Abstract

The hysteresis properties in bistable polarization switching (PS) of vertical-cavity surface-emitting lasers (VCSELs) induced by variable-polarization optical feedback (VPOF) are investigated numerically. We mainly concentrate on the influence of sweep rate of the polarizer angle on the bistable PS for the cases with different feedback strengths and feedback delays. The output in the time domain and the representation on the Poincaré sphere plot are further presented to describe the two PS processes. The results show that the size of the hysteresis cycle of the PS follows a power-law relationship versus the sweep rate of the polarizer angle, and the feedback strength and feedback delay can modify the hysteresis properties significantly. A larger feedback strength leads to a narrower hysteresis loop, while a larger feedback delay gives rise to a wider hysteresis loop. Therefore the VPOF provides a new method for obtaining the controllable bistable PS in VCSELs, which is potentially interesting for applications that require polarization-bistable VCSELs.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  6. 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]
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    [CrossRef]
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    [CrossRef]
  9. C. Masoller and N. B. Abraham, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback through a quarter-wave plate,” Appl. Phys. Lett. 74, 1078–1080 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
  11. 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]
  12. F. Prati, P. Caccia, M. Bache, and F. Castelli, “Analysis of elliptically polarized states in vertical-cavity-surface-emitting lasers,” Phys. Rev. A 69, 033810 (2004).
    [CrossRef]
  13. Y. 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]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  17. Y. 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]
  18. R. Vicente, J. Mulet, C. R. Mirasso, and M. Sciamanna, “Bistable polarization switching in mutually coupled vertical-cavity surface-emitting lasers,” Opt. Lett. 31, 996–998 (2006).
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    [CrossRef]
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    [CrossRef] [PubMed]
  21. C. Masoller, M. S. Torre, and P. Mandel, “Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting lasers,” J. Appl. Phys. 99, 026108 (2006).
    [CrossRef]
  22. 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]
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    [CrossRef]
  24. L. Khaykovich, T. Galfsky, Z. Shotan, and N. Gross, “TE-TM coupled mode dynamics in a semiconductor laser subject to feedback with variably rotated polarization,” Opt. Commun. 282, 2059–2061 (2009).
    [CrossRef]
  25. S. Xiang, W. Pan, L. Yan, B. Luo, N. Jiang, K. Wen, X. Zou, and L. Yang, “Polarization degree of vertical-cavity surface-emitting lasers subject to optical feedback with controllable polarization,” J. Opt. Soc. Am. B 27, 476–483 (2010).
    [CrossRef]
  26. S. Ramanujan, G. P. Agrawal, J. M. Chwalek, and H. Winful, “Elliptical polarization emission from GaAlAs laser diodes in an external cavity configuration,” IEEE J. Quantum Electron. 32, 213–221 (1996).
    [CrossRef]
  27. L. Chrostowski, B. Faraji, W. Hofmann, M. C. Amann, S. Wieczorek, and W. W. Chow, “40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 μm VCSELs,” IEEE J. Sel. Top. Quantum Electron. 13, 1200–1208 (2007).
    [CrossRef]
  28. C. Masoller and N. B. Abraham, “Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59, 3021–3031 (1999).
    [CrossRef]

2010 (1)

2009 (3)

2008 (3)

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]

W. L. Zhang, W. Pan, B. Luo, X. H. Zuo, and M. Y. Wang, “Polarization switching and hysteresis of VCSELs with time-varying optical injection,” IEEE J. Sel. Top. Quantum Electron. 14, 889–894 (2008).
[CrossRef]

W. L. Zhang, W. Pan, B. Luo, X. F. Li, X. H. Zuo, and M. Y. Wang, “Polarization-resolved dynamics of asymmetrically coupled vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 25, 153–158 (2008).
[CrossRef]

2007 (2)

L. Chrostowski, B. Faraji, W. Hofmann, M. C. Amann, S. Wieczorek, and W. W. Chow, “40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 μm VCSELs,” IEEE J. Sel. Top. Quantum Electron. 13, 1200–1208 (2007).
[CrossRef]

I. Gatare, K. Panajotov, and M. Sciamanna, “Frequency-induced polarization bistability in vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. A 75, 023804 (2007).
[CrossRef]

2006 (3)

2005 (2)

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. 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. 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]

F. Prati, P. Caccia, M. Bache, and F. Castelli, “Analysis of elliptically polarized states in vertical-cavity-surface-emitting lasers,” Phys. Rev. A 69, 033810 (2004).
[CrossRef]

2003 (1)

2000 (1)

M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, “Anatomy of a polarization switch of a vertical-cavity semiconductor laser,” Phys. Rev. Lett. 84, 4337–4340 (2000).
[CrossRef] [PubMed]

1999 (3)

C. Masoller and N. B. Abraham, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback through a quarter-wave plate,” Appl. Phys. Lett. 74, 1078–1080 (1999).
[CrossRef]

K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, and H. Thienpont, “Data transparent reconfigurable optical interconnections using polarization switching in VCSEL’s induced by optical injection,” IEEE Photon. Technol. Lett. 11, 985–987 (1999).
[CrossRef]

C. Masoller and N. B. Abraham, “Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59, 3021–3031 (1999).
[CrossRef]

1998 (1)

M. P. van Exter, R. F. M. Hendriks, and J. P. Woerdman, “Physical insight into the polarization dynamics of semiconductor vertical-cavity lasers,” Phys. Rev. A 57, 2080–2090 (1998).
[CrossRef]

1997 (2)

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]

H. Kawaguchi, “Bistable laser diodes and their applications: state of the art,” IEEE J. Sel. Top. Quantum Electron. 3, 1254–1270 (1997).
[CrossRef]

1996 (1)

S. Ramanujan, G. P. Agrawal, J. M. Chwalek, and H. Winful, “Elliptical polarization emission from GaAlAs laser diodes in an external cavity configuration,” IEEE J. Quantum Electron. 32, 213–221 (1996).
[CrossRef]

1995 (1)

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]

1994 (1)

1993 (1)

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 2999–3001 (1993).
[CrossRef]

Abraham, N. B.

C. Masoller and N. B. Abraham, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback through a quarter-wave plate,” Appl. Phys. Lett. 74, 1078–1080 (1999).
[CrossRef]

C. Masoller and N. B. Abraham, “Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59, 3021–3031 (1999).
[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]

Agrawal, G. P.

S. Ramanujan, G. P. Agrawal, J. M. Chwalek, and H. Winful, “Elliptical polarization emission from GaAlAs laser diodes in an external cavity configuration,” IEEE J. Quantum Electron. 32, 213–221 (1996).
[CrossRef]

Amann, M. C.

L. Chrostowski, B. Faraji, W. Hofmann, M. C. Amann, S. Wieczorek, and W. W. Chow, “40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 μm VCSELs,” IEEE J. Sel. Top. Quantum Electron. 13, 1200–1208 (2007).
[CrossRef]

Asom, M. T.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 2999–3001 (1993).
[CrossRef]

Bache, M.

F. Prati, P. Caccia, M. Bache, and F. Castelli, “Analysis of elliptically polarized states in vertical-cavity-surface-emitting lasers,” Phys. Rev. A 69, 033810 (2004).
[CrossRef]

Berghmans, F.

K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, and H. Thienpont, “Data transparent reconfigurable optical interconnections using polarization switching in VCSEL’s induced by optical injection,” IEEE Photon. Technol. Lett. 11, 985–987 (1999).
[CrossRef]

Besnard, P.

Blin, S.

Blondel, M.

Caccia, P.

F. Prati, P. Caccia, M. Bache, and F. Castelli, “Analysis of elliptically polarized states in vertical-cavity-surface-emitting lasers,” Phys. Rev. A 69, 033810 (2004).
[CrossRef]

Castelli, F.

F. Prati, P. Caccia, M. Bache, and F. Castelli, “Analysis of elliptically polarized states in vertical-cavity-surface-emitting lasers,” Phys. Rev. A 69, 033810 (2004).
[CrossRef]

Chow, W. W.

L. Chrostowski, B. Faraji, W. Hofmann, M. C. Amann, S. Wieczorek, and W. W. Chow, “40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 μm VCSELs,” IEEE J. Sel. Top. Quantum Electron. 13, 1200–1208 (2007).
[CrossRef]

Chrostowski, L.

L. Chrostowski, B. Faraji, W. Hofmann, M. C. Amann, S. Wieczorek, and W. W. Chow, “40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 μm VCSELs,” IEEE J. Sel. Top. Quantum Electron. 13, 1200–1208 (2007).
[CrossRef]

Chwalek, J. M.

S. Ramanujan, G. P. Agrawal, J. M. Chwalek, and H. Winful, “Elliptical polarization emission from GaAlAs laser diodes in an external cavity configuration,” IEEE J. Quantum Electron. 32, 213–221 (1996).
[CrossRef]

Dagenais, M.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 2999–3001 (1993).
[CrossRef]

Danckaert, J.

K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, and H. Thienpont, “Data transparent reconfigurable optical interconnections using polarization switching in VCSEL’s induced by optical injection,” IEEE Photon. Technol. Lett. 11, 985–987 (1999).
[CrossRef]

Faraji, B.

L. Chrostowski, B. Faraji, W. Hofmann, M. C. Amann, S. Wieczorek, and W. W. Chow, “40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 μm VCSELs,” IEEE J. Sel. Top. Quantum Electron. 13, 1200–1208 (2007).
[CrossRef]

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]

Focht, M. W.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 2999–3001 (1993).
[CrossRef]

Gabet, R.

Galfsky, T.

L. Khaykovich, T. Galfsky, Z. Shotan, and N. Gross, “TE-TM coupled mode dynamics in a semiconductor laser subject to feedback with variably rotated polarization,” Opt. Commun. 282, 2059–2061 (2009).
[CrossRef]

Gatare, I.

I. Gatare, K. Panajotov, and M. Sciamanna, “Frequency-induced polarization bistability in vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. A 75, 023804 (2007).
[CrossRef]

Gross, N.

L. Khaykovich, T. Galfsky, Z. Shotan, and N. Gross, “TE-TM coupled mode dynamics in a semiconductor laser subject to feedback with variably rotated polarization,” Opt. Commun. 282, 2059–2061 (2009).
[CrossRef]

Guth, G. D.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 2999–3001 (1993).
[CrossRef]

Hendriks, R. F. M.

M. P. van Exter, R. F. M. Hendriks, and J. P. Woerdman, “Physical insight into the polarization dynamics of semiconductor vertical-cavity lasers,” Phys. Rev. A 57, 2080–2090 (1998).
[CrossRef]

Hofmann, W.

L. Chrostowski, B. Faraji, W. Hofmann, M. C. Amann, S. Wieczorek, and W. W. Chow, “40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 μm VCSELs,” IEEE J. Sel. Top. Quantum Electron. 13, 1200–1208 (2007).
[CrossRef]

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]

Y. 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. 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]

Jiang, N.

Jiang, S.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 2999–3001 (1993).
[CrossRef]

Ju, R.

Y. 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]

Kawaguchi, H.

H. Kawaguchi, “Bistable laser diodes and their applications: state of the art,” IEEE J. Sel. Top. Quantum Electron. 3, 1254–1270 (1997).
[CrossRef]

Khaykovich, L.

L. Khaykovich, T. Galfsky, Z. Shotan, and N. Gross, “TE-TM coupled mode dynamics in a semiconductor laser subject to feedback with variably rotated polarization,” Opt. Commun. 282, 2059–2061 (2009).
[CrossRef]

Kojima, K.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 2999–3001 (1993).
[CrossRef]

Leibenguth, R. E.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 2999–3001 (1993).
[CrossRef]

Li, X. F.

Lugiato, L. A.

Luo, B.

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 lasers,” 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 P. Mandel, “Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting lasers,” J. Appl. Phys. 99, 026108 (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. 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]

C. Masoller and N. B. Abraham, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback through a quarter-wave plate,” Appl. Phys. Lett. 74, 1078–1080 (1999).
[CrossRef]

C. Masoller and N. B. Abraham, “Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59, 3021–3031 (1999).
[CrossRef]

Mégret, P.

Mirasso, C. R.

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]

Morgan, R. A.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 2999–3001 (1993).
[CrossRef]

Mulet, J.

Pan, W.

Pan, Z. G.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 2999–3001 (1993).
[CrossRef]

Panajotov, K.

I. Gatare, K. Panajotov, and M. Sciamanna, “Frequency-induced polarization bistability in vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. A 75, 023804 (2007).
[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]

K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, and H. Thienpont, “Data transparent reconfigurable optical interconnections using polarization switching in VCSEL’s induced by optical injection,” IEEE Photon. Technol. Lett. 11, 985–987 (1999).
[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]

Peeters, M.

K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, and H. Thienpont, “Data transparent reconfigurable optical interconnections using polarization switching in VCSEL’s induced by optical injection,” IEEE Photon. Technol. Lett. 11, 985–987 (1999).
[CrossRef]

Prati, F.

F. Prati, P. Caccia, M. Bache, and F. Castelli, “Analysis of elliptically polarized states in vertical-cavity-surface-emitting lasers,” Phys. Rev. A 69, 033810 (2004).
[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]

F. Prati, M. Travagnin, and L. A. Lugiato, “Optical switching and logic gates with vertical cavity surface-emitting lasers,” Opt. Lett. 19, 1991–1993 (1994).
[CrossRef] [PubMed]

Ramanujan, S.

S. Ramanujan, G. P. Agrawal, J. M. Chwalek, and H. Winful, “Elliptical polarization emission from GaAlAs laser diodes in an external cavity configuration,” IEEE J. Quantum Electron. 32, 213–221 (1996).
[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]

Sciamanna, M.

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]

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]

Y. 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. 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]

Shotan, Z.

L. Khaykovich, T. Galfsky, Z. Shotan, and N. Gross, “TE-TM coupled mode dynamics in a semiconductor laser subject to feedback with variably rotated polarization,” Opt. Commun. 282, 2059–2061 (2009).
[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]

Y. 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. 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]

Thienpont, H.

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]

K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, and H. Thienpont, “Data transparent reconfigurable optical interconnections using polarization switching in VCSEL’s induced by optical injection,” IEEE Photon. Technol. Lett. 11, 985–987 (1999).
[CrossRef]

Torre, M. S.

C. Masoller, M. S. Torre, and P. Mandel, “Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting lasers,” J. Appl. Phys. 99, 026108 (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]

Travagnin, M.

van Exter, M. P.

M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, “Anatomy of a polarization switch of a vertical-cavity semiconductor laser,” Phys. Rev. Lett. 84, 4337–4340 (2000).
[CrossRef] [PubMed]

M. P. van Exter, R. F. M. Hendriks, and J. P. Woerdman, “Physical insight into the polarization dynamics of semiconductor vertical-cavity lasers,” Phys. Rev. A 57, 2080–2090 (1998).
[CrossRef]

Vaudel, O.

Veretennicoff, I.

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]

K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, and H. Thienpont, “Data transparent reconfigurable optical interconnections using polarization switching in VCSEL’s induced by optical injection,” IEEE Photon. Technol. Lett. 11, 985–987 (1999).
[CrossRef]

Verschaffelt, G.

K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, and H. Thienpont, “Data transparent reconfigurable optical interconnections using polarization switching in VCSEL’s induced by optical injection,” IEEE Photon. Technol. Lett. 11, 985–987 (1999).
[CrossRef]

Vicente, R.

Wang, M. Y.

W. L. Zhang, W. Pan, B. Luo, X. F. Li, X. H. Zuo, and M. Y. Wang, “Polarization-resolved dynamics of asymmetrically coupled vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 25, 153–158 (2008).
[CrossRef]

W. L. Zhang, W. Pan, B. Luo, X. H. Zuo, and M. Y. Wang, “Polarization switching and hysteresis of VCSELs with time-varying optical injection,” IEEE J. Sel. Top. Quantum Electron. 14, 889–894 (2008).
[CrossRef]

Wen, K.

Wieczorek, S.

L. Chrostowski, B. Faraji, W. Hofmann, M. C. Amann, S. Wieczorek, and W. W. Chow, “40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 μm VCSELs,” IEEE J. Sel. Top. Quantum Electron. 13, 1200–1208 (2007).
[CrossRef]

Willemsen, M. B.

M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, “Anatomy of a polarization switch of a vertical-cavity semiconductor laser,” Phys. Rev. Lett. 84, 4337–4340 (2000).
[CrossRef] [PubMed]

Winful, H.

S. Ramanujan, G. P. Agrawal, J. M. Chwalek, and H. Winful, “Elliptical polarization emission from GaAlAs laser diodes in an external cavity configuration,” IEEE J. Quantum Electron. 32, 213–221 (1996).
[CrossRef]

Woerdman, J. P.

M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, “Anatomy of a polarization switch of a vertical-cavity semiconductor laser,” Phys. Rev. Lett. 84, 4337–4340 (2000).
[CrossRef] [PubMed]

M. P. van Exter, R. F. M. Hendriks, and J. P. Woerdman, “Physical insight into the polarization dynamics of semiconductor vertical-cavity lasers,” Phys. Rev. A 57, 2080–2090 (1998).
[CrossRef]

Xiang, S.

Yan, L.

Yang, L.

Zhang, W. L.

W. L. Zhang, W. Pan, B. Luo, X. F. Li, X. H. Zuo, and M. Y. Wang, “Polarization-resolved dynamics of asymmetrically coupled vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 25, 153–158 (2008).
[CrossRef]

W. L. Zhang, W. Pan, B. Luo, X. H. Zuo, and M. Y. Wang, “Polarization switching and hysteresis of VCSELs with time-varying optical injection,” IEEE J. Sel. Top. Quantum Electron. 14, 889–894 (2008).
[CrossRef]

Zou, X.

Zuo, X. H.

W. L. Zhang, W. Pan, B. Luo, X. F. Li, X. H. Zuo, and M. Y. Wang, “Polarization-resolved dynamics of asymmetrically coupled vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 25, 153–158 (2008).
[CrossRef]

W. L. Zhang, W. Pan, B. Luo, X. H. Zuo, and M. Y. Wang, “Polarization switching and hysteresis of VCSELs with time-varying optical injection,” IEEE J. Sel. Top. Quantum Electron. 14, 889–894 (2008).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 2999–3001 (1993).
[CrossRef]

C. Masoller and N. B. Abraham, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback through a quarter-wave plate,” Appl. Phys. Lett. 74, 1078–1080 (1999).
[CrossRef]

IEEE J. Quantum Electron. (4)

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]

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. 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]

S. Ramanujan, G. P. Agrawal, J. M. Chwalek, and H. Winful, “Elliptical polarization emission from GaAlAs laser diodes in an external cavity configuration,” IEEE J. Quantum Electron. 32, 213–221 (1996).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (3)

L. Chrostowski, B. Faraji, W. Hofmann, M. C. Amann, S. Wieczorek, and W. W. Chow, “40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 μm VCSELs,” IEEE J. Sel. Top. Quantum Electron. 13, 1200–1208 (2007).
[CrossRef]

W. L. Zhang, W. Pan, B. Luo, X. H. Zuo, and M. Y. Wang, “Polarization switching and hysteresis of VCSELs with time-varying optical injection,” IEEE J. Sel. Top. Quantum Electron. 14, 889–894 (2008).
[CrossRef]

H. Kawaguchi, “Bistable laser diodes and their applications: state of the art,” IEEE J. Sel. Top. Quantum Electron. 3, 1254–1270 (1997).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, and H. Thienpont, “Data transparent reconfigurable optical interconnections using polarization switching in VCSEL’s induced by optical injection,” IEEE Photon. Technol. Lett. 11, 985–987 (1999).
[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 lasers,” J. Appl. Phys. 99, 026108 (2006).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

L. Khaykovich, T. Galfsky, Z. Shotan, and N. Gross, “TE-TM coupled mode dynamics in a semiconductor laser subject to feedback with variably rotated polarization,” Opt. Commun. 282, 2059–2061 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

Phys. Rev. A (6)

F. Prati, P. Caccia, M. Bache, and F. Castelli, “Analysis of elliptically polarized states in vertical-cavity-surface-emitting lasers,” Phys. Rev. A 69, 033810 (2004).
[CrossRef]

C. Masoller and N. B. Abraham, “Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59, 3021–3031 (1999).
[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]

I. Gatare, K. Panajotov, and M. Sciamanna, “Frequency-induced polarization bistability in vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. A 75, 023804 (2007).
[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]

M. P. van Exter, R. F. M. Hendriks, and J. P. Woerdman, “Physical insight into the polarization dynamics of semiconductor vertical-cavity lasers,” Phys. Rev. A 57, 2080–2090 (1998).
[CrossRef]

Phys. Rev. Lett. (1)

M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, “Anatomy of a polarization switch of a vertical-cavity semiconductor laser,” Phys. Rev. Lett. 84, 4337–4340 (2000).
[CrossRef] [PubMed]

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Figures (11)

Fig. 1
Fig. 1

Schematic illustration of VCSEL with a RP in the external cavity: VCSEL, vertical-cavity surface-emitting laser; ML, microscopic lens; BS, beam splitter; RP, rotating polarizer; M, mirror; NDF, neutral density filter; ISO, optical isolator.

Fig. 2
Fig. 2

Polarization-resolved intensities as a function of the polarizer angles. The left (right) column corresponds to the XP (YP) mode; the solid (dotted) line with circles (stars) corresponds to increasing (decreasing) θ p . (a) T = 225   ns , (b) T = 450   ns , (c) T = 900   ns .

Fig. 3
Fig. 3

(a) Values of the PS points for increasing θ p (circles) and decreasing θ p (triangles) versus T in logarithmic-linear plot. (b) Hysteresis width versus 1 / T in log-log plot. The solid line indicates the fit: ln ( θ p i θ p d ) = a   ln ( 1 / T ) + b , with a = 0.89 , b = 7.59 .

Fig. 4
Fig. 4

Output in the time domain for both XP (left column) and YP (right column) modes, with T = 225   ns . (a),(b) XP mode; (c),(d) YP mode.

Fig. 5
Fig. 5

Evolutions of polarization state plotted on the normalized Poincaré sphere for VCSEL with T = 225   ns .

Fig. 6
Fig. 6

Same as Fig. 4 but for γ s = 10 ns 1 . The solid line indicates the fit: ln ( θ p i θ p d ) = a   ln ( 1 / T ) + b , with a = 0.78 , b = 7.21 .

Fig. 7
Fig. 7

Same as Fig. 4 but for γ s = 500 ns 1 . The solid line indicates the fit: ln ( θ p i θ p d ) = a   ln ( 1 / T ) + b , with a = 0.82 , b = 7.24 .

Fig. 8
Fig. 8

Polarization-resolved intensities as a function of θ P for T = 225   ns ; the solid (dotted) line with circles (stars) corresponds to increasing (decreasing) θ p . (a) γ = 5 ns 1 , (b) γ = 10 ns 1 , (c) γ = 20 ns 1 .

Fig. 9
Fig. 9

Values of the PS points for increasing θ p (circles) and decreasing θ p (triangles) versus γ. (a) T = 90   ns , (b) T = 225   ns .

Fig. 10
Fig. 10

Polarization-resolved intensities as a function of θ P for T = 225   ns ; the solid (dotted) line with circles (stars) corresponds to increasing (decreasing) θ p . (a) τ = 2   ns , (b) τ = 5   ns , (c) τ = 8   ns .

Fig. 11
Fig. 11

Values of the PS points for increasing θ p (circles) and decreasing θ p (triangles) versus τ. (a) T = 90   ns , (b) T = 225   ns .

Equations (4)

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E ̇ x = k ( 1 + i α ) [ ( N 1 ) E x + i n E y ] ( γ a + i γ p ) E x + γ E x ( t τ ) cos 2 ( θ p ) e i ω τ + γ E y ( t τ ) cos ( θ p ) sin ( θ p ) e i ω τ ,
E ̇ y = k ( 1 + i α ) [ ( N 1 ) E y i n E x ] + ( γ a + i γ p ) E y + γ E x ( t τ ) sin ( θ p ) cos ( θ p ) e i ω τ + γ E y ( t τ ) sin 2 ( θ p ) e i ω τ ,
N ̇ = γ N [ μ N ( 1 + | E x | 2 + | E y | 2 ) + i n ( E x E y E y E x ) ] ,
n ̇ = γ s n γ N [ n ( | E x | 2 + | E y | 2 ) + i N ( E y E x E x E y ) ] ,

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