Abstract

We present a comprehensive study of the bifurcation routes in a generic model of a two-polarization-mode semiconductor laser when subject to orthogonal optical injection, relevant to a single-transverse-mode vertical-cavity surface-emitting laser. For positive detunings, polarization switching (PS) occurs as the intensity of the noninjected mode gradually decreases and eventually shuts down, in some cases accompanied along the way by the onset and the subsequent vanishing of relaxation oscillations. We identify a Hopf bifurcation on a two-polarization-mode solution, which supports the onset of relaxation oscillation time-periodic dynamics in both injected (x-linearly polarized) and noninjected (y-linearly polarized) modes. For sufficiently large negative detunings, PS is a sharp transition occurring either at the injection-locking point or at a subcritical Hopf bifurcation and is often part of a hysteresis cycle.

© 2009 Optical Society of America

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  1. V. Kovanis, A. Gavrielides, T. Simpson, and J. M. Liu, “Instabilities and chaos in optically injected semiconductor lasers,” Appl. Phys. Lett. 67, 2780-2782 (1995).
    [CrossRef]
  2. T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclassic. Opt. 9, 765-784 (1997).
    [CrossRef]
  3. S. Wieczorek, B. Krauskopf, and D. Lenstra, “A unifying view of bifurcations in a semiconductor laser subject to optical injection,” Opt. Commun. 172, 279-295 (1999).
    [CrossRef]
  4. S. Piazzolla, P. Spano, and M. Tamburrini, “Small signal analysis of frequency chirping in injection-locked semiconductor lasers,” IEEE J. Quantum Electron. 22, 2219-2223 (1986).
    [CrossRef]
  5. J. M. Liu, H. Chen, X. Meng, and T. Simpson, “Modulation bandwidth, noise, and stability of a semiconductor laser subject to strong injection locking,” IEEE Photon. Technol. Lett. 9, 1325-1327 (1997).
    [CrossRef]
  6. X. J. Meng, T. Chau, and M. C. Wu, “Experimental demonstration of modulation bandwidth enhancement in distributed feedback lasers with external light injection,” Electron. Lett. 34, 2031-2032 (1998).
    [CrossRef]
  7. P. K. A. Wai, L. Xu, L. F. K. Lui, L. Y. Chan, and C. C. Lee, “All-optical add-drop node for optical packet-switched networks,” Opt. Lett. 30, 1515-1517 (2005).
    [CrossRef] [PubMed]
  8. S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber AM-to-FM upconversion using an optically injected semiconductor laser,” Opt. Lett. 31, 2254-2256 (2006).
    [CrossRef] [PubMed]
  9. K. Choquette, D. Richie, and R. Leibenguth, “Temperature dependence of gain-guided vertical-cavity surface emitting laser polarization,” Appl. Phys. Lett. 64, 2062-2064 (1994).
    [CrossRef]
  10. 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]
  11. K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B. Ryvkin, H. Thienpont, and I. Veretennicoff, “Polarization behavior of vertical-cavity surface-emitting lasers: experiments, models and applications,” AIP Conf. Proc. 560, 403-417 (2001).
    [CrossRef]
  12. M. Sciamanna, A. Valle, P. Mégret, M. Blondel, and K. Panajotov, “Nonlinear polarization dynamics in directly modulated vertical-cavity surface-emitting lasers,” Phys. Rev. E 68, 016207 (2003).
    [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]
  14. M. Arizaleta Arteaga, M. López-Amo, H. Thienpont, and K. Panajotov, “Role of external cavity reflectivity for achieving polarization control and stabilization of vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 90, 031117 (2007).
    [CrossRef]
  15. 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]
  16. H. Kawaguchi, “Bistable laser diodes and their applications: state of the art,” IEEE J. Sel. Top. Quantum Electron. 3, 1254-1270 (1997).
    [CrossRef]
  17. J. Buesa Altés, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42, 198-207 (2006).
    [CrossRef]
  18. 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]
  19. 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]
  20. M. Sciamanna, “Nonlinear dynamics and polarization properties of externally driven semiconductor lasers,” Ph.D. dissertation (Mons Engineering Faculty, 2004).
  21. M. P. van Exter, A. Al-Remawi, and J. P. Woerdman, “Polarization fluctuations demonstrate nonlinear anisotropy of a vertical-cavity semiconductor laser,” Phys. Rev. Lett. 80, 4875-4878 (1998).
    [CrossRef]
  22. M. Sciamanna and K. Panajotov, “Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers,” Phys. Rev. A 73, 023811 (2006).
    [CrossRef]
  23. K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization and transverse-mode dynamics in optically-injected and gain-switched vertical-cavity surface-emitting lasers” IEEE J. Quantum Electron. (accepted for publication).
  24. I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
    [CrossRef]
  25. M. Sciamanna, I. Gatare, and K. Panajotov, in Proceedings of the International Commission for Optics (ICO-21) 2008 Congress, p. 287 (2008).
  26. J. Danckaert, B. Nagler, J. Albert, K. Panajotov, I. Veretennicoff, and T. Erneux, “Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers,” Opt. Commun. 201, 129-137 (2002).
    [CrossRef]
  27. A. Valle, J. Sarma, and K. A. Shore, “Spatial hole burning effect on the dynamic of VCSELs,” IEEE J. Quantum Electron. 31, 1423-1431 (1995).
    [CrossRef]
  28. I. Gatare, M. Sciamanna, M. Nizette, H. Thienpont, and K. Panajotov, “Excitation of a two-mode limit cycle dynamics on the route to polarization switching in a VCSEL subject to orthogonal optical injection,” Proc. SPIE 6997, 699713 (2008).
    [CrossRef]
  29. B. S. Ryvkin, K. Panajotov, E. A. Avrutin, I. Veretennicoff, and H. Thienpont, “Optical-injection-induced polarization switching in polarization-bistable vertical-cavity surface-emitting lasers,” J. Appl. Phys. 96, 6002-6007 (2004).
    [CrossRef]
  30. S. Wieczorek, I. B. Simpson, B. Krauskopf, and D. Lenstra, “Bifurcation transitions in an optically injected diode laser: theory and experiment,” Opt. Commun. 215, 125-134 (2003).
    [CrossRef]
  31. E. J. Doedel, H. B. Keller, and J. P. Kernevez, “Numerical analysis and control of bifurcation problems (I) bifurcation in finite dimensions,” Int. J. Bifurcat. Chaos 1, 493-520 (1991).
    [CrossRef]
  32. S. Wieczorek, I. B. Simpson, B. Krauskopf, and D. Lenstra, “Global quantitative predictions of complex laser dynamics,” Phys. Rev. E 65, 045207(R) (2002).
    [CrossRef]
  33. S. K. Hwang and J. M. Liu, “Dynamical characteristics of an optically injected semiconductor laser,” Opt. Commun. 183, 195-205 (2000).
    [CrossRef]
  34. T. Mori, Y. Yamayoshi, and H. Kawaguchi, “Low-switching-energy and high-repetition-frequency all-optical flip-flop operations of a polarization bistable vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 88, 101102-101104 (2006).
    [CrossRef]

2008 (1)

I. Gatare, M. Sciamanna, M. Nizette, H. Thienpont, and K. Panajotov, “Excitation of a two-mode limit cycle dynamics on the route to polarization switching in a VCSEL subject to orthogonal optical injection,” Proc. SPIE 6997, 699713 (2008).
[CrossRef]

2007 (2)

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
[CrossRef]

M. Arizaleta Arteaga, M. López-Amo, H. Thienpont, and K. Panajotov, “Role of external cavity reflectivity for achieving polarization control and stabilization of vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 90, 031117 (2007).
[CrossRef]

2006 (4)

S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber AM-to-FM upconversion using an optically injected semiconductor laser,” Opt. Lett. 31, 2254-2256 (2006).
[CrossRef] [PubMed]

M. Sciamanna and K. Panajotov, “Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers,” Phys. Rev. A 73, 023811 (2006).
[CrossRef]

T. Mori, Y. Yamayoshi, and H. Kawaguchi, “Low-switching-energy and high-repetition-frequency all-optical flip-flop operations of a polarization bistable vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 88, 101102-101104 (2006).
[CrossRef]

J. Buesa Altés, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42, 198-207 (2006).
[CrossRef]

2005 (1)

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]

B. S. Ryvkin, K. Panajotov, E. A. Avrutin, I. Veretennicoff, and H. Thienpont, “Optical-injection-induced polarization switching in polarization-bistable vertical-cavity surface-emitting lasers,” J. Appl. Phys. 96, 6002-6007 (2004).
[CrossRef]

2003 (2)

S. Wieczorek, I. B. Simpson, B. Krauskopf, and D. Lenstra, “Bifurcation transitions in an optically injected diode laser: theory and experiment,” Opt. Commun. 215, 125-134 (2003).
[CrossRef]

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

2002 (2)

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

S. Wieczorek, I. B. Simpson, B. Krauskopf, and D. Lenstra, “Global quantitative predictions of complex laser dynamics,” Phys. Rev. E 65, 045207(R) (2002).
[CrossRef]

2001 (2)

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]

K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B. Ryvkin, H. Thienpont, and I. Veretennicoff, “Polarization behavior of vertical-cavity surface-emitting lasers: experiments, models and applications,” AIP Conf. Proc. 560, 403-417 (2001).
[CrossRef]

2000 (1)

S. K. Hwang and J. M. Liu, “Dynamical characteristics of an optically injected semiconductor laser,” Opt. Commun. 183, 195-205 (2000).
[CrossRef]

1999 (1)

S. Wieczorek, B. Krauskopf, and D. Lenstra, “A unifying view of bifurcations in a semiconductor laser subject to optical injection,” Opt. Commun. 172, 279-295 (1999).
[CrossRef]

1998 (2)

X. J. Meng, T. Chau, and M. C. Wu, “Experimental demonstration of modulation bandwidth enhancement in distributed feedback lasers with external light injection,” Electron. Lett. 34, 2031-2032 (1998).
[CrossRef]

M. P. van Exter, A. Al-Remawi, and J. P. Woerdman, “Polarization fluctuations demonstrate nonlinear anisotropy of a vertical-cavity semiconductor laser,” Phys. Rev. Lett. 80, 4875-4878 (1998).
[CrossRef]

1997 (4)

J. M. Liu, H. Chen, X. Meng, and T. Simpson, “Modulation bandwidth, noise, and stability of a semiconductor laser subject to strong injection locking,” IEEE Photon. Technol. Lett. 9, 1325-1327 (1997).
[CrossRef]

T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclassic. Opt. 9, 765-784 (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]

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

1995 (3)

V. Kovanis, A. Gavrielides, T. Simpson, and J. M. Liu, “Instabilities and chaos in optically injected semiconductor lasers,” Appl. Phys. Lett. 67, 2780-2782 (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]

A. Valle, J. Sarma, and K. A. Shore, “Spatial hole burning effect on the dynamic of VCSELs,” IEEE J. Quantum Electron. 31, 1423-1431 (1995).
[CrossRef]

1994 (1)

K. Choquette, D. Richie, and R. Leibenguth, “Temperature dependence of gain-guided vertical-cavity surface emitting laser polarization,” Appl. Phys. Lett. 64, 2062-2064 (1994).
[CrossRef]

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]

1991 (1)

E. J. Doedel, H. B. Keller, and J. P. Kernevez, “Numerical analysis and control of bifurcation problems (I) bifurcation in finite dimensions,” Int. J. Bifurcat. Chaos 1, 493-520 (1991).
[CrossRef]

1986 (1)

S. Piazzolla, P. Spano, and M. Tamburrini, “Small signal analysis of frequency chirping in injection-locked semiconductor lasers,” IEEE J. Quantum Electron. 22, 2219-2223 (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]

Albert, J.

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

K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B. Ryvkin, H. Thienpont, and I. Veretennicoff, “Polarization behavior of vertical-cavity surface-emitting lasers: experiments, models and applications,” AIP Conf. Proc. 560, 403-417 (2001).
[CrossRef]

Al-Remawi, A.

M. P. van Exter, A. Al-Remawi, and J. P. Woerdman, “Polarization fluctuations demonstrate nonlinear anisotropy of a vertical-cavity semiconductor laser,” Phys. Rev. Lett. 80, 4875-4878 (1998).
[CrossRef]

Arizaleta Arteaga, M.

M. Arizaleta Arteaga, M. López-Amo, H. Thienpont, and K. Panajotov, “Role of external cavity reflectivity for achieving polarization control and stabilization of vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 90, 031117 (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]

Avrutin, E. A.

B. S. Ryvkin, K. Panajotov, E. A. Avrutin, I. Veretennicoff, and H. Thienpont, “Optical-injection-induced polarization switching in polarization-bistable vertical-cavity surface-emitting lasers,” J. Appl. Phys. 96, 6002-6007 (2004).
[CrossRef]

Blondel, M.

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

Buesa Altés, J.

J. Buesa Altés, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42, 198-207 (2006).
[CrossRef]

Chan, L. Y.

Chan, S. C.

Chau, T.

X. J. Meng, T. Chau, and M. C. Wu, “Experimental demonstration of modulation bandwidth enhancement in distributed feedback lasers with external light injection,” Electron. Lett. 34, 2031-2032 (1998).
[CrossRef]

Chen, H.

J. M. Liu, H. Chen, X. Meng, and T. Simpson, “Modulation bandwidth, noise, and stability of a semiconductor laser subject to strong injection locking,” IEEE Photon. Technol. Lett. 9, 1325-1327 (1997).
[CrossRef]

Choquette, K.

K. Choquette, D. Richie, and R. Leibenguth, “Temperature dependence of gain-guided vertical-cavity surface emitting laser polarization,” Appl. Phys. Lett. 64, 2062-2064 (1994).
[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.

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

K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B. Ryvkin, H. Thienpont, and I. Veretennicoff, “Polarization behavior of vertical-cavity surface-emitting lasers: experiments, models and applications,” AIP Conf. Proc. 560, 403-417 (2001).
[CrossRef]

Doedel, E. J.

E. J. Doedel, H. B. Keller, and J. P. Kernevez, “Numerical analysis and control of bifurcation problems (I) bifurcation in finite dimensions,” Int. J. Bifurcat. Chaos 1, 493-520 (1991).
[CrossRef]

Erneux, T.

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

Gatare, I.

I. Gatare, M. Sciamanna, M. Nizette, H. Thienpont, and K. Panajotov, “Excitation of a two-mode limit cycle dynamics on the route to polarization switching in a VCSEL subject to orthogonal optical injection,” Proc. SPIE 6997, 699713 (2008).
[CrossRef]

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
[CrossRef]

J. Buesa Altés, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42, 198-207 (2006).
[CrossRef]

M. Sciamanna, I. Gatare, and K. Panajotov, in Proceedings of the International Commission for Optics (ICO-21) 2008 Congress, p. 287 (2008).

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization and transverse-mode dynamics in optically-injected and gain-switched vertical-cavity surface-emitting lasers” IEEE J. Quantum Electron. (accepted for publication).

Gavrielides, A.

V. Kovanis, A. Gavrielides, T. Simpson, and J. M. Liu, “Instabilities and chaos in optically injected semiconductor lasers,” Appl. Phys. Lett. 67, 2780-2782 (1995).
[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]

Hong, Y.

Huang, K. F.

T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclassic. Opt. 9, 765-784 (1997).
[CrossRef]

Hwang, S. K.

S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber AM-to-FM upconversion using an optically injected semiconductor laser,” Opt. Lett. 31, 2254-2256 (2006).
[CrossRef] [PubMed]

S. K. Hwang and J. M. Liu, “Dynamical characteristics of an optically injected semiconductor laser,” Opt. Commun. 183, 195-205 (2000).
[CrossRef]

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]

Kawaguchi, H.

T. Mori, Y. Yamayoshi, and H. Kawaguchi, “Low-switching-energy and high-repetition-frequency all-optical flip-flop operations of a polarization bistable vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 88, 101102-101104 (2006).
[CrossRef]

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

Keller, H. B.

E. J. Doedel, H. B. Keller, and J. P. Kernevez, “Numerical analysis and control of bifurcation problems (I) bifurcation in finite dimensions,” Int. J. Bifurcat. Chaos 1, 493-520 (1991).
[CrossRef]

Kernevez, J. P.

E. J. Doedel, H. B. Keller, and J. P. Kernevez, “Numerical analysis and control of bifurcation problems (I) bifurcation in finite dimensions,” Int. J. Bifurcat. Chaos 1, 493-520 (1991).
[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]

Kovanis, V.

V. Kovanis, A. Gavrielides, T. Simpson, and J. M. Liu, “Instabilities and chaos in optically injected semiconductor lasers,” Appl. Phys. Lett. 67, 2780-2782 (1995).
[CrossRef]

Krauskopf, B.

S. Wieczorek, I. B. Simpson, B. Krauskopf, and D. Lenstra, “Bifurcation transitions in an optically injected diode laser: theory and experiment,” Opt. Commun. 215, 125-134 (2003).
[CrossRef]

S. Wieczorek, I. B. Simpson, B. Krauskopf, and D. Lenstra, “Global quantitative predictions of complex laser dynamics,” Phys. Rev. E 65, 045207(R) (2002).
[CrossRef]

S. Wieczorek, B. Krauskopf, and D. Lenstra, “A unifying view of bifurcations in a semiconductor laser subject to optical injection,” Opt. Commun. 172, 279-295 (1999).
[CrossRef]

Lee, C. C.

Leibenguth, R.

K. Choquette, D. Richie, and R. Leibenguth, “Temperature dependence of gain-guided vertical-cavity surface emitting laser polarization,” Appl. Phys. Lett. 64, 2062-2064 (1994).
[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]

Lenstra, D.

S. Wieczorek, I. B. Simpson, B. Krauskopf, and D. Lenstra, “Bifurcation transitions in an optically injected diode laser: theory and experiment,” Opt. Commun. 215, 125-134 (2003).
[CrossRef]

S. Wieczorek, I. B. Simpson, B. Krauskopf, and D. Lenstra, “Global quantitative predictions of complex laser dynamics,” Phys. Rev. E 65, 045207(R) (2002).
[CrossRef]

S. Wieczorek, B. Krauskopf, and D. Lenstra, “A unifying view of bifurcations in a semiconductor laser subject to optical injection,” Opt. Commun. 172, 279-295 (1999).
[CrossRef]

Liu, J. M.

S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber AM-to-FM upconversion using an optically injected semiconductor laser,” Opt. Lett. 31, 2254-2256 (2006).
[CrossRef] [PubMed]

S. K. Hwang and J. M. Liu, “Dynamical characteristics of an optically injected semiconductor laser,” Opt. Commun. 183, 195-205 (2000).
[CrossRef]

J. M. Liu, H. Chen, X. Meng, and T. Simpson, “Modulation bandwidth, noise, and stability of a semiconductor laser subject to strong injection locking,” IEEE Photon. Technol. Lett. 9, 1325-1327 (1997).
[CrossRef]

T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclassic. Opt. 9, 765-784 (1997).
[CrossRef]

V. Kovanis, A. Gavrielides, T. Simpson, and J. M. Liu, “Instabilities and chaos in optically injected semiconductor lasers,” Appl. Phys. Lett. 67, 2780-2782 (1995).
[CrossRef]

López-Amo, M.

M. Arizaleta Arteaga, M. López-Amo, H. Thienpont, and K. Panajotov, “Role of external cavity reflectivity for achieving polarization control and stabilization of vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 90, 031117 (2007).
[CrossRef]

Lui, L. F. K.

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]

Mégret, P.

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

Meng, X.

J. M. Liu, H. Chen, X. Meng, and T. Simpson, “Modulation bandwidth, noise, and stability of a semiconductor laser subject to strong injection locking,” IEEE Photon. Technol. Lett. 9, 1325-1327 (1997).
[CrossRef]

Meng, X. J.

X. J. Meng, T. Chau, and M. C. Wu, “Experimental demonstration of modulation bandwidth enhancement in distributed feedback lasers with external light injection,” Electron. Lett. 34, 2031-2032 (1998).
[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]

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]

Mori, T.

T. Mori, Y. Yamayoshi, and H. Kawaguchi, “Low-switching-energy and high-repetition-frequency all-optical flip-flop operations of a polarization bistable vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 88, 101102-101104 (2006).
[CrossRef]

Nagler, B.

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

K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B. Ryvkin, H. Thienpont, and I. Veretennicoff, “Polarization behavior of vertical-cavity surface-emitting lasers: experiments, models and applications,” AIP Conf. Proc. 560, 403-417 (2001).
[CrossRef]

Nizette, M.

I. Gatare, M. Sciamanna, M. Nizette, H. Thienpont, and K. Panajotov, “Excitation of a two-mode limit cycle dynamics on the route to polarization switching in a VCSEL subject to orthogonal optical injection,” Proc. SPIE 6997, 699713 (2008).
[CrossRef]

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
[CrossRef]

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, M. Sciamanna, M. Nizette, H. Thienpont, and K. Panajotov, “Excitation of a two-mode limit cycle dynamics on the route to polarization switching in a VCSEL subject to orthogonal optical injection,” Proc. SPIE 6997, 699713 (2008).
[CrossRef]

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
[CrossRef]

M. Arizaleta Arteaga, M. López-Amo, H. Thienpont, and K. Panajotov, “Role of external cavity reflectivity for achieving polarization control and stabilization of vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 90, 031117 (2007).
[CrossRef]

J. Buesa Altés, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42, 198-207 (2006).
[CrossRef]

M. Sciamanna and K. Panajotov, “Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers,” Phys. Rev. A 73, 023811 (2006).
[CrossRef]

B. S. Ryvkin, K. Panajotov, E. A. Avrutin, I. Veretennicoff, and H. Thienpont, “Optical-injection-induced polarization switching in polarization-bistable vertical-cavity surface-emitting lasers,” J. Appl. Phys. 96, 6002-6007 (2004).
[CrossRef]

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

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

K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B. Ryvkin, H. Thienpont, and I. Veretennicoff, “Polarization behavior of vertical-cavity surface-emitting lasers: experiments, models and applications,” AIP Conf. Proc. 560, 403-417 (2001).
[CrossRef]

M. Sciamanna, I. Gatare, and K. Panajotov, in Proceedings of the International Commission for Optics (ICO-21) 2008 Congress, p. 287 (2008).

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization and transverse-mode dynamics in optically-injected and gain-switched vertical-cavity surface-emitting lasers” IEEE J. Quantum Electron. (accepted for publication).

Peeters, M.

K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B. Ryvkin, H. Thienpont, and I. Veretennicoff, “Polarization behavior of vertical-cavity surface-emitting lasers: experiments, models and applications,” AIP Conf. Proc. 560, 403-417 (2001).
[CrossRef]

Piazzolla, S.

S. Piazzolla, P. Spano, and M. Tamburrini, “Small signal analysis of frequency chirping in injection-locked semiconductor lasers,” IEEE J. Quantum Electron. 22, 2219-2223 (1986).
[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]

Richie, D.

K. Choquette, D. Richie, and R. Leibenguth, “Temperature dependence of gain-guided vertical-cavity surface emitting laser polarization,” Appl. Phys. Lett. 64, 2062-2064 (1994).
[CrossRef]

Ryvkin, B.

K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B. Ryvkin, H. Thienpont, and I. Veretennicoff, “Polarization behavior of vertical-cavity surface-emitting lasers: experiments, models and applications,” AIP Conf. Proc. 560, 403-417 (2001).
[CrossRef]

Ryvkin, B. S.

B. S. Ryvkin, K. Panajotov, E. A. Avrutin, I. Veretennicoff, and H. Thienpont, “Optical-injection-induced polarization switching in polarization-bistable vertical-cavity surface-emitting lasers,” J. Appl. Phys. 96, 6002-6007 (2004).
[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]

Sarma, J.

A. Valle, J. Sarma, and K. A. Shore, “Spatial hole burning effect on the dynamic of VCSELs,” IEEE J. Quantum Electron. 31, 1423-1431 (1995).
[CrossRef]

Sciamanna, M.

I. Gatare, M. Sciamanna, M. Nizette, H. Thienpont, and K. Panajotov, “Excitation of a two-mode limit cycle dynamics on the route to polarization switching in a VCSEL subject to orthogonal optical injection,” Proc. SPIE 6997, 699713 (2008).
[CrossRef]

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
[CrossRef]

M. Sciamanna and K. Panajotov, “Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers,” Phys. Rev. A 73, 023811 (2006).
[CrossRef]

J. Buesa Altés, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42, 198-207 (2006).
[CrossRef]

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

M. Sciamanna, “Nonlinear dynamics and polarization properties of externally driven semiconductor lasers,” Ph.D. dissertation (Mons Engineering Faculty, 2004).

M. Sciamanna, I. Gatare, and K. Panajotov, in Proceedings of the International Commission for Optics (ICO-21) 2008 Congress, p. 287 (2008).

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization and transverse-mode dynamics in optically-injected and gain-switched vertical-cavity surface-emitting lasers” IEEE J. Quantum Electron. (accepted for publication).

Shore, K. A.

Simpson, I. B.

S. Wieczorek, I. B. Simpson, B. Krauskopf, and D. Lenstra, “Bifurcation transitions in an optically injected diode laser: theory and experiment,” Opt. Commun. 215, 125-134 (2003).
[CrossRef]

S. Wieczorek, I. B. Simpson, B. Krauskopf, and D. Lenstra, “Global quantitative predictions of complex laser dynamics,” Phys. Rev. E 65, 045207(R) (2002).
[CrossRef]

Simpson, T.

J. M. Liu, H. Chen, X. Meng, and T. Simpson, “Modulation bandwidth, noise, and stability of a semiconductor laser subject to strong injection locking,” IEEE Photon. Technol. Lett. 9, 1325-1327 (1997).
[CrossRef]

V. Kovanis, A. Gavrielides, T. Simpson, and J. M. Liu, “Instabilities and chaos in optically injected semiconductor lasers,” Appl. Phys. Lett. 67, 2780-2782 (1995).
[CrossRef]

Simpson, T. B.

T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclassic. Opt. 9, 765-784 (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]

Spano, P.

S. Piazzolla, P. Spano, and M. Tamburrini, “Small signal analysis of frequency chirping in injection-locked semiconductor lasers,” IEEE J. Quantum Electron. 22, 2219-2223 (1986).
[CrossRef]

Spencer, P. S.

Tai, K.

T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclassic. Opt. 9, 765-784 (1997).
[CrossRef]

Tamburrini, M.

S. Piazzolla, P. Spano, and M. Tamburrini, “Small signal analysis of frequency chirping in injection-locked semiconductor lasers,” IEEE J. Quantum Electron. 22, 2219-2223 (1986).
[CrossRef]

Thienpont, H.

I. Gatare, M. Sciamanna, M. Nizette, H. Thienpont, and K. Panajotov, “Excitation of a two-mode limit cycle dynamics on the route to polarization switching in a VCSEL subject to orthogonal optical injection,” Proc. SPIE 6997, 699713 (2008).
[CrossRef]

M. Arizaleta Arteaga, M. López-Amo, H. Thienpont, and K. Panajotov, “Role of external cavity reflectivity for achieving polarization control and stabilization of vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 90, 031117 (2007).
[CrossRef]

J. Buesa Altés, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42, 198-207 (2006).
[CrossRef]

B. S. Ryvkin, K. Panajotov, E. A. Avrutin, I. Veretennicoff, and H. Thienpont, “Optical-injection-induced polarization switching in polarization-bistable vertical-cavity surface-emitting lasers,” J. Appl. Phys. 96, 6002-6007 (2004).
[CrossRef]

K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B. Ryvkin, H. Thienpont, and I. Veretennicoff, “Polarization behavior of vertical-cavity surface-emitting lasers: experiments, models and applications,” AIP Conf. Proc. 560, 403-417 (2001).
[CrossRef]

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization and transverse-mode dynamics in optically-injected and gain-switched vertical-cavity surface-emitting lasers” IEEE J. Quantum Electron. (accepted for publication).

Valle, A.

M. Sciamanna, A. Valle, P. Mégret, 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, J. Sarma, and K. A. Shore, “Spatial hole burning effect on the dynamic of VCSELs,” IEEE J. Quantum Electron. 31, 1423-1431 (1995).
[CrossRef]

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization and transverse-mode dynamics in optically-injected and gain-switched vertical-cavity surface-emitting lasers” IEEE J. Quantum Electron. (accepted for publication).

van Exter, M. P.

M. P. van Exter, A. Al-Remawi, and J. P. Woerdman, “Polarization fluctuations demonstrate nonlinear anisotropy of a vertical-cavity semiconductor laser,” Phys. Rev. Lett. 80, 4875-4878 (1998).
[CrossRef]

Veretennicoff, I.

B. S. Ryvkin, K. Panajotov, E. A. Avrutin, I. Veretennicoff, and H. Thienpont, “Optical-injection-induced polarization switching in polarization-bistable vertical-cavity surface-emitting lasers,” J. Appl. Phys. 96, 6002-6007 (2004).
[CrossRef]

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

K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B. Ryvkin, H. Thienpont, and I. Veretennicoff, “Polarization behavior of vertical-cavity surface-emitting lasers: experiments, models and applications,” AIP Conf. Proc. 560, 403-417 (2001).
[CrossRef]

Verschaffelt, G.

K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B. Ryvkin, H. Thienpont, and I. Veretennicoff, “Polarization behavior of vertical-cavity surface-emitting lasers: experiments, models and applications,” AIP Conf. Proc. 560, 403-417 (2001).
[CrossRef]

Wai, P. K. A.

Wieczorek, S.

S. Wieczorek, I. B. Simpson, B. Krauskopf, and D. Lenstra, “Bifurcation transitions in an optically injected diode laser: theory and experiment,” Opt. Commun. 215, 125-134 (2003).
[CrossRef]

S. Wieczorek, I. B. Simpson, B. Krauskopf, and D. Lenstra, “Global quantitative predictions of complex laser dynamics,” Phys. Rev. E 65, 045207(R) (2002).
[CrossRef]

S. Wieczorek, B. Krauskopf, and D. Lenstra, “A unifying view of bifurcations in a semiconductor laser subject to optical injection,” Opt. Commun. 172, 279-295 (1999).
[CrossRef]

Woerdman, J. P.

M. P. van Exter, A. Al-Remawi, and J. P. Woerdman, “Polarization fluctuations demonstrate nonlinear anisotropy of a vertical-cavity semiconductor laser,” Phys. Rev. Lett. 80, 4875-4878 (1998).
[CrossRef]

Wu, M. C.

X. J. Meng, T. Chau, and M. C. Wu, “Experimental demonstration of modulation bandwidth enhancement in distributed feedback lasers with external light injection,” Electron. Lett. 34, 2031-2032 (1998).
[CrossRef]

Xu, L.

Yamayoshi, Y.

T. Mori, Y. Yamayoshi, and H. Kawaguchi, “Low-switching-energy and high-repetition-frequency all-optical flip-flop operations of a polarization bistable vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 88, 101102-101104 (2006).
[CrossRef]

AIP Conf. Proc. (1)

K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B. Ryvkin, H. Thienpont, and I. Veretennicoff, “Polarization behavior of vertical-cavity surface-emitting lasers: experiments, models and applications,” AIP Conf. Proc. 560, 403-417 (2001).
[CrossRef]

Appl. Phys. Lett. (6)

M. Arizaleta Arteaga, M. López-Amo, H. Thienpont, and K. Panajotov, “Role of external cavity reflectivity for achieving polarization control and stabilization of vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 90, 031117 (2007).
[CrossRef]

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]

V. Kovanis, A. Gavrielides, T. Simpson, and J. M. Liu, “Instabilities and chaos in optically injected semiconductor lasers,” Appl. Phys. Lett. 67, 2780-2782 (1995).
[CrossRef]

K. Choquette, D. Richie, and R. Leibenguth, “Temperature dependence of gain-guided vertical-cavity surface emitting laser polarization,” Appl. Phys. Lett. 64, 2062-2064 (1994).
[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. Mori, Y. Yamayoshi, and H. Kawaguchi, “Low-switching-energy and high-repetition-frequency all-optical flip-flop operations of a polarization bistable vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 88, 101102-101104 (2006).
[CrossRef]

Electron. Lett. (1)

X. J. Meng, T. Chau, and M. C. Wu, “Experimental demonstration of modulation bandwidth enhancement in distributed feedback lasers with external light injection,” Electron. Lett. 34, 2031-2032 (1998).
[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]

S. Piazzolla, P. Spano, and M. Tamburrini, “Small signal analysis of frequency chirping in injection-locked semiconductor lasers,” IEEE J. Quantum Electron. 22, 2219-2223 (1986).
[CrossRef]

J. Buesa Altés, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42, 198-207 (2006).
[CrossRef]

A. Valle, J. Sarma, and K. A. Shore, “Spatial hole burning effect on the dynamic of VCSELs,” IEEE J. Quantum Electron. 31, 1423-1431 (1995).
[CrossRef]

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

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)

J. M. Liu, H. Chen, X. Meng, and T. Simpson, “Modulation bandwidth, noise, and stability of a semiconductor laser subject to strong injection locking,” IEEE Photon. Technol. Lett. 9, 1325-1327 (1997).
[CrossRef]

Int. J. Bifurcat. Chaos (1)

E. J. Doedel, H. B. Keller, and J. P. Kernevez, “Numerical analysis and control of bifurcation problems (I) bifurcation in finite dimensions,” Int. J. Bifurcat. Chaos 1, 493-520 (1991).
[CrossRef]

J. Appl. Phys. (1)

B. S. Ryvkin, K. Panajotov, E. A. Avrutin, I. Veretennicoff, and H. Thienpont, “Optical-injection-induced polarization switching in polarization-bistable vertical-cavity surface-emitting lasers,” J. Appl. Phys. 96, 6002-6007 (2004).
[CrossRef]

Opt. Commun. (4)

S. Wieczorek, I. B. Simpson, B. Krauskopf, and D. Lenstra, “Bifurcation transitions in an optically injected diode laser: theory and experiment,” Opt. Commun. 215, 125-134 (2003).
[CrossRef]

S. K. Hwang and J. M. Liu, “Dynamical characteristics of an optically injected semiconductor laser,” Opt. Commun. 183, 195-205 (2000).
[CrossRef]

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

S. Wieczorek, B. Krauskopf, and D. Lenstra, “A unifying view of bifurcations in a semiconductor laser subject to optical injection,” Opt. Commun. 172, 279-295 (1999).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (3)

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]

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
[CrossRef]

M. Sciamanna and K. Panajotov, “Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers,” Phys. Rev. A 73, 023811 (2006).
[CrossRef]

Phys. Rev. E (2)

S. Wieczorek, I. B. Simpson, B. Krauskopf, and D. Lenstra, “Global quantitative predictions of complex laser dynamics,” Phys. Rev. E 65, 045207(R) (2002).
[CrossRef]

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

Phys. Rev. Lett. (1)

M. P. van Exter, A. Al-Remawi, and J. P. Woerdman, “Polarization fluctuations demonstrate nonlinear anisotropy of a vertical-cavity semiconductor laser,” Phys. Rev. Lett. 80, 4875-4878 (1998).
[CrossRef]

Proc. SPIE (1)

I. Gatare, M. Sciamanna, M. Nizette, H. Thienpont, and K. Panajotov, “Excitation of a two-mode limit cycle dynamics on the route to polarization switching in a VCSEL subject to orthogonal optical injection,” Proc. SPIE 6997, 699713 (2008).
[CrossRef]

Quantum Semiclassic. Opt. (1)

T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclassic. Opt. 9, 765-784 (1997).
[CrossRef]

Other (3)

M. Sciamanna, I. Gatare, and K. Panajotov, in Proceedings of the International Commission for Optics (ICO-21) 2008 Congress, p. 287 (2008).

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization and transverse-mode dynamics in optically-injected and gain-switched vertical-cavity surface-emitting lasers” IEEE J. Quantum Electron. (accepted for publication).

M. Sciamanna, “Nonlinear dynamics and polarization properties of externally driven semiconductor lasers,” Ph.D. dissertation (Mons Engineering Faculty, 2004).

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Figures (12)

Fig. 1
Fig. 1

Bifurcation diagram showing the maxima and the minima of the intensities of the x-LP (black) and y-LP (gray) modes as a function of increasing injection strength κ, when the detuning is fixed at (a) Δ ν = 15 , (b) Δ ν = 5 , (c) Δ ν = 0 , and (d) Δ ν = 10   GHz . The labels with arrows— S N , H y 1 , H x y 1 , H x y 2 , B r 1 , and B r 2 —refer to the crossing of bifurcation curves described in Section 4.

Fig. 2
Fig. 2

Polarization-resolved intensities, time traces, and optical spectra showing a PS scenario involving limit-cycle dynamics in the x LP for a detuning of Δ ν = 5   GHz , when increasing the injection strength κ: (a1)–(a3) κ = 0.0015 , unlocked y-LP mode; (b1)–(b3) κ = 0.0030 , limit cycle in the x-LP mode; and (c1)–(c3) κ = 0.004 , injection locking after PS is achieved. In the spectra black (gray) corresponds to the x-LP (y-LP) mode.

Fig. 3
Fig. 3

Polarization-resolved intensities, time traces, and optical spectra showing a PS scenario involving a two-mode limit-cycle dynamics for a detuning of Δ ν = 0   GHz , when increasing the injection strength κ: (a1)–(a3) κ = 0.0006 , unlocked y-LP mode ; (b1)–(b3) κ = 0.00108 , limit cycle in both the x-LP and y-LP modes; (c1)–(c3) κ = 0.0015 , limit cycle in the x-LP mode after PS is achieved. In the spectra black (gray) corresponds to the x-LP (y-LP) mode.

Fig. 4
Fig. 4

Polarization-resolved intensities, time traces, and optical spectra showing a PS scenario involving two-polarization-mode limit-cycle dynamics for a detuning of Δ ν = 10   GHz , when increasing the injection strength κ: (a1)–(a3) κ = 0.00035 , unlocked x-LP mode; (b1)–(b3) κ = 0.00055 , limit cycle in both the x- and y-LP modes; (c1)–(c3) κ = 0.0011 , injection locking after PS is achieved. In the spectra black (gray) corresponds to the x-LP (y-LP) mode.

Fig. 5
Fig. 5

Dependence on the detuning of the frequency of limit-cycle dynamics in the x-LP (black) and y-LP (gray) modes. The frequencies of the limit cycles in x- and y-LP modes correspond to the frequency offset of peaks, which appears on both sides of, respectively, ν M L and ν y [see Fig. 4(b3)].

Fig. 6
Fig. 6

Continuation of bifurcation curves in the ( κ , Δ ν ) plane. Black (gray) denotes supercritical (subcritical) bifurcation. The dotted curves indicate the bifurcation scenarios analyzed in Figs. 1, 7. The black circles indicate numerically computed PS points when increasing κ for fixed detuning. The inset provides a close view of a region of the mapping where different bifurcation curves intersect. Labels indicating each bifurcation curve are explained in the text.

Fig. 7
Fig. 7

Bifurcation diagram showing the maxima and the minima of the intensities of the x-LP (black) and y-LP (gray) modes for increasing (left panels) and decreasing (right panels) injection strength κ when the detuning is fixed at (a1), (a2) Δ ν = 20 and (b1), (b2) Δ ν = 35   GHz .

Fig. 8
Fig. 8

Polarization-resolved intensities time traces and optical spectra showing PS scenario for a detuning of Δ ν = 20   GHz , when increasing the injection strength κ: (a1)–(a3) κ = 0.00165 , quasiperiodic dynamics; (b1), (b2) κ = 0.0019 , nearly chaotic dynamics; and (c1), (c2) κ = 0.0024 , injection locking after PS is achieved. In the spectra black (gray) corresponds to the x-LP (y-LP) mode.

Fig. 9
Fig. 9

Continuation of bifurcation curves in the ( κ , Δ ν ) plane. In addition to bifurcation curves represented in Fig. 6, a pattern of fold bifurcations of a periodic solution is shown by thick black lines (labeled FLC).

Fig. 10
Fig. 10

Continuation of bifurcation curves in the ( κ , Δ ν ) plane for ζ x = 0.71 and ζ y = 0.75 , other parameters remain the same as for Sections 3, 4, 5. Black (gray) denotes supercritical (subcritical) bifurcation. Labels indicating each bifurcation curve have been explained in Section 4.

Fig. 11
Fig. 11

Impact of gain difference, Δ ζ = ζ y ζ x , on the bifurcation mechanisms H y 1 , H x y 1 , and B r 2 for a representative detuning Δ ν = 0   GHz : ζ y is tuned by fixing ( ζ x = 0.71 ) . Other parameters remain the same as for Sections 3, 4, 5.

Fig. 12
Fig. 12

Bifurcation mapping for α = 2.5 , other parameters remain the same as in Sections 3, 4, 5, e.g., ζ x = 0.71 and ζ y = 0.74 . Black (gray) denotes supercritical (subcritical) bifurcation. Labels indicating each bifurcation curve have been explained in Section 4.

Tables (1)

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Table 1 Parameters Used for the Simulation of the Injected VCSEL

Equations (11)

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d E x d t = 1 2 ( 1 + j α x ) [ Γ x G x 1 τ p x ] E x + κ i 2 π j Δ ν x E x ,
d E y d t = 1 2 ( 1 + j α y ) [ Γ y G y 1 τ p y ] E y 2 π j Δ ν y E y ,
d N d t = J e V N τ e G x | E x | 2 G y | E y | 2 .
G x = v g g x ( N N t r x ) ( 1 ε x x | E x | 2 ε x y | E y | 2 ) ,
G y = v g g y ( N N t r y ) ( 1 ε y x | E x | 2 ε y y | E y | 2 ) ,
d X d T = 1 2 ( 1 + j α ) [ ζ x Z ( 1 | X | 2 ε | Y | 2 ) 1 ] X + κ j δ x X ,
d Y d T = 1 2 ( 1 + j α ) [ ζ y Z ( 1 ε | X | 2 | Y | 2 ) 1 ] Y j δ y Y ,
d Z d T = R i s ( Z + 1 ) η x Z ( 1 | X | 2 ε | Y | 2 ) | X | 2 η y Z ( 1 ε | X | 2 | Y | 2 ) | Y | 2 .
d X d T = 1 2 ( 1 + j α ) [ ζ x Z ( 1 | X | 2 ε P ) 1 ] X + κ E i j δ X ,
d P d T = [ ζ y Z ( 1 ε | X | 2 P ) 1 ] P ,
d Z d T = R i s ( Z + 1 ) η x Z ( 1 | X | 2 ε P ) | X | 2 η y Z ( 1 ε | X | 2 P ) P ,

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