Abstract

We consider an electro-optic phase chaos system with two feedback loops organized in a parallel configuration such that the dynamics of one of the loops remains internal. We show that this configuration intrinsically conceals in the transmitted variable the internal delay times, which are critical for decoding. The scheme also allows for the inclusion, in a very efficient way, of a digital key generated as a long pseudorandom binary sequence. A single digital key can operate both in the internal and transmitted variables leading to a large sensitivity of the synchronization to a key-mismatch. The combination of intrinsic delay time concealment and digital key selectivity provides the basis for a large enhancement of the confidentiality in chaos-based communications.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Donati and C.R. Mirasso, “Feature section on optical chaos and applications to cryptography,” IEEE J. Quantum Electron.38, 1138–1184 (2002).
    [CrossRef]
  2. R. Lavrov, M. Peil, M. Jacquot, L. Larger, V. Udaltsov, and J. Dudley, “Electro-optic delay oscillator with nonlocal nonlinearity: Optical phase dynamics, chaos, and synchronization,” Phys. Rev. E80, 026207/1–9 (2009).
    [CrossRef]
  3. J. P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett.80, 2249–2252 (1998).
    [CrossRef]
  4. L. Larger, J. P. Goedgebuer, and F. Delorme, “Optical encryption system using hyperchaos generated by an optoelectronic wavelength oscillator,” Phys. Rev. E57, 6618–6624 (1998).
    [CrossRef]
  5. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C.R. Mirasso, L. Pesquera, and K.A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature438, 343–346 (2005).
    [CrossRef] [PubMed]
  6. R. Lavrov, M. Jacquot, and L. Larger, “Nonlocal nonlinear electro-optic Phase dynamics demonstrating 10Gbs/s chaos communications,” IEEE J. Quantum Electron.46, 1430–1435 (2010).
    [CrossRef]
  7. X. Li, W. Pan, B. Luo, and D. Ma, “Mismatch robustness and security of chaotic optical communications based on injection-locking chaos synchronization,” IEEE J. Quantum Electron.42, 953–960 (2006).
    [CrossRef]
  8. Y. Chembo Kouomou, P. Colet, N. Gastaud, and L. Larger, “Effect of parameter mismatch on the synchronization of semiconductor lasers with electrooptical feedback,” Phys. Rev. E69, 056226/1–15 (2004).
  9. V.S. Udaltsov, J.-P. Goedgebuer, L. Larger, J.-B. Cuenot, Pascal Levy, and W.T. Rhodes, “Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations,” Phys. Lett. A308, 54–60 (2003).
    [CrossRef]
  10. S. Ortín, J. Gutiérrez, L. Pesquera, and H. Vasquez, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A351, 133–141 (2005).
    [CrossRef]
  11. C. R. Mirasso, P. Colet, and P. García-Fernández, “Synchronization of chaotic semicondcutor lasers: Application to encoded communications,” Phot. Tech. Lett.8, 299–301 (1996).
    [CrossRef]
  12. L. Larger, J. Goedgebuer, and V. Udaltsov, “Ikeda-based nonlinear delayed dynamics for application to secure optical transmission systems using chaos,” Comptes Rendus Physique5, 669–681 (2004).
    [CrossRef]
  13. M. C. Soriano, P. Colet, and C. R. Mirasso, “Security implications of open- and closed-loop receivers in all-optical chaos-based communications,” IEEE Photon. Technol. Lett.21, 426–428 (2009).
    [CrossRef]
  14. R. M. Nguimdo, P. Colet, and C. R. Mirasso, “Electro-optic delay devices with double feedback,” IEEE J. Quantum Electron.46, 1436–1443 (2010).
    [CrossRef]
  15. U. Leonora, M. Santagiustina, and V. Annovazzi-Lodi, “Enhancing chaotic communication performances by Manchester coding”, IEEE Phot. Tech. Lett.20, 401–403 (2008).
    [CrossRef]
  16. V. Z. Tronciu, C. Mirasso, P. Colet, M. Hamacher, M. Benedetti, V. Vercesi, and V. Annovazzi-Lodi, “Chaos generation and synchronization using an integrated source with an air gap,” IEEE J. Quantum Electron.46, 1840–1846 (2010).
    [CrossRef]
  17. R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett.81, 558–561 (1998).
    [CrossRef]
  18. M.D. Prokhorov, V.I. Ponomarenko, A.S. Karavaev, and B.P. Bezruchko, “Reconstruction of time-delayed feedback systems from time series,” Physica D203, 209–223 (2005).
    [CrossRef]
  19. L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso, and C. R. Mirasso, “Permutation-information-theory approach to unveil delay dynamics from time-series analysis,” Phys. Rev. E82, 046212/1–9 (2010).
    [CrossRef]
  20. D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, “Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback,” Opt. Lett.32, 2960 (2007).
    [CrossRef] [PubMed]
  21. D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron.45, 879–891 (2009).
    [CrossRef]
  22. R. M. Nguimdo, M. C. Soriano, and P. Colet, “Role of the phase in the identification of delay time in semiconductor lasers with optical feedback,” Opt. Lett.36, 4332–4334 (2011).
    [CrossRef] [PubMed]
  23. R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett.37, 2541–2544 (2012).
    [CrossRef] [PubMed]
  24. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron.16, 347 (1980)
    [CrossRef]
  25. J. Hizanidis, S. Deligiannidis, A. Bogris, and D. Syvridis, “Enhancement of chaos encryption potential by combining all-optical and electrooptical chaos generators,” IEEE J. Quantum Electron.46, 1642–1649 (2010).
    [CrossRef]
  26. H. C. Wang, K. P. Ho, H. K. Chen, and H. C. Lu, J. Lightw. Technol. “Phase and amplitude responses of narrow-band optical filter measured by microwave network analyzer,” J. Lightwave Technol.24, 5075 (2006)
    [CrossRef]
  27. L. Zimmermann, K. Voigt, G. Winzer, K. Petermann, and C. M. Weinert, “C-band optical 90°-hybrids based on silicon-on-insulator 4 × 4 waveguide couplers,” IEEE Photon. Technol. Lett.21 (3), 143 (2009).
    [CrossRef]
  28. R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett.107, 034103/1–4 (2011).
    [CrossRef]
  29. R. M. Nguimdo, R. Lavrov, P. Colet, M. Jacquot, Y. K. Chembo, and L. Larger, “Effect of fiber dispersion on broadband chaos communications implemented by electro-optic nonlinear delay phase dynamics,” J. Lightwave Technol.28, 2688–2616 (2010).
    [CrossRef]
  30. A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express, vol. 18, 5188–5198, 2010.
    [CrossRef] [PubMed]
  31. K. Pyragas, “Synchronization of coupled time-delay systems: Analytical estimations,” Phys. Rev. E58, 3067–3071 (1998).
    [CrossRef]

2012 (1)

2011 (2)

R. M. Nguimdo, M. C. Soriano, and P. Colet, “Role of the phase in the identification of delay time in semiconductor lasers with optical feedback,” Opt. Lett.36, 4332–4334 (2011).
[CrossRef] [PubMed]

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett.107, 034103/1–4 (2011).
[CrossRef]

2010 (7)

L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso, and C. R. Mirasso, “Permutation-information-theory approach to unveil delay dynamics from time-series analysis,” Phys. Rev. E82, 046212/1–9 (2010).
[CrossRef]

J. Hizanidis, S. Deligiannidis, A. Bogris, and D. Syvridis, “Enhancement of chaos encryption potential by combining all-optical and electrooptical chaos generators,” IEEE J. Quantum Electron.46, 1642–1649 (2010).
[CrossRef]

A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express, vol. 18, 5188–5198, 2010.
[CrossRef] [PubMed]

R. M. Nguimdo, R. Lavrov, P. Colet, M. Jacquot, Y. K. Chembo, and L. Larger, “Effect of fiber dispersion on broadband chaos communications implemented by electro-optic nonlinear delay phase dynamics,” J. Lightwave Technol.28, 2688–2616 (2010).
[CrossRef]

R. Lavrov, M. Jacquot, and L. Larger, “Nonlocal nonlinear electro-optic Phase dynamics demonstrating 10Gbs/s chaos communications,” IEEE J. Quantum Electron.46, 1430–1435 (2010).
[CrossRef]

R. M. Nguimdo, P. Colet, and C. R. Mirasso, “Electro-optic delay devices with double feedback,” IEEE J. Quantum Electron.46, 1436–1443 (2010).
[CrossRef]

V. Z. Tronciu, C. Mirasso, P. Colet, M. Hamacher, M. Benedetti, V. Vercesi, and V. Annovazzi-Lodi, “Chaos generation and synchronization using an integrated source with an air gap,” IEEE J. Quantum Electron.46, 1840–1846 (2010).
[CrossRef]

2009 (4)

M. C. Soriano, P. Colet, and C. R. Mirasso, “Security implications of open- and closed-loop receivers in all-optical chaos-based communications,” IEEE Photon. Technol. Lett.21, 426–428 (2009).
[CrossRef]

R. Lavrov, M. Peil, M. Jacquot, L. Larger, V. Udaltsov, and J. Dudley, “Electro-optic delay oscillator with nonlocal nonlinearity: Optical phase dynamics, chaos, and synchronization,” Phys. Rev. E80, 026207/1–9 (2009).
[CrossRef]

L. Zimmermann, K. Voigt, G. Winzer, K. Petermann, and C. M. Weinert, “C-band optical 90°-hybrids based on silicon-on-insulator 4 × 4 waveguide couplers,” IEEE Photon. Technol. Lett.21 (3), 143 (2009).
[CrossRef]

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron.45, 879–891 (2009).
[CrossRef]

2008 (1)

U. Leonora, M. Santagiustina, and V. Annovazzi-Lodi, “Enhancing chaotic communication performances by Manchester coding”, IEEE Phot. Tech. Lett.20, 401–403 (2008).
[CrossRef]

2007 (1)

2006 (2)

H. C. Wang, K. P. Ho, H. K. Chen, and H. C. Lu, J. Lightw. Technol. “Phase and amplitude responses of narrow-band optical filter measured by microwave network analyzer,” J. Lightwave Technol.24, 5075 (2006)
[CrossRef]

X. Li, W. Pan, B. Luo, and D. Ma, “Mismatch robustness and security of chaotic optical communications based on injection-locking chaos synchronization,” IEEE J. Quantum Electron.42, 953–960 (2006).
[CrossRef]

2005 (3)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C.R. Mirasso, L. Pesquera, and K.A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature438, 343–346 (2005).
[CrossRef] [PubMed]

S. Ortín, J. Gutiérrez, L. Pesquera, and H. Vasquez, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A351, 133–141 (2005).
[CrossRef]

M.D. Prokhorov, V.I. Ponomarenko, A.S. Karavaev, and B.P. Bezruchko, “Reconstruction of time-delayed feedback systems from time series,” Physica D203, 209–223 (2005).
[CrossRef]

2004 (2)

L. Larger, J. Goedgebuer, and V. Udaltsov, “Ikeda-based nonlinear delayed dynamics for application to secure optical transmission systems using chaos,” Comptes Rendus Physique5, 669–681 (2004).
[CrossRef]

Y. Chembo Kouomou, P. Colet, N. Gastaud, and L. Larger, “Effect of parameter mismatch on the synchronization of semiconductor lasers with electrooptical feedback,” Phys. Rev. E69, 056226/1–15 (2004).

2003 (1)

V.S. Udaltsov, J.-P. Goedgebuer, L. Larger, J.-B. Cuenot, Pascal Levy, and W.T. Rhodes, “Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations,” Phys. Lett. A308, 54–60 (2003).
[CrossRef]

2002 (1)

S. Donati and C.R. Mirasso, “Feature section on optical chaos and applications to cryptography,” IEEE J. Quantum Electron.38, 1138–1184 (2002).
[CrossRef]

1998 (4)

J. P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett.80, 2249–2252 (1998).
[CrossRef]

L. Larger, J. P. Goedgebuer, and F. Delorme, “Optical encryption system using hyperchaos generated by an optoelectronic wavelength oscillator,” Phys. Rev. E57, 6618–6624 (1998).
[CrossRef]

R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett.81, 558–561 (1998).
[CrossRef]

K. Pyragas, “Synchronization of coupled time-delay systems: Analytical estimations,” Phys. Rev. E58, 3067–3071 (1998).
[CrossRef]

1996 (1)

C. R. Mirasso, P. Colet, and P. García-Fernández, “Synchronization of chaotic semicondcutor lasers: Application to encoded communications,” Phot. Tech. Lett.8, 299–301 (1996).
[CrossRef]

1980 (1)

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

Annovazzi-Lodi, V.

V. Z. Tronciu, C. Mirasso, P. Colet, M. Hamacher, M. Benedetti, V. Vercesi, and V. Annovazzi-Lodi, “Chaos generation and synchronization using an integrated source with an air gap,” IEEE J. Quantum Electron.46, 1840–1846 (2010).
[CrossRef]

U. Leonora, M. Santagiustina, and V. Annovazzi-Lodi, “Enhancing chaotic communication performances by Manchester coding”, IEEE Phot. Tech. Lett.20, 401–403 (2008).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C.R. Mirasso, L. Pesquera, and K.A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature438, 343–346 (2005).
[CrossRef] [PubMed]

Argyris, A.

A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express, vol. 18, 5188–5198, 2010.
[CrossRef] [PubMed]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C.R. Mirasso, L. Pesquera, and K.A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature438, 343–346 (2005).
[CrossRef] [PubMed]

Benedetti, M.

V. Z. Tronciu, C. Mirasso, P. Colet, M. Hamacher, M. Benedetti, V. Vercesi, and V. Annovazzi-Lodi, “Chaos generation and synchronization using an integrated source with an air gap,” IEEE J. Quantum Electron.46, 1840–1846 (2010).
[CrossRef]

Bezruchko, B.P.

M.D. Prokhorov, V.I. Ponomarenko, A.S. Karavaev, and B.P. Bezruchko, “Reconstruction of time-delayed feedback systems from time series,” Physica D203, 209–223 (2005).
[CrossRef]

Bogris, A.

A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express, vol. 18, 5188–5198, 2010.
[CrossRef] [PubMed]

J. Hizanidis, S. Deligiannidis, A. Bogris, and D. Syvridis, “Enhancement of chaos encryption potential by combining all-optical and electrooptical chaos generators,” IEEE J. Quantum Electron.46, 1642–1649 (2010).
[CrossRef]

Bünner, M. J.

R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett.81, 558–561 (1998).
[CrossRef]

Chembo, Y. K.

Chembo Kouomou, Y.

Y. Chembo Kouomou, P. Colet, N. Gastaud, and L. Larger, “Effect of parameter mismatch on the synchronization of semiconductor lasers with electrooptical feedback,” Phys. Rev. E69, 056226/1–15 (2004).

Chen, H. K.

Citrin, D. S.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron.45, 879–891 (2009).
[CrossRef]

D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, “Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback,” Opt. Lett.32, 2960 (2007).
[CrossRef] [PubMed]

Colet, P.

R. M. Nguimdo, M. C. Soriano, and P. Colet, “Role of the phase in the identification of delay time in semiconductor lasers with optical feedback,” Opt. Lett.36, 4332–4334 (2011).
[CrossRef] [PubMed]

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett.107, 034103/1–4 (2011).
[CrossRef]

R. M. Nguimdo, P. Colet, and C. R. Mirasso, “Electro-optic delay devices with double feedback,” IEEE J. Quantum Electron.46, 1436–1443 (2010).
[CrossRef]

V. Z. Tronciu, C. Mirasso, P. Colet, M. Hamacher, M. Benedetti, V. Vercesi, and V. Annovazzi-Lodi, “Chaos generation and synchronization using an integrated source with an air gap,” IEEE J. Quantum Electron.46, 1840–1846 (2010).
[CrossRef]

R. M. Nguimdo, R. Lavrov, P. Colet, M. Jacquot, Y. K. Chembo, and L. Larger, “Effect of fiber dispersion on broadband chaos communications implemented by electro-optic nonlinear delay phase dynamics,” J. Lightwave Technol.28, 2688–2616 (2010).
[CrossRef]

M. C. Soriano, P. Colet, and C. R. Mirasso, “Security implications of open- and closed-loop receivers in all-optical chaos-based communications,” IEEE Photon. Technol. Lett.21, 426–428 (2009).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C.R. Mirasso, L. Pesquera, and K.A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature438, 343–346 (2005).
[CrossRef] [PubMed]

Y. Chembo Kouomou, P. Colet, N. Gastaud, and L. Larger, “Effect of parameter mismatch on the synchronization of semiconductor lasers with electrooptical feedback,” Phys. Rev. E69, 056226/1–15 (2004).

C. R. Mirasso, P. Colet, and P. García-Fernández, “Synchronization of chaotic semicondcutor lasers: Application to encoded communications,” Phot. Tech. Lett.8, 299–301 (1996).
[CrossRef]

Cuenot, J.-B.

V.S. Udaltsov, J.-P. Goedgebuer, L. Larger, J.-B. Cuenot, Pascal Levy, and W.T. Rhodes, “Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations,” Phys. Lett. A308, 54–60 (2003).
[CrossRef]

Danckaert, J.

Deligiannidis, S.

J. Hizanidis, S. Deligiannidis, A. Bogris, and D. Syvridis, “Enhancement of chaos encryption potential by combining all-optical and electrooptical chaos generators,” IEEE J. Quantum Electron.46, 1642–1649 (2010).
[CrossRef]

Delorme, F.

L. Larger, J. P. Goedgebuer, and F. Delorme, “Optical encryption system using hyperchaos generated by an optoelectronic wavelength oscillator,” Phys. Rev. E57, 6618–6624 (1998).
[CrossRef]

Donati, S.

S. Donati and C.R. Mirasso, “Feature section on optical chaos and applications to cryptography,” IEEE J. Quantum Electron.38, 1138–1184 (2002).
[CrossRef]

Dudley, J.

R. Lavrov, M. Peil, M. Jacquot, L. Larger, V. Udaltsov, and J. Dudley, “Electro-optic delay oscillator with nonlocal nonlinearity: Optical phase dynamics, chaos, and synchronization,” Phys. Rev. E80, 026207/1–9 (2009).
[CrossRef]

Fischer, I.

L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso, and C. R. Mirasso, “Permutation-information-theory approach to unveil delay dynamics from time-series analysis,” Phys. Rev. E82, 046212/1–9 (2010).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C.R. Mirasso, L. Pesquera, and K.A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature438, 343–346 (2005).
[CrossRef] [PubMed]

García-Fernández, P.

C. R. Mirasso, P. Colet, and P. García-Fernández, “Synchronization of chaotic semicondcutor lasers: Application to encoded communications,” Phot. Tech. Lett.8, 299–301 (1996).
[CrossRef]

Garcia-Ojalvo, J.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C.R. Mirasso, L. Pesquera, and K.A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature438, 343–346 (2005).
[CrossRef] [PubMed]

Gastaud, N.

Y. Chembo Kouomou, P. Colet, N. Gastaud, and L. Larger, “Effect of parameter mismatch on the synchronization of semiconductor lasers with electrooptical feedback,” Phys. Rev. E69, 056226/1–15 (2004).

Giaquinta, A.

R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett.81, 558–561 (1998).
[CrossRef]

Goedgebuer, J.

L. Larger, J. Goedgebuer, and V. Udaltsov, “Ikeda-based nonlinear delayed dynamics for application to secure optical transmission systems using chaos,” Comptes Rendus Physique5, 669–681 (2004).
[CrossRef]

Goedgebuer, J. P.

L. Larger, J. P. Goedgebuer, and F. Delorme, “Optical encryption system using hyperchaos generated by an optoelectronic wavelength oscillator,” Phys. Rev. E57, 6618–6624 (1998).
[CrossRef]

J. P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett.80, 2249–2252 (1998).
[CrossRef]

Goedgebuer, J.-P.

V.S. Udaltsov, J.-P. Goedgebuer, L. Larger, J.-B. Cuenot, Pascal Levy, and W.T. Rhodes, “Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations,” Phys. Lett. A308, 54–60 (2003).
[CrossRef]

Grivas, E.

Gutiérrez, J.

S. Ortín, J. Gutiérrez, L. Pesquera, and H. Vasquez, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A351, 133–141 (2005).
[CrossRef]

Hamacher, M.

V. Z. Tronciu, C. Mirasso, P. Colet, M. Hamacher, M. Benedetti, V. Vercesi, and V. Annovazzi-Lodi, “Chaos generation and synchronization using an integrated source with an air gap,” IEEE J. Quantum Electron.46, 1840–1846 (2010).
[CrossRef]

A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express, vol. 18, 5188–5198, 2010.
[CrossRef] [PubMed]

Hegger, R.

R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett.81, 558–561 (1998).
[CrossRef]

Hizanidis, J.

J. Hizanidis, S. Deligiannidis, A. Bogris, and D. Syvridis, “Enhancement of chaos encryption potential by combining all-optical and electrooptical chaos generators,” IEEE J. Quantum Electron.46, 1642–1649 (2010).
[CrossRef]

Ho, K. P.

Jacquot, M.

R. M. Nguimdo, R. Lavrov, P. Colet, M. Jacquot, Y. K. Chembo, and L. Larger, “Effect of fiber dispersion on broadband chaos communications implemented by electro-optic nonlinear delay phase dynamics,” J. Lightwave Technol.28, 2688–2616 (2010).
[CrossRef]

R. Lavrov, M. Jacquot, and L. Larger, “Nonlocal nonlinear electro-optic Phase dynamics demonstrating 10Gbs/s chaos communications,” IEEE J. Quantum Electron.46, 1430–1435 (2010).
[CrossRef]

R. Lavrov, M. Peil, M. Jacquot, L. Larger, V. Udaltsov, and J. Dudley, “Electro-optic delay oscillator with nonlocal nonlinearity: Optical phase dynamics, chaos, and synchronization,” Phys. Rev. E80, 026207/1–9 (2009).
[CrossRef]

Kantz, H.

R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett.81, 558–561 (1998).
[CrossRef]

Karavaev, A.S.

M.D. Prokhorov, V.I. Ponomarenko, A.S. Karavaev, and B.P. Bezruchko, “Reconstruction of time-delayed feedback systems from time series,” Physica D203, 209–223 (2005).
[CrossRef]

Kobayashi, K.

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

Lang, R.

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

Larger, L.

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett.107, 034103/1–4 (2011).
[CrossRef]

R. Lavrov, M. Jacquot, and L. Larger, “Nonlocal nonlinear electro-optic Phase dynamics demonstrating 10Gbs/s chaos communications,” IEEE J. Quantum Electron.46, 1430–1435 (2010).
[CrossRef]

R. M. Nguimdo, R. Lavrov, P. Colet, M. Jacquot, Y. K. Chembo, and L. Larger, “Effect of fiber dispersion on broadband chaos communications implemented by electro-optic nonlinear delay phase dynamics,” J. Lightwave Technol.28, 2688–2616 (2010).
[CrossRef]

R. Lavrov, M. Peil, M. Jacquot, L. Larger, V. Udaltsov, and J. Dudley, “Electro-optic delay oscillator with nonlocal nonlinearity: Optical phase dynamics, chaos, and synchronization,” Phys. Rev. E80, 026207/1–9 (2009).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C.R. Mirasso, L. Pesquera, and K.A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature438, 343–346 (2005).
[CrossRef] [PubMed]

L. Larger, J. Goedgebuer, and V. Udaltsov, “Ikeda-based nonlinear delayed dynamics for application to secure optical transmission systems using chaos,” Comptes Rendus Physique5, 669–681 (2004).
[CrossRef]

Y. Chembo Kouomou, P. Colet, N. Gastaud, and L. Larger, “Effect of parameter mismatch on the synchronization of semiconductor lasers with electrooptical feedback,” Phys. Rev. E69, 056226/1–15 (2004).

V.S. Udaltsov, J.-P. Goedgebuer, L. Larger, J.-B. Cuenot, Pascal Levy, and W.T. Rhodes, “Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations,” Phys. Lett. A308, 54–60 (2003).
[CrossRef]

J. P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett.80, 2249–2252 (1998).
[CrossRef]

L. Larger, J. P. Goedgebuer, and F. Delorme, “Optical encryption system using hyperchaos generated by an optoelectronic wavelength oscillator,” Phys. Rev. E57, 6618–6624 (1998).
[CrossRef]

Lavrov, R.

R. Lavrov, M. Jacquot, and L. Larger, “Nonlocal nonlinear electro-optic Phase dynamics demonstrating 10Gbs/s chaos communications,” IEEE J. Quantum Electron.46, 1430–1435 (2010).
[CrossRef]

R. M. Nguimdo, R. Lavrov, P. Colet, M. Jacquot, Y. K. Chembo, and L. Larger, “Effect of fiber dispersion on broadband chaos communications implemented by electro-optic nonlinear delay phase dynamics,” J. Lightwave Technol.28, 2688–2616 (2010).
[CrossRef]

R. Lavrov, M. Peil, M. Jacquot, L. Larger, V. Udaltsov, and J. Dudley, “Electro-optic delay oscillator with nonlocal nonlinearity: Optical phase dynamics, chaos, and synchronization,” Phys. Rev. E80, 026207/1–9 (2009).
[CrossRef]

Leonora, U.

U. Leonora, M. Santagiustina, and V. Annovazzi-Lodi, “Enhancing chaotic communication performances by Manchester coding”, IEEE Phot. Tech. Lett.20, 401–403 (2008).
[CrossRef]

Levy, Pascal

V.S. Udaltsov, J.-P. Goedgebuer, L. Larger, J.-B. Cuenot, Pascal Levy, and W.T. Rhodes, “Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations,” Phys. Lett. A308, 54–60 (2003).
[CrossRef]

Li, X.

X. Li, W. Pan, B. Luo, and D. Ma, “Mismatch robustness and security of chaotic optical communications based on injection-locking chaos synchronization,” IEEE J. Quantum Electron.42, 953–960 (2006).
[CrossRef]

Locquet, A.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron.45, 879–891 (2009).
[CrossRef]

D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, “Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback,” Opt. Lett.32, 2960 (2007).
[CrossRef] [PubMed]

Lu, H. C.

Luo, B.

X. Li, W. Pan, B. Luo, and D. Ma, “Mismatch robustness and security of chaotic optical communications based on injection-locking chaos synchronization,” IEEE J. Quantum Electron.42, 953–960 (2006).
[CrossRef]

Ma, D.

X. Li, W. Pan, B. Luo, and D. Ma, “Mismatch robustness and security of chaotic optical communications based on injection-locking chaos synchronization,” IEEE J. Quantum Electron.42, 953–960 (2006).
[CrossRef]

Mirasso, C.

V. Z. Tronciu, C. Mirasso, P. Colet, M. Hamacher, M. Benedetti, V. Vercesi, and V. Annovazzi-Lodi, “Chaos generation and synchronization using an integrated source with an air gap,” IEEE J. Quantum Electron.46, 1840–1846 (2010).
[CrossRef]

Mirasso, C. R.

R. M. Nguimdo, P. Colet, and C. R. Mirasso, “Electro-optic delay devices with double feedback,” IEEE J. Quantum Electron.46, 1436–1443 (2010).
[CrossRef]

L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso, and C. R. Mirasso, “Permutation-information-theory approach to unveil delay dynamics from time-series analysis,” Phys. Rev. E82, 046212/1–9 (2010).
[CrossRef]

M. C. Soriano, P. Colet, and C. R. Mirasso, “Security implications of open- and closed-loop receivers in all-optical chaos-based communications,” IEEE Photon. Technol. Lett.21, 426–428 (2009).
[CrossRef]

C. R. Mirasso, P. Colet, and P. García-Fernández, “Synchronization of chaotic semicondcutor lasers: Application to encoded communications,” Phot. Tech. Lett.8, 299–301 (1996).
[CrossRef]

Mirasso, C.R.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C.R. Mirasso, L. Pesquera, and K.A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature438, 343–346 (2005).
[CrossRef] [PubMed]

S. Donati and C.R. Mirasso, “Feature section on optical chaos and applications to cryptography,” IEEE J. Quantum Electron.38, 1138–1184 (2002).
[CrossRef]

Nguimdo, R. M.

Ortin, S.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron.45, 879–891 (2009).
[CrossRef]

Ortín, S.

S. Ortín, J. Gutiérrez, L. Pesquera, and H. Vasquez, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A351, 133–141 (2005).
[CrossRef]

Pan, W.

X. Li, W. Pan, B. Luo, and D. Ma, “Mismatch robustness and security of chaotic optical communications based on injection-locking chaos synchronization,” IEEE J. Quantum Electron.42, 953–960 (2006).
[CrossRef]

Peil, M.

R. Lavrov, M. Peil, M. Jacquot, L. Larger, V. Udaltsov, and J. Dudley, “Electro-optic delay oscillator with nonlocal nonlinearity: Optical phase dynamics, chaos, and synchronization,” Phys. Rev. E80, 026207/1–9 (2009).
[CrossRef]

Pesquera, L.

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett.107, 034103/1–4 (2011).
[CrossRef]

S. Ortín, J. Gutiérrez, L. Pesquera, and H. Vasquez, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A351, 133–141 (2005).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C.R. Mirasso, L. Pesquera, and K.A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature438, 343–346 (2005).
[CrossRef] [PubMed]

Petermann, K.

L. Zimmermann, K. Voigt, G. Winzer, K. Petermann, and C. M. Weinert, “C-band optical 90°-hybrids based on silicon-on-insulator 4 × 4 waveguide couplers,” IEEE Photon. Technol. Lett.21 (3), 143 (2009).
[CrossRef]

Ponomarenko, V.I.

M.D. Prokhorov, V.I. Ponomarenko, A.S. Karavaev, and B.P. Bezruchko, “Reconstruction of time-delayed feedback systems from time series,” Physica D203, 209–223 (2005).
[CrossRef]

Porte, H.

J. P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett.80, 2249–2252 (1998).
[CrossRef]

Prokhorov, M.D.

M.D. Prokhorov, V.I. Ponomarenko, A.S. Karavaev, and B.P. Bezruchko, “Reconstruction of time-delayed feedback systems from time series,” Physica D203, 209–223 (2005).
[CrossRef]

Pyragas, K.

K. Pyragas, “Synchronization of coupled time-delay systems: Analytical estimations,” Phys. Rev. E58, 3067–3071 (1998).
[CrossRef]

Rhodes, W.T.

V.S. Udaltsov, J.-P. Goedgebuer, L. Larger, J.-B. Cuenot, Pascal Levy, and W.T. Rhodes, “Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations,” Phys. Lett. A308, 54–60 (2003).
[CrossRef]

Rontani, D.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron.45, 879–891 (2009).
[CrossRef]

D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, “Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback,” Opt. Lett.32, 2960 (2007).
[CrossRef] [PubMed]

Rosso, O. A.

L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso, and C. R. Mirasso, “Permutation-information-theory approach to unveil delay dynamics from time-series analysis,” Phys. Rev. E82, 046212/1–9 (2010).
[CrossRef]

Santagiustina, M.

U. Leonora, M. Santagiustina, and V. Annovazzi-Lodi, “Enhancing chaotic communication performances by Manchester coding”, IEEE Phot. Tech. Lett.20, 401–403 (2008).
[CrossRef]

Sciamanna, M.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron.45, 879–891 (2009).
[CrossRef]

D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, “Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback,” Opt. Lett.32, 2960 (2007).
[CrossRef] [PubMed]

Shore, K.A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C.R. Mirasso, L. Pesquera, and K.A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature438, 343–346 (2005).
[CrossRef] [PubMed]

Soriano, M. C.

R. M. Nguimdo, M. C. Soriano, and P. Colet, “Role of the phase in the identification of delay time in semiconductor lasers with optical feedback,” Opt. Lett.36, 4332–4334 (2011).
[CrossRef] [PubMed]

L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso, and C. R. Mirasso, “Permutation-information-theory approach to unveil delay dynamics from time-series analysis,” Phys. Rev. E82, 046212/1–9 (2010).
[CrossRef]

M. C. Soriano, P. Colet, and C. R. Mirasso, “Security implications of open- and closed-loop receivers in all-optical chaos-based communications,” IEEE Photon. Technol. Lett.21, 426–428 (2009).
[CrossRef]

Syvridis, D.

A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express, vol. 18, 5188–5198, 2010.
[CrossRef] [PubMed]

J. Hizanidis, S. Deligiannidis, A. Bogris, and D. Syvridis, “Enhancement of chaos encryption potential by combining all-optical and electrooptical chaos generators,” IEEE J. Quantum Electron.46, 1642–1649 (2010).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C.R. Mirasso, L. Pesquera, and K.A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature438, 343–346 (2005).
[CrossRef] [PubMed]

Tronciu, V. Z.

V. Z. Tronciu, C. Mirasso, P. Colet, M. Hamacher, M. Benedetti, V. Vercesi, and V. Annovazzi-Lodi, “Chaos generation and synchronization using an integrated source with an air gap,” IEEE J. Quantum Electron.46, 1840–1846 (2010).
[CrossRef]

Udaltsov, V.

R. Lavrov, M. Peil, M. Jacquot, L. Larger, V. Udaltsov, and J. Dudley, “Electro-optic delay oscillator with nonlocal nonlinearity: Optical phase dynamics, chaos, and synchronization,” Phys. Rev. E80, 026207/1–9 (2009).
[CrossRef]

L. Larger, J. Goedgebuer, and V. Udaltsov, “Ikeda-based nonlinear delayed dynamics for application to secure optical transmission systems using chaos,” Comptes Rendus Physique5, 669–681 (2004).
[CrossRef]

Udaltsov, V.S.

V.S. Udaltsov, J.-P. Goedgebuer, L. Larger, J.-B. Cuenot, Pascal Levy, and W.T. Rhodes, “Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations,” Phys. Lett. A308, 54–60 (2003).
[CrossRef]

Van der Sande, G.

Vasquez, H.

S. Ortín, J. Gutiérrez, L. Pesquera, and H. Vasquez, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A351, 133–141 (2005).
[CrossRef]

Vercesi, V.

V. Z. Tronciu, C. Mirasso, P. Colet, M. Hamacher, M. Benedetti, V. Vercesi, and V. Annovazzi-Lodi, “Chaos generation and synchronization using an integrated source with an air gap,” IEEE J. Quantum Electron.46, 1840–1846 (2010).
[CrossRef]

Verschaffelt, G.

Voigt, K.

L. Zimmermann, K. Voigt, G. Winzer, K. Petermann, and C. M. Weinert, “C-band optical 90°-hybrids based on silicon-on-insulator 4 × 4 waveguide couplers,” IEEE Photon. Technol. Lett.21 (3), 143 (2009).
[CrossRef]

Wang, H. C.

Weinert, C. M.

L. Zimmermann, K. Voigt, G. Winzer, K. Petermann, and C. M. Weinert, “C-band optical 90°-hybrids based on silicon-on-insulator 4 × 4 waveguide couplers,” IEEE Photon. Technol. Lett.21 (3), 143 (2009).
[CrossRef]

Winzer, G.

L. Zimmermann, K. Voigt, G. Winzer, K. Petermann, and C. M. Weinert, “C-band optical 90°-hybrids based on silicon-on-insulator 4 × 4 waveguide couplers,” IEEE Photon. Technol. Lett.21 (3), 143 (2009).
[CrossRef]

Zimmermann, L.

L. Zimmermann, K. Voigt, G. Winzer, K. Petermann, and C. M. Weinert, “C-band optical 90°-hybrids based on silicon-on-insulator 4 × 4 waveguide couplers,” IEEE Photon. Technol. Lett.21 (3), 143 (2009).
[CrossRef]

Zunino, L.

L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso, and C. R. Mirasso, “Permutation-information-theory approach to unveil delay dynamics from time-series analysis,” Phys. Rev. E82, 046212/1–9 (2010).
[CrossRef]

Comptes Rendus Physique (1)

L. Larger, J. Goedgebuer, and V. Udaltsov, “Ikeda-based nonlinear delayed dynamics for application to secure optical transmission systems using chaos,” Comptes Rendus Physique5, 669–681 (2004).
[CrossRef]

IEEE J. Quantum Electron. (8)

R. M. Nguimdo, P. Colet, and C. R. Mirasso, “Electro-optic delay devices with double feedback,” IEEE J. Quantum Electron.46, 1436–1443 (2010).
[CrossRef]

V. Z. Tronciu, C. Mirasso, P. Colet, M. Hamacher, M. Benedetti, V. Vercesi, and V. Annovazzi-Lodi, “Chaos generation and synchronization using an integrated source with an air gap,” IEEE J. Quantum Electron.46, 1840–1846 (2010).
[CrossRef]

S. Donati and C.R. Mirasso, “Feature section on optical chaos and applications to cryptography,” IEEE J. Quantum Electron.38, 1138–1184 (2002).
[CrossRef]

R. Lavrov, M. Jacquot, and L. Larger, “Nonlocal nonlinear electro-optic Phase dynamics demonstrating 10Gbs/s chaos communications,” IEEE J. Quantum Electron.46, 1430–1435 (2010).
[CrossRef]

X. Li, W. Pan, B. Luo, and D. Ma, “Mismatch robustness and security of chaotic optical communications based on injection-locking chaos synchronization,” IEEE J. Quantum Electron.42, 953–960 (2006).
[CrossRef]

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron.45, 879–891 (2009).
[CrossRef]

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

J. Hizanidis, S. Deligiannidis, A. Bogris, and D. Syvridis, “Enhancement of chaos encryption potential by combining all-optical and electrooptical chaos generators,” IEEE J. Quantum Electron.46, 1642–1649 (2010).
[CrossRef]

IEEE Phot. Tech. Lett. (1)

U. Leonora, M. Santagiustina, and V. Annovazzi-Lodi, “Enhancing chaotic communication performances by Manchester coding”, IEEE Phot. Tech. Lett.20, 401–403 (2008).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

M. C. Soriano, P. Colet, and C. R. Mirasso, “Security implications of open- and closed-loop receivers in all-optical chaos-based communications,” IEEE Photon. Technol. Lett.21, 426–428 (2009).
[CrossRef]

L. Zimmermann, K. Voigt, G. Winzer, K. Petermann, and C. M. Weinert, “C-band optical 90°-hybrids based on silicon-on-insulator 4 × 4 waveguide couplers,” IEEE Photon. Technol. Lett.21 (3), 143 (2009).
[CrossRef]

J. Lightwave Technol. (2)

Nature (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C.R. Mirasso, L. Pesquera, and K.A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature438, 343–346 (2005).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (3)

Phot. Tech. Lett. (1)

C. R. Mirasso, P. Colet, and P. García-Fernández, “Synchronization of chaotic semicondcutor lasers: Application to encoded communications,” Phot. Tech. Lett.8, 299–301 (1996).
[CrossRef]

Phys. Lett. A (1)

V.S. Udaltsov, J.-P. Goedgebuer, L. Larger, J.-B. Cuenot, Pascal Levy, and W.T. Rhodes, “Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations,” Phys. Lett. A308, 54–60 (2003).
[CrossRef]

Phys. Rev. E (5)

Y. Chembo Kouomou, P. Colet, N. Gastaud, and L. Larger, “Effect of parameter mismatch on the synchronization of semiconductor lasers with electrooptical feedback,” Phys. Rev. E69, 056226/1–15 (2004).

L. Larger, J. P. Goedgebuer, and F. Delorme, “Optical encryption system using hyperchaos generated by an optoelectronic wavelength oscillator,” Phys. Rev. E57, 6618–6624 (1998).
[CrossRef]

R. Lavrov, M. Peil, M. Jacquot, L. Larger, V. Udaltsov, and J. Dudley, “Electro-optic delay oscillator with nonlocal nonlinearity: Optical phase dynamics, chaos, and synchronization,” Phys. Rev. E80, 026207/1–9 (2009).
[CrossRef]

L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso, and C. R. Mirasso, “Permutation-information-theory approach to unveil delay dynamics from time-series analysis,” Phys. Rev. E82, 046212/1–9 (2010).
[CrossRef]

K. Pyragas, “Synchronization of coupled time-delay systems: Analytical estimations,” Phys. Rev. E58, 3067–3071 (1998).
[CrossRef]

Phys. Rev. Lett. (3)

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett.107, 034103/1–4 (2011).
[CrossRef]

R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett.81, 558–561 (1998).
[CrossRef]

J. P. Goedgebuer, L. Larger, and H. Porte, “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett.80, 2249–2252 (1998).
[CrossRef]

Physica A (1)

S. Ortín, J. Gutiérrez, L. Pesquera, and H. Vasquez, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A351, 133–141 (2005).
[CrossRef]

Physica D (1)

M.D. Prokhorov, V.I. Ponomarenko, A.S. Karavaev, and B.P. Bezruchko, “Reconstruction of time-delayed feedback systems from time series,” Physica D203, 209–223 (2005).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Transmitter and receiver setup in the parallel configuration: SL: semiconductor laser, PM: phase modulator, MZI: imbalanced Mach-Zehnder interferometer, PD: photodiode, x1(t) and x2(t) are the dimensionless output voltages of the RF drivers for the external and the internal loops while R(t) and m(t) are the pseudo-random bit sequence and message, respectively. Sub-index 1 refers to the loop whose output is transmitted while 2 refers to the internal loop.

Fig. 2
Fig. 2

Autocorrelation function C(s) (a) and delayed mutual information DMI(s) (b) of x1(t) without PRBS (red line), and with a PRBS of amplitude π/2 at 3 Gb/s (black). A time series of length 10 μs with 107 data points was used.

Fig. 3
Fig. 3

Autocorrelation function C(s) (a) and delayed mutual information DMI(s) (b) of x1(t) without PRBS (red line), and with a PRBS of amplitude of π/2 at 3 Gb/s (black). Parameters as in Fig. 2 but with δT1 = δT2 = 400 ps.

Fig. 4
Fig. 4

a) Autocorrelation function C(s) for the variable xsum(t) = x1(t)+ x2(t) considering the same parameters as in Fig. 2(b) Cross correlation between x1(t) and x2(t) as function of the mismatch in the differential delay time ξ = (δT2δT1)/δT1 for (•) ϕ1 = π/4 and ϕ2 = π/8 and (▵) ϕ1 = ϕ2 = π/4, considering δT1 = 400 ps.

Fig. 5
Fig. 5

Absolute value of the peaks in C(s) (a), and DMI (b), at T2 (•), T2 + δT2 (∇) as a function of mismatch ξ = (δT2δT1)/δT1 considering δT1 = 400 ps. Solid line and bars correspond to the background mean value and standard deviation. A series of length 267 times T was used.

Fig. 6
Fig. 6

(a) Largest conditional Lyapunov exponent (LCLE) versus G2 considering G1 = 5, (b) Synchronization error σ in logarithmic scale.

Fig. 7
Fig. 7

Influence of the PRBS-mismatch ratio η on (a) Synchronization evaluated through the root-mean square synchronization error σ without the message, and (b) on the BER for a 10Gb/s message. We have considered a PRBS R(t) of length 215 = 32768 bits generated at 3 Gb/s, G1 = 5 and G2 = 0 (□), G2 = 2 (▵), G2 = 3 (•).

Equations (11)

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

x i + τ i d x i d t + 1 θ i u i = G i cos 2 [ Δ ( x 1 + x 2 ) T i + Δ ( R + m ) T i + ϕ i ] ,
C ( s ) = [ x ( t ) x ( t ) ] [ x s ( t ) x ( t ) ] [ x ( t ) x ( t ) ] 2 ,
D M I ( s ) = x ( t ) , x s ( t ) p ( x ( t ) , x s ( t ) ) ln p ( x ( t ) , x s ( t ) ) p ( x ( t ) ) p ( x s ( t ) ) ) ,
X i ( ω ) ( 1 + j ω τ i + 1 j ω θ i ) = G i e j ω T i FT { cos 2 [ Δ ¯ ( x 1 + x 2 ) δ T i + Δ ¯ ( R ) δ T i + ϕ i ] } ,
X 1 ( ω ) X 2 ( ω ) = G 1 ( 1 + j ω τ 2 + 1 j ω θ 2 ) G 2 ( 1 + j ω τ 1 + 1 j ω θ 1 ) exp [ j ω ( T 1 T 2 ) ] .
y i + τ i d y i d t + 1 θ i v i = G i cos 2 [ Δ ( x 1 + y 2 ) T i + Δ ( R + m ) T i + ϕ i ] ,
P cos 2 [ Δ ¯ ( x 1 + m y 1 ) δ T m ]
λ L = lim t 1 t ln { [ T D 0 δ 1 2 ( t + t ) d t ] 1 / 2 [ T D 0 δ 1 2 ( t ) d t ] 1 / 2 } .
δ i + τ i δ i d t + 1 θ i ε i = G i Δ ( δ 2 ) T i sin [ 2 Δ ( x 1 + x 2 ) T i + 2 Δ ( R ) T i + 2 ϕ i ] ,
λ L = 1 4 τ 1 / θ 1 1 2 τ 1 1 θ 1 .
δ i + τ i d δ i d t + 1 θ i ε i = G i sin [ Δ ( δ 2 ) T i + Δ ( R R ) T i ] × sin [ 2 Δ ( x 1 + y 1 ) T i + Δ ( δ 2 ) T i + Δ ( R + R + 2 m ) T i + 2 ϕ i ] .

Metrics