Abstract

The formation and evolution of dual-wavelength solitons in passively mode-locked fiber soliton lasers are investigated both numerically and experimentally. By solving the Ginzburg–Landau equation and taking the gain profile into account, mode-locked soliton emissions at 1532 and 1555 nm are achieved simultaneously. Numerical results show that the two solitons exhibit the same intensity and duration, indicating that the dual-wavelength pulses possess the soliton energy quantization effect. In the process of pulse–pulse collisions, two solitons pass through each other and maintain their properties, qualitatively distinct from single-wavelength solitons that never overlap each other. The dual-wavelength mode-locked operation evolves into single-wavelength mode locking with the decrease of the pumping strength. The dual-peak gain spectrum of erbium-doped fiber and the birefringence-induced cavity filtering effect play crucial roles in the formation of dual-wavelength solitons. Numerical results agree well with analytical solutions and experimental observations. Our study provides an optional method of measuring the fiber dispersion by means of the dual-wavelength solitons.

© 2012 Optical Society of America

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2012 (3)

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
[CrossRef]

L. Yun and X. Liu, “Generation and propagation of bound-state pulses in a passively mode-locked figure-eight laser,” IEEE Photon. J. 4, 512–519 (2012).
[CrossRef]

R. Gumenyuk and O. G. Okhotnikov, “Temporal control of vector soliton bunching by slow/fast saturable absorption,” J. Opt. Soc. Am. B 29, 1–7 (2012).
[CrossRef]

2011 (5)

2010 (10)

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

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

X. M. Liu, “Dynamic evolution of temporal dissipative-soliton molecules in large normal path-averaged dispersion fiber lasers,” Phys. Rev. A 82, 063834 (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]

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]

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

H. B. Sun, X. Liu, Y. K. Gong, X. H. Li, and L. R. Wang, “Broadly tunable dual-wavelength erbium-doped fiber ring laser based on a high birefringence fiber loop mirror,” Laser Phys. 20, 522–527 (2010).
[CrossRef]

X. H. Li, X. M. Liu, Y. Gong, H. Sun, L. Wang, and K. Lu, “A novel erbium/ytterbium co-doped distributed feedback fiber laser with single-polarization and unidirectional output,” Laser Phys. Lett. 7, 55–59 (2010).
[CrossRef]

W. H. Renninger, A. Chong, and F. W. Wise, “Area theorem and energy quantization for dissipative optical solitons,” J. Opt. Soc. Am. B 27, 1978–1982 (2010).
[CrossRef]

X. H. Li, X. M. Liu, X. H. Hu, L. R. Wang, H. Lu, Y. S. Wang, and W. Zhao, “Long-cavity passively mode-locked fiber ring laser with high-energy rectangular-shape pulses in anomalous dispersion regime,” Opt. Lett. 35, 3249–3251 (2010).
[CrossRef]

2009 (4)

2008 (7)

F. Wang, A. G. Rozhin, V. Scardaci, Z. Sun, F. Hennrich, I. H. White, W. I. Milne, and A. C. Ferrari, “Wideband-tuneable, nanotube mode-locked, fibre laser,” Nat. Nanotech. 3, 738–742 (2008).
[CrossRef]

X. Liu, Y. Chung, A. Lin, W. Zhao, K. Q. Lu, Y. S. Wang, and T. Y. Zhang, “Tunable and switchable multi-wavelength erbium-doped fiber laser with highly nonlinear photonic crystal fiber and polarization controllers,” Laser Phys. Lett. 5, 904–907 (2008).
[CrossRef]

X. Liu, T. Wang, C. Shu, L. R. Wang, A. Lin, K. Q. Lu, T. Y. Zhang, and W. Zhao, “Passively harmonic mode-locked erbium-doped fiber soliton laser with a nonlinear polarization rotation,” Laser Phys. 18, 1357–1361 (2008).
[CrossRef]

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Analysis of soliton pattern formation in passively mode-locked fiber lasers,” Phys. Rev. A 78, 043806 (2008).
[CrossRef]

H. Xu, D. Lei, S. Wen, X. Fu, J. Zhang, Y. Shao, L. Zhang, H. Zhang, and D. Fan, “Observation of central wavelength dynamics in erbium-doped fiber ring laser,” Opt. Express 16, 7169–7174 (2008).
[CrossRef]

L. M. Zhao, D. Y. Tang, H. Zhang, X. Wu, and N. Xiang, “Soliton trapping in fiber lasers,” Opt. Express 16, 9528–9533 (2008).
[CrossRef]

G. Q. Xie, D. Y. Tang, H. Luo, H. J. Zhang, H. H. Yu, J. Y. Wang, X. T. Tao, M. H. Jiang, and L. J. Qian, “Dual-wavelength synchronously mode-locked Nd:CNGG laser,” Opt. Lett. 33, 1872–1874 (2008).
[CrossRef]

2007 (1)

X. M. Liu, “A novel dual-wavelength DFB fiber laser based on symmetrical FBG structure,” IEEE Photon. Technol. Lett. 19, 632–634 (2007).
[CrossRef]

2006 (1)

2005 (5)

X. M. Liu, X. Yang, F. Lu, J. Ng, X. Zhou, and C. Lu, “Stable and uniform dual-wavelength erbium-doped fiber laser based on fiber Bragg gratings and photonic crystal fiber,” Opt. Express 13, 142–147 (2005).
[CrossRef]

V. Roy, M. Olivier, F. Babin, and M. Piche, “Dynamics of periodic pulse collisions in a strongly dissipative-dispersive system,” Phys. Rev. Lett. 94, 203903 (2005).
[CrossRef]

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]

X. Liu, X. Zhou, X. Tang, J. Ng, J. Hao, T. Y. Chai, E. Leong, and C. Lu, “Switchable and tunable multiwavelength erbium-doped fiber laser with fiber Bragg gratings and photonic crystal fiber,” IEEE Photon. Technol. Lett. 17, 1626–1628 (2005).
[CrossRef]

X. Liu and C. Lu, “Self-stabilizing effect of four-wave mixing and its applications on multiwavelength erbium-doped fiber lasers,” IEEE Photon. Technol. Lett. 17, 2541–2543 (2005).
[CrossRef]

2004 (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, 213902 (2004).
[CrossRef]

2003 (1)

X. Liu and B. Lee, “A fast method for nonlinear Schrödinger equation,” IEEE Photon. Technol. Lett. 15, 1549–1551 (2003).
[CrossRef]

2002 (1)

D. Pudo, L. R. Chen, D. Giannone, L. Zhang, and I. Bennion, “Actively mode-locked tunable dual-wavelength erbium-doped fiber laser,” IEEE Photon. Technol. Lett. 14, 143–145 (2002).
[CrossRef]

2000 (1)

G. E. Town, L. Chen, and P. W. E. Smith, “Dual wavelength mode-locked fiber laser,” IEEE Photon. Technol. Lett. 12, 1459–1461 (2000).
[CrossRef]

1997 (2)

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]

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg-Landau equation,” Phys. Rev. Lett. 79, 4047–4051 (1997).
[CrossRef]

1996 (1)

H. A. Haus and W. S. William, “Solitons in optical communications,” Rev. Mod. Phys. 68, 423–444 (1996).
[CrossRef]

1992 (2)

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Panye, “Selfstarting passively mode-locked fiber ring soliton laser exploiting nonlinear polarization rotation,” Electron. Lett. 28, 1391–1393 (1992).
[CrossRef]

S. R. Friberg and K. W. DeLong, “Breakup of bound higher-order solitons,” Opt. Lett. 17, 979–981 (1992).
[CrossRef]

1981 (1)

M. Tateda, N. Shibata, and S. Seikai, “Interferometric method for chromatic dispersion measurement in a single-mode optical fiber,” IEEE J. Quantum Electron. 17, 404–407 (1981).
[CrossRef]

Agrawal, G. P.

Akhmediev, N.

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
[CrossRef]

Akhmediev, N. N.

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg-Landau equation,” Phys. Rev. Lett. 79, 4047–4051 (1997).
[CrossRef]

Ankiewicz, A.

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg-Landau equation,” Phys. Rev. Lett. 79, 4047–4051 (1997).
[CrossRef]

Babin, F.

V. Roy, M. Olivier, F. Babin, and M. Piche, “Dynamics of periodic pulse collisions in a strongly dissipative-dispersive system,” Phys. Rev. Lett. 94, 203903 (2005).
[CrossRef]

Babin, S. A.

Bennion, I.

D. Pudo, L. R. Chen, D. Giannone, L. Zhang, and I. Bennion, “Actively mode-locked tunable dual-wavelength erbium-doped fiber laser,” IEEE Photon. Technol. Lett. 14, 143–145 (2002).
[CrossRef]

Buckley, J.

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, 213902 (2004).
[CrossRef]

Chai, T. Y.

X. Liu, X. Zhou, X. Tang, J. Ng, J. Hao, T. Y. Chai, E. Leong, and C. Lu, “Switchable and tunable multiwavelength erbium-doped fiber laser with fiber Bragg gratings and photonic crystal fiber,” IEEE Photon. Technol. Lett. 17, 1626–1628 (2005).
[CrossRef]

Chen, L.

G. E. Town, L. Chen, and P. W. E. Smith, “Dual wavelength mode-locked fiber laser,” IEEE Photon. Technol. Lett. 12, 1459–1461 (2000).
[CrossRef]

Chen, L. R.

D. Pudo, L. R. Chen, D. Giannone, L. Zhang, and I. Bennion, “Actively mode-locked tunable dual-wavelength erbium-doped fiber laser,” IEEE Photon. Technol. Lett. 14, 143–145 (2002).
[CrossRef]

Chong, A.

Chung, Y.

X. Liu, Y. Chung, A. Lin, W. Zhao, K. Q. Lu, Y. S. Wang, and T. Y. Zhang, “Tunable and switchable multi-wavelength erbium-doped fiber laser with highly nonlinear photonic crystal fiber and polarization controllers,” Laser Phys. Lett. 5, 904–907 (2008).
[CrossRef]

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, 213902 (2004).
[CrossRef]

DeLong, K. W.

Fan, D.

Fedoruk, M. P.

Ferrari, A. C.

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]

F. Wang, A. G. Rozhin, V. Scardaci, Z. Sun, F. Hennrich, I. H. White, W. I. Milne, and A. C. Ferrari, “Wideband-tuneable, nanotube mode-locked, fibre laser,” Nat. Nanotech. 3, 738–742 (2008).
[CrossRef]

Friberg, S. R.

Fu, X.

Giannone, D.

D. Pudo, L. R. Chen, D. Giannone, L. Zhang, and I. Bennion, “Actively mode-locked tunable dual-wavelength erbium-doped fiber laser,” IEEE Photon. Technol. Lett. 14, 143–145 (2002).
[CrossRef]

Gong, Y.

X. H. Li, X. M. Liu, Y. Gong, H. Sun, L. Wang, and K. Lu, “A novel erbium/ytterbium co-doped distributed feedback fiber laser with single-polarization and unidirectional output,” Laser Phys. Lett. 7, 55–59 (2010).
[CrossRef]

Gong, Y. K.

H. B. Sun, X. Liu, Y. K. Gong, X. H. Li, and L. R. Wang, “Broadly tunable dual-wavelength erbium-doped fiber ring laser based on a high birefringence fiber loop mirror,” Laser Phys. 20, 522–527 (2010).
[CrossRef]

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]

Grelu, P.

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6, 84–92 (2012).
[CrossRef]

Gumenyuk, R.

Haboucha, A.

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Analysis of soliton pattern formation in passively mode-locked fiber lasers,” Phys. Rev. A 78, 043806 (2008).
[CrossRef]

Hao, J.

X. Liu, X. Zhou, X. Tang, J. Ng, J. Hao, T. Y. Chai, E. Leong, and C. Lu, “Switchable and tunable multiwavelength erbium-doped fiber laser with fiber Bragg gratings and photonic crystal fiber,” IEEE Photon. Technol. Lett. 17, 1626–1628 (2005).
[CrossRef]

Hasan, T.

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. 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]

H. A. Haus and W. S. William, “Solitons in optical communications,” Rev. Mod. Phys. 68, 423–444 (1996).
[CrossRef]

Hennrich, F.

F. Wang, A. G. Rozhin, V. Scardaci, Z. Sun, F. Hennrich, I. H. White, W. I. Milne, and A. C. Ferrari, “Wideband-tuneable, nanotube mode-locked, fibre laser,” Nat. Nanotech. 3, 738–742 (2008).
[CrossRef]

Hu, X. H.

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, 213902 (2004).
[CrossRef]

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]

Jiang, M. H.

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]

Kharenko, D. S.

Kobtsev, S.

Komarov, A.

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Analysis of soliton pattern formation in passively mode-locked fiber lasers,” Phys. Rev. A 78, 043806 (2008).
[CrossRef]

Kukarin, S.

Latkin, A.

Leblond, H.

A. Haboucha, H. Leblond, M. Salhi, A. Komarov, and F. Sanchez, “Analysis of soliton pattern formation in passively mode-locked fiber lasers,” Phys. Rev. A 78, 043806 (2008).
[CrossRef]

Lee, B.

X. Liu and B. Lee, “A fast method for nonlinear Schrödinger equation,” IEEE Photon. Technol. Lett. 15, 1549–1551 (2003).
[CrossRef]

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X. Liu, X. Zhou, X. Tang, J. Ng, J. Hao, T. Y. Chai, E. Leong, and C. Lu, “Switchable and tunable multiwavelength erbium-doped fiber laser with fiber Bragg gratings and photonic crystal fiber,” IEEE Photon. Technol. Lett. 17, 1626–1628 (2005).
[CrossRef]

Li, X. H.

H. B. Sun, X. Liu, Y. K. Gong, X. H. Li, and L. R. Wang, “Broadly tunable dual-wavelength erbium-doped fiber ring laser based on a high birefringence fiber loop mirror,” Laser Phys. 20, 522–527 (2010).
[CrossRef]

X. H. Li, X. M. Liu, Y. Gong, H. Sun, L. Wang, and K. Lu, “A novel erbium/ytterbium co-doped distributed feedback fiber laser with single-polarization and unidirectional output,” Laser Phys. Lett. 7, 55–59 (2010).
[CrossRef]

X. H. Li, X. M. Liu, X. H. Hu, L. R. Wang, H. Lu, Y. S. Wang, and W. Zhao, “Long-cavity passively mode-locked fiber ring laser with high-energy rectangular-shape pulses in anomalous dispersion regime,” Opt. Lett. 35, 3249–3251 (2010).
[CrossRef]

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X. Liu, Y. Chung, A. Lin, W. Zhao, K. Q. Lu, Y. S. Wang, and T. Y. Zhang, “Tunable and switchable multi-wavelength erbium-doped fiber laser with highly nonlinear photonic crystal fiber and polarization controllers,” Laser Phys. Lett. 5, 904–907 (2008).
[CrossRef]

X. Liu, T. Wang, C. Shu, L. R. Wang, A. Lin, K. Q. Lu, T. Y. Zhang, and W. Zhao, “Passively harmonic mode-locked erbium-doped fiber soliton laser with a nonlinear polarization rotation,” Laser Phys. 18, 1357–1361 (2008).
[CrossRef]

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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]

Liu, X.

L. Yun and X. Liu, “Generation and propagation of bound-state pulses in a passively mode-locked figure-eight laser,” IEEE Photon. J. 4, 512–519 (2012).
[CrossRef]

H. B. Sun, X. Liu, Y. K. Gong, X. H. Li, and L. R. Wang, “Broadly tunable dual-wavelength erbium-doped fiber ring laser based on a high birefringence fiber loop mirror,” Laser Phys. 20, 522–527 (2010).
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[CrossRef]

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X. Liu, “Dissipative soliton evolution in ultra-large normal-cavity-dispersion fiber lasers,” Opt. Express 17, 9549–9557 (2009).
[CrossRef]

X. Liu, “Numerical and experimental investigation of dissipative solitons in passively mode-locked fiber lasers with large net-normal-dispersion and high nonlinearity,” Opt. Express 17, 22401–22416 (2009).
[CrossRef]

X. Liu, Y. Chung, A. Lin, W. Zhao, K. Q. Lu, Y. S. Wang, and T. Y. Zhang, “Tunable and switchable multi-wavelength erbium-doped fiber laser with highly nonlinear photonic crystal fiber and polarization controllers,” Laser Phys. Lett. 5, 904–907 (2008).
[CrossRef]

X. Liu, T. Wang, C. Shu, L. R. Wang, A. Lin, K. Q. Lu, T. Y. Zhang, and W. Zhao, “Passively harmonic mode-locked erbium-doped fiber soliton laser with a nonlinear polarization rotation,” Laser Phys. 18, 1357–1361 (2008).
[CrossRef]

X. Liu, X. Zhou, X. Tang, J. Ng, J. Hao, T. Y. Chai, E. Leong, and C. Lu, “Switchable and tunable multiwavelength erbium-doped fiber laser with fiber Bragg gratings and photonic crystal fiber,” IEEE Photon. Technol. Lett. 17, 1626–1628 (2005).
[CrossRef]

X. Liu and C. Lu, “Self-stabilizing effect of four-wave mixing and its applications on multiwavelength erbium-doped fiber lasers,” IEEE Photon. Technol. Lett. 17, 2541–2543 (2005).
[CrossRef]

X. Liu and B. Lee, “A fast method for nonlinear Schrödinger equation,” IEEE Photon. Technol. Lett. 15, 1549–1551 (2003).
[CrossRef]

Liu, X. M.

X. M. Liu, “Soliton formation and evolution in passively-mode-locked lasers with ultralong anomalous-dispersion fibers,” Phys. Rev. A 84, 023835 (2011).
[CrossRef]

X. M. Liu, “Interaction and motion of solitons in passively-mode-locked fiber lasers,” Phys. Rev. A 84, 053828 (2011).
[CrossRef]

X. M. Liu, “Coexistence of strong and weak pulses in a fiber laser with largely anomalous dispersion,” Opt. Express 19, 5874–5887 (2011).
[CrossRef]

X. H. Li, X. M. Liu, X. H. Hu, L. R. Wang, H. Lu, Y. S. Wang, and W. Zhao, “Long-cavity passively mode-locked fiber ring laser with high-energy rectangular-shape pulses in anomalous dispersion regime,” Opt. Lett. 35, 3249–3251 (2010).
[CrossRef]

X. M. Liu, “Dynamic evolution of temporal dissipative-soliton molecules in large normal path-averaged dispersion fiber lasers,” Phys. Rev. A 82, 063834 (2010).
[CrossRef]

X. H. Li, X. M. Liu, Y. Gong, H. Sun, L. Wang, and K. Lu, “A novel erbium/ytterbium co-doped distributed feedback fiber laser with single-polarization and unidirectional output,” Laser Phys. Lett. 7, 55–59 (2010).
[CrossRef]

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]

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

X. M. Liu, “A novel dual-wavelength DFB fiber laser based on symmetrical FBG structure,” IEEE Photon. Technol. Lett. 19, 632–634 (2007).
[CrossRef]

X. M. Liu, X. Yang, F. Lu, J. Ng, X. Zhou, and C. Lu, “Stable and uniform dual-wavelength erbium-doped fiber laser based on fiber Bragg gratings and photonic crystal fiber,” Opt. Express 13, 142–147 (2005).
[CrossRef]

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X. M. Liu, X. Yang, F. Lu, J. Ng, X. Zhou, and C. Lu, “Stable and uniform dual-wavelength erbium-doped fiber laser based on fiber Bragg gratings and photonic crystal fiber,” Opt. Express 13, 142–147 (2005).
[CrossRef]

X. Liu, X. Zhou, X. Tang, J. Ng, J. Hao, T. Y. Chai, E. Leong, and C. Lu, “Switchable and tunable multiwavelength erbium-doped fiber laser with fiber Bragg gratings and photonic crystal fiber,” IEEE Photon. Technol. Lett. 17, 1626–1628 (2005).
[CrossRef]

X. Liu and C. Lu, “Self-stabilizing effect of four-wave mixing and its applications on multiwavelength erbium-doped fiber lasers,” IEEE Photon. Technol. Lett. 17, 2541–2543 (2005).
[CrossRef]

Lu, F.

Lu, H.

Lu, K.

X. H. Li, X. M. Liu, Y. Gong, H. Sun, L. Wang, and K. Lu, “A novel erbium/ytterbium co-doped distributed feedback fiber laser with single-polarization and unidirectional output,” Laser Phys. Lett. 7, 55–59 (2010).
[CrossRef]

Lu, K. Q.

X. Liu, Y. Chung, A. Lin, W. Zhao, K. Q. Lu, Y. S. Wang, and T. Y. Zhang, “Tunable and switchable multi-wavelength erbium-doped fiber laser with highly nonlinear photonic crystal fiber and polarization controllers,” Laser Phys. Lett. 5, 904–907 (2008).
[CrossRef]

X. Liu, T. Wang, C. Shu, L. R. Wang, A. Lin, K. Q. Lu, T. Y. Zhang, and W. Zhao, “Passively harmonic mode-locked erbium-doped fiber soliton laser with a nonlinear polarization rotation,” Laser Phys. 18, 1357–1361 (2008).
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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).
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V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Panye, “Selfstarting passively mode-locked fiber ring soliton laser exploiting nonlinear polarization rotation,” Electron. Lett. 28, 1391–1393 (1992).
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X. M. Liu, X. Yang, F. Lu, J. Ng, X. Zhou, and C. Lu, “Stable and uniform dual-wavelength erbium-doped fiber laser based on fiber Bragg gratings and photonic crystal fiber,” Opt. Express 13, 142–147 (2005).
[CrossRef]

X. Liu, X. Zhou, X. Tang, J. Ng, J. Hao, T. Y. Chai, E. Leong, and C. Lu, “Switchable and tunable multiwavelength erbium-doped fiber laser with fiber Bragg gratings and photonic crystal fiber,” IEEE Photon. Technol. Lett. 17, 1626–1628 (2005).
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V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Panye, “Selfstarting passively mode-locked fiber ring soliton laser exploiting nonlinear polarization rotation,” Electron. Lett. 28, 1391–1393 (1992).
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D. Pudo, L. R. Chen, D. Giannone, L. Zhang, and I. Bennion, “Actively mode-locked tunable dual-wavelength erbium-doped fiber laser,” IEEE Photon. Technol. Lett. 14, 143–145 (2002).
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Renninger, W. H.

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V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Panye, “Selfstarting passively mode-locked fiber ring soliton laser exploiting nonlinear polarization rotation,” Electron. Lett. 28, 1391–1393 (1992).
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V. Roy, M. Olivier, F. Babin, and M. Piche, “Dynamics of periodic pulse collisions in a strongly dissipative-dispersive system,” Phys. Rev. Lett. 94, 203903 (2005).
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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]

F. Wang, A. G. Rozhin, V. Scardaci, Z. Sun, F. Hennrich, I. H. White, W. I. Milne, and A. C. Ferrari, “Wideband-tuneable, nanotube mode-locked, fibre laser,” Nat. Nanotech. 3, 738–742 (2008).
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F. Wang, A. G. Rozhin, V. Scardaci, Z. Sun, F. Hennrich, I. H. White, W. I. Milne, and A. C. Ferrari, “Wideband-tuneable, nanotube mode-locked, fibre laser,” Nat. Nanotech. 3, 738–742 (2008).
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X. Liu, T. Wang, C. Shu, L. R. Wang, A. Lin, K. Q. Lu, T. Y. Zhang, and W. Zhao, “Passively harmonic mode-locked erbium-doped fiber soliton laser with a nonlinear polarization rotation,” Laser Phys. 18, 1357–1361 (2008).
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X. H. Li, X. M. Liu, Y. Gong, H. Sun, L. Wang, and K. Lu, “A novel erbium/ytterbium co-doped distributed feedback fiber laser with single-polarization and unidirectional output,” Laser Phys. Lett. 7, 55–59 (2010).
[CrossRef]

Sun, H. B.

H. B. Sun, X. Liu, Y. K. Gong, X. H. Li, and L. R. Wang, “Broadly tunable dual-wavelength erbium-doped fiber ring laser based on a high birefringence fiber loop mirror,” Laser Phys. 20, 522–527 (2010).
[CrossRef]

Sun, Z.

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]

F. Wang, A. G. Rozhin, V. Scardaci, Z. Sun, F. Hennrich, I. H. White, W. I. Milne, and A. C. Ferrari, “Wideband-tuneable, nanotube mode-locked, fibre laser,” Nat. Nanotech. 3, 738–742 (2008).
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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).
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Tang, D. Y.

Tang, X.

X. Liu, X. Zhou, X. Tang, J. Ng, J. Hao, T. Y. Chai, E. Leong, and C. Lu, “Switchable and tunable multiwavelength erbium-doped fiber laser with fiber Bragg gratings and photonic crystal fiber,” IEEE Photon. Technol. Lett. 17, 1626–1628 (2005).
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M. Tateda, N. Shibata, and S. Seikai, “Interferometric method for chromatic dispersion measurement in a single-mode optical fiber,” IEEE J. Quantum Electron. 17, 404–407 (1981).
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G. E. Town, L. Chen, and P. W. E. Smith, “Dual wavelength mode-locked fiber laser,” IEEE Photon. Technol. Lett. 12, 1459–1461 (2000).
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Wang, F.

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).
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F. Wang, A. G. Rozhin, V. Scardaci, Z. Sun, F. Hennrich, I. H. White, W. I. Milne, and A. C. Ferrari, “Wideband-tuneable, nanotube mode-locked, fibre laser,” Nat. Nanotech. 3, 738–742 (2008).
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Wang, L.

X. H. Li, X. M. Liu, Y. Gong, H. Sun, L. Wang, and K. Lu, “A novel erbium/ytterbium co-doped distributed feedback fiber laser with single-polarization and unidirectional output,” Laser Phys. Lett. 7, 55–59 (2010).
[CrossRef]

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H. B. Sun, X. Liu, Y. K. Gong, X. H. Li, and L. R. Wang, “Broadly tunable dual-wavelength erbium-doped fiber ring laser based on a high birefringence fiber loop mirror,” Laser Phys. 20, 522–527 (2010).
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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]

X. H. Li, X. M. Liu, X. H. Hu, L. R. Wang, H. Lu, Y. S. Wang, and W. Zhao, “Long-cavity passively mode-locked fiber ring laser with high-energy rectangular-shape pulses in anomalous dispersion regime,” Opt. Lett. 35, 3249–3251 (2010).
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X. Liu, T. Wang, C. Shu, L. R. Wang, A. Lin, K. Q. Lu, T. Y. Zhang, and W. Zhao, “Passively harmonic mode-locked erbium-doped fiber soliton laser with a nonlinear polarization rotation,” Laser Phys. 18, 1357–1361 (2008).
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X. H. Li, X. M. Liu, X. H. Hu, L. R. Wang, H. Lu, Y. S. Wang, and W. Zhao, “Long-cavity passively mode-locked fiber ring laser with high-energy rectangular-shape pulses in anomalous dispersion regime,” Opt. Lett. 35, 3249–3251 (2010).
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X. Liu, Y. Chung, A. Lin, W. Zhao, K. Q. Lu, Y. S. Wang, and T. Y. Zhang, “Tunable and switchable multi-wavelength erbium-doped fiber laser with highly nonlinear photonic crystal fiber and polarization controllers,” Laser Phys. Lett. 5, 904–907 (2008).
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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).
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F. Wang, A. G. Rozhin, V. Scardaci, Z. Sun, F. Hennrich, I. H. White, W. I. Milne, and A. C. Ferrari, “Wideband-tuneable, nanotube mode-locked, fibre laser,” Nat. Nanotech. 3, 738–742 (2008).
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L. Yun and X. Liu, “Generation and propagation of bound-state pulses in a passively mode-locked figure-eight laser,” IEEE Photon. J. 4, 512–519 (2012).
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Zhang, T. Y.

X. Liu, T. Wang, C. Shu, L. R. Wang, A. Lin, K. Q. Lu, T. Y. Zhang, and W. Zhao, “Passively harmonic mode-locked erbium-doped fiber soliton laser with a nonlinear polarization rotation,” Laser Phys. 18, 1357–1361 (2008).
[CrossRef]

X. Liu, Y. Chung, A. Lin, W. Zhao, K. Q. Lu, Y. S. Wang, and T. Y. Zhang, “Tunable and switchable multi-wavelength erbium-doped fiber laser with highly nonlinear photonic crystal fiber and polarization controllers,” Laser Phys. Lett. 5, 904–907 (2008).
[CrossRef]

Zhao, B.

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]

Zhao, L. M.

Zhao, W.

X. H. Li, X. M. Liu, X. H. Hu, L. R. Wang, H. Lu, Y. S. Wang, and W. Zhao, “Long-cavity passively mode-locked fiber ring laser with high-energy rectangular-shape pulses in anomalous dispersion regime,” Opt. Lett. 35, 3249–3251 (2010).
[CrossRef]

X. Liu, Y. Chung, A. Lin, W. Zhao, K. Q. Lu, Y. S. Wang, and T. Y. Zhang, “Tunable and switchable multi-wavelength erbium-doped fiber laser with highly nonlinear photonic crystal fiber and polarization controllers,” Laser Phys. Lett. 5, 904–907 (2008).
[CrossRef]

X. Liu, T. Wang, C. Shu, L. R. Wang, A. Lin, K. Q. Lu, T. Y. Zhang, and W. Zhao, “Passively harmonic mode-locked erbium-doped fiber soliton laser with a nonlinear polarization rotation,” Laser Phys. 18, 1357–1361 (2008).
[CrossRef]

Zhou, X.

X. Liu, X. Zhou, X. Tang, J. Ng, J. Hao, T. Y. Chai, E. Leong, and C. Lu, “Switchable and tunable multiwavelength erbium-doped fiber laser with fiber Bragg gratings and photonic crystal fiber,” IEEE Photon. Technol. Lett. 17, 1626–1628 (2005).
[CrossRef]

X. M. Liu, X. Yang, F. Lu, J. Ng, X. Zhou, and C. Lu, “Stable and uniform dual-wavelength erbium-doped fiber laser based on fiber Bragg gratings and photonic crystal fiber,” Opt. Express 13, 142–147 (2005).
[CrossRef]

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]

Electron. Lett. (1)

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Panye, “Selfstarting passively mode-locked fiber ring soliton laser exploiting nonlinear polarization rotation,” Electron. Lett. 28, 1391–1393 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Tateda, N. Shibata, and S. Seikai, “Interferometric method for chromatic dispersion measurement in a single-mode optical fiber,” IEEE J. Quantum Electron. 17, 404–407 (1981).
[CrossRef]

IEEE Photon. J. (1)

L. Yun and X. Liu, “Generation and propagation of bound-state pulses in a passively mode-locked figure-eight laser,” IEEE Photon. J. 4, 512–519 (2012).
[CrossRef]

IEEE Photon. Technol. Lett. (6)

X. Liu, X. Zhou, X. Tang, J. Ng, J. Hao, T. Y. Chai, E. Leong, and C. Lu, “Switchable and tunable multiwavelength erbium-doped fiber laser with fiber Bragg gratings and photonic crystal fiber,” IEEE Photon. Technol. Lett. 17, 1626–1628 (2005).
[CrossRef]

X. M. Liu, “A novel dual-wavelength DFB fiber laser based on symmetrical FBG structure,” IEEE Photon. Technol. Lett. 19, 632–634 (2007).
[CrossRef]

X. Liu and C. Lu, “Self-stabilizing effect of four-wave mixing and its applications on multiwavelength erbium-doped fiber lasers,” IEEE Photon. Technol. Lett. 17, 2541–2543 (2005).
[CrossRef]

X. Liu and B. Lee, “A fast method for nonlinear Schrödinger equation,” IEEE Photon. Technol. Lett. 15, 1549–1551 (2003).
[CrossRef]

D. Pudo, L. R. Chen, D. Giannone, L. Zhang, and I. Bennion, “Actively mode-locked tunable dual-wavelength erbium-doped fiber laser,” IEEE Photon. Technol. Lett. 14, 143–145 (2002).
[CrossRef]

G. E. Town, L. Chen, and P. W. E. Smith, “Dual wavelength mode-locked fiber laser,” IEEE Photon. Technol. Lett. 12, 1459–1461 (2000).
[CrossRef]

J. Opt. Soc. Am. B (4)

Laser Phys. (2)

X. Liu, T. Wang, C. Shu, L. R. Wang, A. Lin, K. Q. Lu, T. Y. Zhang, and W. Zhao, “Passively harmonic mode-locked erbium-doped fiber soliton laser with a nonlinear polarization rotation,” Laser Phys. 18, 1357–1361 (2008).
[CrossRef]

H. B. Sun, X. Liu, Y. K. Gong, X. H. Li, and L. R. Wang, “Broadly tunable dual-wavelength erbium-doped fiber ring laser based on a high birefringence fiber loop mirror,” Laser Phys. 20, 522–527 (2010).
[CrossRef]

Laser Phys. Lett. (3)

X. Liu, Y. Chung, A. Lin, W. Zhao, K. Q. Lu, Y. S. Wang, and T. Y. Zhang, “Tunable and switchable multi-wavelength erbium-doped fiber laser with highly nonlinear photonic crystal fiber and polarization controllers,” Laser Phys. Lett. 5, 904–907 (2008).
[CrossRef]

X. H. Li, X. M. Liu, Y. Gong, H. Sun, L. Wang, and K. Lu, “A novel erbium/ytterbium co-doped distributed feedback fiber laser with single-polarization and unidirectional output,” Laser Phys. Lett. 7, 55–59 (2010).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

(a) Pulse profiles and (b) optical spectrum for dual-wavelength mode locking when Es is 14 pJ.

Fig. 2.
Fig. 2.

Evolution of dual-wavelength mode locking in (a) temporal and (b) spectral domains. A noise signal is initialized for the first round trip. Due to the combined effects of fiber chromatic dispersion and different operating wavelengths, two mode-locked pulses separate from each other with the increase of the round-trip number.

Fig. 3.
Fig. 3.

Dual-wavelength soliton collision in (a) temporal and (b) spectral domains. Two pulses pass through each other and maintain their properties after the interaction.

Fig. 4.
Fig. 4.

Pulse evolution from dual- to single-wavelength mode locking in (a) temporal and (b) spectral domains. Insets in (a) and (b) show the pulse profile and output spectrum for single-wavelength mode locking. Here Es=7pJ; the other parameters are the same as in Fig. 2.

Fig. 5.
Fig. 5.

Analytical solution of the dual-wavelength soliton propagation and interaction.

Fig. 6.
Fig. 6.

Schematic diagram of the dual-wavelength soliton fiber laser. PS-ISO, polarization-sensitive isolator; PC, polarization controller; SMF, single-mode fiber; WDM, wavelength-division multiplexer; EDF, erbium-doped fiber; OC, output coupler.

Fig. 7.
Fig. 7.

(a) Optical spectrum, (b) pulse train, and (c) RF spectrum for the dual-wavelength mode-locked soliton operation. The pump power is fixed at 48 mW. The inset in (a) shows the gain spectra observed in the fiber laser. From top to bottom, the pump powers are 40, 30, and 20 mW, respectively.

Fig. 8.
Fig. 8.

(a) Optical spectrum and (b) autocorrelation trace of single-wavelength solitons at 28 mW. Other experimental settings are the same as in Fig. 7.

Equations (11)

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uz=iβu+δutik222ut2+iγ(|u|2+23|v|2)u+g2u+g2Ωg2ut2,vz=iβvδvtik222vt2+iγ(|v|2+23|u|2)v+g2v+g2Ωg2vt2.
g=g0/(1+Ep/Es),
uz=ik222ut2+iγ|u|2u.
u(z,t)=sech[(tβ1z)/T0]exp[iz|k2|/(2T02)].
u(z,t,λ1,λ2)=sech[(tβλ1z)/T0]exp[iz|k2|/(2T02)]+sech[(tβλ2z)/T0]exp[iz|k2|/(2T02)].
u(z,t,λ1,λ2)=sech[(tΔβ2z)/T0]exp[iz|k2|/(2T02)]+sech[(t+Δβ2z)/T0]exp[iz|k2|/(2T02)],
Δβ=2πcλ1λ2(λ2λ1)|k2|.
ΔT=LDdλ.
T1=nL/c,
T2=T1+ΔT.
Δf=1T11T2=c2Ddλn2(L+LDdλc/n).

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