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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 8 — Apr. 11, 2011
  • pp: 7616–7624
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Observations of four types of pulses in a fiber laser with large net-normal dispersion

Leiran Wang, Xueming Liu, Yongkang Gong, Dong Mao, and Lina Duan  »View Author Affiliations


Optics Express, Vol. 19, Issue 8, pp. 7616-7624 (2011)
http://dx.doi.org/10.1364/OE.19.007616


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Abstract

Four different types of pulses are experimentally obtained in one erbium-doped all-fiber laser with large net-normal dispersion. The proposed laser can deliver the rectangular-spectrum (RS), Gaussian-spectrum (GS), broadband-spectrum (BS), and noise-like pulses by appropriately adjusting the polarization states. These kinds of pulses have distinctly different characteristics. The RS pulses can easily be compressed to femtosecond level whereas the pulse energy is restricted by the trend of multi-pulse shaping with excessive pump. The GS and BS pulses always maintain the single-pulse operation with much higher pulse-energy and accumulate much more chirp. After launching the pulses into the photonic-crystal fiber, the supercontinuum can be generated with the bandwidth of >700 nm by the BS pulses and of ~400 nm by the GS pulses, whereas it can hardly be generated by the RS pulses. The physical mechanisms behind the continuum generation are qualitatively investigated relating to different operating regimes. This work could help to a deeper insight of the normal-dispersion pulses.

© 2011 OSA

1. Introduction

Mode-locked fiber lasers have been extensively investigated for their important practical and potential applications [1

1. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, Boston, 2007).

6

6. A. Komarov, H. Leblond, and F. Sanchez, “Multistablility and hysteresis phenomena in passive mode-locked lasers,” Phys. Rev. A 71, 053809 (2005). [CrossRef]

]. Conventional chirp-free soliton formed by the balance of self-phase modulation (SPM) and negative group-velocity dispersion (GVD) has attracted considerable attention thanks to the ultra-short duration and stable operation features, however, its pulse energy is limited at a low level (typically ~0.1 nJ) according to the soliton area theorem [4

4. L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B 65, 277–294 (1997). [CrossRef]

]. With appropriate intracavity dispersion management (DM), the average peak power is effectively lowered and consequently the nonlinear phase shift is restricted in the stretched-pulse fiber lasers. The implement of the DM technique allows a significant increase of the pulse energy, representatively up to ~1 nJ level [5

5. K. Tamura, E. P. Ippen, H. A. Haus, and L. E. Nelson, “77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser,” Opt. Lett. 18(13), 1080–1082 (1993). [CrossRef] [PubMed]

]. Furthermore, the self-similar pulse that could tolerate strong nonlinearity without wave breaking scales up the pulse energy to ~10 nJ, which is restricted by the finite gain bandwidth [7

7. F. Ö. 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). [CrossRef] [PubMed]

,8

8. J. R. Buckley, F. W. Wise, F. O. Ilday, and T. Sosnowski, “Femtosecond fiber lasers with pulse energies above 10 nJ,” Opt. Lett. 30(14), 1888–1890 (2005). [CrossRef] [PubMed]

]. The accumulation of excessive nonlinear phase shift usually induces the pulse to break up, so the management of the nonlinearity is required to construct the high-energy fiber lasers [9

9. X. Liu, L. Wang, X. Li, H. Sun, A. Lin, K. Lu, Y. Wang, and W. Zhao, “Multistability evolution and hysteresis phenomena of dissipative solitons in a passively mode-locked fiber laser with large normal cavity dispersion,” Opt. Express 17(10), 8506–8512 (2009). [CrossRef] [PubMed]

]. Recently, a new type of pulses named as dissipative solitons (DSs) is realized in fiber lasers with normal cavity dispersion [10

10. N. Akhmediev and A. Ankiewicz, “Dissipative Solitons,” in Lecture Notes in Physics, Vol. 661 (Springer, Berlin, 2005).

14

14. L. R. Wang, X. M. Liu, and Y. K. Gong, “Giant-chirp oscillator for ultra-large net-normal-dispersion fiber lasers,” Laser Phys. Lett. 7, 63–67 (2010). [CrossRef]

]. Based on the impactful DS technique, pulse energy can be enlarged by even four orders of magnitude than that of conventional solitons [15

15. B. Ortaç, M. Baumgartl, J. Limpert, and A. Tünnermann, “Approaching microjoule-level pulse energy with mode-locked femtosecond fiber lasers,” Opt. Lett. 34(10), 1585–1587 (2009). [CrossRef] [PubMed]

]. The enhanced self-amplitude modulation (SAM) through spectral filtering (SF) effect in all-normal-dispersion lasers can stabilize the mode-locking of highly chirped pulses with unprecedented energies [15

15. B. Ortaç, M. Baumgartl, J. Limpert, and A. Tünnermann, “Approaching microjoule-level pulse energy with mode-locked femtosecond fiber lasers,” Opt. Lett. 34(10), 1585–1587 (2009). [CrossRef] [PubMed]

17

17. X. Liu, “Mechanism of high-energy pulse generation without wave breaking in mode-locked fiber lasers,” Phys. Rev. A 82, 053808 (2010). [CrossRef]

]. Pulse evolutions without wave breaking in a strongly dissipative-dispersive laser system have been adequately investigated both numerically and experimentally [10

10. N. Akhmediev and A. Ankiewicz, “Dissipative Solitons,” in Lecture Notes in Physics, Vol. 661 (Springer, Berlin, 2005).

18

18. W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78, 023830 (2008). [CrossRef]

]. In addition, DSs are also found to be reachable in the negative dispersion regime, described as the dissipative soliton resonances [19

19. W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances in the anomalous dispersion regime,” Phys. Rev. A 79, 033840 (2009). [CrossRef]

]. Moreover, many potent means are employed to boost the pulse energy to a higher level, e.g., introducing the large-mode-area fibers into the laser cavity [20

20. M. Baumgartl, B. Ortaç, C. Lecaplain, A. Hideur, J. Limpert, and A. Tünnermann, “Sub-80 fs dissipative soliton large-mode-area fiber laser,” Opt. Lett. 35(13), 2311–2313 (2010). [CrossRef] [PubMed]

], stretching the cavity length [21

21. H. Sayinc, D. Mortag, D. Wandt, J. Neumann, and D. Kracht, “Sub-100 fs pulses from a low repetition rate Yb-doped fiber laser,” Opt. Express 17(7), 5731–5735 (2009). [CrossRef] [PubMed]

], and mode-locking the laser with new materials such as the atomic layer graphene [22

22. H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17(20), 17630–17635 (2009). [CrossRef] [PubMed]

] or the single-wall carbon nanotubes [23

23. Z. Sun, A. G. Rozhin, F. Wang, T. Hasan, D. Popa, W. O’Neill, and A. C. Ferrari, “A compact, high power, ultrafast laser mode-locked by carbon nanotubes,” Appl. Phys. Lett. 95, 253102 (2009). [CrossRef]

]. However, most of the reported DSs are within only one category that is characterized by steep spectral edges with limited bandwidths, i.e., exhibiting a nearly rectangular-spectrum (RS) shape which is induced by the strong SF effect [14

14. L. R. Wang, X. M. Liu, and Y. K. Gong, “Giant-chirp oscillator for ultra-large net-normal-dispersion fiber lasers,” Laser Phys. Lett. 7, 63–67 (2010). [CrossRef]

,15

15. B. Ortaç, M. Baumgartl, J. Limpert, and A. Tünnermann, “Approaching microjoule-level pulse energy with mode-locked femtosecond fiber lasers,” Opt. Lett. 34(10), 1585–1587 (2009). [CrossRef] [PubMed]

,20

20. M. Baumgartl, B. Ortaç, C. Lecaplain, A. Hideur, J. Limpert, and A. Tünnermann, “Sub-80 fs dissipative soliton large-mode-area fiber laser,” Opt. Lett. 35(13), 2311–2313 (2010). [CrossRef] [PubMed]

,23

23. Z. Sun, A. G. Rozhin, F. Wang, T. Hasan, D. Popa, W. O’Neill, and A. C. Ferrari, “A compact, high power, ultrafast laser mode-locked by carbon nanotubes,” Appl. Phys. Lett. 95, 253102 (2009). [CrossRef]

]. Furthermore, the pulse energies of such DSs are limited by the trend of multi-pulse shaping with excessive pump [9

9. X. Liu, L. Wang, X. Li, H. Sun, A. Lin, K. Lu, Y. Wang, and W. Zhao, “Multistability evolution and hysteresis phenomena of dissipative solitons in a passively mode-locked fiber laser with large normal cavity dispersion,” Opt. Express 17(10), 8506–8512 (2009). [CrossRef] [PubMed]

,14

14. L. R. Wang, X. M. Liu, and Y. K. Gong, “Giant-chirp oscillator for ultra-large net-normal-dispersion fiber lasers,” Laser Phys. Lett. 7, 63–67 (2010). [CrossRef]

,24

24. J. W. Lou, M. Currie, and F. K. Fatemi, “Experimental measurements of solitary pulse characteristics from an all-normal-dispersion Yb-doped fiber laser,” Opt. Express 15(8), 4960–4965 (2007). [CrossRef] [PubMed]

]. It is reasonable to imagine that there exist different operation regimes in DS laser cavities, where the pulse energy can be accumulated to a much higher level through a simple way such as widening the pulse width in spectral or temporal domain. However, up to now, the comprehensive research based on the different operation regimes is deficient.

In this paper, we have experimentally obtained different types of pulses in a compact erbium-doped fiber laser with large net-normal dispersion. Adjusting the polarization states while keeping all the other cavity parameters fixed, the proposed laser oscillator can deliver the rectangular-spectrum (RS), Gaussian-spectrum (GS), broadband-spectrum (BS), and noise-like (NL) pulses, respectively. The RS pulse can easily be compressed to femtosecond level with a segment of single-mode-fiber, whereas its energy is limited to a low level of ~1.1 nJ. The GS pulse always maintains the single-pulse operation during the evolution and be potential for accumulating much higher energy through dramatically stretching its pulse duration without wave breaking. Compared with low-peak-power GS pulses resulting from large pulse durations, the BS pulses profiting from the broad bandwidth (3-dB bandwidth of ~81 nm) can also realize high pulse energy (~70 nJ) and support high peak power (~5 kW). According to the experimental results, it is suggested that the switching of operation regimes is essentially determined by the different SAM effects during the pulse-shaping processes. The different intrinsic characteristics of the pulses are further identified through the supercontinuum generation after launching them into the photonic-crystal-fiber. The proposed laser design can find important potentials in high-energy pulse generation/amplification systems for its compact, all-fiber, and low-cost features. Our work could also help to a deeper insight of the normal-dispersion pulses.

2. Experimental setup

The configuration of the fiber laser system is schematically shown in Fig. 1
Fig. 1 Schematic diagram of the experimental setup. P f: forward pump, P b: backward pump.
. Two 980-nm laser diodes are coupled into the laser cavity with two 980/1550 nm wavelength-division-multiplexers (WDMs). A ~20-m-long erbium-doped fiber (EDF) with the dispersion parameter D of about −42 ps/nm.km at 1550 nm contributes to the large-normal dispersion. The other fibers in the cavity are the single-mode-fiber (SMF) with D of ~17 ps/nm.km. The fundamental frequency and net dispersion of the cavity are estimated as ~8.2 MHz and about + 1 ps2, respectively. A polarization-sensitive isolator (PS-ISO) together with two polarization controllers (PCs: PC-1 and PC-2) can act as an equivalent saturable absorber, and the nonlinear polarization rotation (NPR) technique is utilized to modelock the laser. A fiber-pigtailed coupler (OC, 50% output) works as the output port. A segment of standard SMF or positive dispersion-compensation-fiber (DCF) with the D of about −120 ps/km.nm is used to investigate the compression of emitted pulses. Moreover, a 100-m near-zero-dispersion-flattened at 1550 nm highly-nonlinear photonic-crystal-fiber (PCF, Crystal Fiber, NL-1550-NEG-1) with the nonlinear coefficient of ~11 (W⋅km)−1 is employed to further investigate the nonlinear effects. An autocorrelator (AC, APE Pulsecheck), an optical spectrum analyzer (OSA, Yokogawa AQ6370B), an 11-GHz digital storage oscilloscope (DSO, LeCroy SDA) together with a 70-GHz photodetector (PD, U2T XPDV3120R), and a 44-GHz radio frequency analyzer (RFA, Agilent PSA) with a 50-GHz PD (U2T XPDV2020R) are used to measure the output pulses.

3. Experimental results

Self-started mode locking can be realized by appropriately adjusting the polarization state at sufficient pump. When the pump power P is beyond a threshold value, e.g., P f = 20 mW and P b = 40 mW, the proposed laser cavity emits the typical RS pulse characterized by the steep spectral edges and restricted bandwidth, as shown in Fig. 2a
Fig. 2 RS pulse operation: (a) optical spectrum, (b) autocorrelation trace for the original chirped DS, (c) autocorrelation trace for dechirped pulse, and (d) rf spectrum.
, which is generally understood as arising from the strong SF effect [15

15. B. Ortaç, M. Baumgartl, J. Limpert, and A. Tünnermann, “Approaching microjoule-level pulse energy with mode-locked femtosecond fiber lasers,” Opt. Lett. 34(10), 1585–1587 (2009). [CrossRef] [PubMed]

,20

20. M. Baumgartl, B. Ortaç, C. Lecaplain, A. Hideur, J. Limpert, and A. Tünnermann, “Sub-80 fs dissipative soliton large-mode-area fiber laser,” Opt. Lett. 35(13), 2311–2313 (2010). [CrossRef] [PubMed]

,23

23. Z. Sun, A. G. Rozhin, F. Wang, T. Hasan, D. Popa, W. O’Neill, and A. C. Ferrari, “A compact, high power, ultrafast laser mode-locked by carbon nanotubes,” Appl. Phys. Lett. 95, 253102 (2009). [CrossRef]

]. The 3-dB bandwidth of the RS pulse is estimated as ~14.0 nm. The corresponding autocorrelation trace takes on a Gaussian shape, and its 3-dB width is given by ~22.3 ps (Fig. 2b). The original highly-chirped RS pulse can be compressed by negative dispersion devices, e.g., the width of autocorrelation trace becomes to ~430 fs after a ~54-m-long standard SMF with the D of ~17 ps/nm.km (Fig. 2c). According to the experimental result, it is suggested that the chirp across the RS pulse is almost linear. The corresponding rf spectrum with a high signal-to-noise ratio (SNR) of ~80 dB indicates the stable mode locking operation (Fig. 2d).

The RS pulse is promising for its compressibility and has been the primary issue for investigation of normal-dispersion pulses in the past [20

20. M. Baumgartl, B. Ortaç, C. Lecaplain, A. Hideur, J. Limpert, and A. Tünnermann, “Sub-80 fs dissipative soliton large-mode-area fiber laser,” Opt. Lett. 35(13), 2311–2313 (2010). [CrossRef] [PubMed]

,23

23. Z. Sun, A. G. Rozhin, F. Wang, T. Hasan, D. Popa, W. O’Neill, and A. C. Ferrari, “A compact, high power, ultrafast laser mode-locked by carbon nanotubes,” Appl. Phys. Lett. 95, 253102 (2009). [CrossRef]

]. However, its single-pulse energy E is severely limited by the trend of multi-pulse shaping with excessive pump [9

9. X. Liu, L. Wang, X. Li, H. Sun, A. Lin, K. Lu, Y. Wang, and W. Zhao, “Multistability evolution and hysteresis phenomena of dissipative solitons in a passively mode-locked fiber laser with large normal cavity dispersion,” Opt. Express 17(10), 8506–8512 (2009). [CrossRef] [PubMed]

,14

14. L. R. Wang, X. M. Liu, and Y. K. Gong, “Giant-chirp oscillator for ultra-large net-normal-dispersion fiber lasers,” Laser Phys. Lett. 7, 63–67 (2010). [CrossRef]

,24

24. J. W. Lou, M. Currie, and F. K. Fatemi, “Experimental measurements of solitary pulse characteristics from an all-normal-dispersion Yb-doped fiber laser,” Opt. Express 15(8), 4960–4965 (2007). [CrossRef] [PubMed]

]. For the proposed laser, the E is ~1.1 nJ with an average output power of ~9 mW for Fig. 2. In addition, if a Gaussian pulse shape is assumed, the pulse duration is given by ~15.8 ps and the peak power P peak of chirped RS pulse is ~70 W; while if a Sech2 pulse shape is assumed the pulse duration is ~14.5 ps, corresponding to the P peak of ~76 W. One can see that the two P peak values with different assumed pulse shapes are rather close, so in this paper we investigate the pulse properties with the former result for the purpose of conciseness. At the maximum pump of P f = P b = 550 mW, as many as 15 pulses could be emitted simultaneously from the cavity. So the RS operation fails to support high-energy pulses. In order to realize high-energy pulse output, the cavity should maintain the single-pulse operation under strong pump. In order to clearly show the switching of operation regimes for further investigation, here the orientation of PC-1 for the aforementioned RS pulse state is schematically denoted as angle “ϕ1” in the rhumb, as shown in Fig. 1. Keeping all the other cavity parameters fixed except the polarization state of PC-1, i.e., only rotating the orientation of the squeeze of PC-1 anticlockwise from “ϕ1” to “ϕ2” (Fig. 1), we further achieve another kind of GS pulse in the same oscillator, as shown in Fig. 3
Fig. 3 GS pulse operation: (a) optical spectra and (b) autocorrelation traces at P f = P b = 100, 300, and 500 mW from bottom to top, respectively. (c) Oscilloscope trace and (d) rf spectrum at P f = P b = 500 mW.
. At this stage, the laser cavity emits only one GS pulse at the maximum available pump of P f = P b = 550 mW, instead of multi-pulse shaping as the RS pulse operation does. With the increase of P, the 3-dB bandwidth of the GS pulse keeps almost constant (slightly changing within the range of 10 to 11 nm), as depicted in Fig. 3(a). The corresponding autocorrelation traces at different pump powers are depicted in Fig. 3(b). According to the autocorrelation theory, the quasi-triangular profile indicates that the original pulse has an approximately rectangular shape in the temporal domain, which is verified by the oscilloscope trace (Fig. 3(c)). The stable mode locking operation is further confirmed by the rf spectrum with a high SNR (Fig. 3d). Interestingly, the temporal and spectral profiles of the RS pulse are almost reversed from that of the GS pulses. As shown in Fig. 3(b), the durations of the GS pulses are ~100 ps, ~290 ps, and ~440 ps at P f = P b = 100 mW, 300 mW, and 500 mW, respectively. Profiting from the monotonously widening of the pulse duration with the increase of pump power, the GS pulse can accumulate much more energy without wave breaking than the RS pulse does. At the maximum available pump, the cavity delivers GS pulse with an average output power of ~230 mW and E of ~28.0 nJ.

Due to the large pulse duration, the peak power of GS pulse is relatively low, e.g., the P peak is ~64 W which is close to that of the RS pulse. The peak power almost keeps constant during the evolution (e.g., P peak is ~50 W at P f = P b = 100 mW and ~52 W at P f = P b = 300 mW). Moreover, we find that it is hard to compress the GS pulse by SMF. The duration of GS pulses keep almost constant after propagation through SMF with the length from ~10 m to ~300 m (corresponding to the dispersion from about −0.22 ps2 to about −6.6 ps2). With longer SMF the pulse duration broadens dramatically, e.g., after 700-m SMF the pulse duration approaches ~800 ps. Moreover, the GS pulses can nor be compressed by DCF. The pulse durations keep enlarging with the lengthening of DCF. For example, after ~20-m DCF the pulse duration becomes ~850 ps which is almost twice of the initial value (~440 ps). So it is reasonable to conclude that the GS pulse contains a mass of nonlinearity. Actually, the frequency chirp is linear and low across the central region whereas it is nonlinear and strong at both the head and tail of the pulse, in which way the pulse can resist the influence of strong dispersion in the cavity and maintain the wave-breaking-free mode-locking operation in the high energy regime [16

16. X. Liu, “Pulse evolution without wave breaking in a strongly dissipative-dispersive laser system,” Phys. Rev. A 81, 053819 (2010). [CrossRef]

]. It is worth noting that the situations here are rather different from that in the negative dispersion regime where the dissipative soliton resonances (DSRs) are realized [19

19. W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances in the anomalous dispersion regime,” Phys. Rev. A 79, 033840 (2009). [CrossRef]

]. Although the temporal/spectral profiles and evolution processes of GS pulse are similar to that in DSR, however, for the latter case the pulse is almost linearly chirped [19

19. W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances in the anomalous dispersion regime,” Phys. Rev. A 79, 033840 (2009). [CrossRef]

].

To exclude the suspicion of the NL pulse operation, here we also present the state of the typical NL “pulse” output from the proposed laser cavity as shown in Fig. 4
Fig. 4 NL pulse operation: (a) optical spectra, (b) autocorrelation trace, and (c) rf spectrum.
. The NL operation regime is achieved by rotating the orientation of the squeeze of PC-1 clockwise from “ϕ1” to “ϕ3” while maintaining all the other cavity parameters unchanged (Fig. 1). For relatively low pump power, the laser operates in the continuous-wave (CW) regime with a center wavelength of around 1563 nm (Fig. 4a). With the enhancement of pump power, the NL pulse is emitted exhibiting a peculiar spectrum profile with a broader bandwidth (~39 nm) and a characteristic spike on the autocorrelation trace [25

25. 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). [CrossRef] [PubMed]

]. As shown in Fig. 4(b), one can see that the spike does not appear on zero time-delay of autocorrelation trace (about 4 ps biased to left side of the center), which may be attributed to the admissible experimental error induced by the limitation of the practical autocorrelator (e.g., the response time, resolution, and sampling points). Meanwhile, there are two obvious side lobes on the rf spectrum of the NL pulse and the SNR is lower (Fig. 4c), which is due to the inherent instability for the NL operation. Comparatively, the operation regime for the GS pulse is obviously distinct from that of the NL pulse. The NL pulse is trivial due to its low peak power and incoherence, so more detailed discussions are not presented here.

According to the results discussed above, the RS and GS pulse could realize either multi-pulse or high-energy operation, but both fail to achieve high peak power. Therefore, a very different operation regime is required to achieve pulses that can support both high pulse energy and peak power. Remarkablely, a kind of BS pulse is achieved through further adjusting the polarization state of the proposed laser cavity, i.e., rotating the orientation of the squeeze of PC-1 anticlockwise from “ϕ1” to “ϕ4” while keeping all the other cavity parameters fixed (Fig. 1). As shown in Fig. 5(a)
Fig. 5 BS pulse operation: (a) optical spectra, (b) autocorrelation trace, (c) oscilloscope trace, and (d) rf spectra (inset: 1-GHz span range).
, the BS pulse exhibits a unique top-flattened spectral profile with the 3-dB bandwidth as large as ~81 nm which even breaks through the gain bandwidth of EDF. The width of the Gaussian-shape autocorrelation trace is estimated as ~19.7 ps (Fig. 2b). Further checking the pulse with the high-speed DSO and RFA (Figs. 5c and 5d), the stable single-pulse mode-locking operation can be confirmed with the uniform pulse sequence over a large range and a high SNR of >75 dB. At the maximum pump, the average output power is about 288 mW. So the cavity can support the BS pulse with E of 70 nJ and P peak of as high as ~5 kW (the pulse duration is estimated as is ~14.0 ps if a Gaussian pulse shape is assumed). As the central wavelength relating to CW operation locates on the short wavelength side of the spectrum, the BS pulse is expected to be influenced by the strong nonlinear effects such as the SPM and the intrapulse stimulated Raman scattering (SRS) process resulting from its high peak power. In addition, the BS pulse is also hard to be compressed by linear-dispersion devices just like the case for GS pulse. The BS pulse duration enlarges dramatically with the lengthening of either SMF or DCF fiber. For example, after 100-m SMF the pulse duration becomes about 3 times larger than the initial value of ~20 ps (autocorrelation width), while after 20-m DCF it becomes almost 6 times larger. According to the experimental results, it is suggested that the chirp for the BS pulse could be nonlinear across the pulse because of the strong nonlinearity induced during the pulse-shaping process. Furthermore, the spectrum of BS pulse is much broader compared with the NL operation due to the stronger nonlinearity, since the SRS effect could be lacked for the NL pulse due to its lower peak power. Thus, the operation regime of the BS pulse is quite distinct from that of the NL pulse.

The numerical studies show that with the increase of nonlinear gain, the normal-dispersion pulse can become narrower with higher intensity and broader spectrum [26

26. N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, “Roadmap to ultra-short record high-energy pulses out of laser oscillators,” Phys. Lett. A 372, 3124–3128 (2008). [CrossRef]

]. The situation in the current laser cavity is similar, and the BS pulse can accumulate high energy through the widening of pulse spectrum. One can see that the property in the temporal (spectral) domain of the BS pulse is a little similar to that in the spectral (temporal) domain of the GS pulse (e.g., the profile and the dramatically stretching feature), which is very reasonable considering the Fourier-transform theory. However, they realize the high-energy output in different ways (i.e., the BS pulse through broadening its spectrum whereas the GS pulse through broadening its duration), and the BS pulse could also bear very high peak power.

We further investigate the pulses by launching them directly into the highly-nonlinear PCF. As shown in Fig. 6
Fig. 6 SC generation in the PCF with different types of input pulses.
, supercontinuum (SC) is hardly generated when the RS pulse with low peak power (~70 W) is employed as the pump source. However, the situation for GS pulse is very different and obvious SC with a bandwidth of ~400 nm is generated. Although the GS pulse also exhibits a low pulse peak power P peak (~64 W), its pulse duration is large, which helps to the SC generation [1

1. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, Boston, 2007).

]. Moreover, the broadest SC can be achieved if the BS pulse with the strongest P peak (at kW level) is utilized. Here the exact bandwidth of SC is not given because of the experimental implement limitation (i.e., the scan range for the used OSA is limited to 1700 nm). We could make a reasonable estimation of >700 nm (10-dB bandwidth) considering the evolving trend of the spectrum profile and on the basis of the four-wave-mixing theory, which further confirms the high peak power feature of the BS pulse.

Numerical simulations with the complex Ginzburg-Landau model have revealed that the dissipative nonlinear systems admit abundant dynamic regimes, e.g., the pulsating solitons, period doubling, and chaotic solitons can coexist in a mode-locked laser and respectively correspond to a solution in a certain region of the parameter space [27

27. A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg-Landau model for ring fiber lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(2 Pt 2), 025604 (2005). [CrossRef] [PubMed]

,28

28. N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(5 Pt 2), 056602 (2001). [CrossRef] [PubMed]

]. Thus, one can obtain different operation regimes by transforming the parameter regions in a dissipative-dispersive system. According to the experimental results, different operation regimes can be achieved in the same laser oscillator with different polarization states and pump powers. The proposed laser system based on NPR technique allows simple and convenient adjustment of the equivalent saturable absorber effect, which enables the realization of a variety of pulse generation regimes. Since different orientations of the squeezer of PC-1 correspond to different intensity transmissions of light, the RS, GS, NL, and BS pulse operation regimes can be realized respectively by simply rotating the squeeze while keeping the other cavity parameters fixed. According to the experimental results, all the stable mode-locking states (i.e., the RS, GS, BS pulses) are achieved through rotating the squeeze orientation in one direction (i.e., clockwise from ϕ1 to ϕ2, and ϕ4), however, the NL pulse is achieve by rotating the squeeze in another direction (i.e., anticlockwise from ϕ1 to ϕ3). It may indicate that the mode-locked states locate closely in the parameter regions whereas the noised states lie in the regions far away from that for the stable pulses. Actually, there exist different cavity feedback regions for fiber lasers employing the NPR technique with either normal [6

6. A. Komarov, H. Leblond, and F. Sanchez, “Multistablility and hysteresis phenomena in passive mode-locked lasers,” Phys. Rev. A 71, 053809 (2005). [CrossRef]

] or anomalous cavity dispersion [29

29. D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72, 043816 (2005). [CrossRef]

], which supply the positive/negative gain during the pulse-shaping process depending on different nonlinear phase delay. In addition, for fiber lasers with normal cavity dispersion, it is believed that the enhanced SAM from both the NPR and SF effect can cut off not only the temporal but also the spectral wings of a pulse, which facilitates the self-consisting evolution and leads to stable mode locking [15

15. B. Ortaç, M. Baumgartl, J. Limpert, and A. Tünnermann, “Approaching microjoule-level pulse energy with mode-locked femtosecond fiber lasers,” Opt. Lett. 34(10), 1585–1587 (2009). [CrossRef] [PubMed]

,17

17. X. Liu, “Mechanism of high-energy pulse generation without wave breaking in mode-locked fiber lasers,” Phys. Rev. A 82, 053808 (2010). [CrossRef]

,20

20. M. Baumgartl, B. Ortaç, C. Lecaplain, A. Hideur, J. Limpert, and A. Tünnermann, “Sub-80 fs dissipative soliton large-mode-area fiber laser,” Opt. Lett. 35(13), 2311–2313 (2010). [CrossRef] [PubMed]

]. Such dissipative processes presumably have to be exploited at a rather great degree to balance the gain and loss and play a dominate role in the pulse generation, so the normal-dispersion pulses can be regarded as dissipative solitons (DSs) [10

10. N. Akhmediev and A. Ankiewicz, “Dissipative Solitons,” in Lecture Notes in Physics, Vol. 661 (Springer, Berlin, 2005).

18

18. W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78, 023830 (2008). [CrossRef]

]. Thanks to the DS theory, here the switching of different operation regimes of the proposed fiber laser can be well understood. It is suggested that changing the strength of the NPR effect can affect the intracavity nonlinear gain and consequently the different pulse-shaping mechanisms, since the pulse is formed by the combination of the NPR, SF, and other nonlinear effects. In other words, different effects play roles on different levels during the pulse-shaping process. For example, the positive cavity feedback region is relatively small for the RS pulse with low E, and the SF effect may dominate the forming process of a single RS pulse, resulting in the rigidly limited bandwidth. Yet the NPR effect manifests itself through the multiple-pulse shaping. Furthermore, pulses with higher E can be generated with a larger positive cavity feedback region [6

6. A. Komarov, H. Leblond, and F. Sanchez, “Multistablility and hysteresis phenomena in passive mode-locked lasers,” Phys. Rev. A 71, 053809 (2005). [CrossRef]

,29

29. D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72, 043816 (2005). [CrossRef]

]. So the GS and BS pulses with much higher energy than the RS pulse are emitted at higher P without wave breaking via the variation of polarization states, and evolve in their respective manners through different SAM effects. The GS pulse employs both the NPR and SF effect to realize self-consisting propagation in the cavity as described in Ref [17

17. X. Liu, “Mechanism of high-energy pulse generation without wave breaking in mode-locked fiber lasers,” Phys. Rev. A 82, 053808 (2010). [CrossRef]

]. Although the bandwidth of the GS pulse is also limited within the gain bandwidth of the EDF, the SF effect is weakened, which can be obviously deduced from the smooth spectral profile instead of sharp edges for the RS pulse. Comparatively, for the BS pulse, the SF effect may be absent which can be intuitively verified from the ultrabroad bandwidth, and the NPR as well as other nonlinear effects (e.g., the intrapulse SRS effect) dominate over the pulse-shaping process. In addition, since the gain fiber employed in the proposed cavity is rather long and the net cavity dispersion is very large, pulses with broader spectrum and higher energy can be achieved [30

30. J. H. Lee, U. C. Ryu, and N. Park, “Passive erbium-doped fiber seed photon generator for high-power Er(3+)-doped fiber fluorescent sources with an 80-nm bandwidth,” Opt. Lett. 24(5), 279–281 (1999). [CrossRef]

,31

31. M. Baumgartl, B. Ortaç, J. Limpert, and A. Tünnermann, “Passively mode-locked chirped-pulse fiber oscillators: Study on dispersion,” in Advanced Solid-State Photonics (Optical Society of America, 2009), paper TuB3.

]. Therefore, the proposed all-fiber laser design can find important potentials in high-energy pulse generation and amplification systems for its compact, easy-adjustable, and low-cost features.

4. Conclusions

We have experimentally observed four types of pulses in the same compact erbium-doped all-fiber laser with strong net-normal dispersion. With different polarization states (note that all the other cavity parameters are fixed), our laser oscillator can emit the RS, GS, BS, and NL pulses, respectively. The RS pulse is promising for the compressibility to femtosecond level whereas its pulse energy is restricted by the trend of multi-pulse shaping with excessive pump. The GS and BS pulses always maintain the single-pulse operation during the evolution and can accumulate much higher energy through the dramatically widening of the pulse duration and spectral width, respectively. After launching the pulses into PCF, different supercontinua are achieved, which further indicates distinct characteristics of the pulses. It is found that the switching of different operation regimes is determined directly by the NPR effect and essentially by the different enhanced SAM effect during the pulse-shaping processes. This work could help to a deeper insight of the pulses operating in the normal-dispersion regime.

Acknowledgments

This work was supported by the “Hundreds of Talents Programs” of the Chinese Academy of Sciences and by the National Natural Science Foundation of China under Grants 10874239 and 10604066. Corresponding author (X. Liu). Tel.: + 862988881560; fax: + 862988887603; electronic mail: liuxueming72@yahoo.com and liuxm@opt.ac.cn.

References and links

1.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, Boston, 2007).

2.

A. Martinez, K. Fuse, B. Xu, and S. Yamashita, “Optical deposition of graphene and carbon nanotubes in a fiber ferrule for passive mode-locked lasing,” Opt. Express 18(22), 23054–23061 (2010). [CrossRef] [PubMed]

3.

J. H. Im, S. Y. Choi, F. Rotermund, and D. I. Yeom, “All-fiber Er-doped dissipative soliton laser based on evanescent field interaction with carbon nanotube saturable absorber,” Opt. Express 18(21), 22141–22146 (2010). [CrossRef] [PubMed]

4.

L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B 65, 277–294 (1997). [CrossRef]

5.

K. Tamura, E. P. Ippen, H. A. Haus, and L. E. Nelson, “77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser,” Opt. Lett. 18(13), 1080–1082 (1993). [CrossRef] [PubMed]

6.

A. Komarov, H. Leblond, and F. Sanchez, “Multistablility and hysteresis phenomena in passive mode-locked lasers,” Phys. Rev. A 71, 053809 (2005). [CrossRef]

7.

F. Ö. 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). [CrossRef] [PubMed]

8.

J. R. Buckley, F. W. Wise, F. O. Ilday, and T. Sosnowski, “Femtosecond fiber lasers with pulse energies above 10 nJ,” Opt. Lett. 30(14), 1888–1890 (2005). [CrossRef] [PubMed]

9.

X. Liu, L. Wang, X. Li, H. Sun, A. Lin, K. Lu, Y. Wang, and W. Zhao, “Multistability evolution and hysteresis phenomena of dissipative solitons in a passively mode-locked fiber laser with large normal cavity dispersion,” Opt. Express 17(10), 8506–8512 (2009). [CrossRef] [PubMed]

10.

N. Akhmediev and A. Ankiewicz, “Dissipative Solitons,” in Lecture Notes in Physics, Vol. 661 (Springer, Berlin, 2005).

11.

X. M. Liu, “Hysteresis phenomena and multipulse formation of a dissipative system in a passively mode-locked fiber laser,” Phys. Rev. A 81, 023811 (2010). [CrossRef]

12.

N. N. Rozanov, “Dissipative optical solitons,” J. Opt. Technol. 76, 187–198 (2009). [CrossRef]

13.

A. Cabasse, G. Martel, and J. L. Oudar, “High power dissipative soliton in an Erbium-doped fiber laser mode-locked with a high modulation depth saturable absorber mirror,” Opt. Express 17(12), 9537–9542 (2009). [CrossRef] [PubMed]

14.

L. R. Wang, X. M. Liu, and Y. K. Gong, “Giant-chirp oscillator for ultra-large net-normal-dispersion fiber lasers,” Laser Phys. Lett. 7, 63–67 (2010). [CrossRef]

15.

B. Ortaç, M. Baumgartl, J. Limpert, and A. Tünnermann, “Approaching microjoule-level pulse energy with mode-locked femtosecond fiber lasers,” Opt. Lett. 34(10), 1585–1587 (2009). [CrossRef] [PubMed]

16.

X. Liu, “Pulse evolution without wave breaking in a strongly dissipative-dispersive laser system,” Phys. Rev. A 81, 053819 (2010). [CrossRef]

17.

X. Liu, “Mechanism of high-energy pulse generation without wave breaking in mode-locked fiber lasers,” Phys. Rev. A 82, 053808 (2010). [CrossRef]

18.

W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78, 023830 (2008). [CrossRef]

19.

W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances in the anomalous dispersion regime,” Phys. Rev. A 79, 033840 (2009). [CrossRef]

20.

M. Baumgartl, B. Ortaç, C. Lecaplain, A. Hideur, J. Limpert, and A. Tünnermann, “Sub-80 fs dissipative soliton large-mode-area fiber laser,” Opt. Lett. 35(13), 2311–2313 (2010). [CrossRef] [PubMed]

21.

H. Sayinc, D. Mortag, D. Wandt, J. Neumann, and D. Kracht, “Sub-100 fs pulses from a low repetition rate Yb-doped fiber laser,” Opt. Express 17(7), 5731–5735 (2009). [CrossRef] [PubMed]

22.

H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17(20), 17630–17635 (2009). [CrossRef] [PubMed]

23.

Z. Sun, A. G. Rozhin, F. Wang, T. Hasan, D. Popa, W. O’Neill, and A. C. Ferrari, “A compact, high power, ultrafast laser mode-locked by carbon nanotubes,” Appl. Phys. Lett. 95, 253102 (2009). [CrossRef]

24.

J. W. Lou, M. Currie, and F. K. Fatemi, “Experimental measurements of solitary pulse characteristics from an all-normal-dispersion Yb-doped fiber laser,” Opt. Express 15(8), 4960–4965 (2007). [CrossRef] [PubMed]

25.

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). [CrossRef] [PubMed]

26.

N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, “Roadmap to ultra-short record high-energy pulses out of laser oscillators,” Phys. Lett. A 372, 3124–3128 (2008). [CrossRef]

27.

A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg-Landau model for ring fiber lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(2 Pt 2), 025604 (2005). [CrossRef] [PubMed]

28.

N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(5 Pt 2), 056602 (2001). [CrossRef] [PubMed]

29.

D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72, 043816 (2005). [CrossRef]

30.

J. H. Lee, U. C. Ryu, and N. Park, “Passive erbium-doped fiber seed photon generator for high-power Er(3+)-doped fiber fluorescent sources with an 80-nm bandwidth,” Opt. Lett. 24(5), 279–281 (1999). [CrossRef]

31.

M. Baumgartl, B. Ortaç, J. Limpert, and A. Tünnermann, “Passively mode-locked chirped-pulse fiber oscillators: Study on dispersion,” in Advanced Solid-State Photonics (Optical Society of America, 2009), paper TuB3.

OCIS Codes
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(140.0140) Lasers and laser optics : Lasers and laser optics
(140.3500) Lasers and laser optics : Lasers, erbium
(140.4050) Lasers and laser optics : Mode-locked lasers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: February 25, 2011
Revised Manuscript: March 27, 2011
Manuscript Accepted: March 28, 2011
Published: April 5, 2011

Citation
Leiran Wang, Xueming Liu, Yongkang Gong, Dong Mao, and Lina Duan, "Observations of four types of pulses in a fiber laser with large net-normal dispersion," Opt. Express 19, 7616-7624 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-8-7616


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References

  1. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, Boston, 2007).
  2. A. Martinez, K. Fuse, B. Xu, and S. Yamashita, “Optical deposition of graphene and carbon nanotubes in a fiber ferrule for passive mode-locked lasing,” Opt. Express 18(22), 23054–23061 (2010). [CrossRef] [PubMed]
  3. J. H. Im, S. Y. Choi, F. Rotermund, and D. I. Yeom, “All-fiber Er-doped dissipative soliton laser based on evanescent field interaction with carbon nanotube saturable absorber,” Opt. Express 18(21), 22141–22146 (2010). [CrossRef] [PubMed]
  4. L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, “Ultrashort-pulse fiber ring lasers,” Appl. Phys. B 65, 277–294 (1997). [CrossRef]
  5. K. Tamura, E. P. Ippen, H. A. Haus, and L. E. Nelson, “77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser,” Opt. Lett. 18(13), 1080–1082 (1993). [CrossRef] [PubMed]
  6. A. Komarov, H. Leblond, and F. Sanchez, “Multistablility and hysteresis phenomena in passive mode-locked lasers,” Phys. Rev. A 71, 053809 (2005). [CrossRef]
  7. F. Ö. 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). [CrossRef] [PubMed]
  8. J. R. Buckley, F. W. Wise, F. O. Ilday, and T. Sosnowski, “Femtosecond fiber lasers with pulse energies above 10 nJ,” Opt. Lett. 30(14), 1888–1890 (2005). [CrossRef] [PubMed]
  9. X. Liu, L. Wang, X. Li, H. Sun, A. Lin, K. Lu, Y. Wang, and W. Zhao, “Multistability evolution and hysteresis phenomena of dissipative solitons in a passively mode-locked fiber laser with large normal cavity dispersion,” Opt. Express 17(10), 8506–8512 (2009). [CrossRef] [PubMed]
  10. N. Akhmediev and A. Ankiewicz, “Dissipative Solitons,” in Lecture Notes in Physics, Vol. 661 (Springer, Berlin, 2005).
  11. X. M. Liu, “Hysteresis phenomena and multipulse formation of a dissipative system in a passively mode-locked fiber laser,” Phys. Rev. A 81, 023811 (2010). [CrossRef]
  12. N. N. Rozanov, “Dissipative optical solitons,” J. Opt. Technol. 76, 187–198 (2009). [CrossRef]
  13. A. Cabasse, G. Martel, and J. L. Oudar, “High power dissipative soliton in an Erbium-doped fiber laser mode-locked with a high modulation depth saturable absorber mirror,” Opt. Express 17(12), 9537–9542 (2009). [CrossRef] [PubMed]
  14. L. R. Wang, X. M. Liu, and Y. K. Gong, “Giant-chirp oscillator for ultra-large net-normal-dispersion fiber lasers,” Laser Phys. Lett. 7, 63–67 (2010). [CrossRef]
  15. B. Ortaç, M. Baumgartl, J. Limpert, and A. Tünnermann, “Approaching microjoule-level pulse energy with mode-locked femtosecond fiber lasers,” Opt. Lett. 34(10), 1585–1587 (2009). [CrossRef] [PubMed]
  16. X. Liu, “Pulse evolution without wave breaking in a strongly dissipative-dispersive laser system,” Phys. Rev. A 81, 053819 (2010). [CrossRef]
  17. X. Liu, “Mechanism of high-energy pulse generation without wave breaking in mode-locked fiber lasers,” Phys. Rev. A 82, 053808 (2010). [CrossRef]
  18. W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78, 023830 (2008). [CrossRef]
  19. W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances in the anomalous dispersion regime,” Phys. Rev. A 79, 033840 (2009). [CrossRef]
  20. M. Baumgartl, B. Ortaç, C. Lecaplain, A. Hideur, J. Limpert, and A. Tünnermann, “Sub-80 fs dissipative soliton large-mode-area fiber laser,” Opt. Lett. 35(13), 2311–2313 (2010). [CrossRef] [PubMed]
  21. H. Sayinc, D. Mortag, D. Wandt, J. Neumann, and D. Kracht, “Sub-100 fs pulses from a low repetition rate Yb-doped fiber laser,” Opt. Express 17(7), 5731–5735 (2009). [CrossRef] [PubMed]
  22. H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17(20), 17630–17635 (2009). [CrossRef] [PubMed]
  23. Z. Sun, A. G. Rozhin, F. Wang, T. Hasan, D. Popa, W. O’Neill, and A. C. Ferrari, “A compact, high power, ultrafast laser mode-locked by carbon nanotubes,” Appl. Phys. Lett. 95, 253102 (2009). [CrossRef]
  24. J. W. Lou, M. Currie, and F. K. Fatemi, “Experimental measurements of solitary pulse characteristics from an all-normal-dispersion Yb-doped fiber laser,” Opt. Express 15(8), 4960–4965 (2007). [CrossRef] [PubMed]
  25. 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). [CrossRef] [PubMed]
  26. N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, “Roadmap to ultra-short record high-energy pulses out of laser oscillators,” Phys. Lett. A 372, 3124–3128 (2008). [CrossRef]
  27. A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg-Landau model for ring fiber lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(2 Pt 2), 025604 (2005). [CrossRef] [PubMed]
  28. N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(5 Pt 2), 056602 (2001). [CrossRef] [PubMed]
  29. D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72, 043816 (2005). [CrossRef]
  30. J. H. Lee, U. C. Ryu, and N. Park, “Passive erbium-doped fiber seed photon generator for high-power Er(3+)-doped fiber fluorescent sources with an 80-nm bandwidth,” Opt. Lett. 24(5), 279–281 (1999). [CrossRef]
  31. M. Baumgartl, B. Ortaç, J. Limpert, and A. Tünnermann, “Passively mode-locked chirped-pulse fiber oscillators: Study on dispersion,” in Advanced Solid-State Photonics (Optical Society of America, 2009), paper TuB3.

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