Abstract

The practical application of chaotic optical communications has been limited by two aspects: the difficulty in concealing the time delay - a critical security parameter in feedback chaotic systems, and the difficulty of significantly enlarging the key space without complicating the implementation. Here we propose an architecture to break the above limits. By introducing a frequency-dependent group delay module with frequency tuning resolution of 1 MHz into the chaotic feedback loop, we demonstrate excellent time delay concealment effect, and an additional huge key space of 1048 can be achieved at the same time. The effectiveness is proved by both numerical simulation and experiment. Besides, the proposed scheme is compatible with the existing commercial optical communication systems, thus pave the way for high-speed secure optical communications.

© 2016 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  14. S. Ortin, J. M. Gutie-rezc, L. Pesqueraa, and H. Vasqueza, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A 351, 133–141 (2005).
  15. 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).
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    [Crossref]
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    [Crossref]
  21. R. M. Nguimdo, P. Colet, and C. Mirasso, “Electro-optic delay devices with double feedback,” IEEE J. Quantum Electron. 46(10), 1436–1443 (2010).
    [Crossref]
  22. J. Hizanidis, S. Deligiannidis, A. Bogris, and D. Syvridis, “Enhancement of chaos encryption potential by combining all-optical and electro-optical chaos generators,” IEEE J. Quantum Electron. 46(11), 1642–1649 (2010).
    [Crossref]
  23. R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett. 107(3), 034103 (2011).
    [Crossref] [PubMed]
  24. R. M. Nguimdo and P. Colet, “Electro-optic phase chaos systems with an internal variable and a digital key,” Opt. Express 20(23), 25333–25344 (2012).
    [Crossref] [PubMed]
  25. Z. Wang, “Optical Steganography Over a Public DPSK Channel with Asynchronous Detection,” IEEE J. Quantum Electron. 13, 48–50 (2011).
  26. Z. Wang, M. P. Fok, L. Xu, J. Chang, and P. R. Prucnal, “Improving the privacy of optical steganography with temporal phase masks,” Opt. Express 18(6), 6079–6088 (2010).
    [Crossref] [PubMed]
  27. N. Kostinski, K. Kravtsov, and P. R. Prucnal, “Demonstration of an all-optical OCDMA encryption and decryption system with variable two-code keying,” IEEE Photon. Technol. Lett. 20(24), 2045–2047 (2008).
    [Crossref]
  28. S. S. Li, Q. Liu, and S. C. Chan, “Distributed feedbacks for time-delay signature suppression of chaos generated from a semiconductor laser,” IEEE Photon. J. 4(5), 1930–1935 (2012).
    [Crossref]
  29. J. R. Kuttler and G. D. Dockery, “Theoretical description of the parabolic approximation/Fourier split-step method of representing electromagnetic propagation in the troposphere,” Radio Sci. 26(2), 381–393 (1991).
    [Crossref]

2013 (1)

G. Aromataris and V. Annovazzi-Lodi, “Enhancing privacy of chaotic communications by double masking,” IEEE J. Quantum Electron. 49(11), 955–959 (2013).
[Crossref]

2012 (3)

Y. Wu, “Can fixed time delay signature be concealed in chaotic semiconductor laser with optical feedback?” IEEE J. Quantum Electron. 48(11), 1371–1379 (2012).
[Crossref]

S. S. Li, Q. Liu, and S. C. Chan, “Distributed feedbacks for time-delay signature suppression of chaos generated from a semiconductor laser,” IEEE Photon. J. 4(5), 1930–1935 (2012).
[Crossref]

R. M. Nguimdo and P. Colet, “Electro-optic phase chaos systems with an internal variable and a digital key,” Opt. Express 20(23), 25333–25344 (2012).
[Crossref] [PubMed]

2011 (2)

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett. 107(3), 034103 (2011).
[Crossref] [PubMed]

Z. Wang, “Optical Steganography Over a Public DPSK Channel with Asynchronous Detection,” IEEE J. Quantum Electron. 13, 48–50 (2011).

2010 (4)

Z. Wang, M. P. Fok, L. Xu, J. Chang, and P. R. Prucnal, “Improving the privacy of optical steganography with temporal phase masks,” Opt. Express 18(6), 6079–6088 (2010).
[Crossref] [PubMed]

R. M. Nguimdo, P. Colet, and C. Mirasso, “Electro-optic delay devices with double feedback,” IEEE J. Quantum Electron. 46(10), 1436–1443 (2010).
[Crossref]

J. Hizanidis, S. Deligiannidis, A. Bogris, and D. Syvridis, “Enhancement of chaos encryption potential by combining all-optical and electro-optical chaos generators,” IEEE J. Quantum Electron. 46(11), 1642–1649 (2010).
[Crossref]

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

2009 (3)

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. E Stat. Nonlin. Soft Matter Phys. 80(2), 026207 (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), 879–1891 (2009).
[Crossref]

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]

2008 (3)

N. Kostinski, K. Kravtsov, and P. R. Prucnal, “Demonstration of an all-optical OCDMA encryption and decryption system with variable two-code keying,” IEEE Photon. Technol. Lett. 20(24), 2045–2047 (2008).
[Crossref]

L. Ursini, M. Santagiustina, and V. Annovazzi Lodi, “Enhancing Chaotic Communication Performances by Manchester Coding,” IEEE Photonics Technol. Lett. 20(6), 401–403 (2008).
[Crossref]

S. Ortin, M. Jacquot, L. Pesquera, M. Peil, and L. Larger, “Time delay extraction in chaotic cryptosystems base on optoelectronic feedback with variable delay,” Proc. SPIE 699, 0E. 1–12 (2008).

2007 (1)

2005 (4)

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]

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

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, and I. Fischer, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).

S. Ortin, J. M. Gutie-rezc, L. Pesqueraa, and H. Vasqueza, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A 351, 133–141 (2005).

2004 (2)

W. H. Kye, M. Choi, M. W. Kim, S. Y. Lee, S. Rim, C. M. Kim, and Y. J. Park, “Synchronization of delayed systems in the presence of delay time modulation,” Phys. Lett. A 322(5-6), 338–343 (2004).
[Crossref]

N. Gastaud, S. Poinsot, L. Larger, J.-M. Merolla, M. Hanna, J.-P. Goedgebuer, and F. Malassenet, “Electro-optical chaos for multi-10 Gbit/s optical transmissions,” Electron. Lett. 40(14), 898–899 (2004).
[Crossref]

2001 (1)

1998 (1)

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

1994 (1)

1993 (1)

K. M. Cuomo and A. V. Oppenheim, “Circuit implementation of synchronized chaos with applications to communications,” Phys. Rev. Lett. 71(1), 65–68 (1993).
[Crossref] [PubMed]

1991 (1)

J. R. Kuttler and G. D. Dockery, “Theoretical description of the parabolic approximation/Fourier split-step method of representing electromagnetic propagation in the troposphere,” Radio Sci. 26(2), 381–393 (1991).
[Crossref]

1990 (1)

L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett. 64(8), 821–824 (1990).
[Crossref] [PubMed]

Annovazzi Lodi, V.

L. Ursini, M. Santagiustina, and V. Annovazzi Lodi, “Enhancing Chaotic Communication Performances by Manchester Coding,” IEEE Photonics Technol. Lett. 20(6), 401–403 (2008).
[Crossref]

Annovazzi-Lodi, V.

G. Aromataris and V. Annovazzi-Lodi, “Enhancing privacy of chaotic communications by double masking,” IEEE J. Quantum Electron. 49(11), 955–959 (2013).
[Crossref]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, and I. Fischer, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).

Argyris, A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, and I. Fischer, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).

Aromataris, G.

G. Aromataris and V. Annovazzi-Lodi, “Enhancing privacy of chaotic communications by double masking,” IEEE J. Quantum Electron. 49(11), 955–959 (2013).
[Crossref]

Bogris, A.

J. Hizanidis, S. Deligiannidis, A. Bogris, and D. Syvridis, “Enhancement of chaos encryption potential by combining all-optical and electro-optical chaos generators,” IEEE J. Quantum Electron. 46(11), 1642–1649 (2010).
[Crossref]

Carroll, T. L.

L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett. 64(8), 821–824 (1990).
[Crossref] [PubMed]

Chan, S. C.

S. S. Li, Q. Liu, and S. C. Chan, “Distributed feedbacks for time-delay signature suppression of chaos generated from a semiconductor laser,” IEEE Photon. J. 4(5), 1930–1935 (2012).
[Crossref]

Chang, J.

Choi, M.

W. H. Kye, M. Choi, M. W. Kim, S. Y. Lee, S. Rim, C. M. Kim, and Y. J. Park, “Synchronization of delayed systems in the presence of delay time modulation,” Phys. Lett. A 322(5-6), 338–343 (2004).
[Crossref]

Citrin, D. S.

Colet, P.

R. M. Nguimdo and P. Colet, “Electro-optic phase chaos systems with an internal variable and a digital key,” Opt. Express 20(23), 25333–25344 (2012).
[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(3), 034103 (2011).
[Crossref] [PubMed]

R. M. Nguimdo, P. Colet, and C. Mirasso, “Electro-optic delay devices with double feedback,” IEEE J. Quantum Electron. 46(10), 1436–1443 (2010).
[Crossref]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, and I. Fischer, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).

P. Colet and R. Roy, “Digital communication with synchronized chaotic lasers,” Opt. Lett. 19(24), 2056–2058 (1994).
[Crossref] [PubMed]

Cuomo, K. M.

K. M. Cuomo and A. V. Oppenheim, “Circuit implementation of synchronized chaos with applications to communications,” Phys. Rev. Lett. 71(1), 65–68 (1993).
[Crossref] [PubMed]

Deligiannidis, S.

J. Hizanidis, S. Deligiannidis, A. Bogris, and D. Syvridis, “Enhancement of chaos encryption potential by combining all-optical and electro-optical chaos generators,” IEEE J. Quantum Electron. 46(11), 1642–1649 (2010).
[Crossref]

Dockery, G. D.

J. R. Kuttler and G. D. Dockery, “Theoretical description of the parabolic approximation/Fourier split-step method of representing electromagnetic propagation in the troposphere,” Radio Sci. 26(2), 381–393 (1991).
[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. E Stat. Nonlin. Soft Matter Phys. 80(2), 026207 (2009).
[Crossref] [PubMed]

Fischer, I.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, and I. Fischer, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).

Fok, M. P.

Gastaud, N.

N. Gastaud, S. Poinsot, L. Larger, J.-M. Merolla, M. Hanna, J.-P. Goedgebuer, and F. Malassenet, “Electro-optical chaos for multi-10 Gbit/s optical transmissions,” Electron. Lett. 40(14), 898–899 (2004).
[Crossref]

Goedgebuer, J. P.

Goedgebuer, J.-P.

N. Gastaud, S. Poinsot, L. Larger, J.-M. Merolla, M. Hanna, J.-P. Goedgebuer, and F. Malassenet, “Electro-optical chaos for multi-10 Gbit/s optical transmissions,” Electron. Lett. 40(14), 898–899 (2004).
[Crossref]

Gutie-rezc, J. M.

S. Ortin, J. M. Gutie-rezc, L. Pesqueraa, and H. Vasqueza, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A 351, 133–141 (2005).

Hanna, M.

N. Gastaud, S. Poinsot, L. Larger, J.-M. Merolla, M. Hanna, J.-P. Goedgebuer, and F. Malassenet, “Electro-optical chaos for multi-10 Gbit/s optical transmissions,” Electron. Lett. 40(14), 898–899 (2004).
[Crossref]

Hizanidis, J.

J. Hizanidis, S. Deligiannidis, A. Bogris, and D. Syvridis, “Enhancement of chaos encryption potential by combining all-optical and electro-optical chaos generators,” IEEE J. Quantum Electron. 46(11), 1642–1649 (2010).
[Crossref]

Jacquot, M.

R. Lavrov, M. Jacquot, and L. Larger, “Nonlocal nonlinear electro-optic phase dynamics demonstrating 10 Gb/s chaos communications,” IEEE J. Quantum Electron. 46(10), 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. E Stat. Nonlin. Soft Matter Phys. 80(2), 026207 (2009).
[Crossref] [PubMed]

S. Ortin, M. Jacquot, L. Pesquera, M. Peil, and L. Larger, “Time delay extraction in chaotic cryptosystems base on optoelectronic feedback with variable delay,” Proc. SPIE 699, 0E. 1–12 (2008).

Kim, C. M.

W. H. Kye, M. Choi, M. W. Kim, S. Y. Lee, S. Rim, C. M. Kim, and Y. J. Park, “Synchronization of delayed systems in the presence of delay time modulation,” Phys. Lett. A 322(5-6), 338–343 (2004).
[Crossref]

Kim, M. W.

W. H. Kye, M. Choi, M. W. Kim, S. Y. Lee, S. Rim, C. M. Kim, and Y. J. Park, “Synchronization of delayed systems in the presence of delay time modulation,” Phys. Lett. A 322(5-6), 338–343 (2004).
[Crossref]

Kostinski, N.

N. Kostinski, K. Kravtsov, and P. R. Prucnal, “Demonstration of an all-optical OCDMA encryption and decryption system with variable two-code keying,” IEEE Photon. Technol. Lett. 20(24), 2045–2047 (2008).
[Crossref]

Kravtsov, K.

N. Kostinski, K. Kravtsov, and P. R. Prucnal, “Demonstration of an all-optical OCDMA encryption and decryption system with variable two-code keying,” IEEE Photon. Technol. Lett. 20(24), 2045–2047 (2008).
[Crossref]

Kuttler, J. R.

J. R. Kuttler and G. D. Dockery, “Theoretical description of the parabolic approximation/Fourier split-step method of representing electromagnetic propagation in the troposphere,” Radio Sci. 26(2), 381–393 (1991).
[Crossref]

Kye, W. H.

W. H. Kye, M. Choi, M. W. Kim, S. Y. Lee, S. Rim, C. M. Kim, and Y. J. Park, “Synchronization of delayed systems in the presence of delay time modulation,” Phys. Lett. A 322(5-6), 338–343 (2004).
[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(3), 034103 (2011).
[Crossref] [PubMed]

R. Lavrov, M. Jacquot, and L. Larger, “Nonlocal nonlinear electro-optic phase dynamics demonstrating 10 Gb/s chaos communications,” IEEE J. Quantum Electron. 46(10), 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. E Stat. Nonlin. Soft Matter Phys. 80(2), 026207 (2009).
[Crossref] [PubMed]

S. Ortin, M. Jacquot, L. Pesquera, M. Peil, and L. Larger, “Time delay extraction in chaotic cryptosystems base on optoelectronic feedback with variable delay,” Proc. SPIE 699, 0E. 1–12 (2008).

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, and I. Fischer, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).

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]

N. Gastaud, S. Poinsot, L. Larger, J.-M. Merolla, M. Hanna, J.-P. Goedgebuer, and F. Malassenet, “Electro-optical chaos for multi-10 Gbit/s optical transmissions,” Electron. Lett. 40(14), 898–899 (2004).
[Crossref]

Lavrov, R.

R. Lavrov, M. Jacquot, and L. Larger, “Nonlocal nonlinear electro-optic phase dynamics demonstrating 10 Gb/s chaos communications,” IEEE J. Quantum Electron. 46(10), 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. E Stat. Nonlin. Soft Matter Phys. 80(2), 026207 (2009).
[Crossref] [PubMed]

Lee, S. Y.

W. H. Kye, M. Choi, M. W. Kim, S. Y. Lee, S. Rim, C. M. Kim, and Y. J. Park, “Synchronization of delayed systems in the presence of delay time modulation,” Phys. Lett. A 322(5-6), 338–343 (2004).
[Crossref]

Li, S. S.

S. S. Li, Q. Liu, and S. C. Chan, “Distributed feedbacks for time-delay signature suppression of chaos generated from a semiconductor laser,” IEEE Photon. J. 4(5), 1930–1935 (2012).
[Crossref]

Liu, J. M.

Liu, Q.

S. S. Li, Q. Liu, and S. C. Chan, “Distributed feedbacks for time-delay signature suppression of chaos generated from a semiconductor laser,” IEEE Photon. J. 4(5), 1930–1935 (2012).
[Crossref]

Locquet, A.

Malassenet, F.

N. Gastaud, S. Poinsot, L. Larger, J.-M. Merolla, M. Hanna, J.-P. Goedgebuer, and F. Malassenet, “Electro-optical chaos for multi-10 Gbit/s optical transmissions,” Electron. Lett. 40(14), 898–899 (2004).
[Crossref]

Merolla, J.-M.

N. Gastaud, S. Poinsot, L. Larger, J.-M. Merolla, M. Hanna, J.-P. Goedgebuer, and F. Malassenet, “Electro-optical chaos for multi-10 Gbit/s optical transmissions,” Electron. Lett. 40(14), 898–899 (2004).
[Crossref]

Mirasso, C.

R. M. Nguimdo, P. Colet, and C. Mirasso, “Electro-optic delay devices with double feedback,” IEEE J. Quantum Electron. 46(10), 1436–1443 (2010).
[Crossref]

Nguimdo, R. M.

R. M. Nguimdo and P. Colet, “Electro-optic phase chaos systems with an internal variable and a digital key,” Opt. Express 20(23), 25333–25344 (2012).
[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(3), 034103 (2011).
[Crossref] [PubMed]

R. M. Nguimdo, P. Colet, and C. Mirasso, “Electro-optic delay devices with double feedback,” IEEE J. Quantum Electron. 46(10), 1436–1443 (2010).
[Crossref]

Oppenheim, A. V.

K. M. Cuomo and A. V. Oppenheim, “Circuit implementation of synchronized chaos with applications to communications,” Phys. Rev. Lett. 71(1), 65–68 (1993).
[Crossref] [PubMed]

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), 879–1891 (2009).
[Crossref]

S. Ortin, M. Jacquot, L. Pesquera, M. Peil, and L. Larger, “Time delay extraction in chaotic cryptosystems base on optoelectronic feedback with variable delay,” Proc. SPIE 699, 0E. 1–12 (2008).

S. Ortin, J. M. Gutie-rezc, L. Pesqueraa, and H. Vasqueza, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A 351, 133–141 (2005).

Park, Y. J.

W. H. Kye, M. Choi, M. W. Kim, S. Y. Lee, S. Rim, C. M. Kim, and Y. J. Park, “Synchronization of delayed systems in the presence of delay time modulation,” Phys. Lett. A 322(5-6), 338–343 (2004).
[Crossref]

Paul, J.

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

Pecora, L. M.

L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett. 64(8), 821–824 (1990).
[Crossref] [PubMed]

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. E Stat. Nonlin. Soft Matter Phys. 80(2), 026207 (2009).
[Crossref] [PubMed]

S. Ortin, M. Jacquot, L. Pesquera, M. Peil, and L. Larger, “Time delay extraction in chaotic cryptosystems base on optoelectronic feedback with variable delay,” Proc. SPIE 699, 0E. 1–12 (2008).

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(3), 034103 (2011).
[Crossref] [PubMed]

S. Ortin, M. Jacquot, L. Pesquera, M. Peil, and L. Larger, “Time delay extraction in chaotic cryptosystems base on optoelectronic feedback with variable delay,” Proc. SPIE 699, 0E. 1–12 (2008).

Pesqueraa, L.

S. Ortin, J. M. Gutie-rezc, L. Pesqueraa, and H. Vasqueza, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A 351, 133–141 (2005).

Poinsot, S.

N. Gastaud, S. Poinsot, L. Larger, J.-M. Merolla, M. Hanna, J.-P. Goedgebuer, and F. Malassenet, “Electro-optical chaos for multi-10 Gbit/s optical transmissions,” Electron. Lett. 40(14), 898–899 (2004).
[Crossref]

Prucnal, P. R.

Z. Wang, M. P. Fok, L. Xu, J. Chang, and P. R. Prucnal, “Improving the privacy of optical steganography with temporal phase masks,” Opt. Express 18(6), 6079–6088 (2010).
[Crossref] [PubMed]

N. Kostinski, K. Kravtsov, and P. R. Prucnal, “Demonstration of an all-optical OCDMA encryption and decryption system with variable two-code keying,” IEEE Photon. Technol. Lett. 20(24), 2045–2047 (2008).
[Crossref]

Rim, S.

W. H. Kye, M. Choi, M. W. Kim, S. Y. Lee, S. Rim, C. M. Kim, and Y. J. Park, “Synchronization of delayed systems in the presence of delay time modulation,” Phys. Lett. A 322(5-6), 338–343 (2004).
[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(7), 879–1891 (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]

Roy, R.

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

P. Colet and R. Roy, “Digital communication with synchronized chaotic lasers,” Opt. Lett. 19(24), 2056–2058 (1994).
[Crossref] [PubMed]

Santagiustina, M.

L. Ursini, M. Santagiustina, and V. Annovazzi Lodi, “Enhancing Chaotic Communication Performances by Manchester Coding,” IEEE Photonics Technol. Lett. 20(6), 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(7), 879–1891 (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]

Shore, K. A.

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

Syvridis, D.

J. Hizanidis, S. Deligiannidis, A. Bogris, and D. Syvridis, “Enhancement of chaos encryption potential by combining all-optical and electro-optical chaos generators,” IEEE J. Quantum Electron. 46(11), 1642–1649 (2010).
[Crossref]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, and I. Fischer, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).

Tang, S.

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. E Stat. Nonlin. Soft Matter Phys. 80(2), 026207 (2009).
[Crossref] [PubMed]

Udaltsov, V. S.

Ursini, L.

L. Ursini, M. Santagiustina, and V. Annovazzi Lodi, “Enhancing Chaotic Communication Performances by Manchester Coding,” IEEE Photonics Technol. Lett. 20(6), 401–403 (2008).
[Crossref]

VanWiggeren, G. D.

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

Vasqueza, H.

S. Ortin, J. M. Gutie-rezc, L. Pesqueraa, and H. Vasqueza, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A 351, 133–141 (2005).

Wang, Z.

Z. Wang, “Optical Steganography Over a Public DPSK Channel with Asynchronous Detection,” IEEE J. Quantum Electron. 13, 48–50 (2011).

Z. Wang, M. P. Fok, L. Xu, J. Chang, and P. R. Prucnal, “Improving the privacy of optical steganography with temporal phase masks,” Opt. Express 18(6), 6079–6088 (2010).
[Crossref] [PubMed]

Wu, J. G.

Wu, Y.

Y. Wu, “Can fixed time delay signature be concealed in chaotic semiconductor laser with optical feedback?” IEEE J. Quantum Electron. 48(11), 1371–1379 (2012).
[Crossref]

Wu, Z. M.

Xia, G. Q.

Xu, L.

Electron. Lett. (1)

N. Gastaud, S. Poinsot, L. Larger, J.-M. Merolla, M. Hanna, J.-P. Goedgebuer, and F. Malassenet, “Electro-optical chaos for multi-10 Gbit/s optical transmissions,” Electron. Lett. 40(14), 898–899 (2004).
[Crossref]

IEEE J. Quantum Electron. (7)

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), 879–1891 (2009).
[Crossref]

Y. Wu, “Can fixed time delay signature be concealed in chaotic semiconductor laser with optical feedback?” IEEE J. Quantum Electron. 48(11), 1371–1379 (2012).
[Crossref]

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

G. Aromataris and V. Annovazzi-Lodi, “Enhancing privacy of chaotic communications by double masking,” IEEE J. Quantum Electron. 49(11), 955–959 (2013).
[Crossref]

R. M. Nguimdo, P. Colet, and C. Mirasso, “Electro-optic delay devices with double feedback,” IEEE J. Quantum Electron. 46(10), 1436–1443 (2010).
[Crossref]

J. Hizanidis, S. Deligiannidis, A. Bogris, and D. Syvridis, “Enhancement of chaos encryption potential by combining all-optical and electro-optical chaos generators,” IEEE J. Quantum Electron. 46(11), 1642–1649 (2010).
[Crossref]

Z. Wang, “Optical Steganography Over a Public DPSK Channel with Asynchronous Detection,” IEEE J. Quantum Electron. 13, 48–50 (2011).

IEEE Photon. J. (1)

S. S. Li, Q. Liu, and S. C. Chan, “Distributed feedbacks for time-delay signature suppression of chaos generated from a semiconductor laser,” IEEE Photon. J. 4(5), 1930–1935 (2012).
[Crossref]

IEEE Photon. Technol. Lett. (2)

N. Kostinski, K. Kravtsov, and P. R. Prucnal, “Demonstration of an all-optical OCDMA encryption and decryption system with variable two-code keying,” IEEE Photon. Technol. Lett. 20(24), 2045–2047 (2008).
[Crossref]

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

IEEE Photonics Technol. Lett. (1)

L. Ursini, M. Santagiustina, and V. Annovazzi Lodi, “Enhancing Chaotic Communication Performances by Manchester Coding,” IEEE Photonics Technol. Lett. 20(6), 401–403 (2008).
[Crossref]

J. Opt. Technol. (1)

Nature (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, and I. Fischer, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature 438, 343–346 (2005).

Opt. Express (3)

Opt. Lett. (3)

Phys. Lett. A (1)

W. H. Kye, M. Choi, M. W. Kim, S. Y. Lee, S. Rim, C. M. Kim, and Y. J. Park, “Synchronization of delayed systems in the presence of delay time modulation,” Phys. Lett. A 322(5-6), 338–343 (2004).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

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. E Stat. Nonlin. Soft Matter Phys. 80(2), 026207 (2009).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett. 64(8), 821–824 (1990).
[Crossref] [PubMed]

K. M. Cuomo and A. V. Oppenheim, “Circuit implementation of synchronized chaos with applications to communications,” Phys. Rev. Lett. 71(1), 65–68 (1993).
[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(3), 034103 (2011).
[Crossref] [PubMed]

Physica A (1)

S. Ortin, J. M. Gutie-rezc, L. Pesqueraa, and H. Vasqueza, “Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction,” Physica A 351, 133–141 (2005).

Proc. SPIE (1)

S. Ortin, M. Jacquot, L. Pesquera, M. Peil, and L. Larger, “Time delay extraction in chaotic cryptosystems base on optoelectronic feedback with variable delay,” Proc. SPIE 699, 0E. 1–12 (2008).

Radio Sci. (1)

J. R. Kuttler and G. D. Dockery, “Theoretical description of the parabolic approximation/Fourier split-step method of representing electromagnetic propagation in the troposphere,” Radio Sci. 26(2), 381–393 (1991).
[Crossref]

Science (1)

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

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Figures (5)

Fig. 1
Fig. 1 System architecture.
Fig. 2
Fig. 2 (a) Schematic architecture of the FDGD module, (b) the group delay spectra of three individual G-T etalons and (c) the superposed group delay spectra of 16 cascaded G-T etalons.
Fig. 3
Fig. 3 Chaotic time series (a) (b) (c) (d), corresponding RF spectrums (e) (f) (g) (h) and optical spectrums (i) (j) (k) (l). Black lines in each figures represent the situation without feedback. (a) (e) (i) represents chaotic system without FDGD. (b) (f) (j) represent chaotic system with FDGD where the group delay curve is linear within the chaotic spectrum with a 2000ps/nm dispersion. (c) (g) (k) represents chaotic system with FDGD where the group delay curve is linear within the chaotic spectrum with a 1000ps/nm dispersion. (d) (h) (l) represents chaotic system with FDGD where the group delay curve is irregular within the chaotic spectrum.
Fig. 4
Fig. 4 Evidence of TDS concealment. To ensure reliable time delay concealment capability, we tested two different group delay curves in parabolic and linear shape, which are plotted in (a) (b), the corresponding TDS concealment ability is demonstrated in time domain (c) (d) (e) (f) and frequency domain (g) (h), both from numerical calculation (c) (d) and experimental demonstration (e) (f) (g) (h). Contrast between the situations with (black line) and without (red line) FDGD are distinguished by different colors in each figure.
Fig. 5
Fig. 5 BER variation of the decrypted signal with the frequency mismatch of the FDGD modules in emitter and receiver. (a) The FDGD modules in emitter and receiver have a single G-T etalon configuration. (b) The FDGD modules in emitter and receiver have 16 cascaded G-T etalons. The insets show corresponding eye diagrams. Black lines represent the BER results without decryption. Red and blue lines represent the evolution of BER according to the frequency mismatch of the center-positioned and edge-positioned etalon in FDGD module, respectively.

Equations (12)

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H(ω)= r e iδ 1r e iδ ,
δ= 4πnd λ cosθ,
H i (ω)=exp{ i φ i (ω) }=exp{ i ω τ i ( ω )d ω },
φ i (ω)=arctg (1 r i )sin δ i 2 r i (1+ r i )cos δ i ,
τ i (ω)= 2 n i d i cos δ i c 1 r i 2 r i cos δ i (1+ r i ) ,
H(ω)= i=1 i=16 H i (ω)= exp{ iφ(ω) }=exp{ i ω τ( ω )d ω },
φ(ω)= i=1 i=N φ i (ω) ,
τ(ω)= i=1 i=N τ i (ω) ,
E(t)= 1 2 E 0 { 1+ e πV(t) v π + π V B V DC },
E (t)= F 1 { F[ E(t-T)+ α m m(tT) ] e iφ(ω) },
V 1 (t)+ τ 1 d V 1 (t) dt + 1 θ 1 t 0 t V 1 ( t )d t = G 1 S 1 | E 1 (t T 1 ) | 2 ,
V 2 (t)+ τ 2 d V 2 (t) dt + 1 θ 2 t 0 t V 2 ( t )d t = G 2 S 2 | E 2 (t T 2 ) | 2 ,

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