Abstract

We analyze the transverse profiles of oxide-confined vertical-cavity laser diodes as a function of aperture size. For small apertures we demonstrate that thermal lensing can be the dominant effect in determining the transverse resonator properties. We also analyze pattern formation in lasers with large apertures where we observe the appearance of tilted waves.

© 1999 Optical Society of America

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  1. D. L. Huffaker, D. G. Deppe, K. Kumar, and T. J. Rogers, “Native-oxide defined ring contact for low threshold vertical-cavity lasers,” Appl. Phys. Lett. 65, 97–99 (1994).
    [CrossRef]
  2. K. D. Choquette, R. P. Schneider, Jr., K. L. Lear, and K. M. Geib, “Low threshold voltage vertical-cavity lasers fabricated by selective oxidation,” Electron. Lett. 30, 2043–2044 (1994).
    [CrossRef]
  3. K. L. Lear, K. D. Choquette, R. P. Schneider, Jr., S. P. Kilcoyne, and K. M. Geib, “Selectively oxidised vertical-cavity surface emitting lasers with 50% power conversion efficiency,” Electron. Lett. 31, 208–208 (1995).
    [CrossRef]
  4. G. M. Yang, M. H. MacDougal, and P. D. Dapkus, “Ultralow threshold current vertical-cavity surface-emitting lasers obtained with selective oxidation,” Electron. Lett. 31, 886–886 (1995).
    [CrossRef]
  5. K. L. Lear and R. P. Schneider, Jr., “Uniparabolic mirror grading for vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 68, 605–607 (1996).
    [CrossRef]
  6. L. A. Lugiato, M. Brambilla, and A. Gatti, Advances in Atomic, Molecular and Optical Physics, B. Bedersen and H. Walther, eds. (Academic, San Diego, Calif., 1999).
  7. S. P. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, “Pattern formation in the transverse section of a laser with a large Fresnel number,” Phys. Rev. Lett. 82, 1434–1437 (1999).
    [CrossRef]
  8. S. P. Hegarty, G. Huyet, J. G. McInerney, K. D. Choquette, K. M. Geib, and H. Q. Hou, “Size dependence of transverse mode structure in oxide-confined vertical-cavity laser diodes,” Appl. Phys. Lett. 73, 596–598 (1998).
    [CrossRef]
  9. K. D. Choquette, W. W. Chow, G. R. Hadley, H. Q. Hou, and K. M. Geib, “Scalability of small-aperture selectively oxidised vertical cavity lasers,” Appl. Phys. Lett. 70, 823–825 (1997).
    [CrossRef]
  10. E. R. Hegblom, D. I. Babic, B. J. Thibeult, and L. A. Coldren, “Estimation of scattering losses in dielectrically apertured vertical cavity lasers,” Appl. Phys. Lett. 68, 1757–1759 (1996).
    [CrossRef]
  11. A. Yariv, Quantum Electronics (Wiley, New York, 1967).
  12. Y. G. Zhao and J. G. McInerney, “Transient temperature response of vertical-cavity surface-emitting semiconductor lasers,” IEEE J. Quantum Electron. 31, 1668–1673 (1995).
    [CrossRef]
  13. T.-H. Oh, D. L. Huffaker, and D. G. Deppe, “Size effects in small oxide confined vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 69, 3152–3154 (1996).
    [CrossRef]
  14. M. Cross and P. Hohenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993).
    [CrossRef]
  15. N. Abraham, P. Mandel, and L. Narducci, Progress in Optics, E. Wolf, ed. (North-Holland, New York, 1988), Vol. XXV, pp. 1–190.
  16. T. Ackemann, Y. Logvin, A. Heuer, and W. Lange, “Transition between positive and negative hexagons in optical pattern formation,” Phys. Rev. Lett. 75, 3450–3453 (1995).
    [CrossRef] [PubMed]
  17. F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, “Vortices and defect statistics in 2-dimensional optical chaos,” Phys. Rev. Lett. 67, 3749–3752 (1991).
    [CrossRef] [PubMed]
  18. A. V. Mamaev and M. Saffman, “Pattern formation in a linear photorefractive oscillator,” Opt. Commun. 128, 281–286 (1996).
    [CrossRef]
  19. K. Staliunas, G. Slekys, and C. O. Weiss, “Nonlinear pattern formation in active optical systems: shocks, domains of tilted waves, and cross-roll patterns,” Phys. Rev. Lett. 79, 2658–2661 (1997).
    [CrossRef]
  20. E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, “2-dimensional crystals and quasi-crystals in nonlinear optics,” Phys. Rev. Lett. 74, 258–261 (1995).
    [CrossRef] [PubMed]
  21. R. Lefever, L. A. Lugiato, W. Kaige, N. B. Abraham, and P. Mandel, “Phase dynamics of transverse diffraction patterns in the laser,” Phys. Lett. A 135, 254–256 (1989).
    [CrossRef]
  22. P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
    [CrossRef]
  23. G. L. Oppo, G. D’Alessandro, and W. J. Firth, “Spatiotemporal instabilities of lasers in models reduced via center manifold techniques of lasers in models reduced via center manifold techniques,” Phys. Rev. A 44, 4712–4720 (1991).
    [CrossRef] [PubMed]
  24. G. D’Alessandro, A. J. Kent, and G.-L. Oppo, “Centre manifold reduction of laser equations with transverse effects: an approach based on modal expansion,” Opt. Commun. 131, 172–194 (1996).
    [CrossRef]
  25. J. Lega, J. V. Moloney, and A. C. Newell, “Swift–Hohenberg equation for lasers,” Phys. Rev. Lett. 73, 2978–2981 (1994); “Universal description of laser dynamics near-threshold,” 83, 478–498 (1995).
    [CrossRef] [PubMed]
  26. M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, “Spatial soliton pixels in semiconductor devices,” Phys. Rev. Lett. 79, 2042–2045 (1997).
    [CrossRef]
  27. G. Huyet, C. M. Martinoni, J. R. Tredicce, and S. Rica, “Spatiotemporal dynamics of lasers with a large Fresnel number,” Phys. Rev. Lett. 75, 4027–4030 (1994); G. Huyet and J. R. Tredicce, “Spatio-temporal chaos in the transverse section of lasers,” Physica D 96, 209–214 (1996); G. Huyet, C. Mathis, and J. R. Tredicce, “Dynamics of annular lasers,” Opt. Commun. OPCOB8 127, 257–262 (1996).
    [CrossRef]
  28. G. Huyet and S. Rica, “Spatio-temporal instabilities in the transverse patterns of lasers,” Physica D 96, 215–229 (1996).
    [CrossRef]
  29. D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergneaux, and P. Glorieux, “2 dimensional optical lattices in a CO2 laser,” Phys. Rev. A 46, 5955–5958 (1992); E. Louvergneaux, D. Hennequin, D. Dangoisse, and P. Glorieux, “Transverse mode competition in a CO2 laser,” Phys. Rev. A 53, 4435–4438 (1996).
    [CrossRef] [PubMed]
  30. S. Balle, “Effective 2-level-model with asymmetric gain for laser-diodes,” Opt. Commun. 119, 227–235 (1995).
    [CrossRef]
  31. T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney, and C. Z. Ning, “Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers,” Phys. Rev. A 58, 3279–3292 (1998).
    [CrossRef]
  32. W. W. Chow, K. D. Choquette, M. Hagerot-Crawford, K. L. Lear, and G. R. Hadley, “Design, fabrication, and performance of infrared and visible vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 1810–1824 (1997).
    [CrossRef]
  33. J. Martin-Regalado, S. Balle, and M. San Miguel, “Polarization and transverse-mode dynamics of gain-guided vertical-cavity surface-emitting lasers,” Opt. Lett. 22, 460–462 (1997).
    [CrossRef] [PubMed]
  34. M. van Exter, A. Al-Remawi, and J. Woerdman, “Polarization fluctuations demonstrate nonlinear anisotropy of avertical-cavity semiconductor laser,” Phys. Rev. Lett. 80, 4875–4878 (1998).
    [CrossRef]
  35. D. L. Huffaker, H. Deng, Q. Deng, and D. G. Deppe, “Ring and stripe oxide-confined vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 69, 3477–3479 (1996).
    [CrossRef]
  36. H. Li, T. L. Lucas, J. G. McInerney, and R. A. Morgan, “Transverse modes and patterns of electrically pumped vertical-cavity surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1619–1635 (1994).
    [CrossRef]
  37. G. K. Harkness, W. J. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, “Boundary effects in large-aspect-ratio lasers,” Phys. Rev. A 50, 4310–4317 (1994).
    [CrossRef] [PubMed]
  38. P. Coullet, T. Frisch, and F. Plaza, “Sources and sinks of wave patterns,” Physica D 62, 75–79 (1993).
    [CrossRef]
  39. R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, “Transverse mode of vertical cavity top surface emitting lasers,” IEEE Photon. Technol. Lett. 4, 374–377 (1993).
    [CrossRef]
  40. C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamics, polarization and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
    [CrossRef]

1999 (1)

S. P. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, “Pattern formation in the transverse section of a laser with a large Fresnel number,” Phys. Rev. Lett. 82, 1434–1437 (1999).
[CrossRef]

1998 (3)

S. P. Hegarty, G. Huyet, J. G. McInerney, K. D. Choquette, K. M. Geib, and H. Q. Hou, “Size dependence of transverse mode structure in oxide-confined vertical-cavity laser diodes,” Appl. Phys. Lett. 73, 596–598 (1998).
[CrossRef]

T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney, and C. Z. Ning, “Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers,” Phys. Rev. A 58, 3279–3292 (1998).
[CrossRef]

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

1997 (5)

J. Martin-Regalado, S. Balle, and M. San Miguel, “Polarization and transverse-mode dynamics of gain-guided vertical-cavity surface-emitting lasers,” Opt. Lett. 22, 460–462 (1997).
[CrossRef] [PubMed]

W. W. Chow, K. D. Choquette, M. Hagerot-Crawford, K. L. Lear, and G. R. Hadley, “Design, fabrication, and performance of infrared and visible vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 1810–1824 (1997).
[CrossRef]

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, “Spatial soliton pixels in semiconductor devices,” Phys. Rev. Lett. 79, 2042–2045 (1997).
[CrossRef]

K. D. Choquette, W. W. Chow, G. R. Hadley, H. Q. Hou, and K. M. Geib, “Scalability of small-aperture selectively oxidised vertical cavity lasers,” Appl. Phys. Lett. 70, 823–825 (1997).
[CrossRef]

K. Staliunas, G. Slekys, and C. O. Weiss, “Nonlinear pattern formation in active optical systems: shocks, domains of tilted waves, and cross-roll patterns,” Phys. Rev. Lett. 79, 2658–2661 (1997).
[CrossRef]

1996 (7)

T.-H. Oh, D. L. Huffaker, and D. G. Deppe, “Size effects in small oxide confined vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 69, 3152–3154 (1996).
[CrossRef]

E. R. Hegblom, D. I. Babic, B. J. Thibeult, and L. A. Coldren, “Estimation of scattering losses in dielectrically apertured vertical cavity lasers,” Appl. Phys. Lett. 68, 1757–1759 (1996).
[CrossRef]

G. Huyet and S. Rica, “Spatio-temporal instabilities in the transverse patterns of lasers,” Physica D 96, 215–229 (1996).
[CrossRef]

K. L. Lear and R. P. Schneider, Jr., “Uniparabolic mirror grading for vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 68, 605–607 (1996).
[CrossRef]

A. V. Mamaev and M. Saffman, “Pattern formation in a linear photorefractive oscillator,” Opt. Commun. 128, 281–286 (1996).
[CrossRef]

G. D’Alessandro, A. J. Kent, and G.-L. Oppo, “Centre manifold reduction of laser equations with transverse effects: an approach based on modal expansion,” Opt. Commun. 131, 172–194 (1996).
[CrossRef]

D. L. Huffaker, H. Deng, Q. Deng, and D. G. Deppe, “Ring and stripe oxide-confined vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 69, 3477–3479 (1996).
[CrossRef]

1995 (6)

S. Balle, “Effective 2-level-model with asymmetric gain for laser-diodes,” Opt. Commun. 119, 227–235 (1995).
[CrossRef]

Y. G. Zhao and J. G. McInerney, “Transient temperature response of vertical-cavity surface-emitting semiconductor lasers,” IEEE J. Quantum Electron. 31, 1668–1673 (1995).
[CrossRef]

K. L. Lear, K. D. Choquette, R. P. Schneider, Jr., S. P. Kilcoyne, and K. M. Geib, “Selectively oxidised vertical-cavity surface emitting lasers with 50% power conversion efficiency,” Electron. Lett. 31, 208–208 (1995).
[CrossRef]

G. M. Yang, M. H. MacDougal, and P. D. Dapkus, “Ultralow threshold current vertical-cavity surface-emitting lasers obtained with selective oxidation,” Electron. Lett. 31, 886–886 (1995).
[CrossRef]

T. Ackemann, Y. Logvin, A. Heuer, and W. Lange, “Transition between positive and negative hexagons in optical pattern formation,” Phys. Rev. Lett. 75, 3450–3453 (1995).
[CrossRef] [PubMed]

E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, “2-dimensional crystals and quasi-crystals in nonlinear optics,” Phys. Rev. Lett. 74, 258–261 (1995).
[CrossRef] [PubMed]

1994 (4)

D. L. Huffaker, D. G. Deppe, K. Kumar, and T. J. Rogers, “Native-oxide defined ring contact for low threshold vertical-cavity lasers,” Appl. Phys. Lett. 65, 97–99 (1994).
[CrossRef]

K. D. Choquette, R. P. Schneider, Jr., K. L. Lear, and K. M. Geib, “Low threshold voltage vertical-cavity lasers fabricated by selective oxidation,” Electron. Lett. 30, 2043–2044 (1994).
[CrossRef]

H. Li, T. L. Lucas, J. G. McInerney, and R. A. Morgan, “Transverse modes and patterns of electrically pumped vertical-cavity surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1619–1635 (1994).
[CrossRef]

G. K. Harkness, W. J. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, “Boundary effects in large-aspect-ratio lasers,” Phys. Rev. A 50, 4310–4317 (1994).
[CrossRef] [PubMed]

1993 (3)

P. Coullet, T. Frisch, and F. Plaza, “Sources and sinks of wave patterns,” Physica D 62, 75–79 (1993).
[CrossRef]

R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, “Transverse mode of vertical cavity top surface emitting lasers,” IEEE Photon. Technol. Lett. 4, 374–377 (1993).
[CrossRef]

M. Cross and P. Hohenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993).
[CrossRef]

1991 (3)

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, “Vortices and defect statistics in 2-dimensional optical chaos,” Phys. Rev. Lett. 67, 3749–3752 (1991).
[CrossRef] [PubMed]

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamics, polarization and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

G. L. Oppo, G. D’Alessandro, and W. J. Firth, “Spatiotemporal instabilities of lasers in models reduced via center manifold techniques of lasers in models reduced via center manifold techniques,” Phys. Rev. A 44, 4712–4720 (1991).
[CrossRef] [PubMed]

1989 (2)

R. Lefever, L. A. Lugiato, W. Kaige, N. B. Abraham, and P. Mandel, “Phase dynamics of transverse diffraction patterns in the laser,” Phys. Lett. A 135, 254–256 (1989).
[CrossRef]

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
[CrossRef]

Abraham, N. B.

R. Lefever, L. A. Lugiato, W. Kaige, N. B. Abraham, and P. Mandel, “Phase dynamics of transverse diffraction patterns in the laser,” Phys. Lett. A 135, 254–256 (1989).
[CrossRef]

Ackemann, T.

T. Ackemann, Y. Logvin, A. Heuer, and W. Lange, “Transition between positive and negative hexagons in optical pattern formation,” Phys. Rev. Lett. 75, 3450–3453 (1995).
[CrossRef] [PubMed]

Al-Remawi, A.

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

Arecchi, F. T.

E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, “2-dimensional crystals and quasi-crystals in nonlinear optics,” Phys. Rev. Lett. 74, 258–261 (1995).
[CrossRef] [PubMed]

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, “Vortices and defect statistics in 2-dimensional optical chaos,” Phys. Rev. Lett. 67, 3749–3752 (1991).
[CrossRef] [PubMed]

Asom, M. T.

R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, “Transverse mode of vertical cavity top surface emitting lasers,” IEEE Photon. Technol. Lett. 4, 374–377 (1993).
[CrossRef]

Babic, D. I.

E. R. Hegblom, D. I. Babic, B. J. Thibeult, and L. A. Coldren, “Estimation of scattering losses in dielectrically apertured vertical cavity lasers,” Appl. Phys. Lett. 68, 1757–1759 (1996).
[CrossRef]

Balle, S.

Brambilla, M.

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, “Spatial soliton pixels in semiconductor devices,” Phys. Rev. Lett. 79, 2042–2045 (1997).
[CrossRef]

Callis, S. E.

R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, “Transverse mode of vertical cavity top surface emitting lasers,” IEEE Photon. Technol. Lett. 4, 374–377 (1993).
[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, “Dynamics, polarization and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

Choquette, K. D.

S. P. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, “Pattern formation in the transverse section of a laser with a large Fresnel number,” Phys. Rev. Lett. 82, 1434–1437 (1999).
[CrossRef]

S. P. Hegarty, G. Huyet, J. G. McInerney, K. D. Choquette, K. M. Geib, and H. Q. Hou, “Size dependence of transverse mode structure in oxide-confined vertical-cavity laser diodes,” Appl. Phys. Lett. 73, 596–598 (1998).
[CrossRef]

W. W. Chow, K. D. Choquette, M. Hagerot-Crawford, K. L. Lear, and G. R. Hadley, “Design, fabrication, and performance of infrared and visible vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 1810–1824 (1997).
[CrossRef]

K. D. Choquette, W. W. Chow, G. R. Hadley, H. Q. Hou, and K. M. Geib, “Scalability of small-aperture selectively oxidised vertical cavity lasers,” Appl. Phys. Lett. 70, 823–825 (1997).
[CrossRef]

K. L. Lear, K. D. Choquette, R. P. Schneider, Jr., S. P. Kilcoyne, and K. M. Geib, “Selectively oxidised vertical-cavity surface emitting lasers with 50% power conversion efficiency,” Electron. Lett. 31, 208–208 (1995).
[CrossRef]

K. D. Choquette, R. P. Schneider, Jr., K. L. Lear, and K. M. Geib, “Low threshold voltage vertical-cavity lasers fabricated by selective oxidation,” Electron. Lett. 30, 2043–2044 (1994).
[CrossRef]

Chow, W. W.

K. D. Choquette, W. W. Chow, G. R. Hadley, H. Q. Hou, and K. M. Geib, “Scalability of small-aperture selectively oxidised vertical cavity lasers,” Appl. Phys. Lett. 70, 823–825 (1997).
[CrossRef]

W. W. Chow, K. D. Choquette, M. Hagerot-Crawford, K. L. Lear, and G. R. Hadley, “Design, fabrication, and performance of infrared and visible vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 1810–1824 (1997).
[CrossRef]

Coldren, L. A.

E. R. Hegblom, D. I. Babic, B. J. Thibeult, and L. A. Coldren, “Estimation of scattering losses in dielectrically apertured vertical cavity lasers,” Appl. Phys. Lett. 68, 1757–1759 (1996).
[CrossRef]

Coullet, P.

P. Coullet, T. Frisch, and F. Plaza, “Sources and sinks of wave patterns,” Physica D 62, 75–79 (1993).
[CrossRef]

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
[CrossRef]

Cross, M.

M. Cross and P. Hohenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993).
[CrossRef]

D’Alessandro, G.

G. D’Alessandro, A. J. Kent, and G.-L. Oppo, “Centre manifold reduction of laser equations with transverse effects: an approach based on modal expansion,” Opt. Commun. 131, 172–194 (1996).
[CrossRef]

G. L. Oppo, G. D’Alessandro, and W. J. Firth, “Spatiotemporal instabilities of lasers in models reduced via center manifold techniques of lasers in models reduced via center manifold techniques,” Phys. Rev. A 44, 4712–4720 (1991).
[CrossRef] [PubMed]

Dapkus, P. D.

G. M. Yang, M. H. MacDougal, and P. D. Dapkus, “Ultralow threshold current vertical-cavity surface-emitting lasers obtained with selective oxidation,” Electron. Lett. 31, 886–886 (1995).
[CrossRef]

Deng, H.

D. L. Huffaker, H. Deng, Q. Deng, and D. G. Deppe, “Ring and stripe oxide-confined vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 69, 3477–3479 (1996).
[CrossRef]

Deng, Q.

D. L. Huffaker, H. Deng, Q. Deng, and D. G. Deppe, “Ring and stripe oxide-confined vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 69, 3477–3479 (1996).
[CrossRef]

Deppe, D. G.

D. L. Huffaker, H. Deng, Q. Deng, and D. G. Deppe, “Ring and stripe oxide-confined vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 69, 3477–3479 (1996).
[CrossRef]

T.-H. Oh, D. L. Huffaker, and D. G. Deppe, “Size effects in small oxide confined vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 69, 3152–3154 (1996).
[CrossRef]

D. L. Huffaker, D. G. Deppe, K. Kumar, and T. J. Rogers, “Native-oxide defined ring contact for low threshold vertical-cavity lasers,” Appl. Phys. Lett. 65, 97–99 (1994).
[CrossRef]

Firth, W. J.

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, “Spatial soliton pixels in semiconductor devices,” Phys. Rev. Lett. 79, 2042–2045 (1997).
[CrossRef]

G. K. Harkness, W. J. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, “Boundary effects in large-aspect-ratio lasers,” Phys. Rev. A 50, 4310–4317 (1994).
[CrossRef] [PubMed]

G. L. Oppo, G. D’Alessandro, and W. J. Firth, “Spatiotemporal instabilities of lasers in models reduced via center manifold techniques of lasers in models reduced via center manifold techniques,” Phys. Rev. A 44, 4712–4720 (1991).
[CrossRef] [PubMed]

Florez, L. T.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamics, polarization and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

Focht, M. W.

R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, “Transverse mode of vertical cavity top surface emitting lasers,” IEEE Photon. Technol. Lett. 4, 374–377 (1993).
[CrossRef]

Frisch, T.

P. Coullet, T. Frisch, and F. Plaza, “Sources and sinks of wave patterns,” Physica D 62, 75–79 (1993).
[CrossRef]

Geddes, J. B.

G. K. Harkness, W. J. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, “Boundary effects in large-aspect-ratio lasers,” Phys. Rev. A 50, 4310–4317 (1994).
[CrossRef] [PubMed]

Geib, K. M.

S. P. Hegarty, G. Huyet, J. G. McInerney, K. D. Choquette, K. M. Geib, and H. Q. Hou, “Size dependence of transverse mode structure in oxide-confined vertical-cavity laser diodes,” Appl. Phys. Lett. 73, 596–598 (1998).
[CrossRef]

K. D. Choquette, W. W. Chow, G. R. Hadley, H. Q. Hou, and K. M. Geib, “Scalability of small-aperture selectively oxidised vertical cavity lasers,” Appl. Phys. Lett. 70, 823–825 (1997).
[CrossRef]

K. L. Lear, K. D. Choquette, R. P. Schneider, Jr., S. P. Kilcoyne, and K. M. Geib, “Selectively oxidised vertical-cavity surface emitting lasers with 50% power conversion efficiency,” Electron. Lett. 31, 208–208 (1995).
[CrossRef]

K. D. Choquette, R. P. Schneider, Jr., K. L. Lear, and K. M. Geib, “Low threshold voltage vertical-cavity lasers fabricated by selective oxidation,” Electron. Lett. 30, 2043–2044 (1994).
[CrossRef]

Giacomelli, G.

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, “Vortices and defect statistics in 2-dimensional optical chaos,” Phys. Rev. Lett. 67, 3749–3752 (1991).
[CrossRef] [PubMed]

Gil, L.

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
[CrossRef]

Guth, G. D.

R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, “Transverse mode of vertical cavity top surface emitting lasers,” IEEE Photon. Technol. Lett. 4, 374–377 (1993).
[CrossRef]

Hadley, G. R.

W. W. Chow, K. D. Choquette, M. Hagerot-Crawford, K. L. Lear, and G. R. Hadley, “Design, fabrication, and performance of infrared and visible vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 1810–1824 (1997).
[CrossRef]

K. D. Choquette, W. W. Chow, G. R. Hadley, H. Q. Hou, and K. M. Geib, “Scalability of small-aperture selectively oxidised vertical cavity lasers,” Appl. Phys. Lett. 70, 823–825 (1997).
[CrossRef]

Hagerot-Crawford, M.

W. W. Chow, K. D. Choquette, M. Hagerot-Crawford, K. L. Lear, and G. R. Hadley, “Design, fabrication, and performance of infrared and visible vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 1810–1824 (1997).
[CrossRef]

Harbison, J. P.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamics, polarization and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

Harkness, G. K.

T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney, and C. Z. Ning, “Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers,” Phys. Rev. A 58, 3279–3292 (1998).
[CrossRef]

G. K. Harkness, W. J. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, “Boundary effects in large-aspect-ratio lasers,” Phys. Rev. A 50, 4310–4317 (1994).
[CrossRef] [PubMed]

Hasnain, G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamics, polarization and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

Hegarty, S. P.

S. P. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, “Pattern formation in the transverse section of a laser with a large Fresnel number,” Phys. Rev. Lett. 82, 1434–1437 (1999).
[CrossRef]

S. P. Hegarty, G. Huyet, J. G. McInerney, K. D. Choquette, K. M. Geib, and H. Q. Hou, “Size dependence of transverse mode structure in oxide-confined vertical-cavity laser diodes,” Appl. Phys. Lett. 73, 596–598 (1998).
[CrossRef]

Hegblom, E. R.

E. R. Hegblom, D. I. Babic, B. J. Thibeult, and L. A. Coldren, “Estimation of scattering losses in dielectrically apertured vertical cavity lasers,” Appl. Phys. Lett. 68, 1757–1759 (1996).
[CrossRef]

Heuer, A.

T. Ackemann, Y. Logvin, A. Heuer, and W. Lange, “Transition between positive and negative hexagons in optical pattern formation,” Phys. Rev. Lett. 75, 3450–3453 (1995).
[CrossRef] [PubMed]

Hohenberg, P.

M. Cross and P. Hohenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993).
[CrossRef]

Hou, H. Q.

S. P. Hegarty, G. Huyet, J. G. McInerney, K. D. Choquette, K. M. Geib, and H. Q. Hou, “Size dependence of transverse mode structure in oxide-confined vertical-cavity laser diodes,” Appl. Phys. Lett. 73, 596–598 (1998).
[CrossRef]

K. D. Choquette, W. W. Chow, G. R. Hadley, H. Q. Hou, and K. M. Geib, “Scalability of small-aperture selectively oxidised vertical cavity lasers,” Appl. Phys. Lett. 70, 823–825 (1997).
[CrossRef]

Huffaker, D. L.

T.-H. Oh, D. L. Huffaker, and D. G. Deppe, “Size effects in small oxide confined vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 69, 3152–3154 (1996).
[CrossRef]

D. L. Huffaker, H. Deng, Q. Deng, and D. G. Deppe, “Ring and stripe oxide-confined vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 69, 3477–3479 (1996).
[CrossRef]

D. L. Huffaker, D. G. Deppe, K. Kumar, and T. J. Rogers, “Native-oxide defined ring contact for low threshold vertical-cavity lasers,” Appl. Phys. Lett. 65, 97–99 (1994).
[CrossRef]

Huyet, G.

S. P. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, “Pattern formation in the transverse section of a laser with a large Fresnel number,” Phys. Rev. Lett. 82, 1434–1437 (1999).
[CrossRef]

S. P. Hegarty, G. Huyet, J. G. McInerney, K. D. Choquette, K. M. Geib, and H. Q. Hou, “Size dependence of transverse mode structure in oxide-confined vertical-cavity laser diodes,” Appl. Phys. Lett. 73, 596–598 (1998).
[CrossRef]

G. Huyet and S. Rica, “Spatio-temporal instabilities in the transverse patterns of lasers,” Physica D 96, 215–229 (1996).
[CrossRef]

Indik, R. A.

T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney, and C. Z. Ning, “Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers,” Phys. Rev. A 58, 3279–3292 (1998).
[CrossRef]

Kaige, W.

R. Lefever, L. A. Lugiato, W. Kaige, N. B. Abraham, and P. Mandel, “Phase dynamics of transverse diffraction patterns in the laser,” Phys. Lett. A 135, 254–256 (1989).
[CrossRef]

Kent, A. J.

G. D’Alessandro, A. J. Kent, and G.-L. Oppo, “Centre manifold reduction of laser equations with transverse effects: an approach based on modal expansion,” Opt. Commun. 131, 172–194 (1996).
[CrossRef]

Kilcoyne, S. P.

K. L. Lear, K. D. Choquette, R. P. Schneider, Jr., S. P. Kilcoyne, and K. M. Geib, “Selectively oxidised vertical-cavity surface emitting lasers with 50% power conversion efficiency,” Electron. Lett. 31, 208–208 (1995).
[CrossRef]

Kojima, K.

R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, “Transverse mode of vertical cavity top surface emitting lasers,” IEEE Photon. Technol. Lett. 4, 374–377 (1993).
[CrossRef]

Kumar, K.

D. L. Huffaker, D. G. Deppe, K. Kumar, and T. J. Rogers, “Native-oxide defined ring contact for low threshold vertical-cavity lasers,” Appl. Phys. Lett. 65, 97–99 (1994).
[CrossRef]

Lange, W.

T. Ackemann, Y. Logvin, A. Heuer, and W. Lange, “Transition between positive and negative hexagons in optical pattern formation,” Phys. Rev. Lett. 75, 3450–3453 (1995).
[CrossRef] [PubMed]

Lear, K. L.

W. W. Chow, K. D. Choquette, M. Hagerot-Crawford, K. L. Lear, and G. R. Hadley, “Design, fabrication, and performance of infrared and visible vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 1810–1824 (1997).
[CrossRef]

K. L. Lear and R. P. Schneider, Jr., “Uniparabolic mirror grading for vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 68, 605–607 (1996).
[CrossRef]

K. L. Lear, K. D. Choquette, R. P. Schneider, Jr., S. P. Kilcoyne, and K. M. Geib, “Selectively oxidised vertical-cavity surface emitting lasers with 50% power conversion efficiency,” Electron. Lett. 31, 208–208 (1995).
[CrossRef]

K. D. Choquette, R. P. Schneider, Jr., K. L. Lear, and K. M. Geib, “Low threshold voltage vertical-cavity lasers fabricated by selective oxidation,” Electron. Lett. 30, 2043–2044 (1994).
[CrossRef]

Lefever, R.

R. Lefever, L. A. Lugiato, W. Kaige, N. B. Abraham, and P. Mandel, “Phase dynamics of transverse diffraction patterns in the laser,” Phys. Lett. A 135, 254–256 (1989).
[CrossRef]

Li, H.

H. Li, T. L. Lucas, J. G. McInerney, and R. A. Morgan, “Transverse modes and patterns of electrically pumped vertical-cavity surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1619–1635 (1994).
[CrossRef]

Logvin, Y.

T. Ackemann, Y. Logvin, A. Heuer, and W. Lange, “Transition between positive and negative hexagons in optical pattern formation,” Phys. Rev. Lett. 75, 3450–3453 (1995).
[CrossRef] [PubMed]

Lucas, T. L.

H. Li, T. L. Lucas, J. G. McInerney, and R. A. Morgan, “Transverse modes and patterns of electrically pumped vertical-cavity surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1619–1635 (1994).
[CrossRef]

Lugiato, L. A.

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, “Spatial soliton pixels in semiconductor devices,” Phys. Rev. Lett. 79, 2042–2045 (1997).
[CrossRef]

R. Lefever, L. A. Lugiato, W. Kaige, N. B. Abraham, and P. Mandel, “Phase dynamics of transverse diffraction patterns in the laser,” Phys. Lett. A 135, 254–256 (1989).
[CrossRef]

MacDougal, M. H.

G. M. Yang, M. H. MacDougal, and P. D. Dapkus, “Ultralow threshold current vertical-cavity surface-emitting lasers obtained with selective oxidation,” Electron. Lett. 31, 886–886 (1995).
[CrossRef]

Mamaev, A. V.

A. V. Mamaev and M. Saffman, “Pattern formation in a linear photorefractive oscillator,” Opt. Commun. 128, 281–286 (1996).
[CrossRef]

Mandel, P.

R. Lefever, L. A. Lugiato, W. Kaige, N. B. Abraham, and P. Mandel, “Phase dynamics of transverse diffraction patterns in the laser,” Phys. Lett. A 135, 254–256 (1989).
[CrossRef]

Martin-Regalado, J.

McInerney, J. G.

S. P. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, “Pattern formation in the transverse section of a laser with a large Fresnel number,” Phys. Rev. Lett. 82, 1434–1437 (1999).
[CrossRef]

S. P. Hegarty, G. Huyet, J. G. McInerney, K. D. Choquette, K. M. Geib, and H. Q. Hou, “Size dependence of transverse mode structure in oxide-confined vertical-cavity laser diodes,” Appl. Phys. Lett. 73, 596–598 (1998).
[CrossRef]

Y. G. Zhao and J. G. McInerney, “Transient temperature response of vertical-cavity surface-emitting semiconductor lasers,” IEEE J. Quantum Electron. 31, 1668–1673 (1995).
[CrossRef]

H. Li, T. L. Lucas, J. G. McInerney, and R. A. Morgan, “Transverse modes and patterns of electrically pumped vertical-cavity surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1619–1635 (1994).
[CrossRef]

Moloney, J. V.

T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney, and C. Z. Ning, “Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers,” Phys. Rev. A 58, 3279–3292 (1998).
[CrossRef]

G. K. Harkness, W. J. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, “Boundary effects in large-aspect-ratio lasers,” Phys. Rev. A 50, 4310–4317 (1994).
[CrossRef] [PubMed]

Morgan, R. A.

H. Li, T. L. Lucas, J. G. McInerney, and R. A. Morgan, “Transverse modes and patterns of electrically pumped vertical-cavity surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1619–1635 (1994).
[CrossRef]

R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, “Transverse mode of vertical cavity top surface emitting lasers,” IEEE Photon. Technol. Lett. 4, 374–377 (1993).
[CrossRef]

Ning, C. Z.

T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney, and C. Z. Ning, “Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers,” Phys. Rev. A 58, 3279–3292 (1998).
[CrossRef]

Oh, T.-H.

T.-H. Oh, D. L. Huffaker, and D. G. Deppe, “Size effects in small oxide confined vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 69, 3152–3154 (1996).
[CrossRef]

Oppo, G. L.

G. L. Oppo, G. D’Alessandro, and W. J. Firth, “Spatiotemporal instabilities of lasers in models reduced via center manifold techniques of lasers in models reduced via center manifold techniques,” Phys. Rev. A 44, 4712–4720 (1991).
[CrossRef] [PubMed]

Oppo, G.-L.

G. D’Alessandro, A. J. Kent, and G.-L. Oppo, “Centre manifold reduction of laser equations with transverse effects: an approach based on modal expansion,” Opt. Commun. 131, 172–194 (1996).
[CrossRef]

Pampaloni, E.

E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, “2-dimensional crystals and quasi-crystals in nonlinear optics,” Phys. Rev. Lett. 74, 258–261 (1995).
[CrossRef] [PubMed]

Plaza, F.

P. Coullet, T. Frisch, and F. Plaza, “Sources and sinks of wave patterns,” Physica D 62, 75–79 (1993).
[CrossRef]

Prati, F.

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, “Spatial soliton pixels in semiconductor devices,” Phys. Rev. Lett. 79, 2042–2045 (1997).
[CrossRef]

Ramazza, P. L.

E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, “2-dimensional crystals and quasi-crystals in nonlinear optics,” Phys. Rev. Lett. 74, 258–261 (1995).
[CrossRef] [PubMed]

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, “Vortices and defect statistics in 2-dimensional optical chaos,” Phys. Rev. Lett. 67, 3749–3752 (1991).
[CrossRef] [PubMed]

Residori, S.

E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, “2-dimensional crystals and quasi-crystals in nonlinear optics,” Phys. Rev. Lett. 74, 258–261 (1995).
[CrossRef] [PubMed]

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, “Vortices and defect statistics in 2-dimensional optical chaos,” Phys. Rev. Lett. 67, 3749–3752 (1991).
[CrossRef] [PubMed]

Rica, S.

G. Huyet and S. Rica, “Spatio-temporal instabilities in the transverse patterns of lasers,” Physica D 96, 215–229 (1996).
[CrossRef]

Rocca, F.

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
[CrossRef]

Rogers, L. E.

R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, “Transverse mode of vertical cavity top surface emitting lasers,” IEEE Photon. Technol. Lett. 4, 374–377 (1993).
[CrossRef]

Rogers, T. J.

D. L. Huffaker, D. G. Deppe, K. Kumar, and T. J. Rogers, “Native-oxide defined ring contact for low threshold vertical-cavity lasers,” Appl. Phys. Lett. 65, 97–99 (1994).
[CrossRef]

Rossler, T.

T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney, and C. Z. Ning, “Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers,” Phys. Rev. A 58, 3279–3292 (1998).
[CrossRef]

Saffman, M.

A. V. Mamaev and M. Saffman, “Pattern formation in a linear photorefractive oscillator,” Opt. Commun. 128, 281–286 (1996).
[CrossRef]

San Miguel, M.

Schneider Jr., R. P.

K. L. Lear and R. P. Schneider, Jr., “Uniparabolic mirror grading for vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 68, 605–607 (1996).
[CrossRef]

K. L. Lear, K. D. Choquette, R. P. Schneider, Jr., S. P. Kilcoyne, and K. M. Geib, “Selectively oxidised vertical-cavity surface emitting lasers with 50% power conversion efficiency,” Electron. Lett. 31, 208–208 (1995).
[CrossRef]

K. D. Choquette, R. P. Schneider, Jr., K. L. Lear, and K. M. Geib, “Low threshold voltage vertical-cavity lasers fabricated by selective oxidation,” Electron. Lett. 30, 2043–2044 (1994).
[CrossRef]

Slekys, G.

K. Staliunas, G. Slekys, and C. O. Weiss, “Nonlinear pattern formation in active optical systems: shocks, domains of tilted waves, and cross-roll patterns,” Phys. Rev. Lett. 79, 2658–2661 (1997).
[CrossRef]

Spinelli, L.

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, “Spatial soliton pixels in semiconductor devices,” Phys. Rev. Lett. 79, 2042–2045 (1997).
[CrossRef]

Staliunas, K.

K. Staliunas, G. Slekys, and C. O. Weiss, “Nonlinear pattern formation in active optical systems: shocks, domains of tilted waves, and cross-roll patterns,” Phys. Rev. Lett. 79, 2658–2661 (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, “Dynamics, polarization and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

Thibeult, B. J.

E. R. Hegblom, D. I. Babic, B. J. Thibeult, and L. A. Coldren, “Estimation of scattering losses in dielectrically apertured vertical cavity lasers,” Appl. Phys. Lett. 68, 1757–1759 (1996).
[CrossRef]

van Exter, M.

M. van Exter, A. Al-Remawi, and J. Woerdman, “Polarization fluctuations demonstrate nonlinear anisotropy of avertical-cavity semiconductor laser,” Phys. Rev. Lett. 80, 4875–4878 (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, “Dynamics, polarization and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

Weiss, C. O.

K. Staliunas, G. Slekys, and C. O. Weiss, “Nonlinear pattern formation in active optical systems: shocks, domains of tilted waves, and cross-roll patterns,” Phys. Rev. Lett. 79, 2658–2661 (1997).
[CrossRef]

Woerdman, J.

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

Wright, E. M.

G. K. Harkness, W. J. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, “Boundary effects in large-aspect-ratio lasers,” Phys. Rev. A 50, 4310–4317 (1994).
[CrossRef] [PubMed]

Yang, G. M.

G. M. Yang, M. H. MacDougal, and P. D. Dapkus, “Ultralow threshold current vertical-cavity surface-emitting lasers obtained with selective oxidation,” Electron. Lett. 31, 886–886 (1995).
[CrossRef]

Zhao, Y. G.

Y. G. Zhao and J. G. McInerney, “Transient temperature response of vertical-cavity surface-emitting semiconductor lasers,” IEEE J. Quantum Electron. 31, 1668–1673 (1995).
[CrossRef]

Appl. Phys. Lett. (7)

D. L. Huffaker, D. G. Deppe, K. Kumar, and T. J. Rogers, “Native-oxide defined ring contact for low threshold vertical-cavity lasers,” Appl. Phys. Lett. 65, 97–99 (1994).
[CrossRef]

S. P. Hegarty, G. Huyet, J. G. McInerney, K. D. Choquette, K. M. Geib, and H. Q. Hou, “Size dependence of transverse mode structure in oxide-confined vertical-cavity laser diodes,” Appl. Phys. Lett. 73, 596–598 (1998).
[CrossRef]

K. D. Choquette, W. W. Chow, G. R. Hadley, H. Q. Hou, and K. M. Geib, “Scalability of small-aperture selectively oxidised vertical cavity lasers,” Appl. Phys. Lett. 70, 823–825 (1997).
[CrossRef]

E. R. Hegblom, D. I. Babic, B. J. Thibeult, and L. A. Coldren, “Estimation of scattering losses in dielectrically apertured vertical cavity lasers,” Appl. Phys. Lett. 68, 1757–1759 (1996).
[CrossRef]

K. L. Lear and R. P. Schneider, Jr., “Uniparabolic mirror grading for vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 68, 605–607 (1996).
[CrossRef]

T.-H. Oh, D. L. Huffaker, and D. G. Deppe, “Size effects in small oxide confined vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 69, 3152–3154 (1996).
[CrossRef]

D. L. Huffaker, H. Deng, Q. Deng, and D. G. Deppe, “Ring and stripe oxide-confined vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 69, 3477–3479 (1996).
[CrossRef]

Chaos Solitons Fractals (1)

H. Li, T. L. Lucas, J. G. McInerney, and R. A. Morgan, “Transverse modes and patterns of electrically pumped vertical-cavity surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1619–1635 (1994).
[CrossRef]

Electron. Lett. (3)

K. D. Choquette, R. P. Schneider, Jr., K. L. Lear, and K. M. Geib, “Low threshold voltage vertical-cavity lasers fabricated by selective oxidation,” Electron. Lett. 30, 2043–2044 (1994).
[CrossRef]

K. L. Lear, K. D. Choquette, R. P. Schneider, Jr., S. P. Kilcoyne, and K. M. Geib, “Selectively oxidised vertical-cavity surface emitting lasers with 50% power conversion efficiency,” Electron. Lett. 31, 208–208 (1995).
[CrossRef]

G. M. Yang, M. H. MacDougal, and P. D. Dapkus, “Ultralow threshold current vertical-cavity surface-emitting lasers obtained with selective oxidation,” Electron. Lett. 31, 886–886 (1995).
[CrossRef]

IEEE J. Quantum Electron. (3)

Y. G. Zhao and J. G. McInerney, “Transient temperature response of vertical-cavity surface-emitting semiconductor lasers,” IEEE J. Quantum Electron. 31, 1668–1673 (1995).
[CrossRef]

W. W. Chow, K. D. Choquette, M. Hagerot-Crawford, K. L. Lear, and G. R. Hadley, “Design, fabrication, and performance of infrared and visible vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 1810–1824 (1997).
[CrossRef]

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamics, polarization and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, “Transverse mode of vertical cavity top surface emitting lasers,” IEEE Photon. Technol. Lett. 4, 374–377 (1993).
[CrossRef]

Opt. Commun. (4)

S. Balle, “Effective 2-level-model with asymmetric gain for laser-diodes,” Opt. Commun. 119, 227–235 (1995).
[CrossRef]

A. V. Mamaev and M. Saffman, “Pattern formation in a linear photorefractive oscillator,” Opt. Commun. 128, 281–286 (1996).
[CrossRef]

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
[CrossRef]

G. D’Alessandro, A. J. Kent, and G.-L. Oppo, “Centre manifold reduction of laser equations with transverse effects: an approach based on modal expansion,” Opt. Commun. 131, 172–194 (1996).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (1)

R. Lefever, L. A. Lugiato, W. Kaige, N. B. Abraham, and P. Mandel, “Phase dynamics of transverse diffraction patterns in the laser,” Phys. Lett. A 135, 254–256 (1989).
[CrossRef]

Phys. Rev. A (3)

G. L. Oppo, G. D’Alessandro, and W. J. Firth, “Spatiotemporal instabilities of lasers in models reduced via center manifold techniques of lasers in models reduced via center manifold techniques,” Phys. Rev. A 44, 4712–4720 (1991).
[CrossRef] [PubMed]

T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney, and C. Z. Ning, “Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers,” Phys. Rev. A 58, 3279–3292 (1998).
[CrossRef]

G. K. Harkness, W. J. Firth, J. B. Geddes, J. V. Moloney, and E. M. Wright, “Boundary effects in large-aspect-ratio lasers,” Phys. Rev. A 50, 4310–4317 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (7)

K. Staliunas, G. Slekys, and C. O. Weiss, “Nonlinear pattern formation in active optical systems: shocks, domains of tilted waves, and cross-roll patterns,” Phys. Rev. Lett. 79, 2658–2661 (1997).
[CrossRef]

E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, “2-dimensional crystals and quasi-crystals in nonlinear optics,” Phys. Rev. Lett. 74, 258–261 (1995).
[CrossRef] [PubMed]

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, “Spatial soliton pixels in semiconductor devices,” Phys. Rev. Lett. 79, 2042–2045 (1997).
[CrossRef]

S. P. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, “Pattern formation in the transverse section of a laser with a large Fresnel number,” Phys. Rev. Lett. 82, 1434–1437 (1999).
[CrossRef]

T. Ackemann, Y. Logvin, A. Heuer, and W. Lange, “Transition between positive and negative hexagons in optical pattern formation,” Phys. Rev. Lett. 75, 3450–3453 (1995).
[CrossRef] [PubMed]

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, “Vortices and defect statistics in 2-dimensional optical chaos,” Phys. Rev. Lett. 67, 3749–3752 (1991).
[CrossRef] [PubMed]

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

Physica D (2)

P. Coullet, T. Frisch, and F. Plaza, “Sources and sinks of wave patterns,” Physica D 62, 75–79 (1993).
[CrossRef]

G. Huyet and S. Rica, “Spatio-temporal instabilities in the transverse patterns of lasers,” Physica D 96, 215–229 (1996).
[CrossRef]

Rev. Mod. Phys. (1)

M. Cross and P. Hohenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993).
[CrossRef]

Other (6)

N. Abraham, P. Mandel, and L. Narducci, Progress in Optics, E. Wolf, ed. (North-Holland, New York, 1988), Vol. XXV, pp. 1–190.

L. A. Lugiato, M. Brambilla, and A. Gatti, Advances in Atomic, Molecular and Optical Physics, B. Bedersen and H. Walther, eds. (Academic, San Diego, Calif., 1999).

A. Yariv, Quantum Electronics (Wiley, New York, 1967).

D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergneaux, and P. Glorieux, “2 dimensional optical lattices in a CO2 laser,” Phys. Rev. A 46, 5955–5958 (1992); E. Louvergneaux, D. Hennequin, D. Dangoisse, and P. Glorieux, “Transverse mode competition in a CO2 laser,” Phys. Rev. A 53, 4435–4438 (1996).
[CrossRef] [PubMed]

G. Huyet, C. M. Martinoni, J. R. Tredicce, and S. Rica, “Spatiotemporal dynamics of lasers with a large Fresnel number,” Phys. Rev. Lett. 75, 4027–4030 (1994); G. Huyet and J. R. Tredicce, “Spatio-temporal chaos in the transverse section of lasers,” Physica D 96, 209–214 (1996); G. Huyet, C. Mathis, and J. R. Tredicce, “Dynamics of annular lasers,” Opt. Commun. OPCOB8 127, 257–262 (1996).
[CrossRef]

J. Lega, J. V. Moloney, and A. C. Newell, “Swift–Hohenberg equation for lasers,” Phys. Rev. Lett. 73, 2978–2981 (1994); “Universal description of laser dynamics near-threshold,” 83, 478–498 (1995).
[CrossRef] [PubMed]

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Figures (24)

Fig. 1
Fig. 1

Structure of a VCSEL with dielectric oxide-confining layers.

Fig. 2
Fig. 2

Transverse-mode spectra of a 10 µm×10 µm VCSEL with threshold at 3.6 mA. The measurement did not include polarization elements, and only modes that lase over a large current range were recorded.

Fig. 3
Fig. 3

Threshold current density of VCSEL’s with reduced optical confinement as a function of aperture size.

Fig. 4
Fig. 4

Wavelength of a 1 µm×1 µm VCSEL as a function of current. The laser is operated dc, and the threshold current is 1.3 mA.

Fig. 5
Fig. 5

Spectrum of a 1 µm×1 µm VCSEL as a function of current. The squares correspond to the wavelength of the fundamental mode; the stars, to the first-order transverse mode. The laser is operated dc, and the threshold current is 1.3 mA.

Fig. 6
Fig. 6

Wavelength separation between zeroth- and first-order modes versus current of a 1 µm×1 µm VCSEL.

Fig. 7
Fig. 7

Rate of change of mode separation with current versus device size.

Fig. 8
Fig. 8

FWHM of fundamental mode at 1.1 times threshold as a function of device size. A line of mode size equals aperture size has been included for clarity.

Fig. 9
Fig. 9

Pulse response of the laser intensity with low average heating of the active region. Pump, 1.8 mA; period, 20 µs; pulsewidth, 1 µs. Top curve, current pulse; bottom curve, laser intensity.

Fig. 10
Fig. 10

Far-field width of 1 µm×1 µm VCSEL emission for different duty-cycle pulses. Pulse period in all cases is 10 µs. On times: dotted curve, 100 ns; solid curve, 200 ns, dashed curve, 500 ns; dotted–dashed curve, 1 µs; triple-dotted–dashed curve, 2 µs; long-dashed curve, 5 µs.

Fig. 11
Fig. 11

Plot of threshold current versus heat sink temperature for 5 µm×5 µm devices.

Fig. 12
Fig. 12

Methods used to obtain near-field (top) and far-field (bottom) intensity distributions. A lens of high numerical aperture (NA, 0.68) was used to focus the highly divergent emission onto a distant CCD array to obtain a magnified image. For the far field, a piece of paper was mounted to act as a diffusion screen, and the scattered light imaged by a CCD camera.

Fig. 13
Fig. 13

(a) Near-field distribution for a 5 µm×5 µm device at 2.5 times threshold. (b) Corresponding optical spectrum. The temperature is 18 °C.

Fig. 14
Fig. 14

Near field corresponding to the six biggest peaks in the optical spectrum shown in Fig. 13.

Fig. 15
Fig. 15

(a) Vertical and (b) horizontal polarization of near-field distribution for corresponding to Fig. 14(e).

Fig. 16
Fig. 16

(a) Far-field distribution of the laser intensity at 1.05 threshold and at the heat sink temperature of 15 °C. (b) Corresponding near-field distribution.

Fig. 17
Fig. 17

(a) j-polarized optical spectrum of the pattern shown in Fig. 1. (b) i-polarized optical spectrum of the same pattern.

Fig. 18
Fig. 18

Laser wavelength as a function of wafer position for both small and large VCSEL’s. Squares correspond to small-Fresnel-number lasers; points, to large-Fresnel-number lasers. The small lasers operate in the fundamental Gaussian mode and reveal the cavity resonance frequency. The large lasers are free to choose either a superposition of spatial modes or standing waves. The data demonstrate the qualitative change that results from the transition from negative to positive detuning.

Fig. 19
Fig. 19

Shift of highly divergent mode emission wavelength with heat sink temperature at constant injection current. Although the positive detuning of the laser dictates that the mode is a standing wave close to the gain peak frequency, the boundary conditions discretize the allowed frequencies.

Fig. 20
Fig. 20

(a) Far-field distribution of the laser intensity at 1.3 times threshold and at a heat sink temperature of 15 °C. (b) Corresponding optical spectrum.

Fig. 21
Fig. 21

(a) Far field at 1.6 times threshold and heat sink temperature of 15 °C. (b) Corresponding near field filtered to pass only h polarization.

Fig. 22
Fig. 22

(a) Far field at 2.0 times threshold and heat sink temperature of 15 °C. (b) Corresponding near field.

Fig. 23
Fig. 23

cw stability diagram for the modes of a 25-µm VCSEL versus current and heat sink temperature. Triangles, highly divergent outermost ring; squares, second most divergent ring; diamonds, orthogonal polarization; asterisks, third most divergent ring; plus signs, low-divergence modes.

Fig. 24
Fig. 24

Average near-field intensities for broad-area VCSEL’s operating pulsed with a period of 10 µs and a peak injection current of 5ith. The duty cycles are as follows: (a) 0.04%, (b) 0.1%, (c) 0.5%, (d) 5%, (e) 10%, (f) 20%, (g) 50%, (h) 60%.

Equations (6)

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Δν=c/2πnz,
tE=-κ[(1-iδ)-i(a/2)2]E-κP,
tP=-γ[NE+(1+iδ)P],
tN=-γ[N-J-12(E*P+EP*)],
ω=-κγκ+γa2k2,
Jth=1+δ+ωγ2.

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