Abstract

Time-delay signature of chaos in mutually coupled vertical-cavity surface-emitting lasers subject to polarization rotated optical injection has been investigated experimentally. Autocorrelation function and permutation entropy are used to quantitatively identify the time-delay signature of chaos. The experiment results show that the time-delay signature is sensitive to the polarization rotated angle. Minimum time-delay signature has been observed in the intermediate polarization rotated angle for the lower bias current. This is in good agreement with the theoretical prediction. At higher bias currents, the lower time-delay signature has been obtained with parallel optical injection.

© 2013 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. L. Y. Zhang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, and N. Q. Li, “Conceal time-delay signature of mutually coupled vertical-cavity surface-emitting lasers by variable polarization optical injection,” IEEE Photon. Technol. Lett.24(19), 1693–1695 (2012).
    [CrossRef]
  21. P. Xiao, Z.-M. Wu, J.-G. Wu, L. Jiang, T. Deng, X. Tang, L. Fan, and G.-Q. Xia, “Time-delay signature concealment of chaotic output in a vertical-cavity surface-emitting laser with double variable-polarization optical feedback,” Opt. Commun.286, 339–343 (2013).
    [CrossRef]
  22. S. Priyadarshi, Y. Hong, I. Pierce, and K. A. Shore, “Experimental investigations of time-delay signature concealment in chaotic external cavity VCSELs subject to variable optical polarization-angle of feedback,” IEEE J. Sel. Top. Quantum Electron.19(4), 1700707 (2013).
    [CrossRef]
  23. C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Phys. Rev. Lett.88(17), 174102 (2002).
    [CrossRef] [PubMed]
  24. S. Bandyopadhyay, Y. H. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELs,” Opt. Commun.202(1-3), 145–154 (2002).
    [CrossRef]

2013 (4)

Z.-Q. Zhong, Z.-M. Wu, J.-G. Wu, and G.-Q. Xia, “Time-delay signature suppression of polarization-resolved chaos outputs from two mutually coupled VCSELs,” IEEE Photonics J.5(2), 1500409 (2013).
[CrossRef]

P. Xiao, Z.-M. Wu, J.-G. Wu, L. Jiang, T. Deng, X. Tang, L. Fan, and G.-Q. Xia, “Time-delay signature concealment of chaotic output in a vertical-cavity surface-emitting laser with double variable-polarization optical feedback,” Opt. Commun.286, 339–343 (2013).
[CrossRef]

S. Priyadarshi, Y. Hong, I. Pierce, and K. A. Shore, “Experimental investigations of time-delay signature concealment in chaotic external cavity VCSELs subject to variable optical polarization-angle of feedback,” IEEE J. Sel. Top. Quantum Electron.19(4), 1700707 (2013).
[CrossRef]

A. B. Wang, Y. B. Yang, B. J. Wang, B. B. Zhang, L. Li, and Y. C. Wang, “Generation of wideband chaos with suppressed time-delay signature by delayed self-interference,” Opt. Express21(7), 8701–8710 (2013).
[CrossRef] [PubMed]

2012 (4)

J.-G. Wu, Z.-M. Wu, G.-Q. Xia, and G.-Y. Feng, “Evolution of time delay signature of chaos generated in a mutually delay-coupled semiconductor lasers system,” Opt. Express20(2), 1741–1753 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-2-1741 .
[CrossRef] [PubMed]

L. Y. Zhang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, and N. Q. Li, “Conceal time-delay signature of mutually coupled vertical-cavity surface-emitting lasers by variable polarization optical injection,” IEEE Photon. Technol. Lett.24(19), 1693–1695 (2012).
[CrossRef]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, and X. H. Zou, “Loss of time delay signature in Broadband cascade-coupled semiconductor lasers,” IEEE Photon. Technol. Lett.24(23), 2187–2190 (2012).
[CrossRef]

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

2011 (2)

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

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, and H. N. Zhu, “Conceal time-delay signature of chaotic vertical-cavity surface-emitting lasers by variable-polarization optical feedback,” Opt. Commun.284(24), 5758–5765 (2011).
[CrossRef]

2010 (2)

2009 (1)

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE J. Quantum Electron.45(7), 879–891 (2009).
[CrossRef]

2008 (2)

Y. C. Wang, B. J. Wang, and A. B. Wang, “Chaotic correlation optical time domain reflectometer utilizing laser diode,” IEEE Photon. Technol. Lett.20(19), 1636–1638 (2008).
[CrossRef]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008).
[CrossRef]

2007 (1)

M. Sciamanna, I. Gatare, A. Locquet, and K. Panajotov, “Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.75(5), 056213 (2007).
[CrossRef] [PubMed]

2005 (2)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature438(7066), 343–346 (2005).
[CrossRef] [PubMed]

K. E. Chlouverakis and M. J. Adams, “Optoelectronic realisation of NOR logic gate using chaotic two-section lasers,” Electron. Lett.41(6), 359–360 (2005).
[CrossRef]

2004 (2)

2003 (1)

2002 (2)

C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Phys. Rev. Lett.88(17), 174102 (2002).
[CrossRef] [PubMed]

S. Bandyopadhyay, Y. H. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELs,” Opt. Commun.202(1-3), 145–154 (2002).
[CrossRef]

2001 (1)

C. Masoller, “Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback,” Phys. Rev. Lett.86(13), 2782–2785 (2001).
[CrossRef] [PubMed]

Adams, M. J.

K. E. Chlouverakis and M. J. Adams, “Optoelectronic realisation of NOR logic gate using chaotic two-section lasers,” Electron. Lett.41(6), 359–360 (2005).
[CrossRef]

Aida, H.

Amano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008).
[CrossRef]

Annovazzi-Lodi, V.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature438(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. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature438(7066), 343–346 (2005).
[CrossRef] [PubMed]

Aviad, Y.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics4(1), 58–61 (2010).
[CrossRef]

Bandt, C.

C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Phys. Rev. Lett.88(17), 174102 (2002).
[CrossRef] [PubMed]

Bandyopadhyay, S.

S. Bandyopadhyay, Y. H. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELs,” Opt. Commun.202(1-3), 145–154 (2002).
[CrossRef]

Chan, S.-C.

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

Chlouverakis, K. E.

K. E. Chlouverakis and M. J. Adams, “Optoelectronic realisation of NOR logic gate using chaotic two-section lasers,” Electron. Lett.41(6), 359–360 (2005).
[CrossRef]

Citrin, D. S.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE J. Quantum Electron.45(7), 879–891 (2009).
[CrossRef]

Cohen, E.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics4(1), 58–61 (2010).
[CrossRef]

Colet, P.

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

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 fiber-optic links,” Nature438(7066), 343–346 (2005).
[CrossRef] [PubMed]

Davis, P.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express18(6), 5512–5524 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-6-5512 .
[CrossRef] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008).
[CrossRef]

Deng, T.

P. Xiao, Z.-M. Wu, J.-G. Wu, L. Jiang, T. Deng, X. Tang, L. Fan, and G.-Q. Xia, “Time-delay signature concealment of chaotic output in a vertical-cavity surface-emitting laser with double variable-polarization optical feedback,” Opt. Commun.286, 339–343 (2013).
[CrossRef]

Fan, L.

P. Xiao, Z.-M. Wu, J.-G. Wu, L. Jiang, T. Deng, X. Tang, L. Fan, and G.-Q. Xia, “Time-delay signature concealment of chaotic output in a vertical-cavity surface-emitting laser with double variable-polarization optical feedback,” Opt. Commun.286, 339–343 (2013).
[CrossRef]

Feng, G.-Y.

Fischer, I.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature438(7066), 343–346 (2005).
[CrossRef] [PubMed]

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 fiber-optic links,” Nature438(7066), 343–346 (2005).
[CrossRef] [PubMed]

Gatare, I.

M. Sciamanna, I. Gatare, A. Locquet, and K. Panajotov, “Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.75(5), 056213 (2007).
[CrossRef] [PubMed]

Harayama, T.

Hirano, K.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express18(6), 5512–5524 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-6-5512 .
[CrossRef] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008).
[CrossRef]

Hong, Y.

S. Priyadarshi, Y. Hong, I. Pierce, and K. A. Shore, “Experimental investigations of time-delay signature concealment in chaotic external cavity VCSELs subject to variable optical polarization-angle of feedback,” IEEE J. Sel. Top. Quantum Electron.19(4), 1700707 (2013).
[CrossRef]

Hong, Y. H.

Y. H. Hong, M. W. Lee, P. S. Spencer, and K. A. Shore, “Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers,” Opt. Lett.29(11), 1215–1217 (2004).
[CrossRef] [PubMed]

S. Bandyopadhyay, Y. H. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELs,” Opt. Commun.202(1-3), 145–154 (2002).
[CrossRef]

Inoue, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008).
[CrossRef]

Jiang, L.

P. Xiao, Z.-M. Wu, J.-G. Wu, L. Jiang, T. Deng, X. Tang, L. Fan, and G.-Q. Xia, “Time-delay signature concealment of chaotic output in a vertical-cavity surface-emitting laser with double variable-polarization optical feedback,” Opt. Commun.286, 339–343 (2013).
[CrossRef]

Jiang, N.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, and H. N. Zhu, “Conceal time-delay signature of chaotic vertical-cavity surface-emitting lasers by variable-polarization optical feedback,” Opt. Commun.284(24), 5758–5765 (2011).
[CrossRef]

Kanter, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics4(1), 58–61 (2010).
[CrossRef]

Kurashige, T.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008).
[CrossRef]

Larger, L.

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

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 fiber-optic links,” Nature438(7066), 343–346 (2005).
[CrossRef] [PubMed]

Lee, M. W.

Li, L.

Li, N. Q.

L. Y. Zhang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, and N. Q. Li, “Conceal time-delay signature of mutually coupled vertical-cavity surface-emitting lasers by variable polarization optical injection,” IEEE Photon. Technol. Lett.24(19), 1693–1695 (2012).
[CrossRef]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, and X. H. Zou, “Loss of time delay signature in Broadband cascade-coupled semiconductor lasers,” IEEE Photon. Technol. Lett.24(23), 2187–2190 (2012).
[CrossRef]

Li, S.-S.

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

Lin, F. Y.

F. Y. Lin and J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron.10(5), 991–997 (2004).
[CrossRef]

Liu, J. M.

F. Y. Lin and J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron.10(5), 991–997 (2004).
[CrossRef]

Liu, Q.

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

Locquet, A.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE J. Quantum Electron.45(7), 879–891 (2009).
[CrossRef]

M. Sciamanna, I. Gatare, A. Locquet, and K. Panajotov, “Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.75(5), 056213 (2007).
[CrossRef] [PubMed]

Luo, B.

L. Y. Zhang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, and N. Q. Li, “Conceal time-delay signature of mutually coupled vertical-cavity surface-emitting lasers by variable polarization optical injection,” IEEE Photon. Technol. Lett.24(19), 1693–1695 (2012).
[CrossRef]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, and X. H. Zou, “Loss of time delay signature in Broadband cascade-coupled semiconductor lasers,” IEEE Photon. Technol. Lett.24(23), 2187–2190 (2012).
[CrossRef]

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, and H. N. Zhu, “Conceal time-delay signature of chaotic vertical-cavity surface-emitting lasers by variable-polarization optical feedback,” Opt. Commun.284(24), 5758–5765 (2011).
[CrossRef]

Masoller, C.

C. Masoller, “Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback,” Phys. Rev. Lett.86(13), 2782–2785 (2001).
[CrossRef] [PubMed]

Mirasso, C. R.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature438(7066), 343–346 (2005).
[CrossRef] [PubMed]

Morikatsu, S.

Naito, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008).
[CrossRef]

Nguimdo, R. M.

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

Ohtsubo, J.

Ohyagi, K.

Okumura, H.

Oowada, I.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008).
[CrossRef]

Ortin, S.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE J. Quantum Electron.45(7), 879–891 (2009).
[CrossRef]

Pan, W.

L. Y. Zhang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, and N. Q. Li, “Conceal time-delay signature of mutually coupled vertical-cavity surface-emitting lasers by variable polarization optical injection,” IEEE Photon. Technol. Lett.24(19), 1693–1695 (2012).
[CrossRef]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, and X. H. Zou, “Loss of time delay signature in Broadband cascade-coupled semiconductor lasers,” IEEE Photon. Technol. Lett.24(23), 2187–2190 (2012).
[CrossRef]

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, and H. N. Zhu, “Conceal time-delay signature of chaotic vertical-cavity surface-emitting lasers by variable-polarization optical feedback,” Opt. Commun.284(24), 5758–5765 (2011).
[CrossRef]

Panajotov, K.

M. Sciamanna, I. Gatare, A. Locquet, and K. Panajotov, “Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.75(5), 056213 (2007).
[CrossRef] [PubMed]

Pesquera, L.

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

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 fiber-optic links,” Nature438(7066), 343–346 (2005).
[CrossRef] [PubMed]

Pierce, I.

S. Priyadarshi, Y. Hong, I. Pierce, and K. A. Shore, “Experimental investigations of time-delay signature concealment in chaotic external cavity VCSELs subject to variable optical polarization-angle of feedback,” IEEE J. Sel. Top. Quantum Electron.19(4), 1700707 (2013).
[CrossRef]

Pompe, B.

C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Phys. Rev. Lett.88(17), 174102 (2002).
[CrossRef] [PubMed]

Priyadarshi, S.

S. Priyadarshi, Y. Hong, I. Pierce, and K. A. Shore, “Experimental investigations of time-delay signature concealment in chaotic external cavity VCSELs subject to variable optical polarization-angle of feedback,” IEEE J. Sel. Top. Quantum Electron.19(4), 1700707 (2013).
[CrossRef]

Reidler, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics4(1), 58–61 (2010).
[CrossRef]

Rontani, D.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE J. Quantum Electron.45(7), 879–891 (2009).
[CrossRef]

Rosenbluh, M.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics4(1), 58–61 (2010).
[CrossRef]

Sciamanna, M.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE J. Quantum Electron.45(7), 879–891 (2009).
[CrossRef]

M. Sciamanna, I. Gatare, A. Locquet, and K. Panajotov, “Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.75(5), 056213 (2007).
[CrossRef] [PubMed]

Shiki, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008).
[CrossRef]

Shore, K. A.

S. Priyadarshi, Y. Hong, I. Pierce, and K. A. Shore, “Experimental investigations of time-delay signature concealment in chaotic external cavity VCSELs subject to variable optical polarization-angle of feedback,” IEEE J. Sel. Top. Quantum Electron.19(4), 1700707 (2013).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature438(7066), 343–346 (2005).
[CrossRef] [PubMed]

Y. H. Hong, M. W. Lee, P. S. Spencer, and K. A. Shore, “Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers,” Opt. Lett.29(11), 1215–1217 (2004).
[CrossRef] [PubMed]

S. Bandyopadhyay, Y. H. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELs,” Opt. Commun.202(1-3), 145–154 (2002).
[CrossRef]

Someya, H.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008).
[CrossRef]

Spencer, P. S.

Y. H. Hong, M. W. Lee, P. S. Spencer, and K. A. Shore, “Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers,” Opt. Lett.29(11), 1215–1217 (2004).
[CrossRef] [PubMed]

S. Bandyopadhyay, Y. H. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELs,” Opt. Commun.202(1-3), 145–154 (2002).
[CrossRef]

Syvridis, D.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature438(7066), 343–346 (2005).
[CrossRef] [PubMed]

Takiguchi, Y.

Tang, X.

P. Xiao, Z.-M. Wu, J.-G. Wu, L. Jiang, T. Deng, X. Tang, L. Fan, and G.-Q. Xia, “Time-delay signature concealment of chaotic output in a vertical-cavity surface-emitting laser with double variable-polarization optical feedback,” Opt. Commun.286, 339–343 (2013).
[CrossRef]

Uchida, A.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express18(6), 5512–5524 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-6-5512 .
[CrossRef] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008).
[CrossRef]

Wang, A. B.

A. B. Wang, Y. B. Yang, B. J. Wang, B. B. Zhang, L. Li, and Y. C. Wang, “Generation of wideband chaos with suppressed time-delay signature by delayed self-interference,” Opt. Express21(7), 8701–8710 (2013).
[CrossRef] [PubMed]

Y. C. Wang, B. J. Wang, and A. B. Wang, “Chaotic correlation optical time domain reflectometer utilizing laser diode,” IEEE Photon. Technol. Lett.20(19), 1636–1638 (2008).
[CrossRef]

Wang, B. J.

A. B. Wang, Y. B. Yang, B. J. Wang, B. B. Zhang, L. Li, and Y. C. Wang, “Generation of wideband chaos with suppressed time-delay signature by delayed self-interference,” Opt. Express21(7), 8701–8710 (2013).
[CrossRef] [PubMed]

Y. C. Wang, B. J. Wang, and A. B. Wang, “Chaotic correlation optical time domain reflectometer utilizing laser diode,” IEEE Photon. Technol. Lett.20(19), 1636–1638 (2008).
[CrossRef]

Wang, Y. C.

A. B. Wang, Y. B. Yang, B. J. Wang, B. B. Zhang, L. Li, and Y. C. Wang, “Generation of wideband chaos with suppressed time-delay signature by delayed self-interference,” Opt. Express21(7), 8701–8710 (2013).
[CrossRef] [PubMed]

Y. C. Wang, B. J. Wang, and A. B. Wang, “Chaotic correlation optical time domain reflectometer utilizing laser diode,” IEEE Photon. Technol. Lett.20(19), 1636–1638 (2008).
[CrossRef]

Wu, J.-G.

Z.-Q. Zhong, Z.-M. Wu, J.-G. Wu, and G.-Q. Xia, “Time-delay signature suppression of polarization-resolved chaos outputs from two mutually coupled VCSELs,” IEEE Photonics J.5(2), 1500409 (2013).
[CrossRef]

P. Xiao, Z.-M. Wu, J.-G. Wu, L. Jiang, T. Deng, X. Tang, L. Fan, and G.-Q. Xia, “Time-delay signature concealment of chaotic output in a vertical-cavity surface-emitting laser with double variable-polarization optical feedback,” Opt. Commun.286, 339–343 (2013).
[CrossRef]

J.-G. Wu, Z.-M. Wu, G.-Q. Xia, and G.-Y. Feng, “Evolution of time delay signature of chaos generated in a mutually delay-coupled semiconductor lasers system,” Opt. Express20(2), 1741–1753 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-2-1741 .
[CrossRef] [PubMed]

Wu, Z.-M.

P. Xiao, Z.-M. Wu, J.-G. Wu, L. Jiang, T. Deng, X. Tang, L. Fan, and G.-Q. Xia, “Time-delay signature concealment of chaotic output in a vertical-cavity surface-emitting laser with double variable-polarization optical feedback,” Opt. Commun.286, 339–343 (2013).
[CrossRef]

Z.-Q. Zhong, Z.-M. Wu, J.-G. Wu, and G.-Q. Xia, “Time-delay signature suppression of polarization-resolved chaos outputs from two mutually coupled VCSELs,” IEEE Photonics J.5(2), 1500409 (2013).
[CrossRef]

J.-G. Wu, Z.-M. Wu, G.-Q. Xia, and G.-Y. Feng, “Evolution of time delay signature of chaos generated in a mutually delay-coupled semiconductor lasers system,” Opt. Express20(2), 1741–1753 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-2-1741 .
[CrossRef] [PubMed]

Xia, G.-Q.

P. Xiao, Z.-M. Wu, J.-G. Wu, L. Jiang, T. Deng, X. Tang, L. Fan, and G.-Q. Xia, “Time-delay signature concealment of chaotic output in a vertical-cavity surface-emitting laser with double variable-polarization optical feedback,” Opt. Commun.286, 339–343 (2013).
[CrossRef]

Z.-Q. Zhong, Z.-M. Wu, J.-G. Wu, and G.-Q. Xia, “Time-delay signature suppression of polarization-resolved chaos outputs from two mutually coupled VCSELs,” IEEE Photonics J.5(2), 1500409 (2013).
[CrossRef]

J.-G. Wu, Z.-M. Wu, G.-Q. Xia, and G.-Y. Feng, “Evolution of time delay signature of chaos generated in a mutually delay-coupled semiconductor lasers system,” Opt. Express20(2), 1741–1753 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-2-1741 .
[CrossRef] [PubMed]

Xiang, S. Y.

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, and X. H. Zou, “Loss of time delay signature in Broadband cascade-coupled semiconductor lasers,” IEEE Photon. Technol. Lett.24(23), 2187–2190 (2012).
[CrossRef]

L. Y. Zhang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, and N. Q. Li, “Conceal time-delay signature of mutually coupled vertical-cavity surface-emitting lasers by variable polarization optical injection,” IEEE Photon. Technol. Lett.24(19), 1693–1695 (2012).
[CrossRef]

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, and H. N. Zhu, “Conceal time-delay signature of chaotic vertical-cavity surface-emitting lasers by variable-polarization optical feedback,” Opt. Commun.284(24), 5758–5765 (2011).
[CrossRef]

Xiao, P.

P. Xiao, Z.-M. Wu, J.-G. Wu, L. Jiang, T. Deng, X. Tang, L. Fan, and G.-Q. Xia, “Time-delay signature concealment of chaotic output in a vertical-cavity surface-emitting laser with double variable-polarization optical feedback,” Opt. Commun.286, 339–343 (2013).
[CrossRef]

Yamazaki, T.

Yan, L. S.

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, and X. H. Zou, “Loss of time delay signature in Broadband cascade-coupled semiconductor lasers,” IEEE Photon. Technol. Lett.24(23), 2187–2190 (2012).
[CrossRef]

L. Y. Zhang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, and N. Q. Li, “Conceal time-delay signature of mutually coupled vertical-cavity surface-emitting lasers by variable polarization optical injection,” IEEE Photon. Technol. Lett.24(19), 1693–1695 (2012).
[CrossRef]

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, and H. N. Zhu, “Conceal time-delay signature of chaotic vertical-cavity surface-emitting lasers by variable-polarization optical feedback,” Opt. Commun.284(24), 5758–5765 (2011).
[CrossRef]

Yang, L.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, and H. N. Zhu, “Conceal time-delay signature of chaotic vertical-cavity surface-emitting lasers by variable-polarization optical feedback,” Opt. Commun.284(24), 5758–5765 (2011).
[CrossRef]

Yang, Y. B.

Yoshimori, S.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express18(6), 5512–5524 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-6-5512 .
[CrossRef] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008).
[CrossRef]

Yoshimura, K.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express18(6), 5512–5524 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-6-5512 .
[CrossRef] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008).
[CrossRef]

Zhang, B. B.

Zhang, L. Y.

L. Y. Zhang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, and N. Q. Li, “Conceal time-delay signature of mutually coupled vertical-cavity surface-emitting lasers by variable polarization optical injection,” IEEE Photon. Technol. Lett.24(19), 1693–1695 (2012).
[CrossRef]

Zhong, Z.-Q.

Z.-Q. Zhong, Z.-M. Wu, J.-G. Wu, and G.-Q. Xia, “Time-delay signature suppression of polarization-resolved chaos outputs from two mutually coupled VCSELs,” IEEE Photonics J.5(2), 1500409 (2013).
[CrossRef]

Zhu, H. N.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, and H. N. Zhu, “Conceal time-delay signature of chaotic vertical-cavity surface-emitting lasers by variable-polarization optical feedback,” Opt. Commun.284(24), 5758–5765 (2011).
[CrossRef]

Zou, X. H.

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, and X. H. Zou, “Loss of time delay signature in Broadband cascade-coupled semiconductor lasers,” IEEE Photon. Technol. Lett.24(23), 2187–2190 (2012).
[CrossRef]

L. Y. Zhang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, and N. Q. Li, “Conceal time-delay signature of mutually coupled vertical-cavity surface-emitting lasers by variable polarization optical injection,” IEEE Photon. Technol. Lett.24(19), 1693–1695 (2012).
[CrossRef]

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, and H. N. Zhu, “Conceal time-delay signature of chaotic vertical-cavity surface-emitting lasers by variable-polarization optical feedback,” Opt. Commun.284(24), 5758–5765 (2011).
[CrossRef]

Electron. Lett. (1)

K. E. Chlouverakis and M. J. Adams, “Optoelectronic realisation of NOR logic gate using chaotic two-section lasers,” Electron. Lett.41(6), 359–360 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE J. Quantum Electron.45(7), 879–891 (2009).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

S. Priyadarshi, Y. Hong, I. Pierce, and K. A. Shore, “Experimental investigations of time-delay signature concealment in chaotic external cavity VCSELs subject to variable optical polarization-angle of feedback,” IEEE J. Sel. Top. Quantum Electron.19(4), 1700707 (2013).
[CrossRef]

F. Y. Lin and J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron.10(5), 991–997 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

L. Y. Zhang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, and N. Q. Li, “Conceal time-delay signature of mutually coupled vertical-cavity surface-emitting lasers by variable polarization optical injection,” IEEE Photon. Technol. Lett.24(19), 1693–1695 (2012).
[CrossRef]

Y. C. Wang, B. J. Wang, and A. B. Wang, “Chaotic correlation optical time domain reflectometer utilizing laser diode,” IEEE Photon. Technol. Lett.20(19), 1636–1638 (2008).
[CrossRef]

N. Q. Li, W. Pan, S. Y. Xiang, L. S. Yan, B. Luo, and X. H. Zou, “Loss of time delay signature in Broadband cascade-coupled semiconductor lasers,” IEEE Photon. Technol. Lett.24(23), 2187–2190 (2012).
[CrossRef]

IEEE Photonics J. (2)

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

Z.-Q. Zhong, Z.-M. Wu, J.-G. Wu, and G.-Q. Xia, “Time-delay signature suppression of polarization-resolved chaos outputs from two mutually coupled VCSELs,” IEEE Photonics J.5(2), 1500409 (2013).
[CrossRef]

Nat. Photonics (2)

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008).
[CrossRef]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics4(1), 58–61 (2010).
[CrossRef]

Nature (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fiber-optic links,” Nature438(7066), 343–346 (2005).
[CrossRef] [PubMed]

Opt. Commun. (3)

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Jiang, L. Yang, and H. N. Zhu, “Conceal time-delay signature of chaotic vertical-cavity surface-emitting lasers by variable-polarization optical feedback,” Opt. Commun.284(24), 5758–5765 (2011).
[CrossRef]

P. Xiao, Z.-M. Wu, J.-G. Wu, L. Jiang, T. Deng, X. Tang, L. Fan, and G.-Q. Xia, “Time-delay signature concealment of chaotic output in a vertical-cavity surface-emitting laser with double variable-polarization optical feedback,” Opt. Commun.286, 339–343 (2013).
[CrossRef]

S. Bandyopadhyay, Y. H. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELs,” Opt. Commun.202(1-3), 145–154 (2002).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

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

M. Sciamanna, I. Gatare, A. Locquet, and K. Panajotov, “Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.75(5), 056213 (2007).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

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

C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Phys. Rev. Lett.88(17), 174102 (2002).
[CrossRef] [PubMed]

C. Masoller, “Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback,” Phys. Rev. Lett.86(13), 2782–2785 (2001).
[CrossRef] [PubMed]

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Figures (9)

Fig. 1
Fig. 1

Experimental setup. BS-beamsplitter; HWP- half wave plate; ATTN- optical variable attenuator; ISO-isolator; PD – photodetector; OSC -oscilloscope

Fig. 2
Fig. 2

Polarization-resolved L-I curve of (a) VCSEL1, (b) VCSEL2

Fig. 3
Fig. 3

The time trace (first column), autocorrelation coefficient curve (second column) and the PE curves (third column) of the X-polarization of VCSEL 2 with a fixed optical injection ratio of −9.4dB and Δf = 0. The polarization rotated angles are 0° (top row), 60° (middle row) and 90° (bottom row).

Fig. 4
Fig. 4

The amplitude Cp of the X-polarization of VCSEL2 as a function of polarization rotated angle when the optical injection ratio of VCSEL2 is −9.4dB

Fig. 5
Fig. 5

The amplitude Cp of the X-polarization of VCSEL2 as a function of polarization rotated angle with the different injection ratio. The squares, circles, up triangles and down triangles are for the injection ratio of −8.8 dB, −9.4dB, −14.7dB and −16.5dB, respectively.

Fig. 6
Fig. 6

The power ratio of VCSEL2 as a function of polarization rotated angle.

Fig. 7
Fig. 7

The amplitude Cp of VCSEL2 as a function of polarization rotated angle. The squares, circles and triangles are for X-polarization, Y-polarization and the total power, respectively.

Fig. 8
Fig. 8

The amplitude Cp of the total power of VCSEL2 as a function of polarization rotated angle with the different bias currents.

Fig. 9
Fig. 9

The amplitude Cp of the total power of VCSEL2 as a function of the frequency detuning

Equations (4)

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

C(Δt)= <[I(t+Δt)<I(t+Δt)>][I(t)<I(t)>]>) < [I(t+Δt)<I(t+Δt)>] 2 >< [I(t)<I(t)>] 2 > ,
P( π )= #{t|tNMn+1; S q  has type π} NMn+1 ,
h(p)= p(π)logp(π),
R= P x P y ,

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