High-repetition-rate, stretch-lens-based actively-mode-locked femtosecond fiber laser

Ruixin Wang; Yitang Dai; Feifei Yin; Kun Xu; Li Yan; Jianqiang Li; Jintong Lin

doi:10.1364/OE.21.020923

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

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

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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)

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Related Topics
Table of Contents Category
- Lasers and Laser Optics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Optical communications (060.4510)
- Lasers, fiber (140.3510)
- Lasers, pulsed (140.3538)

About this Article
History
- Original Manuscript: May 6, 2013
- Revised Manuscript: August 9, 2013
- Manuscript Accepted: August 19, 2013
- Published: August 30, 2013

Accessible

Open Access

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.

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References

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Author
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Publication

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]
A. Chong, J. Buckley, W. Renninger, and F. Wise, “All-normal-dispersion femtosecond fiber laser,” Opt. Express 14(21), 10095–10100 (2006).
[Crossref] [PubMed]
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]
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]
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]
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]
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]
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]
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]
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]
B. H. Kolner and M. Nazarathy, “Temporal imaging with a time lens,” Opt. Lett. 14(12), 630–632 (1989).
[Crossref] [PubMed]
J. van Howe and C. Xu, “Ultrafast optical signal processing based upon space-time dualities,” J. Lightwave Technol. 24(7), 2649–2662 (2006).
[Crossref]
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.
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]
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]
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]
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]
R. Nagar, D. Abraham, and G. Eisenstein, “Pure phase-modulation mode locking in semiconductor lasers,” Opt. Lett. 17(16), 1119–1121 (1992).
[Crossref] [PubMed]
G. P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Academic Press, 2008).
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]
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]
Finisar Corporation, “Programmable narrow-band filtering using the WaveShaper 1000E and WaveShaper 4000E,” product whitepaper.
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]

2013 (1)

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]

2004 (2)

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]

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]

2002 (1)

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]

2000 (3)

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]

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]

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]

1998 (1)

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]

1996 (1)

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]

1995 (1)

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]

1992 (2)

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]

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

1989 (1)

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

Abraham, D.

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

Anderson, D.

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]

Andrekson, P. A.

Bakhshi, B.

Buckley, J.

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

Buckley, J. R.

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]

Carruthers, T. F.

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]

Chen, Y.

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]

Chong, A.

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

Clark, W. G.

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]

Dai, Y. T.

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]

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]

Desaix, M.

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]

Duling III, I. N.

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]

Eisenstein, G.

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

Grein, M. E.

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]

Haus, H. A.

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]

Horowitz, M.

Hosako, I.

Hsiang, W.-W.

Ilday, F. Ö.

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]

Ippen, E. P.

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]

Ji, Y. F.

Jiang, L. A.

Kawanishi, T.

Kolner, B. H.

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

Kubota, H.

Lai, Y.

Li, J.

Li, J. Q.

Li, Y.

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]

Lin, C.-Y.

Lin, J.

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]

Lin, J. T.

Lisak, M.

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]

McNeilage, C.

Menyuk, C. R.

Morohashi, I.

Nagar, R.

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

Nakazawa, M.

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]

Nazarathy, M.

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

Nelson, L. E.

Quiroga-Teixeiro, M. L.

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]

Renninger, W.

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

Sahara, A.

Sakamoto, T.

Searls, J. H.

Sotobayashi, H.

Tamura, K.

Tien, M.-F.

Tumura, K.

van Howe, J.

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

Wang, R. X.

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]

Windeler, R. S.

Wise, F.

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

Wise, F. W.

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]

Wu, J.

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]

Xu, C.

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]

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

Xu, K.

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]

Yan, L.

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]

Yin, F. F.

Yoshida, E.

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]

IEEE J. Quantum Electron. (3)

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]

IEEE Photon. Technol. Lett. (2)

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]

J. Lightwave Technol. (1)

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

J. Opt. Soc. Am. B (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]

Laser Phys. Lett. (1)

Opt. Express (3)

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]

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

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]

Opt. Lett. (7)

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

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

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]

Phys. Rev. Lett. (1)

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]

Other (4)

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

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.

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]

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

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Fig. 1

Illustration of the fiber laser cavity elements used for the proposed model. AM: amplitude modulator. PM:phase modulator.

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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.

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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.

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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.

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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).

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Tables (1)

Table 1 Parameters Uused in the Ssimulation

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Equations (4)

Equations on this page are rendered with MathJax. Learn more.

u (t) = \sqrt{P_{0}} \exp [- \frac{t^{2}}{2 τ^{2}} (1 - i C)] = \sqrt{P_{0}} \exp (- \frac{t^{2}}{2 q}),

q_{o u t} = \frac{A q_{i n} + B}{C q_{i n} + D},

T_{A M} T_{P M} T_{D} T_{G} = [\begin{matrix} 1 & \frac{2 g}{Ω_{g}^{2}} - 2 i β_{2} L \\ M ω^{2} / 2 - i Δ_{m} ω^{2} & 1 \end{matrix}] .

q = \sqrt{\frac{(M ω^{2} / 2 - i Δ_{m} ω^{2})}{(\frac{2 g}{Ω_{g}^{2}} - 2 i β_{2} L)}} .

Parameter	Value	Parameter	Value
AM (T_AM)	$[\begin{matrix} 1 & 0 \\ M ω^{2} / 2 & 1 \end{matrix}]$	PM (T_PM)	$[\begin{matrix} 1 & 0 \\ - i Δ_{m} ω^{2} & 1 \end{matrix}]$
Dispersive line (T_D)	$[\begin{matrix} 1 & - 2 i β_{2} L \\ 0 & 1 \end{matrix}]$	Gain bandwidth (T_G)	$[\begin{matrix} 1 & \frac{2 g}{Ω_{g}^{2}} \\ 0 & 1 \end{matrix}]$
Small-signal gain (g), EDF	3 m⁻¹	AM modulation depth (M,)	1 (V/V_π)
Gain bandwidth, EDF (Ω_g)	30 nm	PM modulation depth (Δ_m)	From 0.2 to 10 (V/V_π)
RF frequency (ω/2π)	10 GHz	Fiber dispersion (β₂), SMF	18 ps/nm/km
Gain saturation power (E_sat), EDF	50 mW	Fiber dispersion (β₂), EDF	32 ps/nm/km
Length (L), SMF	From 10 to 510 m

Abstract

References

2013 (1)

2012 (1)

2009 (2)

2006 (2)

2005 (1)

2004 (2)

2002 (1)

2000 (3)

1998 (1)

1996 (1)

1995 (1)

1992 (2)

1989 (1)

Abraham, D.

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