Abstract

We investigate the evolution of nonlinear dynamic behaviors of two polarization components (x-PC and y-PC), as well as the interplay of polarization bistability, frequency detuning and injection strength in the vertical cavity surface emitting laser with optical injection. Specifically, by encoding two logic inputs and one clock input in the amplitude of the light from a sampled grating distributed Bragg reflector laser, and by decoding two output logic responses from the x-PC and y-PC emitted by the laser, we demonstrate two parallel data-selection computing. The correct logic output encoded in two emitted PCs response for as short as 100 ps bit time and the response bit time of the correct logic output encoded in the y-PC may be 67 ps by the optimization of the injection strength. The probability of a correct response is controlled by the interplay of the bit time, the injection strength and noise strength, and is equal to 1 in a wide region of the injection strength and noise strength. The chaotic data-selection computing in an optically VCSEL offer interesting perspectives for applications where noise is unavoidable and fast switching is required.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. K. Myneni, T. A. Barr, B. R. Reed, S. D. Pethel, and N. J. Corron, “High-precision ranging using a chaotic laser pulse train,” Appl. Phys. Lett. 78(11), 1496–1498 (2001).
    [Crossref]
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  5. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. Alan Shore, “Chaos based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
    [Crossref] [PubMed]
  6. Q. Li, T. Deng, Z. M. Wu, and G. Q. Xia, “Security-Enhanced Bidirectional Long-Distance Chaos Secure Communication,” Chin. J. Lasers 45(1), 0106001 (2018).
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  7. C. T. Lin and C. P. Jou, “Controlling chaos by GA-based reinforcement learning neural network,” IEEE Trans. Neural. Netw. 10(4), 846–859 (1999).
    [Crossref]
  8. S. Y. Xiang, Y. H. Zhang, J. K. Gong, X. X. Guo, L. Lin, and Y. Hao, “STDP-Based Unsupervised Spike Pattern Learning in a Photonic Spiking Neural Network With VCSELs and VCSOAs,” IEEE J. Sel. Top. Quantum Electron. 25(6), 1700109 (2019).
    [Crossref]
  9. X. J. Yao, X. Tang, Z. M. Wu, and G. Q. Xia, “Multi-channel physical random number generation based on two orthogonally mutually coupled 1550 nm vertical-cavity surface-emitting lasers,” Acta Phys. Sinica 67(2), 024204 (2018).
  10. S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of Chaos Time Delay Signature in a Ring Network Consisting of Three Semiconductor Lasers Coupled With Heterogeneous Delays,” J. Light. Technol. 34(18), 4221–4227 (2016).
    [Crossref]
  11. Y. Wang, S. Y. Xiang, B. Wang, X. Y. Cao, A. J. Wen, and Y. Hao, “Time-delay signature concealment and physical random bits generation in mutually coupled semiconductor lasers with FBG filtered injection,” Opt. Express 27(6), 8446–8455 (2019).
    [Crossref] [PubMed]
  12. K. Murali, S. Sinha, and I. R. Mohamed, “Chaos computing: experimental realization of NOR gate using a simple chaotic circuit,” Phys. Lett. A 339(1–2), 39–44 (2005).
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  13. M. Beyki and M. Yaghoobi, “Chaotic logic gate: A new approach in set and design by genetic algorithm,” Chaos, Solitons & Fractals 77, 247–252 (2015).
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  14. B. Kia, A. Dari, W. L. Ditto, and M. L. Spano, “Unstable periodic orbits and noise in chaos computing,” Chaos: An Interdiscip. J. Nonlinear Sci.,  21(4), 074520 (2011).
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  15. L. L. Li, J. Wu, J. F. Qiu, B. B. Wu, K. Xu, X. B. Hong, Y. Li, and J. T. Lin, “Reconfigurable all-optical logic gate using four-wave mixing (FWM) in HNLF for NRZ-PolSK signal,” Opt. Commun. 283(19), 3608–3612 (2010).
    [Crossref]
  16. Y.B. Tang, Y. P. Tang, H. W. Jiang, W. F. Ji, Y. J. Wu, and X. F. Chen, “Proposal for simultaneous all-optical AND, NOR, and XNOR logic gates using QPM cascading nonlinear effects in two PPLNs,” Chin. Opt. Lett. 11(6), 66–69 (2013).
  17. F. Nian, “The Characteristic of Polarization Chaos and Coherence of Semiconductor Optical Amplifier-Based Fiber Ring Laser,” Acta Opt. Sinica 28(1), 128–131 (2008).
    [Crossref]
  18. Z. Q. Zhong, Z. M. Wu, and G. Q. Xia, “Experimental investigation on the time-delay signature of chaotic output from a 1550 nm VCSEL subject to FBG feedback,” Photonics. Res 5(1), 6–10 (2017).
    [Crossref]
  19. N. Jiang, C. Xue, D. Liu, Y. Lv, and K. Qiu, “Secure key distribution based on chaos synchronization of VCSELs subject to symmetric random-polarization optical injection,” Opt. Lett. 42(6), 1055–1058 (2017).
    [Crossref] [PubMed]
  20. C. H. Uy, D. Rontani, S. Breuer, and M. Sciamanna, “Non-local correlations via chaotic itinerancy in VCSEL with optical feedback,” Opt. Express 25(6), 6914–6926 (2017).
    [Crossref] [PubMed]
  21. Y. Y. Xie, J. C. Li, C. He, Z. D. Zhang, T. T. Song, C. J. Xu, and G. J. Wang, “Long-distance multi-channel bidirectional chaos communication based on synchronized VCSELs subject to chaotic signal injection,” Opt. Commun. 377, 1–9 (2016).
    [Crossref]
  22. X. J. Yang, J. J. Chen, G. Q. Xia, J.G. Wu, and Z. M. Wu, “Analyses of the time-delay signature and bandwidth of the chaotic output from a master-slave vertical-cavity surface-emitting laser dynamical system,” Acta Phys. Sinica 64(22), 224213 (2015).
  23. B. B. Su, J. J. Chen, Z. M. Wu, and G. Q. Xia, “Performances of time-delay signature and bandwidth of the chaos generated by a vertical-cavity surface-emitting laser under chaotic optical injection,” Acta Phys. Sinica 66(24), 224206 (2017).
  24. P. Xu, G. Q. Xia, Z. M. Wu, Q. Li, X. D. Lin, X. Tang, L. Fan, and T. Deng, “Circular Polarization Switching and Ploarization Bistability of Optically Pumped 1300 nm Spin Vertical-Cavity Surface-Emitting Lasers,” Acta Phys. Sinica 45(4), 0401002 (2018).
  25. Q. Liang, L. Fan, J. Y. Yang, Z. M. Wu, and G. Q. Xia, “Narrow-linewidth Photonic Microwave Acquisition Based on an Optically Injected 1550 nm Vertical-cavity Surface-emitting Laser under Optoelectronic Negative Feedback,” Acta Phys. Sinica 46(3), 0314001 (2018).
    [Crossref]
  26. W. Y. Yang, G. Q. Xia, Y. S. Hou, Z. F. Jiang, T. Deng, and Z. M. Wu, “Experimental Investigation on Nonlinear Dynamics of a Multi-transverse Mode 1550 nm Vertical-cavity Surface-emitting Laser Subject to Parallel Optical Injection,” Acta Phys. Sinica 47(7), 0714002 (2018).
    [Crossref]
  27. J. Zamora-Munt and C. Masoller, “Numerical implementation of a VCSEL-based stochastic logic gate via polarization bistability,” Opt. Express 18(16), 16418–16429 (2010).
    [Crossref] [PubMed]
  28. S. L. Yan, “All-optical and combinational optoelectronic logic gates using chaotic synchronization of coupling-feedback semiconductor lasers and amplitude modulation (in chinese),” Chin. Sci. Bull 56(16), 1264–1271 (2011).
    [Crossref]
  29. K. P. Singh and S. Sinha, “Enhancement of "logical" responses by noise in a bistable optical system,” Phy. Reve. 83(4 Pt 2), 046219 (2011).
  30. D. Z. Zhong, W. Luo, and G. L. Xu, “Controllable all-optical stochastic logic gates and their delay storages based on the cascaded VCSELs with optical-injection,” Chin. Phys. B 25(9), 342–354 (2016).
    [Crossref]
  31. D. Z. Zhong, W. Luo, G. L. Xu, and Z. Z. Xiao, “Recongurable dynamic all-optical chaotic logic operations in an optically injected VCSEL,” Chin. Phys. B 26(12), 261–271 (2017).
    [Crossref]
  32. J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface- emitting lasers,” IEEE J. Quantum Electron 33(5), 765–783 (1997).
    [Crossref]
  33. M. F. Salvide, C. Masoller, and M. S. Torre, “All-optical stochastic logic gate based on a VCSEL with tunable optical injection,” IEEE J. Quantum Electron. 49(10), 886–893 (2013).
    [Crossref]

2019 (3)

2018 (5)

X. J. Yao, X. Tang, Z. M. Wu, and G. Q. Xia, “Multi-channel physical random number generation based on two orthogonally mutually coupled 1550 nm vertical-cavity surface-emitting lasers,” Acta Phys. Sinica 67(2), 024204 (2018).

Q. Li, T. Deng, Z. M. Wu, and G. Q. Xia, “Security-Enhanced Bidirectional Long-Distance Chaos Secure Communication,” Chin. J. Lasers 45(1), 0106001 (2018).
[Crossref]

P. Xu, G. Q. Xia, Z. M. Wu, Q. Li, X. D. Lin, X. Tang, L. Fan, and T. Deng, “Circular Polarization Switching and Ploarization Bistability of Optically Pumped 1300 nm Spin Vertical-Cavity Surface-Emitting Lasers,” Acta Phys. Sinica 45(4), 0401002 (2018).

Q. Liang, L. Fan, J. Y. Yang, Z. M. Wu, and G. Q. Xia, “Narrow-linewidth Photonic Microwave Acquisition Based on an Optically Injected 1550 nm Vertical-cavity Surface-emitting Laser under Optoelectronic Negative Feedback,” Acta Phys. Sinica 46(3), 0314001 (2018).
[Crossref]

W. Y. Yang, G. Q. Xia, Y. S. Hou, Z. F. Jiang, T. Deng, and Z. M. Wu, “Experimental Investigation on Nonlinear Dynamics of a Multi-transverse Mode 1550 nm Vertical-cavity Surface-emitting Laser Subject to Parallel Optical Injection,” Acta Phys. Sinica 47(7), 0714002 (2018).
[Crossref]

2017 (5)

B. B. Su, J. J. Chen, Z. M. Wu, and G. Q. Xia, “Performances of time-delay signature and bandwidth of the chaos generated by a vertical-cavity surface-emitting laser under chaotic optical injection,” Acta Phys. Sinica 66(24), 224206 (2017).

D. Z. Zhong, W. Luo, G. L. Xu, and Z. Z. Xiao, “Recongurable dynamic all-optical chaotic logic operations in an optically injected VCSEL,” Chin. Phys. B 26(12), 261–271 (2017).
[Crossref]

Z. Q. Zhong, Z. M. Wu, and G. Q. Xia, “Experimental investigation on the time-delay signature of chaotic output from a 1550 nm VCSEL subject to FBG feedback,” Photonics. Res 5(1), 6–10 (2017).
[Crossref]

N. Jiang, C. Xue, D. Liu, Y. Lv, and K. Qiu, “Secure key distribution based on chaos synchronization of VCSELs subject to symmetric random-polarization optical injection,” Opt. Lett. 42(6), 1055–1058 (2017).
[Crossref] [PubMed]

C. H. Uy, D. Rontani, S. Breuer, and M. Sciamanna, “Non-local correlations via chaotic itinerancy in VCSEL with optical feedback,” Opt. Express 25(6), 6914–6926 (2017).
[Crossref] [PubMed]

2016 (3)

Y. Y. Xie, J. C. Li, C. He, Z. D. Zhang, T. T. Song, C. J. Xu, and G. J. Wang, “Long-distance multi-channel bidirectional chaos communication based on synchronized VCSELs subject to chaotic signal injection,” Opt. Commun. 377, 1–9 (2016).
[Crossref]

S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of Chaos Time Delay Signature in a Ring Network Consisting of Three Semiconductor Lasers Coupled With Heterogeneous Delays,” J. Light. Technol. 34(18), 4221–4227 (2016).
[Crossref]

D. Z. Zhong, W. Luo, and G. L. Xu, “Controllable all-optical stochastic logic gates and their delay storages based on the cascaded VCSELs with optical-injection,” Chin. Phys. B 25(9), 342–354 (2016).
[Crossref]

2015 (2)

X. J. Yang, J. J. Chen, G. Q. Xia, J.G. Wu, and Z. M. Wu, “Analyses of the time-delay signature and bandwidth of the chaotic output from a master-slave vertical-cavity surface-emitting laser dynamical system,” Acta Phys. Sinica 64(22), 224213 (2015).

M. Beyki and M. Yaghoobi, “Chaotic logic gate: A new approach in set and design by genetic algorithm,” Chaos, Solitons & Fractals 77, 247–252 (2015).
[Crossref]

2013 (2)

M. F. Salvide, C. Masoller, and M. S. Torre, “All-optical stochastic logic gate based on a VCSEL with tunable optical injection,” IEEE J. Quantum Electron. 49(10), 886–893 (2013).
[Crossref]

Y.B. Tang, Y. P. Tang, H. W. Jiang, W. F. Ji, Y. J. Wu, and X. F. Chen, “Proposal for simultaneous all-optical AND, NOR, and XNOR logic gates using QPM cascading nonlinear effects in two PPLNs,” Chin. Opt. Lett. 11(6), 66–69 (2013).

2012 (1)

2011 (3)

S. L. Yan, “All-optical and combinational optoelectronic logic gates using chaotic synchronization of coupling-feedback semiconductor lasers and amplitude modulation (in chinese),” Chin. Sci. Bull 56(16), 1264–1271 (2011).
[Crossref]

K. P. Singh and S. Sinha, “Enhancement of "logical" responses by noise in a bistable optical system,” Phy. Reve. 83(4 Pt 2), 046219 (2011).

B. Kia, A. Dari, W. L. Ditto, and M. L. Spano, “Unstable periodic orbits and noise in chaos computing,” Chaos: An Interdiscip. J. Nonlinear Sci.,  21(4), 074520 (2011).
[Crossref]

2010 (2)

L. L. Li, J. Wu, J. F. Qiu, B. B. Wu, K. Xu, X. B. Hong, Y. Li, and J. T. Lin, “Reconfigurable all-optical logic gate using four-wave mixing (FWM) in HNLF for NRZ-PolSK signal,” Opt. Commun. 283(19), 3608–3612 (2010).
[Crossref]

J. Zamora-Munt and C. Masoller, “Numerical implementation of a VCSEL-based stochastic logic gate via polarization bistability,” Opt. Express 18(16), 16418–16429 (2010).
[Crossref] [PubMed]

2008 (1)

F. Nian, “The Characteristic of Polarization Chaos and Coherence of Semiconductor Optical Amplifier-Based Fiber Ring Laser,” Acta Opt. Sinica 28(1), 128–131 (2008).
[Crossref]

2005 (2)

K. Murali, S. Sinha, and I. R. Mohamed, “Chaos computing: experimental realization of NOR gate using a simple chaotic circuit,” Phys. Lett. A 339(1–2), 39–44 (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. Alan Shore, “Chaos based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

2001 (1)

K. Myneni, T. A. Barr, B. R. Reed, S. D. Pethel, and N. J. Corron, “High-precision ranging using a chaotic laser pulse train,” Appl. Phys. Lett. 78(11), 1496–1498 (2001).
[Crossref]

1999 (1)

C. T. Lin and C. P. Jou, “Controlling chaos by GA-based reinforcement learning neural network,” IEEE Trans. Neural. Netw. 10(4), 846–859 (1999).
[Crossref]

1997 (1)

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface- emitting lasers,” IEEE J. Quantum Electron 33(5), 765–783 (1997).
[Crossref]

1995 (1)

J. Y. Gao, J. H. Huang, Z. R. Zheng, Y. Jiang, Y. Zhang, and G. X. Jin, “Hybrid bostable system and its application to dynamic memory,” Opt. Eng. 34(3), 790–794 (1995).
[Crossref]

Abraham, N. B.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface- emitting lasers,” IEEE J. Quantum Electron 33(5), 765–783 (1997).
[Crossref]

Alan Shore, K.

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

Argyris, A.

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

Barr, T. A.

K. Myneni, T. A. Barr, B. R. Reed, S. D. Pethel, and N. J. Corron, “High-precision ranging using a chaotic laser pulse train,” Appl. Phys. Lett. 78(11), 1496–1498 (2001).
[Crossref]

Beyki, M.

M. Beyki and M. Yaghoobi, “Chaotic logic gate: A new approach in set and design by genetic algorithm,” Chaos, Solitons & Fractals 77, 247–252 (2015).
[Crossref]

Breuer, S.

Cao, X. Y.

Chen, J. J.

B. B. Su, J. J. Chen, Z. M. Wu, and G. Q. Xia, “Performances of time-delay signature and bandwidth of the chaos generated by a vertical-cavity surface-emitting laser under chaotic optical injection,” Acta Phys. Sinica 66(24), 224206 (2017).

X. J. Yang, J. J. Chen, G. Q. Xia, J.G. Wu, and Z. M. Wu, “Analyses of the time-delay signature and bandwidth of the chaotic output from a master-slave vertical-cavity surface-emitting laser dynamical system,” Acta Phys. Sinica 64(22), 224213 (2015).

Chen, X. F.

Y.B. Tang, Y. P. Tang, H. W. Jiang, W. F. Ji, Y. J. Wu, and X. F. Chen, “Proposal for simultaneous all-optical AND, NOR, and XNOR logic gates using QPM cascading nonlinear effects in two PPLNs,” Chin. Opt. Lett. 11(6), 66–69 (2013).

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. Alan Shore, “Chaos based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Corron, N. J.

K. Myneni, T. A. Barr, B. R. Reed, S. D. Pethel, and N. J. Corron, “High-precision ranging using a chaotic laser pulse train,” Appl. Phys. Lett. 78(11), 1496–1498 (2001).
[Crossref]

Dari, A.

B. Kia, A. Dari, W. L. Ditto, and M. L. Spano, “Unstable periodic orbits and noise in chaos computing,” Chaos: An Interdiscip. J. Nonlinear Sci.,  21(4), 074520 (2011).
[Crossref]

Deng, T.

Q. Li, T. Deng, Z. M. Wu, and G. Q. Xia, “Security-Enhanced Bidirectional Long-Distance Chaos Secure Communication,” Chin. J. Lasers 45(1), 0106001 (2018).
[Crossref]

W. Y. Yang, G. Q. Xia, Y. S. Hou, Z. F. Jiang, T. Deng, and Z. M. Wu, “Experimental Investigation on Nonlinear Dynamics of a Multi-transverse Mode 1550 nm Vertical-cavity Surface-emitting Laser Subject to Parallel Optical Injection,” Acta Phys. Sinica 47(7), 0714002 (2018).
[Crossref]

P. Xu, G. Q. Xia, Z. M. Wu, Q. Li, X. D. Lin, X. Tang, L. Fan, and T. Deng, “Circular Polarization Switching and Ploarization Bistability of Optically Pumped 1300 nm Spin Vertical-Cavity Surface-Emitting Lasers,” Acta Phys. Sinica 45(4), 0401002 (2018).

Ditto, W. L.

B. Kia, A. Dari, W. L. Ditto, and M. L. Spano, “Unstable periodic orbits and noise in chaos computing,” Chaos: An Interdiscip. J. Nonlinear Sci.,  21(4), 074520 (2011).
[Crossref]

Duport, F.

Fan, L.

Q. Liang, L. Fan, J. Y. Yang, Z. M. Wu, and G. Q. Xia, “Narrow-linewidth Photonic Microwave Acquisition Based on an Optically Injected 1550 nm Vertical-cavity Surface-emitting Laser under Optoelectronic Negative Feedback,” Acta Phys. Sinica 46(3), 0314001 (2018).
[Crossref]

P. Xu, G. Q. Xia, Z. M. Wu, Q. Li, X. D. Lin, X. Tang, L. Fan, and T. Deng, “Circular Polarization Switching and Ploarization Bistability of Optically Pumped 1300 nm Spin Vertical-Cavity Surface-Emitting Lasers,” Acta Phys. Sinica 45(4), 0401002 (2018).

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. Alan Shore, “Chaos based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Gao, J. Y.

J. Y. Gao, J. H. Huang, Z. R. Zheng, Y. Jiang, Y. Zhang, and G. X. Jin, “Hybrid bostable system and its application to dynamic memory,” Opt. Eng. 34(3), 790–794 (1995).
[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. Alan Shore, “Chaos based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Gong, J. K.

S. Y. Xiang, Y. H. Zhang, J. K. Gong, X. X. Guo, L. Lin, and Y. Hao, “STDP-Based Unsupervised Spike Pattern Learning in a Photonic Spiking Neural Network With VCSELs and VCSOAs,” IEEE J. Sel. Top. Quantum Electron. 25(6), 1700109 (2019).
[Crossref]

Guo, X. X.

S. Y. Xiang, Y. H. Zhang, J. K. Gong, X. X. Guo, L. Lin, and Y. Hao, “STDP-Based Unsupervised Spike Pattern Learning in a Photonic Spiking Neural Network With VCSELs and VCSOAs,” IEEE J. Sel. Top. Quantum Electron. 25(6), 1700109 (2019).
[Crossref]

S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of Chaos Time Delay Signature in a Ring Network Consisting of Three Semiconductor Lasers Coupled With Heterogeneous Delays,” J. Light. Technol. 34(18), 4221–4227 (2016).
[Crossref]

Haelterman, M.

Hao, Y.

S. Y. Xiang, Y. H. Zhang, J. K. Gong, X. X. Guo, L. Lin, and Y. Hao, “STDP-Based Unsupervised Spike Pattern Learning in a Photonic Spiking Neural Network With VCSELs and VCSOAs,” IEEE J. Sel. Top. Quantum Electron. 25(6), 1700109 (2019).
[Crossref]

Y. Wang, S. Y. Xiang, B. Wang, X. Y. Cao, A. J. Wen, and Y. Hao, “Time-delay signature concealment and physical random bits generation in mutually coupled semiconductor lasers with FBG filtered injection,” Opt. Express 27(6), 8446–8455 (2019).
[Crossref] [PubMed]

He, C.

Y. Y. Xie, J. C. Li, C. He, Z. D. Zhang, T. T. Song, C. J. Xu, and G. J. Wang, “Long-distance multi-channel bidirectional chaos communication based on synchronized VCSELs subject to chaotic signal injection,” Opt. Commun. 377, 1–9 (2016).
[Crossref]

Hong, X. B.

L. L. Li, J. Wu, J. F. Qiu, B. B. Wu, K. Xu, X. B. Hong, Y. Li, and J. T. Lin, “Reconfigurable all-optical logic gate using four-wave mixing (FWM) in HNLF for NRZ-PolSK signal,” Opt. Commun. 283(19), 3608–3612 (2010).
[Crossref]

Hou, Y. S.

W. Y. Yang, G. Q. Xia, Y. S. Hou, Z. F. Jiang, T. Deng, and Z. M. Wu, “Experimental Investigation on Nonlinear Dynamics of a Multi-transverse Mode 1550 nm Vertical-cavity Surface-emitting Laser Subject to Parallel Optical Injection,” Acta Phys. Sinica 47(7), 0714002 (2018).
[Crossref]

Huang, J. H.

J. Y. Gao, J. H. Huang, Z. R. Zheng, Y. Jiang, Y. Zhang, and G. X. Jin, “Hybrid bostable system and its application to dynamic memory,” Opt. Eng. 34(3), 790–794 (1995).
[Crossref]

Ji, W. F.

Y.B. Tang, Y. P. Tang, H. W. Jiang, W. F. Ji, Y. J. Wu, and X. F. Chen, “Proposal for simultaneous all-optical AND, NOR, and XNOR logic gates using QPM cascading nonlinear effects in two PPLNs,” Chin. Opt. Lett. 11(6), 66–69 (2013).

Jiang, H. W.

Y.B. Tang, Y. P. Tang, H. W. Jiang, W. F. Ji, Y. J. Wu, and X. F. Chen, “Proposal for simultaneous all-optical AND, NOR, and XNOR logic gates using QPM cascading nonlinear effects in two PPLNs,” Chin. Opt. Lett. 11(6), 66–69 (2013).

Jiang, N.

Jiang, Y.

J. Y. Gao, J. H. Huang, Z. R. Zheng, Y. Jiang, Y. Zhang, and G. X. Jin, “Hybrid bostable system and its application to dynamic memory,” Opt. Eng. 34(3), 790–794 (1995).
[Crossref]

Jiang, Z. F.

W. Y. Yang, G. Q. Xia, Y. S. Hou, Z. F. Jiang, T. Deng, and Z. M. Wu, “Experimental Investigation on Nonlinear Dynamics of a Multi-transverse Mode 1550 nm Vertical-cavity Surface-emitting Laser Subject to Parallel Optical Injection,” Acta Phys. Sinica 47(7), 0714002 (2018).
[Crossref]

Jin, G. X.

J. Y. Gao, J. H. Huang, Z. R. Zheng, Y. Jiang, Y. Zhang, and G. X. Jin, “Hybrid bostable system and its application to dynamic memory,” Opt. Eng. 34(3), 790–794 (1995).
[Crossref]

Jou, C. P.

C. T. Lin and C. P. Jou, “Controlling chaos by GA-based reinforcement learning neural network,” IEEE Trans. Neural. Netw. 10(4), 846–859 (1999).
[Crossref]

Kia, B.

B. Kia, A. Dari, W. L. Ditto, and M. L. Spano, “Unstable periodic orbits and noise in chaos computing,” Chaos: An Interdiscip. J. Nonlinear Sci.,  21(4), 074520 (2011).
[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. Alan Shore, “Chaos based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Li, J. C.

Y. Y. Xie, J. C. Li, C. He, Z. D. Zhang, T. T. Song, C. J. Xu, and G. J. Wang, “Long-distance multi-channel bidirectional chaos communication based on synchronized VCSELs subject to chaotic signal injection,” Opt. Commun. 377, 1–9 (2016).
[Crossref]

Li, J. F.

S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of Chaos Time Delay Signature in a Ring Network Consisting of Three Semiconductor Lasers Coupled With Heterogeneous Delays,” J. Light. Technol. 34(18), 4221–4227 (2016).
[Crossref]

Li, L. L.

L. L. Li, J. Wu, J. F. Qiu, B. B. Wu, K. Xu, X. B. Hong, Y. Li, and J. T. Lin, “Reconfigurable all-optical logic gate using four-wave mixing (FWM) in HNLF for NRZ-PolSK signal,” Opt. Commun. 283(19), 3608–3612 (2010).
[Crossref]

Li, Q.

Q. Li, T. Deng, Z. M. Wu, and G. Q. Xia, “Security-Enhanced Bidirectional Long-Distance Chaos Secure Communication,” Chin. J. Lasers 45(1), 0106001 (2018).
[Crossref]

P. Xu, G. Q. Xia, Z. M. Wu, Q. Li, X. D. Lin, X. Tang, L. Fan, and T. Deng, “Circular Polarization Switching and Ploarization Bistability of Optically Pumped 1300 nm Spin Vertical-Cavity Surface-Emitting Lasers,” Acta Phys. Sinica 45(4), 0401002 (2018).

Li, Y.

L. L. Li, J. Wu, J. F. Qiu, B. B. Wu, K. Xu, X. B. Hong, Y. Li, and J. T. Lin, “Reconfigurable all-optical logic gate using four-wave mixing (FWM) in HNLF for NRZ-PolSK signal,” Opt. Commun. 283(19), 3608–3612 (2010).
[Crossref]

Liang, Q.

Q. Liang, L. Fan, J. Y. Yang, Z. M. Wu, and G. Q. Xia, “Narrow-linewidth Photonic Microwave Acquisition Based on an Optically Injected 1550 nm Vertical-cavity Surface-emitting Laser under Optoelectronic Negative Feedback,” Acta Phys. Sinica 46(3), 0314001 (2018).
[Crossref]

Lin, C. T.

C. T. Lin and C. P. Jou, “Controlling chaos by GA-based reinforcement learning neural network,” IEEE Trans. Neural. Netw. 10(4), 846–859 (1999).
[Crossref]

Lin, J. T.

L. L. Li, J. Wu, J. F. Qiu, B. B. Wu, K. Xu, X. B. Hong, Y. Li, and J. T. Lin, “Reconfigurable all-optical logic gate using four-wave mixing (FWM) in HNLF for NRZ-PolSK signal,” Opt. Commun. 283(19), 3608–3612 (2010).
[Crossref]

Lin, L.

S. Y. Xiang, Y. H. Zhang, J. K. Gong, X. X. Guo, L. Lin, and Y. Hao, “STDP-Based Unsupervised Spike Pattern Learning in a Photonic Spiking Neural Network With VCSELs and VCSOAs,” IEEE J. Sel. Top. Quantum Electron. 25(6), 1700109 (2019).
[Crossref]

S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of Chaos Time Delay Signature in a Ring Network Consisting of Three Semiconductor Lasers Coupled With Heterogeneous Delays,” J. Light. Technol. 34(18), 4221–4227 (2016).
[Crossref]

Lin, X. D.

P. Xu, G. Q. Xia, Z. M. Wu, Q. Li, X. D. Lin, X. Tang, L. Fan, and T. Deng, “Circular Polarization Switching and Ploarization Bistability of Optically Pumped 1300 nm Spin Vertical-Cavity Surface-Emitting Lasers,” Acta Phys. Sinica 45(4), 0401002 (2018).

Liu, D.

Luo, W.

D. Z. Zhong, W. Luo, G. L. Xu, and Z. Z. Xiao, “Recongurable dynamic all-optical chaotic logic operations in an optically injected VCSEL,” Chin. Phys. B 26(12), 261–271 (2017).
[Crossref]

D. Z. Zhong, W. Luo, and G. L. Xu, “Controllable all-optical stochastic logic gates and their delay storages based on the cascaded VCSELs with optical-injection,” Chin. Phys. B 25(9), 342–354 (2016).
[Crossref]

Lv, Y.

Martin-Regalado, J.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface- emitting lasers,” IEEE J. Quantum Electron 33(5), 765–783 (1997).
[Crossref]

Masoller, C.

M. F. Salvide, C. Masoller, and M. S. Torre, “All-optical stochastic logic gate based on a VCSEL with tunable optical injection,” IEEE J. Quantum Electron. 49(10), 886–893 (2013).
[Crossref]

J. Zamora-Munt and C. Masoller, “Numerical implementation of a VCSEL-based stochastic logic gate via polarization bistability,” Opt. Express 18(16), 16418–16429 (2010).
[Crossref] [PubMed]

Massar, S.

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. Alan Shore, “Chaos based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Mohamed, I. R.

K. Murali, S. Sinha, and I. R. Mohamed, “Chaos computing: experimental realization of NOR gate using a simple chaotic circuit,” Phys. Lett. A 339(1–2), 39–44 (2005).
[Crossref]

Murali, K.

K. Murali, S. Sinha, and I. R. Mohamed, “Chaos computing: experimental realization of NOR gate using a simple chaotic circuit,” Phys. Lett. A 339(1–2), 39–44 (2005).
[Crossref]

Myneni, K.

K. Myneni, T. A. Barr, B. R. Reed, S. D. Pethel, and N. J. Corron, “High-precision ranging using a chaotic laser pulse train,” Appl. Phys. Lett. 78(11), 1496–1498 (2001).
[Crossref]

Nian, F.

F. Nian, “The Characteristic of Polarization Chaos and Coherence of Semiconductor Optical Amplifier-Based Fiber Ring Laser,” Acta Opt. Sinica 28(1), 128–131 (2008).
[Crossref]

Pan, W.

S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of Chaos Time Delay Signature in a Ring Network Consisting of Three Semiconductor Lasers Coupled With Heterogeneous Delays,” J. Light. Technol. 34(18), 4221–4227 (2016).
[Crossref]

Pesquera, L.

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

Pethel, S. D.

K. Myneni, T. A. Barr, B. R. Reed, S. D. Pethel, and N. J. Corron, “High-precision ranging using a chaotic laser pulse train,” Appl. Phys. Lett. 78(11), 1496–1498 (2001).
[Crossref]

Prati, F.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface- emitting lasers,” IEEE J. Quantum Electron 33(5), 765–783 (1997).
[Crossref]

Qiu, J. F.

L. L. Li, J. Wu, J. F. Qiu, B. B. Wu, K. Xu, X. B. Hong, Y. Li, and J. T. Lin, “Reconfigurable all-optical logic gate using four-wave mixing (FWM) in HNLF for NRZ-PolSK signal,” Opt. Commun. 283(19), 3608–3612 (2010).
[Crossref]

Qiu, K.

Reed, B. R.

K. Myneni, T. A. Barr, B. R. Reed, S. D. Pethel, and N. J. Corron, “High-precision ranging using a chaotic laser pulse train,” Appl. Phys. Lett. 78(11), 1496–1498 (2001).
[Crossref]

Rontani, D.

Salvide, M. F.

M. F. Salvide, C. Masoller, and M. S. Torre, “All-optical stochastic logic gate based on a VCSEL with tunable optical injection,” IEEE J. Quantum Electron. 49(10), 886–893 (2013).
[Crossref]

San Miguel, M.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface- emitting lasers,” IEEE J. Quantum Electron 33(5), 765–783 (1997).
[Crossref]

Schneider, B.

Sciamanna, M.

Singh, K. P.

K. P. Singh and S. Sinha, “Enhancement of "logical" responses by noise in a bistable optical system,” Phy. Reve. 83(4 Pt 2), 046219 (2011).

Sinha, S.

K. P. Singh and S. Sinha, “Enhancement of "logical" responses by noise in a bistable optical system,” Phy. Reve. 83(4 Pt 2), 046219 (2011).

K. Murali, S. Sinha, and I. R. Mohamed, “Chaos computing: experimental realization of NOR gate using a simple chaotic circuit,” Phys. Lett. A 339(1–2), 39–44 (2005).
[Crossref]

Smerieri, A.

Song, T. T.

Y. Y. Xie, J. C. Li, C. He, Z. D. Zhang, T. T. Song, C. J. Xu, and G. J. Wang, “Long-distance multi-channel bidirectional chaos communication based on synchronized VCSELs subject to chaotic signal injection,” Opt. Commun. 377, 1–9 (2016).
[Crossref]

Spano, M. L.

B. Kia, A. Dari, W. L. Ditto, and M. L. Spano, “Unstable periodic orbits and noise in chaos computing,” Chaos: An Interdiscip. J. Nonlinear Sci.,  21(4), 074520 (2011).
[Crossref]

Su, B. B.

B. B. Su, J. J. Chen, Z. M. Wu, and G. Q. Xia, “Performances of time-delay signature and bandwidth of the chaos generated by a vertical-cavity surface-emitting laser under chaotic optical injection,” Acta Phys. Sinica 66(24), 224206 (2017).

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. Alan Shore, “Chaos based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Tang, J. M.

Tang, X.

X. J. Yao, X. Tang, Z. M. Wu, and G. Q. Xia, “Multi-channel physical random number generation based on two orthogonally mutually coupled 1550 nm vertical-cavity surface-emitting lasers,” Acta Phys. Sinica 67(2), 024204 (2018).

P. Xu, G. Q. Xia, Z. M. Wu, Q. Li, X. D. Lin, X. Tang, L. Fan, and T. Deng, “Circular Polarization Switching and Ploarization Bistability of Optically Pumped 1300 nm Spin Vertical-Cavity Surface-Emitting Lasers,” Acta Phys. Sinica 45(4), 0401002 (2018).

Tang, Y. P.

Y.B. Tang, Y. P. Tang, H. W. Jiang, W. F. Ji, Y. J. Wu, and X. F. Chen, “Proposal for simultaneous all-optical AND, NOR, and XNOR logic gates using QPM cascading nonlinear effects in two PPLNs,” Chin. Opt. Lett. 11(6), 66–69 (2013).

Tang, Y.B.

Y.B. Tang, Y. P. Tang, H. W. Jiang, W. F. Ji, Y. J. Wu, and X. F. Chen, “Proposal for simultaneous all-optical AND, NOR, and XNOR logic gates using QPM cascading nonlinear effects in two PPLNs,” Chin. Opt. Lett. 11(6), 66–69 (2013).

Torre, M. S.

M. F. Salvide, C. Masoller, and M. S. Torre, “All-optical stochastic logic gate based on a VCSEL with tunable optical injection,” IEEE J. Quantum Electron. 49(10), 886–893 (2013).
[Crossref]

Uy, C. H.

Wang, B.

Wang, G. J.

Y. Y. Xie, J. C. Li, C. He, Z. D. Zhang, T. T. Song, C. J. Xu, and G. J. Wang, “Long-distance multi-channel bidirectional chaos communication based on synchronized VCSELs subject to chaotic signal injection,” Opt. Commun. 377, 1–9 (2016).
[Crossref]

Wang, Y.

Wen, A. J.

Y. Wang, S. Y. Xiang, B. Wang, X. Y. Cao, A. J. Wen, and Y. Hao, “Time-delay signature concealment and physical random bits generation in mutually coupled semiconductor lasers with FBG filtered injection,” Opt. Express 27(6), 8446–8455 (2019).
[Crossref] [PubMed]

S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of Chaos Time Delay Signature in a Ring Network Consisting of Three Semiconductor Lasers Coupled With Heterogeneous Delays,” J. Light. Technol. 34(18), 4221–4227 (2016).
[Crossref]

Wu, B. B.

L. L. Li, J. Wu, J. F. Qiu, B. B. Wu, K. Xu, X. B. Hong, Y. Li, and J. T. Lin, “Reconfigurable all-optical logic gate using four-wave mixing (FWM) in HNLF for NRZ-PolSK signal,” Opt. Commun. 283(19), 3608–3612 (2010).
[Crossref]

Wu, J.

L. L. Li, J. Wu, J. F. Qiu, B. B. Wu, K. Xu, X. B. Hong, Y. Li, and J. T. Lin, “Reconfigurable all-optical logic gate using four-wave mixing (FWM) in HNLF for NRZ-PolSK signal,” Opt. Commun. 283(19), 3608–3612 (2010).
[Crossref]

Wu, J.G.

X. J. Yang, J. J. Chen, G. Q. Xia, J.G. Wu, and Z. M. Wu, “Analyses of the time-delay signature and bandwidth of the chaotic output from a master-slave vertical-cavity surface-emitting laser dynamical system,” Acta Phys. Sinica 64(22), 224213 (2015).

Wu, Y. J.

Y.B. Tang, Y. P. Tang, H. W. Jiang, W. F. Ji, Y. J. Wu, and X. F. Chen, “Proposal for simultaneous all-optical AND, NOR, and XNOR logic gates using QPM cascading nonlinear effects in two PPLNs,” Chin. Opt. Lett. 11(6), 66–69 (2013).

Wu, Z. M.

X. J. Yao, X. Tang, Z. M. Wu, and G. Q. Xia, “Multi-channel physical random number generation based on two orthogonally mutually coupled 1550 nm vertical-cavity surface-emitting lasers,” Acta Phys. Sinica 67(2), 024204 (2018).

Q. Li, T. Deng, Z. M. Wu, and G. Q. Xia, “Security-Enhanced Bidirectional Long-Distance Chaos Secure Communication,” Chin. J. Lasers 45(1), 0106001 (2018).
[Crossref]

P. Xu, G. Q. Xia, Z. M. Wu, Q. Li, X. D. Lin, X. Tang, L. Fan, and T. Deng, “Circular Polarization Switching and Ploarization Bistability of Optically Pumped 1300 nm Spin Vertical-Cavity Surface-Emitting Lasers,” Acta Phys. Sinica 45(4), 0401002 (2018).

Q. Liang, L. Fan, J. Y. Yang, Z. M. Wu, and G. Q. Xia, “Narrow-linewidth Photonic Microwave Acquisition Based on an Optically Injected 1550 nm Vertical-cavity Surface-emitting Laser under Optoelectronic Negative Feedback,” Acta Phys. Sinica 46(3), 0314001 (2018).
[Crossref]

W. Y. Yang, G. Q. Xia, Y. S. Hou, Z. F. Jiang, T. Deng, and Z. M. Wu, “Experimental Investigation on Nonlinear Dynamics of a Multi-transverse Mode 1550 nm Vertical-cavity Surface-emitting Laser Subject to Parallel Optical Injection,” Acta Phys. Sinica 47(7), 0714002 (2018).
[Crossref]

B. B. Su, J. J. Chen, Z. M. Wu, and G. Q. Xia, “Performances of time-delay signature and bandwidth of the chaos generated by a vertical-cavity surface-emitting laser under chaotic optical injection,” Acta Phys. Sinica 66(24), 224206 (2017).

Z. Q. Zhong, Z. M. Wu, and G. Q. Xia, “Experimental investigation on the time-delay signature of chaotic output from a 1550 nm VCSEL subject to FBG feedback,” Photonics. Res 5(1), 6–10 (2017).
[Crossref]

X. J. Yang, J. J. Chen, G. Q. Xia, J.G. Wu, and Z. M. Wu, “Analyses of the time-delay signature and bandwidth of the chaotic output from a master-slave vertical-cavity surface-emitting laser dynamical system,” Acta Phys. Sinica 64(22), 224213 (2015).

Xia, G. Q.

Q. Li, T. Deng, Z. M. Wu, and G. Q. Xia, “Security-Enhanced Bidirectional Long-Distance Chaos Secure Communication,” Chin. J. Lasers 45(1), 0106001 (2018).
[Crossref]

X. J. Yao, X. Tang, Z. M. Wu, and G. Q. Xia, “Multi-channel physical random number generation based on two orthogonally mutually coupled 1550 nm vertical-cavity surface-emitting lasers,” Acta Phys. Sinica 67(2), 024204 (2018).

P. Xu, G. Q. Xia, Z. M. Wu, Q. Li, X. D. Lin, X. Tang, L. Fan, and T. Deng, “Circular Polarization Switching and Ploarization Bistability of Optically Pumped 1300 nm Spin Vertical-Cavity Surface-Emitting Lasers,” Acta Phys. Sinica 45(4), 0401002 (2018).

Q. Liang, L. Fan, J. Y. Yang, Z. M. Wu, and G. Q. Xia, “Narrow-linewidth Photonic Microwave Acquisition Based on an Optically Injected 1550 nm Vertical-cavity Surface-emitting Laser under Optoelectronic Negative Feedback,” Acta Phys. Sinica 46(3), 0314001 (2018).
[Crossref]

W. Y. Yang, G. Q. Xia, Y. S. Hou, Z. F. Jiang, T. Deng, and Z. M. Wu, “Experimental Investigation on Nonlinear Dynamics of a Multi-transverse Mode 1550 nm Vertical-cavity Surface-emitting Laser Subject to Parallel Optical Injection,” Acta Phys. Sinica 47(7), 0714002 (2018).
[Crossref]

B. B. Su, J. J. Chen, Z. M. Wu, and G. Q. Xia, “Performances of time-delay signature and bandwidth of the chaos generated by a vertical-cavity surface-emitting laser under chaotic optical injection,” Acta Phys. Sinica 66(24), 224206 (2017).

Z. Q. Zhong, Z. M. Wu, and G. Q. Xia, “Experimental investigation on the time-delay signature of chaotic output from a 1550 nm VCSEL subject to FBG feedback,” Photonics. Res 5(1), 6–10 (2017).
[Crossref]

X. J. Yang, J. J. Chen, G. Q. Xia, J.G. Wu, and Z. M. Wu, “Analyses of the time-delay signature and bandwidth of the chaotic output from a master-slave vertical-cavity surface-emitting laser dynamical system,” Acta Phys. Sinica 64(22), 224213 (2015).

Xiang, S. Y.

S. Y. Xiang, Y. H. Zhang, J. K. Gong, X. X. Guo, L. Lin, and Y. Hao, “STDP-Based Unsupervised Spike Pattern Learning in a Photonic Spiking Neural Network With VCSELs and VCSOAs,” IEEE J. Sel. Top. Quantum Electron. 25(6), 1700109 (2019).
[Crossref]

Y. Wang, S. Y. Xiang, B. Wang, X. Y. Cao, A. J. Wen, and Y. Hao, “Time-delay signature concealment and physical random bits generation in mutually coupled semiconductor lasers with FBG filtered injection,” Opt. Express 27(6), 8446–8455 (2019).
[Crossref] [PubMed]

S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of Chaos Time Delay Signature in a Ring Network Consisting of Three Semiconductor Lasers Coupled With Heterogeneous Delays,” J. Light. Technol. 34(18), 4221–4227 (2016).
[Crossref]

Xiao, Z. Z.

D. Z. Zhong, W. Luo, G. L. Xu, and Z. Z. Xiao, “Recongurable dynamic all-optical chaotic logic operations in an optically injected VCSEL,” Chin. Phys. B 26(12), 261–271 (2017).
[Crossref]

Xie, Y. Y.

Y. Y. Xie, J. C. Li, C. He, Z. D. Zhang, T. T. Song, C. J. Xu, and G. J. Wang, “Long-distance multi-channel bidirectional chaos communication based on synchronized VCSELs subject to chaotic signal injection,” Opt. Commun. 377, 1–9 (2016).
[Crossref]

Xu, C. J.

Y. Y. Xie, J. C. Li, C. He, Z. D. Zhang, T. T. Song, C. J. Xu, and G. J. Wang, “Long-distance multi-channel bidirectional chaos communication based on synchronized VCSELs subject to chaotic signal injection,” Opt. Commun. 377, 1–9 (2016).
[Crossref]

Xu, G. L.

D. Z. Zhong, W. Luo, G. L. Xu, and Z. Z. Xiao, “Recongurable dynamic all-optical chaotic logic operations in an optically injected VCSEL,” Chin. Phys. B 26(12), 261–271 (2017).
[Crossref]

D. Z. Zhong, W. Luo, and G. L. Xu, “Controllable all-optical stochastic logic gates and their delay storages based on the cascaded VCSELs with optical-injection,” Chin. Phys. B 25(9), 342–354 (2016).
[Crossref]

Xu, K.

L. L. Li, J. Wu, J. F. Qiu, B. B. Wu, K. Xu, X. B. Hong, Y. Li, and J. T. Lin, “Reconfigurable all-optical logic gate using four-wave mixing (FWM) in HNLF for NRZ-PolSK signal,” Opt. Commun. 283(19), 3608–3612 (2010).
[Crossref]

Xu, P.

P. Xu, G. Q. Xia, Z. M. Wu, Q. Li, X. D. Lin, X. Tang, L. Fan, and T. Deng, “Circular Polarization Switching and Ploarization Bistability of Optically Pumped 1300 nm Spin Vertical-Cavity Surface-Emitting Lasers,” Acta Phys. Sinica 45(4), 0401002 (2018).

Xue, C.

Xue, C. P.

Yaghoobi, M.

M. Beyki and M. Yaghoobi, “Chaotic logic gate: A new approach in set and design by genetic algorithm,” Chaos, Solitons & Fractals 77, 247–252 (2015).
[Crossref]

Yan, S. L.

S. L. Yan, “All-optical and combinational optoelectronic logic gates using chaotic synchronization of coupling-feedback semiconductor lasers and amplitude modulation (in chinese),” Chin. Sci. Bull 56(16), 1264–1271 (2011).
[Crossref]

Yang, J. Y.

Q. Liang, L. Fan, J. Y. Yang, Z. M. Wu, and G. Q. Xia, “Narrow-linewidth Photonic Microwave Acquisition Based on an Optically Injected 1550 nm Vertical-cavity Surface-emitting Laser under Optoelectronic Negative Feedback,” Acta Phys. Sinica 46(3), 0314001 (2018).
[Crossref]

Yang, W. Y.

W. Y. Yang, G. Q. Xia, Y. S. Hou, Z. F. Jiang, T. Deng, and Z. M. Wu, “Experimental Investigation on Nonlinear Dynamics of a Multi-transverse Mode 1550 nm Vertical-cavity Surface-emitting Laser Subject to Parallel Optical Injection,” Acta Phys. Sinica 47(7), 0714002 (2018).
[Crossref]

Yang, X. J.

X. J. Yang, J. J. Chen, G. Q. Xia, J.G. Wu, and Z. M. Wu, “Analyses of the time-delay signature and bandwidth of the chaotic output from a master-slave vertical-cavity surface-emitting laser dynamical system,” Acta Phys. Sinica 64(22), 224213 (2015).

Yao, X. J.

X. J. Yao, X. Tang, Z. M. Wu, and G. Q. Xia, “Multi-channel physical random number generation based on two orthogonally mutually coupled 1550 nm vertical-cavity surface-emitting lasers,” Acta Phys. Sinica 67(2), 024204 (2018).

Zamora-Munt, J.

Zhang, H.

S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of Chaos Time Delay Signature in a Ring Network Consisting of Three Semiconductor Lasers Coupled With Heterogeneous Delays,” J. Light. Technol. 34(18), 4221–4227 (2016).
[Crossref]

S. Y. Xiang, A. J. Wen, W. Pan, L. Lin, H. Zhang, H. Zhang, X. X. Guo, and J. F. Li, “Suppression of Chaos Time Delay Signature in a Ring Network Consisting of Three Semiconductor Lasers Coupled With Heterogeneous Delays,” J. Light. Technol. 34(18), 4221–4227 (2016).
[Crossref]

Zhang, Y.

J. Y. Gao, J. H. Huang, Z. R. Zheng, Y. Jiang, Y. Zhang, and G. X. Jin, “Hybrid bostable system and its application to dynamic memory,” Opt. Eng. 34(3), 790–794 (1995).
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Zhang, Y. H.

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Figures (6)

Fig. 1
Fig. 1 Schematic diagram of two parallel optical chaotic data-selection computing in an optically injected VCSEL (see texts for the detailed description).
Fig. 2
Fig. 2 Maps of nonlinear dynamic behavior of the optically VCSEL evolution in the parameter space of Einj and Δω. Here, CO: chaotic state; QP: quasi-periodic oscillation; P1: period-one oscillation; P2: period-two oscillation.
Fig. 3
Fig. 3 For Δω = 0 GHz (a) and −80 GHz (b), the bistability evolutions of the x-PC and the y-PC with the amplitude of the injection field. Here, I N x = E x 2; I N y = E y 2; the red-solid line: the x-PC; the black-solid line: the y-PC; the arrows indicate the four-level signals used to encode the logic inputs (see texts in details).
Fig. 4
Fig. 4 For T = 100 ps and T = 67 ps, the implementations of two parallel optical chaotic data-selection computing. Left column: T = 100 ps; right column: T = 67 ps. (a) and (e) show the temporal traces of Δω and Einj; the blue-dashline: the frequency detuning Δω; the red-solid line: the four-level signals Einj; (b) and (f) present the logic data-selection operation between C and the three signals including I1, I2 and I3, where the green, yellow and purple solid lines represent I1, I2 and I3, in turn, and the black-solid line represents the control logic signal C; (c) and (g) show the temporal trace of the output x-PC and the corresponding Y1; (d) and (h) display the temporal trace of the output y-PC and the corresponding Y2.
Fig. 5
Fig. 5 Mappings of the evolutions of the success probability P for the chaotic logic outputs Y1 and Y2 in the parameters of T and Kx (Ky). (a): P of Y1; (b): P of Y2.
Fig. 6
Fig. 6 The success probabilities P for the chaotic logic outputs Y1 and Y2 under the different noise conditions. (a): the success probabilities of Y1; (b): the success probabilities of Y2.

Tables (3)

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Table 1 Numerical values for optical chaotic data-selection logic operation [27].

Tables Icon

Table 2 Combinations of inputs and outputs for chaotic logic selection operations under T = 100 ps.

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Table 3 Combinations of inputs and outputs for chaotic logic selection operations under T = 67 ps.

Equations (20)

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d E x ( t ) d t = k ( 1 + i α ) [ N ( t ) E x ( t ) + i n ( t ) E y ( t ) E x ( t ) ] i ( γ p + Δ ω ) E x γ a E x + β s p γ e N ξ x + K x E inj ,
d E y ( t ) d t = k ( 1 + i α ) [ N ( t ) E y ( t ) i n ( t ) E x ( t ) E y ( t ) ] + i ( γ p Δ ω ) E y + γ a E y + β s p γ e N ξ y + K y E inj ,
d N ( t ) d t = γ e [ N ( 1 + | E x | 2 + | E y | 2 ) ] + γ e μ i γ e n ( E y E x * E x E y * ) ,
d n ( t ) d t = γ s n γ e n ( | E x | 2 + | E y | 2 ) i γ e N ( E y E x * E x E y * ) ,
A x ( i ) = j = 1 M E xi ( j ) M ,
A y ( i ) = j = 1 M E yi ( j ) M ,
A xd MIN 1 = min  { A x ( 1 ) , A x ( 2 ) , ... , A x ( n 0 ) } ,
A ys MAX 1 = max  { A y ( 1 ) , A y ( 2 ) , ... , A y ( n 0 ) } ,
A xs MAX 1 = max  { A x ( 1 ) , A x ( 2 ) , ... , A x ( n 1 ) } ,
A yd MIN 1 = min  { A y ( 1 ) , A y ( 2 ) , ... , A y ( n 1 ) } ,
A xth 1 = A xd MIN 1 + A xs MAX 1 2 ,
A yth 1 = A yd MIN 1 + A ys MAX 1 2 .
A xs MAX 2 = max  { A x ( 1 ) , A x ( 2 ) , ... , A x ( n 0 ) } ,
A yd MIN 2 = min  { A y ( 1 ) , A y ( 2 ) , ... , A y ( n 0 ) } .
A xd MIN 2 = min  { A x ( 1 ) , A x ( 2 ) , ... , A x ( n 1 ) } ,
A yx MAX 2 = max  { A y ( 1 ) , A y ( 2 ) , ... , A y ( n 1 ) } .
A xth 2 = A xd MIN 2 + A xs MAX 2 2 ,
A yth 2 = A yd MIN 2 + A ys MAX 2 2 ,
B x min m = min  { A x ( 1 ) , A x ( 2 ) , ... , A x ( l m ) } , B x max m = max  { A x ( 1 ) , A x ( 2 ) , ... , A x ( l m ) } .
B y min m = min  { A y ( 1 ) , A y ( 2 ) , ... , A y ( l m ) } , B y max m = max  { A y ( 1 ) , A y ( 2 ) , ... , A y ( l m ) } .

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