Abstract

Based on the framework of the spin-flip model (SFM) for GHz level modulation frequency, the polarization performances of current-modulated vertical-cavity surface-emitting lasers (VCSELs) subject to weak optical feedback have been theoretically investigated. The results show that, for type 1 polarization switching (PS), the influences of optical feedback intensity and the current modulation amplitude on the high-frequency modulation response is not obvious. For low-frequency modulation, optical feedback will result in the output of a VCSEL having rich dynamics. A new style PS can be obtained under large-signal modulation through adjusting the modulation frequency. For type 2 PS the situation is more complex, and optical feedback increases the probability of polarization conversion and competition, while also affecting the PS point. The modulation amplitude also affects the output dynamics of the VCSEL.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. H. Hong, R. Ju, P. S. Spencer, and K. A. Shore, “Investigation of polarization bistability in vertical-cavity surface-emitting lasers subjected to optical feedback,” IEEE J. Quantum Electron. 41, 619-624 (2005).
    [CrossRef]
  2. A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron. 43, 322-333 (2007).
    [CrossRef]
  3. W. L. Zhang, W. Pan, B. Luo, X. F. Li, X. H. Zuo, and M. Y. Wang, “Theoretical study on polarization dynamics of VCSELs with negative optoelectronic feedback,” Appl. Opt. 46, 7262-7266 (2007).
    [CrossRef] [PubMed]
  4. M. A. Arteaga, H. J. Unold, J. M. Ostermann, R. Michalzik, H. Thienpont, and K. Panajotov, “Investigation of polarization properties of VCSELs subject to optical feedback from an extremely short external cavity--part I: theoretical analysis,” IEEE J. Quantum Electron. 42, 89-101 (2006).
    [CrossRef]
  5. M. Sciamanna and K. Panajotov, “Two-mode injection locking in vertical-cavity surface-emitting lasers,” Opt. Lett. 30, 2903-2905 (2005).
    [CrossRef] [PubMed]
  6. T. Ackemann, M. Sondermann, and S. Balle, “Self-organization in vertical-cavity surface-emitting lasers: polarization selection and polarization dynamics,” in Proceedings of CAOL 2003, Advanced Optoelectronics and Lasers, 2003 (IEEE, 2003), pp. 75-77.
  7. J. S. Gustavsson, Å. Haglund, E. Söderberg, J. Vukušić, P. Modh, P. Jedrasik, and A. Larsson, “Mode and polarization control in VCSELS using shallow surface structures,” IET Optoelectron. 1, 197-205 (2007).
    [CrossRef]
  8. A. Honmayounfar and M. J. Adams, “Locking bandwidth and birefringence effects for polarized optical injection in vertical-cavity surface-emitting lasers,” Opt. Commun. 269, 119-127 (2007).
    [CrossRef]
  9. D. Z. Zhong, G. Q. Xia, Z. M. Wu, and X. H. Jia, “Complete chaotic synchronization characteristics of the linear-polarization mode of vertical-cavity surface-emitting semiconductor lasers with isotropic optical feedback,” Opt. Commun. 281, 1698-1709 (2008).
    [CrossRef]
  10. S. F. Liu, G. Q. Xia, X. Tang, Y. Fan, Z. Y. Li, and Z. M. Wu, “Influence of the light injection on the chaotic carrier fundamental frequency of the VCSELs with optical feedback,” Proc. SPIE 6824, 682410 (2007).
    [CrossRef]
  11. H. J. Kong, Z. M. Wu, C. X. Hu, J. F. Liao, Q. Yang, and G. Q. Xia, “Studying the nonlinear dynamic characteristics of an optically injection vertical-cavity surface-emitting laser,” Proc. SPIE 6839, 68390V (2007).
    [CrossRef]
  12. M. S. Miguel, Q. Feng, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52, 1728-1739 (1995).
    [CrossRef]
  13. J. M. Regalado, F. Prati, M. S. Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 765-783 (1997).
    [CrossRef]
  14. Y. H. Hong, P. S. Spencer, and K. A. Shore, “Experimental study of polarization switching of vertical-cavity surface-emitting lasers as a dynamical bifurcation,” Opt. Lett. 31, 748-750 (2006).
    [CrossRef] [PubMed]
  15. J. Danckaert, B. Nagler, J. Albert, K. Panajotov,I. Veretnnicoff, and T. Erneux, “Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers,” Opt. Commun. 201, 129-137 (2002).
    [CrossRef]
  16. P. Besnard, M. L. Chsrès, G. Stéphan, and F. Robert, “Switching between polarized modes of a vertical-cavity surface-emitting laser by isotropic optical feedback,” J. Opt. Soc. Am. B 16, 1059-1063 (1999).
    [CrossRef]
  17. C. Masoller and M. S. Torre, “Influence of optical feedback on the polarization switching of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 483-489 (2005).
    [CrossRef]
  18. J. Paul, C. Masoller, Y. H. Hong, P. S. Spencer, and K. A. Shore, “Impact of orthogonal optical feedback on the polarization switching of vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 16, 1987-1994 (2007).
    [CrossRef]
  19. Y. H. Hong, P. S. Spencer, and K. A. Shore, “Suppression of polarization switching in vertical-cavity surface-emitting lasers by use of optical feedback,” Opt. Lett. 29, 2151-2153 (2004).
    [CrossRef] [PubMed]
  20. M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28, 1543-1545 (2003).
    [CrossRef] [PubMed]
  21. W. L. Zhang, W. Pan, B. Luo, X. F. Li, X. H. Zou, and M. Y. Wang, “Polarization switching of mutually coupled vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 24, 1276-1282 (2007).
    [CrossRef]
  22. J. Albert, G. Van der Sande, B. Nagler, K. Pannajotov, I. Veretennicoff, J. Danckaert, and T. Erneux, “The effects of nonlinear gain on the stability of semi-degenerate two-mode semiconductor lasers: a case study on VCSELs,” Opt. Commun. 248, 527-534 (2005).
    [CrossRef]
  23. M. Sciamanna, F. Rogister, P. Mégret, and M. Blondel, “Numerical observation of in-phase and out-of-phase pulses in the polarization modes of a VCSEL operating in the low-frequency fluctuations regime,” in Proceedings Symposium of IEEE/LEOS Benelux Chapter (IEEE, 2002), pp. 155-158.
  24. Y. Matsui, D. Vakhshoori, P. D. Wang, P. L. Chen, C. C. Lu, M. Jiang, K. Knopp, S. Burroughs, and P. Tayebati, “Complete polarization mode control of long-wavelength tunable vertical-cavity surface-emitting lasers over 65-nm tuning, up to 14-mw output power,” IEEE J. Quantum Electron. 39, 1037-1048 (2003).
    [CrossRef]
  25. B. Ryvkin, K. Panajotov, A. Georgievski, J. Danckaert, M. Peeters, and G. Verschaffelt, “Effect of photon-energy-dependent loss and gain mechanisms on polarization switching in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 16, 2016-2112 (1999).
    [CrossRef]
  26. G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248-2250 (2002).
    [CrossRef]
  27. M. Sciamanna, A. Valle, P. Megret, M. Blondel, and K. Panajotov, “Nonlinear polarization dynamics in directly modulated vertical-cavity surface-emitting lasers,” Phys. Rev. E 68, 016207 (2003).
    [CrossRef]
  28. C. Masoller, M. S. Torre, and K. A. Shore, “Polarization dynamics of current-modulated vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 43, 1047-1082 (2007).
    [CrossRef]
  29. M. S. Torre, C. Masoller, P. Mandel, and K. A. Shore, “Transverse-mode dynamics in directly modulated vertical-cavity surface-emitting lasers with optical feedback,” IEEE J. Quantum Electron. 40, 620-628 (2004).
    [CrossRef]
  30. Y. H. Hong, S. Bandyopadhyay, and K. A. Shore, “Spectral signatures of the dynamics of current-modulated vertical-cavity surface-emitting lasers subject to optical feedback,” J. Opt. Soc. Am. B 22, 2350-2356 (2005).
    [CrossRef]
  31. Y. H. Hong, J. Paul, P. S. Spencer, and K. A. Shore, “Influence of low-frequency modulation on polarization switching of VCSELs subject to optical feedback,” IEEE J. Quantum Electron. 44, 30-35 (2008).
    [CrossRef]
  32. A. Valle, M. Sciamanna, and K. Panajotov, “Irregular pulsating polarization dynamics in gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 44, 136-143 (2008).
    [CrossRef]
  33. A. Valle, M. Sciamanna, and K. Panajotov, “Nonlinear dynamics of the polarization of multitransverse mode vertical-cavity surface-emitting lasers under current modulation,” Phys. Rev. E 76, 046206 (2007).
    [CrossRef]

2008 (3)

D. Z. Zhong, G. Q. Xia, Z. M. Wu, and X. H. Jia, “Complete chaotic synchronization characteristics of the linear-polarization mode of vertical-cavity surface-emitting semiconductor lasers with isotropic optical feedback,” Opt. Commun. 281, 1698-1709 (2008).
[CrossRef]

Y. H. Hong, J. Paul, P. S. Spencer, and K. A. Shore, “Influence of low-frequency modulation on polarization switching of VCSELs subject to optical feedback,” IEEE J. Quantum Electron. 44, 30-35 (2008).
[CrossRef]

A. Valle, M. Sciamanna, and K. Panajotov, “Irregular pulsating polarization dynamics in gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 44, 136-143 (2008).
[CrossRef]

2007 (10)

A. Valle, M. Sciamanna, and K. Panajotov, “Nonlinear dynamics of the polarization of multitransverse mode vertical-cavity surface-emitting lasers under current modulation,” Phys. Rev. E 76, 046206 (2007).
[CrossRef]

C. Masoller, M. S. Torre, and K. A. Shore, “Polarization dynamics of current-modulated vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 43, 1047-1082 (2007).
[CrossRef]

W. L. Zhang, W. Pan, B. Luo, X. F. Li, X. H. Zou, and M. Y. Wang, “Polarization switching of mutually coupled vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 24, 1276-1282 (2007).
[CrossRef]

W. L. Zhang, W. Pan, B. Luo, X. F. Li, X. H. Zuo, and M. Y. Wang, “Theoretical study on polarization dynamics of VCSELs with negative optoelectronic feedback,” Appl. Opt. 46, 7262-7266 (2007).
[CrossRef] [PubMed]

S. F. Liu, G. Q. Xia, X. Tang, Y. Fan, Z. Y. Li, and Z. M. Wu, “Influence of the light injection on the chaotic carrier fundamental frequency of the VCSELs with optical feedback,” Proc. SPIE 6824, 682410 (2007).
[CrossRef]

H. J. Kong, Z. M. Wu, C. X. Hu, J. F. Liao, Q. Yang, and G. Q. Xia, “Studying the nonlinear dynamic characteristics of an optically injection vertical-cavity surface-emitting laser,” Proc. SPIE 6839, 68390V (2007).
[CrossRef]

J. S. Gustavsson, Å. Haglund, E. Söderberg, J. Vukušić, P. Modh, P. Jedrasik, and A. Larsson, “Mode and polarization control in VCSELS using shallow surface structures,” IET Optoelectron. 1, 197-205 (2007).
[CrossRef]

A. Honmayounfar and M. J. Adams, “Locking bandwidth and birefringence effects for polarized optical injection in vertical-cavity surface-emitting lasers,” Opt. Commun. 269, 119-127 (2007).
[CrossRef]

J. Paul, C. Masoller, Y. H. Hong, P. S. Spencer, and K. A. Shore, “Impact of orthogonal optical feedback on the polarization switching of vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 16, 1987-1994 (2007).
[CrossRef]

A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron. 43, 322-333 (2007).
[CrossRef]

2006 (2)

M. A. Arteaga, H. J. Unold, J. M. Ostermann, R. Michalzik, H. Thienpont, and K. Panajotov, “Investigation of polarization properties of VCSELs subject to optical feedback from an extremely short external cavity--part I: theoretical analysis,” IEEE J. Quantum Electron. 42, 89-101 (2006).
[CrossRef]

Y. H. Hong, P. S. Spencer, and K. A. Shore, “Experimental study of polarization switching of vertical-cavity surface-emitting lasers as a dynamical bifurcation,” Opt. Lett. 31, 748-750 (2006).
[CrossRef] [PubMed]

2005 (5)

M. Sciamanna and K. Panajotov, “Two-mode injection locking in vertical-cavity surface-emitting lasers,” Opt. Lett. 30, 2903-2905 (2005).
[CrossRef] [PubMed]

Y. H. Hong, S. Bandyopadhyay, and K. A. Shore, “Spectral signatures of the dynamics of current-modulated vertical-cavity surface-emitting lasers subject to optical feedback,” J. Opt. Soc. Am. B 22, 2350-2356 (2005).
[CrossRef]

C. Masoller and M. S. Torre, “Influence of optical feedback on the polarization switching of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 483-489 (2005).
[CrossRef]

J. Albert, G. Van der Sande, B. Nagler, K. Pannajotov, I. Veretennicoff, J. Danckaert, and T. Erneux, “The effects of nonlinear gain on the stability of semi-degenerate two-mode semiconductor lasers: a case study on VCSELs,” Opt. Commun. 248, 527-534 (2005).
[CrossRef]

Y. H. Hong, R. Ju, P. S. Spencer, and K. A. Shore, “Investigation of polarization bistability in vertical-cavity surface-emitting lasers subjected to optical feedback,” IEEE J. Quantum Electron. 41, 619-624 (2005).
[CrossRef]

2004 (2)

Y. H. Hong, P. S. Spencer, and K. A. Shore, “Suppression of polarization switching in vertical-cavity surface-emitting lasers by use of optical feedback,” Opt. Lett. 29, 2151-2153 (2004).
[CrossRef] [PubMed]

M. S. Torre, C. Masoller, P. Mandel, and K. A. Shore, “Transverse-mode dynamics in directly modulated vertical-cavity surface-emitting lasers with optical feedback,” IEEE J. Quantum Electron. 40, 620-628 (2004).
[CrossRef]

2003 (3)

M. Sciamanna, A. Valle, P. Megret, M. Blondel, and K. Panajotov, “Nonlinear polarization dynamics in directly modulated vertical-cavity surface-emitting lasers,” Phys. Rev. E 68, 016207 (2003).
[CrossRef]

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28, 1543-1545 (2003).
[CrossRef] [PubMed]

Y. Matsui, D. Vakhshoori, P. D. Wang, P. L. Chen, C. C. Lu, M. Jiang, K. Knopp, S. Burroughs, and P. Tayebati, “Complete polarization mode control of long-wavelength tunable vertical-cavity surface-emitting lasers over 65-nm tuning, up to 14-mw output power,” IEEE J. Quantum Electron. 39, 1037-1048 (2003).
[CrossRef]

2002 (2)

G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248-2250 (2002).
[CrossRef]

J. Danckaert, B. Nagler, J. Albert, K. Panajotov,I. Veretnnicoff, and T. Erneux, “Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers,” Opt. Commun. 201, 129-137 (2002).
[CrossRef]

1999 (2)

B. Ryvkin, K. Panajotov, A. Georgievski, J. Danckaert, M. Peeters, and G. Verschaffelt, “Effect of photon-energy-dependent loss and gain mechanisms on polarization switching in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 16, 2016-2112 (1999).
[CrossRef]

P. Besnard, M. L. Chsrès, G. Stéphan, and F. Robert, “Switching between polarized modes of a vertical-cavity surface-emitting laser by isotropic optical feedback,” J. Opt. Soc. Am. B 16, 1059-1063 (1999).
[CrossRef]

1997 (1)

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

1995 (1)

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

Abraham, N. B.

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

Ackemann, T.

T. Ackemann, M. Sondermann, and S. Balle, “Self-organization in vertical-cavity surface-emitting lasers: polarization selection and polarization dynamics,” in Proceedings of CAOL 2003, Advanced Optoelectronics and Lasers, 2003 (IEEE, 2003), pp. 75-77.

Adams, M. J.

A. Honmayounfar and M. J. Adams, “Locking bandwidth and birefringence effects for polarized optical injection in vertical-cavity surface-emitting lasers,” Opt. Commun. 269, 119-127 (2007).
[CrossRef]

Albert, J.

J. Albert, G. Van der Sande, B. Nagler, K. Pannajotov, I. Veretennicoff, J. Danckaert, and T. Erneux, “The effects of nonlinear gain on the stability of semi-degenerate two-mode semiconductor lasers: a case study on VCSELs,” Opt. Commun. 248, 527-534 (2005).
[CrossRef]

G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248-2250 (2002).
[CrossRef]

J. Danckaert, B. Nagler, J. Albert, K. Panajotov,I. Veretnnicoff, and T. Erneux, “Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers,” Opt. Commun. 201, 129-137 (2002).
[CrossRef]

Arteaga, M. A.

M. A. Arteaga, H. J. Unold, J. M. Ostermann, R. Michalzik, H. Thienpont, and K. Panajotov, “Investigation of polarization properties of VCSELs subject to optical feedback from an extremely short external cavity--part I: theoretical analysis,” IEEE J. Quantum Electron. 42, 89-101 (2006).
[CrossRef]

Balle, S.

T. Ackemann, M. Sondermann, and S. Balle, “Self-organization in vertical-cavity surface-emitting lasers: polarization selection and polarization dynamics,” in Proceedings of CAOL 2003, Advanced Optoelectronics and Lasers, 2003 (IEEE, 2003), pp. 75-77.

Bandyopadhyay, S.

Barbay, S.

G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248-2250 (2002).
[CrossRef]

Besnard, P.

Blondel, M.

M. Sciamanna, A. Valle, P. Megret, M. Blondel, and K. Panajotov, “Nonlinear polarization dynamics in directly modulated vertical-cavity surface-emitting lasers,” Phys. Rev. E 68, 016207 (2003).
[CrossRef]

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28, 1543-1545 (2003).
[CrossRef] [PubMed]

M. Sciamanna, F. Rogister, P. Mégret, and M. Blondel, “Numerical observation of in-phase and out-of-phase pulses in the polarization modes of a VCSEL operating in the low-frequency fluctuations regime,” in Proceedings Symposium of IEEE/LEOS Benelux Chapter (IEEE, 2002), pp. 155-158.

Burroughs, S.

Y. Matsui, D. Vakhshoori, P. D. Wang, P. L. Chen, C. C. Lu, M. Jiang, K. Knopp, S. Burroughs, and P. Tayebati, “Complete polarization mode control of long-wavelength tunable vertical-cavity surface-emitting lasers over 65-nm tuning, up to 14-mw output power,” IEEE J. Quantum Electron. 39, 1037-1048 (2003).
[CrossRef]

Chen, P. L.

Y. Matsui, D. Vakhshoori, P. D. Wang, P. L. Chen, C. C. Lu, M. Jiang, K. Knopp, S. Burroughs, and P. Tayebati, “Complete polarization mode control of long-wavelength tunable vertical-cavity surface-emitting lasers over 65-nm tuning, up to 14-mw output power,” IEEE J. Quantum Electron. 39, 1037-1048 (2003).
[CrossRef]

Chsrès, M. L.

Danckaert, J.

J. Albert, G. Van der Sande, B. Nagler, K. Pannajotov, I. Veretennicoff, J. Danckaert, and T. Erneux, “The effects of nonlinear gain on the stability of semi-degenerate two-mode semiconductor lasers: a case study on VCSELs,” Opt. Commun. 248, 527-534 (2005).
[CrossRef]

G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248-2250 (2002).
[CrossRef]

J. Danckaert, B. Nagler, J. Albert, K. Panajotov,I. Veretnnicoff, and T. Erneux, “Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers,” Opt. Commun. 201, 129-137 (2002).
[CrossRef]

B. Ryvkin, K. Panajotov, A. Georgievski, J. Danckaert, M. Peeters, and G. Verschaffelt, “Effect of photon-energy-dependent loss and gain mechanisms on polarization switching in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 16, 2016-2112 (1999).
[CrossRef]

Erneux, T.

J. Albert, G. Van der Sande, B. Nagler, K. Pannajotov, I. Veretennicoff, J. Danckaert, and T. Erneux, “The effects of nonlinear gain on the stability of semi-degenerate two-mode semiconductor lasers: a case study on VCSELs,” Opt. Commun. 248, 527-534 (2005).
[CrossRef]

J. Danckaert, B. Nagler, J. Albert, K. Panajotov,I. Veretnnicoff, and T. Erneux, “Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers,” Opt. Commun. 201, 129-137 (2002).
[CrossRef]

Fan, Y.

S. F. Liu, G. Q. Xia, X. Tang, Y. Fan, Z. Y. Li, and Z. M. Wu, “Influence of the light injection on the chaotic carrier fundamental frequency of the VCSELs with optical feedback,” Proc. SPIE 6824, 682410 (2007).
[CrossRef]

Feng, Q.

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

Gatare, I.

A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron. 43, 322-333 (2007).
[CrossRef]

Georgievski, A.

B. Ryvkin, K. Panajotov, A. Georgievski, J. Danckaert, M. Peeters, and G. Verschaffelt, “Effect of photon-energy-dependent loss and gain mechanisms on polarization switching in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 16, 2016-2112 (1999).
[CrossRef]

Giacomelli, G.

G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248-2250 (2002).
[CrossRef]

Gustavsson, J. S.

J. S. Gustavsson, Å. Haglund, E. Söderberg, J. Vukušić, P. Modh, P. Jedrasik, and A. Larsson, “Mode and polarization control in VCSELS using shallow surface structures,” IET Optoelectron. 1, 197-205 (2007).
[CrossRef]

Haglund, Å.

J. S. Gustavsson, Å. Haglund, E. Söderberg, J. Vukušić, P. Modh, P. Jedrasik, and A. Larsson, “Mode and polarization control in VCSELS using shallow surface structures,” IET Optoelectron. 1, 197-205 (2007).
[CrossRef]

Hong, Y. H.

Y. H. Hong, J. Paul, P. S. Spencer, and K. A. Shore, “Influence of low-frequency modulation on polarization switching of VCSELs subject to optical feedback,” IEEE J. Quantum Electron. 44, 30-35 (2008).
[CrossRef]

J. Paul, C. Masoller, Y. H. Hong, P. S. Spencer, and K. A. Shore, “Impact of orthogonal optical feedback on the polarization switching of vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 16, 1987-1994 (2007).
[CrossRef]

Y. H. Hong, P. S. Spencer, and K. A. Shore, “Experimental study of polarization switching of vertical-cavity surface-emitting lasers as a dynamical bifurcation,” Opt. Lett. 31, 748-750 (2006).
[CrossRef] [PubMed]

Y. H. Hong, S. Bandyopadhyay, and K. A. Shore, “Spectral signatures of the dynamics of current-modulated vertical-cavity surface-emitting lasers subject to optical feedback,” J. Opt. Soc. Am. B 22, 2350-2356 (2005).
[CrossRef]

Y. H. Hong, R. Ju, P. S. Spencer, and K. A. Shore, “Investigation of polarization bistability in vertical-cavity surface-emitting lasers subjected to optical feedback,” IEEE J. Quantum Electron. 41, 619-624 (2005).
[CrossRef]

Y. H. Hong, P. S. Spencer, and K. A. Shore, “Suppression of polarization switching in vertical-cavity surface-emitting lasers by use of optical feedback,” Opt. Lett. 29, 2151-2153 (2004).
[CrossRef] [PubMed]

Honmayounfar, A.

A. Honmayounfar and M. J. Adams, “Locking bandwidth and birefringence effects for polarized optical injection in vertical-cavity surface-emitting lasers,” Opt. Commun. 269, 119-127 (2007).
[CrossRef]

Hu, C. X.

H. J. Kong, Z. M. Wu, C. X. Hu, J. F. Liao, Q. Yang, and G. Q. Xia, “Studying the nonlinear dynamic characteristics of an optically injection vertical-cavity surface-emitting laser,” Proc. SPIE 6839, 68390V (2007).
[CrossRef]

Jedrasik, P.

J. S. Gustavsson, Å. Haglund, E. Söderberg, J. Vukušić, P. Modh, P. Jedrasik, and A. Larsson, “Mode and polarization control in VCSELS using shallow surface structures,” IET Optoelectron. 1, 197-205 (2007).
[CrossRef]

Jia, X. H.

D. Z. Zhong, G. Q. Xia, Z. M. Wu, and X. H. Jia, “Complete chaotic synchronization characteristics of the linear-polarization mode of vertical-cavity surface-emitting semiconductor lasers with isotropic optical feedback,” Opt. Commun. 281, 1698-1709 (2008).
[CrossRef]

Jiang, M.

Y. Matsui, D. Vakhshoori, P. D. Wang, P. L. Chen, C. C. Lu, M. Jiang, K. Knopp, S. Burroughs, and P. Tayebati, “Complete polarization mode control of long-wavelength tunable vertical-cavity surface-emitting lasers over 65-nm tuning, up to 14-mw output power,” IEEE J. Quantum Electron. 39, 1037-1048 (2003).
[CrossRef]

Ju, R.

Y. H. Hong, R. Ju, P. S. Spencer, and K. A. Shore, “Investigation of polarization bistability in vertical-cavity surface-emitting lasers subjected to optical feedback,” IEEE J. Quantum Electron. 41, 619-624 (2005).
[CrossRef]

Knopp, K.

Y. Matsui, D. Vakhshoori, P. D. Wang, P. L. Chen, C. C. Lu, M. Jiang, K. Knopp, S. Burroughs, and P. Tayebati, “Complete polarization mode control of long-wavelength tunable vertical-cavity surface-emitting lasers over 65-nm tuning, up to 14-mw output power,” IEEE J. Quantum Electron. 39, 1037-1048 (2003).
[CrossRef]

Kong, H. J.

H. J. Kong, Z. M. Wu, C. X. Hu, J. F. Liao, Q. Yang, and G. Q. Xia, “Studying the nonlinear dynamic characteristics of an optically injection vertical-cavity surface-emitting laser,” Proc. SPIE 6839, 68390V (2007).
[CrossRef]

Larsson, A.

J. S. Gustavsson, Å. Haglund, E. Söderberg, J. Vukušić, P. Modh, P. Jedrasik, and A. Larsson, “Mode and polarization control in VCSELS using shallow surface structures,” IET Optoelectron. 1, 197-205 (2007).
[CrossRef]

Li, X. F.

Li, Z. Y.

S. F. Liu, G. Q. Xia, X. Tang, Y. Fan, Z. Y. Li, and Z. M. Wu, “Influence of the light injection on the chaotic carrier fundamental frequency of the VCSELs with optical feedback,” Proc. SPIE 6824, 682410 (2007).
[CrossRef]

Liao, J. F.

H. J. Kong, Z. M. Wu, C. X. Hu, J. F. Liao, Q. Yang, and G. Q. Xia, “Studying the nonlinear dynamic characteristics of an optically injection vertical-cavity surface-emitting laser,” Proc. SPIE 6839, 68390V (2007).
[CrossRef]

Liu, S. F.

S. F. Liu, G. Q. Xia, X. Tang, Y. Fan, Z. Y. Li, and Z. M. Wu, “Influence of the light injection on the chaotic carrier fundamental frequency of the VCSELs with optical feedback,” Proc. SPIE 6824, 682410 (2007).
[CrossRef]

Lu, C. C.

Y. Matsui, D. Vakhshoori, P. D. Wang, P. L. Chen, C. C. Lu, M. Jiang, K. Knopp, S. Burroughs, and P. Tayebati, “Complete polarization mode control of long-wavelength tunable vertical-cavity surface-emitting lasers over 65-nm tuning, up to 14-mw output power,” IEEE J. Quantum Electron. 39, 1037-1048 (2003).
[CrossRef]

Luo, B.

Mandel, P.

M. S. Torre, C. Masoller, P. Mandel, and K. A. Shore, “Transverse-mode dynamics in directly modulated vertical-cavity surface-emitting lasers with optical feedback,” IEEE J. Quantum Electron. 40, 620-628 (2004).
[CrossRef]

Marin, F.

G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248-2250 (2002).
[CrossRef]

Masoller, C.

C. Masoller, M. S. Torre, and K. A. Shore, “Polarization dynamics of current-modulated vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 43, 1047-1082 (2007).
[CrossRef]

J. Paul, C. Masoller, Y. H. Hong, P. S. Spencer, and K. A. Shore, “Impact of orthogonal optical feedback on the polarization switching of vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 16, 1987-1994 (2007).
[CrossRef]

C. Masoller and M. S. Torre, “Influence of optical feedback on the polarization switching of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 483-489 (2005).
[CrossRef]

M. S. Torre, C. Masoller, P. Mandel, and K. A. Shore, “Transverse-mode dynamics in directly modulated vertical-cavity surface-emitting lasers with optical feedback,” IEEE J. Quantum Electron. 40, 620-628 (2004).
[CrossRef]

Matsui, Y.

Y. Matsui, D. Vakhshoori, P. D. Wang, P. L. Chen, C. C. Lu, M. Jiang, K. Knopp, S. Burroughs, and P. Tayebati, “Complete polarization mode control of long-wavelength tunable vertical-cavity surface-emitting lasers over 65-nm tuning, up to 14-mw output power,” IEEE J. Quantum Electron. 39, 1037-1048 (2003).
[CrossRef]

Megret, P.

M. Sciamanna, A. Valle, P. Megret, M. Blondel, and K. Panajotov, “Nonlinear polarization dynamics in directly modulated vertical-cavity surface-emitting lasers,” Phys. Rev. E 68, 016207 (2003).
[CrossRef]

Mégret, P.

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28, 1543-1545 (2003).
[CrossRef] [PubMed]

M. Sciamanna, F. Rogister, P. Mégret, and M. Blondel, “Numerical observation of in-phase and out-of-phase pulses in the polarization modes of a VCSEL operating in the low-frequency fluctuations regime,” in Proceedings Symposium of IEEE/LEOS Benelux Chapter (IEEE, 2002), pp. 155-158.

Michalzik, R.

M. A. Arteaga, H. J. Unold, J. M. Ostermann, R. Michalzik, H. Thienpont, and K. Panajotov, “Investigation of polarization properties of VCSELs subject to optical feedback from an extremely short external cavity--part I: theoretical analysis,” IEEE J. Quantum Electron. 42, 89-101 (2006).
[CrossRef]

Miguel, M. S.

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

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

Modh, P.

J. S. Gustavsson, Å. Haglund, E. Söderberg, J. Vukušić, P. Modh, P. Jedrasik, and A. Larsson, “Mode and polarization control in VCSELS using shallow surface structures,” IET Optoelectron. 1, 197-205 (2007).
[CrossRef]

Moloney, J. V.

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

Nagler, B.

J. Albert, G. Van der Sande, B. Nagler, K. Pannajotov, I. Veretennicoff, J. Danckaert, and T. Erneux, “The effects of nonlinear gain on the stability of semi-degenerate two-mode semiconductor lasers: a case study on VCSELs,” Opt. Commun. 248, 527-534 (2005).
[CrossRef]

J. Danckaert, B. Nagler, J. Albert, K. Panajotov,I. Veretnnicoff, and T. Erneux, “Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers,” Opt. Commun. 201, 129-137 (2002).
[CrossRef]

Ostermann, J. M.

M. A. Arteaga, H. J. Unold, J. M. Ostermann, R. Michalzik, H. Thienpont, and K. Panajotov, “Investigation of polarization properties of VCSELs subject to optical feedback from an extremely short external cavity--part I: theoretical analysis,” IEEE J. Quantum Electron. 42, 89-101 (2006).
[CrossRef]

Pan, W.

Panajotov, K.

A. Valle, M. Sciamanna, and K. Panajotov, “Irregular pulsating polarization dynamics in gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 44, 136-143 (2008).
[CrossRef]

A. Valle, M. Sciamanna, and K. Panajotov, “Nonlinear dynamics of the polarization of multitransverse mode vertical-cavity surface-emitting lasers under current modulation,” Phys. Rev. E 76, 046206 (2007).
[CrossRef]

A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron. 43, 322-333 (2007).
[CrossRef]

M. A. Arteaga, H. J. Unold, J. M. Ostermann, R. Michalzik, H. Thienpont, and K. Panajotov, “Investigation of polarization properties of VCSELs subject to optical feedback from an extremely short external cavity--part I: theoretical analysis,” IEEE J. Quantum Electron. 42, 89-101 (2006).
[CrossRef]

M. Sciamanna and K. Panajotov, “Two-mode injection locking in vertical-cavity surface-emitting lasers,” Opt. Lett. 30, 2903-2905 (2005).
[CrossRef] [PubMed]

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28, 1543-1545 (2003).
[CrossRef] [PubMed]

M. Sciamanna, A. Valle, P. Megret, M. Blondel, and K. Panajotov, “Nonlinear polarization dynamics in directly modulated vertical-cavity surface-emitting lasers,” Phys. Rev. E 68, 016207 (2003).
[CrossRef]

J. Danckaert, B. Nagler, J. Albert, K. Panajotov,I. Veretnnicoff, and T. Erneux, “Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers,” Opt. Commun. 201, 129-137 (2002).
[CrossRef]

B. Ryvkin, K. Panajotov, A. Georgievski, J. Danckaert, M. Peeters, and G. Verschaffelt, “Effect of photon-energy-dependent loss and gain mechanisms on polarization switching in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 16, 2016-2112 (1999).
[CrossRef]

Pannajotov, K.

J. Albert, G. Van der Sande, B. Nagler, K. Pannajotov, I. Veretennicoff, J. Danckaert, and T. Erneux, “The effects of nonlinear gain on the stability of semi-degenerate two-mode semiconductor lasers: a case study on VCSELs,” Opt. Commun. 248, 527-534 (2005).
[CrossRef]

Paul, J.

Y. H. Hong, J. Paul, P. S. Spencer, and K. A. Shore, “Influence of low-frequency modulation on polarization switching of VCSELs subject to optical feedback,” IEEE J. Quantum Electron. 44, 30-35 (2008).
[CrossRef]

J. Paul, C. Masoller, Y. H. Hong, P. S. Spencer, and K. A. Shore, “Impact of orthogonal optical feedback on the polarization switching of vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 16, 1987-1994 (2007).
[CrossRef]

Peeters, M.

B. Ryvkin, K. Panajotov, A. Georgievski, J. Danckaert, M. Peeters, and G. Verschaffelt, “Effect of photon-energy-dependent loss and gain mechanisms on polarization switching in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 16, 2016-2112 (1999).
[CrossRef]

Prati, F.

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

Regalado, J. M.

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

Robert, F.

Rogister, F.

M. Sciamanna, F. Rogister, P. Mégret, and M. Blondel, “Numerical observation of in-phase and out-of-phase pulses in the polarization modes of a VCSEL operating in the low-frequency fluctuations regime,” in Proceedings Symposium of IEEE/LEOS Benelux Chapter (IEEE, 2002), pp. 155-158.

Ryvkin, B.

B. Ryvkin, K. Panajotov, A. Georgievski, J. Danckaert, M. Peeters, and G. Verschaffelt, “Effect of photon-energy-dependent loss and gain mechanisms on polarization switching in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 16, 2016-2112 (1999).
[CrossRef]

Sciamanna, M.

A. Valle, M. Sciamanna, and K. Panajotov, “Irregular pulsating polarization dynamics in gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 44, 136-143 (2008).
[CrossRef]

A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron. 43, 322-333 (2007).
[CrossRef]

A. Valle, M. Sciamanna, and K. Panajotov, “Nonlinear dynamics of the polarization of multitransverse mode vertical-cavity surface-emitting lasers under current modulation,” Phys. Rev. E 76, 046206 (2007).
[CrossRef]

M. Sciamanna and K. Panajotov, “Two-mode injection locking in vertical-cavity surface-emitting lasers,” Opt. Lett. 30, 2903-2905 (2005).
[CrossRef] [PubMed]

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28, 1543-1545 (2003).
[CrossRef] [PubMed]

M. Sciamanna, A. Valle, P. Megret, M. Blondel, and K. Panajotov, “Nonlinear polarization dynamics in directly modulated vertical-cavity surface-emitting lasers,” Phys. Rev. E 68, 016207 (2003).
[CrossRef]

M. Sciamanna, F. Rogister, P. Mégret, and M. Blondel, “Numerical observation of in-phase and out-of-phase pulses in the polarization modes of a VCSEL operating in the low-frequency fluctuations regime,” in Proceedings Symposium of IEEE/LEOS Benelux Chapter (IEEE, 2002), pp. 155-158.

Shore, K. A.

Y. H. Hong, J. Paul, P. S. Spencer, and K. A. Shore, “Influence of low-frequency modulation on polarization switching of VCSELs subject to optical feedback,” IEEE J. Quantum Electron. 44, 30-35 (2008).
[CrossRef]

J. Paul, C. Masoller, Y. H. Hong, P. S. Spencer, and K. A. Shore, “Impact of orthogonal optical feedback on the polarization switching of vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 16, 1987-1994 (2007).
[CrossRef]

C. Masoller, M. S. Torre, and K. A. Shore, “Polarization dynamics of current-modulated vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 43, 1047-1082 (2007).
[CrossRef]

Y. H. Hong, P. S. Spencer, and K. A. Shore, “Experimental study of polarization switching of vertical-cavity surface-emitting lasers as a dynamical bifurcation,” Opt. Lett. 31, 748-750 (2006).
[CrossRef] [PubMed]

Y. H. Hong, S. Bandyopadhyay, and K. A. Shore, “Spectral signatures of the dynamics of current-modulated vertical-cavity surface-emitting lasers subject to optical feedback,” J. Opt. Soc. Am. B 22, 2350-2356 (2005).
[CrossRef]

Y. H. Hong, R. Ju, P. S. Spencer, and K. A. Shore, “Investigation of polarization bistability in vertical-cavity surface-emitting lasers subjected to optical feedback,” IEEE J. Quantum Electron. 41, 619-624 (2005).
[CrossRef]

M. S. Torre, C. Masoller, P. Mandel, and K. A. Shore, “Transverse-mode dynamics in directly modulated vertical-cavity surface-emitting lasers with optical feedback,” IEEE J. Quantum Electron. 40, 620-628 (2004).
[CrossRef]

Y. H. Hong, P. S. Spencer, and K. A. Shore, “Suppression of polarization switching in vertical-cavity surface-emitting lasers by use of optical feedback,” Opt. Lett. 29, 2151-2153 (2004).
[CrossRef] [PubMed]

Söderberg, E.

J. S. Gustavsson, Å. Haglund, E. Söderberg, J. Vukušić, P. Modh, P. Jedrasik, and A. Larsson, “Mode and polarization control in VCSELS using shallow surface structures,” IET Optoelectron. 1, 197-205 (2007).
[CrossRef]

Sondermann, M.

T. Ackemann, M. Sondermann, and S. Balle, “Self-organization in vertical-cavity surface-emitting lasers: polarization selection and polarization dynamics,” in Proceedings of CAOL 2003, Advanced Optoelectronics and Lasers, 2003 (IEEE, 2003), pp. 75-77.

Spencer, P. S.

Y. H. Hong, J. Paul, P. S. Spencer, and K. A. Shore, “Influence of low-frequency modulation on polarization switching of VCSELs subject to optical feedback,” IEEE J. Quantum Electron. 44, 30-35 (2008).
[CrossRef]

J. Paul, C. Masoller, Y. H. Hong, P. S. Spencer, and K. A. Shore, “Impact of orthogonal optical feedback on the polarization switching of vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 16, 1987-1994 (2007).
[CrossRef]

Y. H. Hong, P. S. Spencer, and K. A. Shore, “Experimental study of polarization switching of vertical-cavity surface-emitting lasers as a dynamical bifurcation,” Opt. Lett. 31, 748-750 (2006).
[CrossRef] [PubMed]

Y. H. Hong, R. Ju, P. S. Spencer, and K. A. Shore, “Investigation of polarization bistability in vertical-cavity surface-emitting lasers subjected to optical feedback,” IEEE J. Quantum Electron. 41, 619-624 (2005).
[CrossRef]

Y. H. Hong, P. S. Spencer, and K. A. Shore, “Suppression of polarization switching in vertical-cavity surface-emitting lasers by use of optical feedback,” Opt. Lett. 29, 2151-2153 (2004).
[CrossRef] [PubMed]

Stéphan, G.

Tang, X.

S. F. Liu, G. Q. Xia, X. Tang, Y. Fan, Z. Y. Li, and Z. M. Wu, “Influence of the light injection on the chaotic carrier fundamental frequency of the VCSELs with optical feedback,” Proc. SPIE 6824, 682410 (2007).
[CrossRef]

Tayebati, P.

Y. Matsui, D. Vakhshoori, P. D. Wang, P. L. Chen, C. C. Lu, M. Jiang, K. Knopp, S. Burroughs, and P. Tayebati, “Complete polarization mode control of long-wavelength tunable vertical-cavity surface-emitting lasers over 65-nm tuning, up to 14-mw output power,” IEEE J. Quantum Electron. 39, 1037-1048 (2003).
[CrossRef]

Thienpont, H.

M. A. Arteaga, H. J. Unold, J. M. Ostermann, R. Michalzik, H. Thienpont, and K. Panajotov, “Investigation of polarization properties of VCSELs subject to optical feedback from an extremely short external cavity--part I: theoretical analysis,” IEEE J. Quantum Electron. 42, 89-101 (2006).
[CrossRef]

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28, 1543-1545 (2003).
[CrossRef] [PubMed]

Torre, M. S.

C. Masoller, M. S. Torre, and K. A. Shore, “Polarization dynamics of current-modulated vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 43, 1047-1082 (2007).
[CrossRef]

C. Masoller and M. S. Torre, “Influence of optical feedback on the polarization switching of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 483-489 (2005).
[CrossRef]

M. S. Torre, C. Masoller, P. Mandel, and K. A. Shore, “Transverse-mode dynamics in directly modulated vertical-cavity surface-emitting lasers with optical feedback,” IEEE J. Quantum Electron. 40, 620-628 (2004).
[CrossRef]

Unold, H. J.

M. A. Arteaga, H. J. Unold, J. M. Ostermann, R. Michalzik, H. Thienpont, and K. Panajotov, “Investigation of polarization properties of VCSELs subject to optical feedback from an extremely short external cavity--part I: theoretical analysis,” IEEE J. Quantum Electron. 42, 89-101 (2006).
[CrossRef]

Vakhshoori, D.

Y. Matsui, D. Vakhshoori, P. D. Wang, P. L. Chen, C. C. Lu, M. Jiang, K. Knopp, S. Burroughs, and P. Tayebati, “Complete polarization mode control of long-wavelength tunable vertical-cavity surface-emitting lasers over 65-nm tuning, up to 14-mw output power,” IEEE J. Quantum Electron. 39, 1037-1048 (2003).
[CrossRef]

Valle, A.

A. Valle, M. Sciamanna, and K. Panajotov, “Irregular pulsating polarization dynamics in gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 44, 136-143 (2008).
[CrossRef]

A. Valle, M. Sciamanna, and K. Panajotov, “Nonlinear dynamics of the polarization of multitransverse mode vertical-cavity surface-emitting lasers under current modulation,” Phys. Rev. E 76, 046206 (2007).
[CrossRef]

A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron. 43, 322-333 (2007).
[CrossRef]

M. Sciamanna, A. Valle, P. Megret, M. Blondel, and K. Panajotov, “Nonlinear polarization dynamics in directly modulated vertical-cavity surface-emitting lasers,” Phys. Rev. E 68, 016207 (2003).
[CrossRef]

Van der Sande, G.

J. Albert, G. Van der Sande, B. Nagler, K. Pannajotov, I. Veretennicoff, J. Danckaert, and T. Erneux, “The effects of nonlinear gain on the stability of semi-degenerate two-mode semiconductor lasers: a case study on VCSELs,” Opt. Commun. 248, 527-534 (2005).
[CrossRef]

Veretennicoff, I.

J. Albert, G. Van der Sande, B. Nagler, K. Pannajotov, I. Veretennicoff, J. Danckaert, and T. Erneux, “The effects of nonlinear gain on the stability of semi-degenerate two-mode semiconductor lasers: a case study on VCSELs,” Opt. Commun. 248, 527-534 (2005).
[CrossRef]

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28, 1543-1545 (2003).
[CrossRef] [PubMed]

G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248-2250 (2002).
[CrossRef]

Veretnnicoff, I.

J. Danckaert, B. Nagler, J. Albert, K. Panajotov,I. Veretnnicoff, and T. Erneux, “Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers,” Opt. Commun. 201, 129-137 (2002).
[CrossRef]

Verschaffelt, G.

G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248-2250 (2002).
[CrossRef]

B. Ryvkin, K. Panajotov, A. Georgievski, J. Danckaert, M. Peeters, and G. Verschaffelt, “Effect of photon-energy-dependent loss and gain mechanisms on polarization switching in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 16, 2016-2112 (1999).
[CrossRef]

Vukušic, J.

J. S. Gustavsson, Å. Haglund, E. Söderberg, J. Vukušić, P. Modh, P. Jedrasik, and A. Larsson, “Mode and polarization control in VCSELS using shallow surface structures,” IET Optoelectron. 1, 197-205 (2007).
[CrossRef]

Wang, M. Y.

Wang, P. D.

Y. Matsui, D. Vakhshoori, P. D. Wang, P. L. Chen, C. C. Lu, M. Jiang, K. Knopp, S. Burroughs, and P. Tayebati, “Complete polarization mode control of long-wavelength tunable vertical-cavity surface-emitting lasers over 65-nm tuning, up to 14-mw output power,” IEEE J. Quantum Electron. 39, 1037-1048 (2003).
[CrossRef]

Wu, Z. M.

D. Z. Zhong, G. Q. Xia, Z. M. Wu, and X. H. Jia, “Complete chaotic synchronization characteristics of the linear-polarization mode of vertical-cavity surface-emitting semiconductor lasers with isotropic optical feedback,” Opt. Commun. 281, 1698-1709 (2008).
[CrossRef]

S. F. Liu, G. Q. Xia, X. Tang, Y. Fan, Z. Y. Li, and Z. M. Wu, “Influence of the light injection on the chaotic carrier fundamental frequency of the VCSELs with optical feedback,” Proc. SPIE 6824, 682410 (2007).
[CrossRef]

H. J. Kong, Z. M. Wu, C. X. Hu, J. F. Liao, Q. Yang, and G. Q. Xia, “Studying the nonlinear dynamic characteristics of an optically injection vertical-cavity surface-emitting laser,” Proc. SPIE 6839, 68390V (2007).
[CrossRef]

Xia, G. Q.

D. Z. Zhong, G. Q. Xia, Z. M. Wu, and X. H. Jia, “Complete chaotic synchronization characteristics of the linear-polarization mode of vertical-cavity surface-emitting semiconductor lasers with isotropic optical feedback,” Opt. Commun. 281, 1698-1709 (2008).
[CrossRef]

H. J. Kong, Z. M. Wu, C. X. Hu, J. F. Liao, Q. Yang, and G. Q. Xia, “Studying the nonlinear dynamic characteristics of an optically injection vertical-cavity surface-emitting laser,” Proc. SPIE 6839, 68390V (2007).
[CrossRef]

S. F. Liu, G. Q. Xia, X. Tang, Y. Fan, Z. Y. Li, and Z. M. Wu, “Influence of the light injection on the chaotic carrier fundamental frequency of the VCSELs with optical feedback,” Proc. SPIE 6824, 682410 (2007).
[CrossRef]

Yang, Q.

H. J. Kong, Z. M. Wu, C. X. Hu, J. F. Liao, Q. Yang, and G. Q. Xia, “Studying the nonlinear dynamic characteristics of an optically injection vertical-cavity surface-emitting laser,” Proc. SPIE 6839, 68390V (2007).
[CrossRef]

Zhang, W. L.

Zhong, D. Z.

D. Z. Zhong, G. Q. Xia, Z. M. Wu, and X. H. Jia, “Complete chaotic synchronization characteristics of the linear-polarization mode of vertical-cavity surface-emitting semiconductor lasers with isotropic optical feedback,” Opt. Commun. 281, 1698-1709 (2008).
[CrossRef]

Zou, X. H.

Zuo, X. H.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248-2250 (2002).
[CrossRef]

IEEE J. Quantum Electron. (10)

C. Masoller, M. S. Torre, and K. A. Shore, “Polarization dynamics of current-modulated vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 43, 1047-1082 (2007).
[CrossRef]

M. S. Torre, C. Masoller, P. Mandel, and K. A. Shore, “Transverse-mode dynamics in directly modulated vertical-cavity surface-emitting lasers with optical feedback,” IEEE J. Quantum Electron. 40, 620-628 (2004).
[CrossRef]

Y. H. Hong, J. Paul, P. S. Spencer, and K. A. Shore, “Influence of low-frequency modulation on polarization switching of VCSELs subject to optical feedback,” IEEE J. Quantum Electron. 44, 30-35 (2008).
[CrossRef]

A. Valle, M. Sciamanna, and K. Panajotov, “Irregular pulsating polarization dynamics in gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 44, 136-143 (2008).
[CrossRef]

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

Y. H. Hong, R. Ju, P. S. Spencer, and K. A. Shore, “Investigation of polarization bistability in vertical-cavity surface-emitting lasers subjected to optical feedback,” IEEE J. Quantum Electron. 41, 619-624 (2005).
[CrossRef]

A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron. 43, 322-333 (2007).
[CrossRef]

M. A. Arteaga, H. J. Unold, J. M. Ostermann, R. Michalzik, H. Thienpont, and K. Panajotov, “Investigation of polarization properties of VCSELs subject to optical feedback from an extremely short external cavity--part I: theoretical analysis,” IEEE J. Quantum Electron. 42, 89-101 (2006).
[CrossRef]

C. Masoller and M. S. Torre, “Influence of optical feedback on the polarization switching of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 483-489 (2005).
[CrossRef]

Y. Matsui, D. Vakhshoori, P. D. Wang, P. L. Chen, C. C. Lu, M. Jiang, K. Knopp, S. Burroughs, and P. Tayebati, “Complete polarization mode control of long-wavelength tunable vertical-cavity surface-emitting lasers over 65-nm tuning, up to 14-mw output power,” IEEE J. Quantum Electron. 39, 1037-1048 (2003).
[CrossRef]

IET Optoelectron. (1)

J. S. Gustavsson, Å. Haglund, E. Söderberg, J. Vukušić, P. Modh, P. Jedrasik, and A. Larsson, “Mode and polarization control in VCSELS using shallow surface structures,” IET Optoelectron. 1, 197-205 (2007).
[CrossRef]

J. Opt. Soc. Am. B (5)

B. Ryvkin, K. Panajotov, A. Georgievski, J. Danckaert, M. Peeters, and G. Verschaffelt, “Effect of photon-energy-dependent loss and gain mechanisms on polarization switching in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 16, 2016-2112 (1999).
[CrossRef]

J. Paul, C. Masoller, Y. H. Hong, P. S. Spencer, and K. A. Shore, “Impact of orthogonal optical feedback on the polarization switching of vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 16, 1987-1994 (2007).
[CrossRef]

P. Besnard, M. L. Chsrès, G. Stéphan, and F. Robert, “Switching between polarized modes of a vertical-cavity surface-emitting laser by isotropic optical feedback,” J. Opt. Soc. Am. B 16, 1059-1063 (1999).
[CrossRef]

Y. H. Hong, S. Bandyopadhyay, and K. A. Shore, “Spectral signatures of the dynamics of current-modulated vertical-cavity surface-emitting lasers subject to optical feedback,” J. Opt. Soc. Am. B 22, 2350-2356 (2005).
[CrossRef]

W. L. Zhang, W. Pan, B. Luo, X. F. Li, X. H. Zou, and M. Y. Wang, “Polarization switching of mutually coupled vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 24, 1276-1282 (2007).
[CrossRef]

Opt. Commun. (4)

J. Albert, G. Van der Sande, B. Nagler, K. Pannajotov, I. Veretennicoff, J. Danckaert, and T. Erneux, “The effects of nonlinear gain on the stability of semi-degenerate two-mode semiconductor lasers: a case study on VCSELs,” Opt. Commun. 248, 527-534 (2005).
[CrossRef]

A. Honmayounfar and M. J. Adams, “Locking bandwidth and birefringence effects for polarized optical injection in vertical-cavity surface-emitting lasers,” Opt. Commun. 269, 119-127 (2007).
[CrossRef]

D. Z. Zhong, G. Q. Xia, Z. M. Wu, and X. H. Jia, “Complete chaotic synchronization characteristics of the linear-polarization mode of vertical-cavity surface-emitting semiconductor lasers with isotropic optical feedback,” Opt. Commun. 281, 1698-1709 (2008).
[CrossRef]

J. Danckaert, B. Nagler, J. Albert, K. Panajotov,I. Veretnnicoff, and T. Erneux, “Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers,” Opt. Commun. 201, 129-137 (2002).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (1)

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

Phys. Rev. E (2)

A. Valle, M. Sciamanna, and K. Panajotov, “Nonlinear dynamics of the polarization of multitransverse mode vertical-cavity surface-emitting lasers under current modulation,” Phys. Rev. E 76, 046206 (2007).
[CrossRef]

M. Sciamanna, A. Valle, P. Megret, M. Blondel, and K. Panajotov, “Nonlinear polarization dynamics in directly modulated vertical-cavity surface-emitting lasers,” Phys. Rev. E 68, 016207 (2003).
[CrossRef]

Proc. SPIE (2)

S. F. Liu, G. Q. Xia, X. Tang, Y. Fan, Z. Y. Li, and Z. M. Wu, “Influence of the light injection on the chaotic carrier fundamental frequency of the VCSELs with optical feedback,” Proc. SPIE 6824, 682410 (2007).
[CrossRef]

H. J. Kong, Z. M. Wu, C. X. Hu, J. F. Liao, Q. Yang, and G. Q. Xia, “Studying the nonlinear dynamic characteristics of an optically injection vertical-cavity surface-emitting laser,” Proc. SPIE 6839, 68390V (2007).
[CrossRef]

Other (2)

T. Ackemann, M. Sondermann, and S. Balle, “Self-organization in vertical-cavity surface-emitting lasers: polarization selection and polarization dynamics,” in Proceedings of CAOL 2003, Advanced Optoelectronics and Lasers, 2003 (IEEE, 2003), pp. 75-77.

M. Sciamanna, F. Rogister, P. Mégret, and M. Blondel, “Numerical observation of in-phase and out-of-phase pulses in the polarization modes of a VCSEL operating in the low-frequency fluctuations regime,” in Proceedings Symposium of IEEE/LEOS Benelux Chapter (IEEE, 2002), pp. 155-158.

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 (13)

Fig. 1
Fig. 1

Averaged output power of x-polarized mode (dotted curve) and y-polarized mode (solid curve) versus dc bias current for different feedback intensities, where (a) type I PS ( γ a = 0.4 ns 1 , γ p = 20 pns 1 ) and (b) type II PS ( γ a = 0.2 ns 1 , γ p = pns 1 ).

Fig. 2
Fig. 2

Intensity extreme values of x-polarized mode (triangles) and y-polarized mode (asterisks) versus modulation frequency for different feedback intensities with A m = 0.01 , where (a) i dc = 1.1 and (b) i dc = 1.2 .

Fig. 3
Fig. 3

Samples of time traces of the x-polarized mode (dotted curve) and y-polarized mode (solid curve) for various modulation frequencies with η = 1.5 ns 1 , i dc = 1.1 , and A m = 0.01 .

Fig. 4
Fig. 4

Modulation responses of VCSEL subject to weak optical feedback at different modulation amplitudes with η = 0.3 ns 1 , where triangles and asterisks stand for the x-polarized mode and y-polarized mode, respectively.

Fig. 5
Fig. 5

Intensity extreme values of x-polarized mode (triangles) and y-polarized mode (asterisks) versus modulation frequency for different feedback intensities with A m = 0.1 and i dc = 1.1 .

Fig. 6
Fig. 6

Samples of time traces of the x-polarized mode (dotted curve) and y-polarized mode (solid curve) for various modulation frequencies with η = 1.5 ns 1 , i dc = 1.1 , and A m = 0.1 .

Fig. 7
Fig. 7

Modulation responses of VCSEL subject to weak optical feedback at different modulation amplitudes with η = 0.3 ns 1 , where triangles and asterisks stand for the x-polarized mode and y-polarized mode, respectively.

Fig. 8
Fig. 8

Intensity extreme values of x-polarized mode (triangles) and y-polarized mode (asterisks) versus modulation frequency under different feedback where intensities for i dc is equal to 1.15, 1.3, and 1.6.

Fig. 9
Fig. 9

Samples of time traces of the x-polarized mode (dotted curve) and y-polarized mode (solid curve) for various modulation frequencies with η = 1.5 ns 1 , i dc = 1.3 , and A m = 0.01 .

Fig. 10
Fig. 10

Modulation responses of VCSEL subject to weak optical feedback at different modulation amplitudes with η = 0.3 ns 1 , where triangles and asterisks stand for the x-polarized mode and y-polarized mode, respectively.

Fig. 11
Fig. 11

Intensity extreme values of x-polarized mode (triangles) and y-polarized mode (asterisks) versus modulation frequency for different feedback intensities with A m = 0.1 and i dc = 1.3 .

Fig. 12
Fig. 12

Samples of time traces of the x-polarized mode (dotted curve) and y-polarized mode (solid curve) for various modulation frequencies with η = 1.5 ns 1 , i dc = 1.3 , and A m = 0.1 .

Fig. 13
Fig. 13

Modulation responses of VCSEL subject to weak optical feedback at different modulation amplitudes with η = 0.3 ns 1 , where triangles and asterisks stand for the x-polarized mode and y-polarized mode, respectively.

Equations (5)

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

d E x d t = k ( 1 + i a ) [ ( N 1 ) E x + i n E y ] ( γ a + i γ p ) E x + η E x ( t τ ) exp ( i ω τ ) ,
d E y d t = k ( 1 + i a ) [ ( N 1 ) E y i n E x ] + ( γ a + i γ p ) E y + η E y ( t τ ) exp ( i ω τ ) ,
d N d t = γ N [ μ N ( 1 + E x 2 + E y 2 ) i n ( E y E x * E x E y * ) ] ,
d n d t = γ s n γ N [ n ( E x 2 + E y 2 ) + i N ( E y E x * E x E y * ) ] .
μ = i dc + A m cos ( 2 π f m t ) ,

Metrics