Abstract

Abstract

The aim of this paper is to use the spin-flip model (SFM) to investigate how the fundamental parameters of birefringence, spin relaxation and pumping affect the dynamics of solitary and optically-injected vertical-cavity surface-emitting lasers (VCSELs). The SFM predicts that a solitary VCSEL can exhibit diverse polarisation behaviour, including elliptical and linear stability, which can be used in polarisation switching. For given values of pumping, spin relaxation and birefringence, we analyse the electric field components, the carrier densities corresponding to spin-up and spin-down, and the relaxation oscillation frequency for a solitary VCSEL and the stability map for an optically-injected VCSEL.

© 2007 Optical Society of America

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  1. 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]
  2. Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, and R. E. Leibenguth, “Optical injection induced polarization in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 2999–3001 (1993).
    [Crossref]
  3. J. B. Altes, 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. Select. Topics in Quantum Electron,  42, 198–207 (2006)
    [Crossref]
  4. M. San Miguel, Q. Feng, and J. V. Moloney, “Light-polarization dynamics in surface-emitting lasers,” Phys. Rev. A 52, 1728–1739 (1995).
    [Crossref] [PubMed]
  5. 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, 765–782 (1997).
    [Crossref]
  6. C-H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Select. Topics in Quantum Electron. 9, 1386–1393 (2003).
    [Crossref]
  7. L. Chrostowski, B. Faraji, W. Hofmann, R. Shau, M. Ortsiefer, and M.-C. Amann, “40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 µm VCSELs”, IEEE 20th International Semiconductor Laser Conference, Hawaii, 2006, Conference Digest pp. 117–118.
    [Crossref]
  8. A. Homayounfar and M. J. Adams, “Locking bandwidth and birefringence effects for polarized optical injection in vertical-cavity surface-emitting lasers,” Opt. Commun. 269, 119–127 (2007).
    [Crossref]
  9. A. Homayounfar and M. J. Adams, “Spin polarized properties of optically injected VCSELs,” phys. stat. sol. (c) 4,604–606 (2007).
    [Crossref]
  10. F. Prati, P. Caccia, M. Bache, and F. Castelli, “Analysis of elliptically polarized states in vertical-cavity-surface-emitting lasers,” Phys. Rev. A 69, 033810-9 (2004).
    [Crossref]
  11. L. Chrostowski, X. Zhao, C. J. Chang-Hasnain, R. Shau, M. Ortsiefer, and M-C. Amann, “50 GHz optically injection-locked 1.55 µm VCSELs,” IEEE Photon. Technol. Lett. 16,367–369 (2006).
    [Crossref]
  12. S. Wieczorek, W. W. Chow, L. Chrostowski, and C. J. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Quantum Electron. 42, 552–562 (2006).
    [Crossref]
  13. H. Li, T. L. Lucas, J. G. McInerney, M. W. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
    [Crossref]
  14. G. Van der Sande, J. Danckaert, I. Veretennicoff, and T. Erneux, “Rate equations for vertical-cavity surface-emitting lasers,” Phys. Rev. A 67, 13809-7 (2003).
    [Crossref]
  15. A. Gahl, S. Balle, and M. San Miguel, “Polarization dynamics of optically pumped VCSELs,” IEEE J. Quantum Electron. 35, 342–351 (1999).
    [Crossref]
  16. S. Wieczorek, B. Krauskopf, T.B. Simpson, and D. Lenstra, “The dynamic complexity of optically injected semiconductor lasers,” Physics Report. 416, 1–128 (2005).
    [Crossref]
  17. T. Erneux, J. Danckaert, K. Panajotov, and I. Veretennicoff, “Two-variable reduction of the San Miguel-Feng-Moloney model for vertical-cavity surface-emitting lasers,” Phys. Rev. A 59, 4660–4667 (1999).
    [Crossref]
  18. R. Tackeuchi, T. Kuroda, S. Muto, Y. Nishikawa, and O. Wada, “Electron spin-relaxation dynamics in GaAs/AlGaAs quantum wells and InGaAs/InP quantum wells,” Jpn. J. Appl. Phys. 38, 4680–4687 (1999).
    [Crossref]
  19. A. Tackeuchi, T. Kuroda, S. Muto, and O. Wada, “Picosecond electron spin-relaxation in GaAs/AlGaAs quantum wells and InGaAs/InP quantum wells,” Physica B 272, 318–323 (1999)
    [Crossref]
  20. S. Adachi, T. Miyashita, S. Takeyama, Y. Takagi, and A. Tackeuchi, “Exciton spin dynamics in GaAs quantum wells,” J. Lumin. 72– 74, 307–308 (1997)
    [Crossref]
  21. S. Akasaki, S. Miyata, T. Kuroda, and A. Tackeuchi, “Exciton spin relaxation dynamics in InGaAs/InP quantum wells,” Appl. Phys. Lett. 85, 2083–2085 (2004).
    [Crossref]
  22. H. Ando, T. Sogawa, and H. Gotoh, “Photon-spin controlled lasing oscillation in surface-emitting lasers,” Appl. Phys. Lett. 73, 566–568 (1998).
    [Crossref]
  23. J. T. Hyland, G. T. Kennedy, A. Miller, and C. C. Button, “Spin relaxation and all optical polarization switching at 1.52 micrometres in InGaAs(P)/InGaAsP multiple quantum wells,” Semicond. Sci. Technol. 14, 215–221 (1999).
    [Crossref]
  24. J. Rudolph, S. Dohrmann, D. Hagele, W. Stolz, and M. Oestreich, “Room-temperature threshold reduction in vertical-cavity surface-emitting lasers by injection of spin-polarized electrons,” Appl. Phys. Lett. 87, 241117 (2005).
    [Crossref]
  25. F. Prati, P. Caccia, and F. Castelli, “Effects of gain saturation on polarization switching in vertical-cavity surface-emitting lasers,” Phys. Rev. A 66, 063811 (2002).
    [Crossref]
  26. Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Haonen, “Polarisation switching in a vertical cavity surface emitting semiconductor laser by frequency detuning,” IEE Proc. Optoelectron. 148, 31–34 (2001).
    [Crossref]
  27. I. Gatare, M. Sciamanna, and K. Panajotov, “Frequency-induced polarization bistability in vertical-cavity surface-emitting lasers,” Phys. Rev. A 75, 023804 (2007).
    [Crossref]
  28. 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]
  29. A. Valle, I. Gatare, K. Panajatov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection”, IEEE J. Quantum Electron. 43, 322–333 (2007).
    [Crossref]
  30. K. E. Chlouverakis and M. J. Adams, “Stability maps of injection-locked laser diodes using the largest Lyapunov exponent,” Opt. Commun. 216, 405–412 (2003).
    [Crossref]

2007 (4)

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

A. Homayounfar and M. J. Adams, “Spin polarized properties of optically injected VCSELs,” phys. stat. sol. (c) 4,604–606 (2007).
[Crossref]

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

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

2006 (4)

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. B. Altes, 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. Select. Topics in Quantum Electron,  42, 198–207 (2006)
[Crossref]

L. Chrostowski, X. Zhao, C. J. Chang-Hasnain, R. Shau, M. Ortsiefer, and M-C. Amann, “50 GHz optically injection-locked 1.55 µm VCSELs,” IEEE Photon. Technol. Lett. 16,367–369 (2006).
[Crossref]

S. Wieczorek, W. W. Chow, L. Chrostowski, and C. J. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Quantum Electron. 42, 552–562 (2006).
[Crossref]

2005 (2)

S. Wieczorek, B. Krauskopf, T.B. Simpson, and D. Lenstra, “The dynamic complexity of optically injected semiconductor lasers,” Physics Report. 416, 1–128 (2005).
[Crossref]

J. Rudolph, S. Dohrmann, D. Hagele, W. Stolz, and M. Oestreich, “Room-temperature threshold reduction in vertical-cavity surface-emitting lasers by injection of spin-polarized electrons,” Appl. Phys. Lett. 87, 241117 (2005).
[Crossref]

2004 (2)

S. Akasaki, S. Miyata, T. Kuroda, and A. Tackeuchi, “Exciton spin relaxation dynamics in InGaAs/InP quantum wells,” Appl. Phys. Lett. 85, 2083–2085 (2004).
[Crossref]

F. Prati, P. Caccia, M. Bache, and F. Castelli, “Analysis of elliptically polarized states in vertical-cavity-surface-emitting lasers,” Phys. Rev. A 69, 033810-9 (2004).
[Crossref]

2003 (3)

C-H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Select. Topics in Quantum Electron. 9, 1386–1393 (2003).
[Crossref]

G. Van der Sande, J. Danckaert, I. Veretennicoff, and T. Erneux, “Rate equations for vertical-cavity surface-emitting lasers,” Phys. Rev. A 67, 13809-7 (2003).
[Crossref]

K. E. Chlouverakis and M. J. Adams, “Stability maps of injection-locked laser diodes using the largest Lyapunov exponent,” Opt. Commun. 216, 405–412 (2003).
[Crossref]

2002 (2)

F. Prati, P. Caccia, and F. Castelli, “Effects of gain saturation on polarization switching in vertical-cavity surface-emitting lasers,” Phys. Rev. A 66, 063811 (2002).
[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]

2001 (1)

Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Haonen, “Polarisation switching in a vertical cavity surface emitting semiconductor laser by frequency detuning,” IEE Proc. Optoelectron. 148, 31–34 (2001).
[Crossref]

1999 (5)

J. T. Hyland, G. T. Kennedy, A. Miller, and C. C. Button, “Spin relaxation and all optical polarization switching at 1.52 micrometres in InGaAs(P)/InGaAsP multiple quantum wells,” Semicond. Sci. Technol. 14, 215–221 (1999).
[Crossref]

A. Gahl, S. Balle, and M. San Miguel, “Polarization dynamics of optically pumped VCSELs,” IEEE J. Quantum Electron. 35, 342–351 (1999).
[Crossref]

T. Erneux, J. Danckaert, K. Panajotov, and I. Veretennicoff, “Two-variable reduction of the San Miguel-Feng-Moloney model for vertical-cavity surface-emitting lasers,” Phys. Rev. A 59, 4660–4667 (1999).
[Crossref]

R. Tackeuchi, T. Kuroda, S. Muto, Y. Nishikawa, and O. Wada, “Electron spin-relaxation dynamics in GaAs/AlGaAs quantum wells and InGaAs/InP quantum wells,” Jpn. J. Appl. Phys. 38, 4680–4687 (1999).
[Crossref]

A. Tackeuchi, T. Kuroda, S. Muto, and O. Wada, “Picosecond electron spin-relaxation in GaAs/AlGaAs quantum wells and InGaAs/InP quantum wells,” Physica B 272, 318–323 (1999)
[Crossref]

1998 (1)

H. Ando, T. Sogawa, and H. Gotoh, “Photon-spin controlled lasing oscillation in surface-emitting lasers,” Appl. Phys. Lett. 73, 566–568 (1998).
[Crossref]

1997 (2)

S. Adachi, T. Miyashita, S. Takeyama, Y. Takagi, and A. Tackeuchi, “Exciton spin dynamics in GaAs quantum wells,” J. Lumin. 72– 74, 307–308 (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, 765–782 (1997).
[Crossref]

1996 (1)

H. Li, T. L. Lucas, J. G. McInerney, M. W. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
[Crossref]

1995 (1)

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

1993 (1)

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, and R. E. Leibenguth, “Optical injection induced polarization in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 2999–3001 (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, 765–782 (1997).
[Crossref]

Adachi, S.

S. Adachi, T. Miyashita, S. Takeyama, Y. Takagi, and A. Tackeuchi, “Exciton spin dynamics in GaAs quantum wells,” J. Lumin. 72– 74, 307–308 (1997)
[Crossref]

Adams, M. J.

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

A. Homayounfar and M. J. Adams, “Spin polarized properties of optically injected VCSELs,” phys. stat. sol. (c) 4,604–606 (2007).
[Crossref]

K. E. Chlouverakis and M. J. Adams, “Stability maps of injection-locked laser diodes using the largest Lyapunov exponent,” Opt. Commun. 216, 405–412 (2003).
[Crossref]

Akasaki, S.

S. Akasaki, S. Miyata, T. Kuroda, and A. Tackeuchi, “Exciton spin relaxation dynamics in InGaAs/InP quantum wells,” Appl. Phys. Lett. 85, 2083–2085 (2004).
[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]

Altes, J. B.

J. B. Altes, 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. Select. Topics in Quantum Electron,  42, 198–207 (2006)
[Crossref]

Amann, M.-C.

L. Chrostowski, B. Faraji, W. Hofmann, R. Shau, M. Ortsiefer, and M.-C. Amann, “40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 µm VCSELs”, IEEE 20th International Semiconductor Laser Conference, Hawaii, 2006, Conference Digest pp. 117–118.
[Crossref]

Amann, M-C.

L. Chrostowski, X. Zhao, C. J. Chang-Hasnain, R. Shau, M. Ortsiefer, and M-C. Amann, “50 GHz optically injection-locked 1.55 µm VCSELs,” IEEE Photon. Technol. Lett. 16,367–369 (2006).
[Crossref]

Ando, H.

H. Ando, T. Sogawa, and H. Gotoh, “Photon-spin controlled lasing oscillation in surface-emitting lasers,” Appl. Phys. Lett. 73, 566–568 (1998).
[Crossref]

Asom, M. T.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, and R. E. Leibenguth, “Optical injection induced polarization 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, 033810-9 (2004).
[Crossref]

Balle, S.

A. Gahl, S. Balle, and M. San Miguel, “Polarization dynamics of optically pumped VCSELs,” IEEE J. Quantum Electron. 35, 342–351 (1999).
[Crossref]

Button, C. C.

J. T. Hyland, G. T. Kennedy, A. Miller, and C. C. Button, “Spin relaxation and all optical polarization switching at 1.52 micrometres in InGaAs(P)/InGaAsP multiple quantum wells,” Semicond. Sci. Technol. 14, 215–221 (1999).
[Crossref]

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, 033810-9 (2004).
[Crossref]

F. Prati, P. Caccia, and F. Castelli, “Effects of gain saturation on polarization switching in vertical-cavity surface-emitting lasers,” Phys. Rev. A 66, 063811 (2002).
[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, 033810-9 (2004).
[Crossref]

F. Prati, P. Caccia, and F. Castelli, “Effects of gain saturation on polarization switching in vertical-cavity surface-emitting lasers,” Phys. Rev. A 66, 063811 (2002).
[Crossref]

Chang, C-H.

C-H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Select. Topics in Quantum Electron. 9, 1386–1393 (2003).
[Crossref]

Chang-Hasnain, C. J.

L. Chrostowski, X. Zhao, C. J. Chang-Hasnain, R. Shau, M. Ortsiefer, and M-C. Amann, “50 GHz optically injection-locked 1.55 µm VCSELs,” IEEE Photon. Technol. Lett. 16,367–369 (2006).
[Crossref]

S. Wieczorek, W. W. Chow, L. Chrostowski, and C. J. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Quantum Electron. 42, 552–562 (2006).
[Crossref]

C-H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Select. Topics in Quantum Electron. 9, 1386–1393 (2003).
[Crossref]

Chlouverakis, K. E.

K. E. Chlouverakis and M. J. Adams, “Stability maps of injection-locked laser diodes using the largest Lyapunov exponent,” Opt. Commun. 216, 405–412 (2003).
[Crossref]

Chow, W. W.

S. Wieczorek, W. W. Chow, L. Chrostowski, and C. J. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Quantum Electron. 42, 552–562 (2006).
[Crossref]

Chrostowski, L.

S. Wieczorek, W. W. Chow, L. Chrostowski, and C. J. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Quantum Electron. 42, 552–562 (2006).
[Crossref]

L. Chrostowski, X. Zhao, C. J. Chang-Hasnain, R. Shau, M. Ortsiefer, and M-C. Amann, “50 GHz optically injection-locked 1.55 µm VCSELs,” IEEE Photon. Technol. Lett. 16,367–369 (2006).
[Crossref]

C-H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Select. Topics in Quantum Electron. 9, 1386–1393 (2003).
[Crossref]

L. Chrostowski, B. Faraji, W. Hofmann, R. Shau, M. Ortsiefer, and M.-C. Amann, “40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 µm VCSELs”, IEEE 20th International Semiconductor Laser Conference, Hawaii, 2006, Conference Digest pp. 117–118.
[Crossref]

Dagenais, M.

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

Danckaert, J.

G. Van der Sande, J. Danckaert, I. Veretennicoff, and T. Erneux, “Rate equations for vertical-cavity surface-emitting lasers,” Phys. Rev. A 67, 13809-7 (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]

T. Erneux, J. Danckaert, K. Panajotov, and I. Veretennicoff, “Two-variable reduction of the San Miguel-Feng-Moloney model for vertical-cavity surface-emitting lasers,” Phys. Rev. A 59, 4660–4667 (1999).
[Crossref]

Dohrmann, S.

J. Rudolph, S. Dohrmann, D. Hagele, W. Stolz, and M. Oestreich, “Room-temperature threshold reduction in vertical-cavity surface-emitting lasers by injection of spin-polarized electrons,” Appl. Phys. Lett. 87, 241117 (2005).
[Crossref]

Erneux, T.

G. Van der Sande, J. Danckaert, I. Veretennicoff, and T. Erneux, “Rate equations for vertical-cavity surface-emitting lasers,” Phys. Rev. A 67, 13809-7 (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]

T. Erneux, J. Danckaert, K. Panajotov, and I. Veretennicoff, “Two-variable reduction of the San Miguel-Feng-Moloney model for vertical-cavity surface-emitting lasers,” Phys. Rev. A 59, 4660–4667 (1999).
[Crossref]

Faraji, B.

L. Chrostowski, B. Faraji, W. Hofmann, R. Shau, M. Ortsiefer, and M.-C. Amann, “40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 µm VCSELs”, IEEE 20th International Semiconductor Laser Conference, Hawaii, 2006, Conference Digest pp. 117–118.
[Crossref]

Feng, Q.

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

Gahl, A.

A. Gahl, S. Balle, and M. San Miguel, “Polarization dynamics of optically pumped VCSELs,” IEEE J. Quantum Electron. 35, 342–351 (1999).
[Crossref]

Gatare, I.

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

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

J. B. Altes, 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. Select. Topics in Quantum Electron,  42, 198–207 (2006)
[Crossref]

Ghisoni, M.

Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Haonen, “Polarisation switching in a vertical cavity surface emitting semiconductor laser by frequency detuning,” IEE Proc. Optoelectron. 148, 31–34 (2001).
[Crossref]

Gotoh, H.

H. Ando, T. Sogawa, and H. Gotoh, “Photon-spin controlled lasing oscillation in surface-emitting lasers,” Appl. Phys. Lett. 73, 566–568 (1998).
[Crossref]

Hagele, D.

J. Rudolph, S. Dohrmann, D. Hagele, W. Stolz, and M. Oestreich, “Room-temperature threshold reduction in vertical-cavity surface-emitting lasers by injection of spin-polarized electrons,” Appl. Phys. Lett. 87, 241117 (2005).
[Crossref]

Haonen, J.

Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Haonen, “Polarisation switching in a vertical cavity surface emitting semiconductor laser by frequency detuning,” IEE Proc. Optoelectron. 148, 31–34 (2001).
[Crossref]

Hofmann, W.

L. Chrostowski, B. Faraji, W. Hofmann, R. Shau, M. Ortsiefer, and M.-C. Amann, “40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 µm VCSELs”, IEEE 20th International Semiconductor Laser Conference, Hawaii, 2006, Conference Digest pp. 117–118.
[Crossref]

Homayounfar, A.

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

A. Homayounfar and M. J. Adams, “Spin polarized properties of optically injected VCSELs,” phys. stat. sol. (c) 4,604–606 (2007).
[Crossref]

Hong, Y.

Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Haonen, “Polarisation switching in a vertical cavity surface emitting semiconductor laser by frequency detuning,” IEE Proc. Optoelectron. 148, 31–34 (2001).
[Crossref]

Hyland, J. T.

J. T. Hyland, G. T. Kennedy, A. Miller, and C. C. Button, “Spin relaxation and all optical polarization switching at 1.52 micrometres in InGaAs(P)/InGaAsP multiple quantum wells,” Semicond. Sci. Technol. 14, 215–221 (1999).
[Crossref]

Jiang, S.

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

Kennedy, G. T.

J. T. Hyland, G. T. Kennedy, A. Miller, and C. C. Button, “Spin relaxation and all optical polarization switching at 1.52 micrometres in InGaAs(P)/InGaAsP multiple quantum wells,” Semicond. Sci. Technol. 14, 215–221 (1999).
[Crossref]

Kojima, K.

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

Krauskopf, B.

S. Wieczorek, B. Krauskopf, T.B. Simpson, and D. Lenstra, “The dynamic complexity of optically injected semiconductor lasers,” Physics Report. 416, 1–128 (2005).
[Crossref]

Kuroda, T.

S. Akasaki, S. Miyata, T. Kuroda, and A. Tackeuchi, “Exciton spin relaxation dynamics in InGaAs/InP quantum wells,” Appl. Phys. Lett. 85, 2083–2085 (2004).
[Crossref]

A. Tackeuchi, T. Kuroda, S. Muto, and O. Wada, “Picosecond electron spin-relaxation in GaAs/AlGaAs quantum wells and InGaAs/InP quantum wells,” Physica B 272, 318–323 (1999)
[Crossref]

R. Tackeuchi, T. Kuroda, S. Muto, Y. Nishikawa, and O. Wada, “Electron spin-relaxation dynamics in GaAs/AlGaAs quantum wells and InGaAs/InP quantum wells,” Jpn. J. Appl. Phys. 38, 4680–4687 (1999).
[Crossref]

Larsson, A.

Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Haonen, “Polarisation switching in a vertical cavity surface emitting semiconductor laser by frequency detuning,” IEE Proc. Optoelectron. 148, 31–34 (2001).
[Crossref]

Leibenguth, R. E.

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

Lenstra, D.

S. Wieczorek, B. Krauskopf, T.B. Simpson, and D. Lenstra, “The dynamic complexity of optically injected semiconductor lasers,” Physics Report. 416, 1–128 (2005).
[Crossref]

Li, H.

H. Li, T. L. Lucas, J. G. McInerney, M. W. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
[Crossref]

Lucas, T. L.

H. Li, T. L. Lucas, J. G. McInerney, M. W. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
[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, 765–782 (1997).
[Crossref]

McInerney, J. G.

H. Li, T. L. Lucas, J. G. McInerney, M. W. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
[Crossref]

Miller, A.

J. T. Hyland, G. T. Kennedy, A. Miller, and C. C. Button, “Spin relaxation and all optical polarization switching at 1.52 micrometres in InGaAs(P)/InGaAsP multiple quantum wells,” Semicond. Sci. Technol. 14, 215–221 (1999).
[Crossref]

Miyashita, T.

S. Adachi, T. Miyashita, S. Takeyama, Y. Takagi, and A. Tackeuchi, “Exciton spin dynamics in GaAs quantum wells,” J. Lumin. 72– 74, 307–308 (1997)
[Crossref]

Miyata, S.

S. Akasaki, S. Miyata, T. Kuroda, and A. Tackeuchi, “Exciton spin relaxation dynamics in InGaAs/InP quantum wells,” Appl. Phys. Lett. 85, 2083–2085 (2004).
[Crossref]

Moloney, J. V.

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

Morgan, R. A.

H. Li, T. L. Lucas, J. G. McInerney, M. W. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
[Crossref]

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

Muto, S.

R. Tackeuchi, T. Kuroda, S. Muto, Y. Nishikawa, and O. Wada, “Electron spin-relaxation dynamics in GaAs/AlGaAs quantum wells and InGaAs/InP quantum wells,” Jpn. J. Appl. Phys. 38, 4680–4687 (1999).
[Crossref]

A. Tackeuchi, T. Kuroda, S. Muto, and O. Wada, “Picosecond electron spin-relaxation in GaAs/AlGaAs quantum wells and InGaAs/InP quantum wells,” Physica B 272, 318–323 (1999)
[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]

Nishikawa, Y.

R. Tackeuchi, T. Kuroda, S. Muto, Y. Nishikawa, and O. Wada, “Electron spin-relaxation dynamics in GaAs/AlGaAs quantum wells and InGaAs/InP quantum wells,” Jpn. J. Appl. Phys. 38, 4680–4687 (1999).
[Crossref]

Oestreich, M.

J. Rudolph, S. Dohrmann, D. Hagele, W. Stolz, and M. Oestreich, “Room-temperature threshold reduction in vertical-cavity surface-emitting lasers by injection of spin-polarized electrons,” Appl. Phys. Lett. 87, 241117 (2005).
[Crossref]

Ortsiefer, M.

L. Chrostowski, X. Zhao, C. J. Chang-Hasnain, R. Shau, M. Ortsiefer, and M-C. Amann, “50 GHz optically injection-locked 1.55 µm VCSELs,” IEEE Photon. Technol. Lett. 16,367–369 (2006).
[Crossref]

L. Chrostowski, B. Faraji, W. Hofmann, R. Shau, M. Ortsiefer, and M.-C. Amann, “40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 µm VCSELs”, IEEE 20th International Semiconductor Laser Conference, Hawaii, 2006, Conference Digest pp. 117–118.
[Crossref]

Pan, Z. G.

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

Panajatov, K.

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

Panajotov, K.

I. Gatare, M. Sciamanna, and K. Panajotov, “Frequency-induced polarization bistability in vertical-cavity surface-emitting lasers,” Phys. Rev. A 75, 023804 (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. B. Altes, 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. Select. Topics in Quantum Electron,  42, 198–207 (2006)
[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]

T. Erneux, J. Danckaert, K. Panajotov, and I. Veretennicoff, “Two-variable reduction of the San Miguel-Feng-Moloney model for vertical-cavity surface-emitting lasers,” Phys. Rev. A 59, 4660–4667 (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, 033810-9 (2004).
[Crossref]

F. Prati, P. Caccia, and F. Castelli, “Effects of gain saturation on polarization switching in vertical-cavity surface-emitting lasers,” Phys. Rev. A 66, 063811 (2002).
[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, 765–782 (1997).
[Crossref]

Rudolph, J.

J. Rudolph, S. Dohrmann, D. Hagele, W. Stolz, and M. Oestreich, “Room-temperature threshold reduction in vertical-cavity surface-emitting lasers by injection of spin-polarized electrons,” Appl. Phys. Lett. 87, 241117 (2005).
[Crossref]

San Miguel, M.

A. Gahl, S. Balle, and M. San Miguel, “Polarization dynamics of optically pumped VCSELs,” IEEE J. Quantum Electron. 35, 342–351 (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, 765–782 (1997).
[Crossref]

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

Sciamanna, M.

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

I. Gatare, M. Sciamanna, and K. Panajotov, “Frequency-induced polarization bistability in vertical-cavity surface-emitting lasers,” Phys. Rev. A 75, 023804 (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. B. Altes, 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. Select. Topics in Quantum Electron,  42, 198–207 (2006)
[Crossref]

Shau, R.

L. Chrostowski, X. Zhao, C. J. Chang-Hasnain, R. Shau, M. Ortsiefer, and M-C. Amann, “50 GHz optically injection-locked 1.55 µm VCSELs,” IEEE Photon. Technol. Lett. 16,367–369 (2006).
[Crossref]

L. Chrostowski, B. Faraji, W. Hofmann, R. Shau, M. Ortsiefer, and M.-C. Amann, “40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 µm VCSELs”, IEEE 20th International Semiconductor Laser Conference, Hawaii, 2006, Conference Digest pp. 117–118.
[Crossref]

Shore, K. A.

Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Haonen, “Polarisation switching in a vertical cavity surface emitting semiconductor laser by frequency detuning,” IEE Proc. Optoelectron. 148, 31–34 (2001).
[Crossref]

Simpson, T.B.

S. Wieczorek, B. Krauskopf, T.B. Simpson, and D. Lenstra, “The dynamic complexity of optically injected semiconductor lasers,” Physics Report. 416, 1–128 (2005).
[Crossref]

Sogawa, T.

H. Ando, T. Sogawa, and H. Gotoh, “Photon-spin controlled lasing oscillation in surface-emitting lasers,” Appl. Phys. Lett. 73, 566–568 (1998).
[Crossref]

Stolz, W.

J. Rudolph, S. Dohrmann, D. Hagele, W. Stolz, and M. Oestreich, “Room-temperature threshold reduction in vertical-cavity surface-emitting lasers by injection of spin-polarized electrons,” Appl. Phys. Lett. 87, 241117 (2005).
[Crossref]

Tackeuchi, A.

S. Akasaki, S. Miyata, T. Kuroda, and A. Tackeuchi, “Exciton spin relaxation dynamics in InGaAs/InP quantum wells,” Appl. Phys. Lett. 85, 2083–2085 (2004).
[Crossref]

A. Tackeuchi, T. Kuroda, S. Muto, and O. Wada, “Picosecond electron spin-relaxation in GaAs/AlGaAs quantum wells and InGaAs/InP quantum wells,” Physica B 272, 318–323 (1999)
[Crossref]

S. Adachi, T. Miyashita, S. Takeyama, Y. Takagi, and A. Tackeuchi, “Exciton spin dynamics in GaAs quantum wells,” J. Lumin. 72– 74, 307–308 (1997)
[Crossref]

Tackeuchi, R.

R. Tackeuchi, T. Kuroda, S. Muto, Y. Nishikawa, and O. Wada, “Electron spin-relaxation dynamics in GaAs/AlGaAs quantum wells and InGaAs/InP quantum wells,” Jpn. J. Appl. Phys. 38, 4680–4687 (1999).
[Crossref]

Takagi, Y.

S. Adachi, T. Miyashita, S. Takeyama, Y. Takagi, and A. Tackeuchi, “Exciton spin dynamics in GaAs quantum wells,” J. Lumin. 72– 74, 307–308 (1997)
[Crossref]

Takeyama, S.

S. Adachi, T. Miyashita, S. Takeyama, Y. Takagi, and A. Tackeuchi, “Exciton spin dynamics in GaAs quantum wells,” J. Lumin. 72– 74, 307–308 (1997)
[Crossref]

Thienpont, H.

J. B. Altes, 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. Select. Topics in Quantum Electron,  42, 198–207 (2006)
[Crossref]

Valle, A.

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

Van der Sande, G.

G. Van der Sande, J. Danckaert, I. Veretennicoff, and T. Erneux, “Rate equations for vertical-cavity surface-emitting lasers,” Phys. Rev. A 67, 13809-7 (2003).
[Crossref]

Veretennicoff, I.

G. Van der Sande, J. Danckaert, I. Veretennicoff, and T. Erneux, “Rate equations for vertical-cavity surface-emitting lasers,” Phys. Rev. A 67, 13809-7 (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]

T. Erneux, J. Danckaert, K. Panajotov, and I. Veretennicoff, “Two-variable reduction of the San Miguel-Feng-Moloney model for vertical-cavity surface-emitting lasers,” Phys. Rev. A 59, 4660–4667 (1999).
[Crossref]

Wada, O.

A. Tackeuchi, T. Kuroda, S. Muto, and O. Wada, “Picosecond electron spin-relaxation in GaAs/AlGaAs quantum wells and InGaAs/InP quantum wells,” Physica B 272, 318–323 (1999)
[Crossref]

R. Tackeuchi, T. Kuroda, S. Muto, Y. Nishikawa, and O. Wada, “Electron spin-relaxation dynamics in GaAs/AlGaAs quantum wells and InGaAs/InP quantum wells,” Jpn. J. Appl. Phys. 38, 4680–4687 (1999).
[Crossref]

Wieczorek, S.

S. Wieczorek, W. W. Chow, L. Chrostowski, and C. J. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Quantum Electron. 42, 552–562 (2006).
[Crossref]

S. Wieczorek, B. Krauskopf, T.B. Simpson, and D. Lenstra, “The dynamic complexity of optically injected semiconductor lasers,” Physics Report. 416, 1–128 (2005).
[Crossref]

Wright, M. W.

H. Li, T. L. Lucas, J. G. McInerney, M. W. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
[Crossref]

Zhao, X.

L. Chrostowski, X. Zhao, C. J. Chang-Hasnain, R. Shau, M. Ortsiefer, and M-C. Amann, “50 GHz optically injection-locked 1.55 µm VCSELs,” IEEE Photon. Technol. Lett. 16,367–369 (2006).
[Crossref]

Appl. Phys. Lett. (4)

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

S. Akasaki, S. Miyata, T. Kuroda, and A. Tackeuchi, “Exciton spin relaxation dynamics in InGaAs/InP quantum wells,” Appl. Phys. Lett. 85, 2083–2085 (2004).
[Crossref]

H. Ando, T. Sogawa, and H. Gotoh, “Photon-spin controlled lasing oscillation in surface-emitting lasers,” Appl. Phys. Lett. 73, 566–568 (1998).
[Crossref]

J. Rudolph, S. Dohrmann, D. Hagele, W. Stolz, and M. Oestreich, “Room-temperature threshold reduction in vertical-cavity surface-emitting lasers by injection of spin-polarized electrons,” Appl. Phys. Lett. 87, 241117 (2005).
[Crossref]

IEE Proc. Optoelectron. (1)

Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Haonen, “Polarisation switching in a vertical cavity surface emitting semiconductor laser by frequency detuning,” IEE Proc. Optoelectron. 148, 31–34 (2001).
[Crossref]

IEEE J. Quantum Electron. (5)

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

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, 765–782 (1997).
[Crossref]

S. Wieczorek, W. W. Chow, L. Chrostowski, and C. J. Chang-Hasnain, “Improved semiconductor-laser dynamics from induced population pulsation,” IEEE J. Quantum Electron. 42, 552–562 (2006).
[Crossref]

H. Li, T. L. Lucas, J. G. McInerney, M. W. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
[Crossref]

A. Gahl, S. Balle, and M. San Miguel, “Polarization dynamics of optically pumped VCSELs,” IEEE J. Quantum Electron. 35, 342–351 (1999).
[Crossref]

IEEE J. Select. Topics in Quantum Electron (1)

J. B. Altes, 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. Select. Topics in Quantum Electron,  42, 198–207 (2006)
[Crossref]

IEEE J. Select. Topics in Quantum Electron. (1)

C-H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Select. Topics in Quantum Electron. 9, 1386–1393 (2003).
[Crossref]

IEEE Photon. Technol. Lett. (1)

L. Chrostowski, X. Zhao, C. J. Chang-Hasnain, R. Shau, M. Ortsiefer, and M-C. Amann, “50 GHz optically injection-locked 1.55 µm VCSELs,” IEEE Photon. Technol. Lett. 16,367–369 (2006).
[Crossref]

J. Lumin. (1)

S. Adachi, T. Miyashita, S. Takeyama, Y. Takagi, and A. Tackeuchi, “Exciton spin dynamics in GaAs quantum wells,” J. Lumin. 72– 74, 307–308 (1997)
[Crossref]

Jpn. J. Appl. Phys. (1)

R. Tackeuchi, T. Kuroda, S. Muto, Y. Nishikawa, and O. Wada, “Electron spin-relaxation dynamics in GaAs/AlGaAs quantum wells and InGaAs/InP quantum wells,” Jpn. J. Appl. Phys. 38, 4680–4687 (1999).
[Crossref]

Opt. Commun. (3)

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

J. 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. E. Chlouverakis and M. J. Adams, “Stability maps of injection-locked laser diodes using the largest Lyapunov exponent,” Opt. Commun. 216, 405–412 (2003).
[Crossref]

Phys. Rev. A (7)

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

F. Prati, P. Caccia, and F. Castelli, “Effects of gain saturation on polarization switching in vertical-cavity surface-emitting lasers,” Phys. Rev. A 66, 063811 (2002).
[Crossref]

F. Prati, P. Caccia, M. Bache, and F. Castelli, “Analysis of elliptically polarized states in vertical-cavity-surface-emitting lasers,” Phys. Rev. A 69, 033810-9 (2004).
[Crossref]

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

T. Erneux, J. Danckaert, K. Panajotov, and I. Veretennicoff, “Two-variable reduction of the San Miguel-Feng-Moloney model for vertical-cavity surface-emitting lasers,” Phys. Rev. A 59, 4660–4667 (1999).
[Crossref]

G. Van der Sande, J. Danckaert, I. Veretennicoff, and T. Erneux, “Rate equations for vertical-cavity surface-emitting lasers,” Phys. Rev. A 67, 13809-7 (2003).
[Crossref]

phys. stat. sol. (c) (1)

A. Homayounfar and M. J. Adams, “Spin polarized properties of optically injected VCSELs,” phys. stat. sol. (c) 4,604–606 (2007).
[Crossref]

Physica B (1)

A. Tackeuchi, T. Kuroda, S. Muto, and O. Wada, “Picosecond electron spin-relaxation in GaAs/AlGaAs quantum wells and InGaAs/InP quantum wells,” Physica B 272, 318–323 (1999)
[Crossref]

Physics Report. (1)

S. Wieczorek, B. Krauskopf, T.B. Simpson, and D. Lenstra, “The dynamic complexity of optically injected semiconductor lasers,” Physics Report. 416, 1–128 (2005).
[Crossref]

Semicond. Sci. Technol. (1)

J. T. Hyland, G. T. Kennedy, A. Miller, and C. C. Button, “Spin relaxation and all optical polarization switching at 1.52 micrometres in InGaAs(P)/InGaAsP multiple quantum wells,” Semicond. Sci. Technol. 14, 215–221 (1999).
[Crossref]

Other (1)

L. Chrostowski, B. Faraji, W. Hofmann, R. Shau, M. Ortsiefer, and M.-C. Amann, “40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 µm VCSELs”, IEEE 20th International Semiconductor Laser Conference, Hawaii, 2006, Conference Digest pp. 117–118.
[Crossref]

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Figures (13)

Fig. 1.
Fig. 1.

Stability diagram for a VCSEL with parameter values from Table 1 and spin relaxation rate γs=20 ns-1. The four regions denote linearly polarised stability for x-LP (LSx, dark grey) and y-LP (LSy, light grey), ES (orange) and instability (white).

Fig. 2.
Fig. 2.

Stability diagram as in Fig. 1, but for a larger value of spin relaxation, γs=40 ns-1, which shifts the critical point where the system is either at LSx or LSy towards higher values of pumping. The red area below the critical point now corresponds to linear bistability (LB). According to the numerical results, below the critical point the extent of LSy slightly exceeds the boundary of (6)

Fig. 3.
Fig. 3.

Enlarged plot of the region of ES of Fig. 1 with points (γp, 2η) denoted by letters of the alphabet. The inset shows the region for normalised pumping below 2η=1.4.

Fig. 4.
Fig. 4.

The polarisation |S| as a function of birefringence rate γp for 2η=1.4 (light blue), 1.5 (pink), 1.6 (grey), 1.7 (dark blue), 1.8 (green), 1.9 (red), 2.0 (black) and 2.1 (orange). The dashed line of Fig. 3 is the starting point of the region of ES (γp-EPmin, 2η), where each curve has its maximum value for |S|.

Fig. 5.
Fig. 5.

Absolute values of difference between the carriers with spin-up and spin-down, m, as a function of birefringence rate γp for the same values of pumping as Fig. 4.

Fig. 6.
Fig. 6.

Total carrier density N as a function of birefringence rate γp for the same values of pumping as Fig. 4.

Fig. 7.
Fig. 7.

(a) Elliptical relaxation oscillation frequency, ν ERO, and (b) ratio of elliptical ROF to linear ROF [ρ=ν EROp,2η)/ν LRO(2η)] as a function of birefringence rate γp for the same values of pumping as Fig. 4.

Fig. 8.
Fig. 8.

Calculated stability map for parameters given in Table 1 and 2η=1.3, γs=40ns-1, γp=9 rad/ns and Kinj=120 ns-1. At Δωy=-2γp=-18 rad/ns EILS is found.

Fig. 9.
Fig. 9.

Calculated stability map for parameters given in Table 1 and 2η=1.5, γs=20 ns-1, γp=18 rad/ns and Kinj=200 ns-1.

Fig. 10.
Fig. 10.

Calculated stability map for parameters given in Table 1 and 2η=2.1, γp=33.5 rad/ns, γs=20 ns-1 and Kinj=300 ns-1.

Fig. 11.
Fig. 11.

Transient behaviour of the dynamic variables for parameters Ey/Esol=0.01, γp=9 rad/ns, (IL,Δω)=(-40 dB, 70 rad/ns). The mean value for m is zero and Ω=87 rad/ns.

Fig. 12.
Fig. 12.

Transient behaviour of the dynamic variables for parameters Ey/Esol=0.01, γp=33.5 rad/ns, (IL,Δω)=(-40 dB, 70 rad/ns). The mean value for m is non-zero and Ω=137 rad/ns.

Fig. 13.
Fig. 13.

Transient behaviour of the dynamic variables for parameters Ey/Esol=0.0316 and an operating point from Fig. 10 (IL,Δω)=(-30 dB, -70 rad/ns).

Tables (3)

Tables Icon

Table 1. Parameter values for two VCSELs with different spin relaxation rates.

Tables Icon

Table 2. Summary of ROF behaviour for Figs. 1 and 2. For small (large) values of γs the area corresponding to γpx-min < γp < γpy-max is LSx (LB) in Figs. 1 and 2.

Tables Icon

Table 3. Colour coding of EP and LP regions

Equations (20)

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dE y dt = 1 2 τ p [ ( N 1 ) E y + m E x sin ( ε Δ ϕ ) cos ε ] + γ a E y
dE x dt = 1 2 τ p [ ( N 1 ) E x m E y sin ( ε + Δ ϕ ) cos ε ] γ a E x
d Δ ϕ dt = m 2 τ p cos ε [ E x E y cos ( ε Δ ϕ ) + E y E x cos ( ε + Δ ϕ ) ] + 2 γ p
dN dt = γ [ N ( 1 + E x 2 + E y 2 ) ( η + + η ) 2 m E y E x sin Δ ϕ ]
dm dt = γ s m + γ ( η + η ) γ [ m ( E x 2 + E y 2 ) ] + 2 γ N E y E x sin Δ ϕ
γ px min = α 2 τ p ( 1 + γ s γ ( 2 η 1 ) )
γ py max = [ γ s + γ ( 2 η 1 ) ] 2 α
2 η = 1 + ( J J th 1 ) ( 1 + τ p n o G n )
S = E + 2 E 2 E + 2 + E 2 = 2 E y E x E x 2 + E y 2 sin Δ ϕ
E y 2 = E x 2 sin ( Δ ϕ ε ) sin ( ε + Δ ϕ )
m = 2 γ γ s NE y E x sin Δ ϕ 1 + γ γ s ( E x 2 + E y 2 )
m 2 γ γ s ( 1 + Δ N ) E y E x sin Δ ϕ
m max < ( 2 η 1 ) ( 1 + Δ N ) γ γ s
ν LRO = 1 2 π ( 2 η 1 ) γ τ p
γ d = η γ
dE y dt = 1 2 τ p [ ( N 1 ) E y + m E x sin ( ε Δ ϕ ) cos ε ] + γ a E y + K inj E inj cos Δ
d ϕ y dt = α ( N 1 ) 2 τ p m 2 τ p E x E y cos ( ε Δ ϕ ) cos ε Δ ω y γ p + 2 α γ a + K inj E inj E y sin Δ
d ϕ x dt = α ( N 1 ) 2 τ p + m 2 τ p E y E x cos ( ε + Δ ϕ ) cos ε Δ ω y γ p
γ d = 1 2 [ γ + G n γ p ( J J th ) ]
ν RO = 1 2 π G n ( J J th ) γ d 2

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