Abstract

Self-induced chaos in a laser diode Twyman–Green interferometer with an optoelectronic delayed feedback is studied. We have experimentally observed the chaotic behavior of the laser output power, which involves period-doubling bifurcation schemes. A linearized stability analysis is performed, which predicts the stability condition. The numerical simulations of the difference equation of the system qualitatively reproduce the results of the experiment. We also discuss the evolution’s route to chaos based on the change of the trajectories in the phase space.

© 1992 Optical Society of America

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References

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  1. F. A. Hopf, D. L. Kaplan, H. M. Gibbs, R. L. Shoemaker, “Bifurcations to chaos in optical bistability,” Phys. Rev. A 25, 2172–2182 (1982).
    [CrossRef]
  2. R. Vallée, C. Delisle, “Mode description of the dynamical evolution of an acousto-optic bistable device,” IEEE J. Quantum Electron. QE-21, 1423–1428 (1985).
    [CrossRef]
  3. H. J. Zhang, J. H. Dai, P. Y. Wang, C. D. Jin, “Bifurcation and chaos in an optically bistable liquid-crystal device,” J. Opt. Soc. Am. B 3, 231–235 (1986).
    [CrossRef]
  4. K. Ikeda, H. Daido, O. Akimoto, “Optical turbulence: chaotic behavior of transmitted light from a ring cavity,” Phys. Rev. Lett. 45, 709–712 (1980).
    [CrossRef]
  5. T. Yoshino, M. Nara, S. Mnatzakanian, B. S. Lee, T. C. Strand, “Laser diode feedback interferometer for stabilization and displacement measurements,” Appl. Opt. 26, 892–897 (1987).
    [CrossRef] [PubMed]
  6. J. Ohtsubo, Y. Liu, “Optical bistability and multistability in an active interferometer,” Opt. Lett. 15, 731–733 (1990).
    [CrossRef] [PubMed]
  7. J. Ohtsubo, Y. Liu, “Optical instability and chaos in an active interferometer,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 50–51 (1990).
    [CrossRef]
  8. Y. Liu, J. Ohtsubo, “Dynamical behavior of an optical nonlinear system using a laser diode active interferometer,” Rep. Grad. School Electron. Sci. Technol. Shizuoka Univ.12, (to be published).
  9. R. H. Abraham, C. D. Shaw, Dynamics: the Geometry of Behavior, Part 2: The Chaotic Behavior (Aerial, Santa Cruz, Calif., 1983), p. 121–126.

1990

1987

1986

1985

R. Vallée, C. Delisle, “Mode description of the dynamical evolution of an acousto-optic bistable device,” IEEE J. Quantum Electron. QE-21, 1423–1428 (1985).
[CrossRef]

1982

F. A. Hopf, D. L. Kaplan, H. M. Gibbs, R. L. Shoemaker, “Bifurcations to chaos in optical bistability,” Phys. Rev. A 25, 2172–2182 (1982).
[CrossRef]

1980

K. Ikeda, H. Daido, O. Akimoto, “Optical turbulence: chaotic behavior of transmitted light from a ring cavity,” Phys. Rev. Lett. 45, 709–712 (1980).
[CrossRef]

Abraham, R. H.

R. H. Abraham, C. D. Shaw, Dynamics: the Geometry of Behavior, Part 2: The Chaotic Behavior (Aerial, Santa Cruz, Calif., 1983), p. 121–126.

Akimoto, O.

K. Ikeda, H. Daido, O. Akimoto, “Optical turbulence: chaotic behavior of transmitted light from a ring cavity,” Phys. Rev. Lett. 45, 709–712 (1980).
[CrossRef]

Dai, J. H.

Daido, H.

K. Ikeda, H. Daido, O. Akimoto, “Optical turbulence: chaotic behavior of transmitted light from a ring cavity,” Phys. Rev. Lett. 45, 709–712 (1980).
[CrossRef]

Delisle, C.

R. Vallée, C. Delisle, “Mode description of the dynamical evolution of an acousto-optic bistable device,” IEEE J. Quantum Electron. QE-21, 1423–1428 (1985).
[CrossRef]

Gibbs, H. M.

F. A. Hopf, D. L. Kaplan, H. M. Gibbs, R. L. Shoemaker, “Bifurcations to chaos in optical bistability,” Phys. Rev. A 25, 2172–2182 (1982).
[CrossRef]

Hopf, F. A.

F. A. Hopf, D. L. Kaplan, H. M. Gibbs, R. L. Shoemaker, “Bifurcations to chaos in optical bistability,” Phys. Rev. A 25, 2172–2182 (1982).
[CrossRef]

Ikeda, K.

K. Ikeda, H. Daido, O. Akimoto, “Optical turbulence: chaotic behavior of transmitted light from a ring cavity,” Phys. Rev. Lett. 45, 709–712 (1980).
[CrossRef]

Jin, C. D.

Kaplan, D. L.

F. A. Hopf, D. L. Kaplan, H. M. Gibbs, R. L. Shoemaker, “Bifurcations to chaos in optical bistability,” Phys. Rev. A 25, 2172–2182 (1982).
[CrossRef]

Lee, B. S.

Liu, Y.

J. Ohtsubo, Y. Liu, “Optical bistability and multistability in an active interferometer,” Opt. Lett. 15, 731–733 (1990).
[CrossRef] [PubMed]

J. Ohtsubo, Y. Liu, “Optical instability and chaos in an active interferometer,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 50–51 (1990).
[CrossRef]

Y. Liu, J. Ohtsubo, “Dynamical behavior of an optical nonlinear system using a laser diode active interferometer,” Rep. Grad. School Electron. Sci. Technol. Shizuoka Univ.12, (to be published).

Mnatzakanian, S.

Nara, M.

Ohtsubo, J.

J. Ohtsubo, Y. Liu, “Optical bistability and multistability in an active interferometer,” Opt. Lett. 15, 731–733 (1990).
[CrossRef] [PubMed]

J. Ohtsubo, Y. Liu, “Optical instability and chaos in an active interferometer,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 50–51 (1990).
[CrossRef]

Y. Liu, J. Ohtsubo, “Dynamical behavior of an optical nonlinear system using a laser diode active interferometer,” Rep. Grad. School Electron. Sci. Technol. Shizuoka Univ.12, (to be published).

Shaw, C. D.

R. H. Abraham, C. D. Shaw, Dynamics: the Geometry of Behavior, Part 2: The Chaotic Behavior (Aerial, Santa Cruz, Calif., 1983), p. 121–126.

Shoemaker, R. L.

F. A. Hopf, D. L. Kaplan, H. M. Gibbs, R. L. Shoemaker, “Bifurcations to chaos in optical bistability,” Phys. Rev. A 25, 2172–2182 (1982).
[CrossRef]

Strand, T. C.

Vallée, R.

R. Vallée, C. Delisle, “Mode description of the dynamical evolution of an acousto-optic bistable device,” IEEE J. Quantum Electron. QE-21, 1423–1428 (1985).
[CrossRef]

Wang, P. Y.

Yoshino, T.

Zhang, H. J.

Appl. Opt.

IEEE J. Quantum Electron.

R. Vallée, C. Delisle, “Mode description of the dynamical evolution of an acousto-optic bistable device,” IEEE J. Quantum Electron. QE-21, 1423–1428 (1985).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. A

F. A. Hopf, D. L. Kaplan, H. M. Gibbs, R. L. Shoemaker, “Bifurcations to chaos in optical bistability,” Phys. Rev. A 25, 2172–2182 (1982).
[CrossRef]

Phys. Rev. Lett.

K. Ikeda, H. Daido, O. Akimoto, “Optical turbulence: chaotic behavior of transmitted light from a ring cavity,” Phys. Rev. Lett. 45, 709–712 (1980).
[CrossRef]

Other

J. Ohtsubo, Y. Liu, “Optical instability and chaos in an active interferometer,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 50–51 (1990).
[CrossRef]

Y. Liu, J. Ohtsubo, “Dynamical behavior of an optical nonlinear system using a laser diode active interferometer,” Rep. Grad. School Electron. Sci. Technol. Shizuoka Univ.12, (to be published).

R. H. Abraham, C. D. Shaw, Dynamics: the Geometry of Behavior, Part 2: The Chaotic Behavior (Aerial, Santa Cruz, Calif., 1983), p. 121–126.

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup. LD, laser diode; PD, photodiode; H.M.’s, half mirrors.

Fig. 2
Fig. 2

Examples of the output powers obtained by the experiment. The parameter values are μ = 0.05, b = 0.8, and κ = 32π. Time evolutions of output power under the bias power (a) Pb = 0.423 mW (b) Pb = 0.430 mW, (c) Pb = 0.473 mW, and (d) Pb = 0.573 mW.

Fig. 3
Fig. 3

Power spectra of the time evolutions on a logarithmic scale, corresponding to the output power signals in Fig. 2.

Fig. 4
Fig. 4

Output power Pout versus bias power Pb, bifurcation diagram theoretically obtained for parameter values of μ = 0.05, κ = 32π, ϕ0 = 0.

Fig. 5
Fig. 5

Trajectories reconstructed from the time series of {Xn}. Fifty point sets of the signals are used in the reconstruction.

Fig. 6
Fig. 6

Trajectories reconstructed by using the data in Figs. 2(a), 2(b), and 2(d).

Equations (3)

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P out ( t ) = P b - μ P out ( t - t r ) { 1 + b cos [ κ P out ( t - t r ) - ϕ 0 ) ] } ,
X n + 1 = P b - μ X n [ 1 + b cos ( κ X n - ϕ 0 ) ] ,
p c sin ( κ p c - ϕ 0 ) = 1 / ( μ κ b ) ,

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