Abstract

We numerically demonstrate multiplexing and demultiplexing of two distinct chaotic optical signals with strongly overlapped spectra, which are generated by mutually coupled external-cavity semiconductor lasers. Demultiplexing is performed by complete chaos synchronization, while the lasers at the receiving end are optically injected with the same multiplexed signal that couples the emitters together. Such a configuration could lead to spectrally efficient chaos-based optical encryption and decryption of multiple data streams.

© 2010 Optical Society of America

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  1. G. D. Van Wiggeren and R. Roy, Science 279, 1198 (1998).
    [CrossRef]
  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, Nature 437, 343 (2005).
    [CrossRef]
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    [CrossRef] [PubMed]
  4. T. Matsuura, A. Uchida, and S. Yoshimori, Opt. Lett. 29, 2731 (2004).
    [CrossRef] [PubMed]
  5. J.-Z. Zhang, A.-B. Wang, J.-F. Wang, and Y.-C. Wang, Opt. Express 17, 6357 (2009).
    [CrossRef] [PubMed]
  6. J. K. White and J. V. Moloney, Phys. Rev. A 59, 2422(1999).
    [CrossRef]
  7. J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, IEEE J. Quantum Electron. 40, 640 (2004).
    [CrossRef]
  8. M. W. Lee and K. A. Shore, Electron. Lett. 40, 614 (2004).
    [CrossRef]
  9. M. W. Lee and K. A. Shore, J. Lightwave Technol. 23, 1068 (2005).
    [CrossRef]
  10. L. Kocarev and U. Parlitz, Phys. Rev. Lett. 74, 5028 (1995).
    [CrossRef] [PubMed]
  11. R. Lang and K. Kobayashi, J. Quantum Electron. 16, 347 (1980).
    [CrossRef]
  12. A. Locquet, C. Masoller, and C. R. Mirasso, Phys. Rev. E 65, 056205 (2002).
    [CrossRef]
  13. A. Sánchez-Díaz, C. R. Mirasso, P. Colet, and P. García-Fernández, IEEE J. Quantum Electron. 35, 292 (1999).
    [CrossRef]

2009 (1)

2005 (2)

M. W. Lee and K. A. Shore, J. Lightwave Technol. 23, 1068 (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, Nature 437, 343 (2005).
[CrossRef]

2004 (3)

J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, IEEE J. Quantum Electron. 40, 640 (2004).
[CrossRef]

M. W. Lee and K. A. Shore, Electron. Lett. 40, 614 (2004).
[CrossRef]

T. Matsuura, A. Uchida, and S. Yoshimori, Opt. Lett. 29, 2731 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (1)

A. Locquet, C. Masoller, and C. R. Mirasso, Phys. Rev. E 65, 056205 (2002).
[CrossRef]

1999 (2)

A. Sánchez-Díaz, C. R. Mirasso, P. Colet, and P. García-Fernández, IEEE J. Quantum Electron. 35, 292 (1999).
[CrossRef]

J. K. White and J. V. Moloney, Phys. Rev. A 59, 2422(1999).
[CrossRef]

1998 (1)

G. D. Van Wiggeren and R. Roy, Science 279, 1198 (1998).
[CrossRef]

1995 (1)

L. Kocarev and U. Parlitz, Phys. Rev. Lett. 74, 5028 (1995).
[CrossRef] [PubMed]

1980 (1)

R. Lang and K. Kobayashi, J. Quantum Electron. 16, 347 (1980).
[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, Nature 437, 343 (2005).
[CrossRef]

Argyris, A.

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, Nature 437, 343 (2005).
[CrossRef]

Buldú, J. M.

J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, IEEE J. Quantum Electron. 40, 640 (2004).
[CrossRef]

Colet, P.

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, Nature 437, 343 (2005).
[CrossRef]

A. Sánchez-Díaz, C. R. Mirasso, P. Colet, and P. García-Fernández, IEEE J. Quantum Electron. 35, 292 (1999).
[CrossRef]

Fischer, I.

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, Nature 437, 343 (2005).
[CrossRef]

García-Fernández, P.

A. Sánchez-Díaz, C. R. Mirasso, P. Colet, and P. García-Fernández, IEEE J. Quantum Electron. 35, 292 (1999).
[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, Nature 437, 343 (2005).
[CrossRef]

J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, IEEE J. Quantum Electron. 40, 640 (2004).
[CrossRef]

Kinugawa, S.

Kobayashi, K.

R. Lang and K. Kobayashi, J. Quantum Electron. 16, 347 (1980).
[CrossRef]

Kocarev, L.

L. Kocarev and U. Parlitz, Phys. Rev. Lett. 74, 5028 (1995).
[CrossRef] [PubMed]

Lang, R.

R. Lang and K. Kobayashi, J. Quantum Electron. 16, 347 (1980).
[CrossRef]

Larger, 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, Nature 437, 343 (2005).
[CrossRef]

Lee, M. W.

M. W. Lee and K. A. Shore, J. Lightwave Technol. 23, 1068 (2005).
[CrossRef]

M. W. Lee and K. A. Shore, Electron. Lett. 40, 614 (2004).
[CrossRef]

Locquet, A.

A. Locquet, C. Masoller, and C. R. Mirasso, Phys. Rev. E 65, 056205 (2002).
[CrossRef]

Masoller, C.

A. Locquet, C. Masoller, and C. R. Mirasso, Phys. Rev. E 65, 056205 (2002).
[CrossRef]

Matsuura, T.

Mirasso, C. R.

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, Nature 437, 343 (2005).
[CrossRef]

A. Locquet, C. Masoller, and C. R. Mirasso, Phys. Rev. E 65, 056205 (2002).
[CrossRef]

A. Sánchez-Díaz, C. R. Mirasso, P. Colet, and P. García-Fernández, IEEE J. Quantum Electron. 35, 292 (1999).
[CrossRef]

Moloney, J. V.

J. K. White and J. V. Moloney, Phys. Rev. A 59, 2422(1999).
[CrossRef]

Parlitz, U.

L. Kocarev and U. Parlitz, Phys. Rev. Lett. 74, 5028 (1995).
[CrossRef] [PubMed]

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, Nature 437, 343 (2005).
[CrossRef]

Roy, R.

G. D. Van Wiggeren and R. Roy, Science 279, 1198 (1998).
[CrossRef]

Sánchez-Díaz, A.

A. Sánchez-Díaz, C. R. Mirasso, P. Colet, and P. García-Fernández, IEEE J. Quantum Electron. 35, 292 (1999).
[CrossRef]

Shore, K. A.

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, Nature 437, 343 (2005).
[CrossRef]

M. W. Lee and K. A. Shore, J. Lightwave Technol. 23, 1068 (2005).
[CrossRef]

M. W. Lee and K. A. Shore, Electron. Lett. 40, 614 (2004).
[CrossRef]

Syvridis, D.

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, Nature 437, 343 (2005).
[CrossRef]

Torrent, M. C.

J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, IEEE J. Quantum Electron. 40, 640 (2004).
[CrossRef]

Uchida, A.

Van Wiggeren, G. D.

G. D. Van Wiggeren and R. Roy, Science 279, 1198 (1998).
[CrossRef]

Wang, A.-B.

Wang, J.-F.

Wang, Y.-C.

White, J. K.

J. K. White and J. V. Moloney, Phys. Rev. A 59, 2422(1999).
[CrossRef]

Yoshimori, S.

Zhang, J.-Z.

Electron. Lett. (1)

M. W. Lee and K. A. Shore, Electron. Lett. 40, 614 (2004).
[CrossRef]

IEEE J. Quantum Electron. (2)

J. M. Buldú, J. García-Ojalvo, and M. C. Torrent, IEEE J. Quantum Electron. 40, 640 (2004).
[CrossRef]

A. Sánchez-Díaz, C. R. Mirasso, P. Colet, and P. García-Fernández, IEEE J. Quantum Electron. 35, 292 (1999).
[CrossRef]

J. Lightwave Technol. (1)

J. Quantum Electron. (1)

R. Lang and K. Kobayashi, J. Quantum Electron. 16, 347 (1980).
[CrossRef]

Nature (1)

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, Nature 437, 343 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

J. K. White and J. V. Moloney, Phys. Rev. A 59, 2422(1999).
[CrossRef]

Phys. Rev. E (1)

A. Locquet, C. Masoller, and C. R. Mirasso, Phys. Rev. E 65, 056205 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

L. Kocarev and U. Parlitz, Phys. Rev. Lett. 74, 5028 (1995).
[CrossRef] [PubMed]

Science (1)

G. D. Van Wiggeren and R. Roy, Science 279, 1198 (1998).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Multiplexing scheme based on optically coupled semiconductor lasers: LD, laser diode (labeled M1, M2 for the masters and S1, S2 for the slaves); CS, current source; M, M f , mirrors; VA 1 , VA 2 , variable attenuators; BS, 50 / 50 beam splitter; OI, optical isolator. E T is the multiplexed field sent to the slave lasers.

Fig. 2
Fig. 2

Synchronization diagrams in planes ( I k = 1 , 2 m ( t Δ τ k ) , I j = 1 , 2 s ( t ) ) without [Case (a)] and with spontaneous- emission noise [Case (b), β s p = 1000 s 1 ]. The operational parameters are the following: J 1 m = J 1 s = 2.75 J th and J 2 m = J 2 s = 2.5 J th; η 11 m = η 11 c = 10 GHz , η 22 m = η 22 c = 15 GHz , and η 12 m = η 21 m = η 12 c = η 21 c = η 1 m η 2 m ; τ 11 m = 1 ns , τ 22 m = 4 ns , τ 11 c = 10 ns , and τ 22 c = 15 ns ; and Δ ω 11 m / s = Δ ω 22 m / s = Δ ω 12 m / m = 0 GHz . The internal parameters are the following: α 1 m , s = 5 , α 2 m , s = 4 , τ p 1 m , s = 2 ps , τ p 2 m , s = 1 ps , γ s 1 m , s = 0.5 GHz , γ s 2 m , s = 1 GHz , ε 1 m , s = 5 × 10 7 , ε 2 m , s = 2.5 × 10 7 , g 1 m , s = 1.5 × 10 4 s 1 , g 2 m , s = 1 × 10 4 s 1 , N 01 m , s = 1.5 × 10 8 , and N 02 m , s = 2 × 10 8 .

Fig. 3
Fig. 3

Optical spectrum of each master laser and of the transmitted signal, calculated using Welch’s method. Free-running (inset) and chaotic spectra are represented. Pa rameters are the same as in Fig. 2.

Equations (4)

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d E k m d t = 1 2 ( 1 + i α k m ) ( G k m 1 / τ p k m ) E k m + F k m + j = 1 n η j k m exp ( i ω 0 j m τ j k m + i Δ ω j k m / m t ) E j m ( t τ j k m ) ,
d E k s d t = 1 2 ( 1 + i α k s ) ( G k s 1 / τ p k s ) E k s + F k s + j = 1 n η j k c exp ( i ω 0 j s τ j k c + i Δ ω j k m / s t ) E j m ( t τ j k c ) ,
d N k m , s d t = J k m , s γ s k m , s N k m , s G k m , s | E k m , s | 2 ,
C j k ( τ ) = [ I j m ( t + τ ) I j m [ I k s ( t ) I k s ] [ I j m ( t + τ ) I j m I k s ( t ) I k s ] 1 / 2 ,

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