Abstract

A new chaos generator is described that produces chaotic fluctuations of the optical-path difference in a coherence modulator driven electrically by a nonlinear delayed-feedback loop. Numerical simulations and experimental results are reported. A closed branch of periodic solutions bounded by a forward and a reverse Hopf bifurcation is observed for the first time, to our knowledge, for this type of nonlinear dynamical system.

© 2001 Optical Society of America

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References

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  1. 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]
  2. P. Glorieux and A. Le Floch, “Nonlinear polarization dynamics in anisotropic lasers,” Opt. Commun. 79, 229–234 (1990).
    [CrossRef]
  3. H. Porte and J.-P. Goedgebuer, “Bistability in wavelength using an electro-optically tuned dye laser,” Opt. Commun. 51, 331–336 (1984).
    [CrossRef]
  4. J.-P. Goedgebuer, L. Larger, H. Porte, and F. Delorme, “Chaos in wavelength with a feedback tunable laser diode,” Phys. Rev. E 57, 2795–2798 (1998).
    [CrossRef]
  5. L. Larger, J.-P. Goedgebuer, and J.-M. Mérolla, “Chaotic oscillator in wavelength: a new setup for investigating differential difference equations describing nonlinear dynamics,” IEEE J. Quantum Electron. 34, 594–601 (1998).
    [CrossRef]
  6. K. Ikeda and M. Mizuno, “Modeling of nonlinear Fabry–Perot resonators by difference–differential equations,” IEEE J. Quantum Electron. 21, 1429–1434 (1985).
    [CrossRef]
  7. J. Y. Gao, J. M. Yuan, and L. M. Narducci, “Instabilities and chaotic behavior in a hybrid bistable system with a short delay,” Opt. Commun. 44, 201–206 (1983).
    [CrossRef]
  8. J. Mørk, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992).
    [CrossRef]
  9. T. Takizawa, Y. Liu, and J. Ohtsubo, “Chaos in a feedback Fabry–Pérot interferometer,” IEEE J. Quantum Electron. 30, 334–338 (1994).
    [CrossRef]
  10. T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51, 4181–4185 (1995).
    [CrossRef] [PubMed]
  11. T. C. Newell, V. Kovanis, and A. Gavrielides, “Experimental demonstration of antimonotonicity: the concurrent creation and destruction of periodic orbits in a driven nonlinear electronic resonator,” Phys. Rev. Lett. 77, 1747–1750 (1996).
    [CrossRef] [PubMed]
  12. H. Porte, J.-P. Goedgebuer, W. Elflein, A. Terras, F. Le Deventec, and N. Butterlin, “Linear phase tracking in a coherence modulation electrical sensor system using integrated LiNbO3 modulator/demodulator,” IEEE J. Sel. Top. Quantum Electron. 2, 319–325 (1996).
    [CrossRef]
  13. J.-P. Goedgebuer, R. Ferrière, and A. Hamel, “Polarization-independent transmission on a single mode fiber using coherence modulation of light,” IEEE J. Quantum Electron. 27, 1963–1967 (1991).
    [CrossRef]
  14. Y. Mazurenko, R. Giust, and J.-P. Goedgebuer, “Spectral coding for secure optical communications using refractive index dispersion,” Opt. Commun. 133, 87–92 (1997).
    [CrossRef]
  15. W. Wells, R. Stone, and E. Miles, “Secure communications by optical homodyne,” IEEE J. Sel. Areas Commun. 11, 770–777 (1993).
    [CrossRef]
  16. B. Wacogne, W. Elflein, C. Pieralli, P. Mollier, H. Porte, and D. A. Jackson, “ Secrecy improvement in confidential coherence modulation by means of new keying structure,” Opt. Commun. 154, 350–358 (1998).
    [CrossRef]
  17. J.-P. Goedgebuer, H. Porte, and A. Hamel, “Electrooptic modulation of multilongitudinal mode laser diodes: demonstration at 850 nm with simultaneous data transmission by coherence multiplexing,” IEEE J. Quantum Electron. 23, 1135–1144 (1987).
    [CrossRef]
  18. F. A. Hopf, D. L. Kaplan, H. M. Gibbs, and R. L. Schoemaker, “Bifurcation to chaos in optical bistability,” Phys. Rev. A 25, 2172–2182 (1982); R. Vallée and C. Delisle, “Mode description of the dynamical evolution of an acousto-optic bistable device,” IEEE J. Quantum Electron. 21, 1423–1428 (1985).
    [CrossRef]

1998 (3)

J.-P. Goedgebuer, L. Larger, H. Porte, and F. Delorme, “Chaos in wavelength with a feedback tunable laser diode,” Phys. Rev. E 57, 2795–2798 (1998).
[CrossRef]

L. Larger, J.-P. Goedgebuer, and J.-M. Mérolla, “Chaotic oscillator in wavelength: a new setup for investigating differential difference equations describing nonlinear dynamics,” IEEE J. Quantum Electron. 34, 594–601 (1998).
[CrossRef]

B. Wacogne, W. Elflein, C. Pieralli, P. Mollier, H. Porte, and D. A. Jackson, “ Secrecy improvement in confidential coherence modulation by means of new keying structure,” Opt. Commun. 154, 350–358 (1998).
[CrossRef]

1997 (1)

Y. Mazurenko, R. Giust, and J.-P. Goedgebuer, “Spectral coding for secure optical communications using refractive index dispersion,” Opt. Commun. 133, 87–92 (1997).
[CrossRef]

1996 (2)

T. C. Newell, V. Kovanis, and A. Gavrielides, “Experimental demonstration of antimonotonicity: the concurrent creation and destruction of periodic orbits in a driven nonlinear electronic resonator,” Phys. Rev. Lett. 77, 1747–1750 (1996).
[CrossRef] [PubMed]

H. Porte, J.-P. Goedgebuer, W. Elflein, A. Terras, F. Le Deventec, and N. Butterlin, “Linear phase tracking in a coherence modulation electrical sensor system using integrated LiNbO3 modulator/demodulator,” IEEE J. Sel. Top. Quantum Electron. 2, 319–325 (1996).
[CrossRef]

1995 (1)

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51, 4181–4185 (1995).
[CrossRef] [PubMed]

1994 (1)

T. Takizawa, Y. Liu, and J. Ohtsubo, “Chaos in a feedback Fabry–Pérot interferometer,” IEEE J. Quantum Electron. 30, 334–338 (1994).
[CrossRef]

1993 (1)

W. Wells, R. Stone, and E. Miles, “Secure communications by optical homodyne,” IEEE J. Sel. Areas Commun. 11, 770–777 (1993).
[CrossRef]

1992 (1)

J. Mørk, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992).
[CrossRef]

1991 (1)

J.-P. Goedgebuer, R. Ferrière, and A. Hamel, “Polarization-independent transmission on a single mode fiber using coherence modulation of light,” IEEE J. Quantum Electron. 27, 1963–1967 (1991).
[CrossRef]

1990 (1)

P. Glorieux and A. Le Floch, “Nonlinear polarization dynamics in anisotropic lasers,” Opt. Commun. 79, 229–234 (1990).
[CrossRef]

1987 (1)

J.-P. Goedgebuer, H. Porte, and A. Hamel, “Electrooptic modulation of multilongitudinal mode laser diodes: demonstration at 850 nm with simultaneous data transmission by coherence multiplexing,” IEEE J. Quantum Electron. 23, 1135–1144 (1987).
[CrossRef]

1985 (1)

K. Ikeda and M. Mizuno, “Modeling of nonlinear Fabry–Perot resonators by difference–differential equations,” IEEE J. Quantum Electron. 21, 1429–1434 (1985).
[CrossRef]

1984 (1)

H. Porte and J.-P. Goedgebuer, “Bistability in wavelength using an electro-optically tuned dye laser,” Opt. Commun. 51, 331–336 (1984).
[CrossRef]

1983 (1)

J. Y. Gao, J. M. Yuan, and L. M. Narducci, “Instabilities and chaotic behavior in a hybrid bistable system with a short delay,” Opt. Commun. 44, 201–206 (1983).
[CrossRef]

1979 (1)

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]

Alsing, P. M.

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51, 4181–4185 (1995).
[CrossRef] [PubMed]

Butterlin, N.

H. Porte, J.-P. Goedgebuer, W. Elflein, A. Terras, F. Le Deventec, and N. Butterlin, “Linear phase tracking in a coherence modulation electrical sensor system using integrated LiNbO3 modulator/demodulator,” IEEE J. Sel. Top. Quantum Electron. 2, 319–325 (1996).
[CrossRef]

Delorme, F.

J.-P. Goedgebuer, L. Larger, H. Porte, and F. Delorme, “Chaos in wavelength with a feedback tunable laser diode,” Phys. Rev. E 57, 2795–2798 (1998).
[CrossRef]

Elflein, W.

B. Wacogne, W. Elflein, C. Pieralli, P. Mollier, H. Porte, and D. A. Jackson, “ Secrecy improvement in confidential coherence modulation by means of new keying structure,” Opt. Commun. 154, 350–358 (1998).
[CrossRef]

H. Porte, J.-P. Goedgebuer, W. Elflein, A. Terras, F. Le Deventec, and N. Butterlin, “Linear phase tracking in a coherence modulation electrical sensor system using integrated LiNbO3 modulator/demodulator,” IEEE J. Sel. Top. Quantum Electron. 2, 319–325 (1996).
[CrossRef]

Ferrière, R.

J.-P. Goedgebuer, R. Ferrière, and A. Hamel, “Polarization-independent transmission on a single mode fiber using coherence modulation of light,” IEEE J. Quantum Electron. 27, 1963–1967 (1991).
[CrossRef]

Gao, J. Y.

J. Y. Gao, J. M. Yuan, and L. M. Narducci, “Instabilities and chaotic behavior in a hybrid bistable system with a short delay,” Opt. Commun. 44, 201–206 (1983).
[CrossRef]

Gavrielides, A.

T. C. Newell, V. Kovanis, and A. Gavrielides, “Experimental demonstration of antimonotonicity: the concurrent creation and destruction of periodic orbits in a driven nonlinear electronic resonator,” Phys. Rev. Lett. 77, 1747–1750 (1996).
[CrossRef] [PubMed]

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51, 4181–4185 (1995).
[CrossRef] [PubMed]

Giust, R.

Y. Mazurenko, R. Giust, and J.-P. Goedgebuer, “Spectral coding for secure optical communications using refractive index dispersion,” Opt. Commun. 133, 87–92 (1997).
[CrossRef]

Glorieux, P.

P. Glorieux and A. Le Floch, “Nonlinear polarization dynamics in anisotropic lasers,” Opt. Commun. 79, 229–234 (1990).
[CrossRef]

Goedgebuer, J.-P.

J.-P. Goedgebuer, L. Larger, H. Porte, and F. Delorme, “Chaos in wavelength with a feedback tunable laser diode,” Phys. Rev. E 57, 2795–2798 (1998).
[CrossRef]

L. Larger, J.-P. Goedgebuer, and J.-M. Mérolla, “Chaotic oscillator in wavelength: a new setup for investigating differential difference equations describing nonlinear dynamics,” IEEE J. Quantum Electron. 34, 594–601 (1998).
[CrossRef]

Y. Mazurenko, R. Giust, and J.-P. Goedgebuer, “Spectral coding for secure optical communications using refractive index dispersion,” Opt. Commun. 133, 87–92 (1997).
[CrossRef]

H. Porte, J.-P. Goedgebuer, W. Elflein, A. Terras, F. Le Deventec, and N. Butterlin, “Linear phase tracking in a coherence modulation electrical sensor system using integrated LiNbO3 modulator/demodulator,” IEEE J. Sel. Top. Quantum Electron. 2, 319–325 (1996).
[CrossRef]

J.-P. Goedgebuer, R. Ferrière, and A. Hamel, “Polarization-independent transmission on a single mode fiber using coherence modulation of light,” IEEE J. Quantum Electron. 27, 1963–1967 (1991).
[CrossRef]

J.-P. Goedgebuer, H. Porte, and A. Hamel, “Electrooptic modulation of multilongitudinal mode laser diodes: demonstration at 850 nm with simultaneous data transmission by coherence multiplexing,” IEEE J. Quantum Electron. 23, 1135–1144 (1987).
[CrossRef]

H. Porte and J.-P. Goedgebuer, “Bistability in wavelength using an electro-optically tuned dye laser,” Opt. Commun. 51, 331–336 (1984).
[CrossRef]

Hamel, A.

J.-P. Goedgebuer, R. Ferrière, and A. Hamel, “Polarization-independent transmission on a single mode fiber using coherence modulation of light,” IEEE J. Quantum Electron. 27, 1963–1967 (1991).
[CrossRef]

J.-P. Goedgebuer, H. Porte, and A. Hamel, “Electrooptic modulation of multilongitudinal mode laser diodes: demonstration at 850 nm with simultaneous data transmission by coherence multiplexing,” IEEE J. Quantum Electron. 23, 1135–1144 (1987).
[CrossRef]

Ikeda, K.

K. Ikeda and M. Mizuno, “Modeling of nonlinear Fabry–Perot resonators by difference–differential equations,” IEEE J. Quantum Electron. 21, 1429–1434 (1985).
[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]

Jackson, D. A.

B. Wacogne, W. Elflein, C. Pieralli, P. Mollier, H. Porte, and D. A. Jackson, “ Secrecy improvement in confidential coherence modulation by means of new keying structure,” Opt. Commun. 154, 350–358 (1998).
[CrossRef]

Kovanis, V.

T. C. Newell, V. Kovanis, and A. Gavrielides, “Experimental demonstration of antimonotonicity: the concurrent creation and destruction of periodic orbits in a driven nonlinear electronic resonator,” Phys. Rev. Lett. 77, 1747–1750 (1996).
[CrossRef] [PubMed]

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51, 4181–4185 (1995).
[CrossRef] [PubMed]

Larger, L.

J.-P. Goedgebuer, L. Larger, H. Porte, and F. Delorme, “Chaos in wavelength with a feedback tunable laser diode,” Phys. Rev. E 57, 2795–2798 (1998).
[CrossRef]

L. Larger, J.-P. Goedgebuer, and J.-M. Mérolla, “Chaotic oscillator in wavelength: a new setup for investigating differential difference equations describing nonlinear dynamics,” IEEE J. Quantum Electron. 34, 594–601 (1998).
[CrossRef]

Le Deventec, F.

H. Porte, J.-P. Goedgebuer, W. Elflein, A. Terras, F. Le Deventec, and N. Butterlin, “Linear phase tracking in a coherence modulation electrical sensor system using integrated LiNbO3 modulator/demodulator,” IEEE J. Sel. Top. Quantum Electron. 2, 319–325 (1996).
[CrossRef]

Le Floch, A.

P. Glorieux and A. Le Floch, “Nonlinear polarization dynamics in anisotropic lasers,” Opt. Commun. 79, 229–234 (1990).
[CrossRef]

Liu, J. M.

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51, 4181–4185 (1995).
[CrossRef] [PubMed]

Liu, Y.

T. Takizawa, Y. Liu, and J. Ohtsubo, “Chaos in a feedback Fabry–Pérot interferometer,” IEEE J. Quantum Electron. 30, 334–338 (1994).
[CrossRef]

Mark, J.

J. Mørk, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992).
[CrossRef]

Mazurenko, Y.

Y. Mazurenko, R. Giust, and J.-P. Goedgebuer, “Spectral coding for secure optical communications using refractive index dispersion,” Opt. Commun. 133, 87–92 (1997).
[CrossRef]

Mérolla, J.-M.

L. Larger, J.-P. Goedgebuer, and J.-M. Mérolla, “Chaotic oscillator in wavelength: a new setup for investigating differential difference equations describing nonlinear dynamics,” IEEE J. Quantum Electron. 34, 594–601 (1998).
[CrossRef]

Miles, E.

W. Wells, R. Stone, and E. Miles, “Secure communications by optical homodyne,” IEEE J. Sel. Areas Commun. 11, 770–777 (1993).
[CrossRef]

Mizuno, M.

K. Ikeda and M. Mizuno, “Modeling of nonlinear Fabry–Perot resonators by difference–differential equations,” IEEE J. Quantum Electron. 21, 1429–1434 (1985).
[CrossRef]

Mollier, P.

B. Wacogne, W. Elflein, C. Pieralli, P. Mollier, H. Porte, and D. A. Jackson, “ Secrecy improvement in confidential coherence modulation by means of new keying structure,” Opt. Commun. 154, 350–358 (1998).
[CrossRef]

Mørk, J.

J. Mørk, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992).
[CrossRef]

Narducci, L. M.

J. Y. Gao, J. M. Yuan, and L. M. Narducci, “Instabilities and chaotic behavior in a hybrid bistable system with a short delay,” Opt. Commun. 44, 201–206 (1983).
[CrossRef]

Newell, T. C.

T. C. Newell, V. Kovanis, and A. Gavrielides, “Experimental demonstration of antimonotonicity: the concurrent creation and destruction of periodic orbits in a driven nonlinear electronic resonator,” Phys. Rev. Lett. 77, 1747–1750 (1996).
[CrossRef] [PubMed]

Ohtsubo, J.

T. Takizawa, Y. Liu, and J. Ohtsubo, “Chaos in a feedback Fabry–Pérot interferometer,” IEEE J. Quantum Electron. 30, 334–338 (1994).
[CrossRef]

Pieralli, C.

B. Wacogne, W. Elflein, C. Pieralli, P. Mollier, H. Porte, and D. A. Jackson, “ Secrecy improvement in confidential coherence modulation by means of new keying structure,” Opt. Commun. 154, 350–358 (1998).
[CrossRef]

Porte, H.

B. Wacogne, W. Elflein, C. Pieralli, P. Mollier, H. Porte, and D. A. Jackson, “ Secrecy improvement in confidential coherence modulation by means of new keying structure,” Opt. Commun. 154, 350–358 (1998).
[CrossRef]

J.-P. Goedgebuer, L. Larger, H. Porte, and F. Delorme, “Chaos in wavelength with a feedback tunable laser diode,” Phys. Rev. E 57, 2795–2798 (1998).
[CrossRef]

H. Porte, J.-P. Goedgebuer, W. Elflein, A. Terras, F. Le Deventec, and N. Butterlin, “Linear phase tracking in a coherence modulation electrical sensor system using integrated LiNbO3 modulator/demodulator,” IEEE J. Sel. Top. Quantum Electron. 2, 319–325 (1996).
[CrossRef]

J.-P. Goedgebuer, H. Porte, and A. Hamel, “Electrooptic modulation of multilongitudinal mode laser diodes: demonstration at 850 nm with simultaneous data transmission by coherence multiplexing,” IEEE J. Quantum Electron. 23, 1135–1144 (1987).
[CrossRef]

H. Porte and J.-P. Goedgebuer, “Bistability in wavelength using an electro-optically tuned dye laser,” Opt. Commun. 51, 331–336 (1984).
[CrossRef]

Simpson, T. B.

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51, 4181–4185 (1995).
[CrossRef] [PubMed]

Stone, R.

W. Wells, R. Stone, and E. Miles, “Secure communications by optical homodyne,” IEEE J. Sel. Areas Commun. 11, 770–777 (1993).
[CrossRef]

Takizawa, T.

T. Takizawa, Y. Liu, and J. Ohtsubo, “Chaos in a feedback Fabry–Pérot interferometer,” IEEE J. Quantum Electron. 30, 334–338 (1994).
[CrossRef]

Terras, A.

H. Porte, J.-P. Goedgebuer, W. Elflein, A. Terras, F. Le Deventec, and N. Butterlin, “Linear phase tracking in a coherence modulation electrical sensor system using integrated LiNbO3 modulator/demodulator,” IEEE J. Sel. Top. Quantum Electron. 2, 319–325 (1996).
[CrossRef]

Tromborg, B.

J. Mørk, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992).
[CrossRef]

Wacogne, B.

B. Wacogne, W. Elflein, C. Pieralli, P. Mollier, H. Porte, and D. A. Jackson, “ Secrecy improvement in confidential coherence modulation by means of new keying structure,” Opt. Commun. 154, 350–358 (1998).
[CrossRef]

Wells, W.

W. Wells, R. Stone, and E. Miles, “Secure communications by optical homodyne,” IEEE J. Sel. Areas Commun. 11, 770–777 (1993).
[CrossRef]

Yuan, J. M.

J. Y. Gao, J. M. Yuan, and L. M. Narducci, “Instabilities and chaotic behavior in a hybrid bistable system with a short delay,” Opt. Commun. 44, 201–206 (1983).
[CrossRef]

IEEE J. Quantum Electron. (6)

J. Mørk, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28, 93–108 (1992).
[CrossRef]

T. Takizawa, Y. Liu, and J. Ohtsubo, “Chaos in a feedback Fabry–Pérot interferometer,” IEEE J. Quantum Electron. 30, 334–338 (1994).
[CrossRef]

L. Larger, J.-P. Goedgebuer, and J.-M. Mérolla, “Chaotic oscillator in wavelength: a new setup for investigating differential difference equations describing nonlinear dynamics,” IEEE J. Quantum Electron. 34, 594–601 (1998).
[CrossRef]

K. Ikeda and M. Mizuno, “Modeling of nonlinear Fabry–Perot resonators by difference–differential equations,” IEEE J. Quantum Electron. 21, 1429–1434 (1985).
[CrossRef]

J.-P. Goedgebuer, R. Ferrière, and A. Hamel, “Polarization-independent transmission on a single mode fiber using coherence modulation of light,” IEEE J. Quantum Electron. 27, 1963–1967 (1991).
[CrossRef]

J.-P. Goedgebuer, H. Porte, and A. Hamel, “Electrooptic modulation of multilongitudinal mode laser diodes: demonstration at 850 nm with simultaneous data transmission by coherence multiplexing,” IEEE J. Quantum Electron. 23, 1135–1144 (1987).
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

W. Wells, R. Stone, and E. Miles, “Secure communications by optical homodyne,” IEEE J. Sel. Areas Commun. 11, 770–777 (1993).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

H. Porte, J.-P. Goedgebuer, W. Elflein, A. Terras, F. Le Deventec, and N. Butterlin, “Linear phase tracking in a coherence modulation electrical sensor system using integrated LiNbO3 modulator/demodulator,” IEEE J. Sel. Top. Quantum Electron. 2, 319–325 (1996).
[CrossRef]

Opt. Commun. (6)

B. Wacogne, W. Elflein, C. Pieralli, P. Mollier, H. Porte, and D. A. Jackson, “ Secrecy improvement in confidential coherence modulation by means of new keying structure,” Opt. Commun. 154, 350–358 (1998).
[CrossRef]

Y. Mazurenko, R. Giust, and J.-P. Goedgebuer, “Spectral coding for secure optical communications using refractive index dispersion,” Opt. Commun. 133, 87–92 (1997).
[CrossRef]

J. Y. Gao, J. M. Yuan, and L. M. Narducci, “Instabilities and chaotic behavior in a hybrid bistable system with a short delay,” Opt. Commun. 44, 201–206 (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]

P. Glorieux and A. Le Floch, “Nonlinear polarization dynamics in anisotropic lasers,” Opt. Commun. 79, 229–234 (1990).
[CrossRef]

H. Porte and J.-P. Goedgebuer, “Bistability in wavelength using an electro-optically tuned dye laser,” Opt. Commun. 51, 331–336 (1984).
[CrossRef]

Phys. Rev. A (1)

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51, 4181–4185 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (1)

J.-P. Goedgebuer, L. Larger, H. Porte, and F. Delorme, “Chaos in wavelength with a feedback tunable laser diode,” Phys. Rev. E 57, 2795–2798 (1998).
[CrossRef]

Phys. Rev. Lett. (1)

T. C. Newell, V. Kovanis, and A. Gavrielides, “Experimental demonstration of antimonotonicity: the concurrent creation and destruction of periodic orbits in a driven nonlinear electronic resonator,” Phys. Rev. Lett. 77, 1747–1750 (1996).
[CrossRef] [PubMed]

Other (1)

F. A. Hopf, D. L. Kaplan, H. M. Gibbs, and R. L. Schoemaker, “Bifurcation to chaos in optical bistability,” Phys. Rev. A 25, 2172–2182 (1982); R. Vallée and C. Delisle, “Mode description of the dynamical evolution of an acousto-optic bistable device,” IEEE J. Quantum Electron. 21, 1423–1428 (1985).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Scheme of the chaotic oscillator.

Fig. 2
Fig. 2

Bifurcation diagrams obtained from numerical simulations: (a) Φ=0 and (b) Φ=π.

Fig. 3
Fig. 3

Experimental characterization of the system: (a) Fringe pattern related to the temporal-coherence degree of the light beam at MZ1 output, (b) zoomed window, and (c) experimental nonlinear MTF used in the device.

Fig. 4
Fig. 4

Experimental bifurcation diagrams: (a) ϕ=0 and (b) ϕ=.

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

I=αP04 1+12Γ(D1-D20)cos[2πσ0(D1-D20)],
Γ(D)=-+P(σ)cos(2πσD)dσ.
P(σ)=P0 2Δσπ exp-4Δσ2σ2,
Γ(D)=P0 exp-π2D24LC2.
I=αP04 1+12 exp-π2(D1-D20)24LC2cos[2πσ0(D1-D20)].
MTF=14 1+12 cos[2πσ0(D1-D20)].
I(V)=αP02 1+12 cosΦ+π VVπ,
V+τ dVdt=KI[V(t-T)].
δD(t)+τ d(δD)dt(t)
=βδD1+12 cos[Φ+2πσ0δD(t-T)],
x(θ)+η dxdθ(θ)=β1+12 cos[x(θ-1)+Φ]=f [x(θ-1)],
η dxdθ(θ)=-x(θ)+f [β, x(θ-1)],
0=-xs+f(β, xs).
η dudθ(θ)=-u(θ)+fx(β, xs)u(θ-1)
ησ=-1+fx(β, xs)exp(-σ).
xs-xc=fβ(βc, xc)1-fx(βc, xc)B,
σ=iω+B(a+ib)+.
a=fxfxx fβ1-fx+fxβ 1+η+(ηω)2[1+η+(ηω)2]2+ω2η4,
f(β, x)=β[1+C cos(x+Φ)],
βc4C2(1-C2)-βc2(1+2C2)-10.
a>0if0<βc<βr (forwardHopfbifurcation),
a<0ifβc>βr (reverseHopfbifurcation),
βr(1+2C2)+1+8C22C2(1-C2).

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