Abstract

We present a novel method for the generation of sub-nanosecond optical pulses in directly modulated vertical-cavity surface-emitting lasers (VCSELs) that operate, on average, below the cw threshold. Using the spin-flip model we demonstrate that irregular optical pulses in two orthogonal linear polarizations can be generated via asymmetric triangular modulation of period of a few nanoseconds, with a slow rising ramp followed by a fast decreasing one. For an optimal modulation asymmetry the effective threshold reduction is about 20%, the pulse amplitude is maximum and the dispersion of the pulse amplitude is minimum.

© 2008 Optical Society of America

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  1. K. Iga, "Surface-emitting laser -its birth and generation of new optoelectronics field," IEEE J. Sel. Top. Quantum Electron.  6, 1201-1215 (2000).
    [CrossRef]
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  3. A. J. Danner, J. J. Raftery, P. O. Leisher, and K. D. Choquette, "Single mode photonic crystal vertical cavity lasers," Appl. Phys. Lett 88, 091114 (2006).
    [CrossRef]
  4. T. Czyszanowski, M. Dems, and K. Panajotov, "Single mode condition and modes discrimination in photoniccrystal 1.3 mu m AlInGaAs/InP VCSEL," Opt. Express 15, 5604-5609 (2007).
    [CrossRef] [PubMed]
  5. S. Boutami, B. Benbakir, J. L. Leclercq, and P. Viktorovitch, "Compact and polarization controlled 1.55 mu m vertical-cavity surface-emitting laser using single-layer photonic crystal mirror," Appl. Phys. Lett. 91, 071105 (2007).
    [CrossRef]
  6. C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez and N. G. Stoffel, "Dynamic, polarization and transverse-mode characteristics of vertical cavity surface emitting lasers," IEEE J. Quantum Electron. 27, 1402-1409 (1991).
    [CrossRef]
  7. K. D. Choquette, R. P. Schneider, K. L. Lear and R. E. Leibenguth, "Gain-dependent polarization properties of vertical-cavity lasers,"IEEE J. Sel. Top. Quantum Electron. 1, 661-666 (1995).
    [CrossRef]
  8. J. S. Gustavsson, A. Haglund, J. A. Vukusic, J. Bengtsson, P. Jedrasik, and A. Larsson, "Efficient and individually controllable mechanisms for mode and polarization selection in VCSELs, based on a common, localized, subwavelength surface grating," Opt. Express 13, 6626-6634 (2005).
    [CrossRef] [PubMed]
  9. M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nat. Photonics 1, 119-122 (2007)
    [CrossRef]
  10. M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A nanoelectromechanical tunable laser," Nat. Photonics 2, 180-184 (2008).
    [CrossRef]
  11. G. P. Agrawal, "Effect of gain nonlinearities on period doubling and chaos in directly modualted semiconductorlasers," Appl. Phys. Lett. 49, 1013-1015 (1986).
    [CrossRef]
  12. S. Bennett, C. M. Snowden, and S. Iezekiel, "Nonlinear dynamics in directly modulated multiple-quantum-well laser diodes," IEEE J. Quantum Electron. 33, 2076-2083 (1997).
    [CrossRef]
  13. H. Lamela, G. Carpintero, and F. J. Mancebo, "Period tripling and chaos in the dynamic behavior of directly modulated diode lasers," IEEE J. Quantum Electron. 34, 1797-1801 (1998).
    [CrossRef]
  14. A. Valle, L. Pesquera, S. I. Turovets, and J. M. Lopez, "Nonlinear dynamics of current-modulated vertical-cavity surface-emitting lasers," Opt. Commun. 208, 173-182 (2002).
    [CrossRef]
  15. 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]
  16. 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]
  17. A. Valle, M. Sciamanna, and K. Panajotov, "Irregular pulsating polarization dynamics in gain-switched verticalcavity surface-emitting lasers," IEEE J. Quantum Electron. 44, 136-143 (2008).
    [CrossRef]
  18. C. Masoller, M. S. Torre, and K. A. Shore, "Polarization dynamics of current-modulated vertical-cavity surfaceemitting lasers," IEEE J. Quantum Electron. 43, 1074-1082 (2007).
    [CrossRef]
  19. C. Masoller, M. S. Torre and P. Mandel, "Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting laser," J. Appl. Phys. 99, 026108 (2006).
    [CrossRef]
  20. J. Paul, C. Masoller, Y. 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]
  21. J. Paul, C. Masoller, P. Mandel, Y. Hong, P. S. Spencer, and K. A. Shore, "Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarization switching of vertical-cavity surface-emitting lasers," Phys. Rev. A 77, 043803 (2008).
    [CrossRef]
  22. C. E. Preda, B. Segard, and P. Glorieux, "Weak temporal ratchet effect by asymmetric modulation of a laser," Opt. Lett. 31, 2347-2349 (2006).
    [CrossRef] [PubMed]
  23. M. San Miguel, Q. Feng, and J. V. Moloney, "Light-polarization dynamics in surface-emitting semiconductor lasers," Phys. Rev. A 52, 1728-1739 (1995).
    [CrossRef] [PubMed]
  24. 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, 765-783 (1997).
    [CrossRef]
  25. T. Ackemann and M. Sondermann, "Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 78, 3574-3576 (2001).
    [CrossRef]
  26. C. Masoller and A. 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]
  27. A. Homayounfar and M. J. Adams, "Analysis of SFM dynamics in solitary and optically-injected VCSELs," Opt. Express 15, 10504-10519 (2007).
  28. L. Illing and M. B. Kennel, "Shaping current waveforms for direct modulation of semiconductor lasers," IEEE J. Quantum Electron. 40, 445-452 (2004).
    [CrossRef]
  29. X. Hachair, S. Barland, J. R. Tredicce, and G. L. Lippi, "Optimization of the switch-on and switch-off transition in a commercial laser," Appl. Opt. 44, 4761-4774 (2005).
    [CrossRef] [PubMed]

2008 (3)

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A nanoelectromechanical tunable laser," Nat. Photonics 2, 180-184 (2008).
[CrossRef]

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

J. Paul, C. Masoller, P. Mandel, Y. Hong, P. S. Spencer, and K. A. Shore, "Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarization switching of vertical-cavity surface-emitting lasers," Phys. Rev. A 77, 043803 (2008).
[CrossRef]

2007 (6)

C. Masoller, M. S. Torre, and K. A. Shore, "Polarization dynamics of current-modulated vertical-cavity surfaceemitting lasers," IEEE J. Quantum Electron. 43, 1074-1082 (2007).
[CrossRef]

S. Boutami, B. Benbakir, J. L. Leclercq, and P. Viktorovitch, "Compact and polarization controlled 1.55 mu m vertical-cavity surface-emitting laser using single-layer photonic crystal mirror," Appl. Phys. Lett. 91, 071105 (2007).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nat. Photonics 1, 119-122 (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]

T. Czyszanowski, M. Dems, and K. Panajotov, "Single mode condition and modes discrimination in photoniccrystal 1.3 mu m AlInGaAs/InP VCSEL," Opt. Express 15, 5604-5609 (2007).
[CrossRef] [PubMed]

A. Homayounfar and M. J. Adams, "Analysis of SFM dynamics in solitary and optically-injected VCSELs," Opt. Express 15, 10504-10519 (2007).

2006 (4)

A. J. Danner, J. J. Raftery, P. O. Leisher, and K. D. Choquette, "Single mode photonic crystal vertical cavity lasers," Appl. Phys. Lett 88, 091114 (2006).
[CrossRef]

J. Paul, C. Masoller, Y. 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]

C. E. Preda, B. Segard, and P. Glorieux, "Weak temporal ratchet effect by asymmetric modulation of a laser," Opt. Lett. 31, 2347-2349 (2006).
[CrossRef] [PubMed]

C. Masoller, M. S. Torre and P. Mandel, "Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting laser," J. Appl. Phys. 99, 026108 (2006).
[CrossRef]

2005 (3)

2004 (1)

L. Illing and M. B. Kennel, "Shaping current waveforms for direct modulation of semiconductor lasers," IEEE J. Quantum Electron. 40, 445-452 (2004).
[CrossRef]

2003 (1)

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]

2002 (1)

A. Valle, L. Pesquera, S. I. Turovets, and J. M. Lopez, "Nonlinear dynamics of current-modulated vertical-cavity surface-emitting lasers," Opt. Commun. 208, 173-182 (2002).
[CrossRef]

2001 (1)

T. Ackemann and M. Sondermann, "Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 78, 3574-3576 (2001).
[CrossRef]

2000 (1)

K. Iga, "Surface-emitting laser -its birth and generation of new optoelectronics field," IEEE J. Sel. Top. Quantum Electron.  6, 1201-1215 (2000).
[CrossRef]

1998 (1)

H. Lamela, G. Carpintero, and F. J. Mancebo, "Period tripling and chaos in the dynamic behavior of directly modulated diode lasers," IEEE J. Quantum Electron. 34, 1797-1801 (1998).
[CrossRef]

1997 (2)

S. Bennett, C. M. Snowden, and S. Iezekiel, "Nonlinear dynamics in directly modulated multiple-quantum-well laser diodes," IEEE J. Quantum Electron. 33, 2076-2083 (1997).
[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, 765-783 (1997).
[CrossRef]

1995 (2)

K. D. Choquette, R. P. Schneider, K. L. Lear and R. E. Leibenguth, "Gain-dependent polarization properties of vertical-cavity lasers,"IEEE J. Sel. Top. Quantum Electron. 1, 661-666 (1995).
[CrossRef]

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

1991 (1)

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez and N. G. Stoffel, "Dynamic, polarization and transverse-mode characteristics of vertical cavity surface emitting lasers," IEEE J. Quantum Electron. 27, 1402-1409 (1991).
[CrossRef]

1986 (1)

G. P. Agrawal, "Effect of gain nonlinearities on period doubling and chaos in directly modualted semiconductorlasers," Appl. Phys. Lett. 49, 1013-1015 (1986).
[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, 765-783 (1997).
[CrossRef]

Ackemann, T.

T. Ackemann and M. Sondermann, "Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 78, 3574-3576 (2001).
[CrossRef]

Adams, M. J.

Agrawal, G. P.

G. P. Agrawal, "Effect of gain nonlinearities on period doubling and chaos in directly modualted semiconductorlasers," Appl. Phys. Lett. 49, 1013-1015 (1986).
[CrossRef]

Barland, S.

Benbakir, B.

S. Boutami, B. Benbakir, J. L. Leclercq, and P. Viktorovitch, "Compact and polarization controlled 1.55 mu m vertical-cavity surface-emitting laser using single-layer photonic crystal mirror," Appl. Phys. Lett. 91, 071105 (2007).
[CrossRef]

Bengtsson, J.

Bennett, S.

S. Bennett, C. M. Snowden, and S. Iezekiel, "Nonlinear dynamics in directly modulated multiple-quantum-well laser diodes," IEEE J. Quantum Electron. 33, 2076-2083 (1997).
[CrossRef]

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]

Boutami, S.

S. Boutami, B. Benbakir, J. L. Leclercq, and P. Viktorovitch, "Compact and polarization controlled 1.55 mu m vertical-cavity surface-emitting laser using single-layer photonic crystal mirror," Appl. Phys. Lett. 91, 071105 (2007).
[CrossRef]

Carpintero, G.

H. Lamela, G. Carpintero, and F. J. Mancebo, "Period tripling and chaos in the dynamic behavior of directly modulated diode lasers," IEEE J. Quantum Electron. 34, 1797-1801 (1998).
[CrossRef]

Chang-Hasnain, C. J.

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A nanoelectromechanical tunable laser," Nat. Photonics 2, 180-184 (2008).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nat. Photonics 1, 119-122 (2007)
[CrossRef]

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez and N. G. Stoffel, "Dynamic, polarization and transverse-mode characteristics of vertical cavity surface emitting lasers," IEEE J. Quantum Electron. 27, 1402-1409 (1991).
[CrossRef]

Choquette, K. D.

A. J. Danner, J. J. Raftery, P. O. Leisher, and K. D. Choquette, "Single mode photonic crystal vertical cavity lasers," Appl. Phys. Lett 88, 091114 (2006).
[CrossRef]

K. D. Choquette, R. P. Schneider, K. L. Lear and R. E. Leibenguth, "Gain-dependent polarization properties of vertical-cavity lasers,"IEEE J. Sel. Top. Quantum Electron. 1, 661-666 (1995).
[CrossRef]

Czyszanowski, T.

Danner, A. J.

A. J. Danner, J. J. Raftery, P. O. Leisher, and K. D. Choquette, "Single mode photonic crystal vertical cavity lasers," Appl. Phys. Lett 88, 091114 (2006).
[CrossRef]

Dems, M.

Feng, Q.

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

Florez, L. T.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez and N. G. Stoffel, "Dynamic, polarization and transverse-mode characteristics of vertical cavity surface emitting lasers," IEEE J. Quantum Electron. 27, 1402-1409 (1991).
[CrossRef]

Glorieux, P.

Gustavsson, J. S.

Hachair, X.

Haglund, A.

Harbison, J. P.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez and N. G. Stoffel, "Dynamic, polarization and transverse-mode characteristics of vertical cavity surface emitting lasers," IEEE J. Quantum Electron. 27, 1402-1409 (1991).
[CrossRef]

Hasnain, G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez and N. G. Stoffel, "Dynamic, polarization and transverse-mode characteristics of vertical cavity surface emitting lasers," IEEE J. Quantum Electron. 27, 1402-1409 (1991).
[CrossRef]

Homayounfar, A.

Hong, Y.

J. Paul, C. Masoller, P. Mandel, Y. Hong, P. S. Spencer, and K. A. Shore, "Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarization switching of vertical-cavity surface-emitting lasers," Phys. Rev. A 77, 043803 (2008).
[CrossRef]

J. Paul, C. Masoller, Y. 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]

Huang, M. C. Y.

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A nanoelectromechanical tunable laser," Nat. Photonics 2, 180-184 (2008).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nat. Photonics 1, 119-122 (2007)
[CrossRef]

Iezekiel, S.

S. Bennett, C. M. Snowden, and S. Iezekiel, "Nonlinear dynamics in directly modulated multiple-quantum-well laser diodes," IEEE J. Quantum Electron. 33, 2076-2083 (1997).
[CrossRef]

Iga, K.

K. Iga, "Surface-emitting laser -its birth and generation of new optoelectronics field," IEEE J. Sel. Top. Quantum Electron.  6, 1201-1215 (2000).
[CrossRef]

Illing, L.

L. Illing and M. B. Kennel, "Shaping current waveforms for direct modulation of semiconductor lasers," IEEE J. Quantum Electron. 40, 445-452 (2004).
[CrossRef]

Jedrasik, P.

Kennel, M. B.

L. Illing and M. B. Kennel, "Shaping current waveforms for direct modulation of semiconductor lasers," IEEE J. Quantum Electron. 40, 445-452 (2004).
[CrossRef]

Lamela, H.

H. Lamela, G. Carpintero, and F. J. Mancebo, "Period tripling and chaos in the dynamic behavior of directly modulated diode lasers," IEEE J. Quantum Electron. 34, 1797-1801 (1998).
[CrossRef]

Larsson, A.

Lear, K. L.

K. D. Choquette, R. P. Schneider, K. L. Lear and R. E. Leibenguth, "Gain-dependent polarization properties of vertical-cavity lasers,"IEEE J. Sel. Top. Quantum Electron. 1, 661-666 (1995).
[CrossRef]

Leclercq, J. L.

S. Boutami, B. Benbakir, J. L. Leclercq, and P. Viktorovitch, "Compact and polarization controlled 1.55 mu m vertical-cavity surface-emitting laser using single-layer photonic crystal mirror," Appl. Phys. Lett. 91, 071105 (2007).
[CrossRef]

Leibenguth, R. E.

K. D. Choquette, R. P. Schneider, K. L. Lear and R. E. Leibenguth, "Gain-dependent polarization properties of vertical-cavity lasers,"IEEE J. Sel. Top. Quantum Electron. 1, 661-666 (1995).
[CrossRef]

Leisher, P. O.

A. J. Danner, J. J. Raftery, P. O. Leisher, and K. D. Choquette, "Single mode photonic crystal vertical cavity lasers," Appl. Phys. Lett 88, 091114 (2006).
[CrossRef]

Lippi, G. L.

Lopez, J. M.

A. Valle, L. Pesquera, S. I. Turovets, and J. M. Lopez, "Nonlinear dynamics of current-modulated vertical-cavity surface-emitting lasers," Opt. Commun. 208, 173-182 (2002).
[CrossRef]

Mancebo, F. J.

H. Lamela, G. Carpintero, and F. J. Mancebo, "Period tripling and chaos in the dynamic behavior of directly modulated diode lasers," IEEE J. Quantum Electron. 34, 1797-1801 (1998).
[CrossRef]

Mandel, P.

J. Paul, C. Masoller, P. Mandel, Y. Hong, P. S. Spencer, and K. A. Shore, "Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarization switching of vertical-cavity surface-emitting lasers," Phys. Rev. A 77, 043803 (2008).
[CrossRef]

C. Masoller, M. S. Torre and P. Mandel, "Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting laser," J. Appl. Phys. 99, 026108 (2006).
[CrossRef]

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, 765-783 (1997).
[CrossRef]

Masoller, C.

J. Paul, C. Masoller, P. Mandel, Y. Hong, P. S. Spencer, and K. A. Shore, "Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarization switching of vertical-cavity surface-emitting lasers," Phys. Rev. A 77, 043803 (2008).
[CrossRef]

C. Masoller, M. S. Torre, and K. A. Shore, "Polarization dynamics of current-modulated vertical-cavity surfaceemitting lasers," IEEE J. Quantum Electron. 43, 1074-1082 (2007).
[CrossRef]

J. Paul, C. Masoller, Y. 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]

C. Masoller, M. S. Torre and P. Mandel, "Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting laser," J. Appl. Phys. 99, 026108 (2006).
[CrossRef]

C. Masoller and A. 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]

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]

Moloney, J. V.

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

Panajotov, K.

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

T. Czyszanowski, M. Dems, and K. Panajotov, "Single mode condition and modes discrimination in photoniccrystal 1.3 mu m AlInGaAs/InP VCSEL," Opt. Express 15, 5604-5609 (2007).
[CrossRef] [PubMed]

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]

Paul, J.

J. Paul, C. Masoller, P. Mandel, Y. Hong, P. S. Spencer, and K. A. Shore, "Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarization switching of vertical-cavity surface-emitting lasers," Phys. Rev. A 77, 043803 (2008).
[CrossRef]

J. Paul, C. Masoller, Y. 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]

Pesquera, L.

A. Valle, L. Pesquera, S. I. Turovets, and J. M. Lopez, "Nonlinear dynamics of current-modulated vertical-cavity surface-emitting lasers," Opt. Commun. 208, 173-182 (2002).
[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, 765-783 (1997).
[CrossRef]

Preda, C. E.

Raftery, J. J.

A. J. Danner, J. J. Raftery, P. O. Leisher, and K. D. Choquette, "Single mode photonic crystal vertical cavity lasers," Appl. Phys. Lett 88, 091114 (2006).
[CrossRef]

San Miguel, M.

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

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

Schneider, R. P.

K. D. Choquette, R. P. Schneider, K. L. Lear and R. E. Leibenguth, "Gain-dependent polarization properties of vertical-cavity lasers,"IEEE J. Sel. Top. Quantum Electron. 1, 661-666 (1995).
[CrossRef]

Sciamanna, M.

A. Valle, M. Sciamanna, and K. Panajotov, "Irregular pulsating polarization dynamics in gain-switched verticalcavity 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]

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]

Segard, B.

Shore, K. A.

J. Paul, C. Masoller, P. Mandel, Y. Hong, P. S. Spencer, and K. A. Shore, "Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarization switching of vertical-cavity surface-emitting lasers," Phys. Rev. A 77, 043803 (2008).
[CrossRef]

C. Masoller, M. S. Torre, and K. A. Shore, "Polarization dynamics of current-modulated vertical-cavity surfaceemitting lasers," IEEE J. Quantum Electron. 43, 1074-1082 (2007).
[CrossRef]

J. Paul, C. Masoller, Y. 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]

Snowden, C. M.

S. Bennett, C. M. Snowden, and S. Iezekiel, "Nonlinear dynamics in directly modulated multiple-quantum-well laser diodes," IEEE J. Quantum Electron. 33, 2076-2083 (1997).
[CrossRef]

Sondermann, M.

T. Ackemann and M. Sondermann, "Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 78, 3574-3576 (2001).
[CrossRef]

Spencer, P. S.

J. Paul, C. Masoller, P. Mandel, Y. Hong, P. S. Spencer, and K. A. Shore, "Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarization switching of vertical-cavity surface-emitting lasers," Phys. Rev. A 77, 043803 (2008).
[CrossRef]

J. Paul, C. Masoller, Y. 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]

Stoffel, N. G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez and N. G. Stoffel, "Dynamic, polarization and transverse-mode characteristics of vertical cavity surface emitting lasers," IEEE J. Quantum Electron. 27, 1402-1409 (1991).
[CrossRef]

Torre, A. S.

C. Masoller and A. 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]

Torre, M. S.

C. Masoller, M. S. Torre, and K. A. Shore, "Polarization dynamics of current-modulated vertical-cavity surfaceemitting lasers," IEEE J. Quantum Electron. 43, 1074-1082 (2007).
[CrossRef]

C. Masoller, M. S. Torre and P. Mandel, "Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting laser," J. Appl. Phys. 99, 026108 (2006).
[CrossRef]

Tredicce, J. R.

Turovets, S. I.

A. Valle, L. Pesquera, S. I. Turovets, and J. M. Lopez, "Nonlinear dynamics of current-modulated vertical-cavity surface-emitting lasers," Opt. Commun. 208, 173-182 (2002).
[CrossRef]

Valle, A.

A. Valle, M. Sciamanna, and K. Panajotov, "Irregular pulsating polarization dynamics in gain-switched verticalcavity 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]

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]

A. Valle, L. Pesquera, S. I. Turovets, and J. M. Lopez, "Nonlinear dynamics of current-modulated vertical-cavity surface-emitting lasers," Opt. Commun. 208, 173-182 (2002).
[CrossRef]

Viktorovitch, P.

S. Boutami, B. Benbakir, J. L. Leclercq, and P. Viktorovitch, "Compact and polarization controlled 1.55 mu m vertical-cavity surface-emitting laser using single-layer photonic crystal mirror," Appl. Phys. Lett. 91, 071105 (2007).
[CrossRef]

Vonlehmen, A. C.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez and N. G. Stoffel, "Dynamic, polarization and transverse-mode characteristics of vertical cavity surface emitting lasers," IEEE J. Quantum Electron. 27, 1402-1409 (1991).
[CrossRef]

Vukusic, J. A.

Zhou, Y.

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A nanoelectromechanical tunable laser," Nat. Photonics 2, 180-184 (2008).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nat. Photonics 1, 119-122 (2007)
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett (1)

A. J. Danner, J. J. Raftery, P. O. Leisher, and K. D. Choquette, "Single mode photonic crystal vertical cavity lasers," Appl. Phys. Lett 88, 091114 (2006).
[CrossRef]

Appl. Phys. Lett. (3)

S. Boutami, B. Benbakir, J. L. Leclercq, and P. Viktorovitch, "Compact and polarization controlled 1.55 mu m vertical-cavity surface-emitting laser using single-layer photonic crystal mirror," Appl. Phys. Lett. 91, 071105 (2007).
[CrossRef]

G. P. Agrawal, "Effect of gain nonlinearities on period doubling and chaos in directly modualted semiconductorlasers," Appl. Phys. Lett. 49, 1013-1015 (1986).
[CrossRef]

T. Ackemann and M. Sondermann, "Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 78, 3574-3576 (2001).
[CrossRef]

IEEE J. Quantum Electron. (8)

C. Masoller and A. 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]

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

C. Masoller, M. S. Torre, and K. A. Shore, "Polarization dynamics of current-modulated vertical-cavity surfaceemitting lasers," IEEE J. Quantum Electron. 43, 1074-1082 (2007).
[CrossRef]

S. Bennett, C. M. Snowden, and S. Iezekiel, "Nonlinear dynamics in directly modulated multiple-quantum-well laser diodes," IEEE J. Quantum Electron. 33, 2076-2083 (1997).
[CrossRef]

H. Lamela, G. Carpintero, and F. J. Mancebo, "Period tripling and chaos in the dynamic behavior of directly modulated diode lasers," IEEE J. Quantum Electron. 34, 1797-1801 (1998).
[CrossRef]

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez and N. G. Stoffel, "Dynamic, polarization and transverse-mode characteristics of vertical cavity surface emitting lasers," IEEE J. Quantum Electron. 27, 1402-1409 (1991).
[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, 765-783 (1997).
[CrossRef]

L. Illing and M. B. Kennel, "Shaping current waveforms for direct modulation of semiconductor lasers," IEEE J. Quantum Electron. 40, 445-452 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron (1)

K. Iga, "Surface-emitting laser -its birth and generation of new optoelectronics field," IEEE J. Sel. Top. Quantum Electron.  6, 1201-1215 (2000).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

K. D. Choquette, R. P. Schneider, K. L. Lear and R. E. Leibenguth, "Gain-dependent polarization properties of vertical-cavity lasers,"IEEE J. Sel. Top. Quantum Electron. 1, 661-666 (1995).
[CrossRef]

J. Appl. Phys. (1)

C. Masoller, M. S. Torre and P. Mandel, "Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting laser," J. Appl. Phys. 99, 026108 (2006).
[CrossRef]

Nat. Photonics (2)

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nat. Photonics 1, 119-122 (2007)
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A nanoelectromechanical tunable laser," Nat. Photonics 2, 180-184 (2008).
[CrossRef]

Opt. Commun. (1)

A. Valle, L. Pesquera, S. I. Turovets, and J. M. Lopez, "Nonlinear dynamics of current-modulated vertical-cavity surface-emitting lasers," Opt. Commun. 208, 173-182 (2002).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. A (2)

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

J. Paul, C. Masoller, P. Mandel, Y. Hong, P. S. Spencer, and K. A. Shore, "Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarization switching of vertical-cavity surface-emitting lasers," Phys. Rev. A 77, 043803 (2008).
[CrossRef]

Phys. Rev. E (2)

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]

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]

Other (1)

H. Thienpont and J. Danckaert, eds., VCSELs and Optical Interconnects, Proc. SPIE 4942, 236-246(2003).

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Figures (3)

Fig. 1.
Fig. 1.

Time traces of the intensities of the orthogonal linear polarization: Ix (red), Iy (blue), and the injection current µ(t) (dashed) for an asymmetry parameter (a) αa =0.8, (b) 0.6 and (c) 0.2. (d) Detail of a pulse in Fig.1(a). (e) Color plot of the average pulse total amplitude, 〈AT 〉, for a fixed modulation amplitude, Δµ=1. (f) and (g) Time averaged intensities, 〈I〉, and pulse amplitudes, 〈A〉, respectively (x polarization (red), y polarization (blue) and total intensity (black)). (h) Normalized standard deviation, σ/〈A〉, of the pulse amplitude vs. the asymmetry parameter, αa . The modulation amplitude is Δµ=1, the period is T=3 ns. The DC value µ0 =0.37 is fixed in captions (a)–(d) and (f)–(g) and is varied in (e).

Fig. 2.
Fig. 2.

(a)–(c) Time averaged intensities [x polarization 〈Ix 〉 (red), y polarization 〈Iy 〉 (blue) and total intensity 〈IT 〉 (black)] vs. average current, µave , for different modulation amplitudes (a) Δµ=1.0, (b) 0.5, and (c) 0.15. (d) Color plot of average total intensity 〈IT 〉. The asymmetry parameter αa =0.8 and the period T=3 ns are fixed.

Fig. 3.
Fig. 3.

(a)–(c) Time averaged pulse amplitudes [x polarization 〈Ax 〈 (red), y polarization 〈Ay 〉 (blue) and total amplitude 〈AT 〉 (black)] vs. average current, µave , for different modulation amplitudes (a) Δµ=1.0, (b) 0.5, and (c) 0.15. (d) Color plot of the average total intensity, 〈IT 〉. Parameters are as in Fig. 2.

Equations (3)

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

d E x , y dt = k ( 1 + i α ) [ ( N 1 ) E x , y ± in E y , x ] ( γ a + i γ p ) E x , y + β sp ξ x , y ,
d N dt = γ N [ μ ( t ) N ( 1 + E x 2 + E y 2 ) in ( E y E x * E x E y * ) ] ,
d n dt = γ s n γ N [ n ( E x 2 + E y 2 ) + iN ( E y E x * E x E y * ) ] ,

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