Abstract

Chaos synchronization in two unidirectionally coupled vertical-cavity surface-emitting lasers (VCSELs) with open-loop configuration is studied numerically. We consider two low-order transverse modes for weakly index-guided VCSELs and investigate the generalized type of chaos synchronization for both global coupling and mode-selective coupling configurations. It is found that the synchronization can be obtained between each mode of the transmitter and the receiver lasers when all modes of the transmitter are injected into the receiver equally and coupled with the corresponding modes of the receiver laser. For mode-selective cases, the modes with strong optical injection can achieve the synchronization; while the rest modes without coupling can not obtain the synchronization any more even though the injection is very strong. The results afford an opportunity to multichannel optical secure communications.

© 2006 Optical Society of America

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  1. K. M. Cuomo, and A. V. Oppenheim, "Circuit implementation of synchronized chaos with applications to communications," Phys. Rev. Lett. 71, 65-68 (1993).
    [CrossRef] [PubMed]
  2. R. Lang, and K. Kobayashi, "External optical feedback effects on semiconductor injection laser properties," IEEE J. Quantum. Electron. 16, 347-355 (1980).
    [CrossRef]
  3. H. Kakiuchida, and J. Ohtsubo, "Characteristics of a semiconductor laser with external feedback," IEEE J. Quantum. Electron. 30, 2087-2097 (1994).
    [CrossRef]
  4. H. Lamela, G. Carpintero, and F. J. Mancebo, "Period tripling and chaos in the dynamic behavior of directly modulated diode lasers," IEEE J. Quantum. Electron. 34, 1797-1801 (1998).
    [CrossRef]
  5. S. Tang, and J. M. Liu, "Chaotic pulsing and quasiperiodic route to chaos in a semiconductor laser with delayed opto-electronic feedback," IEEE J. Quantum. Electron. 37, 329-336 (2001).
    [CrossRef]
  6. F. Y. Lin, and J. M. Liu, "Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback," IEEE J. Quantum. Electron. 39, 562-567 (2003).
    [CrossRef]
  7. T. B. Simpson, "Mapping the nonlinear dynamics of a distributed feedback semiconductor laser subject to external optical injection," Opt. Commun. 215, 135-151 (2003).
    [CrossRef]
  8. X. F. Li, W. Pan, B. Luo, and D. Ma, "Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser," Chaos, Solitons & Fractals 27, 1387-1394 (2006).
    [CrossRef]
  9. X. F. Li, W. Pan, B. Luo, D. Ma, Z. Zhao, and G. Deng, "Theoretical study on controlling nonlinear behaviors of a couple-cavity VCSEL by external optical injection," Chinese Opt. Lett. 2, 278-281 (2004).
  10. G. D. Van Wiggeren, and R. Roy, "Communication with chaotic lasers," Science 279, 1198-1200 (1998).
    [CrossRef]
  11. V. Ahlers, U. Parlitz, and W. Lauterborn, "Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers," Phys. Rev. E 58, 7208-7213 (1998).
    [CrossRef]
  12. J. Ohtsubo, "Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback," IEEE J. Quantum Electron. 38, 1141-1154 (2002).
    [CrossRef]
  13. K. Kusumoto, and J. Ohstubo, "Anticipating synchronization based on optical injection-locking in chaotic semiconductor lasers," IEEE J. Quantum Electron. 39, 1531-1536 (2003).
    [CrossRef]
  14. A. Uchida, Y. Liu, and P. Davis, "Characteristics of chaotic masking in synchronized semiconductor lasers," IEEE J. Quantum Electron. 39, 963-970 (2003).
    [CrossRef]
  15. 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. A63, 031802-1-4(R) (2001).
    [CrossRef]
  16. J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, "Multimode synchronization and communication using unidirectionally coupled semiconductor lasers," IEEE J. Quantum Electron. 40, 640-650 (2004).
    [CrossRef]
  17. H. F. Chen, and J. M. Liu, "Open-loop chaotic synchronization of injection-locked semiconductor lasers with gigahertz range modulation," IEEE J. Quantum Electron. 36, 27-34 (2000).
    [CrossRef]
  18. R. Vicente, T. Pérez, and C. R. Mirasso, "Open- versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1197-1204 (2002).
    [CrossRef]
  19. A. Murakami, "Phase locking and chaos synchronization in injection-locked semiconductor lasers," IEEE J. Quantum Electron. 39, 438-447 (2003).
    [CrossRef]
  20. X. F. Li, W. Pan, B. Luo, and D. Ma, "Effects of unwanted feedback on synchronized chaotic optical communications," Appl. Opt. 45, (2006) (to be published)
    [CrossRef] [PubMed]
  21. Y. Takiguchi, H. Fujino, and J. Ohtsubo, "Experimental synchronization of chaotic oscillations in external cavity semiconductor lasers in low-frequency fluctuation regime," Opt. Lett. 24, 1570-1572 (1999).
    [CrossRef]
  22. H. Fujino and J. Ohtsubo, "Experimental synchronization of chaotic oscillations in external-cavity semiconductor lasers," Opt. Lett. 25, 625-627 (2000).
    [CrossRef]
  23. M. Peil, T. Heil, I. Fischer, and W. Elsäßer, "Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario," Phys. Rev. Lett. 88, 174101-1-4 (2002).
    [CrossRef] [PubMed]
  24. G. Q. Xia, Z. M. Wu, and J. G. Wu, "Theory and simulation of dual-channel optical chaotic communication system," Opt. Express 13, 3445-3453 (2005).
    [CrossRef] [PubMed]
  25. N. Fujiwara, Y. Takiguchi, and J. Ohtsubo, "Observation of the synchronization of chaos in mutually injection vertical-cavity surface-emitting semiconductor lasers," Opt. Lett. 28, 1677-1679 (2003).
    [CrossRef] [PubMed]
  26. S. Sivaprakasam, E. M. Shahverdiec, P. S. Spencer, and K. A. Shore, "Experimental demonstration of anticipating synchronization in chaotic semiconductor lasers with optical feedback," Phys. Rev. Lett. 86, 15401-1-3 (2001).
  27. Y. Hong, M. W. Lee, P. S. Spencer, and K. A. Shore, "Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers,’’Opt. Lett. 29, 1215-1217 (2004).
    [CrossRef] [PubMed]
  28. P. S. Spencer, C. R. Mirasso, P. Colet, and K. A. Shore, "Modeling of optical synchronization of chaotic external-cavity VCSEL’s," IEEE J. Quantum Electron. 34, 1673-1679 (1998).
    [CrossRef]
  29. P. S. Spencer, and C. R. Mirasso, "Analysis of optical chaos synchronization in frequency-detuned external-cavity VCSEL’s," IEEE J. Quantum Electron. 35, 803-809 (1998).
    [CrossRef]
  30. C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, "Dynamic, polarization and transverse mode characteristics of VCSEL’s," IEEE J. Quantum Electron. 27, 1402-1408 (1991).
    [CrossRef]
  31. A. Valle, J. Sarma, and K. A. Shore, "Spatial holeburning effects on the dynamics of vertical cavity surface-emitting laser diodes," IEEE J. Quantum Electron. 31, 1423-1431 (1995).
    [CrossRef]
  32. H. B. Zhang, G. Mrozynski, A. Wallrabenstein, and J. Schrage, "Analysis of transverse mode competition of VCSELs based on a spatially independent model," IEEE J. Quantum Electron. 40, 18-23 (2004).
    [CrossRef]
  33. X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Theoretical analysis of multi-transverse-mode characteristics of vertical-cavity surface-emitting lasers", Semicond. Sci. & Technol. 20, 505-513 (2005).
    [CrossRef]
  34. P. V. Mena, J. J. Morikuni, S. M. Kang, A. V. Harton, and K. W. Wyatt, "A comprehensive circuit-level model of vertical-cavity surface-emitting lasers," IEEE J. Lightwave Technol. 17, 2612-2632 (1999).
    [CrossRef]
  35. J. K. White and J. V. Moloney, "Multichannel communication using an infinite dimensional spatiotemporal chaotic system," Phys. Rev. A 59, 2422-2426 (1999).
    [CrossRef]
  36. S. F. Yu, P. Shum, and N. Q. Ngo, "Performance of optical chaotic communication system using multimode vertical cavity surface emitting lasers," Opt. Commun. 200, 143-152 (2001).
    [CrossRef]

2006 (2)

X. F. Li, W. Pan, B. Luo, and D. Ma, "Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser," Chaos, Solitons & Fractals 27, 1387-1394 (2006).
[CrossRef]

X. F. Li, W. Pan, B. Luo, and D. Ma, "Effects of unwanted feedback on synchronized chaotic optical communications," Appl. Opt. 45, (2006) (to be published)
[CrossRef] [PubMed]

2005 (2)

X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Theoretical analysis of multi-transverse-mode characteristics of vertical-cavity surface-emitting lasers", Semicond. Sci. & Technol. 20, 505-513 (2005).
[CrossRef]

G. Q. Xia, Z. M. Wu, and J. G. Wu, "Theory and simulation of dual-channel optical chaotic communication system," Opt. Express 13, 3445-3453 (2005).
[CrossRef] [PubMed]

2004 (4)

Y. Hong, M. W. Lee, P. S. Spencer, and K. A. Shore, "Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers,’’Opt. Lett. 29, 1215-1217 (2004).
[CrossRef] [PubMed]

H. B. Zhang, G. Mrozynski, A. Wallrabenstein, and J. Schrage, "Analysis of transverse mode competition of VCSELs based on a spatially independent model," IEEE J. Quantum Electron. 40, 18-23 (2004).
[CrossRef]

X. F. Li, W. Pan, B. Luo, D. Ma, Z. Zhao, and G. Deng, "Theoretical study on controlling nonlinear behaviors of a couple-cavity VCSEL by external optical injection," Chinese Opt. Lett. 2, 278-281 (2004).

J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, "Multimode synchronization and communication using unidirectionally coupled semiconductor lasers," IEEE J. Quantum Electron. 40, 640-650 (2004).
[CrossRef]

2003 (6)

K. Kusumoto, and J. Ohstubo, "Anticipating synchronization based on optical injection-locking in chaotic semiconductor lasers," IEEE J. Quantum Electron. 39, 1531-1536 (2003).
[CrossRef]

A. Uchida, Y. Liu, and P. Davis, "Characteristics of chaotic masking in synchronized semiconductor lasers," IEEE J. Quantum Electron. 39, 963-970 (2003).
[CrossRef]

F. Y. Lin, and J. M. Liu, "Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback," IEEE J. Quantum. Electron. 39, 562-567 (2003).
[CrossRef]

T. B. Simpson, "Mapping the nonlinear dynamics of a distributed feedback semiconductor laser subject to external optical injection," Opt. Commun. 215, 135-151 (2003).
[CrossRef]

A. Murakami, "Phase locking and chaos synchronization in injection-locked semiconductor lasers," IEEE J. Quantum Electron. 39, 438-447 (2003).
[CrossRef]

N. Fujiwara, Y. Takiguchi, and J. Ohtsubo, "Observation of the synchronization of chaos in mutually injection vertical-cavity surface-emitting semiconductor lasers," Opt. Lett. 28, 1677-1679 (2003).
[CrossRef] [PubMed]

2002 (3)

M. Peil, T. Heil, I. Fischer, and W. Elsäßer, "Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario," Phys. Rev. Lett. 88, 174101-1-4 (2002).
[CrossRef] [PubMed]

R. Vicente, T. Pérez, and C. R. Mirasso, "Open- versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1197-1204 (2002).
[CrossRef]

J. Ohtsubo, "Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback," IEEE J. Quantum Electron. 38, 1141-1154 (2002).
[CrossRef]

2001 (4)

S. Tang, and J. M. Liu, "Chaotic pulsing and quasiperiodic route to chaos in a semiconductor laser with delayed opto-electronic feedback," IEEE J. Quantum. Electron. 37, 329-336 (2001).
[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. A63, 031802-1-4(R) (2001).
[CrossRef]

S. Sivaprakasam, E. M. Shahverdiec, P. S. Spencer, and K. A. Shore, "Experimental demonstration of anticipating synchronization in chaotic semiconductor lasers with optical feedback," Phys. Rev. Lett. 86, 15401-1-3 (2001).

S. F. Yu, P. Shum, and N. Q. Ngo, "Performance of optical chaotic communication system using multimode vertical cavity surface emitting lasers," Opt. Commun. 200, 143-152 (2001).
[CrossRef]

2000 (2)

H. Fujino and J. Ohtsubo, "Experimental synchronization of chaotic oscillations in external-cavity semiconductor lasers," Opt. Lett. 25, 625-627 (2000).
[CrossRef]

H. F. Chen, and J. M. Liu, "Open-loop chaotic synchronization of injection-locked semiconductor lasers with gigahertz range modulation," IEEE J. Quantum Electron. 36, 27-34 (2000).
[CrossRef]

1999 (3)

Y. Takiguchi, H. Fujino, and J. Ohtsubo, "Experimental synchronization of chaotic oscillations in external cavity semiconductor lasers in low-frequency fluctuation regime," Opt. Lett. 24, 1570-1572 (1999).
[CrossRef]

P. V. Mena, J. J. Morikuni, S. M. Kang, A. V. Harton, and K. W. Wyatt, "A comprehensive circuit-level model of vertical-cavity surface-emitting lasers," IEEE J. Lightwave Technol. 17, 2612-2632 (1999).
[CrossRef]

J. K. White and J. V. Moloney, "Multichannel communication using an infinite dimensional spatiotemporal chaotic system," Phys. Rev. A 59, 2422-2426 (1999).
[CrossRef]

1998 (5)

P. S. Spencer, C. R. Mirasso, P. Colet, and K. A. Shore, "Modeling of optical synchronization of chaotic external-cavity VCSEL’s," IEEE J. Quantum Electron. 34, 1673-1679 (1998).
[CrossRef]

P. S. Spencer, and C. R. Mirasso, "Analysis of optical chaos synchronization in frequency-detuned external-cavity VCSEL’s," IEEE J. Quantum Electron. 35, 803-809 (1998).
[CrossRef]

G. D. Van Wiggeren, and R. Roy, "Communication with chaotic lasers," Science 279, 1198-1200 (1998).
[CrossRef]

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

H. Lamela, G. Carpintero, and F. J. Mancebo, "Period tripling and chaos in the dynamic behavior of directly modulated diode lasers," IEEE J. Quantum. Electron. 34, 1797-1801 (1998).
[CrossRef]

1995 (1)

A. Valle, J. Sarma, and K. A. Shore, "Spatial holeburning effects on the dynamics of vertical cavity surface-emitting laser diodes," IEEE J. Quantum Electron. 31, 1423-1431 (1995).
[CrossRef]

1994 (1)

H. Kakiuchida, and J. Ohtsubo, "Characteristics of a semiconductor laser with external feedback," IEEE J. Quantum. Electron. 30, 2087-2097 (1994).
[CrossRef]

1993 (1)

K. M. Cuomo, and A. V. Oppenheim, "Circuit implementation of synchronized chaos with applications to communications," Phys. Rev. Lett. 71, 65-68 (1993).
[CrossRef] [PubMed]

1991 (1)

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, "Dynamic, polarization and transverse mode characteristics of VCSEL’s," IEEE J. Quantum Electron. 27, 1402-1408 (1991).
[CrossRef]

1980 (1)

R. Lang, and K. Kobayashi, "External optical feedback effects on semiconductor injection laser properties," IEEE J. Quantum. Electron. 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, 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. A63, 031802-1-4(R) (2001).
[CrossRef]

Buldú, J. M.

J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, "Multimode synchronization and communication using unidirectionally coupled semiconductor lasers," IEEE J. Quantum Electron. 40, 640-650 (2004).
[CrossRef]

Carpintero, G.

H. Lamela, G. Carpintero, and F. J. Mancebo, "Period tripling and chaos in the dynamic behavior of directly modulated diode lasers," IEEE J. Quantum. Electron. 34, 1797-1801 (1998).
[CrossRef]

Chang-Hasnain, C. J.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, "Dynamic, polarization and transverse mode characteristics of VCSEL’s," IEEE J. Quantum Electron. 27, 1402-1408 (1991).
[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. A63, 031802-1-4(R) (2001).
[CrossRef]

H. F. Chen, and J. M. Liu, "Open-loop chaotic synchronization of injection-locked semiconductor lasers with gigahertz range modulation," IEEE J. Quantum Electron. 36, 27-34 (2000).
[CrossRef]

Colet, P.

P. S. Spencer, C. R. Mirasso, P. Colet, and K. A. Shore, "Modeling of optical synchronization of chaotic external-cavity VCSEL’s," IEEE J. Quantum Electron. 34, 1673-1679 (1998).
[CrossRef]

Cuomo, K. M.

K. M. Cuomo, and A. V. Oppenheim, "Circuit implementation of synchronized chaos with applications to communications," Phys. Rev. Lett. 71, 65-68 (1993).
[CrossRef] [PubMed]

Davis, P.

A. Uchida, Y. Liu, and P. Davis, "Characteristics of chaotic masking in synchronized semiconductor lasers," IEEE J. Quantum Electron. 39, 963-970 (2003).
[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. A63, 031802-1-4(R) (2001).
[CrossRef]

Deng, G.

X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Theoretical analysis of multi-transverse-mode characteristics of vertical-cavity surface-emitting lasers", Semicond. Sci. & Technol. 20, 505-513 (2005).
[CrossRef]

X. F. Li, W. Pan, B. Luo, D. Ma, Z. Zhao, and G. Deng, "Theoretical study on controlling nonlinear behaviors of a couple-cavity VCSEL by external optical injection," Chinese Opt. Lett. 2, 278-281 (2004).

Elsäßer, W.

M. Peil, T. Heil, I. Fischer, and W. Elsäßer, "Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario," Phys. Rev. Lett. 88, 174101-1-4 (2002).
[CrossRef] [PubMed]

Fischer, I.

M. Peil, T. Heil, I. Fischer, and W. Elsäßer, "Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario," Phys. Rev. Lett. 88, 174101-1-4 (2002).
[CrossRef] [PubMed]

Florez, L. T.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, "Dynamic, polarization and transverse mode characteristics of VCSEL’s," IEEE J. Quantum Electron. 27, 1402-1408 (1991).
[CrossRef]

Fujino, H.

Fujiwara, N.

García-Ojalvo, J.

J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, "Multimode synchronization and communication using unidirectionally coupled semiconductor lasers," IEEE J. Quantum Electron. 40, 640-650 (2004).
[CrossRef]

Harbison, J. P.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, "Dynamic, polarization and transverse mode characteristics of VCSEL’s," IEEE J. Quantum Electron. 27, 1402-1408 (1991).
[CrossRef]

Harton, A. V.

P. V. Mena, J. J. Morikuni, S. M. Kang, A. V. Harton, and K. W. Wyatt, "A comprehensive circuit-level model of vertical-cavity surface-emitting lasers," IEEE J. Lightwave Technol. 17, 2612-2632 (1999).
[CrossRef]

Hasnain, G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, "Dynamic, polarization and transverse mode characteristics of VCSEL’s," IEEE J. Quantum Electron. 27, 1402-1408 (1991).
[CrossRef]

Heil, T.

M. Peil, T. Heil, I. Fischer, and W. Elsäßer, "Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario," Phys. Rev. Lett. 88, 174101-1-4 (2002).
[CrossRef] [PubMed]

Hong, Y.

Kakiuchida, H.

H. Kakiuchida, and J. Ohtsubo, "Characteristics of a semiconductor laser with external feedback," IEEE J. Quantum. Electron. 30, 2087-2097 (1994).
[CrossRef]

Kang, S. M.

P. V. Mena, J. J. Morikuni, S. M. Kang, A. V. Harton, and K. W. Wyatt, "A comprehensive circuit-level model of vertical-cavity surface-emitting lasers," IEEE J. Lightwave Technol. 17, 2612-2632 (1999).
[CrossRef]

Kobayashi, K.

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

Kusumoto, K.

K. Kusumoto, and J. Ohstubo, "Anticipating synchronization based on optical injection-locking in chaotic semiconductor lasers," IEEE J. Quantum Electron. 39, 1531-1536 (2003).
[CrossRef]

Lamela, H.

H. Lamela, G. Carpintero, and F. J. Mancebo, "Period tripling and chaos in the dynamic behavior of directly modulated diode lasers," IEEE J. Quantum. Electron. 34, 1797-1801 (1998).
[CrossRef]

Lang, R.

R. Lang, and K. Kobayashi, "External optical feedback effects on semiconductor injection laser properties," IEEE J. Quantum. Electron. 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]

Lee, M. W.

Li, X. F.

X. F. Li, W. Pan, B. Luo, and D. Ma, "Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser," Chaos, Solitons & Fractals 27, 1387-1394 (2006).
[CrossRef]

X. F. Li, W. Pan, B. Luo, and D. Ma, "Effects of unwanted feedback on synchronized chaotic optical communications," Appl. Opt. 45, (2006) (to be published)
[CrossRef] [PubMed]

X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Theoretical analysis of multi-transverse-mode characteristics of vertical-cavity surface-emitting lasers", Semicond. Sci. & Technol. 20, 505-513 (2005).
[CrossRef]

X. F. Li, W. Pan, B. Luo, D. Ma, Z. Zhao, and G. Deng, "Theoretical study on controlling nonlinear behaviors of a couple-cavity VCSEL by external optical injection," Chinese Opt. Lett. 2, 278-281 (2004).

Lin, F. Y.

F. Y. Lin, and J. M. Liu, "Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback," IEEE J. Quantum. Electron. 39, 562-567 (2003).
[CrossRef]

Liu, J. M.

F. Y. Lin, and J. M. Liu, "Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback," IEEE J. Quantum. Electron. 39, 562-567 (2003).
[CrossRef]

S. Tang, and J. M. Liu, "Chaotic pulsing and quasiperiodic route to chaos in a semiconductor laser with delayed opto-electronic feedback," IEEE J. Quantum. Electron. 37, 329-336 (2001).
[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. A63, 031802-1-4(R) (2001).
[CrossRef]

H. F. Chen, and J. M. Liu, "Open-loop chaotic synchronization of injection-locked semiconductor lasers with gigahertz range modulation," IEEE J. Quantum Electron. 36, 27-34 (2000).
[CrossRef]

Liu, Y.

A. Uchida, Y. Liu, and P. Davis, "Characteristics of chaotic masking in synchronized semiconductor lasers," IEEE J. Quantum Electron. 39, 963-970 (2003).
[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. A63, 031802-1-4(R) (2001).
[CrossRef]

Luo, B.

X. F. Li, W. Pan, B. Luo, and D. Ma, "Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser," Chaos, Solitons & Fractals 27, 1387-1394 (2006).
[CrossRef]

X. F. Li, W. Pan, B. Luo, and D. Ma, "Effects of unwanted feedback on synchronized chaotic optical communications," Appl. Opt. 45, (2006) (to be published)
[CrossRef] [PubMed]

X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Theoretical analysis of multi-transverse-mode characteristics of vertical-cavity surface-emitting lasers", Semicond. Sci. & Technol. 20, 505-513 (2005).
[CrossRef]

X. F. Li, W. Pan, B. Luo, D. Ma, Z. Zhao, and G. Deng, "Theoretical study on controlling nonlinear behaviors of a couple-cavity VCSEL by external optical injection," Chinese Opt. Lett. 2, 278-281 (2004).

Ma, D.

X. F. Li, W. Pan, B. Luo, and D. Ma, "Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser," Chaos, Solitons & Fractals 27, 1387-1394 (2006).
[CrossRef]

X. F. Li, W. Pan, B. Luo, and D. Ma, "Effects of unwanted feedback on synchronized chaotic optical communications," Appl. Opt. 45, (2006) (to be published)
[CrossRef] [PubMed]

X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Theoretical analysis of multi-transverse-mode characteristics of vertical-cavity surface-emitting lasers", Semicond. Sci. & Technol. 20, 505-513 (2005).
[CrossRef]

X. F. Li, W. Pan, B. Luo, D. Ma, Z. Zhao, and G. Deng, "Theoretical study on controlling nonlinear behaviors of a couple-cavity VCSEL by external optical injection," Chinese Opt. Lett. 2, 278-281 (2004).

Mancebo, F. J.

H. Lamela, G. Carpintero, and F. J. Mancebo, "Period tripling and chaos in the dynamic behavior of directly modulated diode lasers," IEEE J. Quantum. Electron. 34, 1797-1801 (1998).
[CrossRef]

Mena, P. V.

P. V. Mena, J. J. Morikuni, S. M. Kang, A. V. Harton, and K. W. Wyatt, "A comprehensive circuit-level model of vertical-cavity surface-emitting lasers," IEEE J. Lightwave Technol. 17, 2612-2632 (1999).
[CrossRef]

Mirasso, C. R.

R. Vicente, T. Pérez, and C. R. Mirasso, "Open- versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1197-1204 (2002).
[CrossRef]

P. S. Spencer, C. R. Mirasso, P. Colet, and K. A. Shore, "Modeling of optical synchronization of chaotic external-cavity VCSEL’s," IEEE J. Quantum Electron. 34, 1673-1679 (1998).
[CrossRef]

P. S. Spencer, and C. R. Mirasso, "Analysis of optical chaos synchronization in frequency-detuned external-cavity VCSEL’s," IEEE J. Quantum Electron. 35, 803-809 (1998).
[CrossRef]

Moloney, J. V.

J. K. White and J. V. Moloney, "Multichannel communication using an infinite dimensional spatiotemporal chaotic system," Phys. Rev. A 59, 2422-2426 (1999).
[CrossRef]

Morikuni, J. J.

P. V. Mena, J. J. Morikuni, S. M. Kang, A. V. Harton, and K. W. Wyatt, "A comprehensive circuit-level model of vertical-cavity surface-emitting lasers," IEEE J. Lightwave Technol. 17, 2612-2632 (1999).
[CrossRef]

Mrozynski, G.

H. B. Zhang, G. Mrozynski, A. Wallrabenstein, and J. Schrage, "Analysis of transverse mode competition of VCSELs based on a spatially independent model," IEEE J. Quantum Electron. 40, 18-23 (2004).
[CrossRef]

Murakami, A.

A. Murakami, "Phase locking and chaos synchronization in injection-locked semiconductor lasers," IEEE J. Quantum Electron. 39, 438-447 (2003).
[CrossRef]

Ngo, N. Q.

S. F. Yu, P. Shum, and N. Q. Ngo, "Performance of optical chaotic communication system using multimode vertical cavity surface emitting lasers," Opt. Commun. 200, 143-152 (2001).
[CrossRef]

Ohstubo, J.

K. Kusumoto, and J. Ohstubo, "Anticipating synchronization based on optical injection-locking in chaotic semiconductor lasers," IEEE J. Quantum Electron. 39, 1531-1536 (2003).
[CrossRef]

Ohtsubo, J.

Oppenheim, A. V.

K. M. Cuomo, and A. V. Oppenheim, "Circuit implementation of synchronized chaos with applications to communications," Phys. Rev. Lett. 71, 65-68 (1993).
[CrossRef] [PubMed]

Pan, W.

X. F. Li, W. Pan, B. Luo, and D. Ma, "Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser," Chaos, Solitons & Fractals 27, 1387-1394 (2006).
[CrossRef]

X. F. Li, W. Pan, B. Luo, and D. Ma, "Effects of unwanted feedback on synchronized chaotic optical communications," Appl. Opt. 45, (2006) (to be published)
[CrossRef] [PubMed]

X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Theoretical analysis of multi-transverse-mode characteristics of vertical-cavity surface-emitting lasers", Semicond. Sci. & Technol. 20, 505-513 (2005).
[CrossRef]

X. F. Li, W. Pan, B. Luo, D. Ma, Z. Zhao, and G. Deng, "Theoretical study on controlling nonlinear behaviors of a couple-cavity VCSEL by external optical injection," Chinese Opt. Lett. 2, 278-281 (2004).

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]

Peil, M.

M. Peil, T. Heil, I. Fischer, and W. Elsäßer, "Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario," Phys. Rev. Lett. 88, 174101-1-4 (2002).
[CrossRef] [PubMed]

Pérez, T.

R. Vicente, T. Pérez, and C. R. Mirasso, "Open- versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1197-1204 (2002).
[CrossRef]

Roy, R.

G. D. Van Wiggeren, and R. Roy, "Communication with chaotic lasers," Science 279, 1198-1200 (1998).
[CrossRef]

Sarma, J.

A. Valle, J. Sarma, and K. A. Shore, "Spatial holeburning effects on the dynamics of vertical cavity surface-emitting laser diodes," IEEE J. Quantum Electron. 31, 1423-1431 (1995).
[CrossRef]

Schrage, J.

H. B. Zhang, G. Mrozynski, A. Wallrabenstein, and J. Schrage, "Analysis of transverse mode competition of VCSELs based on a spatially independent model," IEEE J. Quantum Electron. 40, 18-23 (2004).
[CrossRef]

Shahverdiec, E. M.

S. Sivaprakasam, E. M. Shahverdiec, P. S. Spencer, and K. A. Shore, "Experimental demonstration of anticipating synchronization in chaotic semiconductor lasers with optical feedback," Phys. Rev. Lett. 86, 15401-1-3 (2001).

Shore, K. A.

Y. Hong, M. W. Lee, P. S. Spencer, and K. A. Shore, "Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers,’’Opt. Lett. 29, 1215-1217 (2004).
[CrossRef] [PubMed]

S. Sivaprakasam, E. M. Shahverdiec, P. S. Spencer, and K. A. Shore, "Experimental demonstration of anticipating synchronization in chaotic semiconductor lasers with optical feedback," Phys. Rev. Lett. 86, 15401-1-3 (2001).

P. S. Spencer, C. R. Mirasso, P. Colet, and K. A. Shore, "Modeling of optical synchronization of chaotic external-cavity VCSEL’s," IEEE J. Quantum Electron. 34, 1673-1679 (1998).
[CrossRef]

A. Valle, J. Sarma, and K. A. Shore, "Spatial holeburning effects on the dynamics of vertical cavity surface-emitting laser diodes," IEEE J. Quantum Electron. 31, 1423-1431 (1995).
[CrossRef]

Shum, P.

S. F. Yu, P. Shum, and N. Q. Ngo, "Performance of optical chaotic communication system using multimode vertical cavity surface emitting lasers," Opt. Commun. 200, 143-152 (2001).
[CrossRef]

Simpson, T. B.

T. B. Simpson, "Mapping the nonlinear dynamics of a distributed feedback semiconductor laser subject to external optical injection," Opt. Commun. 215, 135-151 (2003).
[CrossRef]

Sivaprakasam, S.

S. Sivaprakasam, E. M. Shahverdiec, P. S. Spencer, and K. A. Shore, "Experimental demonstration of anticipating synchronization in chaotic semiconductor lasers with optical feedback," Phys. Rev. Lett. 86, 15401-1-3 (2001).

Spencer, P. S.

Y. Hong, M. W. Lee, P. S. Spencer, and K. A. Shore, "Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers,’’Opt. Lett. 29, 1215-1217 (2004).
[CrossRef] [PubMed]

S. Sivaprakasam, E. M. Shahverdiec, P. S. Spencer, and K. A. Shore, "Experimental demonstration of anticipating synchronization in chaotic semiconductor lasers with optical feedback," Phys. Rev. Lett. 86, 15401-1-3 (2001).

P. S. Spencer, and C. R. Mirasso, "Analysis of optical chaos synchronization in frequency-detuned external-cavity VCSEL’s," IEEE J. Quantum Electron. 35, 803-809 (1998).
[CrossRef]

P. S. Spencer, C. R. Mirasso, P. Colet, and K. A. Shore, "Modeling of optical synchronization of chaotic external-cavity VCSEL’s," IEEE J. Quantum Electron. 34, 1673-1679 (1998).
[CrossRef]

Stoffel, N. G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, "Dynamic, polarization and transverse mode characteristics of VCSEL’s," IEEE J. Quantum Electron. 27, 1402-1408 (1991).
[CrossRef]

Takiguchi, Y.

Tang, S.

S. Tang, and J. M. Liu, "Chaotic pulsing and quasiperiodic route to chaos in a semiconductor laser with delayed opto-electronic feedback," IEEE J. Quantum. Electron. 37, 329-336 (2001).
[CrossRef]

Torrent, M. C.

J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, "Multimode synchronization and communication using unidirectionally coupled semiconductor lasers," IEEE J. Quantum Electron. 40, 640-650 (2004).
[CrossRef]

Uchida, A.

A. Uchida, Y. Liu, and P. Davis, "Characteristics of chaotic masking in synchronized semiconductor lasers," IEEE J. Quantum Electron. 39, 963-970 (2003).
[CrossRef]

Valle, A.

A. Valle, J. Sarma, and K. A. Shore, "Spatial holeburning effects on the dynamics of vertical cavity surface-emitting laser diodes," IEEE J. Quantum Electron. 31, 1423-1431 (1995).
[CrossRef]

Van Wiggeren, G. D.

G. D. Van Wiggeren, and R. Roy, "Communication with chaotic lasers," Science 279, 1198-1200 (1998).
[CrossRef]

Vicente, R.

R. Vicente, T. Pérez, and C. R. Mirasso, "Open- versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1197-1204 (2002).
[CrossRef]

Von Lehmen, A. C.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, "Dynamic, polarization and transverse mode characteristics of VCSEL’s," IEEE J. Quantum Electron. 27, 1402-1408 (1991).
[CrossRef]

Wallrabenstein, A.

H. B. Zhang, G. Mrozynski, A. Wallrabenstein, and J. Schrage, "Analysis of transverse mode competition of VCSELs based on a spatially independent model," IEEE J. Quantum Electron. 40, 18-23 (2004).
[CrossRef]

White, J. K.

J. K. White and J. V. Moloney, "Multichannel communication using an infinite dimensional spatiotemporal chaotic system," Phys. Rev. A 59, 2422-2426 (1999).
[CrossRef]

Wu, J. G.

Wu, Z. M.

Wyatt, K. W.

P. V. Mena, J. J. Morikuni, S. M. Kang, A. V. Harton, and K. W. Wyatt, "A comprehensive circuit-level model of vertical-cavity surface-emitting lasers," IEEE J. Lightwave Technol. 17, 2612-2632 (1999).
[CrossRef]

Xia, G. Q.

Yu, S. F.

S. F. Yu, P. Shum, and N. Q. Ngo, "Performance of optical chaotic communication system using multimode vertical cavity surface emitting lasers," Opt. Commun. 200, 143-152 (2001).
[CrossRef]

Zhang, H. B.

H. B. Zhang, G. Mrozynski, A. Wallrabenstein, and J. Schrage, "Analysis of transverse mode competition of VCSELs based on a spatially independent model," IEEE J. Quantum Electron. 40, 18-23 (2004).
[CrossRef]

Zhao, Z.

X. F. Li, W. Pan, B. Luo, D. Ma, Z. Zhao, and G. Deng, "Theoretical study on controlling nonlinear behaviors of a couple-cavity VCSEL by external optical injection," Chinese Opt. Lett. 2, 278-281 (2004).

Appl. Opt. (1)

X. F. Li, W. Pan, B. Luo, and D. Ma, "Effects of unwanted feedback on synchronized chaotic optical communications," Appl. Opt. 45, (2006) (to be published)
[CrossRef] [PubMed]

Chaos, Solitons & Fractals (1)

X. F. Li, W. Pan, B. Luo, and D. Ma, "Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser," Chaos, Solitons & Fractals 27, 1387-1394 (2006).
[CrossRef]

Chinese Opt. Lett. (1)

X. F. Li, W. Pan, B. Luo, D. Ma, Z. Zhao, and G. Deng, "Theoretical study on controlling nonlinear behaviors of a couple-cavity VCSEL by external optical injection," Chinese Opt. Lett. 2, 278-281 (2004).

IEEE J. Lightwave Technol. (1)

P. V. Mena, J. J. Morikuni, S. M. Kang, A. V. Harton, and K. W. Wyatt, "A comprehensive circuit-level model of vertical-cavity surface-emitting lasers," IEEE J. Lightwave Technol. 17, 2612-2632 (1999).
[CrossRef]

IEEE J. Quantum Electron. (12)

P. S. Spencer, C. R. Mirasso, P. Colet, and K. A. Shore, "Modeling of optical synchronization of chaotic external-cavity VCSEL’s," IEEE J. Quantum Electron. 34, 1673-1679 (1998).
[CrossRef]

P. S. Spencer, and C. R. Mirasso, "Analysis of optical chaos synchronization in frequency-detuned external-cavity VCSEL’s," IEEE J. Quantum Electron. 35, 803-809 (1998).
[CrossRef]

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, "Dynamic, polarization and transverse mode characteristics of VCSEL’s," IEEE J. Quantum Electron. 27, 1402-1408 (1991).
[CrossRef]

A. Valle, J. Sarma, and K. A. Shore, "Spatial holeburning effects on the dynamics of vertical cavity surface-emitting laser diodes," IEEE J. Quantum Electron. 31, 1423-1431 (1995).
[CrossRef]

H. B. Zhang, G. Mrozynski, A. Wallrabenstein, and J. Schrage, "Analysis of transverse mode competition of VCSELs based on a spatially independent model," IEEE J. Quantum Electron. 40, 18-23 (2004).
[CrossRef]

J. Ohtsubo, "Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback," IEEE J. Quantum Electron. 38, 1141-1154 (2002).
[CrossRef]

K. Kusumoto, and J. Ohstubo, "Anticipating synchronization based on optical injection-locking in chaotic semiconductor lasers," IEEE J. Quantum Electron. 39, 1531-1536 (2003).
[CrossRef]

A. Uchida, Y. Liu, and P. Davis, "Characteristics of chaotic masking in synchronized semiconductor lasers," IEEE J. Quantum Electron. 39, 963-970 (2003).
[CrossRef]

J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, "Multimode synchronization and communication using unidirectionally coupled semiconductor lasers," IEEE J. Quantum Electron. 40, 640-650 (2004).
[CrossRef]

H. F. Chen, and J. M. Liu, "Open-loop chaotic synchronization of injection-locked semiconductor lasers with gigahertz range modulation," IEEE J. Quantum Electron. 36, 27-34 (2000).
[CrossRef]

R. Vicente, T. Pérez, and C. R. Mirasso, "Open- versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1197-1204 (2002).
[CrossRef]

A. Murakami, "Phase locking and chaos synchronization in injection-locked semiconductor lasers," IEEE J. Quantum Electron. 39, 438-447 (2003).
[CrossRef]

IEEE J. Quantum. Electron. (5)

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

H. Kakiuchida, and J. Ohtsubo, "Characteristics of a semiconductor laser with external feedback," IEEE J. Quantum. Electron. 30, 2087-2097 (1994).
[CrossRef]

H. Lamela, G. Carpintero, and F. J. Mancebo, "Period tripling and chaos in the dynamic behavior of directly modulated diode lasers," IEEE J. Quantum. Electron. 34, 1797-1801 (1998).
[CrossRef]

S. Tang, and J. M. Liu, "Chaotic pulsing and quasiperiodic route to chaos in a semiconductor laser with delayed opto-electronic feedback," IEEE J. Quantum. Electron. 37, 329-336 (2001).
[CrossRef]

F. Y. Lin, and J. M. Liu, "Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback," IEEE J. Quantum. Electron. 39, 562-567 (2003).
[CrossRef]

Opt. Commun. (2)

T. B. Simpson, "Mapping the nonlinear dynamics of a distributed feedback semiconductor laser subject to external optical injection," Opt. Commun. 215, 135-151 (2003).
[CrossRef]

S. F. Yu, P. Shum, and N. Q. Ngo, "Performance of optical chaotic communication system using multimode vertical cavity surface emitting lasers," Opt. Commun. 200, 143-152 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (2)

J. K. White and J. V. Moloney, "Multichannel communication using an infinite dimensional spatiotemporal chaotic system," Phys. Rev. A 59, 2422-2426 (1999).
[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. A63, 031802-1-4(R) (2001).
[CrossRef]

Phys. Rev. E (1)

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. (3)

K. M. Cuomo, and A. V. Oppenheim, "Circuit implementation of synchronized chaos with applications to communications," Phys. Rev. Lett. 71, 65-68 (1993).
[CrossRef] [PubMed]

M. Peil, T. Heil, I. Fischer, and W. Elsäßer, "Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario," Phys. Rev. Lett. 88, 174101-1-4 (2002).
[CrossRef] [PubMed]

S. Sivaprakasam, E. M. Shahverdiec, P. S. Spencer, and K. A. Shore, "Experimental demonstration of anticipating synchronization in chaotic semiconductor lasers with optical feedback," Phys. Rev. Lett. 86, 15401-1-3 (2001).

Science (1)

G. D. Van Wiggeren, and R. Roy, "Communication with chaotic lasers," Science 279, 1198-1200 (1998).
[CrossRef]

Semicond. Sci. & Technol. (1)

X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Theoretical analysis of multi-transverse-mode characteristics of vertical-cavity surface-emitting lasers", Semicond. Sci. & Technol. 20, 505-513 (2005).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Chaotic series of (a) modal powers, (b) optical phases, and (c) carrier density. Here, k =8ns -1 and Lext =2cm. The solid and the dot lines stand for LP01 and LP11 modes, respectively.

Fig. 2.
Fig. 2.

Output power of the transmitter (first column) and the receiver (second column) in generalized synchronization regime, where k =8ns -1 , Lext =2cm , kc =533ns -1 , and Lc =0cm. The results for the total output power, the LP01 mode power, and the LP11 mode power are given in the first, second and third rows, respectively. The corresponding correlation curves are plotted in the third column.

Fig. 3.
Fig. 3.

Time series [(a) and (c)] and power spectra [(b) and (d)] of the mode powers of the transmitter and receiver lasers. Here, the black and gray lines correspond to the LP01 and LP11 modes, respectively. The feedback and coupling conditions are k = 8ns -1 , τ = 1ns , kc =533ns -1, and τc =3ns.

Fig. 4.
Fig. 4.

Variations of correlation coefficients C(∆t) with respect to temporal delay ∆t, where (a), (b), and (c) correspond to the total power, the LP01 mode power, and the LP11 mode power, respectively. The feedback and coupling conditions are k = 8ns -1 , τ = 1ns, kc =533ns -1 , and τc = 3ns. Here, the global maximum is observed at ∆t = 1ns , which corresponds to the propagation delay of the chaotic carrier from the transmitter to the receiver.

Fig. 5.
Fig. 5.

As Fig. 2 but only LP01 mode of the transmitter is injected into the receiver laser.

Fig. 6.
Fig. 6.

As Fig. 2 but only LP11 mode of the transmitter is injected into the receiver laser.

Fig. 7.
Fig. 7.

Variations of correlation coefficient C(∆t = 0ns) with respect to the injection parameter kc for different coupling conditions. Thick solid, thin solid, and dot lines correspond to the global injection, LP01 mode injection, and LP11 mode injection cases, respectively. The parameters are the same to those of Fig. 2.

Tables (1)

Tables Icon

Table 1. Propagation constants and eigenvalues of LP01 and LP11 modes.

Equations (11)

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

E i ( r , φ , t ) = E i ( t ) ψ i r φ
ψ i r φ = c i [ J i 1 ( u i r R core ) J i 1 ( u i ) ] cos [ ( i 1 ) φ ] r < R core
ψ i r φ = c i [ K i 1 ( w i r R core ) K i 1 ( w i ) ] cos [ ( i 1 ) φ ] r > R core
1 π R clad 2 0 2 π 0 R clad ψ i r φ 2 rdrdφ = 1
u i J i ( u i ) J i 1 ( u i ) = w i K i ( w i ) K i 1 ( w i )
d E i ( m ) ( t ) dt = 1 j β c 2 ( Γ z G i ( m ) 1 τ p ) E i ( m ) ( t ) + k E i ( m ) ( t τ ) exp [ j ω i ( m ) τ ]
d E i ( s ) ( t ) dt = 1 j β c 2 ( Γ z G i ( s ) 1 τ p ) E i ( s ) ( t ) + k c E i ( m ) ( t τ c ) exp [ j ω i ( m ) τ c ] exp ( j 2 π Δ υt )
N m s r t t = D n 2 N m s r t + I ( r ) qV N m s r t τ e
i v g g 0 [ N m s r t N 0 ] E i m s ( t ) 2 1 2 π 0 2 π ψ i r φ 2
G i ( m , s ) = 1 π R clad 2 0 2 π 0 R lade v g g 0 [ N ( m , s ) ( r , t ) N 0 ] ψ i ( r , φ ) 2 rdrdφ
C ( Δ t ) = { P m , i ( t Δ t ) P m , i ( t Δ t ) } { P m , i ( t ) P s , i ( t ) } { P m , i ( t Δ t ) P s , i ( t Δ t ) } 2 { P s , i ( t ) P s , i ( t ) } 2

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