Abstract

We demonstrate a stable conventional soliton in a Tm-doped hybrid mode-locked fiber laser by employing a homemade all-fiber Lyot filter (AFLF) and a single-wall carbon nanotube. The AFLF, designed by sandwiching a piece of polarization-maintained fiber (PMF) with two 45° tilted fiber gratings inscribed by a UV laser in PMF with a phase-mask scanning technique, shows large filter depth of 9  dB and small insertion loss of 0.8  dB. By optimizing the free spectral range of the AFLF, the Kelly sidebands of a conventional soliton centered at 1966.4 nm can be dramatically suppressed without impairing the main shape of the soliton spectrum. It gives the pulse duration of 1.18 ps and bandwidth of 3.8 nm. By adjusting the temperature of the PMF of the AFLF from 7°C to 60°C, wavelength tunable soliton pulses ranging from 1971.62 nm to 1952.63 nm are also obtained. The generated soliton pulses can be precisely tuned between 1971.62 nm and 1952.63 nm by controlling the temperature of the AFLF.

© 2019 Chinese Laser Press

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References

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2016 (1)

2015 (2)

2014 (2)

2013 (3)

2012 (6)

2011 (1)

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, “Spectral sidebands and multipulse formation in passively mode-locked lasers,” Phys. Rev. A 83, 043831 (2011).
[Crossref]

2010 (3)

Z. Sun, T. Hasan, F. Wang, A. G. Rozhin, I. H. White, and A. C. Ferrari, “Ultrafast stretched-pulse fiber laser mode-locked by carbon nanotubes,” Nano Res. 3, 404–411 (2010).
[Crossref]

Z. Sun, D. Popa, T. Hasan, F. Torrisi, F. Wang, E. J. R. Kelleher, J. C. Travers, V. Nicolosi, and A. C. Ferrari, “A stable, wideband tunable, near transform-limited, graphene-mode-locked, ultrafast laser,” Nano Res. 3, 653–660 (2010).
[Crossref]

K. Özgören and F. Ö. Ilday, “All-fiber all-normal dispersion laser with a fiber-based Lyot filter,” Opt. Lett. 35, 1296–1298 (2010).
[Crossref]

2009 (2)

B. Farrow and P. V. Kamat, “CdSe quantum dot sensitized solar cells. Shuttling electrons through stacked carbon nanocups,” J. Am. Chem. Soc. 131, 11124–11131 (2009).
[Crossref]

M. E. Fermann and I. Hartl, “Ultrafast fiber laser technology,” IEEE J. Sel. Top. Quantum 15, 191–206 (2009).
[Crossref]

2006 (1)

2001 (1)

1998 (1)

F. X. Kurtner, J. A. der Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers-what’s the difference?” IEEE J. Sel. Top. Quantum 4, 159–168 (1998).
[Crossref]

1997 (1)

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]

1994 (2)

M. L. Dennis and I. N. Duling, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30, 1469–1477 (1994).
[Crossref]

K. Tamura, C. R. Doerr, H. A. Haus, and E. P. Ippen, “Soliton fiber ring laser stabilization and tuning with a broad intracavity filter,” IEEE Photon. Technol. Lett. 6, 697–699 (1994).
[Crossref]

1993 (4)

M. E. Fermann, M. J. Andrejco, M. L. Stock, Y. Silberberg, and A. M. Weiner, “Passive mode locking in erbium fiber lasers with negative group delay,” Appl. Phys. Lett. 62, 910–912 (1993).
[Crossref]

M. Nakazawa, E. Yoshida, T. Sugawa, and Y. Kimura, “Continuum suppressed, uniformly repetitive 136 fs pulse generation from an erbium-doped fibre laser with nonlinear polarisation rotation,” Electron. Lett. 29, 1327–1329 (1993).
[Crossref]

M. J. Guy, D. U. Noske, and J. R. Taylor, “Generation of femtosecond soliton pulses by passive mode locking of an ytterbium-erbium figure-of-eight fiber laser,” Opt. Lett. 18, 1447–1449 (1993).
[Crossref]

D. U. Noske and J. R. Taylor, “Spectral and temporal stabilisation of a diode-pumped ytterbium-erbium fibre soliton laser,” Electron. Lett. 29, 2200–2202 (1993).
[Crossref]

1992 (1)

S. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28, 806–807 (1992).
[Crossref]

1975 (1)

H. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE J. Quantum Electron. 11, 736–746 (1975).
[Crossref]

Abramski, K. M.

Andrejco, M. J.

M. E. Fermann, M. J. Andrejco, M. L. Stock, Y. Silberberg, and A. M. Weiner, “Passive mode locking in erbium fiber lasers with negative group delay,” Appl. Phys. Lett. 62, 910–912 (1993).
[Crossref]

Bekker, A.

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, “Spectral sidebands and multipulse formation in passively mode-locked lasers,” Phys. Rev. A 83, 043831 (2011).
[Crossref]

Boguslawski, J.

Byer, R. L.

Chen, Y.

Cui, Y.

X. Liu, D. Han, Z. Sun, C. Zeng, H. Lu, D. Mao, Y. Cui, and F. Wang, “Versatile multi-wavelength ultrafast fiber laser mode-locked by carbon nanotubes,” Sci. Rep. 3, 2718 (2013).
[Crossref]

Dennis, M. L.

M. L. Dennis and I. N. Duling, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30, 1469–1477 (1994).
[Crossref]

der Au, J. A.

F. X. Kurtner, J. A. der Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers-what’s the difference?” IEEE J. Sel. Top. Quantum 4, 159–168 (1998).
[Crossref]

Digonnet, M. J. F.

Doerr, C. R.

K. Tamura, C. R. Doerr, H. A. Haus, and E. P. Ippen, “Soliton fiber ring laser stabilization and tuning with a broad intracavity filter,” IEEE Photon. Technol. Lett. 6, 697–699 (1994).
[Crossref]

Duling, I. N.

M. L. Dennis and I. N. Duling, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30, 1469–1477 (1994).
[Crossref]

Farrow, B.

B. Farrow and P. V. Kamat, “CdSe quantum dot sensitized solar cells. Shuttling electrons through stacked carbon nanocups,” J. Am. Chem. Soc. 131, 11124–11131 (2009).
[Crossref]

Fermann, M. E.

M. E. Fermann and I. Hartl, “Ultrafast fiber laser technology,” IEEE J. Sel. Top. Quantum 15, 191–206 (2009).
[Crossref]

M. E. Fermann, M. J. Andrejco, M. L. Stock, Y. Silberberg, and A. M. Weiner, “Passive mode locking in erbium fiber lasers with negative group delay,” Appl. Phys. Lett. 62, 910–912 (1993).
[Crossref]

Ferrari, A. C.

Z. Sun, D. Popa, T. Hasan, F. Torrisi, F. Wang, E. J. R. Kelleher, J. C. Travers, V. Nicolosi, and A. C. Ferrari, “A stable, wideband tunable, near transform-limited, graphene-mode-locked, ultrafast laser,” Nano Res. 3, 653–660 (2010).
[Crossref]

Z. Sun, T. Hasan, F. Wang, A. G. Rozhin, I. H. White, and A. C. Ferrari, “Ultrafast stretched-pulse fiber laser mode-locked by carbon nanotubes,” Nano Res. 3, 404–411 (2010).
[Crossref]

Fischer, B.

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, “Spectral sidebands and multipulse formation in passively mode-locked lasers,” Phys. Rev. A 83, 043831 (2011).
[Crossref]

Gat, O.

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, “Spectral sidebands and multipulse formation in passively mode-locked lasers,” Phys. Rev. A 83, 043831 (2011).
[Crossref]

Geng, J.

Q. Wang, J. Geng, T. Luo, and S. Jiang, “2 μm mode-locked fiber laser,” Proc. SPIE 8237, 82371N (2012).
[Crossref]

Guina, M.

Guy, M. J.

Han, D.

X. Liu, D. Han, Z. Sun, C. Zeng, H. Lu, D. Mao, Y. Cui, and F. Wang, “Versatile multi-wavelength ultrafast fiber laser mode-locked by carbon nanotubes,” Sci. Rep. 3, 2718 (2013).
[Crossref]

Han, S.

Hartl, I.

M. E. Fermann and I. Hartl, “Ultrafast fiber laser technology,” IEEE J. Sel. Top. Quantum 15, 191–206 (2009).
[Crossref]

Hasan, T.

Z. Sun, D. Popa, T. Hasan, F. Torrisi, F. Wang, E. J. R. Kelleher, J. C. Travers, V. Nicolosi, and A. C. Ferrari, “A stable, wideband tunable, near transform-limited, graphene-mode-locked, ultrafast laser,” Nano Res. 3, 653–660 (2010).
[Crossref]

Z. Sun, T. Hasan, F. Wang, A. G. Rozhin, I. H. White, and A. C. Ferrari, “Ultrafast stretched-pulse fiber laser mode-locked by carbon nanotubes,” Nano Res. 3, 404–411 (2010).
[Crossref]

Haus, H.

H. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE J. Quantum Electron. 11, 736–746 (1975).
[Crossref]

Haus, H. A.

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]

K. Tamura, C. R. Doerr, H. A. Haus, and E. P. Ippen, “Soliton fiber ring laser stabilization and tuning with a broad intracavity filter,” IEEE Photon. Technol. Lett. 6, 697–699 (1994).
[Crossref]

He, Y.

Hu, Y.

Huang, S.

Ilday, F. Ö.

Ippen, E. P.

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]

K. Tamura, C. R. Doerr, H. A. Haus, and E. P. Ippen, “Soliton fiber ring laser stabilization and tuning with a broad intracavity filter,” IEEE Photon. Technol. Lett. 6, 697–699 (1994).
[Crossref]

Jiang, S.

Q. Wang, J. Geng, T. Luo, and S. Jiang, “2 μm mode-locked fiber laser,” Proc. SPIE 8237, 82371N (2012).
[Crossref]

Jones, D. J.

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]

Kamat, P. V.

B. Farrow and P. V. Kamat, “CdSe quantum dot sensitized solar cells. Shuttling electrons through stacked carbon nanocups,” J. Am. Chem. Soc. 131, 11124–11131 (2009).
[Crossref]

Keinonen, J.

Kelleher, E. J. R.

Z. Sun, D. Popa, T. Hasan, F. Torrisi, F. Wang, E. J. R. Kelleher, J. C. Travers, V. Nicolosi, and A. C. Ferrari, “A stable, wideband tunable, near transform-limited, graphene-mode-locked, ultrafast laser,” Nano Res. 3, 653–660 (2010).
[Crossref]

Keller, U.

F. X. Kurtner, J. A. der Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers-what’s the difference?” IEEE J. Sel. Top. Quantum 4, 159–168 (1998).
[Crossref]

Kelly, S.

S. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28, 806–807 (1992).
[Crossref]

Kieu, K.

Kim, S.

Kim, S. W.

Kim, Y.

Kim, Y. J.

Kimura, Y.

M. Nakazawa, E. Yoshida, T. Sugawa, and Y. Kimura, “Continuum suppressed, uniformly repetitive 136 fs pulse generation from an erbium-doped fibre laser with nonlinear polarisation rotation,” Electron. Lett. 29, 1327–1329 (1993).
[Crossref]

Kowalczyk, M.

Kurtner, F. X.

F. X. Kurtner, J. A. der Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers-what’s the difference?” IEEE J. Sel. Top. Quantum 4, 159–168 (1998).
[Crossref]

Li, C.

Li, H.

Li, J.

Li, Z.

Lin, R.

Liu, X.

X. Liu, D. Han, Z. Sun, C. Zeng, H. Lu, D. Mao, Y. Cui, and F. Wang, “Versatile multi-wavelength ultrafast fiber laser mode-locked by carbon nanotubes,” Sci. Rep. 3, 2718 (2013).
[Crossref]

L. Yun, X. Liu, and D. Mao, “Observation of dual-wavelength dissipative solitons in a figure-eight erbium-doped fiber laser,” Opt. Express 20, 20992–20997 (2012).
[Crossref]

Liu, Y.

Lu, H.

X. Liu, D. Han, Z. Sun, C. Zeng, H. Lu, D. Mao, Y. Cui, and F. Wang, “Versatile multi-wavelength ultrafast fiber laser mode-locked by carbon nanotubes,” Sci. Rep. 3, 2718 (2013).
[Crossref]

Lu, R.

Lu, S.

Luo, H.

Luo, T.

Q. Wang, J. Geng, T. Luo, and S. Jiang, “2 μm mode-locked fiber laser,” Proc. SPIE 8237, 82371N (2012).
[Crossref]

Macherzynski, W.

Mansuripur, M.

Mao, D.

X. Liu, D. Han, Z. Sun, C. Zeng, H. Lu, D. Mao, Y. Cui, and F. Wang, “Versatile multi-wavelength ultrafast fiber laser mode-locked by carbon nanotubes,” Sci. Rep. 3, 2718 (2013).
[Crossref]

L. Yun, X. Liu, and D. Mao, “Observation of dual-wavelength dissipative solitons in a figure-eight erbium-doped fiber laser,” Opt. Express 20, 20992–20997 (2012).
[Crossref]

Mars, K.

Mikula, A.

Mo, K.

Mou, C.

Nakazawa, M.

M. Nakazawa, E. Yoshida, T. Sugawa, and Y. Kimura, “Continuum suppressed, uniformly repetitive 136 fs pulse generation from an erbium-doped fibre laser with nonlinear polarisation rotation,” Electron. Lett. 29, 1327–1329 (1993).
[Crossref]

Nelson, L. E.

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]

Nicolosi, V.

Z. Sun, D. Popa, T. Hasan, F. Torrisi, F. Wang, E. J. R. Kelleher, J. C. Travers, V. Nicolosi, and A. C. Ferrari, “A stable, wideband tunable, near transform-limited, graphene-mode-locked, ultrafast laser,” Nano Res. 3, 653–660 (2010).
[Crossref]

Noske, D. U.

M. J. Guy, D. U. Noske, and J. R. Taylor, “Generation of femtosecond soliton pulses by passive mode locking of an ytterbium-erbium figure-of-eight fiber laser,” Opt. Lett. 18, 1447–1449 (1993).
[Crossref]

D. U. Noske and J. R. Taylor, “Spectral and temporal stabilisation of a diode-pumped ytterbium-erbium fibre soliton laser,” Electron. Lett. 29, 2200–2202 (1993).
[Crossref]

Okhotnikov, O. G.

Özgören, K.

Paletko, P.

Park, J.

Park, S.

Popa, D.

Z. Sun, D. Popa, T. Hasan, F. Torrisi, F. Wang, E. J. R. Kelleher, J. C. Travers, V. Nicolosi, and A. C. Ferrari, “A stable, wideband tunable, near transform-limited, graphene-mode-locked, ultrafast laser,” Nano Res. 3, 653–660 (2010).
[Crossref]

Rozhin, A. G.

Z. Sun, T. Hasan, F. Wang, A. G. Rozhin, I. H. White, and A. C. Ferrari, “Ultrafast stretched-pulse fiber laser mode-locked by carbon nanotubes,” Nano Res. 3, 404–411 (2010).
[Crossref]

Rudy, C. W.

Sajavaara, T.

Silberberg, Y.

M. E. Fermann, M. J. Andrejco, M. L. Stock, Y. Silberberg, and A. M. Weiner, “Passive mode locking in erbium fiber lasers with negative group delay,” Appl. Phys. Lett. 62, 910–912 (1993).
[Crossref]

Smulakovsky, V.

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, “Spectral sidebands and multipulse formation in passively mode-locked lasers,” Phys. Rev. A 83, 043831 (2011).
[Crossref]

Sobon, G.

Sotor, J.

Stock, M. L.

M. E. Fermann, M. J. Andrejco, M. L. Stock, Y. Silberberg, and A. M. Weiner, “Passive mode locking in erbium fiber lasers with negative group delay,” Appl. Phys. Lett. 62, 910–912 (1993).
[Crossref]

Sugawa, T.

M. Nakazawa, E. Yoshida, T. Sugawa, and Y. Kimura, “Continuum suppressed, uniformly repetitive 136 fs pulse generation from an erbium-doped fibre laser with nonlinear polarisation rotation,” Electron. Lett. 29, 1327–1329 (1993).
[Crossref]

Sun, Z.

J. Li, Z. Yan, Z. Sun, H. Luo, Y. He, Z. Li, Y. Liu, and L. Zhang, “Thulium-doped all-fiber mode-locked laser based on NPR and 45°-tilted fiber grating,” Opt. Express 22, 31020–31028 (2014).
[Crossref]

X. Liu, D. Han, Z. Sun, C. Zeng, H. Lu, D. Mao, Y. Cui, and F. Wang, “Versatile multi-wavelength ultrafast fiber laser mode-locked by carbon nanotubes,” Sci. Rep. 3, 2718 (2013).
[Crossref]

Z. Sun, T. Hasan, F. Wang, A. G. Rozhin, I. H. White, and A. C. Ferrari, “Ultrafast stretched-pulse fiber laser mode-locked by carbon nanotubes,” Nano Res. 3, 404–411 (2010).
[Crossref]

Z. Sun, D. Popa, T. Hasan, F. Torrisi, F. Wang, E. J. R. Kelleher, J. C. Travers, V. Nicolosi, and A. C. Ferrari, “A stable, wideband tunable, near transform-limited, graphene-mode-locked, ultrafast laser,” Nano Res. 3, 653–660 (2010).
[Crossref]

Tamura, K.

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]

K. Tamura, C. R. Doerr, H. A. Haus, and E. P. Ippen, “Soliton fiber ring laser stabilization and tuning with a broad intracavity filter,” IEEE Photon. Technol. Lett. 6, 697–699 (1994).
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Tang, D.

Taylor, J. R.

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[Crossref]

Travers, J. C.

Z. Sun, D. Popa, T. Hasan, F. Torrisi, F. Wang, E. J. R. Kelleher, J. C. Travers, V. Nicolosi, and A. C. Ferrari, “A stable, wideband tunable, near transform-limited, graphene-mode-locked, ultrafast laser,” Nano Res. 3, 653–660 (2010).
[Crossref]

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Vainionpää, A.

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[Crossref]

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[Crossref]

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Wang, Q.

Q. Wang, J. Geng, T. Luo, and S. Jiang, “2 μm mode-locked fiber laser,” Proc. SPIE 8237, 82371N (2012).
[Crossref]

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Wang, Z.

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Appl. Phys. B (1)

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]

Appl. Phys. Lett. (1)

M. E. Fermann, M. J. Andrejco, M. L. Stock, Y. Silberberg, and A. M. Weiner, “Passive mode locking in erbium fiber lasers with negative group delay,” Appl. Phys. Lett. 62, 910–912 (1993).
[Crossref]

Electron. Lett. (3)

M. Nakazawa, E. Yoshida, T. Sugawa, and Y. Kimura, “Continuum suppressed, uniformly repetitive 136 fs pulse generation from an erbium-doped fibre laser with nonlinear polarisation rotation,” Electron. Lett. 29, 1327–1329 (1993).
[Crossref]

D. U. Noske and J. R. Taylor, “Spectral and temporal stabilisation of a diode-pumped ytterbium-erbium fibre soliton laser,” Electron. Lett. 29, 2200–2202 (1993).
[Crossref]

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[Crossref]

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[Crossref]

IEEE Photon. Technol. Lett. (1)

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[Crossref]

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J. Lightwave Technol. (2)

Nano Res. (2)

Z. Sun, T. Hasan, F. Wang, A. G. Rozhin, I. H. White, and A. C. Ferrari, “Ultrafast stretched-pulse fiber laser mode-locked by carbon nanotubes,” Nano Res. 3, 404–411 (2010).
[Crossref]

Z. Sun, D. Popa, T. Hasan, F. Torrisi, F. Wang, E. J. R. Kelleher, J. C. Travers, V. Nicolosi, and A. C. Ferrari, “A stable, wideband tunable, near transform-limited, graphene-mode-locked, ultrafast laser,” Nano Res. 3, 653–660 (2010).
[Crossref]

Opt. Express (7)

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Y. Wang, J. Li, B. Zhai, Y. Hu, K. Mo, R. Lu, and Y. Liu, “Tunable and switchable dual-wavelength mode-locked Tm3+-doped fiber laser based on a fiber taper,” Opt. Express 24, 15299–15306 (2016).
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Opt. Lett. (7)

Phys. Rev. A (1)

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, “Spectral sidebands and multipulse formation in passively mode-locked lasers,” Phys. Rev. A 83, 043831 (2011).
[Crossref]

Proc. SPIE (1)

Q. Wang, J. Geng, T. Luo, and S. Jiang, “2 μm mode-locked fiber laser,” Proc. SPIE 8237, 82371N (2012).
[Crossref]

Sci. Rep. (1)

X. Liu, D. Han, Z. Sun, C. Zeng, H. Lu, D. Mao, Y. Cui, and F. Wang, “Versatile multi-wavelength ultrafast fiber laser mode-locked by carbon nanotubes,” Sci. Rep. 3, 2718 (2013).
[Crossref]

Supplementary Material (1)

NameDescription
» Visualization 1       spectrum evolution

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Figures (4)

Fig. 1.
Fig. 1. (a) Configuration of our AFLF consisting of two 45°-TFGs segmented by a PMF cavity and corresponding polarization state and phase delay evolutions as the light passes through each portion (inset); (b) theoretically calculated and (c) experimentally measured transmission spectra using PMFs with different lengths of 20 cm, 30 cm, 40 cm, 50 cm, and 60 cm; and (d) experimentally measured and theoretically calculated bandwidths of the AFLF as a function of the PMF length.
Fig. 2.
Fig. 2. Experimental setup of hybrid mode-locked Tm-doped fiber laser based on an AFLF.
Fig. 3.
Fig. 3. Performances of mode-locked fiber lasers based on the AFLF with an FSR of 20.8 nm: (a) spectra from seed lasers with/without the AFLF, (b) autocorrelation traces corresponding to (a), (c) pulse waveform and sequence on oscilloscope, and (d) RF spectra with scanning range of 50 kHz and 500 MHz (inset).
Fig. 4.
Fig. 4. (a) Theoretically calculated transmission spectra of the AFLF at different temperatures, (b) theoretically calculated wavelength shift of the AFLF as a function of temperature, (c) experimentally measured spectra at different temperatures, and (d) experimentally measured center wavelength as a function of temperature.

Equations (8)

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M=[sin2βcosβsinβsinβcosβcos2β][eiΔφcos2α+sin2α(eiΔφ1)cosαsinα(eiΔφ1)cosαsinαeiΔφsin2α+cos2α][0001][11],
T=cos2(2α+β)+cos2(Δφ/2)sin2αsin2(α+β),
Δφ=2πLPMΔnλ,
Tmax=Max[cos2β,cos2(2α+β)],Tmin=Max[cos2β,cos2(2α+β)].
T=cos2(Δφ/2).
λmaxm=LPMΔnm,λminm=2LPMΔn2m+1,
FSRλ2LPMΔn.
dλminm=LheatingλminmLPM(dLheatingLheatingdT+dΔnΔndT)ΔT,