Abstract

We report on the experimental observation of Fermi-Pasta-Ulam (FPU) recurrence in a passively mode-locked fiber ring laser. The spectral sidebands of a CW component generated due to the modulation instability grow up periodically as a result of the reversibility of the effect, demonstrating the existence of FPU recurrence.

© 2003 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 2001), Chap. 5.
  2. K. Tai, A. Hasegawa, and A. Tomita, “Observation of the modulation instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
    [Crossref] [PubMed]
  3. G. P. Agrawal, “Modulation instability in erbium-doped fiber amplifiers,” IEEE Photon. Tech. Lett. 4, 562–564 (1992).
    [Crossref]
  4. D. Y. Tang, W. S. Man, H. Y. Tam, and M. S. Demokan, “Modulation instability in a fiber laser induced by periodic dispersion variation,” Phys. Rev. A 61, 023804 (2000).
    [Crossref]
  5. E. Fermi, J. Pasta, and H. C. Ulam, “Studies of nonlinear problems,” in Collected Papers of Enrico Fermi, E. Segre, ed. Vol 2, 977–988 (1965).
  6. Nail N. Akhmediev, “Déjà vu in optics,” Nature 413, 267 (2001).
    [Crossref] [PubMed]
  7. G. V. Simaeys, P. Emplit, and M. Haelerman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).
    [PubMed]
  8. S. Namiki, E. P. Ippen, H. A. Haus, and K. Tamura, “Relaxation oscillation behavior in polarization additive pulse mode-locked fiber ring lasers,” Appl. Phys. Lett. 69, 3969–3971 (1996).
    [Crossref]
  9. C. J. Chen, P. K. A. Wai, and C. R. Menyuk, “Soliton fiber ring laser,” Opt. Lett. 17, 417–419 (1992).
    [Crossref] [PubMed]
  10. W. S. Man, H. Y. Tam, M. S. Demokan, P. K. A. Wai, and D. Y. Tang, “Mechanism of intrinsic wavelength tuning and sideband asymmetry in a passively mode-locked soliton fiber ring laser,” J. Opt. Soc. Am. B 17, 28–33 (2000)
    [Crossref]
  11. B. Zhao, D. Y. Tang, P. Shum, W. S. Man, H. Y. Tam, Y. D. Gong, and C. Lu, “Passively harmonic mode locking of twin-pulse solitons in an erbium-doped fiber ring laser,” Opt. Comm. (to be published).

2001 (2)

Nail N. Akhmediev, “Déjà vu in optics,” Nature 413, 267 (2001).
[Crossref] [PubMed]

G. V. Simaeys, P. Emplit, and M. Haelerman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).
[PubMed]

2000 (2)

W. S. Man, H. Y. Tam, M. S. Demokan, P. K. A. Wai, and D. Y. Tang, “Mechanism of intrinsic wavelength tuning and sideband asymmetry in a passively mode-locked soliton fiber ring laser,” J. Opt. Soc. Am. B 17, 28–33 (2000)
[Crossref]

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

1996 (1)

S. Namiki, E. P. Ippen, H. A. Haus, and K. Tamura, “Relaxation oscillation behavior in polarization additive pulse mode-locked fiber ring lasers,” Appl. Phys. Lett. 69, 3969–3971 (1996).
[Crossref]

1992 (2)

G. P. Agrawal, “Modulation instability in erbium-doped fiber amplifiers,” IEEE Photon. Tech. Lett. 4, 562–564 (1992).
[Crossref]

C. J. Chen, P. K. A. Wai, and C. R. Menyuk, “Soliton fiber ring laser,” Opt. Lett. 17, 417–419 (1992).
[Crossref] [PubMed]

1986 (1)

K. Tai, A. Hasegawa, and A. Tomita, “Observation of the modulation instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[Crossref] [PubMed]

Agrawal, G. P.

G. P. Agrawal, “Modulation instability in erbium-doped fiber amplifiers,” IEEE Photon. Tech. Lett. 4, 562–564 (1992).
[Crossref]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 2001), Chap. 5.

Akhmediev, Nail N.

Nail N. Akhmediev, “Déjà vu in optics,” Nature 413, 267 (2001).
[Crossref] [PubMed]

Chen, C. J.

Demokan, M. S.

W. S. Man, H. Y. Tam, M. S. Demokan, P. K. A. Wai, and D. Y. Tang, “Mechanism of intrinsic wavelength tuning and sideband asymmetry in a passively mode-locked soliton fiber ring laser,” J. Opt. Soc. Am. B 17, 28–33 (2000)
[Crossref]

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

Emplit, P.

G. V. Simaeys, P. Emplit, and M. Haelerman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).
[PubMed]

Fermi, E.

E. Fermi, J. Pasta, and H. C. Ulam, “Studies of nonlinear problems,” in Collected Papers of Enrico Fermi, E. Segre, ed. Vol 2, 977–988 (1965).

Gong, Y. D.

B. Zhao, D. Y. Tang, P. Shum, W. S. Man, H. Y. Tam, Y. D. Gong, and C. Lu, “Passively harmonic mode locking of twin-pulse solitons in an erbium-doped fiber ring laser,” Opt. Comm. (to be published).

Haelerman, M.

G. V. Simaeys, P. Emplit, and M. Haelerman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).
[PubMed]

Hasegawa, A.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of the modulation instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[Crossref] [PubMed]

Haus, H. A.

S. Namiki, E. P. Ippen, H. A. Haus, and K. Tamura, “Relaxation oscillation behavior in polarization additive pulse mode-locked fiber ring lasers,” Appl. Phys. Lett. 69, 3969–3971 (1996).
[Crossref]

Ippen, E. P.

S. Namiki, E. P. Ippen, H. A. Haus, and K. Tamura, “Relaxation oscillation behavior in polarization additive pulse mode-locked fiber ring lasers,” Appl. Phys. Lett. 69, 3969–3971 (1996).
[Crossref]

Lu, C.

B. Zhao, D. Y. Tang, P. Shum, W. S. Man, H. Y. Tam, Y. D. Gong, and C. Lu, “Passively harmonic mode locking of twin-pulse solitons in an erbium-doped fiber ring laser,” Opt. Comm. (to be published).

Man, W. S.

W. S. Man, H. Y. Tam, M. S. Demokan, P. K. A. Wai, and D. Y. Tang, “Mechanism of intrinsic wavelength tuning and sideband asymmetry in a passively mode-locked soliton fiber ring laser,” J. Opt. Soc. Am. B 17, 28–33 (2000)
[Crossref]

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

B. Zhao, D. Y. Tang, P. Shum, W. S. Man, H. Y. Tam, Y. D. Gong, and C. Lu, “Passively harmonic mode locking of twin-pulse solitons in an erbium-doped fiber ring laser,” Opt. Comm. (to be published).

Menyuk, C. R.

Namiki, S.

S. Namiki, E. P. Ippen, H. A. Haus, and K. Tamura, “Relaxation oscillation behavior in polarization additive pulse mode-locked fiber ring lasers,” Appl. Phys. Lett. 69, 3969–3971 (1996).
[Crossref]

Pasta, J.

E. Fermi, J. Pasta, and H. C. Ulam, “Studies of nonlinear problems,” in Collected Papers of Enrico Fermi, E. Segre, ed. Vol 2, 977–988 (1965).

Shum, P.

B. Zhao, D. Y. Tang, P. Shum, W. S. Man, H. Y. Tam, Y. D. Gong, and C. Lu, “Passively harmonic mode locking of twin-pulse solitons in an erbium-doped fiber ring laser,” Opt. Comm. (to be published).

Simaeys, G. V.

G. V. Simaeys, P. Emplit, and M. Haelerman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).
[PubMed]

Tai, K.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of the modulation instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[Crossref] [PubMed]

Tam, H. Y.

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

W. S. Man, H. Y. Tam, M. S. Demokan, P. K. A. Wai, and D. Y. Tang, “Mechanism of intrinsic wavelength tuning and sideband asymmetry in a passively mode-locked soliton fiber ring laser,” J. Opt. Soc. Am. B 17, 28–33 (2000)
[Crossref]

B. Zhao, D. Y. Tang, P. Shum, W. S. Man, H. Y. Tam, Y. D. Gong, and C. Lu, “Passively harmonic mode locking of twin-pulse solitons in an erbium-doped fiber ring laser,” Opt. Comm. (to be published).

Tamura, K.

S. Namiki, E. P. Ippen, H. A. Haus, and K. Tamura, “Relaxation oscillation behavior in polarization additive pulse mode-locked fiber ring lasers,” Appl. Phys. Lett. 69, 3969–3971 (1996).
[Crossref]

Tang, D. Y.

W. S. Man, H. Y. Tam, M. S. Demokan, P. K. A. Wai, and D. Y. Tang, “Mechanism of intrinsic wavelength tuning and sideband asymmetry in a passively mode-locked soliton fiber ring laser,” J. Opt. Soc. Am. B 17, 28–33 (2000)
[Crossref]

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

B. Zhao, D. Y. Tang, P. Shum, W. S. Man, H. Y. Tam, Y. D. Gong, and C. Lu, “Passively harmonic mode locking of twin-pulse solitons in an erbium-doped fiber ring laser,” Opt. Comm. (to be published).

Tomita, A.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of the modulation instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[Crossref] [PubMed]

Ulam, H. C.

E. Fermi, J. Pasta, and H. C. Ulam, “Studies of nonlinear problems,” in Collected Papers of Enrico Fermi, E. Segre, ed. Vol 2, 977–988 (1965).

Wai, P. K. A.

Zhao, B.

B. Zhao, D. Y. Tang, P. Shum, W. S. Man, H. Y. Tam, Y. D. Gong, and C. Lu, “Passively harmonic mode locking of twin-pulse solitons in an erbium-doped fiber ring laser,” Opt. Comm. (to be published).

Appl. Phys. Lett. (1)

S. Namiki, E. P. Ippen, H. A. Haus, and K. Tamura, “Relaxation oscillation behavior in polarization additive pulse mode-locked fiber ring lasers,” Appl. Phys. Lett. 69, 3969–3971 (1996).
[Crossref]

IEEE Photon. Tech. Lett. (1)

G. P. Agrawal, “Modulation instability in erbium-doped fiber amplifiers,” IEEE Photon. Tech. Lett. 4, 562–564 (1992).
[Crossref]

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

Nature (1)

Nail N. Akhmediev, “Déjà vu in optics,” Nature 413, 267 (2001).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Rev. A (1)

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

Phys. Rev. Lett. (2)

K. Tai, A. Hasegawa, and A. Tomita, “Observation of the modulation instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[Crossref] [PubMed]

G. V. Simaeys, P. Emplit, and M. Haelerman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).
[PubMed]

Other (3)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 2001), Chap. 5.

E. Fermi, J. Pasta, and H. C. Ulam, “Studies of nonlinear problems,” in Collected Papers of Enrico Fermi, E. Segre, ed. Vol 2, 977–988 (1965).

B. Zhao, D. Y. Tang, P. Shum, W. S. Man, H. Y. Tam, Y. D. Gong, and C. Lu, “Passively harmonic mode locking of twin-pulse solitons in an erbium-doped fiber ring laser,” Opt. Comm. (to be published).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of the laser setup. PI: polarization dependent isolator; PC: polarization controller; WDM: wavelength division multiplexer; EDF: erbium-doped fiber; DSF: dispersion-shifted fiber.

Fig. 2.
Fig. 2.

A typical optical spectrum of the laser output when the CW lasing coexists with the single-pulse solitons in the cavity.

Fig. 3.
Fig. 3.

Enlarged views of the CW component under different pump power. (a): with P=100mW; (b) and (c): P=157mW. All the three conditions are measured under the same polarization setting.

Fig. 4.
Fig. 4.

The oscilloscope trace of the output under the same operation condition as Fig. 3(a) and Fig. 3(c). A recurrence period of around 7ms is clearly observed.

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