Abstract

In this paper, evolution of time delay (TD) signature of chaos generated in a mutual delay-coupled semiconductor lasers (MDC-SLs) system is investigated experimentally and theoretically. Two statistical methods, including self-correlation function (SF) and permutation entropy (PE), are used to estimate the TD signature of chaotic time series. Through extracting the characteristic peak from the SF curve, a series of TD signature evolution maps are firstly obtained in the parameter space of coupled strength and frequency detuning. Meantime, the influences of injection current on the evolution maps of TD signature have been discussed, and the optimum scope of TD signature suppression is also specified. An overall qualitative agreement between our theoretical and experimental results is obtained.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279(5354), 1198–1200 (1998).
    [CrossRef] [PubMed]
  2. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
    [CrossRef] [PubMed]
  3. F.-Y. Lin and J.-M. Liu, “Diverse waveform generation using semiconductor lasers for radar and microwave applications,” IEEE J. Quantum Electron. 40(6), 682–689 (2004).
    [CrossRef]
  4. F.-Y. Lin and J.-M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10(5), 991–997 (2004).
    [CrossRef]
  5. M. Peil, I. Fischer, W. Elsäßer, S. Bakić, N. Damaschke, C. Tropea, S. Stry, and J. Sacher, “Rainbow refractometry with a tailored incoherent semiconductor laser source,” Appl. Phys. Lett. 89(9), 091106 (2006).
    [CrossRef]
  6. A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
    [CrossRef]
  7. I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102 (2009).
    [CrossRef] [PubMed]
  8. I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
    [CrossRef]
  9. A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010).
    [CrossRef] [PubMed]
  10. J. Ohtsubo, “Semiconductor Lasers: Stability, Instability and chaos,” Second Ed., Springer-Verlag, Berlin Heidelberg (2008).
  11. R. Vicente, J. Dauden, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron. 41(4), 541–548 (2005).
    [CrossRef]
  12. J. Paul, M. W. Lee, and K. A. Shore, “3.5-GHz signal transmission in an all-optical chaotic communication scheme using 1550-nm diode lasers,” IEEE Photon. Technol. Lett. 17(4), 920–922 (2005).
    [CrossRef]
  13. T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett. 86(5), 795–798 (2001).
    [CrossRef] [PubMed]
  14. E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 046201 (2006).
    [CrossRef] [PubMed]
  15. R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett. 32(4), 403–405 (2007).
    [CrossRef] [PubMed]
  16. W. L. Zhang, W. Pan, B. Luo, X. H. Zou, M. Y. Wang, and Z. Zhou, “Chaos synchronization communication using extremely unsymmetrical bidirectional injections,” Opt. Lett. 33(3), 237–239 (2008).
    [CrossRef] [PubMed]
  17. J. F. Martinez Avila and J. R. Rios Leite, “Time delays in the synchronization of chaotic coupled lasers with feedback,” Opt. Express 17(24), 21442–21451 (2009).
    [CrossRef] [PubMed]
  18. T. Deng, G. Q. Xia, Z. M. Wu, X. D. Lin, and J. G. Wu, “Chaos synchronization in mutually coupled semiconductor lasers with asymmetrical bias currents,” Opt. Express 19(9), 8762–8773 (2011).
    [CrossRef] [PubMed]
  19. H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys. 65(4), 1331–1392 (1993).
    [CrossRef]
  20. M. J. Bünner, M. Popp, T. Meyer, A. Kittel, and J. Parisi, “Tool to recover scalar time-delay systems from experimental time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(4), R3082–R3085 (1996).
    [CrossRef] [PubMed]
  21. H. Voss and J. Kurths, “Reconstruction of nonlinear time-delayed feedback models from optical data,” Chaos Solitons Fractals 10, 805–809 (1999).
  22. A. C. Fowler and G. Kember, “Delay recognition in chaotic time series,” Phys. Lett. A 175(6), 402–408 (1993).
    [CrossRef]
  23. M. D. Prokhorov, V. I. Ponomarenko, A. S. Karavaev, and B. P. Bezruchko, “Reconstruction of time-delayed feedback systems from time series,” Physica D 203(3-4), 209–223 (2005).
    [CrossRef]
  24. M. J. Bünner, T. Meyer, A. Kittel, and J. Parisi, “Recovery of the time-evolution equation of time-delay systems from time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(5), 5083–5089 (1997).
    [CrossRef]
  25. R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett. 81(3), 558–561 (1998).
    [CrossRef]
  26. S. Ortin, J. M. Gutierrez, L. Pesquera, and H. Vasquez, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A 351(1), 133–141 (2005).
    [CrossRef]
  27. V. S. Udaltsov, L. Larger, J. P. Goedgebuer, A. Locquet, and D. S. Citrin, “Time delay identification in chaotic cryptosystems ruled by delay-differential equations,” J. Opt. Technol. 72(5), 373–377 (2005).
    [CrossRef]
  28. 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(20), 2960–2962 (2007).
    [CrossRef] [PubMed]
  29. 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(7), 879–891 (2009).
    [CrossRef]
  30. J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
    [CrossRef] [PubMed]
  31. J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
    [CrossRef] [PubMed]
  32. C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Phys. Rev. Lett. 88(17), 174102 (2002).
    [CrossRef] [PubMed]
  33. 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. E Stat. Nonlin. Soft Matter Phys. 82(4), 046212 (2010).
    [CrossRef] [PubMed]
  34. M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
    [CrossRef]
  35. C. Zhou and C. H. Lai, “Extracting messages masked by chaotic signals of time-delay systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(1), 320–323 (1999).
    [CrossRef] [PubMed]
  36. V. S. Udaltsov, J. P. Goedgebuer, L. Larger, J. B. Cuenot, P. Levy, and W. T. Rhodes, “Cracking chaos-based encryption system ruled by nonlinear time delay differential equations,” Phys. Lett. A 308(1), 54–60 (2003).
    [CrossRef]
  37. 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(7), 426–428 (2009).
    [CrossRef]
  38. M. W. Lee, P. Rees, K. A. Shore, S. Ortin, L. Pesquera, and A. Valle, “Dynamical characterisation of laser diode subject to double optical feedback for chaotic optical communications,” IEE Proc., Optoelectron. 152(2), 97–102 (2005).
    [CrossRef]
  39. J. G. Wu, G. Q. Xia, L. P. Cao, and Z. M. Wu, “Experimental investigations on the external cavity time signature in chaotic output of an incoherent optical feedback external cavity semiconductor laser,” Opt. Commun. 282(15), 3153–3156 (2009).
    [CrossRef]
  40. E. M. Shahverdiev and K. A. Shore, “Erasure of time-delay signatures in the output of an opto-electronic feedback laser with modulated delays and chaos synchronisation,” IET Optoelectron. 3(6), 326–330 (2009).
    [CrossRef]
  41. J. G. Wu, Z. M. Wu, X. Tang, X. D. Lin, T. Deng, G. Q. Xia, and G. Y. Feng, “Simultaneous generation of two sets of time delay signature eliminated chaotic signals by using mutually coupled semiconductor lasers,” IEEE Photon. Technol. Lett. 23(12), 759–761 (2011).
    [CrossRef]
  42. 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(22), 4332–4334 (2011).
    [CrossRef] [PubMed]

2011

T. Deng, G. Q. Xia, Z. M. Wu, X. D. Lin, and J. G. Wu, “Chaos synchronization in mutually coupled semiconductor lasers with asymmetrical bias currents,” Opt. Express 19(9), 8762–8773 (2011).
[CrossRef] [PubMed]

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
[CrossRef]

J. G. Wu, Z. M. Wu, X. Tang, X. D. Lin, T. Deng, G. Q. Xia, and G. Y. Feng, “Simultaneous generation of two sets of time delay signature eliminated chaotic signals by using mutually coupled semiconductor lasers,” IEEE Photon. Technol. Lett. 23(12), 759–761 (2011).
[CrossRef]

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(22), 4332–4334 (2011).
[CrossRef] [PubMed]

2010

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. E Stat. Nonlin. Soft Matter Phys. 82(4), 046212 (2010).
[CrossRef] [PubMed]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[CrossRef] [PubMed]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[CrossRef]

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010).
[CrossRef] [PubMed]

2009

J. F. Martinez Avila and J. R. Rios Leite, “Time delays in the synchronization of chaotic coupled lasers with feedback,” Opt. Express 17(24), 21442–21451 (2009).
[CrossRef] [PubMed]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102 (2009).
[CrossRef] [PubMed]

J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
[CrossRef] [PubMed]

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(7), 879–891 (2009).
[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(7), 426–428 (2009).
[CrossRef]

J. G. Wu, G. Q. Xia, L. P. Cao, and Z. M. Wu, “Experimental investigations on the external cavity time signature in chaotic output of an incoherent optical feedback external cavity semiconductor laser,” Opt. Commun. 282(15), 3153–3156 (2009).
[CrossRef]

E. M. Shahverdiev and K. A. Shore, “Erasure of time-delay signatures in the output of an opto-electronic feedback laser with modulated delays and chaos synchronisation,” IET Optoelectron. 3(6), 326–330 (2009).
[CrossRef]

2008

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

W. L. Zhang, W. Pan, B. Luo, X. H. Zou, M. Y. Wang, and Z. Zhou, “Chaos synchronization communication using extremely unsymmetrical bidirectional injections,” Opt. Lett. 33(3), 237–239 (2008).
[CrossRef] [PubMed]

2007

2006

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 046201 (2006).
[CrossRef] [PubMed]

M. Peil, I. Fischer, W. Elsäßer, S. Bakić, N. Damaschke, C. Tropea, S. Stry, and J. Sacher, “Rainbow refractometry with a tailored incoherent semiconductor laser source,” Appl. Phys. Lett. 89(9), 091106 (2006).
[CrossRef]

2005

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[CrossRef] [PubMed]

R. Vicente, J. Dauden, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron. 41(4), 541–548 (2005).
[CrossRef]

J. Paul, M. W. Lee, and K. A. Shore, “3.5-GHz signal transmission in an all-optical chaotic communication scheme using 1550-nm diode lasers,” IEEE Photon. Technol. Lett. 17(4), 920–922 (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 D 203(3-4), 209–223 (2005).
[CrossRef]

S. Ortin, J. M. Gutierrez, L. Pesquera, and H. Vasquez, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A 351(1), 133–141 (2005).
[CrossRef]

V. S. Udaltsov, L. Larger, J. P. Goedgebuer, A. Locquet, and D. S. Citrin, “Time delay identification in chaotic cryptosystems ruled by delay-differential equations,” J. Opt. Technol. 72(5), 373–377 (2005).
[CrossRef]

M. W. Lee, P. Rees, K. A. Shore, S. Ortin, L. Pesquera, and A. Valle, “Dynamical characterisation of laser diode subject to double optical feedback for chaotic optical communications,” IEE Proc., Optoelectron. 152(2), 97–102 (2005).
[CrossRef]

2004

F.-Y. Lin and J.-M. Liu, “Diverse waveform generation using semiconductor lasers for radar and microwave applications,” IEEE J. Quantum Electron. 40(6), 682–689 (2004).
[CrossRef]

F.-Y. Lin and J.-M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10(5), 991–997 (2004).
[CrossRef]

2003

V. S. Udaltsov, J. P. Goedgebuer, L. Larger, J. B. Cuenot, P. Levy, and W. T. Rhodes, “Cracking chaos-based encryption system ruled by nonlinear time delay differential equations,” Phys. Lett. A 308(1), 54–60 (2003).
[CrossRef]

2002

C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Phys. Rev. Lett. 88(17), 174102 (2002).
[CrossRef] [PubMed]

2001

T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett. 86(5), 795–798 (2001).
[CrossRef] [PubMed]

1999

C. Zhou and C. H. Lai, “Extracting messages masked by chaotic signals of time-delay systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(1), 320–323 (1999).
[CrossRef] [PubMed]

H. Voss and J. Kurths, “Reconstruction of nonlinear time-delayed feedback models from optical data,” Chaos Solitons Fractals 10, 805–809 (1999).

1998

R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett. 81(3), 558–561 (1998).
[CrossRef]

G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279(5354), 1198–1200 (1998).
[CrossRef] [PubMed]

1997

M. J. Bünner, T. Meyer, A. Kittel, and J. Parisi, “Recovery of the time-evolution equation of time-delay systems from time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(5), 5083–5089 (1997).
[CrossRef]

1996

M. J. Bünner, M. Popp, T. Meyer, A. Kittel, and J. Parisi, “Tool to recover scalar time-delay systems from experimental time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(4), R3082–R3085 (1996).
[CrossRef] [PubMed]

1993

A. C. Fowler and G. Kember, “Delay recognition in chaotic time series,” Phys. Lett. A 175(6), 402–408 (1993).
[CrossRef]

H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys. 65(4), 1331–1392 (1993).
[CrossRef]

Abarbanel, H. D. I.

H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys. 65(4), 1331–1392 (1993).
[CrossRef]

Amano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Annovazzi-Lodi, V.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[CrossRef] [PubMed]

Argyris, A.

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010).
[CrossRef] [PubMed]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[CrossRef] [PubMed]

Aviad, Y.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[CrossRef]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102 (2009).
[CrossRef] [PubMed]

Bakic, S.

M. Peil, I. Fischer, W. Elsäßer, S. Bakić, N. Damaschke, C. Tropea, S. Stry, and J. Sacher, “Rainbow refractometry with a tailored incoherent semiconductor laser source,” Appl. Phys. Lett. 89(9), 091106 (2006).
[CrossRef]

Bandt, C.

C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Phys. Rev. Lett. 88(17), 174102 (2002).
[CrossRef] [PubMed]

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 D 203(3-4), 209–223 (2005).
[CrossRef]

Bogris, A.

Brown, R.

H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys. 65(4), 1331–1392 (1993).
[CrossRef]

Bünner, M. J.

R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett. 81(3), 558–561 (1998).
[CrossRef]

M. J. Bünner, T. Meyer, A. Kittel, and J. Parisi, “Recovery of the time-evolution equation of time-delay systems from time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(5), 5083–5089 (1997).
[CrossRef]

M. J. Bünner, M. Popp, T. Meyer, A. Kittel, and J. Parisi, “Tool to recover scalar time-delay systems from experimental time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(4), R3082–R3085 (1996).
[CrossRef] [PubMed]

Cao, L. P.

J. G. Wu, G. Q. Xia, L. P. Cao, and Z. M. Wu, “Experimental investigations on the external cavity time signature in chaotic output of an incoherent optical feedback external cavity semiconductor laser,” Opt. Commun. 282(15), 3153–3156 (2009).
[CrossRef]

Citrin, D. S.

Cohen, E.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[CrossRef]

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(22), 4332–4334 (2011).
[CrossRef] [PubMed]

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(7), 426–428 (2009).
[CrossRef]

R. Vicente, J. Dauden, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron. 41(4), 541–548 (2005).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[CrossRef] [PubMed]

Cuenot, J. B.

V. S. Udaltsov, J. P. Goedgebuer, L. Larger, J. B. Cuenot, P. Levy, and W. T. Rhodes, “Cracking chaos-based encryption system ruled by nonlinear time delay differential equations,” Phys. Lett. A 308(1), 54–60 (2003).
[CrossRef]

Damaschke, N.

M. Peil, I. Fischer, W. Elsäßer, S. Bakić, N. Damaschke, C. Tropea, S. Stry, and J. Sacher, “Rainbow refractometry with a tailored incoherent semiconductor laser source,” Appl. Phys. Lett. 89(9), 091106 (2006).
[CrossRef]

Dauden, J.

R. Vicente, J. Dauden, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron. 41(4), 541–548 (2005).
[CrossRef]

Davis, P.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Deligiannidis, S.

Deng, T.

Elsäßer, W.

M. Peil, I. Fischer, W. Elsäßer, S. Bakić, N. Damaschke, C. Tropea, S. Stry, and J. Sacher, “Rainbow refractometry with a tailored incoherent semiconductor laser source,” Appl. Phys. Lett. 89(9), 091106 (2006).
[CrossRef]

Elsässer, W.

T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett. 86(5), 795–798 (2001).
[CrossRef] [PubMed]

Fan, L.

Feng, G. Y.

J. G. Wu, Z. M. Wu, X. Tang, X. D. Lin, T. Deng, G. Q. Xia, and G. Y. Feng, “Simultaneous generation of two sets of time delay signature eliminated chaotic signals by using mutually coupled semiconductor lasers,” IEEE Photon. Technol. Lett. 23(12), 759–761 (2011).
[CrossRef]

Fischer, I.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
[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. E Stat. Nonlin. Soft Matter Phys. 82(4), 046212 (2010).
[CrossRef] [PubMed]

R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett. 32(4), 403–405 (2007).
[CrossRef] [PubMed]

M. Peil, I. Fischer, W. Elsäßer, S. Bakić, N. Damaschke, C. Tropea, S. Stry, and J. Sacher, “Rainbow refractometry with a tailored incoherent semiconductor laser source,” Appl. Phys. Lett. 89(9), 091106 (2006).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[CrossRef] [PubMed]

T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett. 86(5), 795–798 (2001).
[CrossRef] [PubMed]

Fowler, A. C.

A. C. Fowler and G. Kember, “Delay recognition in chaotic time series,” Phys. Lett. A 175(6), 402–408 (1993).
[CrossRef]

García-Ojalvo, J.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[CrossRef] [PubMed]

Giaquinta, A.

R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett. 81(3), 558–561 (1998).
[CrossRef]

Goedgebuer, J. P.

V. S. Udaltsov, L. Larger, J. P. Goedgebuer, A. Locquet, and D. S. Citrin, “Time delay identification in chaotic cryptosystems ruled by delay-differential equations,” J. Opt. Technol. 72(5), 373–377 (2005).
[CrossRef]

V. S. Udaltsov, J. P. Goedgebuer, L. Larger, J. B. Cuenot, P. Levy, and W. T. Rhodes, “Cracking chaos-based encryption system ruled by nonlinear time delay differential equations,” Phys. Lett. A 308(1), 54–60 (2003).
[CrossRef]

Gross, N.

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 046201 (2006).
[CrossRef] [PubMed]

Gutierrez, J. M.

S. Ortin, J. M. Gutierrez, L. Pesquera, and H. Vasquez, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A 351(1), 133–141 (2005).
[CrossRef]

Hegger, R.

R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett. 81(3), 558–561 (1998).
[CrossRef]

Heil, T.

T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett. 86(5), 795–798 (2001).
[CrossRef] [PubMed]

Hirano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Inoue, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Kanter, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[CrossRef]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102 (2009).
[CrossRef] [PubMed]

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 046201 (2006).
[CrossRef] [PubMed]

Kantz, H.

R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett. 81(3), 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 D 203(3-4), 209–223 (2005).
[CrossRef]

Kember, G.

A. C. Fowler and G. Kember, “Delay recognition in chaotic time series,” Phys. Lett. A 175(6), 402–408 (1993).
[CrossRef]

Khaykovich, L.

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 046201 (2006).
[CrossRef] [PubMed]

Kinzel, W.

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 046201 (2006).
[CrossRef] [PubMed]

Kittel, A.

M. J. Bünner, T. Meyer, A. Kittel, and J. Parisi, “Recovery of the time-evolution equation of time-delay systems from time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(5), 5083–5089 (1997).
[CrossRef]

M. J. Bünner, M. Popp, T. Meyer, A. Kittel, and J. Parisi, “Tool to recover scalar time-delay systems from experimental time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(4), R3082–R3085 (1996).
[CrossRef] [PubMed]

Klein, E.

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 046201 (2006).
[CrossRef] [PubMed]

Kopelowitz, E.

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 046201 (2006).
[CrossRef] [PubMed]

Kurashige, T.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Kurths, J.

H. Voss and J. Kurths, “Reconstruction of nonlinear time-delayed feedback models from optical data,” Chaos Solitons Fractals 10, 805–809 (1999).

Lai, C. H.

C. Zhou and C. H. Lai, “Extracting messages masked by chaotic signals of time-delay systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(1), 320–323 (1999).
[CrossRef] [PubMed]

Larger, L.

V. S. Udaltsov, L. Larger, J. P. Goedgebuer, A. Locquet, and D. S. Citrin, “Time delay identification in chaotic cryptosystems ruled by delay-differential equations,” J. Opt. Technol. 72(5), 373–377 (2005).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[CrossRef] [PubMed]

V. S. Udaltsov, J. P. Goedgebuer, L. Larger, J. B. Cuenot, P. Levy, and W. T. Rhodes, “Cracking chaos-based encryption system ruled by nonlinear time delay differential equations,” Phys. Lett. A 308(1), 54–60 (2003).
[CrossRef]

Lee, M. W.

M. W. Lee, P. Rees, K. A. Shore, S. Ortin, L. Pesquera, and A. Valle, “Dynamical characterisation of laser diode subject to double optical feedback for chaotic optical communications,” IEE Proc., Optoelectron. 152(2), 97–102 (2005).
[CrossRef]

J. Paul, M. W. Lee, and K. A. Shore, “3.5-GHz signal transmission in an all-optical chaotic communication scheme using 1550-nm diode lasers,” IEEE Photon. Technol. Lett. 17(4), 920–922 (2005).
[CrossRef]

Levy, P.

V. S. Udaltsov, J. P. Goedgebuer, L. Larger, J. B. Cuenot, P. Levy, and W. T. Rhodes, “Cracking chaos-based encryption system ruled by nonlinear time delay differential equations,” Phys. Lett. A 308(1), 54–60 (2003).
[CrossRef]

Lin, F.-Y.

F.-Y. Lin and J.-M. Liu, “Diverse waveform generation using semiconductor lasers for radar and microwave applications,” IEEE J. Quantum Electron. 40(6), 682–689 (2004).
[CrossRef]

F.-Y. Lin and J.-M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10(5), 991–997 (2004).
[CrossRef]

Lin, X. D.

Liu, J.-M.

F.-Y. Lin and J.-M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10(5), 991–997 (2004).
[CrossRef]

F.-Y. Lin and J.-M. Liu, “Diverse waveform generation using semiconductor lasers for radar and microwave applications,” IEEE J. Quantum Electron. 40(6), 682–689 (2004).
[CrossRef]

Locquet, A.

Luo, B.

Martinez Avila, J. F.

Meyer, T.

M. J. Bünner, T. Meyer, A. Kittel, and J. Parisi, “Recovery of the time-evolution equation of time-delay systems from time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(5), 5083–5089 (1997).
[CrossRef]

M. J. Bünner, M. Popp, T. Meyer, A. Kittel, and J. Parisi, “Tool to recover scalar time-delay systems from experimental time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(4), R3082–R3085 (1996).
[CrossRef] [PubMed]

Mirasso, C. R.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
[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. E Stat. Nonlin. Soft Matter Phys. 82(4), 046212 (2010).
[CrossRef] [PubMed]

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(7), 426–428 (2009).
[CrossRef]

R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett. 32(4), 403–405 (2007).
[CrossRef] [PubMed]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[CrossRef] [PubMed]

T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett. 86(5), 795–798 (2001).
[CrossRef] [PubMed]

Mulet, J.

T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett. 86(5), 795–798 (2001).
[CrossRef] [PubMed]

Naito, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Nguimdo, R. M.

Oowada, I.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

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(7), 879–891 (2009).
[CrossRef]

S. Ortin, J. M. Gutierrez, L. Pesquera, and H. Vasquez, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A 351(1), 133–141 (2005).
[CrossRef]

M. W. Lee, P. Rees, K. A. Shore, S. Ortin, L. Pesquera, and A. Valle, “Dynamical characterisation of laser diode subject to double optical feedback for chaotic optical communications,” IEE Proc., Optoelectron. 152(2), 97–102 (2005).
[CrossRef]

Pan, W.

Parisi, J.

M. J. Bünner, T. Meyer, A. Kittel, and J. Parisi, “Recovery of the time-evolution equation of time-delay systems from time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(5), 5083–5089 (1997).
[CrossRef]

M. J. Bünner, M. Popp, T. Meyer, A. Kittel, and J. Parisi, “Tool to recover scalar time-delay systems from experimental time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(4), R3082–R3085 (1996).
[CrossRef] [PubMed]

Paul, J.

J. Paul, M. W. Lee, and K. A. Shore, “3.5-GHz signal transmission in an all-optical chaotic communication scheme using 1550-nm diode lasers,” IEEE Photon. Technol. Lett. 17(4), 920–922 (2005).
[CrossRef]

Peil, M.

M. Peil, I. Fischer, W. Elsäßer, S. Bakić, N. Damaschke, C. Tropea, S. Stry, and J. Sacher, “Rainbow refractometry with a tailored incoherent semiconductor laser source,” Appl. Phys. Lett. 89(9), 091106 (2006).
[CrossRef]

Pesquera, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[CrossRef] [PubMed]

S. Ortin, J. M. Gutierrez, L. Pesquera, and H. Vasquez, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A 351(1), 133–141 (2005).
[CrossRef]

M. W. Lee, P. Rees, K. A. Shore, S. Ortin, L. Pesquera, and A. Valle, “Dynamical characterisation of laser diode subject to double optical feedback for chaotic optical communications,” IEE Proc., Optoelectron. 152(2), 97–102 (2005).
[CrossRef]

Pikasis, E.

Pompe, B.

C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Phys. Rev. Lett. 88(17), 174102 (2002).
[CrossRef] [PubMed]

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 D 203(3-4), 209–223 (2005).
[CrossRef]

Popp, M.

M. J. Bünner, M. Popp, T. Meyer, A. Kittel, and J. Parisi, “Tool to recover scalar time-delay systems from experimental time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(4), R3082–R3085 (1996).
[CrossRef] [PubMed]

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 D 203(3-4), 209–223 (2005).
[CrossRef]

Rees, P.

M. W. Lee, P. Rees, K. A. Shore, S. Ortin, L. Pesquera, and A. Valle, “Dynamical characterisation of laser diode subject to double optical feedback for chaotic optical communications,” IEE Proc., Optoelectron. 152(2), 97–102 (2005).
[CrossRef]

Reidler, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[CrossRef]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102 (2009).
[CrossRef] [PubMed]

Rhodes, W. T.

V. S. Udaltsov, J. P. Goedgebuer, L. Larger, J. B. Cuenot, P. Levy, and W. T. Rhodes, “Cracking chaos-based encryption system ruled by nonlinear time delay differential equations,” Phys. Lett. A 308(1), 54–60 (2003).
[CrossRef]

Rios Leite, J. R.

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(7), 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(20), 2960–2962 (2007).
[CrossRef] [PubMed]

Rosenbluh, M.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[CrossRef]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102 (2009).
[CrossRef] [PubMed]

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 046201 (2006).
[CrossRef] [PubMed]

Rosso, O. A.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
[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. E Stat. Nonlin. Soft Matter Phys. 82(4), 046212 (2010).
[CrossRef] [PubMed]

Roy, R.

G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279(5354), 1198–1200 (1998).
[CrossRef] [PubMed]

Sacher, J.

M. Peil, I. Fischer, W. Elsäßer, S. Bakić, N. Damaschke, C. Tropea, S. Stry, and J. Sacher, “Rainbow refractometry with a tailored incoherent semiconductor laser source,” Appl. Phys. Lett. 89(9), 091106 (2006).
[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(7), 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(20), 2960–2962 (2007).
[CrossRef] [PubMed]

Shahverdiev, E. M.

E. M. Shahverdiev and K. A. Shore, “Erasure of time-delay signatures in the output of an opto-electronic feedback laser with modulated delays and chaos synchronisation,” IET Optoelectron. 3(6), 326–330 (2009).
[CrossRef]

Shiki, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Shore, K. A.

E. M. Shahverdiev and K. A. Shore, “Erasure of time-delay signatures in the output of an opto-electronic feedback laser with modulated delays and chaos synchronisation,” IET Optoelectron. 3(6), 326–330 (2009).
[CrossRef]

M. W. Lee, P. Rees, K. A. Shore, S. Ortin, L. Pesquera, and A. Valle, “Dynamical characterisation of laser diode subject to double optical feedback for chaotic optical communications,” IEE Proc., Optoelectron. 152(2), 97–102 (2005).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[CrossRef] [PubMed]

J. Paul, M. W. Lee, and K. A. Shore, “3.5-GHz signal transmission in an all-optical chaotic communication scheme using 1550-nm diode lasers,” IEEE Photon. Technol. Lett. 17(4), 920–922 (2005).
[CrossRef]

Sidorowich, J. J.

H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys. 65(4), 1331–1392 (1993).
[CrossRef]

Someya, H.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Soriano, M. C.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
[CrossRef]

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(22), 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. E Stat. Nonlin. Soft Matter Phys. 82(4), 046212 (2010).
[CrossRef] [PubMed]

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(7), 426–428 (2009).
[CrossRef]

Stry, S.

M. Peil, I. Fischer, W. Elsäßer, S. Bakić, N. Damaschke, C. Tropea, S. Stry, and J. Sacher, “Rainbow refractometry with a tailored incoherent semiconductor laser source,” Appl. Phys. Lett. 89(9), 091106 (2006).
[CrossRef]

Syvridis, D.

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010).
[CrossRef] [PubMed]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[CrossRef] [PubMed]

Tang, X.

J. G. Wu, Z. M. Wu, X. Tang, X. D. Lin, T. Deng, G. Q. Xia, and G. Y. Feng, “Simultaneous generation of two sets of time delay signature eliminated chaotic signals by using mutually coupled semiconductor lasers,” IEEE Photon. Technol. Lett. 23(12), 759–761 (2011).
[CrossRef]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[CrossRef] [PubMed]

Toral, R.

R. Vicente, J. Dauden, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron. 41(4), 541–548 (2005).
[CrossRef]

Tropea, C.

M. Peil, I. Fischer, W. Elsäßer, S. Bakić, N. Damaschke, C. Tropea, S. Stry, and J. Sacher, “Rainbow refractometry with a tailored incoherent semiconductor laser source,” Appl. Phys. Lett. 89(9), 091106 (2006).
[CrossRef]

Tsimring, L. S.

H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys. 65(4), 1331–1392 (1993).
[CrossRef]

Uchida, A.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Udaltsov, V. S.

V. S. Udaltsov, L. Larger, J. P. Goedgebuer, A. Locquet, and D. S. Citrin, “Time delay identification in chaotic cryptosystems ruled by delay-differential equations,” J. Opt. Technol. 72(5), 373–377 (2005).
[CrossRef]

V. S. Udaltsov, J. P. Goedgebuer, L. Larger, J. B. Cuenot, P. Levy, and W. T. Rhodes, “Cracking chaos-based encryption system ruled by nonlinear time delay differential equations,” Phys. Lett. A 308(1), 54–60 (2003).
[CrossRef]

Valle, A.

M. W. Lee, P. Rees, K. A. Shore, S. Ortin, L. Pesquera, and A. Valle, “Dynamical characterisation of laser diode subject to double optical feedback for chaotic optical communications,” IEE Proc., Optoelectron. 152(2), 97–102 (2005).
[CrossRef]

VanWiggeren, G. D.

G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279(5354), 1198–1200 (1998).
[CrossRef] [PubMed]

Vasquez, H.

S. Ortin, J. M. Gutierrez, L. Pesquera, and H. Vasquez, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A 351(1), 133–141 (2005).
[CrossRef]

Vicente, R.

R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett. 32(4), 403–405 (2007).
[CrossRef] [PubMed]

R. Vicente, J. Dauden, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron. 41(4), 541–548 (2005).
[CrossRef]

Voss, H.

H. Voss and J. Kurths, “Reconstruction of nonlinear time-delayed feedback models from optical data,” Chaos Solitons Fractals 10, 805–809 (1999).

Wang, M. Y.

Wu, J. G.

T. Deng, G. Q. Xia, Z. M. Wu, X. D. Lin, and J. G. Wu, “Chaos synchronization in mutually coupled semiconductor lasers with asymmetrical bias currents,” Opt. Express 19(9), 8762–8773 (2011).
[CrossRef] [PubMed]

J. G. Wu, Z. M. Wu, X. Tang, X. D. Lin, T. Deng, G. Q. Xia, and G. Y. Feng, “Simultaneous generation of two sets of time delay signature eliminated chaotic signals by using mutually coupled semiconductor lasers,” IEEE Photon. Technol. Lett. 23(12), 759–761 (2011).
[CrossRef]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[CrossRef] [PubMed]

J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
[CrossRef] [PubMed]

J. G. Wu, G. Q. Xia, L. P. Cao, and Z. M. Wu, “Experimental investigations on the external cavity time signature in chaotic output of an incoherent optical feedback external cavity semiconductor laser,” Opt. Commun. 282(15), 3153–3156 (2009).
[CrossRef]

Wu, Z. M.

J. G. Wu, Z. M. Wu, X. Tang, X. D. Lin, T. Deng, G. Q. Xia, and G. Y. Feng, “Simultaneous generation of two sets of time delay signature eliminated chaotic signals by using mutually coupled semiconductor lasers,” IEEE Photon. Technol. Lett. 23(12), 759–761 (2011).
[CrossRef]

T. Deng, G. Q. Xia, Z. M. Wu, X. D. Lin, and J. G. Wu, “Chaos synchronization in mutually coupled semiconductor lasers with asymmetrical bias currents,” Opt. Express 19(9), 8762–8773 (2011).
[CrossRef] [PubMed]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[CrossRef] [PubMed]

J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
[CrossRef] [PubMed]

J. G. Wu, G. Q. Xia, L. P. Cao, and Z. M. Wu, “Experimental investigations on the external cavity time signature in chaotic output of an incoherent optical feedback external cavity semiconductor laser,” Opt. Commun. 282(15), 3153–3156 (2009).
[CrossRef]

Xia, G. Q.

J. G. Wu, Z. M. Wu, X. Tang, X. D. Lin, T. Deng, G. Q. Xia, and G. Y. Feng, “Simultaneous generation of two sets of time delay signature eliminated chaotic signals by using mutually coupled semiconductor lasers,” IEEE Photon. Technol. Lett. 23(12), 759–761 (2011).
[CrossRef]

T. Deng, G. Q. Xia, Z. M. Wu, X. D. Lin, and J. G. Wu, “Chaos synchronization in mutually coupled semiconductor lasers with asymmetrical bias currents,” Opt. Express 19(9), 8762–8773 (2011).
[CrossRef] [PubMed]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[CrossRef] [PubMed]

J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
[CrossRef] [PubMed]

J. G. Wu, G. Q. Xia, L. P. Cao, and Z. M. Wu, “Experimental investigations on the external cavity time signature in chaotic output of an incoherent optical feedback external cavity semiconductor laser,” Opt. Commun. 282(15), 3153–3156 (2009).
[CrossRef]

Yoshimori, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Yoshimura, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Zhang, W. L.

Zhou, C.

C. Zhou and C. H. Lai, “Extracting messages masked by chaotic signals of time-delay systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(1), 320–323 (1999).
[CrossRef] [PubMed]

Zhou, Z.

Zou, X. H.

Zunino, L.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
[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. E Stat. Nonlin. Soft Matter Phys. 82(4), 046212 (2010).
[CrossRef] [PubMed]

Appl. Phys. Lett.

M. Peil, I. Fischer, W. Elsäßer, S. Bakić, N. Damaschke, C. Tropea, S. Stry, and J. Sacher, “Rainbow refractometry with a tailored incoherent semiconductor laser source,” Appl. Phys. Lett. 89(9), 091106 (2006).
[CrossRef]

Chaos Solitons Fractals

H. Voss and J. Kurths, “Reconstruction of nonlinear time-delayed feedback models from optical data,” Chaos Solitons Fractals 10, 805–809 (1999).

IEE Proc., Optoelectron.

M. W. Lee, P. Rees, K. A. Shore, S. Ortin, L. Pesquera, and A. Valle, “Dynamical characterisation of laser diode subject to double optical feedback for chaotic optical communications,” IEE Proc., Optoelectron. 152(2), 97–102 (2005).
[CrossRef]

IEEE J. Quantum Electron.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
[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(7), 879–891 (2009).
[CrossRef]

F.-Y. Lin and J.-M. Liu, “Diverse waveform generation using semiconductor lasers for radar and microwave applications,” IEEE J. Quantum Electron. 40(6), 682–689 (2004).
[CrossRef]

R. Vicente, J. Dauden, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron. 41(4), 541–548 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

F.-Y. Lin and J.-M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10(5), 991–997 (2004).
[CrossRef]

IEEE Photon. Technol. Lett.

J. Paul, M. W. Lee, and K. A. Shore, “3.5-GHz signal transmission in an all-optical chaotic communication scheme using 1550-nm diode lasers,” IEEE Photon. Technol. Lett. 17(4), 920–922 (2005).
[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(7), 426–428 (2009).
[CrossRef]

J. G. Wu, Z. M. Wu, X. Tang, X. D. Lin, T. Deng, G. Q. Xia, and G. Y. Feng, “Simultaneous generation of two sets of time delay signature eliminated chaotic signals by using mutually coupled semiconductor lasers,” IEEE Photon. Technol. Lett. 23(12), 759–761 (2011).
[CrossRef]

IET Optoelectron.

E. M. Shahverdiev and K. A. Shore, “Erasure of time-delay signatures in the output of an opto-electronic feedback laser with modulated delays and chaos synchronisation,” IET Optoelectron. 3(6), 326–330 (2009).
[CrossRef]

J. Opt. Technol.

Nat. Photonics

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[CrossRef]

Nature

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[CrossRef] [PubMed]

Opt. Commun.

J. G. Wu, G. Q. Xia, L. P. Cao, and Z. M. Wu, “Experimental investigations on the external cavity time signature in chaotic output of an incoherent optical feedback external cavity semiconductor laser,” Opt. Commun. 282(15), 3153–3156 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

V. S. Udaltsov, J. P. Goedgebuer, L. Larger, J. B. Cuenot, P. Levy, and W. T. Rhodes, “Cracking chaos-based encryption system ruled by nonlinear time delay differential equations,” Phys. Lett. A 308(1), 54–60 (2003).
[CrossRef]

A. C. Fowler and G. Kember, “Delay recognition in chaotic time series,” Phys. Lett. A 175(6), 402–408 (1993).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

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. E Stat. Nonlin. Soft Matter Phys. 82(4), 046212 (2010).
[CrossRef] [PubMed]

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 046201 (2006).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics

M. J. Bünner, M. Popp, T. Meyer, A. Kittel, and J. Parisi, “Tool to recover scalar time-delay systems from experimental time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(4), R3082–R3085 (1996).
[CrossRef] [PubMed]

C. Zhou and C. H. Lai, “Extracting messages masked by chaotic signals of time-delay systems,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60(1), 320–323 (1999).
[CrossRef] [PubMed]

M. J. Bünner, T. Meyer, A. Kittel, and J. Parisi, “Recovery of the time-evolution equation of time-delay systems from time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(5), 5083–5089 (1997).
[CrossRef]

Phys. Rev. Lett.

R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett. 81(3), 558–561 (1998).
[CrossRef]

C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Phys. Rev. Lett. 88(17), 174102 (2002).
[CrossRef] [PubMed]

T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett. 86(5), 795–798 (2001).
[CrossRef] [PubMed]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102 (2009).
[CrossRef] [PubMed]

Physica A

S. Ortin, J. M. Gutierrez, L. Pesquera, and H. Vasquez, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A 351(1), 133–141 (2005).
[CrossRef]

Physica D

M. D. Prokhorov, V. I. Ponomarenko, A. S. Karavaev, and B. P. Bezruchko, “Reconstruction of time-delayed feedback systems from time series,” Physica D 203(3-4), 209–223 (2005).
[CrossRef]

Rev. Mod. Phys.

H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, “The analysis of observed chaotic data in physical systems,” Rev. Mod. Phys. 65(4), 1331–1392 (1993).
[CrossRef]

Science

G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279(5354), 1198–1200 (1998).
[CrossRef] [PubMed]

Other

J. Ohtsubo, “Semiconductor Lasers: Stability, Instability and chaos,” Second Ed., Springer-Verlag, Berlin Heidelberg (2008).

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 (9)

Fig. 1
Fig. 1

Schematic of the MDC-SLs system. SL: Distributed Feedback Bragg semiconductor laser; PC: polarization controller; VA: variable attenuator; OI: optical isolator; PD: photodetector; OSA: optical spectrum analyzer; PM: optical power meter.

Fig. 2
Fig. 2

Recorded chaotic time series (the first column), associated power spectra (the second column), SF curves (the third column) and PE curves (the fourth column) under fixed frequency detuning ∆f≈0GHz and different κ values, where κ is about 0.0003 (Aa1-Aa4, Ba1-Ba4), 0.0007 (Ab1-Ab4, Bb1-Bb4), 0.0068 (Ac1-Ac4, Bc1-Bc4), 0.023 (Ad1-Ad4, Bd1-Bd4), 0.145 (Ae1-Ae4, Be1-Be4), respectively. A corresponds to SL1, and B is for SL2. The power spectra, SF curves and PE curves are calculated from the recorded chaotic time series with a 1000ns length.

Fig. 3
Fig. 3

Recorded chaotic time series (the first column), associated power spectra (the second column), SF curves (the third column) and PE curves (the forth column) under fixed κ≈0.008 and different frequency detuning ∆f≈9.0GHz (Aa1-Aa4, Ba1-Ba4), ∆f≈5.7GHz (Ab1-Ab4, Bb1-Bb4), ∆f≈-1.1GHz (Ac1-Ac4, Bc1-Bc4), ∆f≈-5.3GHz (Ad1-Ad4, Bd1-Bd4) and ∆f≈-10.8GHz (Ae1-Ae4, Be1-Be4). A corresponds to SL1, and B is for SL2. The power spectra, SF curves and PE curves are calculated from the recorded chaotic time series with a 1000ns length.

Fig. 4
Fig. 4

Evolution maps of TD signature in parameter space of κ and ∆f when κ varies from 0.002 to 0.025 and ∆f changes from −15GHz to 15GHz. The amplitude ρ is the maximum peak of SF curves in time window 52ns<∆t<55ns. The different colors represent different values of amplitude ρ. A corresponds to SL1 and B is for SL2.

Fig. 5
Fig. 5

The evolution maps of TD signature under different injection currents of SLs. The first row: the injection current is 9.64mA (1.18Ith) for SL1 and 10.2mA (1.20Ith) for SL2. The second row: the injection current is 10.53mA (1.29Ith) for SL1 and 11.1mA (1.31Ith) for SL2. The third row: the injection current is 12.2mA (1.49Ith) for SL1 and 12.8mA (1.51Ith) for SL2. The different colors represent different strength of TD signature. A corresponds to SL1, and B is for SL2.

Fig. 6
Fig. 6

Combination of simulated temporal traces of SLs (the first column), power spectra (the second column), SF curves (the third column) and PE curves (the forth column) under fixed ∆f≈0GHz and different values of η, where η is 2ns−1 (Aa1-Aa4, Ba1-Ba4), 2.5ns−1 (Ab1-Ab4, Bb1-Bb4), 7.5ns−1 (Ac1-Ac4, Bc1-Bc4), 15ns−1 (Ad1-Ad4, Bd1-Bd4) and 25ns−1 (Ae1-Ae4, Be1-Be4), respectively. A corresponds to SL1, and B is for SL2. The power spectra, SF curves and PE curves are calculated from the chaotic time series with a 1000ns length.

Fig. 7
Fig. 7

Combination of the simulated temporal traces of SLs (the first column), power spectra (the second column), SF curves (the third column) and PE curves (the forth column) under fixed η≈7.5ns−1 and different values of ∆f, where ∆f≈9.5GHz (Aa1-Aa4, Ba1-Ba4), ∆f≈7GHz (Ab1-Ab4, Bb1-Bb4), ∆f≈0GHz (Ac1-Ac4, Bc1-Bc4), ∆f≈-7GHz (Ad1-Ad4, Bd1-Bd4), ∆f≈-9.5GHz (Ae1-Ae4, Be1-Be4), respectively. A corresponds to SL1, and B is for SL2. The power spectra, SF curves and PE curves are calculated from the chaotic time series with a 1000ns length.

Fig. 8
Fig. 8

Simulated evolution maps of TD signature in the parameter space of η and ∆f for different J of SLs. The first row: J is 1.15Ith for SL1 and SL2;The second row: J is 1.3Ith for SL1 and SL2; The third row: J is 1.5Ith for SL1 and SL2. The different colors represent different strength of TD signature. The amplitude ρ is the maximum peak of SF curves in time window 6ns<∆t<10ns. A corresponds to SL1, and B is for SL2.

Fig. 9
Fig. 9

A: Comparison between incident chaotic time series (red line) from SL1 and regenerated chaotic time series (black line) by SL2. B: Correlation diagram of incident signal and regenerated signal

Equations (4)

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

C(Δt)= ( P(t+Δt) P(t) )( P(t) P(t) ) ( P(t) P(t) 2 P(t+Δt) P(t) 2 ) 1/2
E ˙ 1 (t)= 1 2 (1+i β 1 )[ g 1 ( N 1 (t) N 0 ) 1+ε E 1 (t) 2 1 τ p1 ] E 1 (t)+η E 2 (t τ 2 ) e i2π( f 2 τ 2 +Δft) + F 1 (t)
E ˙ 2 (t)= 1 2 (1+i β 2 )[ g 2 ( N 2 (t) N 0 ) 1+ε E 2 (t) 2 1 τ p2 ] E 2 (t)+η E 1 (t τ 2 ) e i2π( f 1 τ 2 Δft) + F 2 (t)
N ˙ 1,2 (t)=J N 1,2 (t)/ τ N g 1,2 ( N 1,2 (t) N 0 ) 1+ε E 1,2 (t) 2 | E 1,2 (t) | 2

Metrics