Abstract

We investigate theoretically and experimentally the nonlinear dynamics of a synchronously pumped all-fiber passive ring cavity. Our study is based on the use of a specially designed stabilization system that allows for interferometric control of the cavity length. With this system we can achieve stable operation and we are able to perform systematic and reproducible measurements for the characterization of the fundamental nonlinear behaviors of the cavity such as optical bistability, period doubling instabilities, and dissipative modulational instabilities. Through the analysis of the output pulse spectra we show that modulational instability plays a crucial role in the dynamics of the cavity (in particular, in the period-doubling route to chaos) even with normal group-velocity dispersion. A theoretical study of modulational instability in the cavity is presented and is successfully compared with experimental results.

© 1998 Optical Society of America

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  1. J. Mark, L. Y. Liu, K. L. Hall, H. A. Haus, and E. P. Ippen, “Femtosecond pulse generation in a laser with a nonlinear external resonator,” Opt. Lett. 14, 48–50 (1989).
    [CrossRef] [PubMed]
  2. 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]
  3. E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, and D. G. Fursa, “Tunable subpicosecond synchronously pumped fiber Raman laser,” Pis’ma Zh. Eksp. Teor. Fiz. 45, 469–471 (1987) [JETP Lett. 45, 599–601 (1987)].
  4. M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38, 5193–5196 (1988).
    [CrossRef] [PubMed]
  5. M. Haelterman, S. Trillo, and S. Wabnitz, “Generation of ultrahigh repetition rate soliton trains in fibre ring,” Electron. Lett. 29, 119–121 (1993).
    [CrossRef]
  6. S. Wabnitz, “Suppression of interactions in a phase-locked soliton optical memory,” Opt. Lett. 18, 601–603 (1993).
    [CrossRef] [PubMed]
  7. J. García-Mateos, F. Canal, and M. Haelterman, “Passive fiber ring flip-flop memory based on polarization dynamics,” Opt. Commun. 137, 427–436 (1997).
    [CrossRef]
  8. H. M. Gibbs, Optical Bistability: Controlling Light with Light, Quantum Electronics: Principle and Applications (Academic, New York, 1985).
  9. K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).
    [CrossRef]
  10. M. Haelterman, “Simple model for the study of period-doubling instabilities in the nonlinear ring cavity,” Appl. Phys. Lett. 61, 2756–2758 (1992).
    [CrossRef]
  11. M. Haelterman, S. Trillo, and S. Wabnitz, “Polarization multistability and instability in a nonlinear dispersive ring cavity,” J. Opt. Soc. Am. B 11, 446–456 (1994).
    [CrossRef]
  12. M. Haelterman and M. D. Tolley, “Pure polarization period-doubling instability in a Kerr-type nonlinear ring cavity,” Opt. Commun. 108, 165–175 (1994).
    [CrossRef]
  13. M. Haelterman, G. Vitrant, and J. García-Mateos, “Symmetry-breaking bifurcation in synchronously driven fiber cavities,” in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1995), pp. 201–203.
  14. R. Vallée, “Role of the group velocity dispersion in the onset of instabilities in a nonlinear ring cavity,” Opt. Commun. 93, 389–399 (1992).
    [CrossRef]
  15. D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “New class of instabilities in passive optical cavities,” Phys. Rev. Lett. 54, 681–684 (1985).
    [CrossRef] [PubMed]
  16. H. Nakatsuka, S. Asaka, H. Itoh, K. Ikeda, and M. Matsuoka, “Observation of bifurcation to chaos in an all-optical bistable system,” Phys. Rev. Lett. 50, 109–112 (1983).
    [CrossRef]
  17. R. G. Harrison, W. J. Firth, and I. A. Al-Saidi, “Observation of bifurcation to chaos in an all-optical Fabry–Pérot resonator,” Phys. Rev. Lett. 53, 258–261 (1984).
    [CrossRef]
  18. R. Vallée, “Temporal instabilities in the output of an all-fiber ring cavity,” Opt. Commun. 81, 419–426 (1991).
    [CrossRef]
  19. M. B. van der Mark, J. M. Schins, and A. Lagendijk, “Beyond the Ikeda map: a nonlinear optical ring cavity excited with picosecond pulses,” Opt. Commun. 98, 120–126 (1993).
    [CrossRef]
  20. G. Steinmeyer, D. Jaspert, and F. Mitschke, “Observation of a period-doubling sequence in a nonlinear optical fiber ring cavity near zero dispersion,” Opt. Commun. 104, 379–384 (1994).
    [CrossRef]
  21. G. P. Agrawal, Nonlinear Fiber Optics, Optics and Photonics, 2nd ed. (Academic, San Diego, Calif., 1995).
  22. S. Coen, M. Haelterman, Ph. Emplit, L. Delage, and F. Reynaud, “Stable operation of a passive fiber resonator in the bistable and period-doubling regimes,” in Nonlinear Guided Waves and Their Applications, Vol. 15 of 1996 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1996), pp. 173–175.
  23. J. J. Alleman, F. Reynaud, and P. Connes, “Fiber-linked telescope array: description and laboratory tests of a two-channel prototype,” Appl. Opt. 34, 3736–3743 (1995).
    [CrossRef]
  24. Z. Y. Cheng and C. S. Tsai, “A novel integrated acoustooptic frequency shifter,” J. Lightwave Technol. 7, 1575–1580 (1989).
    [CrossRef]
  25. M. Johnson, “In-line fiber-optical polarization transformer,” Appl. Opt. 18, 1288–1289 (1979).
    [CrossRef] [PubMed]
  26. F. Reynaud, “Optical fibre Babinet compensator,” Pure Appl. Opt. 2, 185–188 (1993).
    [CrossRef]
  27. F. Reynaud and J. Boca, “Compensation of thermally induced birefringence fluctuation of bow-tie fibres using an all-fibre babinet compensator,” Pure Appl. Opt. 2, 677–682 (1993).
    [CrossRef]
  28. H. C. Lefevre, “Single-mode fibre fractional wave devices and polarization controllers,” Electron. Lett. 16, 778–780 (1980).
    [CrossRef]
  29. C. Y. Yue, J. D. Peng, Y. B. Liao, and B. K. Zhou, “Fibre ring resonator with finesse of 1260,” Electron. Lett. 24, 622–623 (1988).
    [CrossRef]
  30. L. M. Simohamed, L. Delage, and F. Reynaud, “An optical fiber delay line with 318 mm stroke,” Pure Appl. Opt. 5, 1005–1009 (1996).
    [CrossRef]
  31. L. M. Simohamed and F. Reynaud, “A 2 m stroke optical fiber delay line,” Pure Appl. Opt. 6, L37–L41 (1997), letter to the editor.
    [CrossRef]
  32. M. Haelterman, “Ikeda instability and transverse effects in nonlinear ring resonators,” Opt. Commun. 100, 389–398 (1993).
    [CrossRef]
  33. R. M. Shelby, M. D. Levenson, and S. H. Perlmutter, “Bistability and other effects in a nonlinear fiber-optic ring resonator,” J. Opt. Soc. Am. B 5, 347–357 (1988).
    [CrossRef]
  34. T. Aida and P. Davis, “Oscillation modes of laser diode pumped hybrid bistable system with large delay and application to dynamical memory,” IEEE J. Quantum Electron. 28, 686–699 (1992).
    [CrossRef]
  35. T. Aida and P. Davis, “Oscillation mode selection using bifurcation of chaotic mode transitions in a nonlinear ring resonator,” IEEE J. Quantum Electron. 30, 2986–2997 (1994).
    [CrossRef]
  36. E. Infeld and G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge U. Press, London, 1990).
  37. H. G. Schuster, Deterministic Chaos: An Introduction, 3rd ed. (VCH Verlagsgesellschaft, Weinheim, 1995).
  38. D. Dangoisse, P. Glorieux, and D. Hennequin, “Laser chaotic attractor in crisis,” Phys. Rev. Lett. 57, 2657–2660 (1986).
    [CrossRef] [PubMed]
  39. S. Coen and M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
    [CrossRef]
  40. A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Zh. Eksp. Teor. Fiz. 58, 903 (1970) [Sov. Phys. JETP 31, 486 (1970)].
  41. G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
    [CrossRef] [PubMed]
  42. M. Haelterman, S. Trillo, and S. Wabnitz, “Additive-modulation-instability ring laser in the normal dispersion regime of a fiber,” Opt. Lett. 17, 745–747 (1992).
    [CrossRef] [PubMed]

1997 (3)

J. García-Mateos, F. Canal, and M. Haelterman, “Passive fiber ring flip-flop memory based on polarization dynamics,” Opt. Commun. 137, 427–436 (1997).
[CrossRef]

L. M. Simohamed and F. Reynaud, “A 2 m stroke optical fiber delay line,” Pure Appl. Opt. 6, L37–L41 (1997), letter to the editor.
[CrossRef]

S. Coen and M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
[CrossRef]

1996 (1)

L. M. Simohamed, L. Delage, and F. Reynaud, “An optical fiber delay line with 318 mm stroke,” Pure Appl. Opt. 5, 1005–1009 (1996).
[CrossRef]

1995 (2)

J. J. Alleman, F. Reynaud, and P. Connes, “Fiber-linked telescope array: description and laboratory tests of a two-channel prototype,” Appl. Opt. 34, 3736–3743 (1995).
[CrossRef]

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]

1994 (4)

G. Steinmeyer, D. Jaspert, and F. Mitschke, “Observation of a period-doubling sequence in a nonlinear optical fiber ring cavity near zero dispersion,” Opt. Commun. 104, 379–384 (1994).
[CrossRef]

M. Haelterman and M. D. Tolley, “Pure polarization period-doubling instability in a Kerr-type nonlinear ring cavity,” Opt. Commun. 108, 165–175 (1994).
[CrossRef]

T. Aida and P. Davis, “Oscillation mode selection using bifurcation of chaotic mode transitions in a nonlinear ring resonator,” IEEE J. Quantum Electron. 30, 2986–2997 (1994).
[CrossRef]

M. Haelterman, S. Trillo, and S. Wabnitz, “Polarization multistability and instability in a nonlinear dispersive ring cavity,” J. Opt. Soc. Am. B 11, 446–456 (1994).
[CrossRef]

1993 (6)

S. Wabnitz, “Suppression of interactions in a phase-locked soliton optical memory,” Opt. Lett. 18, 601–603 (1993).
[CrossRef] [PubMed]

M. Haelterman, “Ikeda instability and transverse effects in nonlinear ring resonators,” Opt. Commun. 100, 389–398 (1993).
[CrossRef]

F. Reynaud, “Optical fibre Babinet compensator,” Pure Appl. Opt. 2, 185–188 (1993).
[CrossRef]

F. Reynaud and J. Boca, “Compensation of thermally induced birefringence fluctuation of bow-tie fibres using an all-fibre babinet compensator,” Pure Appl. Opt. 2, 677–682 (1993).
[CrossRef]

M. B. van der Mark, J. M. Schins, and A. Lagendijk, “Beyond the Ikeda map: a nonlinear optical ring cavity excited with picosecond pulses,” Opt. Commun. 98, 120–126 (1993).
[CrossRef]

M. Haelterman, S. Trillo, and S. Wabnitz, “Generation of ultrahigh repetition rate soliton trains in fibre ring,” Electron. Lett. 29, 119–121 (1993).
[CrossRef]

1992 (4)

M. Haelterman, “Simple model for the study of period-doubling instabilities in the nonlinear ring cavity,” Appl. Phys. Lett. 61, 2756–2758 (1992).
[CrossRef]

R. Vallée, “Role of the group velocity dispersion in the onset of instabilities in a nonlinear ring cavity,” Opt. Commun. 93, 389–399 (1992).
[CrossRef]

T. Aida and P. Davis, “Oscillation modes of laser diode pumped hybrid bistable system with large delay and application to dynamical memory,” IEEE J. Quantum Electron. 28, 686–699 (1992).
[CrossRef]

M. Haelterman, S. Trillo, and S. Wabnitz, “Additive-modulation-instability ring laser in the normal dispersion regime of a fiber,” Opt. Lett. 17, 745–747 (1992).
[CrossRef] [PubMed]

1991 (1)

R. Vallée, “Temporal instabilities in the output of an all-fiber ring cavity,” Opt. Commun. 81, 419–426 (1991).
[CrossRef]

1989 (2)

1988 (3)

R. M. Shelby, M. D. Levenson, and S. H. Perlmutter, “Bistability and other effects in a nonlinear fiber-optic ring resonator,” J. Opt. Soc. Am. B 5, 347–357 (1988).
[CrossRef]

C. Y. Yue, J. D. Peng, Y. B. Liao, and B. K. Zhou, “Fibre ring resonator with finesse of 1260,” Electron. Lett. 24, 622–623 (1988).
[CrossRef]

M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38, 5193–5196 (1988).
[CrossRef] [PubMed]

1987 (2)

E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, and D. G. Fursa, “Tunable subpicosecond synchronously pumped fiber Raman laser,” Pis’ma Zh. Eksp. Teor. Fiz. 45, 469–471 (1987) [JETP Lett. 45, 599–601 (1987)].

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
[CrossRef] [PubMed]

1986 (1)

D. Dangoisse, P. Glorieux, and D. Hennequin, “Laser chaotic attractor in crisis,” Phys. Rev. Lett. 57, 2657–2660 (1986).
[CrossRef] [PubMed]

1985 (1)

D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “New class of instabilities in passive optical cavities,” Phys. Rev. Lett. 54, 681–684 (1985).
[CrossRef] [PubMed]

1984 (1)

R. G. Harrison, W. J. Firth, and I. A. Al-Saidi, “Observation of bifurcation to chaos in an all-optical Fabry–Pérot resonator,” Phys. Rev. Lett. 53, 258–261 (1984).
[CrossRef]

1983 (1)

H. Nakatsuka, S. Asaka, H. Itoh, K. Ikeda, and M. Matsuoka, “Observation of bifurcation to chaos in an all-optical bistable system,” Phys. Rev. Lett. 50, 109–112 (1983).
[CrossRef]

1980 (1)

H. C. Lefevre, “Single-mode fibre fractional wave devices and polarization controllers,” Electron. Lett. 16, 778–780 (1980).
[CrossRef]

1979 (2)

M. Johnson, “In-line fiber-optical polarization transformer,” Appl. Opt. 18, 1288–1289 (1979).
[CrossRef] [PubMed]

K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).
[CrossRef]

1970 (1)

A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Zh. Eksp. Teor. Fiz. 58, 903 (1970) [Sov. Phys. JETP 31, 486 (1970)].

Agrawal, G. P.

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
[CrossRef] [PubMed]

Aida, T.

T. Aida and P. Davis, “Oscillation mode selection using bifurcation of chaotic mode transitions in a nonlinear ring resonator,” IEEE J. Quantum Electron. 30, 2986–2997 (1994).
[CrossRef]

T. Aida and P. Davis, “Oscillation modes of laser diode pumped hybrid bistable system with large delay and application to dynamical memory,” IEEE J. Quantum Electron. 28, 686–699 (1992).
[CrossRef]

Alleman, J. J.

J. J. Alleman, F. Reynaud, and P. Connes, “Fiber-linked telescope array: description and laboratory tests of a two-channel prototype,” Appl. Opt. 34, 3736–3743 (1995).
[CrossRef]

Al-Saidi, I. A.

R. G. Harrison, W. J. Firth, and I. A. Al-Saidi, “Observation of bifurcation to chaos in an all-optical Fabry–Pérot resonator,” Phys. Rev. Lett. 53, 258–261 (1984).
[CrossRef]

Asaka, S.

H. Nakatsuka, S. Asaka, H. Itoh, K. Ikeda, and M. Matsuoka, “Observation of bifurcation to chaos in an all-optical bistable system,” Phys. Rev. Lett. 50, 109–112 (1983).
[CrossRef]

Berkhoer, A. L.

A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Zh. Eksp. Teor. Fiz. 58, 903 (1970) [Sov. Phys. JETP 31, 486 (1970)].

Boca, J.

F. Reynaud and J. Boca, “Compensation of thermally induced birefringence fluctuation of bow-tie fibres using an all-fibre babinet compensator,” Pure Appl. Opt. 2, 677–682 (1993).
[CrossRef]

Bolton, S. R.

Canal, F.

J. García-Mateos, F. Canal, and M. Haelterman, “Passive fiber ring flip-flop memory based on polarization dynamics,” Opt. Commun. 137, 427–436 (1997).
[CrossRef]

Chemla, D. S.

Cheng, Z. Y.

Z. Y. Cheng and C. S. Tsai, “A novel integrated acoustooptic frequency shifter,” J. Lightwave Technol. 7, 1575–1580 (1989).
[CrossRef]

Coen, S.

S. Coen and M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
[CrossRef]

Connes, P.

J. J. Alleman, F. Reynaud, and P. Connes, “Fiber-linked telescope array: description and laboratory tests of a two-channel prototype,” Appl. Opt. 34, 3736–3743 (1995).
[CrossRef]

Dangoisse, D.

D. Dangoisse, P. Glorieux, and D. Hennequin, “Laser chaotic attractor in crisis,” Phys. Rev. Lett. 57, 2657–2660 (1986).
[CrossRef] [PubMed]

Davis, P.

T. Aida and P. Davis, “Oscillation mode selection using bifurcation of chaotic mode transitions in a nonlinear ring resonator,” IEEE J. Quantum Electron. 30, 2986–2997 (1994).
[CrossRef]

T. Aida and P. Davis, “Oscillation modes of laser diode pumped hybrid bistable system with large delay and application to dynamical memory,” IEEE J. Quantum Electron. 28, 686–699 (1992).
[CrossRef]

Delage, L.

L. M. Simohamed, L. Delage, and F. Reynaud, “An optical fiber delay line with 318 mm stroke,” Pure Appl. Opt. 5, 1005–1009 (1996).
[CrossRef]

Dianov, E. M.

E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, and D. G. Fursa, “Tunable subpicosecond synchronously pumped fiber Raman laser,” Pis’ma Zh. Eksp. Teor. Fiz. 45, 469–471 (1987) [JETP Lett. 45, 599–601 (1987)].

Firth, W. J.

R. G. Harrison, W. J. Firth, and I. A. Al-Saidi, “Observation of bifurcation to chaos in an all-optical Fabry–Pérot resonator,” Phys. Rev. Lett. 53, 258–261 (1984).
[CrossRef]

Fursa, D. G.

E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, and D. G. Fursa, “Tunable subpicosecond synchronously pumped fiber Raman laser,” Pis’ma Zh. Eksp. Teor. Fiz. 45, 469–471 (1987) [JETP Lett. 45, 599–601 (1987)].

García-Mateos, J.

J. García-Mateos, F. Canal, and M. Haelterman, “Passive fiber ring flip-flop memory based on polarization dynamics,” Opt. Commun. 137, 427–436 (1997).
[CrossRef]

Glorieux, P.

D. Dangoisse, P. Glorieux, and D. Hennequin, “Laser chaotic attractor in crisis,” Phys. Rev. Lett. 57, 2657–2660 (1986).
[CrossRef] [PubMed]

Haelterman, M.

S. Coen and M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
[CrossRef]

J. García-Mateos, F. Canal, and M. Haelterman, “Passive fiber ring flip-flop memory based on polarization dynamics,” Opt. Commun. 137, 427–436 (1997).
[CrossRef]

M. Haelterman, S. Trillo, and S. Wabnitz, “Polarization multistability and instability in a nonlinear dispersive ring cavity,” J. Opt. Soc. Am. B 11, 446–456 (1994).
[CrossRef]

M. Haelterman and M. D. Tolley, “Pure polarization period-doubling instability in a Kerr-type nonlinear ring cavity,” Opt. Commun. 108, 165–175 (1994).
[CrossRef]

M. Haelterman, S. Trillo, and S. Wabnitz, “Generation of ultrahigh repetition rate soliton trains in fibre ring,” Electron. Lett. 29, 119–121 (1993).
[CrossRef]

M. Haelterman, “Ikeda instability and transverse effects in nonlinear ring resonators,” Opt. Commun. 100, 389–398 (1993).
[CrossRef]

M. Haelterman, “Simple model for the study of period-doubling instabilities in the nonlinear ring cavity,” Appl. Phys. Lett. 61, 2756–2758 (1992).
[CrossRef]

M. Haelterman, S. Trillo, and S. Wabnitz, “Additive-modulation-instability ring laser in the normal dispersion regime of a fiber,” Opt. Lett. 17, 745–747 (1992).
[CrossRef] [PubMed]

Hall, K. L.

Harrison, R. G.

R. G. Harrison, W. J. Firth, and I. A. Al-Saidi, “Observation of bifurcation to chaos in an all-optical Fabry–Pérot resonator,” Phys. Rev. Lett. 53, 258–261 (1984).
[CrossRef]

Haus, H. A.

J. Mark, L. Y. Liu, K. L. Hall, H. A. Haus, and E. P. Ippen, “Femtosecond pulse generation in a laser with a nonlinear external resonator,” Opt. Lett. 14, 48–50 (1989).
[CrossRef] [PubMed]

M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38, 5193–5196 (1988).
[CrossRef] [PubMed]

Hennequin, D.

D. Dangoisse, P. Glorieux, and D. Hennequin, “Laser chaotic attractor in crisis,” Phys. Rev. Lett. 57, 2657–2660 (1986).
[CrossRef] [PubMed]

Ikeda, K.

H. Nakatsuka, S. Asaka, H. Itoh, K. Ikeda, and M. Matsuoka, “Observation of bifurcation to chaos in an all-optical bistable system,” Phys. Rev. Lett. 50, 109–112 (1983).
[CrossRef]

K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).
[CrossRef]

Ippen, E. P.

Itoh, H.

H. Nakatsuka, S. Asaka, H. Itoh, K. Ikeda, and M. Matsuoka, “Observation of bifurcation to chaos in an all-optical bistable system,” Phys. Rev. Lett. 50, 109–112 (1983).
[CrossRef]

Jaspert, D.

G. Steinmeyer, D. Jaspert, and F. Mitschke, “Observation of a period-doubling sequence in a nonlinear optical fiber ring cavity near zero dispersion,” Opt. Commun. 104, 379–384 (1994).
[CrossRef]

Johnson, M.

Lagendijk, A.

M. B. van der Mark, J. M. Schins, and A. Lagendijk, “Beyond the Ikeda map: a nonlinear optical ring cavity excited with picosecond pulses,” Opt. Commun. 98, 120–126 (1993).
[CrossRef]

Lefevre, H. C.

H. C. Lefevre, “Single-mode fibre fractional wave devices and polarization controllers,” Electron. Lett. 16, 778–780 (1980).
[CrossRef]

Levenson, M. D.

Liao, Y. B.

C. Y. Yue, J. D. Peng, Y. B. Liao, and B. K. Zhou, “Fibre ring resonator with finesse of 1260,” Electron. Lett. 24, 622–623 (1988).
[CrossRef]

Liu, L. Y.

Mamyshev, P. V.

E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, and D. G. Fursa, “Tunable subpicosecond synchronously pumped fiber Raman laser,” Pis’ma Zh. Eksp. Teor. Fiz. 45, 469–471 (1987) [JETP Lett. 45, 599–601 (1987)].

Mark, J.

Matsuoka, M.

H. Nakatsuka, S. Asaka, H. Itoh, K. Ikeda, and M. Matsuoka, “Observation of bifurcation to chaos in an all-optical bistable system,” Phys. Rev. Lett. 50, 109–112 (1983).
[CrossRef]

McLaughlin, D. W.

D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “New class of instabilities in passive optical cavities,” Phys. Rev. Lett. 54, 681–684 (1985).
[CrossRef] [PubMed]

Mitschke, F.

G. Steinmeyer, D. Jaspert, and F. Mitschke, “Observation of a period-doubling sequence in a nonlinear optical fiber ring cavity near zero dispersion,” Opt. Commun. 104, 379–384 (1994).
[CrossRef]

Moloney, J. V.

D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “New class of instabilities in passive optical cavities,” Phys. Rev. Lett. 54, 681–684 (1985).
[CrossRef] [PubMed]

Nakatsuka, H.

H. Nakatsuka, S. Asaka, H. Itoh, K. Ikeda, and M. Matsuoka, “Observation of bifurcation to chaos in an all-optical bistable system,” Phys. Rev. Lett. 50, 109–112 (1983).
[CrossRef]

Nakazawa, M.

M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38, 5193–5196 (1988).
[CrossRef] [PubMed]

Newell, A. C.

D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “New class of instabilities in passive optical cavities,” Phys. Rev. Lett. 54, 681–684 (1985).
[CrossRef] [PubMed]

Peng, J. D.

C. Y. Yue, J. D. Peng, Y. B. Liao, and B. K. Zhou, “Fibre ring resonator with finesse of 1260,” Electron. Lett. 24, 622–623 (1988).
[CrossRef]

Perlmutter, S. H.

Prokhorov, A. M.

E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, and D. G. Fursa, “Tunable subpicosecond synchronously pumped fiber Raman laser,” Pis’ma Zh. Eksp. Teor. Fiz. 45, 469–471 (1987) [JETP Lett. 45, 599–601 (1987)].

Reynaud, F.

L. M. Simohamed and F. Reynaud, “A 2 m stroke optical fiber delay line,” Pure Appl. Opt. 6, L37–L41 (1997), letter to the editor.
[CrossRef]

L. M. Simohamed, L. Delage, and F. Reynaud, “An optical fiber delay line with 318 mm stroke,” Pure Appl. Opt. 5, 1005–1009 (1996).
[CrossRef]

J. J. Alleman, F. Reynaud, and P. Connes, “Fiber-linked telescope array: description and laboratory tests of a two-channel prototype,” Appl. Opt. 34, 3736–3743 (1995).
[CrossRef]

F. Reynaud, “Optical fibre Babinet compensator,” Pure Appl. Opt. 2, 185–188 (1993).
[CrossRef]

F. Reynaud and J. Boca, “Compensation of thermally induced birefringence fluctuation of bow-tie fibres using an all-fibre babinet compensator,” Pure Appl. Opt. 2, 677–682 (1993).
[CrossRef]

Schins, J. M.

M. B. van der Mark, J. M. Schins, and A. Lagendijk, “Beyond the Ikeda map: a nonlinear optical ring cavity excited with picosecond pulses,” Opt. Commun. 98, 120–126 (1993).
[CrossRef]

Shelby, R. M.

Simohamed, L. M.

L. M. Simohamed and F. Reynaud, “A 2 m stroke optical fiber delay line,” Pure Appl. Opt. 6, L37–L41 (1997), letter to the editor.
[CrossRef]

L. M. Simohamed, L. Delage, and F. Reynaud, “An optical fiber delay line with 318 mm stroke,” Pure Appl. Opt. 5, 1005–1009 (1996).
[CrossRef]

Steinmeyer, G.

G. Steinmeyer, D. Jaspert, and F. Mitschke, “Observation of a period-doubling sequence in a nonlinear optical fiber ring cavity near zero dispersion,” Opt. Commun. 104, 379–384 (1994).
[CrossRef]

Sucha, G.

Suzuki, K.

M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38, 5193–5196 (1988).
[CrossRef] [PubMed]

Tolley, M. D.

M. Haelterman and M. D. Tolley, “Pure polarization period-doubling instability in a Kerr-type nonlinear ring cavity,” Opt. Commun. 108, 165–175 (1994).
[CrossRef]

Trillo, S.

Tsai, C. S.

Z. Y. Cheng and C. S. Tsai, “A novel integrated acoustooptic frequency shifter,” J. Lightwave Technol. 7, 1575–1580 (1989).
[CrossRef]

Vallée, R.

R. Vallée, “Role of the group velocity dispersion in the onset of instabilities in a nonlinear ring cavity,” Opt. Commun. 93, 389–399 (1992).
[CrossRef]

R. Vallée, “Temporal instabilities in the output of an all-fiber ring cavity,” Opt. Commun. 81, 419–426 (1991).
[CrossRef]

van der Mark, M. B.

M. B. van der Mark, J. M. Schins, and A. Lagendijk, “Beyond the Ikeda map: a nonlinear optical ring cavity excited with picosecond pulses,” Opt. Commun. 98, 120–126 (1993).
[CrossRef]

Wabnitz, S.

Weiss, S.

Yue, C. Y.

C. Y. Yue, J. D. Peng, Y. B. Liao, and B. K. Zhou, “Fibre ring resonator with finesse of 1260,” Electron. Lett. 24, 622–623 (1988).
[CrossRef]

Zakharov, V. E.

A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Zh. Eksp. Teor. Fiz. 58, 903 (1970) [Sov. Phys. JETP 31, 486 (1970)].

Zhou, B. K.

C. Y. Yue, J. D. Peng, Y. B. Liao, and B. K. Zhou, “Fibre ring resonator with finesse of 1260,” Electron. Lett. 24, 622–623 (1988).
[CrossRef]

Appl. Opt. (2)

J. J. Alleman, F. Reynaud, and P. Connes, “Fiber-linked telescope array: description and laboratory tests of a two-channel prototype,” Appl. Opt. 34, 3736–3743 (1995).
[CrossRef]

M. Johnson, “In-line fiber-optical polarization transformer,” Appl. Opt. 18, 1288–1289 (1979).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

M. Haelterman, “Simple model for the study of period-doubling instabilities in the nonlinear ring cavity,” Appl. Phys. Lett. 61, 2756–2758 (1992).
[CrossRef]

Electron. Lett. (3)

M. Haelterman, S. Trillo, and S. Wabnitz, “Generation of ultrahigh repetition rate soliton trains in fibre ring,” Electron. Lett. 29, 119–121 (1993).
[CrossRef]

H. C. Lefevre, “Single-mode fibre fractional wave devices and polarization controllers,” Electron. Lett. 16, 778–780 (1980).
[CrossRef]

C. Y. Yue, J. D. Peng, Y. B. Liao, and B. K. Zhou, “Fibre ring resonator with finesse of 1260,” Electron. Lett. 24, 622–623 (1988).
[CrossRef]

IEEE J. Quantum Electron. (2)

T. Aida and P. Davis, “Oscillation modes of laser diode pumped hybrid bistable system with large delay and application to dynamical memory,” IEEE J. Quantum Electron. 28, 686–699 (1992).
[CrossRef]

T. Aida and P. Davis, “Oscillation mode selection using bifurcation of chaotic mode transitions in a nonlinear ring resonator,” IEEE J. Quantum Electron. 30, 2986–2997 (1994).
[CrossRef]

J. Lightwave Technol. (1)

Z. Y. Cheng and C. S. Tsai, “A novel integrated acoustooptic frequency shifter,” J. Lightwave Technol. 7, 1575–1580 (1989).
[CrossRef]

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

JETP Lett. (1)

E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, and D. G. Fursa, “Tunable subpicosecond synchronously pumped fiber Raman laser,” Pis’ma Zh. Eksp. Teor. Fiz. 45, 469–471 (1987) [JETP Lett. 45, 599–601 (1987)].

Opt. Commun. (8)

J. García-Mateos, F. Canal, and M. Haelterman, “Passive fiber ring flip-flop memory based on polarization dynamics,” Opt. Commun. 137, 427–436 (1997).
[CrossRef]

M. Haelterman and M. D. Tolley, “Pure polarization period-doubling instability in a Kerr-type nonlinear ring cavity,” Opt. Commun. 108, 165–175 (1994).
[CrossRef]

R. Vallée, “Role of the group velocity dispersion in the onset of instabilities in a nonlinear ring cavity,” Opt. Commun. 93, 389–399 (1992).
[CrossRef]

R. Vallée, “Temporal instabilities in the output of an all-fiber ring cavity,” Opt. Commun. 81, 419–426 (1991).
[CrossRef]

M. B. van der Mark, J. M. Schins, and A. Lagendijk, “Beyond the Ikeda map: a nonlinear optical ring cavity excited with picosecond pulses,” Opt. Commun. 98, 120–126 (1993).
[CrossRef]

G. Steinmeyer, D. Jaspert, and F. Mitschke, “Observation of a period-doubling sequence in a nonlinear optical fiber ring cavity near zero dispersion,” Opt. Commun. 104, 379–384 (1994).
[CrossRef]

K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).
[CrossRef]

M. Haelterman, “Ikeda instability and transverse effects in nonlinear ring resonators,” Opt. Commun. 100, 389–398 (1993).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (1)

M. Nakazawa, K. Suzuki, and H. A. Haus, “Modulational instability oscillation in nonlinear dispersive ring cavity,” Phys. Rev. A 38, 5193–5196 (1988).
[CrossRef] [PubMed]

Phys. Rev. Lett. (6)

D. W. McLaughlin, J. V. Moloney, and A. C. Newell, “New class of instabilities in passive optical cavities,” Phys. Rev. Lett. 54, 681–684 (1985).
[CrossRef] [PubMed]

H. Nakatsuka, S. Asaka, H. Itoh, K. Ikeda, and M. Matsuoka, “Observation of bifurcation to chaos in an all-optical bistable system,” Phys. Rev. Lett. 50, 109–112 (1983).
[CrossRef]

R. G. Harrison, W. J. Firth, and I. A. Al-Saidi, “Observation of bifurcation to chaos in an all-optical Fabry–Pérot resonator,” Phys. Rev. Lett. 53, 258–261 (1984).
[CrossRef]

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
[CrossRef] [PubMed]

D. Dangoisse, P. Glorieux, and D. Hennequin, “Laser chaotic attractor in crisis,” Phys. Rev. Lett. 57, 2657–2660 (1986).
[CrossRef] [PubMed]

S. Coen and M. Haelterman, “Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber,” Phys. Rev. Lett. 79, 4139–4142 (1997).
[CrossRef]

Pure Appl. Opt. (4)

F. Reynaud, “Optical fibre Babinet compensator,” Pure Appl. Opt. 2, 185–188 (1993).
[CrossRef]

F. Reynaud and J. Boca, “Compensation of thermally induced birefringence fluctuation of bow-tie fibres using an all-fibre babinet compensator,” Pure Appl. Opt. 2, 677–682 (1993).
[CrossRef]

L. M. Simohamed, L. Delage, and F. Reynaud, “An optical fiber delay line with 318 mm stroke,” Pure Appl. Opt. 5, 1005–1009 (1996).
[CrossRef]

L. M. Simohamed and F. Reynaud, “A 2 m stroke optical fiber delay line,” Pure Appl. Opt. 6, L37–L41 (1997), letter to the editor.
[CrossRef]

Sov. Phys. JETP (1)

A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Zh. Eksp. Teor. Fiz. 58, 903 (1970) [Sov. Phys. JETP 31, 486 (1970)].

Other (6)

E. Infeld and G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge U. Press, London, 1990).

H. G. Schuster, Deterministic Chaos: An Introduction, 3rd ed. (VCH Verlagsgesellschaft, Weinheim, 1995).

G. P. Agrawal, Nonlinear Fiber Optics, Optics and Photonics, 2nd ed. (Academic, San Diego, Calif., 1995).

S. Coen, M. Haelterman, Ph. Emplit, L. Delage, and F. Reynaud, “Stable operation of a passive fiber resonator in the bistable and period-doubling regimes,” in Nonlinear Guided Waves and Their Applications, Vol. 15 of 1996 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1996), pp. 173–175.

M. Haelterman, G. Vitrant, and J. García-Mateos, “Symmetry-breaking bifurcation in synchronously driven fiber cavities,” in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1995), pp. 201–203.

H. M. Gibbs, Optical Bistability: Controlling Light with Light, Quantum Electronics: Principle and Applications (Academic, New York, 1985).

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Figures (12)

Fig. 1
Fig. 1

Schematic of the fiber ring cavity.

Fig. 2
Fig. 2

Two resonance sets corresponding to the pump and control beams. For clarity the origins of the intensity axes of both beams are different. Note that the pump beam is here in the linear regime.

Fig. 3
Fig. 3

Experimental setup: Ar, cw argon-ion laser; Ti, cw mode-locked Ti:sapphire laser; OI, optical isolator; BS, 5% beam splitter; AC, autocorrelator; PC, polarization controller; STR, mechanical fiber stretcher; PZT, piezoelectric fiber stretcher; PD, photodetector; S, servo system; G, signal generator.

Fig. 4
Fig. 4

Hysteresis cycles measured with different cavity detunings δ at λ=880 nm.

Fig. 5
Fig. 5

Pulse spectra in the lower and upper branches of the bistable cycle with δ=0.6π and λ=880 nm.

Fig. 6
Fig. 6

Observation of (a), (b) period-2 patterns with δ=0.35π and (c), (d) period-4 patterns with δ=0.65π. Both observations are made at 880 nm with an average input power of 200 mW and 250 mW, respectively.

Fig. 7
Fig. 7

Observation of (a), (b) period-3 and (c), (d) period-6. λ=880 nm, and the average input power is in the range of 250–300 mW.

Fig. 8
Fig. 8

Observation of the output power as a function of δ in the presence of period-3. The figure shows that the period-3 attractor appears embedded in the chaotic region.

Fig. 9
Fig. 9

RF spectrum of period-2 patterns. The spectrum (a) corresponds to Fig. 6(a), while (b) corresponds to Fig. 6(b). f=82 MHz indicates the repetition rate of the pump laser.

Fig. 10
Fig. 10

RF spectra of (a) period-3 and (b) period-4 patterns. The first case corresponds to Fig. 7(a), while the second one corresponds to Fig. 6(d). f=82 MHz indicates the repetition rate of the pump laser.

Fig. 11
Fig. 11

MI gain spectrum: thin (bold) lines indicate cw-MI (P2-MI) sidelobes.

Fig. 12
Fig. 12

Experimental pulse spectrum obtained for δ=0.8π with input powers of (a) 700 W (inset is a vertical zoom) and (b) 450 W. Arrows indicate P2-MI sidelobes. (c) Numerical simulations of (a). These measures were performed with λ=980 nm.

Equations (7)

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Em+1(0, t)=ρEm(L, t)exp(iϕ0)+θEi,
Em(z, t)z=-i β22 2Em(z, t)t2+iγ|Em(z, t)|2Em(z, t),
Po/Pi=(1+F sin2 ϕ/2)-1,
2π2β2Lf2-δ=0.
q±=ρ(p±p2-1),
q±=±1-θ2+4δ-η Ω22|U0|2-δ-η Ω222-3|U0|41/2,
2|U0|2+ηΩl2/2+ϕ0=lπ

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