Abstract

Based on the framework of spin-flip model (SFM), the output characteristics of a 1550 nm vertical-cavity surface-emitting laser (VCSEL) subject to variable-polarization fiber Bragg grating (FBG) feedback (VPFBGF) have been investigated. With the aid of the self-correlation function (SF) and the permutation entropy (PE) function, the time-delay signature (TDS) of chaos in the VPFBGF-VCSEL is evaluated, and then the influences of the operation parameters on the TDS of chaos are analyzed. The results show that the TDS of chaos can be suppressed efficiently through selecting suitable coupling coefficient and feedback rate of the FBG, and is weaker than that of chaos generated by traditional variable-polarization mirror feedback VCSELs (VPMF-VCSELs) or polarization-preserved FBG feedback VCSELs (PPFBGF-VCSELs).

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  39. C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Phys. Rev. Lett. 88(17), 174102 (2002).
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  40. M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
    [CrossRef]
  41. R. Al-Seyab, K. Schires, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of VCSELs subject to optical injection of arbitrary polarization,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1700512 (2013).
    [CrossRef]

2013

S. Priyadarshi, Y. H. 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]

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]

R. Al-Seyab, K. Schires, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of VCSELs subject to optical injection of arbitrary polarization,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1700512 (2013).
[CrossRef]

2012

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

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Q. Li, and L. Y. Zhang, “Enhanced chaotic communication in VCSELs with variable-polarization optical feedback and polarization-preserved optical injection,” Opt. Commun. 285(24), 5293–5301 (2012).
[CrossRef]

2011

J. G. Wu, Z. M. Wu, G. Q. Xia, T. Deng, X. D. Lin, X. Tang, and G. Y. Feng, “Isochronous synchronization between chaotic semiconductor lasers over 40-km fiber links,” IEEE Photon. Technol. Lett. 23(24), 1854–1856 (2011).
[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]

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
[CrossRef]

2010

2009

2008

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. Photon. 2(12), 728–732 (2008).
[CrossRef]

2007

2006

F. Koyama, “Recent advances of VCSEL photonics,” J. Lightwave Technol. 24(12), 4502–4513 (2006).
[CrossRef]

I. Gatare, J. Buesa, H. Thienpont, K. Panajotov, and M. Sciamanna, “Polarization switching bistability and dynamics in vertical-cavity surface-emitting laser under orthogonal optical injection,” Opt. Quantum Electron. 38(4–6), 429–443 (2006).
[CrossRef]

2005

R. Ju, P. S. Spencer, and K. A. Shore, “Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface emitting lasers,” IEEE J. Quantum Electron. 41(12), 1461–1467 (2005).
[CrossRef]

M. W. Lee, P. Rees, K. A. Shore, S. Ortin, L. Pesquera, and A. Valle, “Dynamical characterisation of laser diode subject to double optical feedback for chaotic optical communications,” IEE Proc., Optoelectron. 152(2), 97–102 (2005).
[CrossRef]

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

G. Q. Xia, Z. M. Wu, and J. G. Wu, “Theory and simulation of dual-channel optical chaotic communication system,” Opt. Express 13(9), 3445–3453 (2005).
[CrossRef] [PubMed]

2004

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

2003

V. S. Udaltsov, J. Goedgebuer, L. Larger, J. Cuenot, P. Levy, and W. T. Rhodes, “Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations,” Phys. Lett. A 308(1), 54–60 (2003).
[CrossRef]

F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221(1–3), 173–180 (2003).
[CrossRef]

A. V. Naumenko, N. A. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003).
[CrossRef]

2002

2001

S. Tang and J. M. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback,” IEEE J. Quantum Electron. 37(3), 329–336 (2001).
[CrossRef]

J. García-Ojalvo and R. Roy, “Spatiotemporal communication with synchronized optical chaos,” Phys. Rev. Lett. 86(22), 5204–5207 (2001).
[CrossRef] [PubMed]

T. Heil, I. Fischer, W. Elsäßer, and A. Gavrielides, “Dynamics of semiconductor lasers subject to delayed optical feedback: the short cavity regime,” Phys. Rev. Lett. 87(24), 243901 (2001).
[CrossRef] [PubMed]

2000

C. J. Chang-Hasnain, “Tunable VCSEL,” IEEE J. Sel. Top. Quantum Electron. 6(6), 978–987 (2000).
[CrossRef]

1998

1997

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]

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[CrossRef]

M. J. Bünner, T. Meyer, A. Kittel, and J. Parisi, “Recovery of the time evolution equation of time-delay systems from time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(5), 5083–5089 (1997).
[CrossRef]

1995

M. S. Miguel, Q. Feng, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728–1739 (1995).

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51(5), 4181–4185 (1995).
[CrossRef] [PubMed]

1994

I. Fischer, O. Hess, W. Elsa, and E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73(16), 2188–2191 (1994).
[CrossRef] [PubMed]

1980

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[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]

Ackemann, T.

A. V. Naumenko, N. A. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003).
[CrossRef]

Adams, M. J.

R. Al-Seyab, K. Schires, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of VCSELs subject to optical injection of arbitrary polarization,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1700512 (2013).
[CrossRef]

Agrawal, G. P.

Al-Seyab, R.

R. Al-Seyab, K. Schires, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of VCSELs subject to optical injection of arbitrary polarization,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1700512 (2013).
[CrossRef]

Alsing, P. M.

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51(5), 4181–4185 (1995).
[CrossRef] [PubMed]

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. Photon. 2(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 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. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[CrossRef] [PubMed]

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]

Belmonte, M.

Buesa, J.

I. Gatare, J. Buesa, H. Thienpont, K. Panajotov, and M. Sciamanna, “Polarization switching bistability and dynamics in vertical-cavity surface-emitting laser under orthogonal optical injection,” Opt. Quantum Electron. 38(4–6), 429–443 (2006).
[CrossRef]

Bünner, M. J.

M. J. Bünner, T. Meyer, A. Kittel, and J. Parisi, “Recovery of the time evolution equation of time-delay systems from time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(5), 5083–5089 (1997).
[CrossRef]

Cao, L. P.

J. G. Wu, G. Q. Xia, L. P. Cao, and Z. M. Wu, “Experimental investigations on the external cavity time signature in chaotic output of an incoherent optical feedback external cavity semiconductor laser,” Opt. Commun. 282(15), 3153–3156 (2009).
[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 Photon. J. 4(5), 1930–1935 (2012).
[CrossRef]

Chang-Hasnain, C. J.

C. J. Chang-Hasnain, “Tunable VCSEL,” IEEE J. Sel. Top. Quantum Electron. 6(6), 978–987 (2000).
[CrossRef]

Citrin, D. S.

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 438(7066), 343–346 (2005).
[CrossRef] [PubMed]

Cuenot, J.

V. S. Udaltsov, J. Goedgebuer, L. Larger, J. Cuenot, P. Levy, and W. T. Rhodes, “Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations,” Phys. Lett. A 308(1), 54–60 (2003).
[CrossRef]

Davis, P.

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. Photon. 2(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]

J. G. Wu, Z. M. Wu, G. Q. Xia, T. Deng, X. D. Lin, X. Tang, and G. Y. Feng, “Isochronous synchronization between chaotic semiconductor lasers over 40-km fiber links,” IEEE Photon. Technol. Lett. 23(24), 1854–1856 (2011).
[CrossRef]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[CrossRef] [PubMed]

Elsa, W.

I. Fischer, O. Hess, W. Elsa, and E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73(16), 2188–2191 (1994).
[CrossRef] [PubMed]

Elsäßer, W.

T. Heil, I. Fischer, W. Elsäßer, and A. Gavrielides, “Dynamics of semiconductor lasers subject to delayed optical feedback: the short cavity regime,” Phys. Rev. Lett. 87(24), 243901 (2001).
[CrossRef] [PubMed]

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[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]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[CrossRef] [PubMed]

Feng, G. Y.

J. G. Wu, Z. M. Wu, G. Q. Xia, T. Deng, X. D. Lin, X. Tang, and G. Y. Feng, “Isochronous synchronization between chaotic semiconductor lasers over 40-km fiber links,” IEEE Photon. Technol. Lett. 23(24), 1854–1856 (2011).
[CrossRef]

Feng, Q.

M. S. Miguel, Q. Feng, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728–1739 (1995).

Fischer, I.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
[CrossRef]

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 438(7066), 343–346 (2005).
[CrossRef] [PubMed]

T. Heil, I. Fischer, W. Elsäßer, and A. Gavrielides, “Dynamics of semiconductor lasers subject to delayed optical feedback: the short cavity regime,” Phys. Rev. Lett. 87(24), 243901 (2001).
[CrossRef] [PubMed]

I. Fischer, O. Hess, W. Elsa, and E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73(16), 2188–2191 (1994).
[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 fibre-optic links,” Nature 438(7066), 343–346 (2005).
[CrossRef] [PubMed]

J. García-Ojalvo and R. Roy, “Spatiotemporal communication with synchronized optical chaos,” Phys. Rev. Lett. 86(22), 5204–5207 (2001).
[CrossRef] [PubMed]

Gatare, I.

I. Gatare, J. Buesa, H. Thienpont, K. Panajotov, and M. Sciamanna, “Polarization switching bistability and dynamics in vertical-cavity surface-emitting laser under orthogonal optical injection,” Opt. Quantum Electron. 38(4–6), 429–443 (2006).
[CrossRef]

Gavrielides, A.

T. Heil, I. Fischer, W. Elsäßer, and A. Gavrielides, “Dynamics of semiconductor lasers subject to delayed optical feedback: the short cavity regime,” Phys. Rev. Lett. 87(24), 243901 (2001).
[CrossRef] [PubMed]

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51(5), 4181–4185 (1995).
[CrossRef] [PubMed]

Göbel, E.

I. Fischer, O. Hess, W. Elsa, and E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73(16), 2188–2191 (1994).
[CrossRef] [PubMed]

Goedgebuer, J.

V. S. Udaltsov, J. Goedgebuer, L. Larger, J. Cuenot, P. Levy, and W. T. Rhodes, “Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations,” Phys. Lett. A 308(1), 54–60 (2003).
[CrossRef]

Heil, T.

T. Heil, I. Fischer, W. Elsäßer, and A. Gavrielides, “Dynamics of semiconductor lasers subject to delayed optical feedback: the short cavity regime,” Phys. Rev. Lett. 87(24), 243901 (2001).
[CrossRef] [PubMed]

Henning, I. D.

R. Al-Seyab, K. Schires, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of VCSELs subject to optical injection of arbitrary polarization,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1700512 (2013).
[CrossRef]

Hess, O.

I. Fischer, O. Hess, W. Elsa, and E. Göbel, “High-dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73(16), 2188–2191 (1994).
[CrossRef] [PubMed]

Hirano, 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. Photon. 2(12), 728–732 (2008).
[CrossRef]

Hong, Y. H.

S. Priyadarshi, Y. H. 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]

Hurtado, A.

R. Al-Seyab, K. Schires, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of VCSELs subject to optical injection of arbitrary polarization,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1700512 (2013).
[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. Photon. 2(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]

Ju, R.

R. Ju, P. S. Spencer, and K. A. Shore, “Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface emitting lasers,” IEEE J. Quantum Electron. 41(12), 1461–1467 (2005).
[CrossRef]

Kittel, A.

M. J. Bünner, T. Meyer, A. Kittel, and J. Parisi, “Recovery of the time evolution equation of time-delay systems from time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(5), 5083–5089 (1997).
[CrossRef]

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[CrossRef]

Kovanis, V.

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51(5), 4181–4185 (1995).
[CrossRef] [PubMed]

Koyama, F.

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. Photon. 2(12), 728–732 (2008).
[CrossRef]

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[CrossRef]

Laporta, P.

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 438(7066), 343–346 (2005).
[CrossRef] [PubMed]

V. S. Udaltsov, J. Goedgebuer, L. Larger, J. Cuenot, P. Levy, and W. T. Rhodes, “Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations,” Phys. Lett. A 308(1), 54–60 (2003).
[CrossRef]

Law, J. Y.

Lee, M. W.

M. W. Lee, P. Rees, K. A. Shore, S. Ortin, L. Pesquera, and A. Valle, “Dynamical characterisation of laser diode subject to double optical feedback for chaotic optical communications,” IEE Proc., Optoelectron. 152(2), 97–102 (2005).
[CrossRef]

Levy, P.

V. S. Udaltsov, J. Goedgebuer, L. Larger, J. Cuenot, P. Levy, and W. T. Rhodes, “Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations,” Phys. Lett. A 308(1), 54–60 (2003).
[CrossRef]

Li, N. Q.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Q. Li, and L. Y. Zhang, “Enhanced chaotic communication in VCSELs with variable-polarization optical feedback and polarization-preserved optical injection,” Opt. Commun. 285(24), 5293–5301 (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 Photon. 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]

F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221(1–3), 173–180 (2003).
[CrossRef]

Lin, X. D.

J. G. Wu, Z. M. Wu, G. Q. Xia, T. Deng, X. D. Lin, X. Tang, and G. Y. Feng, “Isochronous synchronization between chaotic semiconductor lasers over 40-km fiber links,” IEEE Photon. Technol. Lett. 23(24), 1854–1856 (2011).
[CrossRef]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[CrossRef] [PubMed]

Liu, J.

Liu, J. M.

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

F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221(1–3), 173–180 (2003).
[CrossRef]

S. Tang and J. M. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback,” IEEE J. Quantum Electron. 37(3), 329–336 (2001).
[CrossRef]

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51(5), 4181–4185 (1995).
[CrossRef] [PubMed]

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 Photon. J. 4(5), 1930–1935 (2012).
[CrossRef]

Locquet, A.

Loiko, N. A.

A. V. Naumenko, N. A. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003).
[CrossRef]

Longhi, S.

Luo, B.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Q. Li, and L. Y. Zhang, “Enhanced chaotic communication in VCSELs with variable-polarization optical feedback and polarization-preserved optical injection,” Opt. Commun. 285(24), 5293–5301 (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]

Marano, M.

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]

Meyer, T.

M. J. Bünner, T. Meyer, A. Kittel, and J. Parisi, “Recovery of the time evolution equation of time-delay systems from time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(5), 5083–5089 (1997).
[CrossRef]

Miguel, M. S.

M. S. Miguel, Q. Feng, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728–1739 (1995).

Mirasso, C. R.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
[CrossRef]

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 438(7066), 343–346 (2005).
[CrossRef] [PubMed]

Moloney, J. V.

M. S. Miguel, Q. Feng, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728–1739 (1995).

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. Photon. 2(12), 728–732 (2008).
[CrossRef]

Naumenko, A. V.

A. V. Naumenko, N. A. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003).
[CrossRef]

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. Photon. 2(12), 728–732 (2008).
[CrossRef]

Ortin, S.

M. W. Lee, P. Rees, K. A. Shore, S. Ortin, L. Pesquera, and A. Valle, “Dynamical characterisation of laser diode subject to double optical feedback for chaotic optical communications,” IEE Proc., Optoelectron. 152(2), 97–102 (2005).
[CrossRef]

Pan, W.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Q. Li, and L. Y. Zhang, “Enhanced chaotic communication in VCSELs with variable-polarization optical feedback and polarization-preserved optical injection,” Opt. Commun. 285(24), 5293–5301 (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.

I. Gatare, J. Buesa, H. Thienpont, K. Panajotov, and M. Sciamanna, “Polarization switching bistability and dynamics in vertical-cavity surface-emitting laser under orthogonal optical injection,” Opt. Quantum Electron. 38(4–6), 429–443 (2006).
[CrossRef]

Parisi, J.

M. J. Bünner, T. Meyer, A. Kittel, and J. Parisi, “Recovery of the time evolution equation of time-delay systems from time series,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56(5), 5083–5089 (1997).
[CrossRef]

Pesquera, L.

M. W. Lee, P. Rees, K. A. Shore, S. Ortin, L. Pesquera, and A. Valle, “Dynamical characterisation of laser diode subject to double optical feedback for chaotic optical communications,” IEE Proc., Optoelectron. 152(2), 97–102 (2005).
[CrossRef]

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

Pierce, I.

S. Priyadarshi, Y. H. 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]

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]

Priyadarshi, S.

S. Priyadarshi, Y. H. 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]

Rees, P.

M. W. Lee, P. Rees, K. A. Shore, S. Ortin, L. Pesquera, and A. Valle, “Dynamical characterisation of laser diode subject to double optical feedback for chaotic optical communications,” IEE Proc., Optoelectron. 152(2), 97–102 (2005).
[CrossRef]

Rhodes, W. T.

V. S. Udaltsov, J. Goedgebuer, L. Larger, J. Cuenot, P. Levy, and W. T. Rhodes, “Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations,” Phys. Lett. A 308(1), 54–60 (2003).
[CrossRef]

Rontani, D.

Rosso, O. A.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
[CrossRef]

Roy, R.

J. García-Ojalvo and R. Roy, “Spatiotemporal communication with synchronized optical chaos,” Phys. Rev. Lett. 86(22), 5204–5207 (2001).
[CrossRef] [PubMed]

G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279(5354), 1198–1200 (1998).
[CrossRef] [PubMed]

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]

Schires, K.

R. Al-Seyab, K. Schires, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of VCSELs subject to optical injection of arbitrary polarization,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1700512 (2013).
[CrossRef]

Sciamanna, M.

D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, “Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback,” Opt. Lett. 32(20), 2960–2962 (2007).
[CrossRef] [PubMed]

I. Gatare, J. Buesa, H. Thienpont, K. Panajotov, and M. Sciamanna, “Polarization switching bistability and dynamics in vertical-cavity surface-emitting laser under orthogonal optical injection,” Opt. Quantum Electron. 38(4–6), 429–443 (2006).
[CrossRef]

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. Photon. 2(12), 728–732 (2008).
[CrossRef]

Shore, K. A.

S. Priyadarshi, Y. H. 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]

R. Ju, P. S. Spencer, and K. A. Shore, “Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface emitting lasers,” IEEE J. Quantum Electron. 41(12), 1461–1467 (2005).
[CrossRef]

M. W. Lee, P. Rees, K. A. Shore, S. Ortin, L. Pesquera, and A. Valle, “Dynamical characterisation of laser diode subject to double optical feedback for chaotic optical communications,” IEE Proc., Optoelectron. 152(2), 97–102 (2005).
[CrossRef]

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

Simpson, T. B.

T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Period-doubling cascades and chaos in a semiconductor laser with optical injection,” Phys. Rev. A 51(5), 4181–4185 (1995).
[CrossRef] [PubMed]

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. Photon. 2(12), 728–732 (2008).
[CrossRef]

Sondermann, M.

A. V. Naumenko, N. A. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003).
[CrossRef]

Soriano, M. C.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
[CrossRef]

Spencer, P. S.

R. Ju, P. S. Spencer, and K. A. Shore, “Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface emitting lasers,” IEEE J. Quantum Electron. 41(12), 1461–1467 (2005).
[CrossRef]

Svelto, O.

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 fibre-optic links,” Nature 438(7066), 343–346 (2005).
[CrossRef] [PubMed]

Tang, S.

S. Tang and J. M. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback,” IEEE J. Quantum Electron. 37(3), 329–336 (2001).
[CrossRef]

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]

J. G. Wu, Z. M. Wu, G. Q. Xia, T. Deng, X. D. Lin, X. Tang, and G. Y. Feng, “Isochronous synchronization between chaotic semiconductor lasers over 40-km fiber links,” IEEE Photon. Technol. Lett. 23(24), 1854–1856 (2011).
[CrossRef]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[CrossRef] [PubMed]

Thienpont, H.

I. Gatare, J. Buesa, H. Thienpont, K. Panajotov, and M. Sciamanna, “Polarization switching bistability and dynamics in vertical-cavity surface-emitting laser under orthogonal optical injection,” Opt. Quantum Electron. 38(4–6), 429–443 (2006).
[CrossRef]

Uchida, A.

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. Photon. 2(12), 728–732 (2008).
[CrossRef]

Udaltsov, V. S.

V. S. Udaltsov, J. Goedgebuer, L. Larger, J. Cuenot, P. Levy, and W. T. Rhodes, “Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations,” Phys. Lett. A 308(1), 54–60 (2003).
[CrossRef]

Valle, A.

M. W. Lee, P. Rees, K. A. Shore, S. Ortin, L. Pesquera, and A. Valle, “Dynamical characterisation of laser diode subject to double optical feedback for chaotic optical communications,” IEE Proc., Optoelectron. 152(2), 97–102 (2005).
[CrossRef]

VanWiggeren, G. D.

G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,” Science 279(5354), 1198–1200 (1998).
[CrossRef] [PubMed]

Vicente, R.

Wang, A. B.

Wang, Y. C.

Wu, J. G.

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, T. Deng, X. D. Lin, X. Tang, and G. Y. Feng, “Isochronous synchronization between chaotic semiconductor lasers over 40-km fiber links,” IEEE Photon. Technol. Lett. 23(24), 1854–1856 (2011).
[CrossRef]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[CrossRef] [PubMed]

J. G. Wu, G. Q. Xia, L. P. Cao, and Z. M. Wu, “Experimental investigations on the external cavity time signature in chaotic output of an incoherent optical feedback external cavity semiconductor laser,” Opt. Commun. 282(15), 3153–3156 (2009).
[CrossRef]

J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
[CrossRef] [PubMed]

G. Q. Xia, Z. M. Wu, and J. G. Wu, “Theory and simulation of dual-channel optical chaotic communication system,” Opt. Express 13(9), 3445–3453 (2005).
[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]

J. G. Wu, Z. M. Wu, G. Q. Xia, T. Deng, X. D. Lin, X. Tang, and G. Y. Feng, “Isochronous synchronization between chaotic semiconductor lasers over 40-km fiber links,” IEEE Photon. Technol. Lett. 23(24), 1854–1856 (2011).
[CrossRef]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[CrossRef] [PubMed]

J. G. Wu, G. Q. Xia, L. P. Cao, and Z. M. Wu, “Experimental investigations on the external cavity time signature in chaotic output of an incoherent optical feedback external cavity semiconductor laser,” Opt. Commun. 282(15), 3153–3156 (2009).
[CrossRef]

J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
[CrossRef] [PubMed]

J. Liu, Z. M. Wu, and G. Q. Xia, “Dual-channel chaos synchronization and communication based on unidirectionally coupled VCSELs with polarization-rotated optical feedback and polarization-rotated optical injection,” Opt. Express 17(15), 12619–12626 (2009).
[CrossRef] [PubMed]

G. Q. Xia, Z. M. Wu, and J. G. Wu, “Theory and simulation of dual-channel optical chaotic communication system,” Opt. Express 13(9), 3445–3453 (2005).
[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]

J. G. Wu, Z. M. Wu, G. Q. Xia, T. Deng, X. D. Lin, X. Tang, and G. Y. Feng, “Isochronous synchronization between chaotic semiconductor lasers over 40-km fiber links,” IEEE Photon. Technol. Lett. 23(24), 1854–1856 (2011).
[CrossRef]

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, “Time delay signature concealment of optical feedback induced chaos in an external cavity semiconductor laser,” Opt. Express 18(7), 6661–6666 (2010).
[CrossRef] [PubMed]

J. G. Wu, G. Q. Xia, L. P. Cao, and Z. M. Wu, “Experimental investigations on the external cavity time signature in chaotic output of an incoherent optical feedback external cavity semiconductor laser,” Opt. Commun. 282(15), 3153–3156 (2009).
[CrossRef]

J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
[CrossRef] [PubMed]

J. Liu, Z. M. Wu, and G. Q. Xia, “Dual-channel chaos synchronization and communication based on unidirectionally coupled VCSELs with polarization-rotated optical feedback and polarization-rotated optical injection,” Opt. Express 17(15), 12619–12626 (2009).
[CrossRef] [PubMed]

G. Q. Xia, Z. M. Wu, and J. G. Wu, “Theory and simulation of dual-channel optical chaotic communication system,” Opt. Express 13(9), 3445–3453 (2005).
[CrossRef] [PubMed]

Xiang, S. Y.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Q. Li, and L. Y. Zhang, “Enhanced chaotic communication in VCSELs with variable-polarization optical feedback and polarization-preserved optical injection,” Opt. Commun. 285(24), 5293–5301 (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]

Yan, L. S.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Q. Li, and L. Y. Zhang, “Enhanced chaotic communication in VCSELs with variable-polarization optical feedback and polarization-preserved optical injection,” Opt. Commun. 285(24), 5293–5301 (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).
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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. Photon. 2(12), 728–732 (2008).
[CrossRef]

Zhang, L. Y.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Q. Li, and L. Y. Zhang, “Enhanced chaotic communication in VCSELs with variable-polarization optical feedback and polarization-preserved optical injection,” Opt. Commun. 285(24), 5293–5301 (2012).
[CrossRef]

Zhao, Q. C.

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.

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Q. Li, and L. Y. Zhang, “Enhanced chaotic communication in VCSELs with variable-polarization optical feedback and polarization-preserved optical injection,” Opt. Commun. 285(24), 5293–5301 (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).
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IEEE J. Sel. Top. Quantum Electron.

R. Al-Seyab, K. Schires, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of VCSELs subject to optical injection of arbitrary polarization,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1700512 (2013).
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IEEE Photon. Technol. Lett.

J. G. Wu, Z. M. Wu, G. Q. Xia, T. Deng, X. D. Lin, X. Tang, and G. Y. Feng, “Isochronous synchronization between chaotic semiconductor lasers over 40-km fiber links,” IEEE Photon. Technol. Lett. 23(24), 1854–1856 (2011).
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F. Koyama, “Recent advances of VCSEL photonics,” J. Lightwave Technol. 24(12), 4502–4513 (2006).
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[CrossRef]

Nature

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 438(7066), 343–346 (2005).
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[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]

J. G. Wu, G. Q. Xia, L. P. Cao, and Z. M. Wu, “Experimental investigations on the external cavity time signature in chaotic output of an incoherent optical feedback external cavity semiconductor laser,” Opt. Commun. 282(15), 3153–3156 (2009).
[CrossRef]

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Q. Li, and L. Y. Zhang, “Enhanced chaotic communication in VCSELs with variable-polarization optical feedback and polarization-preserved optical injection,” Opt. Commun. 285(24), 5293–5301 (2012).
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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of a VESEL with VPFBGF. VCSEL: vertical-cavity surface-emitting laser; AL: aspheric lens; P: polarizer; NDF: neutral density filter; FBG: fiber Bragg grating.

Fig. 2
Fig. 2

Polarization-resolved P-I curve for a solitary VCSEL, where the dashed line and the solid line stand for X- polarized component and Y- polarized component, respectively.

Fig. 3
Fig. 3

Polarization-resolved intensities as functions of θp under η = 10 ns−1 and |κ| = 600 m−1.

Fig. 4
Fig. 4

Total intensity time series (first column), power spectra (second column), SF curves (third column) and PE curves (forth column) of a VPFBGF-VCSEL under η = 12 ns−1 and |κ| = 600 m−1 for θp = 90° (first row), θp = 66° (second row) and θp = 30° (third row).

Fig. 5
Fig. 5

Total intensity time series (first column), power spectra (second column), SF curves (third column) and PE curves (forth column) for a VPFBGF-VCSEL under θp = 60° and |κ| = 600 m−1 for η = 20 ns−1 (first row), 15 ns−1 (second row) and 10 ns−1 (third row), respectively.

Fig. 6
Fig. 6

σ as a function of θp under η = 10 ns−1 and different feedback delay times for a VCSEL subject to optical feedback from a mirror or a FBG with |κ| = 600 m−1.

Fig. 7
Fig. 7

Left column: maps of σ in the parameter space of η and θp for a VCSEL subject to VPFBGF with |κ| = 300 m−1 (a1), |κ| = 600 m−1 (b1), |κ| = 900 m−1 (c1) and VPMF (d1); right column: reflection spectra (blue lines) and group delays (red lines) of the used FBGs (a2, b2, and c2) and mirror (d2), where the dashed lines with arrows label the angle frequencies of the two polarized components of the solitary VCSEL.

Fig. 8
Fig. 8

Dependence of σ on θp in a PPFBGF-VCSEL or a VPFBGF-VCSEL for |κ| = 600 m−1, where (a) η = 5 ns−1, (b) η = 10 ns−1, (c) η = 15 ns−1 and (d) η = 20 ns−1, respectively. Green lines represent PPFBGF while blue lines with asterisks correspond to VPFBGF.

Fig. 9
Fig. 9

Output intensity (red lines with circles) and σ (black lines with squares) as a function of rotating angle of the additional polarizer, where the green lines corresponds to σ calculated from the output chaos signal before passing through the additional polarizer.

Equations (8)

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

d E x dt =k(1+iα)[(N1) E x +in E y ]( γ a +i γ p ) E x +ηr(t)[ E x (tτ) e iθ cos 2 ( θ p )+ E y (tτ) e iθ cos( θ p )sin( θ p )]
d E y dt =k(1+iα)[(N1) E y in E x ]+( γ a +i γ p ) E y +ηr(t)[ E x (tτ) e iθ cos( θ p )sin( θ p )+ E y (tτ) e iθ sin 2 ( θ p )]
dN dt = γ N [μN(1+| E x | 2 +| E y | 2 )+in( E x E y * E y E x * )]
dn dt = γ S n γ N [n(| E x | 2 +| E y | 2 )+iN( E y E x * E x E y * )]
r( Ω )= κsinh( |κ | 2 δ 2 L) δsinh( |κ| δ 2 L)+i |κ| δ 2 cosh( |κ | 2 δ 2 L)
C(Δt)= [I(t+Δt) I(t) ][I(t) I(t) ] I(t+Δt) I(t) 2 I(t) I(t) 2
p(π)= #{m|mND,( I m+1 ,, I m+D )hastypesπ} ND+1
H(D)= p(π) logp(π)

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