Abstract

We study experimentally and numerically the influence of orthogonal optical feedback on the polarization-resolved light versus bias current characteristic (LI curve) of vertical-cavity surface-emitting lasers (VCSELs). The feedback scheme is such that only one linear polarization is selected to be fed back into the laser while the orthogonal polarization is completely suppressed before the output is rotated 90° and reinjected into the laser. We experimentally demonstrate that weak feedback levels modify the polarization switching point only slightly, but as the feedback increases the otherwise depressed mode grows and the hysteresis is suppressed. While polarization-preserved and X-orthogonal feedback have similar effects (X indicates the direction of the polarization selected at threshold), Y-orthogonal feedback strongly modifies the shape of the LI curve, even suppressing the polarization-switching for strong enough feedback. Numerical simulations of the spin-flip model show good qualitative agreement with the observations. We also analyze the influence of various parameters, such as linear birefringence, dichroism, and the spin-flip relaxation rate.

© 2007 Optical Society of America

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  1. Z. G. Pan, S. J. 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]
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    [CrossRef]
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    [CrossRef]
  4. A. Valle, L. Pesquera, and K. A. Shore, "Polarization behavior of birefringent multitransverse mode vertical-cavity surface-emitting lasers," IEEE Photon. Technol. Lett. 9, 557-559 (1997).
    [CrossRef]
  5. B. Ryvkin, K. Panajotov, A. Georgievski, J. Danckaert, M. Peeters, G. Verschaffelt, H. Thienpont, and I. Veretennicoff, "Effect of photon-energy-dependent loss and gain mechanisms on polarization switching in vertical-cavity surface-emitting lasers," J. Opt. Soc. Am. B 16, 2106-2113 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  17. Y. Hong, M. W. Lee, P. S. Spencer, and K. A. Shore, "Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers," Opt. Lett. 29, 1215-1217 (2004).
    [CrossRef] [PubMed]
  18. M. W. Lee, Y. Hong, and K. A. Shore, "Experimental demonstration of VCSEL-based chaotic optical communications," IEEE Photon. Technol. Lett. 16, 2392-2394 (2004).
    [CrossRef]
  19. D. W. Sukow, A. Gavrielides, T. McLachlan, G. Burner, J. Amonette, and J. Miller, "Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields," Phys. Rev. A 74, 023812 (2006).
    [CrossRef]
  20. R. Ju and P. S. Spencer, "Dynamic regimes in semiconductor lasers subject to incoherent optical feedback," J. Lightwave Technol. 23, 2513-2523 (2005).
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  21. A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, "Square-wave self-modulation in diode lasers with polarization-rotated optical feedback," Opt. Lett. 31, 2006-2008 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
  23. H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, "Stable polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 72, 2355-2357 (1998).
    [CrossRef]
  24. M. Sciamanna, F. Rogister, O. Deparis, P. Megret, M. Blondel, and T. Erneux, "Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers," Opt. Lett. 27, 261-263 (2002).
    [CrossRef]
  25. S. Kakuma and R. Ohba, "Practical accurate optical ranging based on polarization self modulation of a vertical-cavity surface-emitting laser diode," Opt. Rev. 10, 511-513 (2003).
    [CrossRef]
  26. J. Javaloyes, J. Mulet, and S. Balle, "Passive mode locking of lasers by crossed-polarization gain modulation," Phys. Rev. Lett. 97, 163902 (2006).
    [CrossRef] [PubMed]
  27. W. L. Zhang, W. Pan, B. Luo, X. H. Zou, and M. Y. Wang, "Polarization dynamics of vertical-cavity surface-emitting lasers with optical feedback," Opt. Eng. (Bellingham) 45, 114202 (2006).
    [CrossRef]

2006 (5)

D. W. Sukow, A. Gavrielides, T. McLachlan, G. Burner, J. Amonette, and J. Miller, "Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields," Phys. Rev. A 74, 023812 (2006).
[CrossRef]

J. Javaloyes, J. Mulet, and S. Balle, "Passive mode locking of lasers by crossed-polarization gain modulation," Phys. Rev. Lett. 97, 163902 (2006).
[CrossRef] [PubMed]

W. L. Zhang, W. Pan, B. Luo, X. H. Zou, and M. Y. Wang, "Polarization dynamics of vertical-cavity surface-emitting lasers with optical feedback," Opt. Eng. (Bellingham) 45, 114202 (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]

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, "Square-wave self-modulation in diode lasers with polarization-rotated optical feedback," Opt. Lett. 31, 2006-2008 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (3)

2003 (3)

A. Scire, J. Mulet, C. R. Mirasso, J. Danckaert, and M. San Miguel, "Polarization message encoding through vectorial chaos synchronization in vertical-cavity surface-emitting lasers," Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

S. Kakuma and R. Ohba, "Practical accurate optical ranging based on polarization self modulation of a vertical-cavity surface-emitting laser diode," Opt. Rev. 10, 511-513 (2003).
[CrossRef]

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

2002 (2)

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]

1999 (3)

1998 (3)

T. Yoshikawa, T. Kawakami, H. Saito, H. Kosaka, M. Kajita, K. Kurihara, Y. Sugimoto, and K. Kasahara, "Polarization-controlled single-mode VCSEL," IEEE J. Quantum Electron. 34, 1009-1015 (1998).
[CrossRef]

A. Valle, L. Pesquera, and K. A. Shore, "Polarization selection and sensitivity of external cavity vertical-cavity surface-emitting laser diodes," IEEE Photon. Technol. Lett. 10, 639-641 (1998).
[CrossRef]

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, "Stable polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 72, 2355-2357 (1998).
[CrossRef]

1997 (3)

T. H. Russell and T. D. Milster, "Polarization switching control in VCSELs," Appl. Phys. Lett. 70, 2520-2522 (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]

A. Valle, L. Pesquera, and K. A. Shore, "Polarization behavior of birefringent multitransverse mode vertical-cavity surface-emitting lasers," IEEE Photon. Technol. Lett. 9, 557-559 (1997).
[CrossRef]

1995 (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]

1993 (2)

Z. G. Pan, S. J. 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]

S. J. Jiang, Z. Q. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, "High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 63, 3545-3547 (1993).
[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]

Amonette, J.

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, "Square-wave self-modulation in diode lasers with polarization-rotated optical feedback," Opt. Lett. 31, 2006-2008 (2006).
[CrossRef] [PubMed]

D. W. Sukow, A. Gavrielides, T. McLachlan, G. Burner, J. Amonette, and J. Miller, "Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields," Phys. Rev. A 74, 023812 (2006).
[CrossRef]

Asom, M. T.

Z. G. Pan, S. J. 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]

Balle, S.

Besnard, P.

Blondel, M.

Burner, G.

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, "Square-wave self-modulation in diode lasers with polarization-rotated optical feedback," Opt. Lett. 31, 2006-2008 (2006).
[CrossRef] [PubMed]

D. W. Sukow, A. Gavrielides, T. McLachlan, G. Burner, J. Amonette, and J. Miller, "Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields," Phys. Rev. A 74, 023812 (2006).
[CrossRef]

Chares, M. L.

Choquette, K. D.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, "Stable polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 72, 2355-2357 (1998).
[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]

Dagenais, M.

S. J. Jiang, Z. Q. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, "High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 63, 3545-3547 (1993).
[CrossRef]

Z. G. Pan, S. J. 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.

A. Scire, J. Mulet, C. R. Mirasso, J. Danckaert, and M. San Miguel, "Polarization message encoding through vectorial chaos synchronization in vertical-cavity surface-emitting lasers," Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

B. Ryvkin, K. Panajotov, A. Georgievski, J. Danckaert, M. Peeters, G. Verschaffelt, H. Thienpont, and I. Veretennicoff, "Effect of photon-energy-dependent loss and gain mechanisms on polarization switching in vertical-cavity surface-emitting lasers," J. Opt. Soc. Am. B 16, 2106-2113 (1999).
[CrossRef]

Deparis, O.

Erneux, T.

Focht, M. W.

Z. G. Pan, S. J. 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]

Gahl, A.

Gavrielides, A.

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, "Square-wave self-modulation in diode lasers with polarization-rotated optical feedback," Opt. Lett. 31, 2006-2008 (2006).
[CrossRef] [PubMed]

D. W. Sukow, A. Gavrielides, T. McLachlan, G. Burner, J. Amonette, and J. Miller, "Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields," Phys. Rev. A 74, 023812 (2006).
[CrossRef]

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, "Stable polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 72, 2355-2357 (1998).
[CrossRef]

Georgievski, A.

Guth, G. D.

Z. G. Pan, S. J. 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]

Hohl, A.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, "Stable polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 72, 2355-2357 (1998).
[CrossRef]

Hong, Y.

Hou, H.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, "Stable polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 72, 2355-2357 (1998).
[CrossRef]

Javaloyes, J.

J. Javaloyes, J. Mulet, and S. Balle, "Passive mode locking of lasers by crossed-polarization gain modulation," Phys. Rev. Lett. 97, 163902 (2006).
[CrossRef] [PubMed]

Jiang, S. J.

Z. G. Pan, S. J. 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]

S. J. Jiang, Z. Q. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, "High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 63, 3545-3547 (1993).
[CrossRef]

Ju, R.

Kajita, M.

T. Yoshikawa, T. Kawakami, H. Saito, H. Kosaka, M. Kajita, K. Kurihara, Y. Sugimoto, and K. Kasahara, "Polarization-controlled single-mode VCSEL," IEEE J. Quantum Electron. 34, 1009-1015 (1998).
[CrossRef]

Kakuma, S.

S. Kakuma and R. Ohba, "Practical accurate optical ranging based on polarization self modulation of a vertical-cavity surface-emitting laser diode," Opt. Rev. 10, 511-513 (2003).
[CrossRef]

Kasahara, K.

T. Yoshikawa, T. Kawakami, H. Saito, H. Kosaka, M. Kajita, K. Kurihara, Y. Sugimoto, and K. Kasahara, "Polarization-controlled single-mode VCSEL," IEEE J. Quantum Electron. 34, 1009-1015 (1998).
[CrossRef]

Kawakami, T.

T. Yoshikawa, T. Kawakami, H. Saito, H. Kosaka, M. Kajita, K. Kurihara, Y. Sugimoto, and K. Kasahara, "Polarization-controlled single-mode VCSEL," IEEE J. Quantum Electron. 34, 1009-1015 (1998).
[CrossRef]

Kojima, K.

S. J. Jiang, Z. Q. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, "High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 63, 3545-3547 (1993).
[CrossRef]

Z. G. Pan, S. J. 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]

Kosaka, H.

T. Yoshikawa, T. Kawakami, H. Saito, H. Kosaka, M. Kajita, K. Kurihara, Y. Sugimoto, and K. Kasahara, "Polarization-controlled single-mode VCSEL," IEEE J. Quantum Electron. 34, 1009-1015 (1998).
[CrossRef]

Kurihara, K.

T. Yoshikawa, T. Kawakami, H. Saito, H. Kosaka, M. Kajita, K. Kurihara, Y. Sugimoto, and K. Kasahara, "Polarization-controlled single-mode VCSEL," IEEE J. Quantum Electron. 34, 1009-1015 (1998).
[CrossRef]

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]

Lee, M. W.

M. W. Lee, Y. Hong, and K. A. Shore, "Experimental demonstration of VCSEL-based chaotic optical communications," IEEE Photon. Technol. Lett. 16, 2392-2394 (2004).
[CrossRef]

Y. Hong, M. W. Lee, P. S. Spencer, and K. A. Shore, "Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers," Opt. Lett. 29, 1215-1217 (2004).
[CrossRef] [PubMed]

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]

Z. G. Pan, S. J. 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, H.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, "Stable polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 72, 2355-2357 (1998).
[CrossRef]

Luo, B.

W. L. Zhang, W. Pan, B. Luo, X. H. Zou, and M. Y. Wang, "Polarization dynamics of vertical-cavity surface-emitting lasers with optical feedback," Opt. Eng. (Bellingham) 45, 114202 (2006).
[CrossRef]

Martin-Regalado, J.

Masoller, C.

McLachlan, T.

D. W. Sukow, A. Gavrielides, T. McLachlan, G. Burner, J. Amonette, and J. Miller, "Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields," Phys. Rev. A 74, 023812 (2006).
[CrossRef]

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, "Square-wave self-modulation in diode lasers with polarization-rotated optical feedback," Opt. Lett. 31, 2006-2008 (2006).
[CrossRef] [PubMed]

Megret, P.

Miller, J.

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, "Square-wave self-modulation in diode lasers with polarization-rotated optical feedback," Opt. Lett. 31, 2006-2008 (2006).
[CrossRef] [PubMed]

D. W. Sukow, A. Gavrielides, T. McLachlan, G. Burner, J. Amonette, and J. Miller, "Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields," Phys. Rev. A 74, 023812 (2006).
[CrossRef]

Milster, T. D.

T. H. Russell and T. D. Milster, "Polarization switching control in VCSELs," Appl. Phys. Lett. 70, 2520-2522 (1997).
[CrossRef]

Mirasso, C. R.

A. Scire, J. Mulet, C. R. Mirasso, J. Danckaert, and M. San Miguel, "Polarization message encoding through vectorial chaos synchronization in vertical-cavity surface-emitting lasers," Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

Morgan, R. A.

Z. G. Pan, S. J. 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]

S. J. Jiang, Z. Q. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, "High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 63, 3545-3547 (1993).
[CrossRef]

Mulet, J.

J. Javaloyes, J. Mulet, and S. Balle, "Passive mode locking of lasers by crossed-polarization gain modulation," Phys. Rev. Lett. 97, 163902 (2006).
[CrossRef] [PubMed]

A. Scire, J. Mulet, C. R. Mirasso, J. Danckaert, and M. San Miguel, "Polarization message encoding through vectorial chaos synchronization in vertical-cavity surface-emitting lasers," Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

Ohba, R.

S. Kakuma and R. Ohba, "Practical accurate optical ranging based on polarization self modulation of a vertical-cavity surface-emitting laser diode," Opt. Rev. 10, 511-513 (2003).
[CrossRef]

Pan, W.

W. L. Zhang, W. Pan, B. Luo, X. H. Zou, and M. Y. Wang, "Polarization dynamics of vertical-cavity surface-emitting lasers with optical feedback," Opt. Eng. (Bellingham) 45, 114202 (2006).
[CrossRef]

Pan, Z. G.

Z. G. Pan, S. J. 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]

Pan, Z. Q.

S. J. Jiang, Z. Q. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, "High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 63, 3545-3547 (1993).
[CrossRef]

Panajotov, K.

Paul, J.

Peeters, M.

Pesquera, L.

A. Valle, L. Pesquera, and K. A. Shore, "Polarization selection and sensitivity of external cavity vertical-cavity surface-emitting laser diodes," IEEE Photon. Technol. Lett. 10, 639-641 (1998).
[CrossRef]

A. Valle, L. Pesquera, and K. A. Shore, "Polarization behavior of birefringent multitransverse mode vertical-cavity surface-emitting lasers," IEEE Photon. Technol. Lett. 9, 557-559 (1997).
[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]

Robert, F.

Rogister, F.

Roy, R.

G. D. VanWiggeren and R. Roy, "Communication with dynamically fluctuating states of light polarization," Phys. Rev. Lett. 88, 097903 (2002).
[CrossRef] [PubMed]

Russell, T. H.

T. H. Russell and T. D. Milster, "Polarization switching control in VCSELs," Appl. Phys. Lett. 70, 2520-2522 (1997).
[CrossRef]

Ryvkin, B.

Saito, H.

T. Yoshikawa, T. Kawakami, H. Saito, H. Kosaka, M. Kajita, K. Kurihara, Y. Sugimoto, and K. Kasahara, "Polarization-controlled single-mode VCSEL," IEEE J. Quantum Electron. 34, 1009-1015 (1998).
[CrossRef]

San Miguel, M.

A. Scire, J. Mulet, C. R. Mirasso, J. Danckaert, and M. San Miguel, "Polarization message encoding through vectorial chaos synchronization in vertical-cavity surface-emitting lasers," Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

S. Balle, E. Tolkachova, M. San Miguel, J. R. Tredicce, J. Martin-Regalado, and A. Gahl, "Mechanisms of polarization switching in single-transverse-mode vertical-cavity surface-emitting lasers: thermal shift and nonlinear semiconductor dynamics," Opt. Lett. 24, 1121-1123 (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]

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.

Scire, A.

A. Scire, J. Mulet, C. R. Mirasso, J. Danckaert, and M. San Miguel, "Polarization message encoding through vectorial chaos synchronization in vertical-cavity surface-emitting lasers," Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

Shore, K. A.

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, 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. W. Lee, Y. Hong, and K. A. Shore, "Experimental demonstration of VCSEL-based chaotic optical communications," IEEE Photon. Technol. Lett. 16, 2392-2394 (2004).
[CrossRef]

Y. Hong, M. W. Lee, P. S. Spencer, and K. A. Shore, "Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers," Opt. Lett. 29, 1215-1217 (2004).
[CrossRef] [PubMed]

A. Valle, L. Pesquera, and K. A. Shore, "Polarization selection and sensitivity of external cavity vertical-cavity surface-emitting laser diodes," IEEE Photon. Technol. Lett. 10, 639-641 (1998).
[CrossRef]

A. Valle, L. Pesquera, and K. A. Shore, "Polarization behavior of birefringent multitransverse mode vertical-cavity surface-emitting lasers," IEEE Photon. Technol. Lett. 9, 557-559 (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.

Stephan, G.

Sugimoto, Y.

T. Yoshikawa, T. Kawakami, H. Saito, H. Kosaka, M. Kajita, K. Kurihara, Y. Sugimoto, and K. Kasahara, "Polarization-controlled single-mode VCSEL," IEEE J. Quantum Electron. 34, 1009-1015 (1998).
[CrossRef]

Sukow, D. W.

D. W. Sukow, A. Gavrielides, T. McLachlan, G. Burner, J. Amonette, and J. Miller, "Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields," Phys. Rev. A 74, 023812 (2006).
[CrossRef]

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, "Square-wave self-modulation in diode lasers with polarization-rotated optical feedback," Opt. Lett. 31, 2006-2008 (2006).
[CrossRef] [PubMed]

Thienpont, H.

Tolkachova, E.

Tredicce, J. R.

Valle, A.

A. Valle, L. Pesquera, and K. A. Shore, "Polarization selection and sensitivity of external cavity vertical-cavity surface-emitting laser diodes," IEEE Photon. Technol. Lett. 10, 639-641 (1998).
[CrossRef]

A. Valle, L. Pesquera, and K. A. Shore, "Polarization behavior of birefringent multitransverse mode vertical-cavity surface-emitting lasers," IEEE Photon. Technol. Lett. 9, 557-559 (1997).
[CrossRef]

VanWiggeren, G. D.

G. D. VanWiggeren and R. Roy, "Communication with dynamically fluctuating states of light polarization," Phys. Rev. Lett. 88, 097903 (2002).
[CrossRef] [PubMed]

Veretennicoff, I.

Verschaffelt, G.

Wang, M. Y.

W. L. Zhang, W. Pan, B. Luo, X. H. Zou, and M. Y. Wang, "Polarization dynamics of vertical-cavity surface-emitting lasers with optical feedback," Opt. Eng. (Bellingham) 45, 114202 (2006).
[CrossRef]

Yoshikawa, T.

T. Yoshikawa, T. Kawakami, H. Saito, H. Kosaka, M. Kajita, K. Kurihara, Y. Sugimoto, and K. Kasahara, "Polarization-controlled single-mode VCSEL," IEEE J. Quantum Electron. 34, 1009-1015 (1998).
[CrossRef]

Zhang, W. L.

W. L. Zhang, W. Pan, B. Luo, X. H. Zou, and M. Y. Wang, "Polarization dynamics of vertical-cavity surface-emitting lasers with optical feedback," Opt. Eng. (Bellingham) 45, 114202 (2006).
[CrossRef]

Zou, X. H.

W. L. Zhang, W. Pan, B. Luo, X. H. Zou, and M. Y. Wang, "Polarization dynamics of vertical-cavity surface-emitting lasers with optical feedback," Opt. Eng. (Bellingham) 45, 114202 (2006).
[CrossRef]

Appl. Phys. Lett. (5)

Z. G. Pan, S. J. 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]

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]

T. H. Russell and T. D. Milster, "Polarization switching control in VCSELs," Appl. Phys. Lett. 70, 2520-2522 (1997).
[CrossRef]

S. J. Jiang, Z. Q. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, "High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 63, 3545-3547 (1993).
[CrossRef]

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, "Stable polarization self-modulation in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 72, 2355-2357 (1998).
[CrossRef]

IEEE J. Quantum Electron. (2)

T. Yoshikawa, T. Kawakami, H. Saito, H. Kosaka, M. Kajita, K. Kurihara, Y. Sugimoto, and K. Kasahara, "Polarization-controlled single-mode VCSEL," IEEE J. Quantum Electron. 34, 1009-1015 (1998).
[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]

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]

IEEE Photon. Technol. Lett. (3)

A. Valle, L. Pesquera, and K. A. Shore, "Polarization behavior of birefringent multitransverse mode vertical-cavity surface-emitting lasers," IEEE Photon. Technol. Lett. 9, 557-559 (1997).
[CrossRef]

A. Valle, L. Pesquera, and K. A. Shore, "Polarization selection and sensitivity of external cavity vertical-cavity surface-emitting laser diodes," IEEE Photon. Technol. Lett. 10, 639-641 (1998).
[CrossRef]

M. W. Lee, Y. Hong, and K. A. Shore, "Experimental demonstration of VCSEL-based chaotic optical communications," IEEE Photon. Technol. Lett. 16, 2392-2394 (2004).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Eng. (Bellingham) (1)

W. L. Zhang, W. Pan, B. Luo, X. H. Zou, and M. Y. Wang, "Polarization dynamics of vertical-cavity surface-emitting lasers with optical feedback," Opt. Eng. (Bellingham) 45, 114202 (2006).
[CrossRef]

Opt. Lett. (7)

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, "Square-wave self-modulation in diode lasers with polarization-rotated optical feedback," Opt. Lett. 31, 2006-2008 (2006).
[CrossRef] [PubMed]

M. Sciamanna, F. Rogister, O. Deparis, P. Megret, M. Blondel, and T. Erneux, "Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers," Opt. Lett. 27, 261-263 (2002).
[CrossRef]

S. Balle, E. Tolkachova, M. San Miguel, J. R. Tredicce, J. Martin-Regalado, and A. Gahl, "Mechanisms of polarization switching in single-transverse-mode vertical-cavity surface-emitting lasers: thermal shift and nonlinear semiconductor dynamics," Opt. Lett. 24, 1121-1123 (1999)
[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]

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

Y. Hong, M. W. Lee, P. S. Spencer, and K. A. Shore, "Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers," Opt. Lett. 29, 1215-1217 (2004).
[CrossRef] [PubMed]

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]

Opt. Rev. (1)

S. Kakuma and R. Ohba, "Practical accurate optical ranging based on polarization self modulation of a vertical-cavity surface-emitting laser diode," Opt. Rev. 10, 511-513 (2003).
[CrossRef]

Phys. Rev. A (1)

D. W. Sukow, A. Gavrielides, T. McLachlan, G. Burner, J. Amonette, and J. Miller, "Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields," Phys. Rev. A 74, 023812 (2006).
[CrossRef]

Phys. Rev. Lett. (3)

J. Javaloyes, J. Mulet, and S. Balle, "Passive mode locking of lasers by crossed-polarization gain modulation," Phys. Rev. Lett. 97, 163902 (2006).
[CrossRef] [PubMed]

G. D. VanWiggeren and R. Roy, "Communication with dynamically fluctuating states of light polarization," Phys. Rev. Lett. 88, 097903 (2002).
[CrossRef] [PubMed]

A. Scire, J. Mulet, C. R. Mirasso, J. Danckaert, and M. San Miguel, "Polarization message encoding through vectorial chaos synchronization in vertical-cavity surface-emitting lasers," Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

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Figures (14)

Fig. 1
Fig. 1

Schematic of experimental setup arrangement. BS, beam splitter; NDF, neutral-density filter; FAR ROT, Faraday rotator; POL, polarizer; M1, M2, mirrors; HWP, half-wave plate; PBS, polarization beam splitter; ISO1, ISO2, optical isolators; D1, D2, photodetectors; OSC, oscilloscope.

Fig. 2
Fig. 2

Polarization-resolved L I curve. (a) First VCSEL. (b) Second VCSEL. The polarization selected at threshold ( x ) is indicated with a black curve, the orthogonal polarization ( y ) is indicated with a gray curve.

Fig. 3
Fig. 3

Polarization-resolved L I characteristic measured experimentally for the (a) free-running laser, (b)–(j) laser with X-orthogonal feedback. The polarization selected at threshold ( X ) is indicated with a black curve, the orthogonal polarization ( Y ) is indicated with a gray curve. The feedback ratios are 22 , 19 , 17.6 , 15.4 , 13.1 , 12.2 , 11 , 9.9 , and 9 dB , respectively.

Fig. 4
Fig. 4

Polarization-resolved L I characteristic measured experimentally for the (a) free-running laser, (b)–(j) laser with Y-orthogonal feedback. The feedback ratios are 22 , 19 , 17.6 , 15.4 , 13.1 , 12.2 , 11 , 9.9 , and 9 dB , respectively.

Fig. 5
Fig. 5

Polarization-resolved L I characteristic measured experimentally for the (a) free-running laser, (b)–(j) laser with polarization preserved feedback. The feedback ratios are 21 , 18.6 , 16.5 , 14.3 , 12.3 , 11.1 , 9.9 , 8.9 , and 7.9 dB , respectively.

Fig. 6
Fig. 6

Influence of X-orthogonal feedback on the second VCSEL device. (a) Free-running laser, (b)–(j) the feedback ratios are 22 , 19 , 17.6 , 15.4 , 13.1 , 12.2 , 11 , 9.9 , and 9 dB , respectively. The polarization selected at threshold ( X ) is indicated with a black curve, the orthogonal polarization ( Y ) is indicated with a gray curve.

Fig. 7
Fig. 7

Influence of Y-orthogonal feedback on the second VCSEL device. (a) Free-running laser, (b)–(j) the feedback ratios are 22 , 19 , 17.6 , 15.4 , 13.1 , 12.2 , 11 , 9.9 , and 9 dB , respectively.

Fig. 8
Fig. 8

Influence of polarization-preserved feedback on the second VCSEL device. (a) Free-running laser, (b)–(j) the feedback ratios are 21 , 18.6 , 16.5 , 14.3 , 12.3 , 11.1 , 9.9 , 8.9 , and 7.9 dB , respectively.

Fig. 9
Fig. 9

Influence of x-orthogonal feedback, for parameters describing the first VCSEL device used in the experiments: γ p = 70 rad ns , other parameters as explained in the text. (a) Free-running laser. (b)–(j) η y 2 increases linearly as η y 2 = a η m 2 , with η m = 70 GHz and a=(a) 0.1 to (j) 1.0. The polarization selected at threshold ( y ) is indicated with a black curve, the orthogonal polarization ( x ) is indicated with a gray curve.

Fig. 10
Fig. 10

Influence of y-orthogonal feedback. (a) Free-running laser. (b)–(j) η x 2 increases linearly: η x 2 = a η m 2 , with η m = 70 GHz and a=(a) 0.1 to (j) 1.0. Other parameters are as in Fig. 9.

Fig. 11
Fig. 11

Influence of polarization-preserved feedback. (a) Free-running laser. (b)–(j) η 2 increases linearly: η 2 = a η m 2 with η m = 7 GHz and a=(a) 0.1 to (j) 1.0. Other parameters are as in Fig. 9.

Fig. 12
Fig. 12

Influence of x-orthogonal feedback for parameters corresponding to type-II PS. γ p = 5 rad ns , γ a = 0.3 ns 1 , and γ s = 50 ns 1 ; other parameters as described in the text. (a) Free-running laser. (b)–(j) η y 2 increases linearly: η y 2 = a η m 2 with η m = 5 GHz and a=from (a) 0.1 to (j) 1.0. The polarization selected at threshold ( x ) is indicated with a black curve, the orthogonal polarization ( y ) is indicated with a gray curve.

Fig. 13
Fig. 13

Influence of y-orthogonal feedback for parameters corresponding to type-II PS. (a) Free-running laser. (b)–(j) η x 2 increases linearly: η x 2 = a η m 2 with η m = 5 GHz and a=(a) 0.1 to (j) 1.0. Other parameters are as in Fig. 12.

Fig. 14
Fig. 14

Influence of polarization-preserved feedback for parameters corresponding to type-II PS. (a) Free-running laser. (b)–(j) η 2 increases linearly: η 2 = a η m 2 with η m = 3 GHz and a=(a) 0.1 to (j) 1.0. Other parameters are as in Fig. 12.

Equations (4)

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E ̇ x , y = k ( 1 + j α ) [ ( N 1 ) E x , y ± j n E y , x ] ( γ a + j γ p ) E x , y + β s p ξ x , y + η x , y E y , x ( t τ ) e i ω τ + η E x , y ( t τ ) e i ω τ ,
N ̇ = γ N [ μ N ( 1 + E x 2 + E y 2 ) + j n ( E y E x * E x E y * ) ] ,
n ̇ = γ s n γ N [ n ( E x 2 + E y 2 ) + j N ( E y E x * E x E y * ) ] .
λ x , y = λ x , y , t h + A J t h ( μ 1 ) ,

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