Abstract

A combined analytical approach to classify soliton dynamics from dissipative soliton to dissipative soliton resonance (DSR) is developed based on the established laser models. The approach, derived from two compatible analytical solutions to the complex cubic-quintic Ginzburg-Landau equation (CQGLE), characterizes the pulse evolution process from both algebraic and physical points of view. The proposed theory is proved to be valid in real world laser oscillators according to numerical simulations, and potentially offers guideline on the design of DSR cavity configurations.

© 2015 Optical Society of America

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  27. W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77(2), 023814 (2008).
    [Crossref]
  28. V. L. Kalashnikov, E. Podivilov, A. Chernykh, S. Naumov, A. Fernandez, R. Graf, and A. Apolonski, “Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment,” New J. Phys. 7(1), 217 (2005).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  34. X. Liu, “Hysteresis phenomena and multipulse formation of a dissipative system in a passively mode-locked fiber laser,” Phys. Rev. A 81(2), 023811 (2010).
    [Crossref]

2015 (1)

2014 (2)

N. Zhao, M. Liu, H. Liu, X. W. Zheng, Q. Y. Ning, A. P. Luo, Z. C. Luo, and W. C. Xu, “Dual-wavelength rectangular pulse Yb-doped fiber laser using a microfiber-based graphene saturable absorber,” Opt. Express 22(9), 10906–10913 (2014).
[Crossref] [PubMed]

Y. Liu, W. Li, X. Shen, C. Wang, Z. Yang, and H. Zeng, “Square nanosecond mode-locked laser based on nonlinear amplifying loop mirror,” IEEE Photonics Technol. Lett. 26(19), 1932–1935 (2014).
[Crossref]

2013 (2)

A. Komarov, F. Amrani, A. Dmitriev, K. Komarov, and F. Sanchez, “Competition and coexistence of ultrashort pulses in passive mode-locked lasers under dissipative-soliton-resonance conditions,” Phys. Rev. A 87(2), 023838 (2013).
[Crossref]

S. K. Wang, Q. Y. Ning, A. P. Luo, Z. B. Lin, Z. C. Luo, and W. C. Xu, “Dissipative soliton resonance in a passively mode-locked figure-eight fiber laser,” Opt. Express 21(2), 2402–2407 (2013).
[Crossref] [PubMed]

2012 (3)

2011 (3)

2010 (3)

2009 (4)

V. L. Kalashnikov, “Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(4), 046606 (2009).
[Crossref] [PubMed]

W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances in the anomalous dispersion regime,” Phys. Rev. A 79(3), 033840 (2009).
[Crossref]

X. Wu, D. Y. Tang, H. Zhang, and L. M. Zhao, “Dissipative soliton resonance in an all-normal-dispersion erbium-doped fiber laser,” Opt. Express 17(7), 5580–5584 (2009).
[Crossref] [PubMed]

E. Ding and J. N. Kutz, “Operating regimes, split-step modeling, and the Haus master mode-locking model,” J. Opt. Soc. Am. B 26(12), 2290–2300 (2009).
[Crossref]

2008 (2)

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78(2), 023830 (2008).
[Crossref]

W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77(2), 023814 (2008).
[Crossref]

2007 (3)

2006 (1)

2005 (3)

V. L. Kalashnikov, E. Podivilov, A. Chernykh, S. Naumov, A. Fernandez, R. Graf, and A. Apolonski, “Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment,” New J. Phys. 7(1), 217 (2005).
[Crossref]

E. Podivilov and V. L. Kalashnikov, “Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation,” J. Exp. Theor. Phys. Lett. 82(8), 467–471 (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(4), 043816 (2005).
[Crossref]

2000 (1)

M. E. Fermann, A. Galvanauskas, and M. Hofer, “Ultrafast pulse sources based on multi-mode optical fibers,” Appl. Phys. B 70(1), S13–S23 (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(2), 277–294 (1997).
[Crossref]

J. M. Soto-Crespo, N. N. Akhmediev, V. V. Afanasjev, and S. Wabnitz, “Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(4), 4783–4796 (1997).
[Crossref]

1995 (1)

F. I. Khatri, J. D. Moores, G. Lenz, and H. A. Haus, “Models for self-limited additive pulse mode-locking,” Opt. Commun. 114(5-6), 447–452 (1995).
[Crossref]

1993 (2)

1991 (1)

D. J. Richardson, R. I. Laming, D. N. Payne, V. Matsas, and M. W. Phillips, “Selfstarting, passively mode-locked erbium fibre ring laser based on the amplifying Sagnac switch,” Electron. Lett. 27(6), 542–544 (1991).
[Crossref]

Afanasjev, V. V.

J. M. Soto-Crespo, N. N. Akhmediev, V. V. Afanasjev, and S. Wabnitz, “Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(4), 4783–4796 (1997).
[Crossref]

Akhmediev, N.

P. Grelu, W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonance as a guideline for high-energy pulse laser oscillators,” J. Opt. Soc. Am. B 27(11), 2336–2341 (2010).
[Crossref]

W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances in the anomalous dispersion regime,” Phys. Rev. A 79(3), 033840 (2009).
[Crossref]

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78(2), 023830 (2008).
[Crossref]

Akhmediev, N. N.

P. Grelu and N. N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012).
[Crossref]

J. M. Soto-Crespo, N. N. Akhmediev, V. V. Afanasjev, and S. Wabnitz, “Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(4), 4783–4796 (1997).
[Crossref]

Amrani, F.

A. Komarov, F. Amrani, A. Dmitriev, K. Komarov, and F. Sanchez, “Competition and coexistence of ultrashort pulses in passive mode-locked lasers under dissipative-soliton-resonance conditions,” Phys. Rev. A 87(2), 023838 (2013).
[Crossref]

Ankiewicz, A.

P. Grelu, W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonance as a guideline for high-energy pulse laser oscillators,” J. Opt. Soc. Am. B 27(11), 2336–2341 (2010).
[Crossref]

W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances in the anomalous dispersion regime,” Phys. Rev. A 79(3), 033840 (2009).
[Crossref]

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78(2), 023830 (2008).
[Crossref]

Apolonski, A.

V. L. Kalashnikov and A. Apolonski, “Energy scalability of mode-locked oscillators: a completely analytical approach to analysis,” Opt. Express 18(25), 25757–25770 (2010).
[Crossref] [PubMed]

V. L. Kalashnikov, E. Podivilov, A. Chernykh, S. Naumov, A. Fernandez, R. Graf, and A. Apolonski, “Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment,” New J. Phys. 7(1), 217 (2005).
[Crossref]

Babin, S. A.

Cai, Z. R.

Cao, W. J.

Chang, W.

P. Grelu, W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonance as a guideline for high-energy pulse laser oscillators,” J. Opt. Soc. Am. B 27(11), 2336–2341 (2010).
[Crossref]

W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances in the anomalous dispersion regime,” Phys. Rev. A 79(3), 033840 (2009).
[Crossref]

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78(2), 023830 (2008).
[Crossref]

Cheng, Z.

Chernykh, A.

V. L. Kalashnikov, E. Podivilov, A. Chernykh, S. Naumov, A. Fernandez, R. Graf, and A. Apolonski, “Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment,” New J. Phys. 7(1), 217 (2005).
[Crossref]

Chong, A.

W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77(2), 023814 (2008).
[Crossref]

A. Chong, W. H. Renninger, and F. W. Wise, “All-normal-dispersion femtosecond fiber laser with pulse energy above 20 nJ,” Opt. Lett. 32(16), 2408–2410 (2007).
[Crossref] [PubMed]

Ding, E.

Dmitriev, A.

A. Komarov, F. Amrani, A. Dmitriev, K. Komarov, and F. Sanchez, “Competition and coexistence of ultrashort pulses in passive mode-locked lasers under dissipative-soliton-resonance conditions,” Phys. Rev. A 87(2), 023838 (2013).
[Crossref]

Duan, L.

Fedoruk, M. P.

Fermann, M. E.

M. E. Fermann, A. Galvanauskas, and M. Hofer, “Ultrafast pulse sources based on multi-mode optical fibers,” Appl. Phys. B 70(1), S13–S23 (2000).
[Crossref]

M. H. Ober, M. Hofer, and M. E. Fermann, “42-fs pulse generation from a mode-locked fiber laser started with a moving mirror,” Opt. Lett. 18(5), 367–369 (1993).
[Crossref] [PubMed]

Fernandez, A.

V. L. Kalashnikov, E. Podivilov, A. Chernykh, S. Naumov, A. Fernandez, R. Graf, and A. Apolonski, “Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment,” New J. Phys. 7(1), 217 (2005).
[Crossref]

Galvanauskas, A.

M. E. Fermann, A. Galvanauskas, and M. Hofer, “Ultrafast pulse sources based on multi-mode optical fibers,” Appl. Phys. B 70(1), S13–S23 (2000).
[Crossref]

Graf, R.

V. L. Kalashnikov, E. Podivilov, A. Chernykh, S. Naumov, A. Fernandez, R. Graf, and A. Apolonski, “Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment,” New J. Phys. 7(1), 217 (2005).
[Crossref]

Grelu, P.

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(2), 277–294 (1997).
[Crossref]

F. I. Khatri, J. D. Moores, G. Lenz, and H. A. Haus, “Models for self-limited additive pulse mode-locking,” Opt. Commun. 114(5-6), 447–452 (1995).
[Crossref]

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

Hofer, M.

M. E. Fermann, A. Galvanauskas, and M. Hofer, “Ultrafast pulse sources based on multi-mode optical fibers,” Appl. Phys. B 70(1), S13–S23 (2000).
[Crossref]

M. H. Ober, M. Hofer, and M. E. Fermann, “42-fs pulse generation from a mode-locked fiber laser started with a moving mirror,” Opt. Lett. 18(5), 367–369 (1993).
[Crossref] [PubMed]

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(2), 277–294 (1997).
[Crossref]

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

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(2), 277–294 (1997).
[Crossref]

Kalashnikov, V. L.

V. L. Kalashnikov and A. Apolonski, “Energy scalability of mode-locked oscillators: a completely analytical approach to analysis,” Opt. Express 18(25), 25757–25770 (2010).
[Crossref] [PubMed]

V. L. Kalashnikov, “Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(4), 046606 (2009).
[Crossref] [PubMed]

V. L. Kalashnikov, E. Podivilov, A. Chernykh, S. Naumov, A. Fernandez, R. Graf, and A. Apolonski, “Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment,” New J. Phys. 7(1), 217 (2005).
[Crossref]

E. Podivilov and V. L. Kalashnikov, “Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation,” J. Exp. Theor. Phys. Lett. 82(8), 467–471 (2005).
[Crossref]

Kharenko, D. S.

Khatri, F. I.

F. I. Khatri, J. D. Moores, G. Lenz, and H. A. Haus, “Models for self-limited additive pulse mode-locking,” Opt. Commun. 114(5-6), 447–452 (1995).
[Crossref]

Komarov, A.

A. Komarov, F. Amrani, A. Dmitriev, K. Komarov, and F. Sanchez, “Competition and coexistence of ultrashort pulses in passive mode-locked lasers under dissipative-soliton-resonance conditions,” Phys. Rev. A 87(2), 023838 (2013).
[Crossref]

Komarov, K.

A. Komarov, F. Amrani, A. Dmitriev, K. Komarov, and F. Sanchez, “Competition and coexistence of ultrashort pulses in passive mode-locked lasers under dissipative-soliton-resonance conditions,” Phys. Rev. A 87(2), 023838 (2013).
[Crossref]

Kutz, J. N.

Laming, R. I.

D. J. Richardson, R. I. Laming, D. N. Payne, V. Matsas, and M. W. Phillips, “Selfstarting, passively mode-locked erbium fibre ring laser based on the amplifying Sagnac switch,” Electron. Lett. 27(6), 542–544 (1991).
[Crossref]

Lenz, G.

F. I. Khatri, J. D. Moores, G. Lenz, and H. A. Haus, “Models for self-limited additive pulse mode-locking,” Opt. Commun. 114(5-6), 447–452 (1995).
[Crossref]

Li, H.

Li, W.

Y. Liu, W. Li, X. Shen, C. Wang, Z. Yang, and H. Zeng, “Square nanosecond mode-locked laser based on nonlinear amplifying loop mirror,” IEEE Photonics Technol. Lett. 26(19), 1932–1935 (2014).
[Crossref]

Limpert, J.

Lin, Z. B.

Liu, A. Q.

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(4), 043816 (2005).
[Crossref]

Liu, H.

Liu, M.

Liu, X.

L. Duan, X. Liu, D. Mao, L. Wang, and G. Wang, “Experimental observation of dissipative soliton resonance in an anomalous-dispersion fiber laser,” Opt. Express 20(1), 265–270 (2012).
[Crossref] [PubMed]

X. Liu, “Hysteresis phenomena and multipulse formation of a dissipative system in a passively mode-locked fiber laser,” Phys. Rev. A 81(2), 023811 (2010).
[Crossref]

Liu, Y.

Y. Liu, W. Li, X. Shen, C. Wang, Z. Yang, and H. Zeng, “Square nanosecond mode-locked laser based on nonlinear amplifying loop mirror,” IEEE Photonics Technol. Lett. 26(19), 1932–1935 (2014).
[Crossref]

Luo, A. P.

Luo, Z. C.

Mao, D.

Matsas, V.

D. J. Richardson, R. I. Laming, D. N. Payne, V. Matsas, and M. W. Phillips, “Selfstarting, passively mode-locked erbium fibre ring laser based on the amplifying Sagnac switch,” Electron. Lett. 27(6), 542–544 (1991).
[Crossref]

Moores, J. D.

F. I. Khatri, J. D. Moores, G. Lenz, and H. A. Haus, “Models for self-limited additive pulse mode-locking,” Opt. Commun. 114(5-6), 447–452 (1995).
[Crossref]

Naumov, S.

V. L. Kalashnikov, E. Podivilov, A. Chernykh, S. Naumov, A. Fernandez, R. Graf, and A. Apolonski, “Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment,” New J. Phys. 7(1), 217 (2005).
[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(2), 277–294 (1997).
[Crossref]

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

Ning, Q. Y.

Ober, M. H.

Ortaç, B.

Payne, D. N.

D. J. Richardson, R. I. Laming, D. N. Payne, V. Matsas, and M. W. Phillips, “Selfstarting, passively mode-locked erbium fibre ring laser based on the amplifying Sagnac switch,” Electron. Lett. 27(6), 542–544 (1991).
[Crossref]

Phillips, M. W.

D. J. Richardson, R. I. Laming, D. N. Payne, V. Matsas, and M. W. Phillips, “Selfstarting, passively mode-locked erbium fibre ring laser based on the amplifying Sagnac switch,” Electron. Lett. 27(6), 542–544 (1991).
[Crossref]

Podivilov, E.

E. Podivilov and V. L. Kalashnikov, “Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation,” J. Exp. Theor. Phys. Lett. 82(8), 467–471 (2005).
[Crossref]

V. L. Kalashnikov, E. Podivilov, A. Chernykh, S. Naumov, A. Fernandez, R. Graf, and A. Apolonski, “Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment,” New J. Phys. 7(1), 217 (2005).
[Crossref]

Podivilov, E. V.

Renninger, W. H.

W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77(2), 023814 (2008).
[Crossref]

A. Chong, W. H. Renninger, and F. W. Wise, “All-normal-dispersion femtosecond fiber laser with pulse energy above 20 nJ,” Opt. Lett. 32(16), 2408–2410 (2007).
[Crossref] [PubMed]

Richardson, D. J.

D. J. Richardson, R. I. Laming, D. N. Payne, V. Matsas, and M. W. Phillips, “Selfstarting, passively mode-locked erbium fibre ring laser based on the amplifying Sagnac switch,” Electron. Lett. 27(6), 542–544 (1991).
[Crossref]

Sanchez, F.

A. Komarov, F. Amrani, A. Dmitriev, K. Komarov, and F. Sanchez, “Competition and coexistence of ultrashort pulses in passive mode-locked lasers under dissipative-soliton-resonance conditions,” Phys. Rev. A 87(2), 023838 (2013).
[Crossref]

Schimpf, D. N.

Schreiber, T.

Shen, X.

Y. Liu, W. Li, X. Shen, C. Wang, Z. Yang, and H. Zeng, “Square nanosecond mode-locked laser based on nonlinear amplifying loop mirror,” IEEE Photonics Technol. Lett. 26(19), 1932–1935 (2014).
[Crossref]

Shlizerman, E.

E. Ding, E. Shlizerman, and J. N. Kutz, “Generalized master equation for high-energy passive mode-locking: the sinusoidal Ginzburg–Landau equation,” IEEE J. Quantum Electron. 47(5), 705–714 (2011).
[Crossref] [PubMed]

Shtyrina, O. V.

Soto-Crespo, J. M.

P. Grelu, W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonance as a guideline for high-energy pulse laser oscillators,” J. Opt. Soc. Am. B 27(11), 2336–2341 (2010).
[Crossref]

W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances in the anomalous dispersion regime,” Phys. Rev. A 79(3), 033840 (2009).
[Crossref]

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78(2), 023830 (2008).
[Crossref]

J. M. Soto-Crespo, N. N. Akhmediev, V. V. Afanasjev, and S. Wabnitz, “Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(4), 4783–4796 (1997).
[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(2), 277–294 (1997).
[Crossref]

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

Tang, D. Y.

Tünnermann, A.

Wabnitz, S.

J. M. Soto-Crespo, N. N. Akhmediev, V. V. Afanasjev, and S. Wabnitz, “Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(4), 4783–4796 (1997).
[Crossref]

Wang, C.

Y. Liu, W. Li, X. Shen, C. Wang, Z. Yang, and H. Zeng, “Square nanosecond mode-locked laser based on nonlinear amplifying loop mirror,” IEEE Photonics Technol. Lett. 26(19), 1932–1935 (2014).
[Crossref]

Wang, G.

Wang, L.

Wang, P.

Wang, S. K.

Wise, F. W.

W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77(2), 023814 (2008).
[Crossref]

A. Chong, W. H. Renninger, and F. W. Wise, “All-normal-dispersion femtosecond fiber laser with pulse energy above 20 nJ,” Opt. Lett. 32(16), 2408–2410 (2007).
[Crossref] [PubMed]

Wu, J.

Wu, X.

Xu, W. C.

Yang, Z.

Y. Liu, W. Li, X. Shen, C. Wang, Z. Yang, and H. Zeng, “Square nanosecond mode-locked laser based on nonlinear amplifying loop mirror,” IEEE Photonics Technol. Lett. 26(19), 1932–1935 (2014).
[Crossref]

Yarutkina, I. A.

Zeng, H.

Y. Liu, W. Li, X. Shen, C. Wang, Z. Yang, and H. Zeng, “Square nanosecond mode-locked laser based on nonlinear amplifying loop mirror,” IEEE Photonics Technol. Lett. 26(19), 1932–1935 (2014).
[Crossref]

Zhang, H.

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(4), 043816 (2005).
[Crossref]

Zhao, L. M.

Zhao, N.

Zheng, X. W.

Appl. Phys. B (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(2), 277–294 (1997).
[Crossref]

M. E. Fermann, A. Galvanauskas, and M. Hofer, “Ultrafast pulse sources based on multi-mode optical fibers,” Appl. Phys. B 70(1), S13–S23 (2000).
[Crossref]

Electron. Lett. (1)

D. J. Richardson, R. I. Laming, D. N. Payne, V. Matsas, and M. W. Phillips, “Selfstarting, passively mode-locked erbium fibre ring laser based on the amplifying Sagnac switch,” Electron. Lett. 27(6), 542–544 (1991).
[Crossref]

IEEE J. Quantum Electron. (1)

E. Ding, E. Shlizerman, and J. N. Kutz, “Generalized master equation for high-energy passive mode-locking: the sinusoidal Ginzburg–Landau equation,” IEEE J. Quantum Electron. 47(5), 705–714 (2011).
[Crossref] [PubMed]

IEEE Photonics Technol. Lett. (1)

Y. Liu, W. Li, X. Shen, C. Wang, Z. Yang, and H. Zeng, “Square nanosecond mode-locked laser based on nonlinear amplifying loop mirror,” IEEE Photonics Technol. Lett. 26(19), 1932–1935 (2014).
[Crossref]

J. Exp. Theor. Phys. Lett. (1)

E. Podivilov and V. L. Kalashnikov, “Heavily-chirped solitary pulses in the normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation,” J. Exp. Theor. Phys. Lett. 82(8), 467–471 (2005).
[Crossref]

J. Opt. Soc. Am. B (3)

Nat. Photonics (1)

P. Grelu and N. N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012).
[Crossref]

New J. Phys. (1)

V. L. Kalashnikov, E. Podivilov, A. Chernykh, S. Naumov, A. Fernandez, R. Graf, and A. Apolonski, “Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment,” New J. Phys. 7(1), 217 (2005).
[Crossref]

Opt. Commun. (1)

F. I. Khatri, J. D. Moores, G. Lenz, and H. A. Haus, “Models for self-limited additive pulse mode-locking,” Opt. Commun. 114(5-6), 447–452 (1995).
[Crossref]

Opt. Express (8)

L. Duan, X. Liu, D. Mao, L. Wang, and G. Wang, “Experimental observation of dissipative soliton resonance in an anomalous-dispersion fiber laser,” Opt. Express 20(1), 265–270 (2012).
[Crossref] [PubMed]

S. K. Wang, Q. Y. Ning, A. P. Luo, Z. B. Lin, Z. C. Luo, and W. C. Xu, “Dissipative soliton resonance in a passively mode-locked figure-eight fiber laser,” Opt. Express 21(2), 2402–2407 (2013).
[Crossref] [PubMed]

N. Zhao, M. Liu, H. Liu, X. W. Zheng, Q. Y. Ning, A. P. Luo, Z. C. Luo, and W. C. Xu, “Dual-wavelength rectangular pulse Yb-doped fiber laser using a microfiber-based graphene saturable absorber,” Opt. Express 22(9), 10906–10913 (2014).
[Crossref] [PubMed]

Z. Cheng, H. Li, and P. Wang, “Simulation of generation of dissipative soliton, dissipative soliton resonance and noise-like pulse in Yb-doped mode-locked fiber lasers,” Opt. Express 23(5), 5972–5981 (2015).
[Crossref] [PubMed]

V. L. Kalashnikov and A. Apolonski, “Energy scalability of mode-locked oscillators: a completely analytical approach to analysis,” Opt. Express 18(25), 25757–25770 (2010).
[Crossref] [PubMed]

T. Schreiber, B. Ortaç, J. Limpert, and A. Tünnermann, “On the study of pulse evolution in ultra-short pulse mode-locked fiber lasers by numerical simulations,” Opt. Express 15(13), 8252–8262 (2007).
[Crossref] [PubMed]

D. N. Schimpf, J. Limpert, and A. Tünnermann, “Controlling the influence of SPM in fiber-based chirped-pulse amplification systems by using an actively shaped parabolic spectrum,” Opt. Express 15(25), 16945–16953 (2007).
[Crossref] [PubMed]

X. Wu, D. Y. Tang, H. Zhang, and L. M. Zhao, “Dissipative soliton resonance in an all-normal-dispersion erbium-doped fiber laser,” Opt. Express 17(7), 5580–5584 (2009).
[Crossref] [PubMed]

Opt. Lett. (6)

Phys. Rev. A (6)

X. Liu, “Hysteresis phenomena and multipulse formation of a dissipative system in a passively mode-locked fiber laser,” Phys. Rev. A 81(2), 023811 (2010).
[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(4), 043816 (2005).
[Crossref]

W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77(2), 023814 (2008).
[Crossref]

A. Komarov, F. Amrani, A. Dmitriev, K. Komarov, and F. Sanchez, “Competition and coexistence of ultrashort pulses in passive mode-locked lasers under dissipative-soliton-resonance conditions,” Phys. Rev. A 87(2), 023838 (2013).
[Crossref]

W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances in the anomalous dispersion regime,” Phys. Rev. A 79(3), 033840 (2009).
[Crossref]

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78(2), 023830 (2008).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

V. L. Kalashnikov, “Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(4), 046606 (2009).
[Crossref] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

J. M. Soto-Crespo, N. N. Akhmediev, V. V. Afanasjev, and S. Wabnitz, “Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(4), 4783–4796 (1997).
[Crossref]

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Figures (11)

Fig. 1
Fig. 1 Three different transition types from non-DSR to DSR condition corresponding to the fixed β (DSR transition I illustrated by red lines) and g-dependent β (DSR transition II and III illustrated by blue lines) in the master diagram.
Fig. 2
Fig. 2 Schematic representation of a ring cavity fiber laser using NPE mode-locking technique. The solid dot A in the picture stands for the initial position per round-trip when averaging.
Fig. 3
Fig. 3 (a),(d) Comparison between the transmission curves Ts and the fitted quadratic function. (b),(e) Comparison between temporal profiles acquired by the full lumped model (CNLS) and master averaged CQGLE. (c),(f) Comparison between spectra acquired by CNLS and CQGLE. (a)-(c) are for oscillator I, (d)-(f) are for oscillator III. The initial condition is ψ0(t) = 5sech(t).
Fig. 4
Fig. 4 Positions of the parameter sets for oscillators I, II and III in the master diagram. The soliton existence region is filled by contour plot of the values of R2 from zero (blue) to high (red) levels.
Fig. 5
Fig. 5 (a) The values of δ in dependence on the gain saturation energy for oscillator I. (b) Limiting intensity, reference intensity, and peak intensity of the pulse versus the gain saturation energy. The inset in (a) shows the evolution of temporal profiles with increasing gain saturation energy.
Fig. 6
Fig. 6 (a) The values of δ varying with the gain saturation energy for oscillator II. (b) Limiting intensity and reference intensity versus the gain saturation energy. The inset in (a) shows the pulse evolution from single-pulse operation to multistability when raising the gain saturation energy.
Fig. 7
Fig. 7 (a) The values of δ versus the increasing gain saturation energy for oscillator III. (b) Limiting intensity and reference intensity with different gain saturation energies. The inset in (a) shows the spectral evolution of the pulses with the increasing pump power, and the gray area in (b) stands for the transmission profile.
Fig. 8
Fig. 8 The values of –D/β and p against different gain saturation energies in the oscillator III.
Fig. 9
Fig. 9 Pulse duration varies with the gain saturation energy. The inset shows the numerically obtained points of linear loss δ and the corresponding fitting curve.
Fig. 10
Fig. 10 Schematic of the regimes representing different soliton dynamics. Top row: limiting intensities and reference intensities varying with the pump power. Middle row: master curves in the master diagram. Bottom row: illustrations of the pulse evolution process with the increasing pump power.
Fig. 11
Fig. 11 (a) Switching power against different cavity lengths. (b) Switching power varying with the fiber nonlinearity. Aside from the cavity length in (a) and nonlinearity in (b), other parameters of the oscillators are identical with those in oscillator I.

Tables (1)

Tables Icon

Table 1 Main abbreviations and symbols of some uncommon ingredients

Equations (22)

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

i ψ z + D 2 ψ tt +γ | ψ | 2 ψ=iδψ+iε | ψ | 2 ψ+iβ ψ tt +iμ | ψ | 4 ψν | ψ | 4 ψ
I( w )= 6πγH( Δ f 2 w 2 ) μ( w 2 + Δ f 2 R 2 ) where Δ f 2 = 3 I s γ D [ ( 1+ βγ Dε )± ( 1+ βγ Dε ) 2 2δ ε I s ] R 2 = 4( 12βγ/Dε ) 3[ ( 1+βγ/Dε )± ( 1+βγ/Dε ) 2 ( 2δ/ε I s ) ] 5 3
I max = D Δ f 2 2γ
y= D Ω 2 I s γ x a 0 ε I s
I( t )= 2 d 0 d 2 + d 2 2 4 d 0 d 4 cosh( 2 d 0 t ) where d 0 = δ β d 2 +Ddβ , d 2 = 2ε 4β3Dd2β d 2 , d 4 = μ 3β2Ddβ d 2
δ+ε I l +μ I l 2 +μΔ=0
3β2Ddβ d 2 = ( μ I l 2 μΔ )( 4β3Dd2β d 2 ) ε I l
d 4 = I l d 2 2( Δ+ I l 2 )
d 2 2 4 d 0 d 4 = d 2 2 Δ/ I l 2 1+Δ/ I l 2
p= 4β3Dd2β d 2 β d 2 +Ddβ 3
I r ± = I s ±Δ I r
I l I r ± = 3δ ε I r ± = 3( I s Δ I r ) 2 I s
I( t )= 3δ μ I s μ 2 I s 2 9μδ/8 cosh( 2t δε/3Dγ )
( ψ n+1 0 )= e gL+iγ | ψ n | 2 L J PBS J Analyzer K( cos( 2γJ/3 ) sin( 2γJ/3 ) sin( 2γJ/3 ) cos( 2γJ/3 ) )K Γ 2 J PC ( ψ n 0 ) where g= g 0 exp( | ψ | 2 / E s ) J PBS =( 1 0 0 0 ), J Analyzer =( cos α 2 sin α 2 sin α 2 cos α 2 ), J PC =( cos α 1 sin α 1 sin α 1 e i α 3 cos α 1 e i α 3 ) K=( e ikL/2 0 0 e ikL/2 );Γ=1+ L 2 ( iD 2 + g Ω 2 ) t 2
ψ n+1 =T( | ψ n | 2 ) e gL+iγ | ψ n | 2 L Γ 2 ψ n where T( | ψ n | 2 )=cos α 2 ( cos α 1 cos( 2γJ/3 ) e ikL +sin α 1 sin( 2γJ/3 ) e i α 3 ) +sin α 2 ( cos α 1 sin( 2γJ/3 )+sin α 1 cos( 2γJ/3 ) e ikLi α 3 )
ψ z =[ ( iD 2 + g Ω 2 ) t 2 +iγ | ψ | 2 +g+log( T( | ψ | 2 ) )/L ]ψ
T s ( | ψ | 2 )=Re[ log( T( | ψ | 2 ) )/L ]
ψ z =[ ( iD 2 + g Ω 2 ) t 2 +i( γ+ b 1 ) | ψ | 2 +i b 2 | ψ | 4 +g+ a 0 + a 1 | ψ | 2 + a 2 | ψ | 4 ]ψ
ψ x z =ik ψ x + iD 2 2 ψ x t 2 +iγ( | ψ x | 2 + 2 3 | ψ y | 2 ) ψ x +i γ 3 ψ x 2 ψ y * +g ψ x + g Ω 2 2 ψ x t 2 ψ y z =ik ψ y + iD 2 2 ψ y t 2 +iγ( | ψ y | 2 + 2 3 | ψ x | 2 ) ψ y +i γ 3 ψ y 2 ψ x * +g ψ y + g Ω 2 2 ψ y t 2
ε( D d 2 /2+3βd+D )=γ( β d 2 3Dd/2+2β )
ν( β d 2 2Dd+3β )=μ( D d 2 /2+4βd+3D/2 )
I( t )= 4 I s /3[ 1 δ exp( E s / E s ) ] 1+ δ exp( E s /2 E s )cosh( 2t 16 μ 2 I s 3 ( 1 δ exp( E s / E s ) )/27Dγ )

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