode-locked lasers, which essential require additional pulse shaping components, such as in-line bandpass filters and dispersion compensators, the SMF-GIMF-SMF structure based mode-locked fiber lasers have many advantages, such as high damage threshold, easy fabrication, simple and low-cost design, and reliable and stable running. However, according to the reported research results with respect to the NL-MMI based mode-locking schemes [27–33], the length of the GIMF needs to be precisely controlled in order to realize the intensitydependent discrimination and generate equivalent saturable absorption behaviour. This mainly attributes to the nonlinear transmission period with the order of magnitude of micron-scale in SMF-GIMF-SMF fiber structure. Therefore, similar to the previous research methods, in this work we experimentally splice a short section of step-index multimode fiber (SIMF) with 105 μm core diameter to the input end of the GIMF with 62.5 μm core diameter so as to relieve the strict restriction on the length of the GIMF. However, in all-normal-dispersion domain, to obtain the effective saturable absorption and spectral filtering, the structure parameters of the all-fiber SA still need to be reasonably managed, which intrinsically affect its modulation depth, center wavelength and losses. In this paper, the optimization of the structure parameters mainly includes lengths and curving curvatures of the GIMF and SIMF, which are crucial for the generation of the fundamental mode-locked bound soliton states. Secondly, for the buildup of the harmonic mode-locked bound soliton states, the optimal pump power is a crucial one. Therefore, in order to realize the harmonic mode-locked bound soliton states controlled in pulse repetition rate, two single-mode laser diodes (LDs) emitting approximately 520 mW average power are effectively combined through a polarization beam combiner and used to realize stronger pumping. And on this basis, through comparative study and repeated experiments, we demonstrate, to the best of our knowledge, the first experiment generation of the fundamental and harmonic modelocked bound soliton states in a NL-MMI based all-normal-dispersion ytterbium-doped fiber laser. Stable bound soliton states can be respectively obtained at 34.4 MHz, 68.8 MHz and 103.3 MHz repetition rates. Furthermore, we also study the evolution dynamics, temporal distribution characteristics and compressibility of the harmonic modelocked bound soliton states, respectively.
Fig. 1. Schematic diagram of the NL-MMI based harmonic mode-locked boundsoliton-state all-normal-dispersion ytterbium-doped fiber laser. WDM: wavelength-division multiplexer; Yb:fiber: ytterbium-doped fiber; CP: coupler; PC: polarization controller; PI-ISO: broadband polarization-independent isolator; SIMF: step-index multimode fiber; GIMF: graded-index multimode fiber.
solid line shows the broadband fluorescent input with 54 nm spectral bandwidth. Fig. 2(b) shows the nonlinear transmittance of the hybrid fiber structure as a function of the peak power intensity. Based on the measured results under certain bending condition, the modulation depth, saturation fluence and non-saturable losses of the SMF-SIMFGIMF-SMF hybrid fiber structure are respectively 5.9%, 1557 MW/cm2 and 90.4%. It should be noted that the measured spectral bandwidth and SA characteristics are not exactly same for different bending of the SMF-SIMF-GIMF-SMF fiber structure, which mainly attribute to the sensitivity of the transmission period for the variations of lengths and curving curvatures of the GIMF and SIMF.
3. Results and discussion For the presented laser configuration, the cavity length is approximately 5.7 m and the overall group-velocity dispersion is estimated to be 0.125 ps2. In addition, due to the large intra-cavity losses generated from the core mismatch between SMF and multimode fibers (GIMF, SIMF), in order to reach the threshold of the self-phase modulation (SPM) and start the NL-MMI based mode-locking operation, higher pump power is necessary. For these above described parameter settings of the GIMF and SIMF, the bound soliton states at the fundamental repetition rate can be obtained under a pump power of 490 mW. Fig. 3(a) and (b) shows the 34.4 MHz fundamental mode-locked pulse trains on the time scales of 20 ns/div and 2 μs/div, respectively. The manifested homogeneous and uniformly equal-amplitude distribution confirms the mode-locked stability. Fig. 3(c) shows the modulated autocorrelation traces, which are typical characteristics of the bound soliton states. The time separation between these two adjacent lateral peaks is 2.4 ps, and the patterned structure is induced by the direct overlap of these two close and consecutive chirped pulses with large normal dispersion [34]. Fig. 3(e) shows the corresponding mode-locked spectrum centered at 1024.7 nm, which is unmodulated and has no periodic modulation fringes as a direct consequence of rotating phase difference. The generation of the bound soliton states with rotating phase difference is theoretically proposed under the framework of the complex Ginzburg-Landau equation [3] and has also been experimentally demonstrated in bulk solid state lasers [16,35]. Furthermore, the manifested spectrum with steep edges is typical characteristic of the all-normal-dispersion dissipative soliton mode-locking fiber laser. Further, in order to reveal the soliton pair structure under the chirp-free situation, dispersion compensation has been performed. After compression, the separation distance between these two adjacent lateral peaks is shortened to 1.2 ps and simultaneously the autocorrelation trace of the central peak has a 275 fs pulse width assuming a sech2 pulse shape, which is three times less than separation of these two adjacent lateral peaks. In the experiment, stable bound soliton states at the fundamental repetition rate can be self-started and maintained provided that the pump power is between 490 mW and 639 mW. Fig. 4 shows the increase of the output power of the fundamental mode-locked bound soliton states with
2. Experiment setup The mode-locked bound-soliton-state all-normal-dispersion fiber laser is schematically shown in Fig. 1. In experiment, the used broadband polarization-independent isolator (PI-ISO) effectively eliminates the possibilities of the spectral filtering and nonlinear polarization evolution mode-locking. Additionally, to achieve more intuitively understanding for the spectral filtering and SA characteristics of the SMFSIMF-GIMF-SMF fiber structure, its spectral bandwidth and nonlinear transmittance properties are respectively measured under certain bending condition by a home-made broadband fluorescent source and an ultrashort pulse fiber laser with 45 MHz repetition rate, 1030 nm center wavelength and 10 ps pulse duration. The measured spectral bandwidth is 17 nm and shown in Fig. 2(a) in blue solid line. The red 2
Optics and Laser Technology 119 (2019) 105626
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Fig. 2. (a) Transmittance spectrum of the SMF-SIMF-GIMF-SMF hybrid fiber structure. Red solid line shows the broadband fluorescent input with 54 nm spectral bandwidth. (b) Nonlinear transmittance of the SMF-SIMF-GIMF-SMF fiber structure. MD: modulation depth; SI: saturable intensity; NL: non-saturable losses. The used SIMF and GIMF respectively have 1 cm and 15 cm in length. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
locking fiber lasers under stronger pumping [35–37]. Further increasing the pump power beyond 639 mW, the fundamental mode-locked bound soliton states are disappeared. As the pump power is uninterruptedly increased to 808 mW, by fine tuning the polarization controllers to optimize the intra-cavity birefringence, we can obtain the equally spaced second harmonic bound-soliton-state modelocking operation, which repetition rate is 68.8 MHz. Under the invariable polarization control, the second harmonic mode-locked bound soliton states can be maintained and stable operation between 808 mW and the maximum pump power of 992 mW. In addition, by carefully adjusting the polarization controllers under the maximum pump power, the third harmonic mode-locked bound soliton states can also be generated. Fig. 5(a) and (b) shows the 68.8 MHz second harmonic mode-locked bound state pulse trains on the time scales of 20 ns/div and 2 μs/div, respectively. The measured pulse trains with equal-amplitude periodic interval distribution confirm the mode-locked stability. Fig. 6(a) shows the variation of the average power of the second harmonic mode-locked bound solitons with the increment of the pump power. In the experiment, the obtained maximum output power is 29 mW for the full pump power. Fig. 6(b) shows the triangular-like intensity autocorrelation trace, which is less modulation on the top of the autocorrelation trace in comparison to the fundamental mode-locked bound soliton states. The bound soliton states with similar intensity distribution characteristics can also exist in the dispersion management Er-doped fiber laser [34]. The time separation between these two adjacent lateral peaks is 2 ps. Fig. 6(c) shows the unmodulated mode-locked optical spectrum as a direct consequence of the rotating phase difference [16,35]. Same as
Fig. 3. Experiment results of the bound soliton states at the 34.4 MHz fundamental mode-locked repetition rate. (a) and (b) Oscilloscope traces on the time scales of 20 ns/div and 2 μs/div. (c) Chirped pulse duration of a close pulse pair. (d) Compressed intensity autocorrelation trace. (e) Mode-locked spectrum.
Fig. 4. Pump power dependence of the output power at the 34.4 MHz fundamental repetition rate.
increasing pump power. The generation of the bound soliton states with rotating phase difference, we think, is the result of the combined action among nonlinear multimodal interference based SA, large bandpass filter losses, saturated gain, nonlinearity (such as cross-phase modulation and cross-amplitude modulation), and large amounts of normal dispersion, and is intrinsic feature of the dissipative soliton mode-
Fig. 5. Oscilloscope traces on the time scales of 20 ns/div and 2 μs/div. 3
Optics and Laser Technology 119 (2019) 105626
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of the combined action by many factors, such as enhanced nonlinear phase modulation, spectral filter, and saturation of nonlinear gain under stronger pumping. 4. Conclusion In summary, we demonstrate the generation of the fundamental and harmonic mode-locked bound soliton states with NL-MMI based allfiber all-normal-dispersion ytterbium-doped fiber laser for the first time to the best of our knowledge. In the presented fiber laser, the SMFSIMF-GIMF-SMF hybrid fiber structure not only acts as a SA, but also works as a bandpass filter for pulse shaping in the spectral and temporal domains. Highly chirped dissipative soliton bound states are generated and the laser characteristics in the spectral and temporal regimes are discussed in detail at different harmonic mode-locked repetition rates. We experimentally attribute the dynamics of the harmonic mode-locked bound soliton states to the complex nonlinear interactions among NLMMI based SA, large bandpass filter losses, saturated gain, nonlinearity (such as cross-phase modulation, cross-amplitude modulation, enhanced self-phase modulation and so on), and large amounts of normal dispersion.
Fig. 6. Experiment results of the bound soliton states at the 68.8 MHz second harmonic mode-locked repetition rate. (a) Pump power dependence of the output power. (b) Chirped pulse duration of a close pulse pair. (c) Mode-locked spectrum. (d) Compressed pulse pair.
Acknowledgments The work is supported by the National Natural Science Foundation of China (Grant No. 61805274 and 61690222), Chinese Academy of Science “Light of West China” Program (Grant No. XAB2016B21) and National Key R&D Program of China (Grant No. 2018YFB1108000), Guangdong Key R&D Program (Grant No. 2018B090904003). Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.optlastec.2019.105626. References [1] Wolfgang Hänsel, Heinar Hoogland, Michele Giunta, Sebastian Schmid, Tilo Steinmetz, Ralf Doubek, Peter Mayer, Sven Dobner, Carsten Cleff, Marc Fischer, Ronald Holzwarth, All polarization-maintaining fiber laser architecture for robust femtosecond pulse generation, Appl. Phys. B 123 (1) (2017) 41. [2] Xueming Liu, Xiankun Yao, Yudong Cui, Real-time observation of the buildup of soliton molecules, Phys. Rev. Lett. 121 (2018) 023905. [3] J.M. Soto-Crespo, N.N. Akhmediev, Multisoliton regime of pulse generation by lasers passively mode locked with a slow saturable absorber, J. Opt. Soc. Am. B 16 (4) (1999) 674–677. [4] N. Akhmediev, J.M. Soto-Crespo, G. Town, Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex GinzburgLandau equation approach, Phys. Rev. E 63 (2001) 056602. [5] J.M. Soto-Crespo, Ph. Grelu, N. Akhmediev, N. Devine, Soliton complexes in dissipative systems: Vibrating, shaking, and mixed soliton pairs, Phys. Rev. E 75 (2007) 016613. [6] W. Chang, A. Ankiewicz, J.M. Soto-Crespo, N. Akhmediev, Dissipative soliton resonances, Phys. Rev. A 78 (2008) 023830. [7] Aleksandr Zavyalov, Rumen Iliew, Oleg Egorov, Falk Lederer, Dissipative soliton molecules with independently evolving or flipping phases in mode-locked fiber lasers, Phys. Rev. A 80 (2009) 043829. [8] Stefan Wabnitz, Optical turbulence in fiber lasers, Opt. Lett. 39 (6) (2014) 1362–1365. [9] M. Stratmann, T. Pagel, F. Mitshke, Experimental observation of temporal soliton molecules, Phys. Rev. Lett. 95 (2005) 143902. [10] Boris A. Malomed, Bound solitons in the nonlinear Schrödinger-Ginzburg-Landau equation, Phys. Rev. A 44 (1991) 6954. [11] N.N. Akhmediev, A. Ankiewicz, J.M. Soto-Crespo, Multisoliton solutions of the complex Ginzburg-Landau equation, Phys. Rev. Lett. 79 (1997) 4047. [12] Lili Gui, Xiaosheng Xiao, Changxi Yang, Observation of various bound solitons in a carbon-nanotube-based erbium fiber laser, J. Opt. Soc. Am. B 30 (1) (2013) 158–164. [13] Huaqiang Qiu, Xiaosheng Xiao, Pan Wang, Changxi Yang, Observation of soliton molecules in a spatiotemporal mode-locked multimode fiber laser, Opt. Lett. 43 (9) (2018) 1982–1985. [14] D.Y. Tang, W.S. Man, H.Y. Tam, P.D. Drummond, Observation of bound states of solitons in a passively mode-locked fiber laser, Phys. Rev. A 64 (2001) 033814. [15] Bülend Ortaç, Alexandr Zaviyalov, Carsten K. Nielsen, Oleg Egorov, Rumen Iliew,
Fig. 7. Experiment results of the bound soliton states at the 103.3 MHz third harmonic mode-locked repetition rate. (a) and (b) Oscilloscope traces on the time scales of 20 ns/div and 2 μs/div. (c) Mode-locked spectrum. (d) Measured chirped intensity autocorrelation trace. (e) Compressed pulse pair.
the case of the fundamental mode-locked bound soliton states, in order to more clearly reveal the soliton pair structure under the chirp-free situation, dispersion compensation has also been performed for the second harmonic mode-locked bound soliton states. After compression, the time separation between these two adjacent lateral peaks is shortened to 1.4 ps. The measured autocorrelation trace of the central peak has a 360 fs pulse width assuming a sech2 pulse shape. Likewise, for the third harmonic mode-locking operation, we study the laser characteristics of the bound states of the dissipative solitons in the spectral and temporal domains. The measured equal-amplitude and uniformly-spaced mode-locking pulse trains, as shown in Fig. 7(a) and (b), demonstrate the mode-locked stability. Fig. 7(c) illustrates the mode-locked output spectrum with 11 nm FWHM and centered at 1024 nm. The measured chirped and compressed intensity autocorrelation traces of the bound soliton states are respectively shown in Fig. 7(d) and (e). After compression, the time separation between these two adjacent lateral peaks is 1.37 ps. The measured autocorrelation trace of the central peak has a 323 fs pulse width assuming a sech2 pulse shape. Similarly, the highly chirped intensity autocorrelation trace is less modulation on the top of the autocorrelation trace in comparison to the fundamental and second harmonic mode-locked bound soliton states. We think the gradually diminished modulation in the autocorrelation traces, as shown in Figs. 6(b) and 7(d), is probably the result 4
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5
Contents lists available at ScienceDirect
Optics and Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Full length article
Observation of dissipative soliton bound states in a nonlinear multimodal interference based all-fiber all-normal-dispersion mode-locking laser
T
⁎
Zhiguo Lv , Zhi Yang, DongDong Song, Feng Li, Yang Yang, Xiaojun Yang, Yishan Wang, Qianglong Li, Wei Zhao State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China
H I GH L IG H T S
soliton states are demonstrated in NL-MMI all-normal-dispersion fiber laser. • Bound to the third harmonic mode-locked bound soliton states can be generated. • Up • The temporal distribution characteristics of bound soliton states have been revealed.
A R T I C LE I N FO
A B S T R A C T
Keywords: Nonlinear multimodal interference Mode-locking Bound soliton states Rotating phase
This work, for the first time, demonstrates the generation of the bound soliton states in a nonlinear multimodal interference (NL-MMI) based ytterbium-doped all-normal-dispersion dissipative soliton mode-locking laser. Further, up to the third harmonic mode-locked bound soliton states with rotating phase difference can be generated under the appropriate optimization of the laser cavity parameters. Furthermore, the evolution dynamics and compressibility of the harmonic mode-locked bound soliton states have also been respectively investigated in order to reveal the temporal distribution characteristics of the highly chirped bound soliton states and inter-pulse separation after dispersion compensation.
1. Introduction Benefiting from the advantages of the integrated and maintenancefree physical design, stable and reliable laser operation, and broad application space, passively mode-locked all-fiber ultrashort pulse lasers have been one of the most popular research subjects for the laser community [1]. In addition to the practicability, passively mode-locked fiber lasers can also be used as the effective measures to investigate and explore the soliton nonlinear dynamics [2]. Under the framework of the complex Ginzburg-Landau equation, by reasonably managing and regulating the resonator cavity parameters (laser gain, losses, nonlinear, dispersion, cavity feedback and so on), various existence forms of soliton solutions can be numerically obtained [3–8]. However, among them, bound soliton states are of great interest due to their contributions to the exploration of the basic physical phenomena and potential applications in optical communications [9]. Since proposed by B. Malomed and Akhmediev et al. [10,11], bound soliton states with different phase differences (such as 0, π, ± π/2 or variable) have been widely demonstrated from anomalous to normal dispersion regimes
⁎
[12,13]. For instance, bound soliton states with locked phase and strongly spectra modulation [14], with independently evolving phase and incomplete spectra modulation [15], with rotating phase difference [16], and with vibrating phase [17] have been respectively realized in 1 μm, 1.5 μm and 2 μm mode-locked ultrashort pulse fiber lasers [18–20]. It is commonly believed that as one of the special multi-pulse states, bound soliton states are originated from the interactions between adjacent solitons [21–23], and are relevant with the dispersion and nonlinear effects under stronger pumping [24,25]. Therefore, in most cases, the investigations of the bound soliton states are performed in both anomalous dispersion and dispersion managed mode-locking regimes. In contrast, in all-normal-dispersion domain, due to the removal of the anomalous dispersion segment and solely spectral filtering based pulse shaping mechanism, this kind of mode-locked fiber laser has great tolerance of the nonlinear phase shift and is relatively difficult to realize high-order pulse splitting to generate bound soliton states. Very recently, graded-index multimode fibers (GIMFs) have received much attention in nonlinear optics regime and become very
Corresponding author. E-mail address: [email protected] (Z. Lv).
https://doi.org/10.1016/j.optlastec.2019.105626 Received 8 March 2019; Received in revised form 6 May 2019; Accepted 9 June 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
Optics and Laser Technology 119 (2019) 105626
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active nonlinear media of research [26]. Especially, the nonlinear multimodal interference (NL-MMI) in GIMF, which was theoretically proposed by Arash Mafi et al. in 2013 [27], has been widely investigated for the generation of the ultrashort pulse mode-locked fiber lasers [28–30]. In experiment, the NL-MMI based saturable absorber (SA) can be easily fabricated by respectively splicing a segment of single mode fiber (SMF) to both ends of the GIMF and constituting an only fiber format SMF-GIMF-SMF structure. More importantly, in addition to act as a SA in the temporal regime, the hybrid fiber structure can also be simultaneously used as a bandpass filter to shape the pulse in the spectrum regime [31,32]. Therefore, compared with the emerging materials (such as carbon nanotubes, few-layer graphene and two-dimensional materials) based all-fiber mode-locked lasers, which essential require additional pulse shaping components, such as in-line bandpass filters and dispersion compensators, the SMF-GIMF-SMF structure based mode-locked fiber lasers have many advantages, such as high damage threshold, easy fabrication, simple and low-cost design, and reliable and stable running. However, according to the reported research results with respect to the NL-MMI based mode-locking schemes [27–33], the length of the GIMF needs to be precisely controlled in order to realize the intensitydependent discrimination and generate equivalent saturable absorption behaviour. This mainly attributes to the nonlinear transmission period with the order of magnitude of micron-scale in SMF-GIMF-SMF fiber structure. Therefore, similar to the previous research methods, in this work we experimentally splice a short section of step-index multimode fiber (SIMF) with 105 μm core diameter to the input end of the GIMF with 62.5 μm core diameter so as to relieve the strict restriction on the length of the GIMF. However, in all-normal-dispersion domain, to obtain the effective saturable absorption and spectral filtering, the structure parameters of the all-fiber SA still need to be reasonably managed, which intrinsically affect its modulation depth, center wavelength and losses. In this paper, the optimization of the structure parameters mainly includes lengths and curving curvatures of the GIMF and SIMF, which are crucial for the generation of the fundamental mode-locked bound soliton states. Secondly, for the buildup of the harmonic mode-locked bound soliton states, the optimal pump power is a crucial one. Therefore, in order to realize the harmonic mode-locked bound soliton states controlled in pulse repetition rate, two single-mode laser diodes (LDs) emitting approximately 520 mW average power are effectively combined through a polarization beam combiner and used to realize stronger pumping. And on this basis, through comparative study and repeated experiments, we demonstrate, to the best of our knowledge, the first experiment generation of the fundamental and harmonic modelocked bound soliton states in a NL-MMI based all-normal-dispersion ytterbium-doped fiber laser. Stable bound soliton states can be respectively obtained at 34.4 MHz, 68.8 MHz and 103.3 MHz repetition rates. Furthermore, we also study the evolution dynamics, temporal distribution characteristics and compressibility of the harmonic modelocked bound soliton states, respectively.
Fig. 1. Schematic diagram of the NL-MMI based harmonic mode-locked boundsoliton-state all-normal-dispersion ytterbium-doped fiber laser. WDM: wavelength-division multiplexer; Yb:fiber: ytterbium-doped fiber; CP: coupler; PC: polarization controller; PI-ISO: broadband polarization-independent isolator; SIMF: step-index multimode fiber; GIMF: graded-index multimode fiber.
solid line shows the broadband fluorescent input with 54 nm spectral bandwidth. Fig. 2(b) shows the nonlinear transmittance of the hybrid fiber structure as a function of the peak power intensity. Based on the measured results under certain bending condition, the modulation depth, saturation fluence and non-saturable losses of the SMF-SIMFGIMF-SMF hybrid fiber structure are respectively 5.9%, 1557 MW/cm2 and 90.4%. It should be noted that the measured spectral bandwidth and SA characteristics are not exactly same for different bending of the SMF-SIMF-GIMF-SMF fiber structure, which mainly attribute to the sensitivity of the transmission period for the variations of lengths and curving curvatures of the GIMF and SIMF.
3. Results and discussion For the presented laser configuration, the cavity length is approximately 5.7 m and the overall group-velocity dispersion is estimated to be 0.125 ps2. In addition, due to the large intra-cavity losses generated from the core mismatch between SMF and multimode fibers (GIMF, SIMF), in order to reach the threshold of the self-phase modulation (SPM) and start the NL-MMI based mode-locking operation, higher pump power is necessary. For these above described parameter settings of the GIMF and SIMF, the bound soliton states at the fundamental repetition rate can be obtained under a pump power of 490 mW. Fig. 3(a) and (b) shows the 34.4 MHz fundamental mode-locked pulse trains on the time scales of 20 ns/div and 2 μs/div, respectively. The manifested homogeneous and uniformly equal-amplitude distribution confirms the mode-locked stability. Fig. 3(c) shows the modulated autocorrelation traces, which are typical characteristics of the bound soliton states. The time separation between these two adjacent lateral peaks is 2.4 ps, and the patterned structure is induced by the direct overlap of these two close and consecutive chirped pulses with large normal dispersion [34]. Fig. 3(e) shows the corresponding mode-locked spectrum centered at 1024.7 nm, which is unmodulated and has no periodic modulation fringes as a direct consequence of rotating phase difference. The generation of the bound soliton states with rotating phase difference is theoretically proposed under the framework of the complex Ginzburg-Landau equation [3] and has also been experimentally demonstrated in bulk solid state lasers [16,35]. Furthermore, the manifested spectrum with steep edges is typical characteristic of the all-normal-dispersion dissipative soliton mode-locking fiber laser. Further, in order to reveal the soliton pair structure under the chirp-free situation, dispersion compensation has been performed. After compression, the separation distance between these two adjacent lateral peaks is shortened to 1.2 ps and simultaneously the autocorrelation trace of the central peak has a 275 fs pulse width assuming a sech2 pulse shape, which is three times less than separation of these two adjacent lateral peaks. In the experiment, stable bound soliton states at the fundamental repetition rate can be self-started and maintained provided that the pump power is between 490 mW and 639 mW. Fig. 4 shows the increase of the output power of the fundamental mode-locked bound soliton states with
2. Experiment setup The mode-locked bound-soliton-state all-normal-dispersion fiber laser is schematically shown in Fig. 1. In experiment, the used broadband polarization-independent isolator (PI-ISO) effectively eliminates the possibilities of the spectral filtering and nonlinear polarization evolution mode-locking. Additionally, to achieve more intuitively understanding for the spectral filtering and SA characteristics of the SMFSIMF-GIMF-SMF fiber structure, its spectral bandwidth and nonlinear transmittance properties are respectively measured under certain bending condition by a home-made broadband fluorescent source and an ultrashort pulse fiber laser with 45 MHz repetition rate, 1030 nm center wavelength and 10 ps pulse duration. The measured spectral bandwidth is 17 nm and shown in Fig. 2(a) in blue solid line. The red 2
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Fig. 2. (a) Transmittance spectrum of the SMF-SIMF-GIMF-SMF hybrid fiber structure. Red solid line shows the broadband fluorescent input with 54 nm spectral bandwidth. (b) Nonlinear transmittance of the SMF-SIMF-GIMF-SMF fiber structure. MD: modulation depth; SI: saturable intensity; NL: non-saturable losses. The used SIMF and GIMF respectively have 1 cm and 15 cm in length. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
locking fiber lasers under stronger pumping [35–37]. Further increasing the pump power beyond 639 mW, the fundamental mode-locked bound soliton states are disappeared. As the pump power is uninterruptedly increased to 808 mW, by fine tuning the polarization controllers to optimize the intra-cavity birefringence, we can obtain the equally spaced second harmonic bound-soliton-state modelocking operation, which repetition rate is 68.8 MHz. Under the invariable polarization control, the second harmonic mode-locked bound soliton states can be maintained and stable operation between 808 mW and the maximum pump power of 992 mW. In addition, by carefully adjusting the polarization controllers under the maximum pump power, the third harmonic mode-locked bound soliton states can also be generated. Fig. 5(a) and (b) shows the 68.8 MHz second harmonic mode-locked bound state pulse trains on the time scales of 20 ns/div and 2 μs/div, respectively. The measured pulse trains with equal-amplitude periodic interval distribution confirm the mode-locked stability. Fig. 6(a) shows the variation of the average power of the second harmonic mode-locked bound solitons with the increment of the pump power. In the experiment, the obtained maximum output power is 29 mW for the full pump power. Fig. 6(b) shows the triangular-like intensity autocorrelation trace, which is less modulation on the top of the autocorrelation trace in comparison to the fundamental mode-locked bound soliton states. The bound soliton states with similar intensity distribution characteristics can also exist in the dispersion management Er-doped fiber laser [34]. The time separation between these two adjacent lateral peaks is 2 ps. Fig. 6(c) shows the unmodulated mode-locked optical spectrum as a direct consequence of the rotating phase difference [16,35]. Same as
Fig. 3. Experiment results of the bound soliton states at the 34.4 MHz fundamental mode-locked repetition rate. (a) and (b) Oscilloscope traces on the time scales of 20 ns/div and 2 μs/div. (c) Chirped pulse duration of a close pulse pair. (d) Compressed intensity autocorrelation trace. (e) Mode-locked spectrum.
Fig. 4. Pump power dependence of the output power at the 34.4 MHz fundamental repetition rate.
increasing pump power. The generation of the bound soliton states with rotating phase difference, we think, is the result of the combined action among nonlinear multimodal interference based SA, large bandpass filter losses, saturated gain, nonlinearity (such as cross-phase modulation and cross-amplitude modulation), and large amounts of normal dispersion, and is intrinsic feature of the dissipative soliton mode-
Fig. 5. Oscilloscope traces on the time scales of 20 ns/div and 2 μs/div. 3
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of the combined action by many factors, such as enhanced nonlinear phase modulation, spectral filter, and saturation of nonlinear gain under stronger pumping. 4. Conclusion In summary, we demonstrate the generation of the fundamental and harmonic mode-locked bound soliton states with NL-MMI based allfiber all-normal-dispersion ytterbium-doped fiber laser for the first time to the best of our knowledge. In the presented fiber laser, the SMFSIMF-GIMF-SMF hybrid fiber structure not only acts as a SA, but also works as a bandpass filter for pulse shaping in the spectral and temporal domains. Highly chirped dissipative soliton bound states are generated and the laser characteristics in the spectral and temporal regimes are discussed in detail at different harmonic mode-locked repetition rates. We experimentally attribute the dynamics of the harmonic mode-locked bound soliton states to the complex nonlinear interactions among NLMMI based SA, large bandpass filter losses, saturated gain, nonlinearity (such as cross-phase modulation, cross-amplitude modulation, enhanced self-phase modulation and so on), and large amounts of normal dispersion.
Fig. 6. Experiment results of the bound soliton states at the 68.8 MHz second harmonic mode-locked repetition rate. (a) Pump power dependence of the output power. (b) Chirped pulse duration of a close pulse pair. (c) Mode-locked spectrum. (d) Compressed pulse pair.
Acknowledgments The work is supported by the National Natural Science Foundation of China (Grant No. 61805274 and 61690222), Chinese Academy of Science “Light of West China” Program (Grant No. XAB2016B21) and National Key R&D Program of China (Grant No. 2018YFB1108000), Guangdong Key R&D Program (Grant No. 2018B090904003). Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.optlastec.2019.105626. References [1] Wolfgang Hänsel, Heinar Hoogland, Michele Giunta, Sebastian Schmid, Tilo Steinmetz, Ralf Doubek, Peter Mayer, Sven Dobner, Carsten Cleff, Marc Fischer, Ronald Holzwarth, All polarization-maintaining fiber laser architecture for robust femtosecond pulse generation, Appl. Phys. B 123 (1) (2017) 41. [2] Xueming Liu, Xiankun Yao, Yudong Cui, Real-time observation of the buildup of soliton molecules, Phys. Rev. Lett. 121 (2018) 023905. [3] J.M. Soto-Crespo, N.N. Akhmediev, Multisoliton regime of pulse generation by lasers passively mode locked with a slow saturable absorber, J. Opt. Soc. Am. B 16 (4) (1999) 674–677. [4] N. Akhmediev, J.M. Soto-Crespo, G. Town, Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex GinzburgLandau equation approach, Phys. Rev. E 63 (2001) 056602. [5] J.M. Soto-Crespo, Ph. Grelu, N. Akhmediev, N. Devine, Soliton complexes in dissipative systems: Vibrating, shaking, and mixed soliton pairs, Phys. Rev. E 75 (2007) 016613. [6] W. Chang, A. Ankiewicz, J.M. Soto-Crespo, N. Akhmediev, Dissipative soliton resonances, Phys. Rev. A 78 (2008) 023830. [7] Aleksandr Zavyalov, Rumen Iliew, Oleg Egorov, Falk Lederer, Dissipative soliton molecules with independently evolving or flipping phases in mode-locked fiber lasers, Phys. Rev. A 80 (2009) 043829. [8] Stefan Wabnitz, Optical turbulence in fiber lasers, Opt. Lett. 39 (6) (2014) 1362–1365. [9] M. Stratmann, T. Pagel, F. Mitshke, Experimental observation of temporal soliton molecules, Phys. Rev. Lett. 95 (2005) 143902. [10] Boris A. Malomed, Bound solitons in the nonlinear Schrödinger-Ginzburg-Landau equation, Phys. Rev. A 44 (1991) 6954. [11] N.N. Akhmediev, A. Ankiewicz, J.M. Soto-Crespo, Multisoliton solutions of the complex Ginzburg-Landau equation, Phys. Rev. Lett. 79 (1997) 4047. [12] Lili Gui, Xiaosheng Xiao, Changxi Yang, Observation of various bound solitons in a carbon-nanotube-based erbium fiber laser, J. Opt. Soc. Am. B 30 (1) (2013) 158–164. [13] Huaqiang Qiu, Xiaosheng Xiao, Pan Wang, Changxi Yang, Observation of soliton molecules in a spatiotemporal mode-locked multimode fiber laser, Opt. Lett. 43 (9) (2018) 1982–1985. [14] D.Y. Tang, W.S. Man, H.Y. Tam, P.D. Drummond, Observation of bound states of solitons in a passively mode-locked fiber laser, Phys. Rev. A 64 (2001) 033814. [15] Bülend Ortaç, Alexandr Zaviyalov, Carsten K. Nielsen, Oleg Egorov, Rumen Iliew,
Fig. 7. Experiment results of the bound soliton states at the 103.3 MHz third harmonic mode-locked repetition rate. (a) and (b) Oscilloscope traces on the time scales of 20 ns/div and 2 μs/div. (c) Mode-locked spectrum. (d) Measured chirped intensity autocorrelation trace. (e) Compressed pulse pair.
the case of the fundamental mode-locked bound soliton states, in order to more clearly reveal the soliton pair structure under the chirp-free situation, dispersion compensation has also been performed for the second harmonic mode-locked bound soliton states. After compression, the time separation between these two adjacent lateral peaks is shortened to 1.4 ps. The measured autocorrelation trace of the central peak has a 360 fs pulse width assuming a sech2 pulse shape. Likewise, for the third harmonic mode-locking operation, we study the laser characteristics of the bound states of the dissipative solitons in the spectral and temporal domains. The measured equal-amplitude and uniformly-spaced mode-locking pulse trains, as shown in Fig. 7(a) and (b), demonstrate the mode-locked stability. Fig. 7(c) illustrates the mode-locked output spectrum with 11 nm FWHM and centered at 1024 nm. The measured chirped and compressed intensity autocorrelation traces of the bound soliton states are respectively shown in Fig. 7(d) and (e). After compression, the time separation between these two adjacent lateral peaks is 1.37 ps. The measured autocorrelation trace of the central peak has a 323 fs pulse width assuming a sech2 pulse shape. Similarly, the highly chirped intensity autocorrelation trace is less modulation on the top of the autocorrelation trace in comparison to the fundamental and second harmonic mode-locked bound soliton states. We think the gradually diminished modulation in the autocorrelation traces, as shown in Figs. 6(b) and 7(d), is probably the result 4
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