Abstract

Dissipative soliton resonance (DSR) is a phenomenon where the energy of a soliton in a dissipative system increases without limit at certain values of the system parameters. We have found that the DSR phenomenon is robust and does not disappear when perturbations are introduced into the model. In particular, parameter management is benign to DSR: the resonance property remains intact even when a pulse experiences periodic changes of system parameters in a laser cavity. We also show that high energy pulses emerging from a laser cavity can be compressed to shorter durations with the help of linear dispersive devices.

© 2008 Optical Society of America

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  3. N. Akhmediev, J. M. Soto-Crespo, and Ph. Grelu, “Roadmap to ultra-short record high-energy pulses out of laser systems,” Phys. Lett. A 372, 3124-3128 (2008).
    [CrossRef]
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    [CrossRef]
  5. H. A. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE J. Quantum Electron. QE-11, 736-746 (1975).
    [CrossRef]
  6. W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77, 023814 (2008).
    [CrossRef]
  7. A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg-Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604(R) (2005).
    [CrossRef]
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    [CrossRef]
  14. F. X. Kartner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, “Control of solid-state laser dynamics by semiconductor devices,” Opt. Eng. (Bellingham) 34, 2024-2036 (1995).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2008 (3)

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

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

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

2005 (1)

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 (1)

T. Katayama and H. Kawaguchi, “Supercontinuum generation and pulse compression in short fibers for optical pulses generated by 1.5 μm optical parametric oscillator,” Jpn. J. Appl. Phys., Part 2 43, L712-L715 (2004).
[CrossRef]

2003 (1)

2002 (1)

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

2000 (1)

B. J. Eggleton, G. Lenz, and N. M. Litchinitser, “Optical pulse compression schemes that use nonlinear Bragg gratings,” Fiber Integr. Opt. 19, 383-421 (2000).
[CrossRef]

1997 (1)

1995 (2)

A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19, 161-238 (1995).
[CrossRef]

F. X. Kartner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, “Control of solid-state laser dynamics by semiconductor devices,” Opt. Eng. (Bellingham) 34, 2024-2036 (1995).
[CrossRef]

1993 (2)

E. A. DeSouza, C. E. Soccolich, W. Pleibel, R. H. Stolen, M. N. Islam, J. R. Simpson, and D. J. DiGiovanni, “Saturable absorber modelocked polarization maintaining erbium-doped fiber laser,” Electron. Lett. 29, 447-449 (1993).
[CrossRef]

P. F. Curley, C. Spielmann, T. Brabec, E. Winter, and F. Krausz, “Periodic pulse evolution in solitary lasers,” J. Opt. Soc. Am. B 10, 1025-1028 (1993).
[CrossRef]

1992 (2)

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse mode-locking and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086-2096 (1992).
[CrossRef]

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Speilmann, E. Wintner, and A. J. Schmit, “Femtosecond solid-state lasers,” IEEE J. Quantum Electron. 28, 2097-2122 (1992).
[CrossRef]

1991 (1)

1982 (1)

D. Grischkowsky and A. C. Balant, “Optical pulse compression based on enhanced frequency chirping,” Appl. Phys. Lett. 41, 1-3 (1982).
[CrossRef]

1975 (1)

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

1969 (1)

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454-458 (1969).
[CrossRef]

Akhmediev, N.

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

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

G. E. Town and N. Akhmediev, “Optical fiber lasers,” in Encyclopedia of Modern Optics, R.D.Guenther, ed. (Academic, 2004), Vol. 2, pp. 475-484.

Ankiewicz, A.

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

Aranson, I. S.

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

Balant, A. C.

D. Grischkowsky and A. C. Balant, “Optical pulse compression based on enhanced frequency chirping,” Appl. Phys. Lett. 41, 1-3 (1982).
[CrossRef]

Bergman, K.

Blow, K. J.

Brabec, T.

P. F. Curley, C. Spielmann, T. Brabec, E. Winter, and F. Krausz, “Periodic pulse evolution in solitary lasers,” J. Opt. Soc. Am. B 10, 1025-1028 (1993).
[CrossRef]

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Speilmann, E. Wintner, and A. J. Schmit, “Femtosecond solid-state lasers,” IEEE J. Quantum Electron. 28, 2097-2122 (1992).
[CrossRef]

Brovelli, L. R.

F. X. Kartner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, “Control of solid-state laser dynamics by semiconductor devices,” Opt. Eng. (Bellingham) 34, 2024-2036 (1995).
[CrossRef]

Calasso, I.

F. X. Kartner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, “Control of solid-state laser dynamics by semiconductor devices,” Opt. Eng. (Bellingham) 34, 2024-2036 (1995).
[CrossRef]

Chang, W.

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

Chong, A.

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

Collings, B. C.

Cundiff, S. T.

Curley, P. F.

P. F. Curley, C. Spielmann, T. Brabec, E. Winter, and F. Krausz, “Periodic pulse evolution in solitary lasers,” J. Opt. Soc. Am. B 10, 1025-1028 (1993).
[CrossRef]

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Speilmann, E. Wintner, and A. J. Schmit, “Femtosecond solid-state lasers,” IEEE J. Quantum Electron. 28, 2097-2122 (1992).
[CrossRef]

DeSouza, E. A.

E. A. DeSouza, C. E. Soccolich, W. Pleibel, R. H. Stolen, M. N. Islam, J. R. Simpson, and D. J. DiGiovanni, “Saturable absorber modelocked polarization maintaining erbium-doped fiber laser,” Electron. Lett. 29, 447-449 (1993).
[CrossRef]

DiGiovanni, D. J.

E. A. DeSouza, C. E. Soccolich, W. Pleibel, R. H. Stolen, M. N. Islam, J. R. Simpson, and D. J. DiGiovanni, “Saturable absorber modelocked polarization maintaining erbium-doped fiber laser,” Electron. Lett. 29, 447-449 (1993).
[CrossRef]

Doran, N. J.

Eggleton, B. J.

B. J. Eggleton, G. Lenz, and N. M. Litchinitser, “Optical pulse compression schemes that use nonlinear Bragg gratings,” Fiber Integr. Opt. 19, 383-421 (2000).
[CrossRef]

Fermann, M. E.

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Speilmann, E. Wintner, and A. J. Schmit, “Femtosecond solid-state lasers,” IEEE J. Quantum Electron. 28, 2097-2122 (1992).
[CrossRef]

Fortier, T. M.

Fujimoto, J. G.

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse mode-locking and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086-2096 (1992).
[CrossRef]

Grelu, Ph.

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

Grischkowsky, D.

D. Grischkowsky and A. C. Balant, “Optical pulse compression based on enhanced frequency chirping,” Appl. Phys. Lett. 41, 1-3 (1982).
[CrossRef]

Haus, H. A.

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse mode-locking and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086-2096 (1992).
[CrossRef]

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

Hofer, M.

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Speilmann, E. Wintner, and A. J. Schmit, “Femtosecond solid-state lasers,” IEEE J. Quantum Electron. 28, 2097-2122 (1992).
[CrossRef]

Ippen, E. P.

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse mode-locking and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086-2096 (1992).
[CrossRef]

Islam, M. N.

E. A. DeSouza, C. E. Soccolich, W. Pleibel, R. H. Stolen, M. N. Islam, J. R. Simpson, and D. J. DiGiovanni, “Saturable absorber modelocked polarization maintaining erbium-doped fiber laser,” Electron. Lett. 29, 447-449 (1993).
[CrossRef]

Jones, D. J.

Kamp, M.

F. X. Kartner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, “Control of solid-state laser dynamics by semiconductor devices,” Opt. Eng. (Bellingham) 34, 2024-2036 (1995).
[CrossRef]

Kartner, F. X.

F. X. Kartner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, “Control of solid-state laser dynamics by semiconductor devices,” Opt. Eng. (Bellingham) 34, 2024-2036 (1995).
[CrossRef]

Katayama, T.

T. Katayama and H. Kawaguchi, “Supercontinuum generation and pulse compression in short fibers for optical pulses generated by 1.5 μm optical parametric oscillator,” Jpn. J. Appl. Phys., Part 2 43, L712-L715 (2004).
[CrossRef]

Kawaguchi, H.

T. Katayama and H. Kawaguchi, “Supercontinuum generation and pulse compression in short fibers for optical pulses generated by 1.5 μm optical parametric oscillator,” Jpn. J. Appl. Phys., Part 2 43, L712-L715 (2004).
[CrossRef]

Keller, U.

F. X. Kartner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, “Control of solid-state laser dynamics by semiconductor devices,” Opt. Eng. (Bellingham) 34, 2024-2036 (1995).
[CrossRef]

Kelly, S. M. J.

Knox, W. H.

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]

Kopf, D.

F. X. Kartner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, “Control of solid-state laser dynamics by semiconductor devices,” Opt. Eng. (Bellingham) 34, 2024-2036 (1995).
[CrossRef]

Kramer, L.

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

Krausz, F.

P. F. Curley, C. Spielmann, T. Brabec, E. Winter, and F. Krausz, “Periodic pulse evolution in solitary lasers,” J. Opt. Soc. Am. B 10, 1025-1028 (1993).
[CrossRef]

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Speilmann, E. Wintner, and A. J. Schmit, “Femtosecond solid-state lasers,” IEEE J. Quantum Electron. 28, 2097-2122 (1992).
[CrossRef]

Kutz, J. 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]

Lenz, G.

B. J. Eggleton, G. Lenz, and N. M. Litchinitser, “Optical pulse compression schemes that use nonlinear Bragg gratings,” Fiber Integr. Opt. 19, 383-421 (2000).
[CrossRef]

Litchinitser, N. M.

B. J. Eggleton, G. Lenz, and N. M. Litchinitser, “Optical pulse compression schemes that use nonlinear Bragg gratings,” Fiber Integr. Opt. 19, 383-421 (2000).
[CrossRef]

Ober, M. H.

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Speilmann, E. Wintner, and A. J. Schmit, “Femtosecond solid-state lasers,” IEEE J. Quantum Electron. 28, 2097-2122 (1992).
[CrossRef]

Pleibel, W.

E. A. DeSouza, C. E. Soccolich, W. Pleibel, R. H. Stolen, M. N. Islam, J. R. Simpson, and D. J. DiGiovanni, “Saturable absorber modelocked polarization maintaining erbium-doped fiber laser,” Electron. Lett. 29, 447-449 (1993).
[CrossRef]

Renninger, W. H.

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

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]

Schmit, A. J.

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Speilmann, E. Wintner, and A. J. Schmit, “Femtosecond solid-state lasers,” IEEE J. Quantum Electron. 28, 2097-2122 (1992).
[CrossRef]

Simpson, J. R.

E. A. DeSouza, C. E. Soccolich, W. Pleibel, R. H. Stolen, M. N. Islam, J. R. Simpson, and D. J. DiGiovanni, “Saturable absorber modelocked polarization maintaining erbium-doped fiber laser,” Electron. Lett. 29, 447-449 (1993).
[CrossRef]

Smith, K.

Soccolich, C. E.

E. A. DeSouza, C. E. Soccolich, W. Pleibel, R. H. Stolen, M. N. Islam, J. R. Simpson, and D. J. DiGiovanni, “Saturable absorber modelocked polarization maintaining erbium-doped fiber laser,” Electron. Lett. 29, 447-449 (1993).
[CrossRef]

Soto-Crespo, J. M.

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

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

Speilmann, C.

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Speilmann, E. Wintner, and A. J. Schmit, “Femtosecond solid-state lasers,” IEEE J. Quantum Electron. 28, 2097-2122 (1992).
[CrossRef]

Spielmann, C.

Stolen, R. H.

E. A. DeSouza, C. E. Soccolich, W. Pleibel, R. H. Stolen, M. N. Islam, J. R. Simpson, and D. J. DiGiovanni, “Saturable absorber modelocked polarization maintaining erbium-doped fiber laser,” Electron. Lett. 29, 447-449 (1993).
[CrossRef]

Town, G. E.

G. E. Town and N. Akhmediev, “Optical fiber lasers,” in Encyclopedia of Modern Optics, R.D.Guenther, ed. (Academic, 2004), Vol. 2, pp. 475-484.

Treacy, E. B.

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454-458 (1969).
[CrossRef]

Tsuda, S.

Weiner, A. M.

A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19, 161-238 (1995).
[CrossRef]

Winter, E.

Wintner, E.

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Speilmann, E. Wintner, and A. J. Schmit, “Femtosecond solid-state lasers,” IEEE J. Quantum Electron. 28, 2097-2122 (1992).
[CrossRef]

Wise, F. W.

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

Appl. Phys. Lett. (1)

D. Grischkowsky and A. C. Balant, “Optical pulse compression based on enhanced frequency chirping,” Appl. Phys. Lett. 41, 1-3 (1982).
[CrossRef]

Electron. Lett. (1)

E. A. DeSouza, C. E. Soccolich, W. Pleibel, R. H. Stolen, M. N. Islam, J. R. Simpson, and D. J. DiGiovanni, “Saturable absorber modelocked polarization maintaining erbium-doped fiber laser,” Electron. Lett. 29, 447-449 (1993).
[CrossRef]

Fiber Integr. Opt. (1)

B. J. Eggleton, G. Lenz, and N. M. Litchinitser, “Optical pulse compression schemes that use nonlinear Bragg gratings,” Fiber Integr. Opt. 19, 383-421 (2000).
[CrossRef]

IEEE J. Quantum Electron. (4)

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

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454-458 (1969).
[CrossRef]

F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, C. Speilmann, E. Wintner, and A. J. Schmit, “Femtosecond solid-state lasers,” IEEE J. Quantum Electron. 28, 2097-2122 (1992).
[CrossRef]

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse mode-locking and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086-2096 (1992).
[CrossRef]

J. Opt. Soc. Am. B (2)

Jpn. J. Appl. Phys., Part 2 (1)

T. Katayama and H. Kawaguchi, “Supercontinuum generation and pulse compression in short fibers for optical pulses generated by 1.5 μm optical parametric oscillator,” Jpn. J. Appl. Phys., Part 2 43, L712-L715 (2004).
[CrossRef]

Opt. Eng. (Bellingham) (1)

F. X. Kartner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, “Control of solid-state laser dynamics by semiconductor devices,” Opt. Eng. (Bellingham) 34, 2024-2036 (1995).
[CrossRef]

Opt. Lett. (2)

Phys. Lett. A (1)

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

Phys. Rev. A (2)

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

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

Phys. Rev. E (1)

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

Prog. Quantum Electron. (1)

A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19, 161-238 (1995).
[CrossRef]

Rev. Mod. Phys. (1)

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

Other (3)

N.Akhmediev and A.Ankiewicz, eds., “Dissipative Solitons,” in Lecture Notes in Physics (Springer-Verlag2005), Vol. 661.
[CrossRef]

G. E. Town and N. Akhmediev, “Optical fiber lasers,” in Encyclopedia of Modern Optics, R.D.Guenther, ed. (Academic, 2004), Vol. 2, pp. 475-484.

G.P.Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic of the model and (b) map of the parameters of the CGLE for a single round trip of the pulse in the cavity. Pulses travel counterclockwise around the nonlinear ( L 1 ) and linear ( L 2 ) sections of the loop. At the coupler, 20% of the light is tapped off, and this enters the compressing piece of fiber.

Fig. 2
Fig. 2

Evolution of the soliton within the dispersion-managed cavity for three consecutive round trips. The pulse shape repeats at the end of each round trip, and hence fixed shape solitons are generated at the output of the oscillator. The system parameters are L 1 = 0.1 , L 2 D 2 = 0.02 , D 1 = 1 , ϵ = 1.0 , δ = 1.1 , β = 0.08 , ν = 0.01 , and μ = 0.003 .

Fig. 3
Fig. 3

Soliton energy, Q, in the L 1 section of the oscillator versus the dispersion parameter, D 1 , for three different values of L 2 D 2 . The solid circle and the solid square show the points for which pulses are compressed (see Fig. 6 below).

Fig. 4
Fig. 4

(a) Pulse profiles, (b) soliton spectra, and (c) phase profiles for three different values of D 1 . The rest of the parameters are shown inside (a).

Fig. 5
Fig. 5

(a) Pulse profiles, (b) soliton spectra, and (c) phase for three different values of L 2 D 2 . The rest of the parameters are shown inside (a). Comparison with Fig. 4 shows that the effect of changing L 2 D 2 is qualitatively the same as the effect of changing D 1 .

Fig. 6
Fig. 6

Pulse profiles before (dashed curves) and after (solid curves) the linear compression of the pulse. The oscillator output pulses (dashed curves) are chosen for the set of parameters shown in Fig. 3 and (a) D 1 = 1.0 (solid circle in Fig. 3 and (b) D 1 = 1.3 (solid square in Fig. 3).

Equations (4)

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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 ,
i ψ z + D 2 2 ψ t t = 0 .
log 10 ( Q ) = 2.8 D + 2.2 ,
D = D 1 + 10 L 2 D 2 .

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