Abstract

We study the dynamics of two vertical-cavity surface-emitting lasers (VCSELs) mutually coupled such that the natural lasing polarization of each laser is rotated by 90 degrees and then is injected into the other laser. Simulations based on the spin-flip model show transient square-wave polarization switchings before a stationary state is reached. The influence of various model parameters on the duration of the stochastic transient time and on the lasers’ dynamics in the stationary state is investigated.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18, 18292 (2010).
  2. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Science (Cambridge University Press, Cambridge, 2001).
    [CrossRef]
  3. A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104114102 (2010).
    [CrossRef] [PubMed]
  4. M. W. Lee, J. Paul, C. Masoller, and K. A. Shore, “Observation of cascade complete chaos synchronisation with zero time lag in laser diodes,” J. Opt. Soc. Am. B 23846 (2006).
    [CrossRef]
  5. I. Fischer, R. Vicente, J. M. Buldu, M. Peil, C. R. Mirasso, M. C. Torrent, and J. Garcia-Ojalvo, “Zero-Lag Long-Range Synchronization via Dynamical Relaying,” Phys. Rev. Lett.97123902 (2006).
    [CrossRef] [PubMed]
  6. N. Jiang, W. Pan, L. Yan, B. Luo, S. Xiang, L. Yang, and D. Zheng, “Isochronal chaos synchronization of semiconductor lasers with multiple time-delayed couplings,” J. Opt. Soc. Am. B 281139 (2011).
    [CrossRef]
  7. M. Ozaki, H. Someya, T. Mihara, A. Uchida, S. Yoshimori, K. Panajotov, and M. Sciamanna, “Leader-laggard relationship of chaos synchronization in mutually coupled vertical-cavity surface-emitting lasers with time delay,” Phys. Rev. A 79026210 (2009).
  8. J. F. Martinez Avila and J. R. Rios Leite, “Time delays in the synchronization of chaotic coupled lasers with feedback,” Opt. Express 1721442 (2009).
    [CrossRef]
  9. M. Y. Kim, R. Roy, J. L. Aron, T. W. Carr, and I. B. Schwartz, “Scaling behavior of laser population dynamics with time-delayed coupling: theory and experiment,” Phys. Rev. Lett. 94088101 (2005).
    [CrossRef] [PubMed]
  10. M. C. Chiang, H. F. Chen, and J. M. Liu, “Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback”, IEEE J. Quantum Electron. 411333 (2005).
    [CrossRef]
  11. D. W. Sukow, K. L. Blackburn, A. R. Spain, K. J. Babcock, J. V. Bennett, and A. Gavrielides, “Experimental synchronization of chaos in diode lasers with polarization-rotated feedback and injection”, Opt. Lett. 292393 (2004).
    [CrossRef] [PubMed]
  12. R. Ju, P. S. Spencer, and K. Alan Shore, “Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 411461 (2005).
    [CrossRef]
  13. D. W. Sukow, A. Gavrielides, T. McLachlan, G. Burner, J. Amonette, and J. Miller, “Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields,” Phys. Rev. A 74023812 (2006).
    [CrossRef]
  14. N. Shibasaki, A. Uchida, S. Yoshimori, and P. Davis, “Characteristics of chaos synchronization in semiconductor lasers subject to polarization-rotated optical feedback,” IEEE J. Quantum Electron. 42, 342 (2006).
    [CrossRef]
  15. D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81025206R (2010).
    [CrossRef]
  16. C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: theory and experiment,” Phys. Rev. A 84023838 (2011).
    [CrossRef]
  17. F. Koyama, “Recent advances of VCSEL photonics,” J. Lightwave Technol. 24, 4502 (2006).
    [CrossRef]
  18. K. H. Jeong, K. H. Kim, S. H. Lee, M. H. Lee, B. S. Yoo, and K. A. Shore, “Optical injection-induced polarization switching dynamics in 1.5 mu m wavelength single-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 20779 (2008).
    [CrossRef]
  19. W. L. Zhang, W. Pan, B. Luo, X. F. Li, X. H. Zou, and M. Y. Wang, “Influence of polarization-selected mutual injection on the polarization-switching dynamics of vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 242472 (2007).
    [CrossRef]
  20. 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, 765 (1997).
    [CrossRef]
  21. A. Hurtado, I. D. Henning, and M. J. Adams, “Different forms of wavelength polarization switching and bistability in a 1.55 m vertical-cavity surface-emitting laser under orthogonally polarized optical injection,” Opt. Lett. 34365 (2009).
    [CrossRef] [PubMed]
  22. M. S. Torre, A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. J. Adams “Polarization switching in long-wavelength VCSELs subject to orthogonal optical injection,” IEEE J. Quantum Electron. 4792 (2011).
    [CrossRef]

2011

N. Jiang, W. Pan, L. Yan, B. Luo, S. Xiang, L. Yang, and D. Zheng, “Isochronal chaos synchronization of semiconductor lasers with multiple time-delayed couplings,” J. Opt. Soc. Am. B 281139 (2011).
[CrossRef]

C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: theory and experiment,” Phys. Rev. A 84023838 (2011).
[CrossRef]

M. S. Torre, A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. J. Adams “Polarization switching in long-wavelength VCSELs subject to orthogonal optical injection,” IEEE J. Quantum Electron. 4792 (2011).
[CrossRef]

2010

D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81025206R (2010).
[CrossRef]

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104114102 (2010).
[CrossRef] [PubMed]

2009

2008

K. H. Jeong, K. H. Kim, S. H. Lee, M. H. Lee, B. S. Yoo, and K. A. Shore, “Optical injection-induced polarization switching dynamics in 1.5 mu m wavelength single-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 20779 (2008).
[CrossRef]

2007

2006

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

M. W. Lee, J. Paul, C. Masoller, and K. A. Shore, “Observation of cascade complete chaos synchronisation with zero time lag in laser diodes,” J. Opt. Soc. Am. B 23846 (2006).
[CrossRef]

D. W. Sukow, A. Gavrielides, T. McLachlan, G. Burner, J. Amonette, and J. Miller, “Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields,” Phys. Rev. A 74023812 (2006).
[CrossRef]

N. Shibasaki, A. Uchida, S. Yoshimori, and P. Davis, “Characteristics of chaos synchronization in semiconductor lasers subject to polarization-rotated optical feedback,” IEEE J. Quantum Electron. 42, 342 (2006).
[CrossRef]

2005

M. Y. Kim, R. Roy, J. L. Aron, T. W. Carr, and I. B. Schwartz, “Scaling behavior of laser population dynamics with time-delayed coupling: theory and experiment,” Phys. Rev. Lett. 94088101 (2005).
[CrossRef] [PubMed]

M. C. Chiang, H. F. Chen, and J. M. Liu, “Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback”, IEEE J. Quantum Electron. 411333 (2005).
[CrossRef]

R. Ju, P. S. Spencer, and K. Alan Shore, “Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 411461 (2005).
[CrossRef]

2004

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, 765 (1997).
[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, 765 (1997).
[CrossRef]

Adams, M. J.

M. S. Torre, A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. J. Adams “Polarization switching in long-wavelength VCSELs subject to orthogonal optical injection,” IEEE J. Quantum Electron. 4792 (2011).
[CrossRef]

A. Hurtado, I. D. Henning, and M. J. Adams, “Different forms of wavelength polarization switching and bistability in a 1.55 m vertical-cavity surface-emitting laser under orthogonally polarized optical injection,” Opt. Lett. 34365 (2009).
[CrossRef] [PubMed]

Alan Shore, K.

R. Ju, P. S. Spencer, and K. Alan Shore, “Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 411461 (2005).
[CrossRef]

Amonette, J.

D. W. Sukow, A. Gavrielides, T. McLachlan, G. Burner, J. Amonette, and J. Miller, “Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields,” Phys. Rev. A 74023812 (2006).
[CrossRef]

Aron, J. L.

M. Y. Kim, R. Roy, J. L. Aron, T. W. Carr, and I. B. Schwartz, “Scaling behavior of laser population dynamics with time-delayed coupling: theory and experiment,” Phys. Rev. Lett. 94088101 (2005).
[CrossRef] [PubMed]

Aviad, Y.

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104114102 (2010).
[CrossRef] [PubMed]

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18, 18292 (2010).

Babcock, K. J.

Bennett, J. V.

Blackburn, K. L.

Buldu, J. M.

I. Fischer, R. Vicente, J. M. Buldu, M. Peil, C. R. Mirasso, M. C. Torrent, and J. Garcia-Ojalvo, “Zero-Lag Long-Range Synchronization via Dynamical Relaying,” Phys. Rev. Lett.97123902 (2006).
[CrossRef] [PubMed]

Burner, G.

D. W. Sukow, A. Gavrielides, T. McLachlan, G. Burner, J. Amonette, and J. Miller, “Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields,” Phys. Rev. A 74023812 (2006).
[CrossRef]

Butkovski, M.

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104114102 (2010).
[CrossRef] [PubMed]

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18, 18292 (2010).

Carr, T. W.

M. Y. Kim, R. Roy, J. L. Aron, T. W. Carr, and I. B. Schwartz, “Scaling behavior of laser population dynamics with time-delayed coupling: theory and experiment,” Phys. Rev. Lett. 94088101 (2005).
[CrossRef] [PubMed]

Chen, H. F.

M. C. Chiang, H. F. Chen, and J. M. Liu, “Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback”, IEEE J. Quantum Electron. 411333 (2005).
[CrossRef]

Chiang, M. C.

M. C. Chiang, H. F. Chen, and J. M. Liu, “Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback”, IEEE J. Quantum Electron. 411333 (2005).
[CrossRef]

Davis, J.

D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81025206R (2010).
[CrossRef]

Davis, P.

N. Shibasaki, A. Uchida, S. Yoshimori, and P. Davis, “Characteristics of chaos synchronization in semiconductor lasers subject to polarization-rotated optical feedback,” IEEE J. Quantum Electron. 42, 342 (2006).
[CrossRef]

Englert, A.

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104114102 (2010).
[CrossRef] [PubMed]

Erneux, T.

D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81025206R (2010).
[CrossRef]

Fischer, I.

I. Fischer, R. Vicente, J. M. Buldu, M. Peil, C. R. Mirasso, M. C. Torrent, and J. Garcia-Ojalvo, “Zero-Lag Long-Range Synchronization via Dynamical Relaying,” Phys. Rev. Lett.97123902 (2006).
[CrossRef] [PubMed]

Garcia-Ojalvo, J.

I. Fischer, R. Vicente, J. M. Buldu, M. Peil, C. R. Mirasso, M. C. Torrent, and J. Garcia-Ojalvo, “Zero-Lag Long-Range Synchronization via Dynamical Relaying,” Phys. Rev. Lett.97123902 (2006).
[CrossRef] [PubMed]

Gavrielides, A.

C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: theory and experiment,” Phys. Rev. A 84023838 (2011).
[CrossRef]

D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81025206R (2010).
[CrossRef]

D. W. Sukow, A. Gavrielides, T. McLachlan, G. Burner, J. Amonette, and J. Miller, “Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields,” Phys. Rev. A 74023812 (2006).
[CrossRef]

D. W. Sukow, K. L. Blackburn, A. R. Spain, K. J. Babcock, J. V. Bennett, and A. Gavrielides, “Experimental synchronization of chaos in diode lasers with polarization-rotated feedback and injection”, Opt. Lett. 292393 (2004).
[CrossRef] [PubMed]

Henning, I. D.

Hurtado, A.

M. S. Torre, A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. J. Adams “Polarization switching in long-wavelength VCSELs subject to orthogonal optical injection,” IEEE J. Quantum Electron. 4792 (2011).
[CrossRef]

A. Hurtado, I. D. Henning, and M. J. Adams, “Different forms of wavelength polarization switching and bistability in a 1.55 m vertical-cavity surface-emitting laser under orthogonally polarized optical injection,” Opt. Lett. 34365 (2009).
[CrossRef] [PubMed]

Jeong, K. H.

K. H. Jeong, K. H. Kim, S. H. Lee, M. H. Lee, B. S. Yoo, and K. A. Shore, “Optical injection-induced polarization switching dynamics in 1.5 mu m wavelength single-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 20779 (2008).
[CrossRef]

Jiang, N.

Ju, R.

R. Ju, P. S. Spencer, and K. Alan Shore, “Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 411461 (2005).
[CrossRef]

Kanter, I.

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104114102 (2010).
[CrossRef] [PubMed]

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18, 18292 (2010).

Kim, K. H.

K. H. Jeong, K. H. Kim, S. H. Lee, M. H. Lee, B. S. Yoo, and K. A. Shore, “Optical injection-induced polarization switching dynamics in 1.5 mu m wavelength single-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 20779 (2008).
[CrossRef]

Kim, M. Y.

M. Y. Kim, R. Roy, J. L. Aron, T. W. Carr, and I. B. Schwartz, “Scaling behavior of laser population dynamics with time-delayed coupling: theory and experiment,” Phys. Rev. Lett. 94088101 (2005).
[CrossRef] [PubMed]

Kinzel, W.

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104114102 (2010).
[CrossRef] [PubMed]

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18, 18292 (2010).

Koyama, F.

Kurths, J.

A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Science (Cambridge University Press, Cambridge, 2001).
[CrossRef]

Lee, K.

D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81025206R (2010).
[CrossRef]

Lee, M. H.

K. H. Jeong, K. H. Kim, S. H. Lee, M. H. Lee, B. S. Yoo, and K. A. Shore, “Optical injection-induced polarization switching dynamics in 1.5 mu m wavelength single-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 20779 (2008).
[CrossRef]

Lee, M. W.

Lee, S. H.

K. H. Jeong, K. H. Kim, S. H. Lee, M. H. Lee, B. S. Yoo, and K. A. Shore, “Optical injection-induced polarization switching dynamics in 1.5 mu m wavelength single-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 20779 (2008).
[CrossRef]

Li, X. F.

Liu, J. M.

M. C. Chiang, H. F. Chen, and J. M. Liu, “Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback”, IEEE J. Quantum Electron. 411333 (2005).
[CrossRef]

Luo, B.

Martinez Avila, J. F.

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, 765 (1997).
[CrossRef]

Masoller, C.

C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: theory and experiment,” Phys. Rev. A 84023838 (2011).
[CrossRef]

M. W. Lee, J. Paul, C. Masoller, and K. A. Shore, “Observation of cascade complete chaos synchronisation with zero time lag in laser diodes,” J. Opt. Soc. Am. B 23846 (2006).
[CrossRef]

McKay, J.

D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81025206R (2010).
[CrossRef]

McLachlan, T.

D. W. Sukow, A. Gavrielides, T. McLachlan, G. Burner, J. Amonette, and J. Miller, “Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields,” Phys. Rev. A 74023812 (2006).
[CrossRef]

Mihara, T.

M. Ozaki, H. Someya, T. Mihara, A. Uchida, S. Yoshimori, K. Panajotov, and M. Sciamanna, “Leader-laggard relationship of chaos synchronization in mutually coupled vertical-cavity surface-emitting lasers with time delay,” Phys. Rev. A 79026210 (2009).

Miller, J.

D. W. Sukow, A. Gavrielides, T. McLachlan, G. Burner, J. Amonette, and J. Miller, “Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields,” Phys. Rev. A 74023812 (2006).
[CrossRef]

Mirasso, C. R.

I. Fischer, R. Vicente, J. M. Buldu, M. Peil, C. R. Mirasso, M. C. Torrent, and J. Garcia-Ojalvo, “Zero-Lag Long-Range Synchronization via Dynamical Relaying,” Phys. Rev. Lett.97123902 (2006).
[CrossRef] [PubMed]

Mooneyham, B.

D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81025206R (2010).
[CrossRef]

Ozaki, M.

M. Ozaki, H. Someya, T. Mihara, A. Uchida, S. Yoshimori, K. Panajotov, and M. Sciamanna, “Leader-laggard relationship of chaos synchronization in mutually coupled vertical-cavity surface-emitting lasers with time delay,” Phys. Rev. A 79026210 (2009).

Pan, W.

Panajotov, K.

M. Ozaki, H. Someya, T. Mihara, A. Uchida, S. Yoshimori, K. Panajotov, and M. Sciamanna, “Leader-laggard relationship of chaos synchronization in mutually coupled vertical-cavity surface-emitting lasers with time delay,” Phys. Rev. A 79026210 (2009).

Paul, J.

Peil, M.

I. Fischer, R. Vicente, J. M. Buldu, M. Peil, C. R. Mirasso, M. C. Torrent, and J. Garcia-Ojalvo, “Zero-Lag Long-Range Synchronization via Dynamical Relaying,” Phys. Rev. Lett.97123902 (2006).
[CrossRef] [PubMed]

Peleg, Y.

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18, 18292 (2010).

Pesquera, L.

M. S. Torre, A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. J. Adams “Polarization switching in long-wavelength VCSELs subject to orthogonal optical injection,” IEEE J. Quantum Electron. 4792 (2011).
[CrossRef]

Pikovsky, A.

A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Science (Cambridge University Press, Cambridge, 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, 765 (1997).
[CrossRef]

Quirce, A.

M. S. Torre, A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. J. Adams “Polarization switching in long-wavelength VCSELs subject to orthogonal optical injection,” IEEE J. Quantum Electron. 4792 (2011).
[CrossRef]

Reidler, I.

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104114102 (2010).
[CrossRef] [PubMed]

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18, 18292 (2010).

Rios Leite, J. R.

Rosenbluh, M.

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104114102 (2010).
[CrossRef] [PubMed]

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18, 18292 (2010).

Rosenblum, M.

A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Science (Cambridge University Press, Cambridge, 2001).
[CrossRef]

Roy, R.

M. Y. Kim, R. Roy, J. L. Aron, T. W. Carr, and I. B. Schwartz, “Scaling behavior of laser population dynamics with time-delayed coupling: theory and experiment,” Phys. Rev. Lett. 94088101 (2005).
[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, 765 (1997).
[CrossRef]

Schwartz, I. B.

M. Y. Kim, R. Roy, J. L. Aron, T. W. Carr, and I. B. Schwartz, “Scaling behavior of laser population dynamics with time-delayed coupling: theory and experiment,” Phys. Rev. Lett. 94088101 (2005).
[CrossRef] [PubMed]

Sciamanna, M.

C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: theory and experiment,” Phys. Rev. A 84023838 (2011).
[CrossRef]

M. Ozaki, H. Someya, T. Mihara, A. Uchida, S. Yoshimori, K. Panajotov, and M. Sciamanna, “Leader-laggard relationship of chaos synchronization in mutually coupled vertical-cavity surface-emitting lasers with time delay,” Phys. Rev. A 79026210 (2009).

Shibasaki, N.

N. Shibasaki, A. Uchida, S. Yoshimori, and P. Davis, “Characteristics of chaos synchronization in semiconductor lasers subject to polarization-rotated optical feedback,” IEEE J. Quantum Electron. 42, 342 (2006).
[CrossRef]

Shore, K. A.

K. H. Jeong, K. H. Kim, S. H. Lee, M. H. Lee, B. S. Yoo, and K. A. Shore, “Optical injection-induced polarization switching dynamics in 1.5 mu m wavelength single-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 20779 (2008).
[CrossRef]

M. W. Lee, J. Paul, C. Masoller, and K. A. Shore, “Observation of cascade complete chaos synchronisation with zero time lag in laser diodes,” J. Opt. Soc. Am. B 23846 (2006).
[CrossRef]

Someya, H.

M. Ozaki, H. Someya, T. Mihara, A. Uchida, S. Yoshimori, K. Panajotov, and M. Sciamanna, “Leader-laggard relationship of chaos synchronization in mutually coupled vertical-cavity surface-emitting lasers with time delay,” Phys. Rev. A 79026210 (2009).

Spain, A. R.

Spencer, P. S.

R. Ju, P. S. Spencer, and K. Alan Shore, “Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 411461 (2005).
[CrossRef]

Sukow, D.

C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: theory and experiment,” Phys. Rev. A 84023838 (2011).
[CrossRef]

D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81025206R (2010).
[CrossRef]

Sukow, D. W.

D. W. Sukow, A. Gavrielides, T. McLachlan, G. Burner, J. Amonette, and J. Miller, “Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields,” Phys. Rev. A 74023812 (2006).
[CrossRef]

D. W. Sukow, K. L. Blackburn, A. R. Spain, K. J. Babcock, J. V. Bennett, and A. Gavrielides, “Experimental synchronization of chaos in diode lasers with polarization-rotated feedback and injection”, Opt. Lett. 292393 (2004).
[CrossRef] [PubMed]

Torre, M. S.

M. S. Torre, A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. J. Adams “Polarization switching in long-wavelength VCSELs subject to orthogonal optical injection,” IEEE J. Quantum Electron. 4792 (2011).
[CrossRef]

Torrent, M. C.

I. Fischer, R. Vicente, J. M. Buldu, M. Peil, C. R. Mirasso, M. C. Torrent, and J. Garcia-Ojalvo, “Zero-Lag Long-Range Synchronization via Dynamical Relaying,” Phys. Rev. Lett.97123902 (2006).
[CrossRef] [PubMed]

Uchida, A.

M. Ozaki, H. Someya, T. Mihara, A. Uchida, S. Yoshimori, K. Panajotov, and M. Sciamanna, “Leader-laggard relationship of chaos synchronization in mutually coupled vertical-cavity surface-emitting lasers with time delay,” Phys. Rev. A 79026210 (2009).

N. Shibasaki, A. Uchida, S. Yoshimori, and P. Davis, “Characteristics of chaos synchronization in semiconductor lasers subject to polarization-rotated optical feedback,” IEEE J. Quantum Electron. 42, 342 (2006).
[CrossRef]

Valle, A.

M. S. Torre, A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. J. Adams “Polarization switching in long-wavelength VCSELs subject to orthogonal optical injection,” IEEE J. Quantum Electron. 4792 (2011).
[CrossRef]

Vicente, R.

I. Fischer, R. Vicente, J. M. Buldu, M. Peil, C. R. Mirasso, M. C. Torrent, and J. Garcia-Ojalvo, “Zero-Lag Long-Range Synchronization via Dynamical Relaying,” Phys. Rev. Lett.97123902 (2006).
[CrossRef] [PubMed]

Wang, M. Y.

Xiang, S.

Yan, L.

Yang, L.

Yoo, B. S.

K. H. Jeong, K. H. Kim, S. H. Lee, M. H. Lee, B. S. Yoo, and K. A. Shore, “Optical injection-induced polarization switching dynamics in 1.5 mu m wavelength single-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 20779 (2008).
[CrossRef]

Yoshimori, S.

M. Ozaki, H. Someya, T. Mihara, A. Uchida, S. Yoshimori, K. Panajotov, and M. Sciamanna, “Leader-laggard relationship of chaos synchronization in mutually coupled vertical-cavity surface-emitting lasers with time delay,” Phys. Rev. A 79026210 (2009).

N. Shibasaki, A. Uchida, S. Yoshimori, and P. Davis, “Characteristics of chaos synchronization in semiconductor lasers subject to polarization-rotated optical feedback,” IEEE J. Quantum Electron. 42, 342 (2006).
[CrossRef]

Zhang, W. L.

Zheng, D.

Zigzag, M.

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104114102 (2010).
[CrossRef] [PubMed]

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18, 18292 (2010).

Zou, X. H.

IEEE J. Quantum Electron.

R. Ju, P. S. Spencer, and K. Alan Shore, “Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 411461 (2005).
[CrossRef]

N. Shibasaki, A. Uchida, S. Yoshimori, and P. Davis, “Characteristics of chaos synchronization in semiconductor lasers subject to polarization-rotated optical feedback,” IEEE J. Quantum Electron. 42, 342 (2006).
[CrossRef]

M. C. Chiang, H. F. Chen, and J. M. Liu, “Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback”, IEEE J. Quantum Electron. 411333 (2005).
[CrossRef]

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, 765 (1997).
[CrossRef]

M. S. Torre, A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. J. Adams “Polarization switching in long-wavelength VCSELs subject to orthogonal optical injection,” IEEE J. Quantum Electron. 4792 (2011).
[CrossRef]

IEEE Photon. Technol. Lett.

K. H. Jeong, K. H. Kim, S. H. Lee, M. H. Lee, B. S. Yoo, and K. A. Shore, “Optical injection-induced polarization switching dynamics in 1.5 mu m wavelength single-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 20779 (2008).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Opt. Express

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18, 18292 (2010).

J. F. Martinez Avila and J. R. Rios Leite, “Time delays in the synchronization of chaotic coupled lasers with feedback,” Opt. Express 1721442 (2009).
[CrossRef]

Opt. Lett.

Phys. Rev. A

M. Ozaki, H. Someya, T. Mihara, A. Uchida, S. Yoshimori, K. Panajotov, and M. Sciamanna, “Leader-laggard relationship of chaos synchronization in mutually coupled vertical-cavity surface-emitting lasers with time delay,” Phys. Rev. A 79026210 (2009).

C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: theory and experiment,” Phys. Rev. A 84023838 (2011).
[CrossRef]

D. W. Sukow, A. Gavrielides, T. McLachlan, G. Burner, J. Amonette, and J. Miller, “Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields,” Phys. Rev. A 74023812 (2006).
[CrossRef]

Phys. Rev. E

D. Sukow, A. Gavrielides, T. Erneux, B. Mooneyham, K. Lee, J. McKay, and J. Davis, “Asymmetric square waves in mutually coupled semiconductor lasers with orthogonal optical injection,” Phys. Rev. E 81025206R (2010).
[CrossRef]

Phys. Rev. Lett.

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104114102 (2010).
[CrossRef] [PubMed]

M. Y. Kim, R. Roy, J. L. Aron, T. W. Carr, and I. B. Schwartz, “Scaling behavior of laser population dynamics with time-delayed coupling: theory and experiment,” Phys. Rev. Lett. 94088101 (2005).
[CrossRef] [PubMed]

Other

I. Fischer, R. Vicente, J. M. Buldu, M. Peil, C. R. Mirasso, M. C. Torrent, and J. Garcia-Ojalvo, “Zero-Lag Long-Range Synchronization via Dynamical Relaying,” Phys. Rev. Lett.97123902 (2006).
[CrossRef] [PubMed]

A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Science (Cambridge University Press, Cambridge, 2001).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Linear stability of the x and y polarized states of the solitary lasers in the parameter space (birefringence, injection current). In the red region only the x polarization is stable, in the blue region, only the y polarization is stable, in the white region, both polarizations are stable and in the green region, neither polarization is stable. The model parameters are: k = 300 ns−1, γn = 2 ns−1, γs = 50 ns−1, γa = 0.4 ns−1 and α = 3. The black circle and square indicate the parameters used for Figs. 3(a) and (b) respectively.

Fig. 2
Fig. 2

Bifurcation diagram for increasing coupling strength. The analytically calculated pure mode solution (black dots) is plotted together with the numerical solution (the extreme values of the oscillations of the x intensity of one laser, I1x in red, and the extreme values of the oscillations of the y intensity of the other laser, I2y in blue). In (a), (b) the coupling is xy, in (c), (d) the coupling is yx. The parameters are μ = 2, γp = 60 rad/ns (a), (b), γp = 4 rad/ns (c), (d), other parameters are as indicated in the text.

Fig. 3
Fig. 3

Transient dynamics towards the “pure-mode” steady-state in which the lasers emit cw orthogonal polarizations. The intensities of the x and y polarizations of the two lasers are plotted vs. time (x red line; y blue line, the intensities were averaged to simulate the finite experimental detection bandwidth). Left panels: the coupling is xy and the parameters are μ = 2.5, γp = 60 rad/ns, η = 60 ns−1; right panels: yx, μ = 1.7, γp = 4 rad/ns, η = 80 ns−1, other parameters as indicated in the text. In both cases after a transient time laser 2 (bottom row) acts as “master laser”, emitting the natural polarization of the stand alone laser (x in the left panels and y in the right panels), while laser 1 (top row) is the “injected laser”, emitting the orthogonal polarization.

Fig. 4
Fig. 4

Left panels: Dynamics of the coupled lasers with xy coupling, μ = 3.5, other parameters as in the left panels of Fig. 3. After the transient laser 1 (top row) is the “master laser” displaying sustained oscillations of the two polarizations (“solitary laser solution”) and laser 2 (bottom row) is the “injected laser” emitting the y polarization with the same oscillation as the master. Right panels: Dynamics of the coupled lasers with weaker coupling strength and yx coupling. After the transient laser 2 (bottom row) is the “injected laser” displaying sustained oscillations of the x polarization and laser 1 (top row) is the “master laser” emitting the y polarization with cw output (μ = 2, γp = 4 rad/ns, η = 50 ns−1).

Fig. 5
Fig. 5

Transient time vs. (a) the noise strength, βsp, and (b) the injection current parameter, μ. For each parameter value we simulated 30 stochastic trajectories, with an integration time of 10 μs (i.e., this is the longest transient time that we can compute). The dashed line indicates the average value. In (a) μ = 2.5, in (b) βsp = 10−5 ns−1, other model parameters are k = 300 ns−1, γn = 2 ns−1, γs = 50 ns−1, γa = 0.4 ns−1, γp = 60 rad ns−1, α = 3, η = 50 ns−1 and τ = 3 ns.

Fig. 6
Fig. 6

As in Fig. 5 but plot of the transient time vs. (a) the delay time, τ, and (b) the coupling strength, η. In (a) η = 50 ns−1, in (b) τ = 3 ns, other model parameters are k = 300 ns−1, γn = 2 ns−1, γs = 50 ns−1, γa = 0.4 ns−1, γp = 60 rad ns−1, α = 3, μ = 2.5 and βsp = 10−5 ns−1.

Fig. 7
Fig. 7

As in Fig. 5 but plot of the transient time vs. (a) the anisotropy parameter, γa, and (b) the spin-flip rate, γs. In (a) γs = 50 ns−1, in (b) γa = 0.4 ns−1, other model parameters are k = 300 ns−1, γn = 2 ns−1, γp = 60 rad ns−1, α = 3, μ = 2.5, βsp = 10−5 ns−1, η = 50 ns−1 and τ = 3 ns.

Fig. 8
Fig. 8

As in Fig. 5 but plot of the transient time vs. the birefringence parameter, γp, for (a) x → y injection and (b) yx injection. In (a) γp = 60 rad ns−1, in (b) γp = 6 rad ns−1, other model parameters are k = 300 ns−1, γn = 2 ns−1, γs = 50 ns−1, γa = 0.4 ns−1, α = 3, μ = 2.5, βsp = 10−5 ns−1, η = 50 ns−1 and τ = 3 ns.

Equations (5)

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

d E ix dt = k ( 1 + j α ) [ ( N i 1 ) E ix + j n i E iy ] ( γ a + j γ p ) E ix + β sp ξ x ( t ) + η y E ( 3 i ) y ( t τ ) ,
d E iy dt = k ( 1 + j α ) [ ( N i 1 ) E i y j n i E ix ] + ( γ a + j γ p ) E iy + β sp ξ y ( t ) + η x E ( 3 i ) x ( t τ ) ,
d N i dt = γ n [ μ + N i ( 1 + | E ix | 2 + | E iy | 2 ) + j n i ( E iy E ix * E ix E iy * ) ] ,
d n i dt = γ s n i γ n [ n i ( | E ix | 2 + | E iy | 2 ) + j N i ( E iy E ix * E ix E iy * ) ] .
( [ Δ + α k ( N 1 ) ] 2 + [ k ( N 1 ) + γ a ] 2 ) I y = η 2 I x ,

Metrics