Abstract

We report on the experimental observation of period-doubling bifurcation and period-doubling route to chaos in a femtosecond soliton fiber laser passively mode locked by using the nonlinear polarization rotation technique. Increasing energy of the solitons circulating in the laser cavity, it was revealed that the intensity pattern of the output solitons experiences a period doubling route to chaos. Period-doubling route to chaos is a universal property of the nonlinear dynamic systems transiting from a stable state to a chaotic state. This experimental result shows that the nonlinear propagation of soliton pulses in the laser cavity is an intrinsic dynamic process, which follows the universal laws of the nonlinear dynamic systems.

©2004 Optical Society of America

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References

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  1. F. Ö. Ilday, F. W. Wise, and T. Sosnowski, “High-energy femtosecond stretched-pulse fiber laser with a nonlinear optical loop mirror,” Opt. Lett. 27, 1531–1533 (2002).
    [Crossref]
  2. M. J. Guy, D. U. Noske, and J. R. Taylor, “Generation of femtosecond soliton pulses by passive mode locking of an ytterbium-erbium figure-of-eight fiber laser,” Opt. Lett. 18, 1447–1449 (1993).
    [Crossref] [PubMed]
  3. D. Y. Tang, W. S. Man, H. Y. Tam, and M. S. Demokan, “Modulational instability in a fiber siliton ring laser induced by periodic dispersion variation,” Phys. Rev. A 61, 023804 (2000).
    [Crossref]
  4. S. M. J. Kelly, K. Smith, K. J. Blow, and N. J. Doran, “Average soliton dynamics of a high-gain erbium fiber laser,” Opt. Lett. 16, 1337–1339 (1991).
    [Crossref] [PubMed]
  5. A. D. Kim, J. N. Kutz, and D. J. Muraki, “Pulse-train uniformity in optical fiber lasers passively mode-locked by nonlinear polarization rotation,” IEEE J. Quantum Electron. 36, 465–471 (2000).
    [Crossref]
  6. Kristin M. Spaulding, Darryl H. Yong, Arnold D. Kim, and J. Nathan Kutz, “Nonlinear dynamics of mode-locking optical fiber ring lasers,” J. Opt. Soc. Am. B 19, 1045–054 (2002).
    [Crossref]
  7. B. Zhao, D. Y. Tang, L. M. Zhao, and P. Shum, “Pulse-train nonuniformity in a fiber soliton ring laser mode-locked by using the nonlinear polarization rotation technique,” Phys. Rev. A 69, 043808 (2004).
    [Crossref]
  8. R. Braun, F. Feudel, and P. Guzdar, “Route to chaos for a two-dimensional externally driven flow,” Phys. Rev. E 58, 1927–1932 (1998).
    [Crossref]
  9. G. Sucha, S. R. Bolton, S. Weiss, and D. S. Chemla, “Period doubling and quasi-periodicity in additive-pulse mode-locked lasers,” Opt. Lett. 20, 1794–1796 (1995).
    [Crossref] [PubMed]
  10. K. Tamura, C. R. Doerr, H. A. Haus, and E. P. Ippen, “Soliton fiber ring laser stabilization and tuning with a broad intracavity filter,” IEEE Phot. Tech. Lett. 6, 697–699 (1994).
    [Crossref]
  11. 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, 1080–1082 (1993).
    [Crossref] [PubMed]
  12. N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
    [Crossref]
  13. Daniel Côté and Henry M. van Driel, “Period doubling of a femtosecond Ti:sapphire laser by total mode locking,” Opt. Lett. 23, 715–717 (1998).
    [Crossref]

2004 (1)

B. Zhao, D. Y. Tang, L. M. Zhao, and P. Shum, “Pulse-train nonuniformity in a fiber soliton ring laser mode-locked by using the nonlinear polarization rotation technique,” Phys. Rev. A 69, 043808 (2004).
[Crossref]

2002 (2)

2000 (2)

D. Y. Tang, W. S. Man, H. Y. Tam, and M. S. Demokan, “Modulational instability in a fiber siliton ring laser induced by periodic dispersion variation,” Phys. Rev. A 61, 023804 (2000).
[Crossref]

A. D. Kim, J. N. Kutz, and D. J. Muraki, “Pulse-train uniformity in optical fiber lasers passively mode-locked by nonlinear polarization rotation,” IEEE J. Quantum Electron. 36, 465–471 (2000).
[Crossref]

1998 (2)

R. Braun, F. Feudel, and P. Guzdar, “Route to chaos for a two-dimensional externally driven flow,” Phys. Rev. E 58, 1927–1932 (1998).
[Crossref]

Daniel Côté and Henry M. van Driel, “Period doubling of a femtosecond Ti:sapphire laser by total mode locking,” Opt. Lett. 23, 715–717 (1998).
[Crossref]

1996 (1)

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[Crossref]

1995 (1)

1994 (1)

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

1993 (2)

1991 (1)

Bennion, I.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[Crossref]

Blow, K. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[Crossref]

S. M. J. Kelly, K. Smith, K. J. Blow, and N. J. Doran, “Average soliton dynamics of a high-gain erbium fiber laser,” Opt. Lett. 16, 1337–1339 (1991).
[Crossref] [PubMed]

Bolton, S. R.

Braun, R.

R. Braun, F. Feudel, and P. Guzdar, “Route to chaos for a two-dimensional externally driven flow,” Phys. Rev. E 58, 1927–1932 (1998).
[Crossref]

Chemla, D. S.

Côté, Daniel

Demokan, M. S.

D. Y. Tang, W. S. Man, H. Y. Tam, and M. S. Demokan, “Modulational instability in a fiber siliton ring laser induced by periodic dispersion variation,” Phys. Rev. A 61, 023804 (2000).
[Crossref]

Doerr, C. R.

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

Doran, N. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[Crossref]

S. M. J. Kelly, K. Smith, K. J. Blow, and N. J. Doran, “Average soliton dynamics of a high-gain erbium fiber laser,” Opt. Lett. 16, 1337–1339 (1991).
[Crossref] [PubMed]

Feudel, F.

R. Braun, F. Feudel, and P. Guzdar, “Route to chaos for a two-dimensional externally driven flow,” Phys. Rev. E 58, 1927–1932 (1998).
[Crossref]

Guy, M. J.

Guzdar, P.

R. Braun, F. Feudel, and P. Guzdar, “Route to chaos for a two-dimensional externally driven flow,” Phys. Rev. E 58, 1927–1932 (1998).
[Crossref]

Haus, H. A.

K. Tamura, C. R. Doerr, H. A. Haus, and E. P. Ippen, “Soliton fiber ring laser stabilization and tuning with a broad intracavity filter,” IEEE Phot. Tech. Lett. 6, 697–699 (1994).
[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, 1080–1082 (1993).
[Crossref] [PubMed]

Ilday, F. Ö.

Ippen, E. P.

K. Tamura, C. R. Doerr, H. A. Haus, and E. P. Ippen, “Soliton fiber ring laser stabilization and tuning with a broad intracavity filter,” IEEE Phot. Tech. Lett. 6, 697–699 (1994).
[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, 1080–1082 (1993).
[Crossref] [PubMed]

Kelly, S. M. J.

Kim, A. D.

A. D. Kim, J. N. Kutz, and D. J. Muraki, “Pulse-train uniformity in optical fiber lasers passively mode-locked by nonlinear polarization rotation,” IEEE J. Quantum Electron. 36, 465–471 (2000).
[Crossref]

Kim, Arnold D.

Knox, F. M.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[Crossref]

Kutz, J. N.

A. D. Kim, J. N. Kutz, and D. J. Muraki, “Pulse-train uniformity in optical fiber lasers passively mode-locked by nonlinear polarization rotation,” IEEE J. Quantum Electron. 36, 465–471 (2000).
[Crossref]

Kutz, J. Nathan

Man, W. S.

D. Y. Tang, W. S. Man, H. Y. Tam, and M. S. Demokan, “Modulational instability in a fiber siliton ring laser induced by periodic dispersion variation,” Phys. Rev. A 61, 023804 (2000).
[Crossref]

Muraki, D. J.

A. D. Kim, J. N. Kutz, and D. J. Muraki, “Pulse-train uniformity in optical fiber lasers passively mode-locked by nonlinear polarization rotation,” IEEE J. Quantum Electron. 36, 465–471 (2000).
[Crossref]

Nelson, L. E.

Noske, D. U.

Shum, P.

B. Zhao, D. Y. Tang, L. M. Zhao, and P. Shum, “Pulse-train nonuniformity in a fiber soliton ring laser mode-locked by using the nonlinear polarization rotation technique,” Phys. Rev. A 69, 043808 (2004).
[Crossref]

Smith, K.

Smith, N. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[Crossref]

Sosnowski, T.

Spaulding, Kristin M.

Sucha, G.

Tam, H. Y.

D. Y. Tang, W. S. Man, H. Y. Tam, and M. S. Demokan, “Modulational instability in a fiber siliton ring laser induced by periodic dispersion variation,” Phys. Rev. A 61, 023804 (2000).
[Crossref]

Tamura, K.

K. Tamura, C. R. Doerr, H. A. Haus, and E. P. Ippen, “Soliton fiber ring laser stabilization and tuning with a broad intracavity filter,” IEEE Phot. Tech. Lett. 6, 697–699 (1994).
[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, 1080–1082 (1993).
[Crossref] [PubMed]

Tang, D. Y.

B. Zhao, D. Y. Tang, L. M. Zhao, and P. Shum, “Pulse-train nonuniformity in a fiber soliton ring laser mode-locked by using the nonlinear polarization rotation technique,” Phys. Rev. A 69, 043808 (2004).
[Crossref]

D. Y. Tang, W. S. Man, H. Y. Tam, and M. S. Demokan, “Modulational instability in a fiber siliton ring laser induced by periodic dispersion variation,” Phys. Rev. A 61, 023804 (2000).
[Crossref]

Taylor, J. R.

van Driel, Henry M.

Weiss, S.

Wise, F. W.

Yong, Darryl H.

Zhao, B.

B. Zhao, D. Y. Tang, L. M. Zhao, and P. Shum, “Pulse-train nonuniformity in a fiber soliton ring laser mode-locked by using the nonlinear polarization rotation technique,” Phys. Rev. A 69, 043808 (2004).
[Crossref]

Zhao, L. M.

B. Zhao, D. Y. Tang, L. M. Zhao, and P. Shum, “Pulse-train nonuniformity in a fiber soliton ring laser mode-locked by using the nonlinear polarization rotation technique,” Phys. Rev. A 69, 043808 (2004).
[Crossref]

Electron. Lett. (1)

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[Crossref]

IEEE J. Quantum Electron. (1)

A. D. Kim, J. N. Kutz, and D. J. Muraki, “Pulse-train uniformity in optical fiber lasers passively mode-locked by nonlinear polarization rotation,” IEEE J. Quantum Electron. 36, 465–471 (2000).
[Crossref]

IEEE Phot. Tech. Lett. (1)

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

J. Opt. Soc. Am. B (1)

Opt. Lett. (6)

Phys. Rev. A (2)

D. Y. Tang, W. S. Man, H. Y. Tam, and M. S. Demokan, “Modulational instability in a fiber siliton ring laser induced by periodic dispersion variation,” Phys. Rev. A 61, 023804 (2000).
[Crossref]

B. Zhao, D. Y. Tang, L. M. Zhao, and P. Shum, “Pulse-train nonuniformity in a fiber soliton ring laser mode-locked by using the nonlinear polarization rotation technique,” Phys. Rev. A 69, 043808 (2004).
[Crossref]

Phys. Rev. E (1)

R. Braun, F. Feudel, and P. Guzdar, “Route to chaos for a two-dimensional externally driven flow,” Phys. Rev. E 58, 1927–1932 (1998).
[Crossref]

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Figures (5)

Fig. 1.
Fig. 1. A schematic of the experimental setup. λ/4: quarter-wave plate; λ/2: half-wave plate; BS: beam splitter; WDM: wavelength-division multiplexer; EDF: erbium doped fiber; OSA: optical spectrum analyzer; PD: photodetector; Osci.: Oscilloscope; SA: rf spectrum analyzer.

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Fig. 2.
Fig. 2. Period-doubling bifurcation to chaos of the soliton trains. (a) Period-one state; (b) Period-two state; (c) Period-four state; (d) Chaotic state. From (a) to (d) the pump intensity is increased.

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Fig. 3.
Fig. 3. Oscilloscope traces of a period-two state of the laser emission.

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Fig. 4.
Fig. 4. Optical spectra of the laser measured in the states of period-one (a) and period-two (b).

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Fig. 5.
Fig. 5. rf spectra of the laser output corresponding to (a) period-one; (b) period-two states.

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