locked thulium-doped fiber lasers - OSA Publishing

Pulse-shaping mechanisms in passively modelocked thulium-doped fiber lasers Huihui Li, Jiang Liu, Zhaochen Cheng, Jia Xu, Fangzhou Tan, and Pu Wang* National Center of Laser Technology; Institute of Laser Engineering, Beijing University of Technology, Beijing 100124, China * [email protected]

Abstract: Different pulse-shaping mechanisms were investigated experimentally and numerically in passively mode-locked thulium-doped fiber lasers. Conventional solitons were demonstrated in a passively semiconductor saturable absorber mirror mode-locked anomalous dispersion thulium-doped fiber laser. With normal dispersion fiber and spectral filter added in cavity, pulse-shaping processes were theoretically analyzed in the presence of dispersion map and dissipation in thuliumdoped fiber lasers. The existence of parabolic pulse as nonlinear attraction was proved and distinct pulse intensity profiles evolution from Gaussian shape to parabolic shape was proposed in dissipative dispersion-managed thulium-doped fiber lasers. ©2015 Optical Society of America OCIS codes: (140.3510) Lasers, fiber; (140.4050) Mode-locked lasers; (140.7090) Ultrafast lasers.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Self-starting passively mode-locked fiber ring soliton laser exploiting nonlinear polarization rotation,” Electron. Lett. 28(15), 1391–1393 (1992). L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B 65(2), 277–294 (1997). J. Liu, Q. Wang, and P. Wang, “High average power picosecond pulse generation from a thulium-doped all-fiber MOPA system,” Opt. Express 20(20), 22442–22447 (2012). N. M. Fried, “Thulium fiber laser lithotripsy: An in vitro analysis of stone fragmentation using a modulated 110watt Thulium fiber laser at 1.94 microm,” Lasers Surg. Med. 37(1), 53–58 (2005). D. Creeden, P. A. Ketteridge, P. A. Budni, S. D. Setzler, Y. E. Young, J. C. McCarthy, K. Zawilski, P. G. Schunemann, T. M. Pollak, E. P. Chicklis, and M. Jiang, “Mid-infrared ZnGeP2 parametric oscillator directly pumped by a pulsed 2 microm Tm-doped fiber laser,” Opt. Lett. 33(4), 315–317 (2008). R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008). L. Nelson, E. Ippen, and H. Haus, “Broadly tunable sub-500 fs pulses from an additive-pulse mode-locked thulium-doped fiber ring laser,” Appl. Phys. Lett. 67(1), 19–21 (1995). P. Wan, L. M. Yang, and J. Liu, “High power 2 µm femtosecond fiber laser,” Opt. Express 21(18), 21374–21379 (2013). A. A. Krylov, M. A. Chernyshova, D. S. Chernykh, A. K. Senatorov, I. M. Tupitsyn, P. G. Kryukov, and E. M. Dianov, “High-power thulium-doped fibre laser with intracavity dispersion management,” Quantum Electron. 42(5), 427–431 (2012). C. Rudy, M. Digonnet, R. Byer, S. Jiang, and Q. Wang, “Thulium-doped Germanosilicate Mode-locked Fiber Lasers,” in Lasers, Sources, and Related Photonic Devices, OSA Technical Digest (CD) (Optical Society of America, 2012), paper FTh4A.4. K. Kieu and F. W. Wise, “Soliton thulium-doped fiber laser with carbon nanotube saturable absorber,” IEEE Photon. Technol. Lett. 21(3), 128–130 (2009). B. G. Bale, S. Boscolo, and S. K. Turitsyn, “Dissipative dispersion-managed solitons in mode-locked lasers,” Opt. Lett. 34(21), 3286–3288 (2009). B. G. Bale, S. Boscolo, J. N. Kutz, and S. K. Turitsyn, “Intracavity dynamics in high-power mode-locked fiber lasers,” Phys. Rev. A 81(3), 033828 (2010). F. Haxsen, A. Ruehl, M. Engelbrecht, D. Wandt, U. Morgner, and D. Kracht, “Stretched-pulse operation of a thulium-doped fiber laser,” Opt. Express 16(25), 20471–20476 (2008). R. Gumenyuk, I. Vartiainen, H. Tuovinen, and O. G. Okhotnikov, “Dissipative dispersion-managed soliton 2 μm thulium/holmium fiber laser,” Opt. Lett. 36(5), 609–611 (2011).

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16. M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84(26 Pt 1), 6010–6013 (2000). 17. F. O. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92(21), 213902 (2004). 18. C. Finot, L. Provost, P. Petropoulos, and D. J. Richardson, “Parabolic pulse generation through passive nonlinear pulse reshaping in a normally dispersive two segment fiber device,” Opt. Express 15(3), 852–864 (2007). 19. M. L. Dennis and I. N. Duling, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30(6), 1469–1477 (1994). 20. Q. Q. Wang, T. Chen, M. S. Li, B. T. Zhang, Y. F. Lu, and K. P. Chen, “All-fiber ultrafast thulium-doped fiber ring laser with dissipative soliton and noise-like output in normal dispersion by single-wall carbon nanotubes,” Appl. Phys. Lett. 103(1), 011103 (2013). 21. K. Kieu, W. H. Renninger, A. Chong, and F. W. Wise, “Sub-100 fs pulses at watt-level powers from a dissipative-soliton fiber laser,” Opt. Lett. 34(5), 593–595 (2009). 22. I. A. Yarutkina and O. V. Shtyrina, “Mathematical modelling of dispersion-managed thulium/holmium fibre lasers,” Quantum Electron. 43(11), 1019–1023 (2013). 23. H. Xia, H. Li, X. Zhang, S. Zhang, X. Tang, and Y. Liu, “Characteristics of dissipative solitons in an all-fiber thulium-doped fiber ring laser,” Opt. Eng. 52(5), 054201 (2013). 24. W. H. Renninger, A. Chong, and F. W. Wise, “Pulse shaping and evolution in normal-dispersion mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 18(1), 389–398 (2012). 25. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6(6), 1159–1166 (1989). 26. 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). 27. H. H. Li, J. Liu, Z. C. Cheng, J. Xu, F. Z. Tan, and P. Wang, “Characteristics of pulses in passively mode-locked thulium-doped fiber laser,” in Advanced Solid State Lasers (Optical Society of America, 2014), paper ATh2A– 34. 28. S. K. Turitsyn, B. G. Bale, and M. P. Fedoruk, “Dispersion-managed solitons in fibre systems and lasers,” Phys. Rep. 521(4), 135–203 (2012). 29. W. J. Tomlinson, R. H. Stolen, and A. M. Johnson, “Optical wave breaking of pulses in nonlinear optical fibers,” Opt. Lett. 10(9), 457–459 (1985). 30. D. Anderson, M. Desaix, M. Lisak, and M. L. Quiroga-Teixeiro, “Wave-breaking in nonlinear optical fibers,” J. Opt. Soc. Am. B 9(8), 1358–1361 (1992). 31. B. Oktem, C. Ülgüdür, and F. Ö. Ilday, “Soliton–similariton fibre laser,” Nat. Photonics 4(5), 307–311 (2010). 32. F. Stutzki, C. Gaida, M. Gebhardt, F. Jansen, A. Wienke, U. Zeitner, F. Fuchs, C. Jauregui, D. Wandt, D. Kracht, J. Limpert, and A. Tünnermann, “152 W average power Tm-doped fiber CPA system,” Opt. Lett. 39(16), 4671– 4674 (2014).

1. Introduction Fiber lasers offer significant advantages such as great stability, maintenance-free operation, and low cost, and have been investigated extensively in the past two decades [1–3]. Nowadays thulium-doped fiber lasers become a subject of growing interest and rapid development because of their increasingly application requirements in medicine [4], mid-IR generation [5] and semiconductor micromachining [6]. In particularly, passively mode-locked thulium-doped fiber lasers have been demonstrated using nonlinear polarization rotation (NPR) [7], semiconductor saturable absorber mirror (SESAM) [8–10], and carbon nanotubebased saturable absorber [11]. Normally, pulse-shaping mechanisms in mode-locked fiber lasers were dominated by group-velocity dispersion (GVD) and nonlinear effects of the constructed fibers. The anomalous dispersion of most silica fiber around 2 μm restricted thulium-doped fiber lasers to conventional soliton regime, and wave breaking or multiple pulsing occurred at high pulse energy. Normal dispersion components and spectral filter were added in thulium-doped fiber lasers reasonably for robust performance of high-power operation. The stable dispersion-managed solutions produced in dispersion-managed cavity were successfully predicted and analyzed in theory [12,13]. The breathing nature of dispersion-managed thulium-doped fiber lasers could effectively reduce the intra-cavity accumulated nonlinear phase shift, and distinctly different pulse evolutions and characteristics of experimental results were observed with different cavity dispersion maps. Haxsen et al. experimentally demonstrated the stretched pulse with reflection grating providing normal dispersion in thulium-doped fiber laser with nearly zero net cavity dispersion [14]. R. Gumenyuk et al. declared the dissipative dispersion-managed soliton in mode-locked thulium-

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Received 16 Dec 2014; revised 12 Feb 2015; accepted 13 Feb 2015; published 2 Mar 2015 9 Mar 2015 | Vol. 23, No. 5 | DOI:10.1364/OE.23.006292 | OPTICS EXPRESS 6293

holmium fiber laser by introducing chirped fiber Bragg grating into laser cavity [15]. Numerical simulation of comparative study strictly to these experimental observations became necessary to define the pulse-shaping mechanisms in dispersion-managed thuliumdoped fiber lasers. However, for better performance, more energetic pulse-shaping dynamics was required in thulium-doped fiber lasers. The demonstration of parabolic pulse in the normally dispersive amplifier, which could propagate at high power without undergoing pulse distortion, has generated a great deal of attention [16,17]. Besides in the active normally dispersive fiber, parabolic pulses could also be formed in passive normal dispersion fiber [18]. In addition to wide-ranging practical significance, the parabolic pulse as nonlinear attraction preserved in dispersion-managed thulium-doped fiber lasers has fundamental research interest. In this paper, conventional solitons with high repetition rate of 108 MHz were obtained experimentally in a passively SESAM mode-locked thulium-doped fiber laser. Pulse-shaping mechanisms of dissipative solitons and stretched pulses with different cavity dispersion maps in dispersion-managed thulium-doped fiber lasers were demonstrated in numerical simulation. With the optimized parameters of cavity components, parabolic pulses were proposed in dispersion-managed thulium-doped fiber lasers. Distinct pulse intensity profiles evolution from Gaussian shape to parabolic shape in thulium-doped fiber lasers was reported for the first time. The spectral filter played a key role as dissipative effect to compensate the excessive nonlinear spectrum expansion in the convergence process. Femtosecond pulse with a peak power of 140 kW could be directly obtained by external dechirped compression. 2. Conventional solitons The conventional soliton thulium-doped fiber laser was constructed in Fig. 1, which had a linear cavity confined between a SESAM on one end and a highly reflective broadband mirror (HR) on the other end. The total length of the fiber laser was ~0.93 m. A segment of 0.6 m long thulium-doped single-clad fiber was used as the gain medium, which had group-velocity dispersion of about −0.064 ps2/m. The core of the thulium-doped gain fiber had a diameter of 9.0 μm and a numerical aperture (NA) of 0.16. Its cladding had a diameter of 125 μm, the core-absorption was ~20 dB/m at 1550 nm. The homemade single-mode continuous wave erbium-doped fiber laser was used as pump source via a 1550/2000 nm wavelength division multiplexer, which had a center wavelength of 1550 nm and maximum output power of 900 mW. The laser was out of the 30% port of the 30/70 tap coupler while the 70% was spliced back into the laser cavity. All the other fiber segments used in the laser cavity were a total length of ~0.33 m standard single-mode fiber (SMF) with GVD of about −0.067 ps2/m. The total net dispersion of the cavity was estimated to be −0.06 ps2 without any dispersion compensating components. The SESAM in the experiment had a modulation depth of 20%, non-saturable loss of 16%, relaxation time of 500 fs, and saturation fluence of 35 μJ/cm2.

Fig. 1. Schematic setup of passively mode-locked thulium-doped fiber laser. SESAM, semiconductor saturable absorber mirror; WDM, 1550/2000 nm wavelength division multiplexer coupler; HR, high-reflectivity broadband mirror.

Stable self-started mode-locked pulses of the thulium-doped fiber laser occurred at about 225 mW incident pump power and the pulse repetition rate was 108 MHz, which agreed with the cavity length. The laser pulses were monitored using a 1 GHz oscilloscope and a 1.8 GHz

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Received 16 Dec 2014; revised 12 Feb 2015; accepted 13 Feb 2015; published 2 Mar 2015 9 Mar 2015 | Vol. 23, No. 5 | DOI:10.1364/OE.23.006292 | OPTICS EXPRESS 6294

InGaAs photodetector. The conventional soliton laser could be stable long-lasting mode locking with single pulse operation in the range of incident pump powers of 225~580 mW.

Fig. 2. (a) Stable pulse train of the conventional soliton thulium-doped fiber laser. (b) Average output power with the increase of incident pump power.

Figure 2(a) showed the measured oscilloscope trace over an 80 ns time scale, the laser emitted single pulses with no pulse breaking or multiple pulse operation. Figure 2(b) showed the average output power with the increase of incident pump power. The results showed that the average output power for the fiber laser could be up to 70 mW at a slope efficiency of 21%, corresponding to single pulse energy of 0.65 nJ, under the pump power of 580 mW. In addition, we also measured the radio frequency (RF) spectrum of the mode-locked thuliumdoped fiber laser using a 7.5 GHz signal analyzer (Agilent N9000A-507) and a fast photodetector with a rising time of 35 ps. The signal-to-background ratio was up to 70 dB, indicating that the passively mode-locked state was stable.

Fig. 3. (a) Optical spectrum (b) Autocorrelation trace at maximum average output power of the conventional soliton in thulium-doped fiber laser. Dashed curve: simulated fit.

Figure 3(a) showed optical spectrum of the mode-locked fiber laser measured by optical spectral analyzer (YOKOGAWA AQ 6375) with resolution of 0.05 nm. It should be noted that for increasing incident pump power above the mode-locking threshold, a slight increase of spectral bandwidth could be observed, and no significant changes of spectral intensity shape could be observed. The center wavelength was 1945 nm and spectral bandwidth (FWHM) was 6.1 nm measured at maximum average output power. It should be noted that several pairs of sidebands were visible on both sides of central wavelength [19]. We performed a numerical simulation, based on the split step Fourier method. The simulation started from quantum noise until steady state was achieved. All the parameters in simulation were similar to those of the experimental setup. The calculated spectral characteristics of mode-locked conventional solitons were consistent with experimental observations, as shown in Fig. 3(a). Similar Kelly sidebands were clearly observed in optical spectrum, which confirmed the typical conventional soliton feature of mode-locked fiber lasers. The sideband positions agreed with the theoretical prediction in the soliton fiber laser cavity. These sidebands would limit the performance of the power and energy amplification and chirped

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Received 16 Dec 2014; revised 12 Feb 2015; accepted 13 Feb 2015; published 2 Mar 2015 9 Mar 2015 | Vol. 23, No. 5 | DOI:10.1364/OE.23.006292 | OPTICS EXPRESS 6295

fiber Bragg grating with normal dispersion could be added in cavity to remove them [8]. The pulse width was characterized by our autocorrelator (FR-103XL). Figure 3(b) was the autocorrelation trace of the conventional soliton in thulium-doped fiber laser. It had a FWHM width of 1.1 ps. If sech2 pulse profile was assumed, the pulse width was 712 fs. The timebandwidth product of the conventional soliton was 0.34 indicating a nearly transform limited pulse operation. The maximum peak power of mode-locked soliton fiber laser was 910 W. Passively SESAM mode-locked thulium-doped fiber lasers with linear configuration were reported in [9,10], femtosecond pulses with higher repetition rate of 108 MHz were obtained in this paper. The balance between nonlinearity of SPM and linear dispersion of GVD dominated in the conservative system. The conventional solitons were used to describe the nonlinear solitary wave solutions of integrable equations. 3. Dispersion-managed solitons Most of silica fibers had anomalous dispersion around 2 μm, specialty normal dispersion fiber was added in thulium-doped fiber laser cavity to break through the conventional soliton regime. Wang et al. declared dissipative soliton with large net normal cavity dispersion in dispersion-managed thulium-doped fiber laser using a segment of normally dispersive fiber (UHNA4) [20]. The narrow core UHNA4 fiber of diameter 2.2 μm and high numerical aperture (NA) of 0.35 was employed in laser to form large net-normal-dispersion cavity. Dissipative solitons have been investigated intensively in all-normal-dispersion (ANDi) ytterbium-doped fiber lasers with additional spectral filter [21]. The concept of dissipation was introduced to dispersion-managed cavity to yield energetic intra-cavity pulse dynamics. The characteristics of pulses in the dispersion-managed thulium-doped fiber laser were mathematically modeled [22,23]. In this section, we focused on the two distinct types of dispersion-managed solitons observed in thulium-doped fiber lasers with different net cavity dispersion values. Dissipative dispersion-managed solitons existed only at high map strengths, namely could be considered as a dissipative soliton that breathed as a direct consequence of the dispersion map [24]. In contrast, stretched pulses were delivered in conservative dispersion-managed lasers operating in anomalous net cavity dispersion regime. To convey insight about pulse formation in dispersion-managed thulium-doped fiber lasers, pulseshaping mechanisms of dissipative dispersion-managed solitons and conservative dispersionmanaged solitons were demonstrated in numerical simulation, and the main differences between them were emphasized. We modeled the pulse propagation in the dispersion-managed thulium-doped fiber laser with the extended nonlinear Schrodinger equation including the effects of dispersion, Kerr nonlinearity, saturated gain with a finite bandwidth and delayed Raman response. i

∞   ∂A β 2 ∂ 2 A ig ( z ) ∂ 2 A α 2 − + γ  A( z , t )  R (τ ) A( z , t − τ ) dτ  = ig ( z ) A + − i A (1) 2 ∂z 2 ∂t ΔΩ g 2 ∂t 2 2 −∞  

A(z,t) is the pulse envelope and t is the time in the co-moving frame. β 2 denote the group velocity dispersion, γ is the nonlinearity parameter, g ( z ) is the saturated gain coefficient given by g ( z) =

g0 1 + E ( z ) ESat

(2)

g0 is the small signal gain coefficient g0 = 4, the gain is saturated with the growth of the total pulse energy E(z) and Esat is the effective saturation energy Esat = 0.5 nJ. The gain spectral dependence is taken into account. The active thulium-doped fiber is characterized by the finite gain bandwidth Δλg = 100 nm, corresponding to the frequency width

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Received 16 Dec 2014; revised 12 Feb 2015; accepted 13 Feb 2015; published 2 Mar 2015 9 Mar 2015 | Vol. 23, No. 5 | DOI:10.1364/OE.23.006292 | OPTICS EXPRESS 6296

ΔΩ g = 2π c Δλg λ0 2

(3)

and Gaussian shape gain in the frequency domain with central wavelength λ0 = 1947 nm. The normalized functional form R(t) can be written as R (t ) = (1 − f R )δ (t ) + f R hR (t )

(4)

The parameter of the delayed Raman response is described by the following equation

hR (t ) =

τ 12 + τ 2 2 exp(− t τ 2 ) sin(t τ 1 ) τ 1τ 2 2

(5)

The parameters τ1 = 12.2 fs, τ2 = 32 fs and fR = 0.18 are chosen to provide a good fit to the actual Raman-gain spectrum [25]. The effective saturable absorber is described by a simplified transfer function   ΔR Aout = Ain  Runsat + ΔR −  2 (1 + A(t ) Psat )  

(6)

Runsat and ΔR corresponds to the unsaturable and saturable reflectivity, Runsat = 0.4, ΔR = 0.37 and Psat is the saturation power Psat = 60 W. We used the standard split-step method to analyze the characteristics of the pulse solutions.

Fig. 4. Schematic of the dispersion-managed thulium-doped fiber laser. TDF, thulium-doped fiber; SA, saturable absorber; OC, output coupler; SMF, single mode fiber; NDF, normal dispersion fiber.

The UHNA4 fiber as normal dispersion fiber (NDF) was used in this numerical simulation section. Pulse evolution was modeled as a consecutive propagation through the laser system elements as shown in Fig. 4. The NDF formed the majority of the cavity. The pulse experienced anomalous GVD and nonlinearity during the thulium-doped fiber and the passive single-mode fiber. The gain fiber was followed by the saturable absorber (SA) and output coupler (OC). The pulse amplitude was reduced by 50% after the OC to account for the output ratio and spliced losses, which could be lumped together without loss of generality. Table 1. The parameters of the numerical model Tm

SMF

NDF

Units

Length

1

6

22

m

Dispersion (β2@1947 nm)

−0.012

−0.067

0.093

ps2/m

Nonlinear coefficient (γ)

0.0011

0.0011

0.0053

W−1m−1

Gain bandwidth (Δλg)

100

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nm

Received 16 Dec 2014; revised 12 Feb 2015; accepted 13 Feb 2015; published 2 Mar 2015 9 Mar 2015 | Vol. 23, No. 5 | DOI:10.1364/OE.23.006292 | OPTICS EXPRESS 6297

Fig. 5. Evolution in the temporal domain from white noise to steady solution.

Parameters of these elements used in the simulations were shown in Table 1. And the parameters of the numerical model corresponded to the realistic experimental setup [20]. Initial white noise was routinely used for modeling of the passively mode-locked thuliumdoped fiber laser. The converged pulses were independent of the initial condition of the simulation, all lay on the cavity parameters. The self-consistent solution could be obtained after a finite number of round-trips, as shown in Fig. 5. The simulation was considered to be reaching a steady state, only when the pulse parameters changed less than 0.0001% with at least 100 round trips in the cavity.

Fig. 6. (a) Pulse shape. Inset: dechirped pulse; Blue curve: frequency chirp; Red dashed curve: Gaussian fit. (b) Optical spectrum of the dissipative dispersion-managed solitons.

The dissipative dispersion-managed solitons could be generated at the net cavity dispersion value of 1.63 ps2, as shown in Fig. 6. The temporal intensity profile went a Gaussian shape, which was a hallmark signature of the dispersion-managed operation. The pulse duration was 47.5 ps. The spectra exhibited the typical steep spectral edges, resemble those generated in the ANDi laser, due to the dissipative effects to compensate for the additional normal dispersion. These characteristics of the dissipative dispersion-managed solitons implied the domination by dispersion map and the dependence on dissipation in this thulium-doped fiber laser. The bandwidth was 4.14 nm, time-bandwidth product (TBP) was calculated as 15.6, the intra-cavity single pulse energy was 1.8 nJ. The pulse had a potentially large nontrivial phase profile across it while avoiding soliton-like instabilities. Since the chirp was largely linear, it could be compressed with an external dispersive delay line composed of fiber, prisms or gratings. In this simulation, after propagating 220-m SMF fiber outside the cavity, the output pulse was dechirped to ~1.5 ps duration which was close to the transform limit 0.44. These theoretical results exhibited the best quantitative agreement with the experimental results in [20]. We pointed out that the dissipative dispersion-managed solitons generated in this thulium-doped fiber laser were, not unique, representative nonlinear waves

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Received 16 Dec 2014; revised 12 Feb 2015; accepted 13 Feb 2015; published 2 Mar 2015 9 Mar 2015 | Vol. 23, No. 5 | DOI:10.1364/OE.23.006292 | OPTICS EXPRESS 6298

of those obtained in net-normal-dispersion mode-locked fiber lasers, which has been theoretically and experimentally investigated [26,27].

Fig. 7. The dissipative dispersion-managed solitons: the intra-cavity evolutions of pulse duration and spectral bandwidth along the cavity position.

The dispersion-managed mode-locked fiber laser consisted of both normal and anomalous dispersion segments, which caused the solitons to temporally broaden and recompress as they propagated along the cavity. As illustrated in Fig. 7, for the positive value of net cavity dispersion β2 = 1.63 ps2, the dissipative dispersion-managed soliton duration decreased along the saturable absorber and SMF and reached a minimum at the beginning of the normal dispersion fiber. The pulses temporally compressed and stretched once each cavity round trip. Theoretical modeling showed that the pulse-shaping process depended on the interaction between dissipative effects and net normal dispersion map. The nonlinear coefficient of NDF was about four times larger than that of SMF and Tm. The high nonlinearity and the large net normal cavity dispersion prompted the involvement of dissipation in the convergence process. The broad gain spectrum 100 nm of the thulium-doped fiber provided limited spectral filtering effect because of the relatively narrow spectral bandwidth 4.14 nm of the mode-locked output [20]. As shown in Fig. 7, the saturable absorber cleaned up the leading and trailing edges of the pulses and narrowed the spectrum bandwidth simultaneously due to the linearly up frequency chirp. Besides providing the amplitude modulation to stabilize the pulse, the saturable absorber as dissipative effect played a key role in the dispersion-managed thuliumdoped fiber laser. To the higher pulse energy, an spectral filter would be added in the nonlinear laser oscillator to supply the stronger dissipative effect.

Fig. 8. (a) Pulse shape. Red dashed curve: Gaussian fit; Blue curve: frequency chirp. (b) Optical spectrum of the conservative dispersion-managed solitons. Red dashed curve: Gaussian fit.

The length of SMF was increased to 40 m to study the characteristics of the stretched pulse with the negative value of net cavity dispersion β2 = −0.65 ps2. In this configuration, the small signal gain coefficient g0 = 3.5, and the effective saturation energy Esat = 0.06 nJ. The numerical results were shown in Fig. 8, the pulse duration was 2.8 ps, spectral width was 4 nm, and time-bandwidth product (TBP) was calculated as 0.8. The single pulse energy was

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Received 16 Dec 2014; revised 12 Feb 2015; accepted 13 Feb 2015; published 2 Mar 2015 9 Mar 2015 | Vol. 23, No. 5 | DOI:10.1364/OE.23.006292 | OPTICS EXPRESS 6299

163 pJ. The temporal and spectral pulse profiles also stayed close to Gaussian shape. The temporal and spectral profile evolutions along the cavity position were shown in Fig. 9. The pulse dynamics of the conservative dispersion-managed solitons were distinctly different from the one of dissipative dispersion-managed solitons. The conservative dispersion-managed solitons stretched and compressed twice each cavity round trip. The pulse duration reached minimum in the middle of SMF and NDF. Periodic soliton evolution was shown in gray portion of Fig. 9 as the pulse propagated along the SMF with anomalous GVD. The temporal and spectral changed resulted from the interplay between the SPM and GVD effects. Soliton effects dominated the evolution in SMF. Distinct evolution was shown in the normal dispersion fiber, the temporal and spectral widths changed consistently during the propagation. Obviously, the spectral filtering effect of SA was much weaker than the effect in dissipative dispersion-managed solitons region. The alternating dispersion reduced the phasematched coupling to resonant sidebands giving cleaner spectra with less dispersive radiation between pulses [28]. The conservative dispersion-managed fiber lasers operated with breathing solutions of the nonlinear wave equation.

Fig. 9. The conservative dispersion-managed solitons: the intra-cavity evolutions of pulse duration and spectral bandwidth along the cavity position.

4. Dissipative solitons

To yield the energetic parabolic pulse-shaping dynamics, we optimized the cavity length with properly managing the intra-cavity dispersion and nonlinear effects. A spectral filter was added in the thulium-doped fiber laser to compensate the excessive nonlinear phase shift. The UHNA4 fiber as normal dispersion fiber, described above, was used in this numerical simulation section. The dissipative soliton evolution was modeled through the laser system elements as shown in Fig. 10.

Fig. 10. Schematic of the thulium-doped fiber ring laser. TDF, thulium-doped fiber; SMF, single mode fiber; NDF, normal dispersion fiber; SA, saturable absorber; Filter, 30 nm Gaussian filter.

Parameters of these elements used in simulations were shown in Table 2. The effective saturation energy of the gain fiber Esat = 8 nJ and the small signal gain coefficient g0 = 7.8. The unsaturable and saturable reflectivity of the saturable absorber, Runsat = 0.06, ΔR = 0.5

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Received 16 Dec 2014; revised 12 Feb 2015; accepted 13 Feb 2015; published 2 Mar 2015 9 Mar 2015 | Vol. 23, No. 5 | DOI:10.1364/OE.23.006292 | OPTICS EXPRESS 6300

and the saturation power Psat = 3000 W. The SA was followed by a 30 nm Gaussian spectral filter. Initial white noise was used for modeling the mode-locked fiber laser and the converged pulses could be obtained after a finite number of round-trips. Table 2. The parameters of the numerical model Tm

SMF

NDF

Filter

Units

Length

0.6

0.3

2

m

Dispersion (β2@1947 nm)

−0.012

−0.067

0.093

ps2/m

Nonlinear coefficient (γ)

0.0011

0.0011

0.0053

W−1m−1

Gain/Filter bandwidth (Δλ)

100

30

nm

Figure 11 showed the different temporal and spectral shapes obtained after the NDF and the Gaussian filter. The distinct properties of the dissipative solitons were studied with the positive value of net cavity dispersion β2 = 0.16 ps2. As shown in Fig. 11, parabolic pulse with 11 ps FWHM pulse duration as local attractor was obtained and the pulse energy was 16.8 nJ. The pulse, with linearly up frequency chirp, showed a good agreement with parabolic fit and the interference fringes on the leading and trailing edges was due to optical wave breaking [29,30]. The pulse width was 3.1 ps with a Gaussian intensity profile after the 30-nm Gaussian filter, and the temporal width increased and intensity profile progressively reshaped to parabolic, during propagation in NDF. The optical FWHM spectral width was 30 nm with Gaussian profile after the spectral filter and broadened to 103 nm (RMS width: 59 nm) after nonlinear spectrum expansion in the NDF.

Fig. 11. (a) Pulse shape and (b) optical spectrum after the NDF. Inset: frequency chirp; Blue dashed curve: parabolic fit. (c) Pulse shape and (d) optical spectrum after the Gaussian filter. Red dotted curve: Gaussian fit.

The intra-cavity evolutions of pulse duration and spectral bandwidth along the cavity position were shown in Fig. 12. The dissipative evolution induced by spectral filter was similar to the one by the saturable absorber described at the previous section. The spectral filter selected a portion of the bandwidth for reinjection. The 30 nm Gaussian spectral filter

#230794 - $15.00 USD (C) 2015 OSA

Received 16 Dec 2014; revised 12 Feb 2015; accepted 13 Feb 2015; published 2 Mar 2015 9 Mar 2015 | Vol. 23, No. 5 | DOI:10.1364/OE.23.006292 | OPTICS EXPRESS 6301

narrowed down the spectrum as the main dissipative process. The pulses temporally compressed and stretched once each cavity round trip. In the NDF, spectral width saturated due to peak power of pulse rapidly decreasing, induced by pulse broadening. The normally dispersive fiber and the strong spectral filtering effect were crucial for the pulse evolution in oscillator with distinct intensity profiles from the Gaussian shape to parabolic shape. In relation to this point, a spectral filter was used in an erbium-doped fiber laser to initiate the transition from similariton to soliton evolution, which represented the most thorough exposition of the intrinsic nonlinear dynamics in mode-locked fiber lasers [31]. The parabolic pulse was numerically explored for different values of the net cavity dispersion and the filter bandwidth. A new equilibrium of the oscillator had to be found when any parameter of cavity components was changed. The time-bandwidth product of the parabolic pulse was calculated as 90. The output pulse could be dechirped to 120 fs with a peak power of 140 kW by extracavity linear dispersive delay line. In comparison to the femtosecond pulses with MW-level peak power obtained from chirped pulse amplification system [8,32], wave-breaking phenomenon was the most fundamental limitation in the fiber-based oscillator, and the spectral interference fringes would degrade the quality of the compressed pulse.

Fig. 12. The parabolic pulses: the intra-cavity evolutions of pulse duration and spectral bandwidth along the cavity position.

In this numerical simulation section, we reported the generation of parabolic pulses in thulium-doped fiber laser with strong dissipative effect of spectral filter. Highly chirped parabolic pulse was demonstrated by passively nonlinear propagation in normal dispersion fiber. As discussed in the previous sections, with the intra-cavity pulse energy increased, the intensity profile of the output pulse gradually changed from sech2, Gaussian to parabolic shape. As we knew, the conventional solitons were nearly free frequency chirp, the dispersion-managed solitons and dissipative solitons with higher energy were always highlychirped. The magnitude of frequency chirp progressively increased from conventional solitons to dispersion-managed solitons to dissipative solitons. It would be interesting to see an unified theory explanation, focused on the pulse energy varying along with corresponding range of the frequency chirp. 5. Conclusion

In conclusion, pulse-shaping mechanisms in passively mode-locked thulium-doped fiber lasers were investigated by experiments and theoretical modeling. Stable passively SESAM mode-locked conventional solitons thulium-doped fiber laser was demonstrated, producing pulses of 712 fs width with high repetition rate of 108 MHz and high pulse energy of 0.65 nJ. Theoretical modeling of dispersion-managed thulium-doped fiber laser showed the best quantitative agreement with experimental results and exhibited distinct evolutions between the dissipative soliton and the stretched pulse. The dissipative dispersion-managed solitons existed in large normal net cavity dispersion regime and temporally compressed and stretched once each cavity round trip. The distinct pulse intensity profiles evolution from the Gaussian shape to parabolic shape was reported in a compact thulium-doped fiber laser oscillator. The

#230794 - $15.00 USD (C) 2015 OSA

Received 16 Dec 2014; revised 12 Feb 2015; accepted 13 Feb 2015; published 2 Mar 2015 9 Mar 2015 | Vol. 23, No. 5 | DOI:10.1364/OE.23.006292 | OPTICS EXPRESS 6302

parabolic pulse could be dechirped to 120 fs with a peak power of 140 kW by extra-cavity linear dispersive delay line. The experimental results and theoretical modeling allowed us for a deeper insight into the pulse-shaping mechanisms at 2 μm wavelength band. The further experimental study on the mechanism of dissipative solitons in passively mode-locked thulium-doped fiber lasers is on-going in our lab. Acknowledgments

The authors acknowledge the financial support from the National Natural Science Foundation of China (NSFC, Nos. 61235010 and 61177048).

#230794 - $15.00 USD (C) 2015 OSA

Received 16 Dec 2014; revised 12 Feb 2015; accepted 13 Feb 2015; published 2 Mar 2015 9 Mar 2015 | Vol. 23, No. 5 | DOI:10.1364/OE.23.006292 | OPTICS EXPRESS 6303