Abstract

A modified spin-flip model is used to investigate the stability of optically-pumped quantum-dot spin-vertical cavity surface-emitting lasers. in terms of pump intensity and polarization. The stability maps exhibit pronounced polarization switching in the stable regions. Periodic oscillations in unstable regions are attributed to competition between spin relaxation and birefringence.

© 2012 Optical Society of America

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  1. P. Bhattacharya, D. Basu, A. Das, and D. Saha, Semicond. Sci. Technol. 26, 014002 (2011).
    [CrossRef]
  2. S. Iba, S. Koh, K. Ikeda, and H. Kawaguchi, Appl. Phys. Lett. 98, 081113 (2011).
    [CrossRef]
  3. A. Gahl, S. Balle, and M. San Miguel, IEEE J. Quantum Electron. 33, 342 (1999).
    [CrossRef]
  4. M. Y. Li, H. Jaehme, H. Soldat, N. C. Gerhardt, M. R. Hofmann, and T. Ackemann, Appl. Phys. Lett. 97, 191114 (2010).
    [CrossRef]
  5. R. K. Al-Seyab, D. Alexandropoulos, I. D. Henning, and M. J. Adams, IEEE Photon. J. 3, 799 (2011).
    [CrossRef]
  6. R. Oszwaldowski, C. Gothgen, and I. Zutic, Phys. Rev. B 82, 085316 (2010).
  7. J. Lee, W. Falls, R. Oszwałdowski, and I. Žutić, Phys. Rev. B 85, 045314 (2012).
  8. J. L. Robb, Y. Chen, A. Timmons, K. C. Hall, O. B. Shchekin, and D. G. Deppe, Appl. Phys. Lett. 90, 153118 (2007).
    [CrossRef]
  9. D. O’Brien, S. P. Hegarty, G. Huyet, and A. V. Uskov, Opt. Lett 29, 1072 (2004).
  10. M. J. Adams and D. Alexandropoulos, “Analysis of quantum-dot spin-VCSELs,” in preparation.
  11. C. Gøthgen, R. Oszwałdowski, A. Petrou, and I. Žutić, Appl. Phys. Lett. 93, 042513 (2008).
    [CrossRef]
  12. M. J. Adams and D. Alexandropoulos, IEEE J. Quantum Electron. 45, 744 (2009).
    [CrossRef]
  13. D. Saha, D. Basu, and P. Bhattacharya, Phys. Rev. B 82, 205309 (2010).
  14. D. Basu, D. Saha, and P. Bhattacharya, Phys. Rev. Lett. 102, 093904 (2009).
    [CrossRef]

2012

J. Lee, W. Falls, R. Oszwałdowski, and I. Žutić, Phys. Rev. B 85, 045314 (2012).

2011

P. Bhattacharya, D. Basu, A. Das, and D. Saha, Semicond. Sci. Technol. 26, 014002 (2011).
[CrossRef]

S. Iba, S. Koh, K. Ikeda, and H. Kawaguchi, Appl. Phys. Lett. 98, 081113 (2011).
[CrossRef]

R. K. Al-Seyab, D. Alexandropoulos, I. D. Henning, and M. J. Adams, IEEE Photon. J. 3, 799 (2011).
[CrossRef]

2010

R. Oszwaldowski, C. Gothgen, and I. Zutic, Phys. Rev. B 82, 085316 (2010).

M. Y. Li, H. Jaehme, H. Soldat, N. C. Gerhardt, M. R. Hofmann, and T. Ackemann, Appl. Phys. Lett. 97, 191114 (2010).
[CrossRef]

D. Saha, D. Basu, and P. Bhattacharya, Phys. Rev. B 82, 205309 (2010).

2009

D. Basu, D. Saha, and P. Bhattacharya, Phys. Rev. Lett. 102, 093904 (2009).
[CrossRef]

M. J. Adams and D. Alexandropoulos, IEEE J. Quantum Electron. 45, 744 (2009).
[CrossRef]

2008

C. Gøthgen, R. Oszwałdowski, A. Petrou, and I. Žutić, Appl. Phys. Lett. 93, 042513 (2008).
[CrossRef]

2007

J. L. Robb, Y. Chen, A. Timmons, K. C. Hall, O. B. Shchekin, and D. G. Deppe, Appl. Phys. Lett. 90, 153118 (2007).
[CrossRef]

2004

D. O’Brien, S. P. Hegarty, G. Huyet, and A. V. Uskov, Opt. Lett 29, 1072 (2004).

1999

A. Gahl, S. Balle, and M. San Miguel, IEEE J. Quantum Electron. 33, 342 (1999).
[CrossRef]

Ackemann, T.

M. Y. Li, H. Jaehme, H. Soldat, N. C. Gerhardt, M. R. Hofmann, and T. Ackemann, Appl. Phys. Lett. 97, 191114 (2010).
[CrossRef]

Adams, M. J.

R. K. Al-Seyab, D. Alexandropoulos, I. D. Henning, and M. J. Adams, IEEE Photon. J. 3, 799 (2011).
[CrossRef]

M. J. Adams and D. Alexandropoulos, IEEE J. Quantum Electron. 45, 744 (2009).
[CrossRef]

M. J. Adams and D. Alexandropoulos, “Analysis of quantum-dot spin-VCSELs,” in preparation.

Alexandropoulos, D.

R. K. Al-Seyab, D. Alexandropoulos, I. D. Henning, and M. J. Adams, IEEE Photon. J. 3, 799 (2011).
[CrossRef]

M. J. Adams and D. Alexandropoulos, IEEE J. Quantum Electron. 45, 744 (2009).
[CrossRef]

M. J. Adams and D. Alexandropoulos, “Analysis of quantum-dot spin-VCSELs,” in preparation.

Al-Seyab, R. K.

R. K. Al-Seyab, D. Alexandropoulos, I. D. Henning, and M. J. Adams, IEEE Photon. J. 3, 799 (2011).
[CrossRef]

Balle, S.

A. Gahl, S. Balle, and M. San Miguel, IEEE J. Quantum Electron. 33, 342 (1999).
[CrossRef]

Basu, D.

P. Bhattacharya, D. Basu, A. Das, and D. Saha, Semicond. Sci. Technol. 26, 014002 (2011).
[CrossRef]

D. Saha, D. Basu, and P. Bhattacharya, Phys. Rev. B 82, 205309 (2010).

D. Basu, D. Saha, and P. Bhattacharya, Phys. Rev. Lett. 102, 093904 (2009).
[CrossRef]

Bhattacharya, P.

P. Bhattacharya, D. Basu, A. Das, and D. Saha, Semicond. Sci. Technol. 26, 014002 (2011).
[CrossRef]

D. Saha, D. Basu, and P. Bhattacharya, Phys. Rev. B 82, 205309 (2010).

D. Basu, D. Saha, and P. Bhattacharya, Phys. Rev. Lett. 102, 093904 (2009).
[CrossRef]

Chen, Y.

J. L. Robb, Y. Chen, A. Timmons, K. C. Hall, O. B. Shchekin, and D. G. Deppe, Appl. Phys. Lett. 90, 153118 (2007).
[CrossRef]

Das, A.

P. Bhattacharya, D. Basu, A. Das, and D. Saha, Semicond. Sci. Technol. 26, 014002 (2011).
[CrossRef]

Deppe, D. G.

J. L. Robb, Y. Chen, A. Timmons, K. C. Hall, O. B. Shchekin, and D. G. Deppe, Appl. Phys. Lett. 90, 153118 (2007).
[CrossRef]

Falls, W.

J. Lee, W. Falls, R. Oszwałdowski, and I. Žutić, Phys. Rev. B 85, 045314 (2012).

Gahl, A.

A. Gahl, S. Balle, and M. San Miguel, IEEE J. Quantum Electron. 33, 342 (1999).
[CrossRef]

Gerhardt, N. C.

M. Y. Li, H. Jaehme, H. Soldat, N. C. Gerhardt, M. R. Hofmann, and T. Ackemann, Appl. Phys. Lett. 97, 191114 (2010).
[CrossRef]

Gothgen, C.

R. Oszwaldowski, C. Gothgen, and I. Zutic, Phys. Rev. B 82, 085316 (2010).

Gøthgen, C.

C. Gøthgen, R. Oszwałdowski, A. Petrou, and I. Žutić, Appl. Phys. Lett. 93, 042513 (2008).
[CrossRef]

Hall, K. C.

J. L. Robb, Y. Chen, A. Timmons, K. C. Hall, O. B. Shchekin, and D. G. Deppe, Appl. Phys. Lett. 90, 153118 (2007).
[CrossRef]

Hegarty, S. P.

D. O’Brien, S. P. Hegarty, G. Huyet, and A. V. Uskov, Opt. Lett 29, 1072 (2004).

Henning, I. D.

R. K. Al-Seyab, D. Alexandropoulos, I. D. Henning, and M. J. Adams, IEEE Photon. J. 3, 799 (2011).
[CrossRef]

Hofmann, M. R.

M. Y. Li, H. Jaehme, H. Soldat, N. C. Gerhardt, M. R. Hofmann, and T. Ackemann, Appl. Phys. Lett. 97, 191114 (2010).
[CrossRef]

Huyet, G.

D. O’Brien, S. P. Hegarty, G. Huyet, and A. V. Uskov, Opt. Lett 29, 1072 (2004).

Iba, S.

S. Iba, S. Koh, K. Ikeda, and H. Kawaguchi, Appl. Phys. Lett. 98, 081113 (2011).
[CrossRef]

Ikeda, K.

S. Iba, S. Koh, K. Ikeda, and H. Kawaguchi, Appl. Phys. Lett. 98, 081113 (2011).
[CrossRef]

Jaehme, H.

M. Y. Li, H. Jaehme, H. Soldat, N. C. Gerhardt, M. R. Hofmann, and T. Ackemann, Appl. Phys. Lett. 97, 191114 (2010).
[CrossRef]

Kawaguchi, H.

S. Iba, S. Koh, K. Ikeda, and H. Kawaguchi, Appl. Phys. Lett. 98, 081113 (2011).
[CrossRef]

Koh, S.

S. Iba, S. Koh, K. Ikeda, and H. Kawaguchi, Appl. Phys. Lett. 98, 081113 (2011).
[CrossRef]

Lee, J.

J. Lee, W. Falls, R. Oszwałdowski, and I. Žutić, Phys. Rev. B 85, 045314 (2012).

Li, M. Y.

M. Y. Li, H. Jaehme, H. Soldat, N. C. Gerhardt, M. R. Hofmann, and T. Ackemann, Appl. Phys. Lett. 97, 191114 (2010).
[CrossRef]

O’Brien, D.

D. O’Brien, S. P. Hegarty, G. Huyet, and A. V. Uskov, Opt. Lett 29, 1072 (2004).

Oszwaldowski, R.

J. Lee, W. Falls, R. Oszwałdowski, and I. Žutić, Phys. Rev. B 85, 045314 (2012).

R. Oszwaldowski, C. Gothgen, and I. Zutic, Phys. Rev. B 82, 085316 (2010).

C. Gøthgen, R. Oszwałdowski, A. Petrou, and I. Žutić, Appl. Phys. Lett. 93, 042513 (2008).
[CrossRef]

Petrou, A.

C. Gøthgen, R. Oszwałdowski, A. Petrou, and I. Žutić, Appl. Phys. Lett. 93, 042513 (2008).
[CrossRef]

Robb, J. L.

J. L. Robb, Y. Chen, A. Timmons, K. C. Hall, O. B. Shchekin, and D. G. Deppe, Appl. Phys. Lett. 90, 153118 (2007).
[CrossRef]

Saha, D.

P. Bhattacharya, D. Basu, A. Das, and D. Saha, Semicond. Sci. Technol. 26, 014002 (2011).
[CrossRef]

D. Saha, D. Basu, and P. Bhattacharya, Phys. Rev. B 82, 205309 (2010).

D. Basu, D. Saha, and P. Bhattacharya, Phys. Rev. Lett. 102, 093904 (2009).
[CrossRef]

San Miguel, M.

A. Gahl, S. Balle, and M. San Miguel, IEEE J. Quantum Electron. 33, 342 (1999).
[CrossRef]

Shchekin, O. B.

J. L. Robb, Y. Chen, A. Timmons, K. C. Hall, O. B. Shchekin, and D. G. Deppe, Appl. Phys. Lett. 90, 153118 (2007).
[CrossRef]

Soldat, H.

M. Y. Li, H. Jaehme, H. Soldat, N. C. Gerhardt, M. R. Hofmann, and T. Ackemann, Appl. Phys. Lett. 97, 191114 (2010).
[CrossRef]

Timmons, A.

J. L. Robb, Y. Chen, A. Timmons, K. C. Hall, O. B. Shchekin, and D. G. Deppe, Appl. Phys. Lett. 90, 153118 (2007).
[CrossRef]

Uskov, A. V.

D. O’Brien, S. P. Hegarty, G. Huyet, and A. V. Uskov, Opt. Lett 29, 1072 (2004).

Zutic, I.

R. Oszwaldowski, C. Gothgen, and I. Zutic, Phys. Rev. B 82, 085316 (2010).

Žutic, I.

J. Lee, W. Falls, R. Oszwałdowski, and I. Žutić, Phys. Rev. B 85, 045314 (2012).

C. Gøthgen, R. Oszwałdowski, A. Petrou, and I. Žutić, Appl. Phys. Lett. 93, 042513 (2008).
[CrossRef]

Appl. Phys. Lett.

M. Y. Li, H. Jaehme, H. Soldat, N. C. Gerhardt, M. R. Hofmann, and T. Ackemann, Appl. Phys. Lett. 97, 191114 (2010).
[CrossRef]

S. Iba, S. Koh, K. Ikeda, and H. Kawaguchi, Appl. Phys. Lett. 98, 081113 (2011).
[CrossRef]

J. L. Robb, Y. Chen, A. Timmons, K. C. Hall, O. B. Shchekin, and D. G. Deppe, Appl. Phys. Lett. 90, 153118 (2007).
[CrossRef]

C. Gøthgen, R. Oszwałdowski, A. Petrou, and I. Žutić, Appl. Phys. Lett. 93, 042513 (2008).
[CrossRef]

IEEE J. Quantum Electron.

M. J. Adams and D. Alexandropoulos, IEEE J. Quantum Electron. 45, 744 (2009).
[CrossRef]

A. Gahl, S. Balle, and M. San Miguel, IEEE J. Quantum Electron. 33, 342 (1999).
[CrossRef]

IEEE Photon. J.

R. K. Al-Seyab, D. Alexandropoulos, I. D. Henning, and M. J. Adams, IEEE Photon. J. 3, 799 (2011).
[CrossRef]

Opt. Lett

D. O’Brien, S. P. Hegarty, G. Huyet, and A. V. Uskov, Opt. Lett 29, 1072 (2004).

Phys. Rev. B

R. Oszwaldowski, C. Gothgen, and I. Zutic, Phys. Rev. B 82, 085316 (2010).

J. Lee, W. Falls, R. Oszwałdowski, and I. Žutić, Phys. Rev. B 85, 045314 (2012).

D. Saha, D. Basu, and P. Bhattacharya, Phys. Rev. B 82, 205309 (2010).

Phys. Rev. Lett.

D. Basu, D. Saha, and P. Bhattacharya, Phys. Rev. Lett. 102, 093904 (2009).
[CrossRef]

Semicond. Sci. Technol.

P. Bhattacharya, D. Basu, A. Das, and D. Saha, Semicond. Sci. Technol. 26, 014002 (2011).
[CrossRef]

Other

M. J. Adams and D. Alexandropoulos, “Analysis of quantum-dot spin-VCSELs,” in preparation.

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Figures (4)

Fig. 1.
Fig. 1.

The six-level system used for the SFM in a QD spin-VCSEL showing the relevant nomenclature.

Fig. 2.
Fig. 2.

Calculated maps of (a) output intensity I and (b) output polarization ε for the parameters γWLs=γQDs=1ps1, γ0=400ns1, γp=20ns1, γa=0, γn=1ns1, κ=250ns1, α=3, and h=1.1995.

Fig. 3.
Fig. 3.

(a) Output intensity map, (b) output polarization map, and (c) time series for the point P=0.6, η=4, calculated for the same parameters as in Fig. 2, except that here γWLs=γQDs=10ns1.

Fig. 4.
Fig. 4.

Time traces of (a) intensities (b) QD carrier densities, and (c) phase for the parameter of Fig. 3 and P=0.2 and η=1.07.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

dE±dt=κ(nQD±1)(1+iα)E±(γa+iγp)E,
dnWL±dt=η±γn+hγn2γonWL±[hnQD±2h]γWLs(nWL+nWL),
dnGS±dt=γonWL±h(hnQD±)γn(h+nQD±)γQDs(nQD+nQD)2γnnQD±|E±|2,
I=|E+|2+|E|2,ε=|E+|2|E|2|E+|2|E|2,η=η++η,P=η+ηη++η.

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