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 ?m 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 ?m 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, X. Zhao, C. J. Chang-Hasnain, R. Shau, M. Ortsiefer and M-C. Amann, "50 GHz optically injection-locked 1.55 ?m 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 ?m 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 ?m 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]

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]

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.

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]

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]

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]

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]

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.

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]

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 ?m VCSELs," IEEE Photon. Technol. Lett. 16,367-369 (2006).
[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. 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.

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]

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]

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 ?m VCSELs," IEEE Photon. Technol. Lett. 16,367-369 (2006).
[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]

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 ?m 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 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 ?m 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]

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]

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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