Abstract

We experimentally and numerically investigated the chaos synchronization characteristics of mutually coupled semiconductor lasers (MCSLs) with asymmetrical bias currents. Experimental results show that, asymmetrical bias current level of two MCSLs has obvious influence on chaos synchronization between them, and stable leader-laggard chaos synchronization can be realized under relatively large asymmetrical bias current levels. Moreover, the influences of frequency detuning and mutually coupling strength between the two lasers on chaos synchronization performance have also been discussed. Theoretical simulations basically conform to our experimental observations.

© 2011 OSA

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  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]
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  24. N. Jiang, W. Pan, L. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28(13), 1978–1986 (2010).
    [CrossRef]
  25. 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]
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    [CrossRef] [PubMed]
  27. M. G. Rosenblum, A. S. Pilovsky, and J. Kurths, “From phase to lag synchronization in coupled chaotic oscillators,” Phys. Rev. Lett. 78(22), 4193–4196 (1997).
    [CrossRef]

2010

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104(11), 114102 (2010).
[CrossRef] [PubMed]

N. Jiang, W. Pan, B. Luo, L. S. Yan, S. Y. Xiang, L. Yang, D. Zheng, and N. Q. Li, “Properties of leader-laggard chaos synchronization in mutually coupled external-cavity semiconductor lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81(6), 066217 (2010).
[CrossRef] [PubMed]

N. Jiang, W. Pan, L. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28(13), 1978–1986 (2010).
[CrossRef]

2009

2008

W. L. Zhang, W. Pan, B. Luo, X. H. Zou, and M. Y. Wang, “One-to-many and many-to-one optical chaos communications using semiconductor lasers,” IEEE Photon. Technol. Lett. 20(9), 712–714 (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

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]

S. L. Yan, “Study of dual-directional high rate secure communication systems using chaotic multiple-quantum-well lasers,” Chin. Phys. 16(11), 3271–3278 (2007).
[CrossRef]

2006

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, “Stable isochronal synchronization of mutually coupled chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066214 (2006).
[CrossRef] [PubMed]

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 437(7066), 343–346 (2005).
[CrossRef]

2003

S. Tang and J. M. Liu, “Chaos synchronization in semiconductor lasers with optoelectronic feedback,” IEEE J. Quantum Electron. 39(6), 708–715 (2003).
[CrossRef]

F. Y. Lin and J. M. Liu, “Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback,” IEEE J. Quantum Electron. 39(4), 562–568 (2003).
[CrossRef]

F. Rogister and J. García-Ojalvo, “Symmetry breaking and high-frequency periodic oscillations in mutually coupled laser diodes,” Opt. Lett. 28(14), 1176–1178 (2003).
[CrossRef] [PubMed]

2002

J. Ohtsubo, “Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,” IEEE J. Quantum Electron. 38(9), 1141–1154 (2002).
[CrossRef]

2001

H. Fujino and J. Ohtsubo, “Synchronization of chaotic oscillations in mutually coupled semiconductor lasers,” Opt. Rev. 8(5), 351–357 (2001).
[CrossRef]

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]

S. Sivaprakasam and K. A. Shore, “Cascaded synchronization of external-cavity laser diodes,” Opt. Lett. 26(5), 253–255 (2001).
[CrossRef]

1999

1997

M. G. Rosenblum, A. S. Pilovsky, and J. Kurths, “From phase to lag synchronization in coupled chaotic oscillators,” Phys. Rev. Lett. 78(22), 4193–4196 (1997).
[CrossRef]

A. Hohl, A. Gavrielides, T. Erneux, and V. Kovanis, “Localized synchronization in two coupled nonidentical semiconductor lasers,” Phys. Rev. Lett. 78(25), 4745–4748 (1997).
[CrossRef]

1994

T. Sugawara, M. Tachikawa, T. Tsukamoto, and T. Shimizu, “Observation of synchronization in laser chaos,” Phys. Rev. Lett. 72(22), 3502–3505 (1994).
[CrossRef] [PubMed]

1992

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: Theory and experiment,” IEEE J. Quantum Electron. 28(1), 93–108 (1992).
[CrossRef]

1990

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

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 437(7066), 343–346 (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, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005).
[CrossRef]

Aviad, Y.

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104(11), 114102 (2010).
[CrossRef] [PubMed]

Butkovski, M.

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104(11), 114102 (2010).
[CrossRef] [PubMed]

Cao, L. P.

T. Deng, G. Q. Xia, L. P. Cao, J. G. Chen, X. D. Lin, and Z. M. Wu, “Bidirectional chaos synchronization and communication in semiconductor lasers with optoelectronic feedback,” Opt. Commun. 282(11), 2243–2249 (2009).
[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]

Chen, J. G.

T. Deng, G. Q. Xia, L. P. Cao, J. G. Chen, X. D. Lin, and Z. M. Wu, “Bidirectional chaos synchronization and communication in semiconductor lasers with optoelectronic feedback,” Opt. Commun. 282(11), 2243–2249 (2009).
[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, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005).
[CrossRef]

Deng, T.

T. Deng, G. Q. Xia, L. P. Cao, J. G. Chen, X. D. Lin, and Z. M. Wu, “Bidirectional chaos synchronization and communication in semiconductor lasers with optoelectronic feedback,” Opt. Commun. 282(11), 2243–2249 (2009).
[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]

Englert, A.

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104(11), 114102 (2010).
[CrossRef] [PubMed]

Erneux, T.

A. Hohl, A. Gavrielides, T. Erneux, and V. Kovanis, “Localized synchronization in two coupled nonidentical semiconductor lasers,” Phys. Rev. Lett. 78(25), 4745–4748 (1997).
[CrossRef]

Fischer, I.

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 437(7066), 343–346 (2005).
[CrossRef]

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]

Fujino, H.

H. Fujino and J. Ohtsubo, “Synchronization of chaotic oscillations in mutually coupled semiconductor lasers,” Opt. Rev. 8(5), 351–357 (2001).
[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 437(7066), 343–346 (2005).
[CrossRef]

F. Rogister and J. García-Ojalvo, “Symmetry breaking and high-frequency periodic oscillations in mutually coupled laser diodes,” Opt. Lett. 28(14), 1176–1178 (2003).
[CrossRef] [PubMed]

Gavrielides, A.

A. Hohl, A. Gavrielides, T. Erneux, and V. Kovanis, “Localized synchronization in two coupled nonidentical semiconductor lasers,” Phys. Rev. Lett. 78(25), 4745–4748 (1997).
[CrossRef]

Gross, N.

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, “Stable isochronal synchronization of mutually coupled chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066214 (2006).
[CrossRef] [PubMed]

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]

Hohl, A.

A. Hohl, A. Gavrielides, T. Erneux, and V. Kovanis, “Localized synchronization in two coupled nonidentical semiconductor lasers,” Phys. Rev. Lett. 78(25), 4745–4748 (1997).
[CrossRef]

Jiang, N.

N. Jiang, W. Pan, B. Luo, L. S. Yan, S. Y. Xiang, L. Yang, D. Zheng, and N. Q. Li, “Properties of leader-laggard chaos synchronization in mutually coupled external-cavity semiconductor lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81(6), 066217 (2010).
[CrossRef] [PubMed]

N. Jiang, W. Pan, L. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28(13), 1978–1986 (2010).
[CrossRef]

Kannari, F.

Kanter, I.

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104(11), 114102 (2010).
[CrossRef] [PubMed]

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, “Stable isochronal synchronization of mutually coupled chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066214 (2006).
[CrossRef] [PubMed]

Khaykovich, L.

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, “Stable isochronal synchronization of mutually coupled chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066214 (2006).
[CrossRef] [PubMed]

Kinzel, W.

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104(11), 114102 (2010).
[CrossRef] [PubMed]

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, “Stable isochronal synchronization of mutually coupled chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066214 (2006).
[CrossRef] [PubMed]

Klein, E.

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, “Stable isochronal synchronization of mutually coupled chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066214 (2006).
[CrossRef] [PubMed]

Kovanis, V.

A. Hohl, A. Gavrielides, T. Erneux, and V. Kovanis, “Localized synchronization in two coupled nonidentical semiconductor lasers,” Phys. Rev. Lett. 78(25), 4745–4748 (1997).
[CrossRef]

Kurths, J.

M. G. Rosenblum, A. S. Pilovsky, and J. Kurths, “From phase to lag synchronization in coupled chaotic oscillators,” Phys. Rev. Lett. 78(22), 4193–4196 (1997).
[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, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 437(7066), 343–346 (2005).
[CrossRef]

Li, N. Q.

N. Jiang, W. Pan, B. Luo, L. S. Yan, S. Y. Xiang, L. Yang, D. Zheng, and N. Q. Li, “Properties of leader-laggard chaos synchronization in mutually coupled external-cavity semiconductor lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81(6), 066217 (2010).
[CrossRef] [PubMed]

Lin, F. Y.

F. Y. Lin and J. M. Liu, “Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback,” IEEE J. Quantum Electron. 39(4), 562–568 (2003).
[CrossRef]

Lin, X. D.

T. Deng, G. Q. Xia, L. P. Cao, J. G. Chen, X. D. Lin, and Z. M. Wu, “Bidirectional chaos synchronization and communication in semiconductor lasers with optoelectronic feedback,” Opt. Commun. 282(11), 2243–2249 (2009).
[CrossRef]

Liu, J.

Liu, J. M.

F. Y. Lin and J. M. Liu, “Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback,” IEEE J. Quantum Electron. 39(4), 562–568 (2003).
[CrossRef]

S. Tang and J. M. Liu, “Chaos synchronization in semiconductor lasers with optoelectronic feedback,” IEEE J. Quantum Electron. 39(6), 708–715 (2003).
[CrossRef]

Luo, B.

N. Jiang, W. Pan, L. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28(13), 1978–1986 (2010).
[CrossRef]

N. Jiang, W. Pan, B. Luo, L. S. Yan, S. Y. Xiang, L. Yang, D. Zheng, and N. Q. Li, “Properties of leader-laggard chaos synchronization in mutually coupled external-cavity semiconductor lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81(6), 066217 (2010).
[CrossRef] [PubMed]

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]

W. L. Zhang, W. Pan, B. Luo, X. H. Zou, and M. Y. Wang, “One-to-many and many-to-one optical chaos communications using semiconductor lasers,” IEEE Photon. Technol. Lett. 20(9), 712–714 (2008).
[CrossRef]

Mark, J.

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: Theory and experiment,” IEEE J. Quantum Electron. 28(1), 93–108 (1992).
[CrossRef]

Mirasso, C. 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]

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 437(7066), 343–346 (2005).
[CrossRef]

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]

Mork, J.

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: Theory and experiment,” IEEE J. Quantum Electron. 28(1), 93–108 (1992).
[CrossRef]

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]

Ogawa, T.

Ohtsubo, J.

J. Ohtsubo, “Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,” IEEE J. Quantum Electron. 38(9), 1141–1154 (2002).
[CrossRef]

H. Fujino and J. Ohtsubo, “Synchronization of chaotic oscillations in mutually coupled semiconductor lasers,” Opt. Rev. 8(5), 351–357 (2001).
[CrossRef]

Pan, W.

N. Jiang, W. Pan, B. Luo, L. S. Yan, S. Y. Xiang, L. Yang, D. Zheng, and N. Q. Li, “Properties of leader-laggard chaos synchronization in mutually coupled external-cavity semiconductor lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81(6), 066217 (2010).
[CrossRef] [PubMed]

N. Jiang, W. Pan, L. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28(13), 1978–1986 (2010).
[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]

W. L. Zhang, W. Pan, B. Luo, X. H. Zou, and M. Y. Wang, “One-to-many and many-to-one optical chaos communications using semiconductor lasers,” IEEE Photon. Technol. Lett. 20(9), 712–714 (2008).
[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]

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 437(7066), 343–346 (2005).
[CrossRef]

Pilovsky, A. S.

M. G. Rosenblum, A. S. Pilovsky, and J. Kurths, “From phase to lag synchronization in coupled chaotic oscillators,” Phys. Rev. Lett. 78(22), 4193–4196 (1997).
[CrossRef]

Reidler, I.

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[CrossRef] [PubMed]

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Figures (13)

Fig. 1
Fig. 1

Experimental setup. SL: semiconductor laser; AL: aspheric lens; BS: beam splitter; OI: optical isolator; PD: photo-detector; NDF: neutral density filter; FC: fiber coupler. The solid lines indicate optical paths, while the dashed lines indicate electronic paths.

Fig. 2
Fig. 2

Power spectra of SL1 and SL2 (left column) and correlation coefficient between the two lasers (right column), where (a) I1 = 1.8Ith1 , I2 = 1.2Ith2 ; (b) I1 = 1.6Ith1 , I2 = 1.55Ith2 ; (c) I1 = 1.2Ith1 , I2 = 1.8Ith2 .

Fig. 3
Fig. 3

Variation of maximal correlation coefficient Cmax with I1 , where I2 is fixed at 1.1Ith2 , 1.2Ith2 and 1.3Ith2 , respectively.

Fig. 4
Fig. 4

Temporal traces of the optical power of SL1 (upper) and SL2 (lower) when two lasers respectively operate at LFFs (a) for I1 = 1.1Ith1 and I2 = 1.1Ith2 and chaos oscillation (b) for I1 = 1.8Ith1 and I2 = 1.1Ith2 , where the temporal trace of SL2 is vertically shifted lower for convenient of comparison with that of SL1.

Fig. 5
Fig. 5

Variation of maximal correlation coefficient Cmax with I1 for I2 = 1.2Ith2 , where curve A corresponds to that temperatures of SL1 And SL2 are respectively stabilized at 24.80 °C and 25.55 °C, and curve B corresponds to temperatures of SL1 And SL2 are respectively stabilized at 24.30 °C and 25.16 °C.

Fig. 6
Fig. 6

Variation of maximal correlation coefficient Cmax with I1 , where I2 is fixed at 1.2Ith 2 and Δf is respectively fixed at 0 GHz, −5 GHz and −10 GHz.

Fig. 7
Fig. 7

Variation of maximal correlation coefficient Cmax with detuning frequency under I1 = 1.8Ith1 , I2 = 1.2Ith2 .

Fig. 8
Fig. 8

Variation of maximal correlation coefficient Cmax with transmissivity T of NDF for I1 = 1.8Ith1 , I2 = 1.2Ith2 and Δf = −5 GHz.

Fig. 9
Fig. 9

Simulated correlation coefficient between SL1 and SL2, where (a) I1 = 1.8Ith1 , I2 = 1.2Ith2 , k = 0.4; (b) I1 = 1.6Ith1 , I2 = 1.55Ith2 , k = 0.4; (c) I1 = 1.2Ith1 , I2 = 1.8Ith2 , k = 0.4.

Fig. 10
Fig. 10

Variation of maximal correlation coefficient Cmax with I1 for I2 = 1.2Ith2 , where the detuning frequency between two lasers are respectively fixed at 0 GHz, −5 GHz and −10 GHz.

Fig. 11
Fig. 11

Variation of maximal correlation coefficient Cmax with frequency detuning between two lasers for I1 = 1.8Ith1 , I2 = 1.2Ith2 and k = 0.4.

Fig. 12
Fig. 12

Variation of maximal correlation coefficient Cmax with coupling coefficient k for I1 = 1.8Ith1 , I2 = 1.2Ith2 and Δf = −5 GHz.

Fig. 13
Fig. 13

Map of maximal correlation coefficient Cmax as function of detuning frequency and coupling coefficient.

Equations (5)

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C ( Δ t ) = [ P 1 ( t ) P 1 ] [ P 2 ( t + Δ t ) P 2 ] { [ P 1 ( t ) P 1 ] 2 P 2 ( t ) P 2 ] 2 } 1 / 2
d E 1 ( t ) d t = 1 2 ( 1 + i α 1 ) [ G 1 1 τ p 1 ] E 1 ( t ) + k τ i n E 2 ( t τ ) e i 2 π ( f 2 τ + Δ f t ) + 2 β N 1 ( t ) ξ e 1
d E 2 ( t ) d t = 1 2 ( 1 + i α 2 ) [ G 2 1 τ p 2 ] E 2 ( t ) + k τ i n E 1 ( t τ ) e i 2 π ( f 1 τ Δ f t ) + 2 β N 2 ( t ) ξ e 2
d N 1 , 2 ( t ) d t = I 1 , 2 e N 1 , 2 ( t ) τ s 1 , 2 G 1 , 2 | E 1 , 2 ( t ) | 2
G 1 , 2 = g 1 , 2 ( N 1.2 N 01 , 2 ) 1 + s | E 1 , 2 | 2

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