Abstract

We have analyzed the effect of the photon energy and temperature dependence of both the gain and the total losses inside the cavity to understand the polarization behavior of vertical-cavity surface-emitting lasers. The assumption that the losses are dominated by free-carrier absorption in the p-doped mirror is made. Developing a new theoretical approach, we are able to predict different polarization switching regimes in which switching occurs from the high- to the low-frequency mode, from the low- to the high-frequency mode, or both consecutively. All these predictions have been experimentally verified by our measurements on GaAs/AlGaAs proton-implanted vertical-cavity surface-emitting lasers.

© 1999 Optical Society of America

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  1. C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Polarization and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
    [CrossRef]
  2. A. K. Jansen van Doorn, M. P. van Exter, and J. P. Woerdman, “Elasto-optic anisotropy and polarization orientation of vertical-cavity surface-emitting semiconductor lasers,” Appl. Phys. Lett. 69, 1041–1043 (1996).
    [CrossRef]
  3. K. D. Choquette, D. A. Richie, and R. E. Leibenguth, “Temperature dependence of gain-guided of vertical-cavity surface-emitting laser polarization,” Appl. Phys. Lett. 64, 2062–2064 (1994).
    [CrossRef]
  4. K. D. Choquette, K. L. Lear, R. E. Leibenguth, and M. T. Asom, “Polarization modulation of vertical-cavity laser diodes,” Appl. Phys. Lett. 64, 2767–2769 (1994).
    [CrossRef]
  5. K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSELs due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
    [CrossRef]
  6. M. P. van Exter, A. K. Jansen van Doorn, and J. P. Woerdman, “Electro-optic effect and birefringence in semiconductor vertical-cavity lasers,” Phys. Rev. A 51, 845–853 (1997).
    [CrossRef]
  7. J. Martin-Regalado, J. L. A. Chilla, J. J. Rocca, and P. Brusenbach, “Polarization switching in vertical-cavity surface-emitting lasers observed at constant active region temperature,” Appl. Phys. Lett. 70, 3350–3352 (1997).
    [CrossRef]
  8. M. P. van Exter, A. Al-Remawi, and J. P. Woerdman, “Polarization fluctuations demonstrate nonlinear anisotropy of a vertical-cavity semiconductor laser,” Phys. Rev. Lett. 80, 4875–4878 (1998).
    [CrossRef]
  9. M. San Miguel, O. Feng, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52, 1728–1739 (1996).
    [CrossRef]
  10. J. Martin-Regalado, M. San Miguel, N. B. Abraham, and F. Prati, “Polarization switching in quantum-well vertical-cavity surface-emitting lasers,” Opt. Lett. 21, 351–353 (1996).
    [CrossRef] [PubMed]
  11. 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]
  12. A. Valle, L. Pesquera, and K. S. Shore, “Polarization behaviour of birefringent multi-transverse mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 9, 557–559 (1997).
    [CrossRef]
  13. J. Martin-Regalado, S. Balle, M. San Miguel, A. Valle, and L. Pesquera, “Polarization and transverse-mode selection in quantum-well vertical-cavity surface-emitting lasers: index- and gain guided devices,” Quantum Semiclass. Opt. 9, 713–736 (1997).
    [CrossRef]
  14. S. Balle, E. Tolkachova, M. San Miguel, J. R. Tredicce, J. Martin-Regalado, and A. Gahl, “Mechanisms of polarization switching in single-transverse-mode verticalcavity surface-emitting lasers: thermal shift and nonlinear semiconductor dynamics,” Opt. Lett. 24, 1121–1123 (1999).
    [CrossRef]
  15. B. Ryvkin and A. Georgievskii, “Polarization selection in VCSELs due to current carrier heating,” Semiconductors 33, 813–819 (1999).
    [CrossRef]
  16. T. E. Sale, Vertical Cavity Surface Emitting Lasers (Wiley, New York, 1995).
  17. M. H. MacDougal, P. D. Dapkus, A. E. Bond, C. K. Lin, and J. Geske, “Design and fabrication of VCSELs with AlxOy–GaAs DBR’s,” IEEE J. Sel. Top. Quantum Electron. 3, 905–915 (1997).
    [CrossRef]
  18. A. H. Kahn, “Theory of the infrared absorption of carriers in germanium and silicon,” Phys. Rev. 97, 1647–1652 (1955).
    [CrossRef]
  19. O. Christensen, “Absorption from neutral acceptors in GaAs and GaP,” Phys. Rev. B 7, 1426–1432 (1973).
    [CrossRef]
  20. R. F. Kazarinov, “Maximum reduction of the threshold current density in double-heterojunction injection lasers,” Sov. Phys. Semicond. 7, 525–531 (1973).
  21. G. E. Giudice, D. V. Kuksenkov, and H. Temkin, “Measurement of differential carrier lifetime in vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 10, 920–922 (1998).
    [CrossRef]
  22. L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, New York, 1995).
  23. Vixel Corporation, 325 Interlocken Parkway, Broomfield, Colo. 80021.

1999 (3)

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]

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

B. Ryvkin and A. Georgievskii, “Polarization selection in VCSELs due to current carrier heating,” Semiconductors 33, 813–819 (1999).
[CrossRef]

1998 (3)

G. E. Giudice, D. V. Kuksenkov, and H. Temkin, “Measurement of differential carrier lifetime in vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 10, 920–922 (1998).
[CrossRef]

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

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSELs due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

1997 (5)

M. P. van Exter, A. K. Jansen van Doorn, and J. P. Woerdman, “Electro-optic effect and birefringence in semiconductor vertical-cavity lasers,” Phys. Rev. A 51, 845–853 (1997).
[CrossRef]

J. Martin-Regalado, J. L. A. Chilla, J. J. Rocca, and P. Brusenbach, “Polarization switching in vertical-cavity surface-emitting lasers observed at constant active region temperature,” Appl. Phys. Lett. 70, 3350–3352 (1997).
[CrossRef]

A. Valle, L. Pesquera, and K. S. Shore, “Polarization behaviour of birefringent multi-transverse mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 9, 557–559 (1997).
[CrossRef]

J. Martin-Regalado, S. Balle, M. San Miguel, A. Valle, and L. Pesquera, “Polarization and transverse-mode selection in quantum-well vertical-cavity surface-emitting lasers: index- and gain guided devices,” Quantum Semiclass. Opt. 9, 713–736 (1997).
[CrossRef]

M. H. MacDougal, P. D. Dapkus, A. E. Bond, C. K. Lin, and J. Geske, “Design and fabrication of VCSELs with AlxOy–GaAs DBR’s,” IEEE J. Sel. Top. Quantum Electron. 3, 905–915 (1997).
[CrossRef]

1996 (3)

M. San Miguel, O. Feng, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52, 1728–1739 (1996).
[CrossRef]

J. Martin-Regalado, M. San Miguel, N. B. Abraham, and F. Prati, “Polarization switching in quantum-well vertical-cavity surface-emitting lasers,” Opt. Lett. 21, 351–353 (1996).
[CrossRef] [PubMed]

A. K. Jansen van Doorn, M. P. van Exter, and J. P. Woerdman, “Elasto-optic anisotropy and polarization orientation of vertical-cavity surface-emitting semiconductor lasers,” Appl. Phys. Lett. 69, 1041–1043 (1996).
[CrossRef]

1994 (2)

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

K. D. Choquette, K. L. Lear, R. E. Leibenguth, and M. T. Asom, “Polarization modulation of vertical-cavity laser diodes,” Appl. Phys. Lett. 64, 2767–2769 (1994).
[CrossRef]

1991 (1)

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Polarization and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

1973 (2)

O. Christensen, “Absorption from neutral acceptors in GaAs and GaP,” Phys. Rev. B 7, 1426–1432 (1973).
[CrossRef]

R. F. Kazarinov, “Maximum reduction of the threshold current density in double-heterojunction injection lasers,” Sov. Phys. Semicond. 7, 525–531 (1973).

1955 (1)

A. H. Kahn, “Theory of the infrared absorption of carriers in germanium and silicon,” Phys. Rev. 97, 1647–1652 (1955).
[CrossRef]

Abraham, N. B.

Al-Remawi, A.

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

Asom, M. T.

K. D. Choquette, K. L. Lear, R. E. Leibenguth, and M. T. Asom, “Polarization modulation of vertical-cavity laser diodes,” Appl. Phys. Lett. 64, 2767–2769 (1994).
[CrossRef]

Balle, S.

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

J. Martin-Regalado, S. Balle, M. San Miguel, A. Valle, and L. Pesquera, “Polarization and transverse-mode selection in quantum-well vertical-cavity surface-emitting lasers: index- and gain guided devices,” Quantum Semiclass. Opt. 9, 713–736 (1997).
[CrossRef]

Bond, A. E.

M. H. MacDougal, P. D. Dapkus, A. E. Bond, C. K. Lin, and J. Geske, “Design and fabrication of VCSELs with AlxOy–GaAs DBR’s,” IEEE J. Sel. Top. Quantum Electron. 3, 905–915 (1997).
[CrossRef]

Brusenbach, P.

J. Martin-Regalado, J. L. A. Chilla, J. J. Rocca, and P. Brusenbach, “Polarization switching in vertical-cavity surface-emitting lasers observed at constant active region temperature,” Appl. Phys. Lett. 70, 3350–3352 (1997).
[CrossRef]

Chang-Hasnain, C. J.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Polarization and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

Chilla, J. L. A.

J. Martin-Regalado, J. L. A. Chilla, J. J. Rocca, and P. Brusenbach, “Polarization switching in vertical-cavity surface-emitting lasers observed at constant active region temperature,” Appl. Phys. Lett. 70, 3350–3352 (1997).
[CrossRef]

Choquette, K. D.

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

K. D. Choquette, K. L. Lear, R. E. Leibenguth, and M. T. Asom, “Polarization modulation of vertical-cavity laser diodes,” Appl. Phys. Lett. 64, 2767–2769 (1994).
[CrossRef]

Christensen, O.

O. Christensen, “Absorption from neutral acceptors in GaAs and GaP,” Phys. Rev. B 7, 1426–1432 (1973).
[CrossRef]

Danckaert, J.

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]

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSELs due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

Dapkus, P. D.

M. H. MacDougal, P. D. Dapkus, A. E. Bond, C. K. Lin, and J. Geske, “Design and fabrication of VCSELs with AlxOy–GaAs DBR’s,” IEEE J. Sel. Top. Quantum Electron. 3, 905–915 (1997).
[CrossRef]

Erneux, T.

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, O.

M. San Miguel, O. Feng, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52, 1728–1739 (1996).
[CrossRef]

Florez, L. T.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Polarization and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

Gahl, A.

Georgievskii, A.

B. Ryvkin and A. Georgievskii, “Polarization selection in VCSELs due to current carrier heating,” Semiconductors 33, 813–819 (1999).
[CrossRef]

Geske, J.

M. H. MacDougal, P. D. Dapkus, A. E. Bond, C. K. Lin, and J. Geske, “Design and fabrication of VCSELs with AlxOy–GaAs DBR’s,” IEEE J. Sel. Top. Quantum Electron. 3, 905–915 (1997).
[CrossRef]

Giudice, G. E.

G. E. Giudice, D. V. Kuksenkov, and H. Temkin, “Measurement of differential carrier lifetime in vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 10, 920–922 (1998).
[CrossRef]

Harbison, J. P.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Polarization and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

Hasnain, G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Polarization and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

Jansen van Doorn, A. K.

M. P. van Exter, A. K. Jansen van Doorn, and J. P. Woerdman, “Electro-optic effect and birefringence in semiconductor vertical-cavity lasers,” Phys. Rev. A 51, 845–853 (1997).
[CrossRef]

A. K. Jansen van Doorn, M. P. van Exter, and J. P. Woerdman, “Elasto-optic anisotropy and polarization orientation of vertical-cavity surface-emitting semiconductor lasers,” Appl. Phys. Lett. 69, 1041–1043 (1996).
[CrossRef]

Kahn, A. H.

A. H. Kahn, “Theory of the infrared absorption of carriers in germanium and silicon,” Phys. Rev. 97, 1647–1652 (1955).
[CrossRef]

Kazarinov, R. F.

R. F. Kazarinov, “Maximum reduction of the threshold current density in double-heterojunction injection lasers,” Sov. Phys. Semicond. 7, 525–531 (1973).

Kuksenkov, D. V.

G. E. Giudice, D. V. Kuksenkov, and H. Temkin, “Measurement of differential carrier lifetime in vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 10, 920–922 (1998).
[CrossRef]

Lear, K. L.

K. D. Choquette, K. L. Lear, R. E. Leibenguth, and M. T. Asom, “Polarization modulation of vertical-cavity laser diodes,” Appl. Phys. Lett. 64, 2767–2769 (1994).
[CrossRef]

Leibenguth, R. E.

K. D. Choquette, K. L. Lear, R. E. Leibenguth, and M. T. Asom, “Polarization modulation of vertical-cavity laser diodes,” Appl. Phys. Lett. 64, 2767–2769 (1994).
[CrossRef]

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

Lin, C. K.

M. H. MacDougal, P. D. Dapkus, A. E. Bond, C. K. Lin, and J. Geske, “Design and fabrication of VCSELs with AlxOy–GaAs DBR’s,” IEEE J. Sel. Top. Quantum Electron. 3, 905–915 (1997).
[CrossRef]

MacDougal, M. H.

M. H. MacDougal, P. D. Dapkus, A. E. Bond, C. K. Lin, and J. Geske, “Design and fabrication of VCSELs with AlxOy–GaAs DBR’s,” IEEE J. Sel. Top. Quantum Electron. 3, 905–915 (1997).
[CrossRef]

Martin-Regalado, J.

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

J. Martin-Regalado, S. Balle, M. San Miguel, A. Valle, and L. Pesquera, “Polarization and transverse-mode selection in quantum-well vertical-cavity surface-emitting lasers: index- and gain guided devices,” Quantum Semiclass. Opt. 9, 713–736 (1997).
[CrossRef]

J. Martin-Regalado, J. L. A. Chilla, J. J. Rocca, and P. Brusenbach, “Polarization switching in vertical-cavity surface-emitting lasers observed at constant active region temperature,” Appl. Phys. Lett. 70, 3350–3352 (1997).
[CrossRef]

J. Martin-Regalado, M. San Miguel, N. B. Abraham, and F. Prati, “Polarization switching in quantum-well vertical-cavity surface-emitting lasers,” Opt. Lett. 21, 351–353 (1996).
[CrossRef] [PubMed]

Moloney, J. V.

M. San Miguel, O. Feng, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52, 1728–1739 (1996).
[CrossRef]

Panajotov, K.

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]

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSELs due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

Peeters, M.

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSELs due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

Pesquera, L.

J. Martin-Regalado, S. Balle, M. San Miguel, A. Valle, and L. Pesquera, “Polarization and transverse-mode selection in quantum-well vertical-cavity surface-emitting lasers: index- and gain guided devices,” Quantum Semiclass. Opt. 9, 713–736 (1997).
[CrossRef]

A. Valle, L. Pesquera, and K. S. Shore, “Polarization behaviour of birefringent multi-transverse mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 9, 557–559 (1997).
[CrossRef]

Prati, F.

Richie, D. A.

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

Rocca, J. J.

J. Martin-Regalado, J. L. A. Chilla, J. J. Rocca, and P. Brusenbach, “Polarization switching in vertical-cavity surface-emitting lasers observed at constant active region temperature,” Appl. Phys. Lett. 70, 3350–3352 (1997).
[CrossRef]

Ryvkin, B.

B. Ryvkin and A. Georgievskii, “Polarization selection in VCSELs due to current carrier heating,” Semiconductors 33, 813–819 (1999).
[CrossRef]

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSELs due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

San Miguel, M.

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

J. Martin-Regalado, S. Balle, M. San Miguel, A. Valle, and L. Pesquera, “Polarization and transverse-mode selection in quantum-well vertical-cavity surface-emitting lasers: index- and gain guided devices,” Quantum Semiclass. Opt. 9, 713–736 (1997).
[CrossRef]

J. Martin-Regalado, M. San Miguel, N. B. Abraham, and F. Prati, “Polarization switching in quantum-well vertical-cavity surface-emitting lasers,” Opt. Lett. 21, 351–353 (1996).
[CrossRef] [PubMed]

M. San Miguel, O. Feng, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52, 1728–1739 (1996).
[CrossRef]

Shore, K. S.

A. Valle, L. Pesquera, and K. S. Shore, “Polarization behaviour of birefringent multi-transverse mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 9, 557–559 (1997).
[CrossRef]

Stoffel, N. G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Polarization and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

Temkin, H.

G. E. Giudice, D. V. Kuksenkov, and H. Temkin, “Measurement of differential carrier lifetime in vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 10, 920–922 (1998).
[CrossRef]

Thienpont, H.

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSELs due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

Tolkachova, E.

Tredicce, J. R.

Valle, A.

J. Martin-Regalado, S. Balle, M. San Miguel, A. Valle, and L. Pesquera, “Polarization and transverse-mode selection in quantum-well vertical-cavity surface-emitting lasers: index- and gain guided devices,” Quantum Semiclass. Opt. 9, 713–736 (1997).
[CrossRef]

A. Valle, L. Pesquera, and K. S. Shore, “Polarization behaviour of birefringent multi-transverse mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 9, 557–559 (1997).
[CrossRef]

van Exter, M. P.

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

M. P. van Exter, A. K. Jansen van Doorn, and J. P. Woerdman, “Electro-optic effect and birefringence in semiconductor vertical-cavity lasers,” Phys. Rev. A 51, 845–853 (1997).
[CrossRef]

A. K. Jansen van Doorn, M. P. van Exter, and J. P. Woerdman, “Elasto-optic anisotropy and polarization orientation of vertical-cavity surface-emitting semiconductor lasers,” Appl. Phys. Lett. 69, 1041–1043 (1996).
[CrossRef]

Veretennicoff, I.

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]

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSELs due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

Von Lehmen, A. C.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Polarization and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

Woerdman, J. P.

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[CrossRef]

M. P. van Exter, A. K. Jansen van Doorn, and J. P. Woerdman, “Electro-optic effect and birefringence in semiconductor vertical-cavity lasers,” Phys. Rev. A 51, 845–853 (1997).
[CrossRef]

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[CrossRef]

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IEEE J. Quantum Electron. (1)

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[CrossRef]

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

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Vixel Corporation, 325 Interlocken Parkway, Broomfield, Colo. 80021.

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Figures (7)

Fig. 1
Fig. 1

Schematic representation of the material gain and the cavity losses as a function of photon energy for three different situations.

Fig. 2
Fig. 2

Temperature dependence of the two terms in the gain derivative [Eq. (9)].

Fig. 3
Fig. 3

Dependence of the gain derivative with respect to the photon energy on ΔT, the difference between the active region temperature at a certain current and the temperature at threshold (solid curves 1–8). For curve 1, ω0 is close to the gain maximum, and Tsub=300 K. Each of curves 2–8 corresponds to a relative increase of the substrate temperature of 4.5 K. The dependence of the loss derivative on the active region temperature rise above threshold is shown by the nearly straight lines. The initial points of these thick and thin solid lines are taken at (αp/αtot)g2000 cm-1 [see Eq. (6)], and Tsub=300 K and Tsub=350 K, correspondingly. The inset shows an enlargement.

Fig. 4
Fig. 4

Polarization-resolved optical output power versus dc injection current characteristic at three different substrate temperatures: (a) Tsub=10 °C, (b) Tsub=15 °C, (c) Tsub=55 °C. The lower (higher) photon energy mode is shown as a full (dashed) curve.

Fig. 5
Fig. 5

Typical scanning Fabry–Perot spectrum at the current of type II switching (J=9 mA, Tsub=15 °C) showing the direction of the switching and the frequency splitting of 12 GHz.

Fig. 6
Fig. 6

(a) Injection current at the type II PS point JPS (diamonds) and at the threshold current Jth (squares) as a function of the laser substrate temperature. (b) Active region temperature at the type II PS current (TPS, diamonds) and at the threshold current (Tth, squares).

Fig. 7
Fig. 7

Schematic representation of the gain and the loss as a function of photon energy for (a) lower and (b) higher cavity temperatures. The lasing mode in each case is indicated by the vertical arrow. Notice that for higher temperatures the gain has to increase, as it has to compensate for the losses in the p-doped DBR mirror, which also increase with temperature. The different cases (A, B, D, and E) depicted are discussed in the text.

Equations (9)

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

dGd(ω)ω0>dαtotd(ω)ω0.
αtot=αp+α0.
αp=Aωω-ΔkTDBR3/2 exp-B ω-ΔkTDBR,
dαtotd(ω)=-αp(ω, TDBR)BkTDBR-321ω-Δ+1ω.
g(ω, TQW, pQW)=Ldαtot(ω, TDBR),
Lddαtotd(ω)ω0=-αp(ω0, TDBR)αtot(ω0, TDBR)g(ω0, TQW, pQW)×BkTDBR-321ω0-Δ+1ω0.
g(ω, TQW, pQW)=αQW(ω)[fn(En, TQW, pQW)+fp(Ep, TQW, pQW)-1],
g(ω, TQW, pQW)αQW(ω)fp[C(ω-Eg),TQW, pQW],
dgd(ω)ω0f0dαQWd(ω)ω0-CαQW(ω0)f0 1-f0kTQW,

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