Abstract

We report on the realization of a hybrid chaos-based communication scheme using three chaotic semiconductor ring lasers (SRLs). In this scheme, two slave SRLs (S-SRLs) are identically driven by a master SRL (M-SRL) subject to delayed optical feedback. Under proper conditions, the S-SRLs are completely synchronized with each other due to the symmetric operation, and they are also synchronized with the M-SRL through the injection-locking effect. The results also show that a message encrypted through chaos shift keying at the M-SRL end can be successfully decrypted by the two S-SRLs, while the two uncoupled S-SRLs allow for dual-channel chaos communication when both counterpropagating modes of one S-SRL are encoded with a message.

© 2013 Optical Society of America

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  1. S. Donati and C. R. Mirasso, “Feature section on optical chaos and applications to cryptography,” IEEE J. Quantum Electron. 38, 1138–1140 (2002).
    [CrossRef]
  2. A. Argyris, D. Syvrids, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343–346 (2005).
    [CrossRef]
  3. R. M. Nguimdo and P. Colet, “Electro-optic phase chaos systems with an internal variable and a digital key,” Opt. Express 20, 25333–25344 (2012).
    [CrossRef]
  4. X. F. Li, W. Pan, B. Luo, and D. Ma, “Mismatch robustness and security of chaotic optical communications based on injection-locking chaos synchronization,” IEEE J. Quantum Electron. 42, 953–960 (2006).
    [CrossRef]
  5. Q. C. Zhao, H. X. Yin, and X. L. Chen, “Long-haul dense wavelength division multiplexing between a chaotic optical secure channel and a conventional fiber-optic channel,” Appl. Opt. 51, 5585–5590 (2012).
    [CrossRef]
  6. S. Sivaprakasam and K. A. Shore, “Signal masking for chaotic optical communications using external-cavity diode lasers,” Opt. Lett. 24, 1200–1202 (1999).
    [CrossRef]
  7. V. Annovazzi-Lodi, S. Donati, and A. Scire, “Synchronization of chaotic injected-lasers systems and its applications to optical cryptography,” IEEE J. Quantum Electron. 32, 953–959 (1996).
    [CrossRef]
  8. V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, and S. Merlo, “Private message transmission by common driving of two chaotic lasers,” IEEE J. Quantum Electron. 46, 258–264 (2010).
    [CrossRef]
  9. N. Q. Li, W. Pan, L. S. Yan, B. Luo, M. F. Xu, Y. L. Tang, N. Jiang, S. Y. Xiang, and Q. Zhang, “Chaotic optical cryptographic communication using a three-semiconductor-laser scheme,” J. Opt. Soc. Am. B 29, 101–108 (2012).
    [CrossRef]
  10. J. Liu, Z. M. Wu, and G. Q. Xia, “Dual-channel chaos synchronization and communication based on unidirectionally coupled VCSELs with polarization-rotated optical feedback and polarization-rotated optical injection,” Opt. Express 17, 12619–12626 (2009).
    [CrossRef]
  11. N. Jiang, W. Pan, B. Luo, S. Y. Xiang, and L. Yang, “Bidirectional dual-channel communication based on polarization-division-multiplexed chaos synchronization in mutually coupled VCSELs,” IEEE Photon. Technol. Lett. 24, 1094–1096 (2012).
    [CrossRef]
  12. L. Chrostowski, and W. Shi, “Monolithic injection-locked high-speed semiconductor ring lasers,” J. Lightwave Technol. 26, 3355–3362 (2008).
    [CrossRef]
  13. S. T. Kingni, G. van der Sande, L. Gelens, T. Erneux, and J. Danckaert, “Direct modulation of semiconductor ring lasers: numerical and asymptotic analysis,” J. Opt. Soc. Am. B 29, 1983–1992 (2012).
    [CrossRef]
  14. R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett. 37, 2541–2543 (2012).
    [CrossRef]
  15. L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multistability in semiconductor ring lasers: theory and experiment,” Phys. Rev. Lett. 102, 193904 (2009).
    [CrossRef]
  16. T. Perez, A. Scire, G. Van der Sande, P. Colet, and C. R. Mirasso, “Bistability and all-optical switching in semiconductor ring lasers,” Opt. Express 15, 12941–12948 (2007).
    [CrossRef]
  17. S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “A semiconductor-based photonic memory cell,” Science 283, 1292–1295 (1999).
    [CrossRef]
  18. M. T. Hill, H. J. S. Dorren, H. T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
    [CrossRef]
  19. S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, and P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express 19, 7439–7450 (2011).
    [CrossRef]
  20. R. M. Nguimdo, G. Verschaffelt, J. Danckaert, X. Leijtens, J. Bolk, and G. Van der Sande, “Fast random bits generation based on a single chaotic semiconductor ring laser,” Opt. Express 20, 28603–28613 (2012).
    [CrossRef]
  21. L. Mashal, G. van der Sande, L. Gelens, J. Danckaert, and G. Verschaffelt, “Square-wave oscillations in semiconductor ring lasers with delayed optical feedback,” Opt. Express 20, 22503–22516 (2012).
    [CrossRef]
  22. I. V. Ermakov, G. van der Sande, and J. Danckaert, “Semiconductor ring laser subject to delayed optical feedback: bifurcations and stability,” Commun. Nonlinear Sci. Numer. Simul. 17, 4767–4779 (2012).
    [CrossRef]
  23. I. V. Ermakov, S. T. Kingni, V. Z. Tronciu, and J. Danckaert, “Chaotic semiconductor ring lasers subject to optical feedback: applications to chaos-based communications,” Opt. Commun. 286, 265–272 (2013).
    [CrossRef]
  24. N. Q. Li, W. Pan, L. S. Yan, B. Luo, X. H. Zou, and S. Y. Xiang, “Enhanced two-channel optical chaotic communication using isochronous synchronization,” IEEE J. Sel. Top. Quantum Electron., doi:10.1109/JSTQE.2012.2210394 (2012).
    [CrossRef]
  25. R. Ju, P. S. Spencer, and K. A. Shore, “Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1461–1467 (2005).
    [CrossRef]
  26. A. Locquet, C. Masoller, and C. R. Mirasso, “Synchronization regimes of optical-feedback-induces chaos in unidirectionally coupled semiconductor lasers,” Phys. Rev. E 65, 056205 (2002).
    [CrossRef]
  27. S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, N. Q. Li, and H. N. Zhu, “Message encoding/decoding using unpredictability-enhanced chaotic VCSELs,” IEEE Photon. Technol. Lett. 24, 1267–1269 (2012).
    [CrossRef]
  28. N. Q. Li, W. Pan, B. Luo, L. S. Yan, X. H. Zou, and S. Y. Xiang, “Multiuser optical communication system based on generalized and complete synchronization,” Optik, doi:10.1016/j.ijleo.2012.09.008 (2012).
    [CrossRef]

2013 (1)

I. V. Ermakov, S. T. Kingni, V. Z. Tronciu, and J. Danckaert, “Chaotic semiconductor ring lasers subject to optical feedback: applications to chaos-based communications,” Opt. Commun. 286, 265–272 (2013).
[CrossRef]

2012 (10)

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, X. Leijtens, J. Bolk, and G. Van der Sande, “Fast random bits generation based on a single chaotic semiconductor ring laser,” Opt. Express 20, 28603–28613 (2012).
[CrossRef]

L. Mashal, G. van der Sande, L. Gelens, J. Danckaert, and G. Verschaffelt, “Square-wave oscillations in semiconductor ring lasers with delayed optical feedback,” Opt. Express 20, 22503–22516 (2012).
[CrossRef]

I. V. Ermakov, G. van der Sande, and J. Danckaert, “Semiconductor ring laser subject to delayed optical feedback: bifurcations and stability,” Commun. Nonlinear Sci. Numer. Simul. 17, 4767–4779 (2012).
[CrossRef]

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, N. Q. Li, and H. N. Zhu, “Message encoding/decoding using unpredictability-enhanced chaotic VCSELs,” IEEE Photon. Technol. Lett. 24, 1267–1269 (2012).
[CrossRef]

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

Q. C. Zhao, H. X. Yin, and X. L. Chen, “Long-haul dense wavelength division multiplexing between a chaotic optical secure channel and a conventional fiber-optic channel,” Appl. Opt. 51, 5585–5590 (2012).
[CrossRef]

N. Q. Li, W. Pan, L. S. Yan, B. Luo, M. F. Xu, Y. L. Tang, N. Jiang, S. Y. Xiang, and Q. Zhang, “Chaotic optical cryptographic communication using a three-semiconductor-laser scheme,” J. Opt. Soc. Am. B 29, 101–108 (2012).
[CrossRef]

S. T. Kingni, G. van der Sande, L. Gelens, T. Erneux, and J. Danckaert, “Direct modulation of semiconductor ring lasers: numerical and asymptotic analysis,” J. Opt. Soc. Am. B 29, 1983–1992 (2012).
[CrossRef]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett. 37, 2541–2543 (2012).
[CrossRef]

N. Jiang, W. Pan, B. Luo, S. Y. Xiang, and L. Yang, “Bidirectional dual-channel communication based on polarization-division-multiplexed chaos synchronization in mutually coupled VCSELs,” IEEE Photon. Technol. Lett. 24, 1094–1096 (2012).
[CrossRef]

2011 (1)

2010 (1)

V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, and S. Merlo, “Private message transmission by common driving of two chaotic lasers,” IEEE J. Quantum Electron. 46, 258–264 (2010).
[CrossRef]

2009 (2)

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multistability in semiconductor ring lasers: theory and experiment,” Phys. Rev. Lett. 102, 193904 (2009).
[CrossRef]

J. Liu, Z. M. Wu, and G. Q. Xia, “Dual-channel chaos synchronization and communication based on unidirectionally coupled VCSELs with polarization-rotated optical feedback and polarization-rotated optical injection,” Opt. Express 17, 12619–12626 (2009).
[CrossRef]

2008 (1)

2007 (1)

2006 (1)

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

2005 (2)

A. Argyris, D. Syvrids, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

R. Ju, P. S. Spencer, and K. A. Shore, “Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1461–1467 (2005).
[CrossRef]

2004 (1)

M. T. Hill, H. J. S. Dorren, H. T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef]

2002 (2)

S. Donati and C. R. Mirasso, “Feature section on optical chaos and applications to cryptography,” IEEE J. Quantum Electron. 38, 1138–1140 (2002).
[CrossRef]

A. Locquet, C. Masoller, and C. R. Mirasso, “Synchronization regimes of optical-feedback-induces chaos in unidirectionally coupled semiconductor lasers,” Phys. Rev. E 65, 056205 (2002).
[CrossRef]

1999 (2)

S. Sivaprakasam and K. A. Shore, “Signal masking for chaotic optical communications using external-cavity diode lasers,” Opt. Lett. 24, 1200–1202 (1999).
[CrossRef]

S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “A semiconductor-based photonic memory cell,” Science 283, 1292–1295 (1999).
[CrossRef]

1996 (1)

V. Annovazzi-Lodi, S. Donati, and A. Scire, “Synchronization of chaotic injected-lasers systems and its applications to optical cryptography,” IEEE J. Quantum Electron. 32, 953–959 (1996).
[CrossRef]

Annovazzi-Lodi, V.

V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, and S. Merlo, “Private message transmission by common driving of two chaotic lasers,” IEEE J. Quantum Electron. 46, 258–264 (2010).
[CrossRef]

A. Argyris, D. Syvrids, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

V. Annovazzi-Lodi, S. Donati, and A. Scire, “Synchronization of chaotic injected-lasers systems and its applications to optical cryptography,” IEEE J. Quantum Electron. 32, 953–959 (1996).
[CrossRef]

Arai, K.

Argyris, A.

A. Argyris, D. Syvrids, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

Aromataris, G.

V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, and S. Merlo, “Private message transmission by common driving of two chaotic lasers,” IEEE J. Quantum Electron. 46, 258–264 (2010).
[CrossRef]

Benedetti, M.

V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, and S. Merlo, “Private message transmission by common driving of two chaotic lasers,” IEEE J. Quantum Electron. 46, 258–264 (2010).
[CrossRef]

Beri, S.

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multistability in semiconductor ring lasers: theory and experiment,” Phys. Rev. Lett. 102, 193904 (2009).
[CrossRef]

Bichler, M.

S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “A semiconductor-based photonic memory cell,” Science 283, 1292–1295 (1999).
[CrossRef]

Binsma, H.

M. T. Hill, H. J. S. Dorren, H. T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef]

Bolk, J.

Chen, X. L.

Chrostowski, L.

Colet, P.

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

T. Perez, A. Scire, G. Van der Sande, P. Colet, and C. R. Mirasso, “Bistability and all-optical switching in semiconductor ring lasers,” Opt. Express 15, 12941–12948 (2007).
[CrossRef]

A. Argyris, D. Syvrids, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

Danckaert, J.

I. V. Ermakov, S. T. Kingni, V. Z. Tronciu, and J. Danckaert, “Chaotic semiconductor ring lasers subject to optical feedback: applications to chaos-based communications,” Opt. Commun. 286, 265–272 (2013).
[CrossRef]

I. V. Ermakov, G. van der Sande, and J. Danckaert, “Semiconductor ring laser subject to delayed optical feedback: bifurcations and stability,” Commun. Nonlinear Sci. Numer. Simul. 17, 4767–4779 (2012).
[CrossRef]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, X. Leijtens, J. Bolk, and G. Van der Sande, “Fast random bits generation based on a single chaotic semiconductor ring laser,” Opt. Express 20, 28603–28613 (2012).
[CrossRef]

L. Mashal, G. van der Sande, L. Gelens, J. Danckaert, and G. Verschaffelt, “Square-wave oscillations in semiconductor ring lasers with delayed optical feedback,” Opt. Express 20, 22503–22516 (2012).
[CrossRef]

S. T. Kingni, G. van der Sande, L. Gelens, T. Erneux, and J. Danckaert, “Direct modulation of semiconductor ring lasers: numerical and asymptotic analysis,” J. Opt. Soc. Am. B 29, 1983–1992 (2012).
[CrossRef]

R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett. 37, 2541–2543 (2012).
[CrossRef]

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multistability in semiconductor ring lasers: theory and experiment,” Phys. Rev. Lett. 102, 193904 (2009).
[CrossRef]

Davis, P.

de Vries, H. T.

M. T. Hill, H. J. S. Dorren, H. T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef]

den Besten, J. H.

M. T. Hill, H. J. S. Dorren, H. T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef]

Donati, S.

S. Donati and C. R. Mirasso, “Feature section on optical chaos and applications to cryptography,” IEEE J. Quantum Electron. 38, 1138–1140 (2002).
[CrossRef]

V. Annovazzi-Lodi, S. Donati, and A. Scire, “Synchronization of chaotic injected-lasers systems and its applications to optical cryptography,” IEEE J. Quantum Electron. 32, 953–959 (1996).
[CrossRef]

Dorren, H. J. S.

M. T. Hill, H. J. S. Dorren, H. T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef]

Ermakov, I. V.

I. V. Ermakov, S. T. Kingni, V. Z. Tronciu, and J. Danckaert, “Chaotic semiconductor ring lasers subject to optical feedback: applications to chaos-based communications,” Opt. Commun. 286, 265–272 (2013).
[CrossRef]

I. V. Ermakov, G. van der Sande, and J. Danckaert, “Semiconductor ring laser subject to delayed optical feedback: bifurcations and stability,” Commun. Nonlinear Sci. Numer. Simul. 17, 4767–4779 (2012).
[CrossRef]

Erneux, T.

Fischer, I.

A. Argyris, D. Syvrids, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

Garcia-Ojalvo, J.

A. Argyris, D. Syvrids, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

Gelens, L.

Harayama, T.

Hill, M. T.

M. T. Hill, H. J. S. Dorren, H. T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef]

Jiang, N.

N. Jiang, W. Pan, B. Luo, S. Y. Xiang, and L. Yang, “Bidirectional dual-channel communication based on polarization-division-multiplexed chaos synchronization in mutually coupled VCSELs,” IEEE Photon. Technol. Lett. 24, 1094–1096 (2012).
[CrossRef]

N. Q. Li, W. Pan, L. S. Yan, B. Luo, M. F. Xu, Y. L. Tang, N. Jiang, S. Y. Xiang, and Q. Zhang, “Chaotic optical cryptographic communication using a three-semiconductor-laser scheme,” J. Opt. Soc. Am. B 29, 101–108 (2012).
[CrossRef]

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, N. Q. Li, and H. N. Zhu, “Message encoding/decoding using unpredictability-enhanced chaotic VCSELs,” IEEE Photon. Technol. Lett. 24, 1267–1269 (2012).
[CrossRef]

Ju, R.

R. Ju, P. S. Spencer, and K. A. Shore, “Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1461–1467 (2005).
[CrossRef]

Khoe, G. D.

M. T. Hill, H. J. S. Dorren, H. T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef]

Kingni, S. T.

I. V. Ermakov, S. T. Kingni, V. Z. Tronciu, and J. Danckaert, “Chaotic semiconductor ring lasers subject to optical feedback: applications to chaos-based communications,” Opt. Commun. 286, 265–272 (2013).
[CrossRef]

S. T. Kingni, G. van der Sande, L. Gelens, T. Erneux, and J. Danckaert, “Direct modulation of semiconductor ring lasers: numerical and asymptotic analysis,” J. Opt. Soc. Am. B 29, 1983–1992 (2012).
[CrossRef]

Kotthaus, J. P.

S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “A semiconductor-based photonic memory cell,” Science 283, 1292–1295 (1999).
[CrossRef]

Larger, L.

A. Argyris, D. Syvrids, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

Leijtens, X.

Leijtens, X. J. M.

M. T. Hill, H. J. S. Dorren, H. T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef]

Li, N. Q.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, N. Q. Li, and H. N. Zhu, “Message encoding/decoding using unpredictability-enhanced chaotic VCSELs,” IEEE Photon. Technol. Lett. 24, 1267–1269 (2012).
[CrossRef]

N. Q. Li, W. Pan, L. S. Yan, B. Luo, M. F. Xu, Y. L. Tang, N. Jiang, S. Y. Xiang, and Q. Zhang, “Chaotic optical cryptographic communication using a three-semiconductor-laser scheme,” J. Opt. Soc. Am. B 29, 101–108 (2012).
[CrossRef]

N. Q. Li, W. Pan, B. Luo, L. S. Yan, X. H. Zou, and S. Y. Xiang, “Multiuser optical communication system based on generalized and complete synchronization,” Optik, doi:10.1016/j.ijleo.2012.09.008 (2012).
[CrossRef]

N. Q. Li, W. Pan, L. S. Yan, B. Luo, X. H. Zou, and S. Y. Xiang, “Enhanced two-channel optical chaotic communication using isochronous synchronization,” IEEE J. Sel. Top. Quantum Electron., doi:10.1109/JSTQE.2012.2210394 (2012).
[CrossRef]

Li, X. F.

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

Liu, J.

Locquet, A.

A. Locquet, C. Masoller, and C. R. Mirasso, “Synchronization regimes of optical-feedback-induces chaos in unidirectionally coupled semiconductor lasers,” Phys. Rev. E 65, 056205 (2002).
[CrossRef]

Luo, B.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, N. Q. Li, and H. N. Zhu, “Message encoding/decoding using unpredictability-enhanced chaotic VCSELs,” IEEE Photon. Technol. Lett. 24, 1267–1269 (2012).
[CrossRef]

N. Q. Li, W. Pan, L. S. Yan, B. Luo, M. F. Xu, Y. L. Tang, N. Jiang, S. Y. Xiang, and Q. Zhang, “Chaotic optical cryptographic communication using a three-semiconductor-laser scheme,” J. Opt. Soc. Am. B 29, 101–108 (2012).
[CrossRef]

N. Jiang, W. Pan, B. Luo, S. Y. Xiang, and L. Yang, “Bidirectional dual-channel communication based on polarization-division-multiplexed chaos synchronization in mutually coupled VCSELs,” IEEE Photon. Technol. Lett. 24, 1094–1096 (2012).
[CrossRef]

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

N. Q. Li, W. Pan, L. S. Yan, B. Luo, X. H. Zou, and S. Y. Xiang, “Enhanced two-channel optical chaotic communication using isochronous synchronization,” IEEE J. Sel. Top. Quantum Electron., doi:10.1109/JSTQE.2012.2210394 (2012).
[CrossRef]

N. Q. Li, W. Pan, B. Luo, L. S. Yan, X. H. Zou, and S. Y. Xiang, “Multiuser optical communication system based on generalized and complete synchronization,” Optik, doi:10.1016/j.ijleo.2012.09.008 (2012).
[CrossRef]

Ma, D.

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

Mashal, L.

Masoller, C.

A. Locquet, C. Masoller, and C. R. Mirasso, “Synchronization regimes of optical-feedback-induces chaos in unidirectionally coupled semiconductor lasers,” Phys. Rev. E 65, 056205 (2002).
[CrossRef]

Merlo, S.

V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, and S. Merlo, “Private message transmission by common driving of two chaotic lasers,” IEEE J. Quantum Electron. 46, 258–264 (2010).
[CrossRef]

Mezosi, G.

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multistability in semiconductor ring lasers: theory and experiment,” Phys. Rev. Lett. 102, 193904 (2009).
[CrossRef]

Mirasso, C. R.

T. Perez, A. Scire, G. Van der Sande, P. Colet, and C. R. Mirasso, “Bistability and all-optical switching in semiconductor ring lasers,” Opt. Express 15, 12941–12948 (2007).
[CrossRef]

A. Argyris, D. Syvrids, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

S. Donati and C. R. Mirasso, “Feature section on optical chaos and applications to cryptography,” IEEE J. Quantum Electron. 38, 1138–1140 (2002).
[CrossRef]

A. Locquet, C. Masoller, and C. R. Mirasso, “Synchronization regimes of optical-feedback-induces chaos in unidirectionally coupled semiconductor lasers,” Phys. Rev. E 65, 056205 (2002).
[CrossRef]

Nguimdo, R. M.

Oei, Y. S.

M. T. Hill, H. J. S. Dorren, H. T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef]

Pan, W.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, N. Q. Li, and H. N. Zhu, “Message encoding/decoding using unpredictability-enhanced chaotic VCSELs,” IEEE Photon. Technol. Lett. 24, 1267–1269 (2012).
[CrossRef]

N. Jiang, W. Pan, B. Luo, S. Y. Xiang, and L. Yang, “Bidirectional dual-channel communication based on polarization-division-multiplexed chaos synchronization in mutually coupled VCSELs,” IEEE Photon. Technol. Lett. 24, 1094–1096 (2012).
[CrossRef]

N. Q. Li, W. Pan, L. S. Yan, B. Luo, M. F. Xu, Y. L. Tang, N. Jiang, S. Y. Xiang, and Q. Zhang, “Chaotic optical cryptographic communication using a three-semiconductor-laser scheme,” J. Opt. Soc. Am. B 29, 101–108 (2012).
[CrossRef]

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

N. Q. Li, W. Pan, B. Luo, L. S. Yan, X. H. Zou, and S. Y. Xiang, “Multiuser optical communication system based on generalized and complete synchronization,” Optik, doi:10.1016/j.ijleo.2012.09.008 (2012).
[CrossRef]

N. Q. Li, W. Pan, L. S. Yan, B. Luo, X. H. Zou, and S. Y. Xiang, “Enhanced two-channel optical chaotic communication using isochronous synchronization,” IEEE J. Sel. Top. Quantum Electron., doi:10.1109/JSTQE.2012.2210394 (2012).
[CrossRef]

Perez, T.

Pesquera, L.

A. Argyris, D. Syvrids, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

Scire, A.

T. Perez, A. Scire, G. Van der Sande, P. Colet, and C. R. Mirasso, “Bistability and all-optical switching in semiconductor ring lasers,” Opt. Express 15, 12941–12948 (2007).
[CrossRef]

V. Annovazzi-Lodi, S. Donati, and A. Scire, “Synchronization of chaotic injected-lasers systems and its applications to optical cryptography,” IEEE J. Quantum Electron. 32, 953–959 (1996).
[CrossRef]

Shi, W.

Shore, K. A.

A. Argyris, D. Syvrids, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

R. Ju, P. S. Spencer, and K. A. Shore, “Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1461–1467 (2005).
[CrossRef]

S. Sivaprakasam and K. A. Shore, “Signal masking for chaotic optical communications using external-cavity diode lasers,” Opt. Lett. 24, 1200–1202 (1999).
[CrossRef]

Sivaprakasam, S.

Smalbrugge, B.

M. T. Hill, H. J. S. Dorren, H. T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef]

Smit, M. K.

M. T. Hill, H. J. S. Dorren, H. T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef]

Sorel, M.

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multistability in semiconductor ring lasers: theory and experiment,” Phys. Rev. Lett. 102, 193904 (2009).
[CrossRef]

Spencer, P. S.

R. Ju, P. S. Spencer, and K. A. Shore, “Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1461–1467 (2005).
[CrossRef]

Sunada, S.

Syvrids, D.

A. Argyris, D. Syvrids, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

Tang, Y. L.

Tronciu, V. Z.

I. V. Ermakov, S. T. Kingni, V. Z. Tronciu, and J. Danckaert, “Chaotic semiconductor ring lasers subject to optical feedback: applications to chaos-based communications,” Opt. Commun. 286, 265–272 (2013).
[CrossRef]

Tsuzuki, K.

Uchida, A.

van der Sande, G.

Verschaffelt, G.

Wegscheider, W.

S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “A semiconductor-based photonic memory cell,” Science 283, 1292–1295 (1999).
[CrossRef]

Wixforth, A.

S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “A semiconductor-based photonic memory cell,” Science 283, 1292–1295 (1999).
[CrossRef]

Wu, Z. M.

Xia, G. Q.

Xiang, S. Y.

N. Q. Li, W. Pan, L. S. Yan, B. Luo, M. F. Xu, Y. L. Tang, N. Jiang, S. Y. Xiang, and Q. Zhang, “Chaotic optical cryptographic communication using a three-semiconductor-laser scheme,” J. Opt. Soc. Am. B 29, 101–108 (2012).
[CrossRef]

N. Jiang, W. Pan, B. Luo, S. Y. Xiang, and L. Yang, “Bidirectional dual-channel communication based on polarization-division-multiplexed chaos synchronization in mutually coupled VCSELs,” IEEE Photon. Technol. Lett. 24, 1094–1096 (2012).
[CrossRef]

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, N. Q. Li, and H. N. Zhu, “Message encoding/decoding using unpredictability-enhanced chaotic VCSELs,” IEEE Photon. Technol. Lett. 24, 1267–1269 (2012).
[CrossRef]

N. Q. Li, W. Pan, L. S. Yan, B. Luo, X. H. Zou, and S. Y. Xiang, “Enhanced two-channel optical chaotic communication using isochronous synchronization,” IEEE J. Sel. Top. Quantum Electron., doi:10.1109/JSTQE.2012.2210394 (2012).
[CrossRef]

N. Q. Li, W. Pan, B. Luo, L. S. Yan, X. H. Zou, and S. Y. Xiang, “Multiuser optical communication system based on generalized and complete synchronization,” Optik, doi:10.1016/j.ijleo.2012.09.008 (2012).
[CrossRef]

Xu, M. F.

Yan, L. S.

N. Q. Li, W. Pan, L. S. Yan, B. Luo, M. F. Xu, Y. L. Tang, N. Jiang, S. Y. Xiang, and Q. Zhang, “Chaotic optical cryptographic communication using a three-semiconductor-laser scheme,” J. Opt. Soc. Am. B 29, 101–108 (2012).
[CrossRef]

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, N. Q. Li, and H. N. Zhu, “Message encoding/decoding using unpredictability-enhanced chaotic VCSELs,” IEEE Photon. Technol. Lett. 24, 1267–1269 (2012).
[CrossRef]

N. Q. Li, W. Pan, B. Luo, L. S. Yan, X. H. Zou, and S. Y. Xiang, “Multiuser optical communication system based on generalized and complete synchronization,” Optik, doi:10.1016/j.ijleo.2012.09.008 (2012).
[CrossRef]

N. Q. Li, W. Pan, L. S. Yan, B. Luo, X. H. Zou, and S. Y. Xiang, “Enhanced two-channel optical chaotic communication using isochronous synchronization,” IEEE J. Sel. Top. Quantum Electron., doi:10.1109/JSTQE.2012.2210394 (2012).
[CrossRef]

Yang, L.

N. Jiang, W. Pan, B. Luo, S. Y. Xiang, and L. Yang, “Bidirectional dual-channel communication based on polarization-division-multiplexed chaos synchronization in mutually coupled VCSELs,” IEEE Photon. Technol. Lett. 24, 1094–1096 (2012).
[CrossRef]

Yin, H. X.

Yoshimura, K.

Zhang, Q.

Zhao, Q. C.

Zhu, H. N.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, N. Q. Li, and H. N. Zhu, “Message encoding/decoding using unpredictability-enhanced chaotic VCSELs,” IEEE Photon. Technol. Lett. 24, 1267–1269 (2012).
[CrossRef]

Zimmermann, S.

S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “A semiconductor-based photonic memory cell,” Science 283, 1292–1295 (1999).
[CrossRef]

Zou, X. H.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, N. Q. Li, and H. N. Zhu, “Message encoding/decoding using unpredictability-enhanced chaotic VCSELs,” IEEE Photon. Technol. Lett. 24, 1267–1269 (2012).
[CrossRef]

N. Q. Li, W. Pan, L. S. Yan, B. Luo, X. H. Zou, and S. Y. Xiang, “Enhanced two-channel optical chaotic communication using isochronous synchronization,” IEEE J. Sel. Top. Quantum Electron., doi:10.1109/JSTQE.2012.2210394 (2012).
[CrossRef]

N. Q. Li, W. Pan, B. Luo, L. S. Yan, X. H. Zou, and S. Y. Xiang, “Multiuser optical communication system based on generalized and complete synchronization,” Optik, doi:10.1016/j.ijleo.2012.09.008 (2012).
[CrossRef]

Appl. Opt. (1)

Commun. Nonlinear Sci. Numer. Simul. (1)

I. V. Ermakov, G. van der Sande, and J. Danckaert, “Semiconductor ring laser subject to delayed optical feedback: bifurcations and stability,” Commun. Nonlinear Sci. Numer. Simul. 17, 4767–4779 (2012).
[CrossRef]

IEEE J. Quantum Electron. (5)

R. Ju, P. S. Spencer, and K. A. Shore, “Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1461–1467 (2005).
[CrossRef]

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

S. Donati and C. R. Mirasso, “Feature section on optical chaos and applications to cryptography,” IEEE J. Quantum Electron. 38, 1138–1140 (2002).
[CrossRef]

V. Annovazzi-Lodi, S. Donati, and A. Scire, “Synchronization of chaotic injected-lasers systems and its applications to optical cryptography,” IEEE J. Quantum Electron. 32, 953–959 (1996).
[CrossRef]

V. Annovazzi-Lodi, G. Aromataris, M. Benedetti, and S. Merlo, “Private message transmission by common driving of two chaotic lasers,” IEEE J. Quantum Electron. 46, 258–264 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

N. Jiang, W. Pan, B. Luo, S. Y. Xiang, and L. Yang, “Bidirectional dual-channel communication based on polarization-division-multiplexed chaos synchronization in mutually coupled VCSELs,” IEEE Photon. Technol. Lett. 24, 1094–1096 (2012).
[CrossRef]

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, N. Q. Li, and H. N. Zhu, “Message encoding/decoding using unpredictability-enhanced chaotic VCSELs,” IEEE Photon. Technol. Lett. 24, 1267–1269 (2012).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (2)

Nature (2)

A. Argyris, D. Syvrids, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

M. T. Hill, H. J. S. Dorren, H. T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[CrossRef]

Opt. Commun. (1)

I. V. Ermakov, S. T. Kingni, V. Z. Tronciu, and J. Danckaert, “Chaotic semiconductor ring lasers subject to optical feedback: applications to chaos-based communications,” Opt. Commun. 286, 265–272 (2013).
[CrossRef]

Opt. Express (6)

Opt. Lett. (2)

Phys. Rev. E (1)

A. Locquet, C. Masoller, and C. R. Mirasso, “Synchronization regimes of optical-feedback-induces chaos in unidirectionally coupled semiconductor lasers,” Phys. Rev. E 65, 056205 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multistability in semiconductor ring lasers: theory and experiment,” Phys. Rev. Lett. 102, 193904 (2009).
[CrossRef]

Science (1)

S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “A semiconductor-based photonic memory cell,” Science 283, 1292–1295 (1999).
[CrossRef]

Other (2)

N. Q. Li, W. Pan, L. S. Yan, B. Luo, X. H. Zou, and S. Y. Xiang, “Enhanced two-channel optical chaotic communication using isochronous synchronization,” IEEE J. Sel. Top. Quantum Electron., doi:10.1109/JSTQE.2012.2210394 (2012).
[CrossRef]

N. Q. Li, W. Pan, B. Luo, L. S. Yan, X. H. Zou, and S. Y. Xiang, “Multiuser optical communication system based on generalized and complete synchronization,” Optik, doi:10.1016/j.ijleo.2012.09.008 (2012).
[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

Architecture for hybrid chaos-based communication scheme. SRL, semiconductor ring laser; CW, clockwise; CCW, counterclockwise; M, modulation module; PD, photodetector; OSC, oscilloscope; m(t), message.

Fig. 2.
Fig. 2.

Schematic of an SRL subject to delayed optical feedback. FR, optical fiber reflector.

Fig. 3.
Fig. 3.

(a) CW temporal outputs of SRLA (upper), SRLB (middle), and SRLC (bottom). CCF curves for (b) CW modes of SRLA and SRLB, (c) CW modes of SRLA and SRLC, and (d) CW modes of SRLB and SRLC.

Fig. 4.
Fig. 4.

(a) CCW temporal outputs of SRLA (upper), SRLB (middle), and SRLC (bottom). CCF curves for (b) CCW modes of SRLA and SRLB, (c) CCW modes of SRLA and SRLC, and (d) CCW modes of SRLB and SRLC.

Fig. 5.
Fig. 5.

Power spectra for (a) CW mode of SRLA, (b) CCW mode of SRLA, (c) CW mode of SRLB, and (d) CCW mode of SRLB.

Fig. 6.
Fig. 6.

XCorr as a function of feedback and coupling strengths for CW (a) and CCW (b) modes. η2A is varied and η1A=2.5ns1.

Fig. 7.
Fig. 7.

XCorr as a function of coupling strength and frequency detuning for CW (a) and CCW (b) modes. Other parameters are as in Fig. 5.

Fig. 8.
Fig. 8.

Illustration of encoding and decoding process for SRLA and SRLB. (a) Original message at 100Mb/s, (b) recovered message, and (c) corresponding eye diagram.

Fig. 9.
Fig. 9.

Illustration of encoding and decoding process for using only one mode. (a), (b) for CW mode; (c), (d) for CCW mode.

Fig. 10.
Fig. 10.

Illustration of encoding and decoding process for dual-channel chaos-based communication. (a)–(c) for CW mode; (d)–(f) for CCW mode. m2(t) at 400Mb/s; m3(t) at 100Mb/s.

Tables (1)

Tables Icon

Table 1. Values of Parameters Used in Our Simulations [21,23]

Equations (8)

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

E˙1A=κ(1+iα)[g1ANA1]E1AkeiϕkE2A+η2AE2A(tτ2A)eiωAτ2A,
E˙2A=κ(1+iα)[g2ANA1]E2AkeiϕkE1A+η1AE1A(tτ1A)eiωAτ1A,
E˙1B=κ(1+iα)[g1BNB1]E1BkeiϕkE2B+kcE1A(tτc)eiωAτc+i2πΔfABt,
E˙2B=κ(1+iα)[g2BNB1]E2BkeiϕkE1B+kcE2A(tτc)eiωAτc+i2πΔfABt,
E˙1C=κ(1+iα)[g1CNC1]E1CkeiϕkE2C+kcE1A(tτc)eiωAτc+i2πΔfACt,
E˙2C=κ(1+iα)[g2CNC1]E2CkeiϕkE1C+kcE2A(tτc)eiωAτc+i2πΔfACt,
N˙A,B,C=γ[μNA,B,Cg1A,1B,1CNA,B,C|E1A,1B,1C|2g2A,2B,2CNA,B,C|E2A,2B,2C|2].
ρij(Δt)=[Pi(t)Pi(t)]·[Pj(tΔt)Pj(tΔt)]|Pi(t)Pi(t)|2·|Pj(tΔt)Pj(tΔt)|2,

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