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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 18 — Sep. 9, 2013
  • pp: 20923–20930
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High-repetition-rate, stretch-lens-based actively-mode-locked femtosecond fiber laser

Ruixin Wang, Yitang Dai, Feifei Yin, Kun Xu, Li Yan, Jianqiang Li, and Jintong Lin  »View Author Affiliations


Optics Express, Vol. 21, Issue 18, pp. 20923-20930 (2013)
http://dx.doi.org/10.1364/OE.21.020923


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Abstract

We propose and demonstrate a novel actively mode-locked fiber laser based on a stretch-type time-lens. The pulse generated by this scheme has high repetition rate and large bandwidth while no nonlinearity is participated. A 10-GHz chirped pulse train with 18-ps duration and 11.6-nm bandwidth is obtained, which is then extra-cavity compressed down to 825 fs. The pulse characteristics dependent on the cavity dispersion and time-lens strength are discussed. Pulse propagation in the laser is similar with dissipative soliton in all-normal-dispersion laser. The results demonstrate that the stretch-lens inside the actively mode-locked laser can effectively broaden the spectral bandwidth, instead of the fiber nonlinearity, which can then support a high-repetition-rate “linear dissipative soliton” pulse shaping in a very compact design.

© 2013 OSA

1. Introduction

Femtosecond fiber lasers are attractive light sources as they offer many advantages such as compact size, maintenance- and alignment-free, and superior thermal handling. Generally, fs-pulse generation in fiber laser relies on the contribution of fiber nonlinearity, which could however induce instability or even collapse of the pulse [1

1. 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). [CrossRef]

]. Moreover, the strong nonlinearity in the cavity requires high pulse energy, so the generation of fs-pulse usually exists in repetition-rate-limited passive mode-locked lasers [2

2. A. Chong, J. Buckley, W. Renninger, and F. Wise, “All-normal-dispersion femtosecond fiber laser,” Opt. Express 14(21), 10095–10100 (2006). [CrossRef] [PubMed]

, 3

3. H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, “Stretched-pulse additive pulse mode-locking in fiber ring lasers: theory and experiment,” IEEE J. Quantum Electron. 31(3), 591–598 (1995). [CrossRef]

], where the repetition rate is fixed by cavity length. To generate high-repetition-rate pulses, actively mode-locked fiber laser is widely employed [4

4. T. F. Carruthers and I. N. Duling III, “10-GHz, 1.3-ps erbium fiber laser employing soliton pulse shortening,” Opt. Lett. 21(23), 1927–1929 (1996). [CrossRef] [PubMed]

10

10. M. E. Grein, H. A. Haus, Y. Chen, and E. P. Ippen, “Quantum-limited timing jitter in actively modelocked lasers,” IEEE J. Quantum Electron. 40(10), 1458–1470 (2004). [CrossRef]

]. However, the pulse train in those lasers is based on soliton pulse shaping, and long cavity is needed to accumulate sufficient nonlinearity, which increases the cavity instability. Besides, the ultra-short pulse is usually sensitive to the in-cavity dispersion and nonlinearity map, which should also be carefully designed.

2. Design rationale and numerical simulations

The structure illustrated in Fig. 1
Fig. 1 Illustration of the fiber laser cavity elements used for the proposed model. AM: amplitude modulator. PM:phase modulator.
is employed to investigate the principle of our actively mode-locked fiber laser. The key elements of such a laser are a segment of Er-doped fiber (EDF), a segment of single-mode fiber (SMF), and components that produce amplitude and phase modulation. When a mode-locked laser cavity consists of several optical elements, one can immediately obtain a steady-state solution (pulse width and chirp) of a mode-locked pulse by using the time-domain ABCD matrix, which is presented by Nakazawa et al. [17

17. M. Nakazawa, H. Kubota, A. Sahara, and K. Tumura, “Time-domain ABCD matrix formalism for laser mode-locking and optical pulse transmission,” IEEE J. Quantum Electron. 34(7), 1075–1081 (1998). [CrossRef]

].

Using the Gaussian approximation, the time domain amplitude expression of a linearly chirped pulse is:
u(t)=P0exp[t22τ2(1iC)]=P0exp(t22q),
(1)
where P0 is the peak power, τ is the 1/e pulse width, C is the dimensionless linear chirp parameter, and q parameter is τ2/(1 + iC). When such a pulse passed through an optical element characterized by ABCD matrix[ABCD], the q parameter at output will satisfy the following ABCD law
qout=Aqin+BCqin+D,
(2)
where qout and qin are the corresponding q parameter at output and input port. The optical components in Fig. 1 described by ABCD matrix is shown in Table 1

Table 1. Parameters Uused in the Ssimulation

table-icon
View This Table
.

The pulse forming process is determined by four primary factors: the amplitude modulation, the phase modulation, the fiber dispersion, and the gain fiber filtering. In our laser, the fiber nonlinearity is negligible, because of the low peak power and long pulse duration. Neglect the multiplication of the B and C matrix elements [17

17. M. Nakazawa, H. Kubota, A. Sahara, and K. Tumura, “Time-domain ABCD matrix formalism for laser mode-locking and optical pulse transmission,” IEEE J. Quantum Electron. 34(7), 1075–1081 (1998). [CrossRef]

], the total ABCD matrix for the active mode locking pulse is
TAMTPMTDTG=[12gΩg22iβ2LMω2/2iΔmω21].
(3)
To obtain the steady-state solution, the self-consistent condition of q should be satisfied, as q(0) = q(L). Introducing Eq. (3) into Eq. (2), we can obtain the analytical expression of the pulse Gaussian factor
q=(Mω2/2iΔmω2)(2gΩg22iβ2L).
(4)
Based on Eq. (4), we draw the pulse properties depending on the cavity dispersion and phase modulation in Fig. 2
Fig. 2 Pulse duration (a) and bandwidth (b) as a function of total cavity dispersion (by changing the SMF length, according to Table 1) and modulation depth of the PM.
.

Figure 2 shows that under large phase modulation depth and small cavity dispersion, pulse with large bandwidth can be obtained in our proposed laser without the participation of fiber nonlinearity. The generated pulse with large chirp has large time-bandwidth product, which is very different from soliton. Although PM is used in our fiber laser, the above pulse properties indicate that the laser is not working at soliton shaping regime [6

6. M. Nakazawa and E. Yoshida, “A 40-GHz 850-fs regeneratively FM mode-locked polarization-maintaining erbium fiber ring laser,” IEEE Photon. Technol. Lett. 12(12), 1613–1615 (2000). [CrossRef]

, 8

8. W.-W. Hsiang, C.-Y. Lin, M.-F. Tien, and Y. Lai, “Direct generation of a 10 GHz 816 fs pulse train from an erbium-fiber soliton laser with asynchronous phase modulation,” Opt. Lett. 30(18), 2493–2495 (2005). [CrossRef] [PubMed]

]. Furthermore, the PM can impose either positive or negative linear chirp onto the pulse [18

18. R. Nagar, D. Abraham, and G. Eisenstein, “Pure phase-modulation mode locking in semiconductor lasers,” Opt. Lett. 17(16), 1119–1121 (1992). [CrossRef] [PubMed]

], so that stable spectral broadening can be achieved by either anomalous or normal cavity dispersion (by changing the sign of the fiber dispersion) under proper timing of the PM, which is very different from the nonlinearity-based spectral broadening: the soliton exists in anomalous-dispersion cavity, while the dissipative soliton exists in a normal-dispersion one.

To illustrate the pulse generation mechanism and reveal the details of pulse shaping in the cavity at different position, we calculate the master equation of mode locking [19

19. G. P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Academic Press, 2008).

]. Assume that the in-cavity fibers are nonlinearity-free. We take no account of the fiber nonlinearity term. As an initial condition, white noise is used. The model is then solved by iterating the initial field until the field becomes constant to ensure that a stable mode-locked pulse operation has been reached after a finite number of traversals of the cavity [20

20. 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]

]. Under the condition of 14-m SMF and 1.7-m EDF, 5π radians phase modulation, and 10-GHz RF signal, a stable solution is obtained as shown in Fig. 3
Fig. 3 Numerical simulation results. (a) Temporal intensity profile with linear chirp, inset: optical spectrum of the pulse. (b) Evolution of pulse width (black) and spectral bandwidth (red) through the laser cavity.
.

The numerical study has revealed the pulse shaping of the proposed actively mode-locked laser, which is explicated in Fig. 3(b) through the evolution of one pulse properties (e.g. the pulse width and bandwidth) along the fiber. In a regular phase-modulation-based active mode locking, the cavity dispersion will de-chirp and compress the pulse after phase modulation, which results in a short and slightly-chirped pulse whose bandwidth is however greatly limited by the dispersion [6

6. M. Nakazawa and E. Yoshida, “A 40-GHz 850-fs regeneratively FM mode-locked polarization-maintaining erbium fiber ring laser,” IEEE Photon. Technol. Lett. 12(12), 1613–1615 (2000). [CrossRef]

, 8

8. W.-W. Hsiang, C.-Y. Lin, M.-F. Tien, and Y. Lai, “Direct generation of a 10 GHz 816 fs pulse train from an erbium-fiber soliton laser with asynchronous phase modulation,” Opt. Lett. 30(18), 2493–2495 (2005). [CrossRef] [PubMed]

] and has to be further broadened by fiber nonlinearity. On the contrary, in our design the cavity dispersion will broaden the temporal pulse. Assume the fiber dispersion is anomalous. By adjusting the phase of the driven-signal, the PM generates a linear and anomalous chirp to the pulse, which is then broadened by the following fiber. In contrast to the conventional fiber laser, where the broad spectrum is provided by the nonlinear effect of high energy ultrashort pulse, the time-lens plays an important role of linear widening in our scheme. However, the intensity windowing by the AM reverses the above changes, both temporally and spectrally due to the linear chirp, and thus restores the pulse after traversal of the cavity. In addition, the EDF has the similar effect as AM because of the gain filtering.

Therefore, the pulse in the linear, time-lens-based laser is similar to the typical dissipative soliton in a nonlinear laser [20

20. 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]

]. The pulse has large linear chirp, and the spectrum profile [Fig. 3(a) inset] has similar property (also refer to the experiment results), due to the similar pulse shaping process. The reason is that the nonlinear phase modulation on a pulse by fiber self-phase-modulation (SPM) is analogous to the quadratic phase modulation by time-lens. Here the presence of the large chirp is critical, which is the same as dissipative soliton in normal-dispersion cavity. The pulse duration under large chirp as well as the matched dispersion is always long, which ensures an effective time-lens modulation to increase the spectrum bandwidth but does not destabilize the pulse.

Since the spectral broadening is induced totally by the pulse-energy-independent time-lens, a high repetition rate is then feasible without nonlinearity. As a result, the fiber length can be shortened greatly, and a very compact design is expected, which could be more stable.

3. Experimental results and discussion

The experimental setup of the proposed actively mode-locked fiber laser is illustrated in Fig. 4
Fig. 4 Schematic of the proposed actively mode-locked fiber laser. RF: RF sinusoidal source. VGA: variable gain amplifier. PL: polarizer. ISO: isolator. PS: phase shifter.
. A 1.7-m Er-doped fiber (EDF) with absorption of 55 dB/m @ 1530 nm is used, which is forward pumped by a 980-nm laser diode through a 980/1550-nm wavelength division multiplexer (WDM). A dual-drive LiNbO3 Mach-Zehnder amplitude modulator (AM; from EOSpace, 10 GHz), one port of which is driven by a RF sinusoidal source (Agilent E8267D, 250 kHz-20 GHz), is employed to realize the active mode locking. Due to the low polarization-dependent loss of the AM, a polarizer is used before to ensure the AM works at the correct polarization state. An isolator is employed for unidirectional operation, and a 30% optical coupler (OC1 in Fig. 4) outputs the laser pulses. A LiNbO3 PM with 10-GHz bandwidth, which is actually the in-cavity time-lens, is driven by the same RF sinusoidal wave which is amplified and carefully synchronized by a phase shifter. Adjusting the phase shifter to make sure the minimum point of the quadratic phase is aligned to the center of the pulse. The EDF and other single mode fibers (SMFs) in the cavity are polarization-maintained to prevent any polarization fluctuation. The total length of the cavity is approximately 17.5 m, corresponding to a fundamental frequency of about 11.4 MHz. Note that a pulse-intensity-feed-forward path, which consists of an optical tunable delay line (ODL), a fast photo detector (PD), and a microwave amplifier (from 75 kHz to 10 GHz) with tunable gain, is employed, which will be explained later.

In our experiment, the frequency of the RF sinusoidal wave is 10.0587 GHz, which is the 882th harmonics, and the pump power is 23.82 dBm. The RF power applied on the PM is 29 dBm, corresponding to a modulation depth of about 4 Vπ. Highly-stable active mode locking is observed, as is shown in Fig. 5
Fig. 5 (a) Oscilloscope trace of output pulse. (b) RF spectrum of the 10 GHz mode-locked pulse train. (c) Optical spectrum of the output pulse and the parabolic phase response of waveshaper. (d) The compressed pulse temporal profile (black line) and Gaussian fit (red circles).
. The pulse is firstly received by a 70-GHz PD and then measured by a high-speed sampling oscilloscope (HP 83485B) whose bandwidth is 40 GHz. The measured full-width at half-maximum (FWHM) of the output pulse is about 18 ps, as shown in Fig. 5(a). Experimentally the supermode noise of the generated 10 GHz optical pulse train is investigated using a RF spectrum analyzer (Agilent N9030A, with analysis bandwidth of 26.5 GHz). The electrical spectrum is plotted in Fig. 5(b). Within the span of 300 MHz, which covers more than 26 times the cavity frequency, the supermode noise suppression ratio is closed to 80 dB, which indicates a stable 10-GHz pulse train.

Different from the conventional actively mode-locked fiber lasers, the proposed scheme includes a pulse-intensity-feed-forward path, as shown in Fig. 4, which is employed to suppress the supermode noise [23

23. K. Xu, R. X. Wang, Y. T. Dai, F. F. Yin, J. Q. Li, Y. F. Ji, and J. T. Lin, “Supermode noise suppression in an actively mode-locked fiber laser with pulse intensity feed-forward and a dual-drive MZM,” Laser Phys. Lett. 10(5), 055108 (2013). [CrossRef]

]. The output optical pulse is firstly converted into electronic signal, and then fed forward to the “negative” port of the dual-drive AM, where the optical pulse is modulated by the reversed intensity profile of itself. Therefore, under the feed-forward control, pulse-to-pulse intensity fluctuation is suppressed with proper feed-forward strength. When the feed-forward loop is switched off, sidebands appear at the cavity-mode spacing with large intensity, and serious pulse-intensity fluctuation occurs in the time domain. Note that the feed-forward path has no relationship with “linear dissipative soliton” pulse shaping. Other than the normally used power-limiting method including nonlinear polarization rotation (NPR), the pulse-intensity-feed-forward scheme is also free from fiber nonlinearity.

4. Conclusion

In conclusion, we have proposed and demonstrated a novel actively mode-locked femtosecond fiber laser scheme, where an optical-power-independent time-lens is employed to spectrally broaden the optical pulse, instead of the conventional fiber nonlinearity. As a result, large bandwidth can be achieved under a high repetition rate and average optical pump power. Experimentally, a de-chirped pulse train with 825-fs duration at 10-GHz repetition rate was generated. Due to the nonlinearity-free requirement, the proposed scheme can be more compact by using integrated modulators and waveguide amplifier, where the bandwidth can be further broadened due to the cut of dispersive fibers. In addition, benefited from the development of digital optical communications, high-speed opto-electronic devices (e.g. modulators, photo detectors and RF drivers) will enable the proposed active mode locking with repetition rate up to 40 GHz or more.

Acknowledgment

This work was supported in part by 973 Program (2012CB315705), National 863 Program (2011AA010306), NSFC Program (61271042, 61107058, and 61120106001), the Fundamental Research Funds for the Central Universities, BUPT Excellent Ph.D. Students Foundation (CX201321), and the Fund of State Key Laboratory of Information Photonics and Optical Communications.

References and links

1.

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). [CrossRef]

2.

A. Chong, J. Buckley, W. Renninger, and F. Wise, “All-normal-dispersion femtosecond fiber laser,” Opt. Express 14(21), 10095–10100 (2006). [CrossRef] [PubMed]

3.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, “Stretched-pulse additive pulse mode-locking in fiber ring lasers: theory and experiment,” IEEE J. Quantum Electron. 31(3), 591–598 (1995). [CrossRef]

4.

T. F. Carruthers and I. N. Duling III, “10-GHz, 1.3-ps erbium fiber laser employing soliton pulse shortening,” Opt. Lett. 21(23), 1927–1929 (1996). [CrossRef] [PubMed]

5.

J. Li, P. A. Andrekson, and B. Bakhshi, “Direct generation of subpicosecond chirp-free pulses at 10 GHz from a nonpolarization maintaining actively mode-locked fiber ring laser,” IEEE Photon. Technol. Lett. 12(9), 1150–1152 (2000). [CrossRef]

6.

M. Nakazawa and E. Yoshida, “A 40-GHz 850-fs regeneratively FM mode-locked polarization-maintaining erbium fiber ring laser,” IEEE Photon. Technol. Lett. 12(12), 1613–1615 (2000). [CrossRef]

7.

T. F. Carruthers, I. N. Duling III, M. Horowitz, and C. R. Menyuk, “Dispersion management in a harmonically mode-locked fiber soliton laser,” Opt. Lett. 25(3), 153–155 (2000). [CrossRef] [PubMed]

8.

W.-W. Hsiang, C.-Y. Lin, M.-F. Tien, and Y. Lai, “Direct generation of a 10 GHz 816 fs pulse train from an erbium-fiber soliton laser with asynchronous phase modulation,” Opt. Lett. 30(18), 2493–2495 (2005). [CrossRef] [PubMed]

9.

M. E. Grein, L. A. Jiang, H. A. Haus, E. P. Ippen, C. McNeilage, J. H. Searls, and R. S. Windeler, “Observation of quantum-limited timing jitter in an active, harmonically mode-locked fiber laser,” Opt. Lett. 27(11), 957–959 (2002). [CrossRef] [PubMed]

10.

M. E. Grein, H. A. Haus, Y. Chen, and E. P. Ippen, “Quantum-limited timing jitter in actively modelocked lasers,” IEEE J. Quantum Electron. 40(10), 1458–1470 (2004). [CrossRef]

11.

B. H. Kolner and M. Nazarathy, “Temporal imaging with a time lens,” Opt. Lett. 14(12), 630–632 (1989). [CrossRef] [PubMed]

12.

J. van Howe and C. Xu, “Ultrafast optical signal processing based upon space-time dualities,” J. Lightwave Technol. 24(7), 2649–2662 (2006). [CrossRef]

13.

Y. T. Dai and C. Xu, “Femtosecond pulses with 1.1 GHz repetition rate generated from a CW laser without mode-locking,” in Conference on Laser and Electro-Optics (CLEO 2009) (Optical Society of America, 2009), paper CMA5.

14.

Y. T. Dai and C. Xu, “Femtosecond pulses with tunable, high repetition rate generated from a CW laser without mode-locking,” in Conference on Optical Fiber Communication (OFC 2009) (Optical Society of America, 2009), paper OWB4. [CrossRef]

15.

Y. T. Dai and C. Xu, “Generation of high repetition rate femtosecond pulses from a CW laser by a time-lens loop,” Opt. Express 17(8), 6584–6590 (2009). [CrossRef] [PubMed]

16.

I. Morohashi, T. Sakamoto, H. Sotobayashi, T. Kawanishi, and I. Hosako, “Broadband wavelength-tunable ultrashort pulse source using a Mach-Zehnder modulator and dispersion-flattened dispersion-decreasing fiber,” Opt. Lett. 34(15), 2297–2299 (2009). [CrossRef] [PubMed]

17.

M. Nakazawa, H. Kubota, A. Sahara, and K. Tumura, “Time-domain ABCD matrix formalism for laser mode-locking and optical pulse transmission,” IEEE J. Quantum Electron. 34(7), 1075–1081 (1998). [CrossRef]

18.

R. Nagar, D. Abraham, and G. Eisenstein, “Pure phase-modulation mode locking in semiconductor lasers,” Opt. Lett. 17(16), 1119–1121 (1992). [CrossRef] [PubMed]

19.

G. P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Academic Press, 2008).

20.

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]

21.

R. X. Wang, Y. T. Dai, L. Yan, J. Wu, K. Xu, Y. Li, and J. Lin, “Dissipative soliton in actively mode-locked fiber laser,” Opt. Express 20(6), 6406–6411 (2012). [CrossRef] [PubMed]

22.

Finisar Corporation, “Programmable narrow-band filtering using the WaveShaper 1000E and WaveShaper 4000E,” product whitepaper.

23.

K. Xu, R. X. Wang, Y. T. Dai, F. F. Yin, J. Q. Li, Y. F. Ji, and J. T. Lin, “Supermode noise suppression in an actively mode-locked fiber laser with pulse intensity feed-forward and a dual-drive MZM,” Laser Phys. Lett. 10(5), 055108 (2013). [CrossRef]

OCIS Codes
(060.4510) Fiber optics and optical communications : Optical communications
(140.3510) Lasers and laser optics : Lasers, fiber
(140.3538) Lasers and laser optics : Lasers, pulsed

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: May 6, 2013
Revised Manuscript: August 9, 2013
Manuscript Accepted: August 19, 2013
Published: August 30, 2013

Citation
Ruixin Wang, Yitang Dai, Feifei Yin, Kun Xu, Li Yan, Jianqiang Li, and Jintong Lin, "High-repetition-rate, stretch-lens-based actively-mode-locked femtosecond fiber laser," Opt. Express 21, 20923-20930 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-18-20923


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References

  1. D. Anderson, M. Desaix, M. Lisak, and M. L. Quiroga-Teixeiro, “Wave breaking in nonlinear-optical fibers,” J. Opt. Soc. Am. B9(8), 1358–1361 (1992). [CrossRef]
  2. A. Chong, J. Buckley, W. Renninger, and F. Wise, “All-normal-dispersion femtosecond fiber laser,” Opt. Express14(21), 10095–10100 (2006). [CrossRef] [PubMed]
  3. H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, “Stretched-pulse additive pulse mode-locking in fiber ring lasers: theory and experiment,” IEEE J. Quantum Electron.31(3), 591–598 (1995). [CrossRef]
  4. T. F. Carruthers and I. N. Duling III, “10-GHz, 1.3-ps erbium fiber laser employing soliton pulse shortening,” Opt. Lett.21(23), 1927–1929 (1996). [CrossRef] [PubMed]
  5. J. Li, P. A. Andrekson, and B. Bakhshi, “Direct generation of subpicosecond chirp-free pulses at 10 GHz from a nonpolarization maintaining actively mode-locked fiber ring laser,” IEEE Photon. Technol. Lett.12(9), 1150–1152 (2000). [CrossRef]
  6. M. Nakazawa and E. Yoshida, “A 40-GHz 850-fs regeneratively FM mode-locked polarization-maintaining erbium fiber ring laser,” IEEE Photon. Technol. Lett.12(12), 1613–1615 (2000). [CrossRef]
  7. T. F. Carruthers, I. N. Duling III, M. Horowitz, and C. R. Menyuk, “Dispersion management in a harmonically mode-locked fiber soliton laser,” Opt. Lett.25(3), 153–155 (2000). [CrossRef] [PubMed]
  8. W.-W. Hsiang, C.-Y. Lin, M.-F. Tien, and Y. Lai, “Direct generation of a 10 GHz 816 fs pulse train from an erbium-fiber soliton laser with asynchronous phase modulation,” Opt. Lett.30(18), 2493–2495 (2005). [CrossRef] [PubMed]
  9. M. E. Grein, L. A. Jiang, H. A. Haus, E. P. Ippen, C. McNeilage, J. H. Searls, and R. S. Windeler, “Observation of quantum-limited timing jitter in an active, harmonically mode-locked fiber laser,” Opt. Lett.27(11), 957–959 (2002). [CrossRef] [PubMed]
  10. M. E. Grein, H. A. Haus, Y. Chen, and E. P. Ippen, “Quantum-limited timing jitter in actively modelocked lasers,” IEEE J. Quantum Electron.40(10), 1458–1470 (2004). [CrossRef]
  11. B. H. Kolner and M. Nazarathy, “Temporal imaging with a time lens,” Opt. Lett.14(12), 630–632 (1989). [CrossRef] [PubMed]
  12. J. van Howe and C. Xu, “Ultrafast optical signal processing based upon space-time dualities,” J. Lightwave Technol.24(7), 2649–2662 (2006). [CrossRef]
  13. Y. T. Dai and C. Xu, “Femtosecond pulses with 1.1 GHz repetition rate generated from a CW laser without mode-locking,” in Conference on Laser and Electro-Optics (CLEO 2009) (Optical Society of America, 2009), paper CMA5.
  14. Y. T. Dai and C. Xu, “Femtosecond pulses with tunable, high repetition rate generated from a CW laser without mode-locking,” in Conference on Optical Fiber Communication (OFC 2009) (Optical Society of America, 2009), paper OWB4. [CrossRef]
  15. Y. T. Dai and C. Xu, “Generation of high repetition rate femtosecond pulses from a CW laser by a time-lens loop,” Opt. Express17(8), 6584–6590 (2009). [CrossRef] [PubMed]
  16. I. Morohashi, T. Sakamoto, H. Sotobayashi, T. Kawanishi, and I. Hosako, “Broadband wavelength-tunable ultrashort pulse source using a Mach-Zehnder modulator and dispersion-flattened dispersion-decreasing fiber,” Opt. Lett.34(15), 2297–2299 (2009). [CrossRef] [PubMed]
  17. M. Nakazawa, H. Kubota, A. Sahara, and K. Tumura, “Time-domain ABCD matrix formalism for laser mode-locking and optical pulse transmission,” IEEE J. Quantum Electron.34(7), 1075–1081 (1998). [CrossRef]
  18. R. Nagar, D. Abraham, and G. Eisenstein, “Pure phase-modulation mode locking in semiconductor lasers,” Opt. Lett.17(16), 1119–1121 (1992). [CrossRef] [PubMed]
  19. G. P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Academic Press, 2008).
  20. 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]
  21. R. X. Wang, Y. T. Dai, L. Yan, J. Wu, K. Xu, Y. Li, and J. Lin, “Dissipative soliton in actively mode-locked fiber laser,” Opt. Express20(6), 6406–6411 (2012). [CrossRef] [PubMed]
  22. Finisar Corporation, “Programmable narrow-band filtering using the WaveShaper 1000E and WaveShaper 4000E,” product whitepaper.
  23. K. Xu, R. X. Wang, Y. T. Dai, F. F. Yin, J. Q. Li, Y. F. Ji, and J. T. Lin, “Supermode noise suppression in an actively mode-locked fiber laser with pulse intensity feed-forward and a dual-drive MZM,” Laser Phys. Lett.10(5), 055108 (2013). [CrossRef]

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