Abstract

Dissipative soliton resonance (DSR) occurs in the close vicinity of a hypersurface in the space of parameters of the equation governing propagation in a dissipative nonlinear medium. Pulsed solutions can acquire virtually unlimited energies as soon as the equation parameters converge toward that specific hypersurface. Here we extend previous studies that have recently unveiled DSRs from the complex cubic-quintic Ginzburg–Landau equation. We clearly confirm the existence of DSR for a wide range of parameters in both regimes of chromatic dispersion, and we establish general features of the ultra-high-energy pulses that can be found close to a DSR. Application to high-energy mode-locked fiber oscillators is discussed.

© 2010 Optical Society of America

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  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, 217 (2005).
    [CrossRef]
  2. T. Schreiber, C. Nielsen, B. Ortaç, J. Limpert, and A. Tunnermann, “Microjoule-level all-polarization-maintaining femtosecond fiber source,” Opt. Lett. 31, 574–576 (2006).
    [CrossRef] [PubMed]
  3. A. Chong, W. Renninger, and F. Wise, “All-normal-dispersion femtosecond fiber laser with pulse energy above 20 nJ,” Opt. Lett. 32, 2408–2410 (2007).
    [CrossRef] [PubMed]
  4. S. Kobtsev, S. Kukarin, and Y. Fedotov, “Ultra-low repetition rate mode-locked fiber laser with high-energy pulses,” Opt. Express 16, 21936–21941 (2008).
    [CrossRef] [PubMed]
  5. C. Lecaplain, B. Ortaç, and A. Hideur, “High-energy femtosecond pulses from a dissipative soliton fiber laser,” Opt. Lett. 34, 3731–3733 (2009).
    [CrossRef] [PubMed]
  6. S. Lefrançois, K. Kieu, Y. Deng, J. Kafka, and F. Wise, “Scaling of dissipative soliton fiber lasers to megawatt peak powers by use of large-area photonic crystal fiber,” Opt. Lett. 35, 1569–1571 (2010).
    [CrossRef] [PubMed]
  7. E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. McCollum, “Double-clad, offset-core Nd fiber laser” in Optical Fiber Sensors, Vol. 2 of 1988 OSA Technical Digest Series (Optical Society of America, 1988), paper PD5.
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    [CrossRef] [PubMed]
  9. A. Fernandez, T. Fuji, A. Poppe, A. Fürbach, F. Krausz, and A. Apolonski, “Chirped-pulse oscillators: a route to high-power femtosecond pulses without external amplification,” Opt. Lett. 29, 1366–1368 (2004).
    [CrossRef] [PubMed]
  10. N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, “Roadmap to ultra-short record high-energy pulses out of laser oscillators,” Phys. Lett. A 372, 3124–3128 (2008).
    [CrossRef]
  11. K. Tamura, E. P. Ippen, and H. A. Haus, “Pulse dynamics in stretched-pulse fiber lasers,” Appl. Phys. Lett. 67, 158–160 (1995).
    [CrossRef]
  12. D. Anderson, M. Desaix, M. Karlsson, M. Lisak, and M. Quiroga-Teixeiro, “Wave-breaking-free pulses in nonlinear optical fibers,” J. Opt. Soc. Am. B 10, 1185–1190 (1993).
    [CrossRef]
  13. F. Ilday, J. Buckley, W. Clark, and F. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).
    [CrossRef] [PubMed]
  14. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
    [CrossRef]
  15. V. L. Kalashnikov and A. Apolonski, “Chirped-pulse oscillators: A unified standpoint,” Phys. Rev. A 79, 043829 (2009).
    [CrossRef]
  16. I. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74, 99–143 (2002).
    [CrossRef]
  17. N.Akhmediev and A.Ankiewicz, eds., Dissipative Solitons (Springer, 2005).
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  18. J. M. Soto-Crespo, M. Grapinet, Ph. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E 70, 066612 (2004).
    [CrossRef]
  19. S. Cundiff, J. M. Soto-Crespo, and N. Akhmediev, “Experimental evidence for soliton explosions,” Phys. Rev. Lett. 88, 073903 (2002).
    [CrossRef] [PubMed]
  20. Ph. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, “Relative phase locking of pulses in a passively mode-locked fiber laser,” J. Opt. Soc. Am. B 20, 863–870 (2003).
    [CrossRef]
  21. N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and Ph. Grelu, “Dissipative soliton interactions inside a fiber laser cavity,” Opt. Fiber Technol. 11, 209–228 (2005).
    [CrossRef]
  22. W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78, 023830 (2008).
    [CrossRef]
  23. W. Chang, J. M. Soto-Crespo, A. Ankiewicz, and N. Akhmediev, “Dissipative soliton resonances in the anomalous dispersion regime,” Phys. Rev. A 79, 033840 (2009).
    [CrossRef]
  24. X. Liu, “Pulse evolution without wave breaking in a strongly dissipative-dispersive laser system,” Phys. Rev. A 81, 053819 (2010).
    [CrossRef]
  25. S. Chen, “Theory of dissipative solitons in complex Ginzburg–Landau systems,” Phys. Rev. E 78, 025601(R) (2008).
    [CrossRef]
  26. V. L. Kalashnikov, “Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg–Landau equation,” Phys. Rev. E 80, 046606 (2009); “Chirped dissipative solitons,” arXiv:1001.4918.
    [CrossRef]
  27. W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances in laser models with parameter management,” J. Opt. Soc. Am. B 25, 1972–1977 (2008).
    [CrossRef]
  28. A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg–Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604(R) (2005).
    [CrossRef]
  29. E. Ding and N. Kutz, “Operating regimes, split-step modeling, and the Haus master mode-locking model,” J. Opt. Soc. Am. B 26, 2290–2300 (2009).
    [CrossRef]

2010 (2)

2009 (5)

V. L. Kalashnikov, “Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg–Landau equation,” Phys. Rev. E 80, 046606 (2009); “Chirped dissipative solitons,” arXiv:1001.4918.
[CrossRef]

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

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

V. L. Kalashnikov and A. Apolonski, “Chirped-pulse oscillators: A unified standpoint,” Phys. Rev. A 79, 043829 (2009).
[CrossRef]

C. Lecaplain, B. Ortaç, and A. Hideur, “High-energy femtosecond pulses from a dissipative soliton fiber laser,” Opt. Lett. 34, 3731–3733 (2009).
[CrossRef] [PubMed]

2008 (5)

N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, “Roadmap to ultra-short record high-energy pulses out of laser oscillators,” Phys. Lett. A 372, 3124–3128 (2008).
[CrossRef]

S. Kobtsev, S. Kukarin, and Y. Fedotov, “Ultra-low repetition rate mode-locked fiber laser with high-energy pulses,” Opt. Express 16, 21936–21941 (2008).
[CrossRef] [PubMed]

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances in laser models with parameter management,” J. Opt. Soc. Am. B 25, 1972–1977 (2008).
[CrossRef]

S. Chen, “Theory of dissipative solitons in complex Ginzburg–Landau systems,” Phys. Rev. E 78, 025601(R) (2008).
[CrossRef]

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

2007 (2)

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, 217 (2005).
[CrossRef]

N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and Ph. Grelu, “Dissipative soliton interactions inside a fiber laser cavity,” Opt. Fiber Technol. 11, 209–228 (2005).
[CrossRef]

A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg–Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604(R) (2005).
[CrossRef]

2004 (3)

A. Fernandez, T. Fuji, A. Poppe, A. Fürbach, F. Krausz, and A. Apolonski, “Chirped-pulse oscillators: a route to high-power femtosecond pulses without external amplification,” Opt. Lett. 29, 1366–1368 (2004).
[CrossRef] [PubMed]

J. M. Soto-Crespo, M. Grapinet, Ph. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E 70, 066612 (2004).
[CrossRef]

F. Ilday, J. Buckley, W. Clark, and F. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (2)

S. Cundiff, J. M. Soto-Crespo, and N. Akhmediev, “Experimental evidence for soliton explosions,” Phys. Rev. Lett. 88, 073903 (2002).
[CrossRef] [PubMed]

I. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74, 99–143 (2002).
[CrossRef]

1995 (1)

K. Tamura, E. P. Ippen, and H. A. Haus, “Pulse dynamics in stretched-pulse fiber lasers,” Appl. Phys. Lett. 67, 158–160 (1995).
[CrossRef]

1993 (1)

1985 (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Akhmediev, N.

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

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

N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, “Roadmap to ultra-short record high-energy pulses out of laser oscillators,” Phys. Lett. A 372, 3124–3128 (2008).
[CrossRef]

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances in laser models with parameter management,” J. Opt. Soc. Am. B 25, 1972–1977 (2008).
[CrossRef]

N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and Ph. Grelu, “Dissipative soliton interactions inside a fiber laser cavity,” Opt. Fiber Technol. 11, 209–228 (2005).
[CrossRef]

J. M. Soto-Crespo, M. Grapinet, Ph. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E 70, 066612 (2004).
[CrossRef]

S. Cundiff, J. M. Soto-Crespo, and N. Akhmediev, “Experimental evidence for soliton explosions,” Phys. Rev. Lett. 88, 073903 (2002).
[CrossRef] [PubMed]

Anderson, D.

Ankiewicz, A.

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

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

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances in laser models with parameter management,” J. Opt. Soc. Am. B 25, 1972–1977 (2008).
[CrossRef]

Apolonski, A.

V. L. Kalashnikov and A. Apolonski, “Chirped-pulse oscillators: A unified standpoint,” Phys. Rev. A 79, 043829 (2009).
[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, 217 (2005).
[CrossRef]

A. Fernandez, T. Fuji, A. Poppe, A. Fürbach, F. Krausz, and A. Apolonski, “Chirped-pulse oscillators: a route to high-power femtosecond pulses without external amplification,” Opt. Lett. 29, 1366–1368 (2004).
[CrossRef] [PubMed]

Aranson, I.

I. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74, 99–143 (2002).
[CrossRef]

Belhache, F.

Buckley, J.

F. Ilday, J. Buckley, W. Clark, and F. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Chang, W.

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

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

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances in laser models with parameter management,” J. Opt. Soc. Am. B 25, 1972–1977 (2008).
[CrossRef]

Chen, S.

S. Chen, “Theory of dissipative solitons in complex Ginzburg–Landau systems,” Phys. Rev. E 78, 025601(R) (2008).
[CrossRef]

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, 217 (2005).
[CrossRef]

Chong, A.

Clark, W.

F. Ilday, J. Buckley, W. Clark, and F. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Cundiff, S.

S. Cundiff, J. M. Soto-Crespo, and N. Akhmediev, “Experimental evidence for soliton explosions,” Phys. Rev. Lett. 88, 073903 (2002).
[CrossRef] [PubMed]

Deng, Y.

Desaix, M.

Ding, E.

Fedotov, Y.

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, 217 (2005).
[CrossRef]

A. Fernandez, T. Fuji, A. Poppe, A. Fürbach, F. Krausz, and A. Apolonski, “Chirped-pulse oscillators: a route to high-power femtosecond pulses without external amplification,” Opt. Lett. 29, 1366–1368 (2004).
[CrossRef] [PubMed]

Fuji, T.

Fürbach, A.

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, 217 (2005).
[CrossRef]

Grapinet, M.

N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and Ph. Grelu, “Dissipative soliton interactions inside a fiber laser cavity,” Opt. Fiber Technol. 11, 209–228 (2005).
[CrossRef]

J. M. Soto-Crespo, M. Grapinet, Ph. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E 70, 066612 (2004).
[CrossRef]

Grelu, Ph.

N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, “Roadmap to ultra-short record high-energy pulses out of laser oscillators,” Phys. Lett. A 372, 3124–3128 (2008).
[CrossRef]

N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and Ph. Grelu, “Dissipative soliton interactions inside a fiber laser cavity,” Opt. Fiber Technol. 11, 209–228 (2005).
[CrossRef]

J. M. Soto-Crespo, M. Grapinet, Ph. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E 70, 066612 (2004).
[CrossRef]

Ph. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, “Relative phase locking of pulses in a passively mode-locked fiber laser,” J. Opt. Soc. Am. B 20, 863–870 (2003).
[CrossRef]

Gutty, F.

Hakimi, F.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. McCollum, “Double-clad, offset-core Nd fiber laser” in Optical Fiber Sensors, Vol. 2 of 1988 OSA Technical Digest Series (Optical Society of America, 1988), paper PD5.

Haus, H. A.

K. Tamura, E. P. Ippen, and H. A. Haus, “Pulse dynamics in stretched-pulse fiber lasers,” Appl. Phys. Lett. 67, 158–160 (1995).
[CrossRef]

Hideur, A.

Ilday, F.

F. Ilday, J. Buckley, W. Clark, and F. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Ippen, E. P.

K. Tamura, E. P. Ippen, and H. A. Haus, “Pulse dynamics in stretched-pulse fiber lasers,” Appl. Phys. Lett. 67, 158–160 (1995).
[CrossRef]

Kafka, J.

Kalashnikov, V. L.

V. L. Kalashnikov and A. Apolonski, “Chirped-pulse oscillators: A unified standpoint,” Phys. Rev. A 79, 043829 (2009).
[CrossRef]

V. L. Kalashnikov, “Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg–Landau equation,” Phys. Rev. E 80, 046606 (2009); “Chirped dissipative solitons,” arXiv:1001.4918.
[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, 217 (2005).
[CrossRef]

Karlsson, M.

Kieu, K.

Kobtsev, S.

Komarov, A.

A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg–Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604(R) (2005).
[CrossRef]

Kramer, L.

I. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74, 99–143 (2002).
[CrossRef]

Krausz, F.

Kukarin, S.

Kutz, N.

Leblond, H.

A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg–Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604(R) (2005).
[CrossRef]

Lecaplain, C.

Lefrançois, S.

Limpert, J.

Lisak, M.

Liu, X.

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

McCollum, B.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. McCollum, “Double-clad, offset-core Nd fiber laser” in Optical Fiber Sensors, Vol. 2 of 1988 OSA Technical Digest Series (Optical Society of America, 1988), paper PD5.

Mourou, G.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[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, 217 (2005).
[CrossRef]

Nielsen, C.

Ortaç, B.

Po, H.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. McCollum, “Double-clad, offset-core Nd fiber laser” in Optical Fiber Sensors, Vol. 2 of 1988 OSA Technical Digest Series (Optical Society of America, 1988), paper PD5.

Podivilov, E.

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, 217 (2005).
[CrossRef]

Poppe, A.

Quiroga-Teixeiro, M.

Renninger, W.

Sanchez, F.

A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg–Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604(R) (2005).
[CrossRef]

Schreiber, T.

Snitzer, E.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. McCollum, “Double-clad, offset-core Nd fiber laser” in Optical Fiber Sensors, Vol. 2 of 1988 OSA Technical Digest Series (Optical Society of America, 1988), paper PD5.

Soto-Crespo, J. M.

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

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

N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, “Roadmap to ultra-short record high-energy pulses out of laser oscillators,” Phys. Lett. A 372, 3124–3128 (2008).
[CrossRef]

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances in laser models with parameter management,” J. Opt. Soc. Am. B 25, 1972–1977 (2008).
[CrossRef]

N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and Ph. Grelu, “Dissipative soliton interactions inside a fiber laser cavity,” Opt. Fiber Technol. 11, 209–228 (2005).
[CrossRef]

J. M. Soto-Crespo, M. Grapinet, Ph. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E 70, 066612 (2004).
[CrossRef]

Ph. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, “Relative phase locking of pulses in a passively mode-locked fiber laser,” J. Opt. Soc. Am. B 20, 863–870 (2003).
[CrossRef]

S. Cundiff, J. M. Soto-Crespo, and N. Akhmediev, “Experimental evidence for soliton explosions,” Phys. Rev. Lett. 88, 073903 (2002).
[CrossRef] [PubMed]

Strickland, D.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Tamura, K.

K. Tamura, E. P. Ippen, and H. A. Haus, “Pulse dynamics in stretched-pulse fiber lasers,” Appl. Phys. Lett. 67, 158–160 (1995).
[CrossRef]

Tumminelli, R.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. McCollum, “Double-clad, offset-core Nd fiber laser” in Optical Fiber Sensors, Vol. 2 of 1988 OSA Technical Digest Series (Optical Society of America, 1988), paper PD5.

Tunnermann, A.

Wise, F.

Appl. Phys. Lett. (1)

K. Tamura, E. P. Ippen, and H. A. Haus, “Pulse dynamics in stretched-pulse fiber lasers,” Appl. Phys. Lett. 67, 158–160 (1995).
[CrossRef]

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

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, 217 (2005).
[CrossRef]

Opt. Commun. (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Opt. Express (1)

Opt. Fiber Technol. (1)

N. Akhmediev, J. M. Soto-Crespo, M. Grapinet, and Ph. Grelu, “Dissipative soliton interactions inside a fiber laser cavity,” Opt. Fiber Technol. 11, 209–228 (2005).
[CrossRef]

Opt. Lett. (6)

Phys. Lett. A (1)

N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, “Roadmap to ultra-short record high-energy pulses out of laser oscillators,” Phys. Lett. A 372, 3124–3128 (2008).
[CrossRef]

Phys. Rev. A (4)

V. L. Kalashnikov and A. Apolonski, “Chirped-pulse oscillators: A unified standpoint,” Phys. Rev. A 79, 043829 (2009).
[CrossRef]

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

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

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

Phys. Rev. E (4)

S. Chen, “Theory of dissipative solitons in complex Ginzburg–Landau systems,” Phys. Rev. E 78, 025601(R) (2008).
[CrossRef]

V. L. Kalashnikov, “Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg–Landau equation,” Phys. Rev. E 80, 046606 (2009); “Chirped dissipative solitons,” arXiv:1001.4918.
[CrossRef]

A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg–Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604(R) (2005).
[CrossRef]

J. M. Soto-Crespo, M. Grapinet, Ph. Grelu, and N. Akhmediev, “Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser,” Phys. Rev. E 70, 066612 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

S. Cundiff, J. M. Soto-Crespo, and N. Akhmediev, “Experimental evidence for soliton explosions,” Phys. Rev. Lett. 88, 073903 (2002).
[CrossRef] [PubMed]

F. Ilday, J. Buckley, W. Clark, and F. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

I. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74, 99–143 (2002).
[CrossRef]

Other (2)

N.Akhmediev and A.Ankiewicz, eds., Dissipative Solitons (Springer, 2005).
[CrossRef]

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. McCollum, “Double-clad, offset-core Nd fiber laser” in Optical Fiber Sensors, Vol. 2 of 1988 OSA Technical Digest Series (Optical Society of America, 1988), paper PD5.

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Figures (5)

Fig. 1
Fig. 1

Contour plot of the energy of stable soliton solution in the two-dimensional parameter space of (dispersion D, nonlinear gain ϵ) in the CGLE. Color scales the pulse energy from low (blue) to high (red) levels. Pulse solutions for the three sets of parameter values denoted by vertical crosses “+,” stars “∗,” and oblique crosses “×” are detailed in the following figures. The dashed line is an analytical approximation to the resonance curve [22].

Fig. 2
Fig. 2

(a) Pulse shape, (b) chirp, and (c) the spectrum transformations near the DSR in the normal dispersion regime. The points on the ϵ - D plane which correspond to these curves are shown by the vertical crosses ( + ) in Fig. 1.

Fig. 3
Fig. 3

(a) Pulse shape, (b) chirp, and (c) the spectrum transformations near the DSR in the anomalous dispersion regime. The points on the ϵ - D plane which correspond to these curves are shown by the stars ( ) in Fig. 1.

Fig. 4
Fig. 4

(a) Pulse shape, (b) chirp, and (c) the spectrum transformations near the lower boundary of the region of soliton existence. The points on the ϵ - D plane which correspond to these curves are shown by the oblique crosses (×) in Fig. 1. When moving toward the lower boundary (when D changes from 0.7 to 0.3), the soliton energy decreases.

Fig. 5
Fig. 5

Comparison between numerical results and trial function approximation of the DSR phenomenon. Pulse energy Q is plotted versus dispersion D showing resonance at D 0.7 . The blue line is the horizontal cut of the Q ( ϵ , D ) surface at ϵ = 0.44 in Fig. 1. Red circles are obtained from the approximation that uses the trial function (6).

Equations (8)

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i ψ z + D 2 ψ t t + | ψ | 2 ψ + ν | ψ | 4 ψ = i δ ψ + i ϵ | ψ | 2 ψ + i β ψ t t + i μ | ψ | 4 ψ .
Q + ,
P = | ψ | max 2 P c w = ϵ + ϵ 2 4 μ δ 2 μ ,
T + ,
C T K ( ϵ , δ , μ , ν , D / β ) .
ψ ( t , z ) = A ( t ) e i φ ( t ) + i Ω z ,
A ( t ) = P [ 1 + ( 1 η ) sinh 2 ( t T ) ] 1 / 2 ,
φ ( t ) = d   ln   A ( t ) + C t t A 2 ( t ) d t ,

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