Abstract

We investigate theoretically the effects of nonlinear phase distortion on synchronization of two identical unidirectionally coupled chaotic semiconductor lasers. When we take into account the self-phase modulation of the transmitted signal in an optical communication channel, we find that distortion severely affects synchronization. The effects of self-phase modulation on synchronization error relative to the power of the transmitting signal and the optical fiber length are studied.

© 2004 Optical Society of America

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References

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  1. I. Fischer, O. Hess, W. Elsässer, and E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
    [CrossRef] [PubMed]
  2. C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photonics Technol. Lett. 8, 299–301 (1996).
    [CrossRef]
  3. V. Annovazzi-Lodi, S. Donati, and A. Scire, “Synchronization of chaotic lasers by optical feedback for cryptographic applications,” IEEE J. Quantum Electron. 33, 1449–1454 (1997).
    [CrossRef]
  4. V. Ahlers, U. Parlitz, and W. Lauterborn, “Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers,” Phys. Rev. E 58, 7208–7213 (1998).
    [CrossRef]
  5. K. V. Volodchenko, V. N. Ivanov, S. H. Gong, M. Choi, Y. J. Park, and C. M. Kim, “Phase synchronization in coupled Nd:YAG lasers,” Opt. Lett. 26, 1406–1408 (2001).
    [CrossRef]
  6. M. Choi, K. V. Volodchenko, S. Rim, W. H. Kye, C. M. Kim, Y. J. Park, and G. U. Kim, “Transition from phase synchronization to complete synchronization in mutually coupled nonidentical Nd:YAG lasers,” Opt. Lett. 28, 1013–1015 (2003).
    [CrossRef] [PubMed]
  7. S. Sivaprakasam and K. Shore, “Demonstration of optical synchronization of chaotic external-cavity laser diodes,” Opt. Lett. 24, 466–468 (1999).
    [CrossRef]
  8. I. Fischer, Y. Liu, and P. Davis, “Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication,” Phys. Rev. A 62, 011801 (2000).
    [CrossRef]
  9. Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802 (2001).
    [CrossRef]
  10. Y. Liu, Y. Takiguchi, P. Davis, T. Aida, and S. Saito, “Experimental observation of complete chaos synchronization in semiconductor lasers,” Appl. Phys. Lett. 80, 4306–4308 (2002).
    [CrossRef]
  11. G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, New York, 1997).
  12. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. QE-16, 347–355 (1980).
    [CrossRef]
  13. T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, “Statistical properties of low-frequency fluctuations during single-mode operation in distributed-feedback lasers: experiments and modeling,” Opt. Lett. 24, 1275–1277 (1999).
    [CrossRef]

2003

2002

Y. Liu, Y. Takiguchi, P. Davis, T. Aida, and S. Saito, “Experimental observation of complete chaos synchronization in semiconductor lasers,” Appl. Phys. Lett. 80, 4306–4308 (2002).
[CrossRef]

2001

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802 (2001).
[CrossRef]

K. V. Volodchenko, V. N. Ivanov, S. H. Gong, M. Choi, Y. J. Park, and C. M. Kim, “Phase synchronization in coupled Nd:YAG lasers,” Opt. Lett. 26, 1406–1408 (2001).
[CrossRef]

2000

I. Fischer, Y. Liu, and P. Davis, “Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication,” Phys. Rev. A 62, 011801 (2000).
[CrossRef]

1999

1998

V. Ahlers, U. Parlitz, and W. Lauterborn, “Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers,” Phys. Rev. E 58, 7208–7213 (1998).
[CrossRef]

1997

V. Annovazzi-Lodi, S. Donati, and A. Scire, “Synchronization of chaotic lasers by optical feedback for cryptographic applications,” IEEE J. Quantum Electron. 33, 1449–1454 (1997).
[CrossRef]

1996

C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photonics Technol. Lett. 8, 299–301 (1996).
[CrossRef]

1994

I. Fischer, O. Hess, W. Elsässer, and E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
[CrossRef] [PubMed]

1980

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. QE-16, 347–355 (1980).
[CrossRef]

Ahlers, V.

V. Ahlers, U. Parlitz, and W. Lauterborn, “Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers,” Phys. Rev. E 58, 7208–7213 (1998).
[CrossRef]

Aida, T.

Y. Liu, Y. Takiguchi, P. Davis, T. Aida, and S. Saito, “Experimental observation of complete chaos synchronization in semiconductor lasers,” Appl. Phys. Lett. 80, 4306–4308 (2002).
[CrossRef]

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802 (2001).
[CrossRef]

Annovazzi-Lodi, V.

V. Annovazzi-Lodi, S. Donati, and A. Scire, “Synchronization of chaotic lasers by optical feedback for cryptographic applications,” IEEE J. Quantum Electron. 33, 1449–1454 (1997).
[CrossRef]

Chen, H. F.

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802 (2001).
[CrossRef]

Choi, M.

Colet, P.

C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photonics Technol. Lett. 8, 299–301 (1996).
[CrossRef]

Davis, P.

Y. Liu, Y. Takiguchi, P. Davis, T. Aida, and S. Saito, “Experimental observation of complete chaos synchronization in semiconductor lasers,” Appl. Phys. Lett. 80, 4306–4308 (2002).
[CrossRef]

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802 (2001).
[CrossRef]

I. Fischer, Y. Liu, and P. Davis, “Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication,” Phys. Rev. A 62, 011801 (2000).
[CrossRef]

Donati, S.

V. Annovazzi-Lodi, S. Donati, and A. Scire, “Synchronization of chaotic lasers by optical feedback for cryptographic applications,” IEEE J. Quantum Electron. 33, 1449–1454 (1997).
[CrossRef]

Elsässer, W.

Fischer, I.

I. Fischer, Y. Liu, and P. Davis, “Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication,” Phys. Rev. A 62, 011801 (2000).
[CrossRef]

T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, “Statistical properties of low-frequency fluctuations during single-mode operation in distributed-feedback lasers: experiments and modeling,” Opt. Lett. 24, 1275–1277 (1999).
[CrossRef]

I. Fischer, O. Hess, W. Elsässer, and E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
[CrossRef] [PubMed]

Garcia-Fernandez, P.

C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photonics Technol. Lett. 8, 299–301 (1996).
[CrossRef]

Göbel, E.

I. Fischer, O. Hess, W. Elsässer, and E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
[CrossRef] [PubMed]

Gong, S. H.

Heil, T.

Hess, O.

I. Fischer, O. Hess, W. Elsässer, and E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
[CrossRef] [PubMed]

Ivanov, V. N.

Kim, C. M.

Kim, G. U.

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. QE-16, 347–355 (1980).
[CrossRef]

Kye, W. H.

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. QE-16, 347–355 (1980).
[CrossRef]

Lauterborn, W.

V. Ahlers, U. Parlitz, and W. Lauterborn, “Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers,” Phys. Rev. E 58, 7208–7213 (1998).
[CrossRef]

Liu, J. M.

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802 (2001).
[CrossRef]

Liu, Y.

Y. Liu, Y. Takiguchi, P. Davis, T. Aida, and S. Saito, “Experimental observation of complete chaos synchronization in semiconductor lasers,” Appl. Phys. Lett. 80, 4306–4308 (2002).
[CrossRef]

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802 (2001).
[CrossRef]

I. Fischer, Y. Liu, and P. Davis, “Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication,” Phys. Rev. A 62, 011801 (2000).
[CrossRef]

Mirasso, C. R.

T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, “Statistical properties of low-frequency fluctuations during single-mode operation in distributed-feedback lasers: experiments and modeling,” Opt. Lett. 24, 1275–1277 (1999).
[CrossRef]

C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photonics Technol. Lett. 8, 299–301 (1996).
[CrossRef]

Mulet, J.

Park, Y. J.

Parlitz, U.

V. Ahlers, U. Parlitz, and W. Lauterborn, “Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers,” Phys. Rev. E 58, 7208–7213 (1998).
[CrossRef]

Rim, S.

Saito, S.

Y. Liu, Y. Takiguchi, P. Davis, T. Aida, and S. Saito, “Experimental observation of complete chaos synchronization in semiconductor lasers,” Appl. Phys. Lett. 80, 4306–4308 (2002).
[CrossRef]

Scire, A.

V. Annovazzi-Lodi, S. Donati, and A. Scire, “Synchronization of chaotic lasers by optical feedback for cryptographic applications,” IEEE J. Quantum Electron. 33, 1449–1454 (1997).
[CrossRef]

Shore, K.

Sivaprakasam, S.

Takiguchi, Y.

Y. Liu, Y. Takiguchi, P. Davis, T. Aida, and S. Saito, “Experimental observation of complete chaos synchronization in semiconductor lasers,” Appl. Phys. Lett. 80, 4306–4308 (2002).
[CrossRef]

Volodchenko, K. V.

Appl. Phys. Lett.

Y. Liu, Y. Takiguchi, P. Davis, T. Aida, and S. Saito, “Experimental observation of complete chaos synchronization in semiconductor lasers,” Appl. Phys. Lett. 80, 4306–4308 (2002).
[CrossRef]

IEEE J. Quantum Electron.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. QE-16, 347–355 (1980).
[CrossRef]

V. Annovazzi-Lodi, S. Donati, and A. Scire, “Synchronization of chaotic lasers by optical feedback for cryptographic applications,” IEEE J. Quantum Electron. 33, 1449–1454 (1997).
[CrossRef]

IEEE Photonics Technol. Lett.

C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, “Synchronization of chaotic semiconductor lasers: application to encoded communications,” IEEE Photonics Technol. Lett. 8, 299–301 (1996).
[CrossRef]

Opt. Lett.

Phys. Rev. A

I. Fischer, Y. Liu, and P. Davis, “Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication,” Phys. Rev. A 62, 011801 (2000).
[CrossRef]

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802 (2001).
[CrossRef]

Phys. Rev. E

V. Ahlers, U. Parlitz, and W. Lauterborn, “Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers,” Phys. Rev. E 58, 7208–7213 (1998).
[CrossRef]

Phys. Rev. Lett.

I. Fischer, O. Hess, W. Elsässer, and E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
[CrossRef] [PubMed]

Other

G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, New York, 1997).

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of an optical communication system based on synchronization of chaos.

Fig. 2
Fig. 2

Synchronization pictures in the low-frequency fluctuations regime for J=1.005Jth: (a) output power waveform of the transmitter, (b) that of the receiver, (c) synchronization error.

Fig. 3
Fig. 3

Synchronization pictures for J=1.3Jth: (a) output power waveform of the transmitter; (b) that of the receiver; (c) synchronization error. The insets in (a) and (b) are the enlarged time series in the region from 30 to 35 ns.

Fig. 4
Fig. 4

Synchronization error versus excess pumping current and propagating distance. (a) Synchronization error versus excess pumping current: solid curve, without averaging; dashed curve, averaged with a 0.1-ns window; dotted curve, averaged with a 1-ns window. (b) Error versus propagating distance: open triangles, J=1.5Jth; filled triangles J=1.1Jth; open circles, J=1.005Jth. Solid curves, without averaging; dotted curves, averaged with a 1-ns window.

Equations (4)

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

dE1,2dt=12(1-iβ)Gn1,2E1,2(t)+ηE1(t-τ1,2)exp(iωτ1,2+ϕNL),
dn1,2dt=(p-1)Jth-γn1,2-(γc+Gn1,2)|E1,2|2,
ϕNL=(γγ¯chc/αλ)|E1|210-6|E1|2.
ϕNL=k(γγ¯c)(hc/λ)|E1|2LT.

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