Abstract

Based on a numerical optical model for calculating threshold material gain in vertical-cavity surface-emitting laser, we investigate the influence of transverse-optical confinement in airpost, regrown, and oxidized structures. In each of these cases, we demonstrate the trade-off that needs to be made between low threshold for the fundamental laser mode and good modal stability.

© 1999 Optical Society of America

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  1. E. R. Hegblom, N. M. Margalit, A. Fiore, and L. A. Coldren, “Small efficient vertical cavity lasers with tapered oxide apertures,” Electron. Lett. 34, 895–897 (1998).
    [Crossref]
  2. D. L. Huffaker and D. G. Deppe, “Improved performance of oxide-confined vertical-cavity surface-emitting lasers using a tunnel injection active region,” Appl. Phys. Lett. 71, 1449–1451 (1997).
    [Crossref]
  3. K. L. Lear, K. D. Choquette, R. P. Schneider, S. P. Kilcoyne, and K. M. Geib, “Selectively oxidized vertical cavity surface emitting lasers with 50% power conversion efficiency,” Electron. Lett. 31, 208–209 (1995).
    [Crossref]
  4. K. D. Choquette, R. P. Schneider, K. L. Lear, and K. M. Geib, “Low threshold voltage vertical cavity lasers fabricated by selective oxidation,” Electron. Lett. 30, 2043–2044 (1994).
    [Crossref]
  5. K. D. Choquette, K. L. Lear, R. P. Schneider, K. M. Geib, J. J. Figiel, and R. Hull, “Fabrication and performance of selectively oxidized vertical cavity lasers,” IEEE Photon. Technol. Lett. 7, 1237–1239 (1995).
    [Crossref]
  6. B. Demeulenaere, P. Bienstman, B. Dhoedt, and R. Baets, “Detailed study of AlAs-oxidized apertures in VCSEL cavities for optimized modal performance,” IEEE J. Quantum Electron. 35, 358–367 (1999).
    [Crossref]
  7. G. R. Hadley, “Effective index model for vertical-cavity surface-emitting lasers,” Opt. Lett. 20, 1483–1485 (1995).
    [Crossref] [PubMed]
  8. G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, “Comprehensive numerical modeling of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 607–616 (1996).
    [Crossref]
  9. G. R. Hadley, “Low-truncation-error finite difference equations for photonics simulation. II. Vertical-cavity surface-emitting lasers,” J. Lightwave Technol. 16, 142–151 (1998).
    [Crossref]
  10. M. J. Noble, J. P. Loehr, and J. A. Lott, “Analysis of microcavity lasing modes using a full-vector weighted index method,” IEEE J. Quantum Electron. 34, 1892–1903 (1998).
    [Crossref]
  11. M. J. Noble, J. P. Loehr, and J. A. Lott, “Semi-analytic calculation of diffraction losses and threshold currents in microcavity VCSELs,” in IEEE LEOS Annual Meeting (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 212–213, paper WI3.
  12. M. J. Noble, J. P. Loehr, and J. A. Lott, “Quasi-exact optical analysis of oxide apertured microcavity VCSEL’s using vector finite elements,” IEEE J. Quantum Electron. 34, 2327–2339 (1998).
    [Crossref]
  13. B. Klein, L. F. Register, K. Hess, D. G. Deppe, and Q. Deng, “Self-consistent Green’s function approach to the analysis of dielectrically apertured vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 3324–3326 (1998).
    [Crossref]
  14. D. Burak and R. Binder, “Cold-cavity vectorial eigenmodes of VCSEL’s,” IEEE J. Quantum Electron. 33, 1205–1215 (1997).
    [Crossref]
  15. R. Kuszelewicz and G. Aubert, “Modal matrix theory for light propagation in laterally restricted stratified media,” J. Opt. Soc. Am. A 14, 3262–3272 (1997).
    [Crossref]
  16. W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990).
  17. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996).
    [Crossref]
  18. S. Rapp, J. Piprek, K. Streubel, J. André, and J. Wallin, “Temperature sensitivity of 1.54 µm vertical cavity lasers with an InP-based Bragg reflector,” IEEE J. Quantum Electron. 33, 1839–1845 (1997).
    [Crossref]
  19. K. Streubel, S. Rapp, J. André, and J. Wallin, “Room-temperature pulsed operation of 1.5 µm vertical cavity lasers with an InP-based Bragg reflector,” IEEE Photon. Technol. Lett. 8, 1121–1123 (1996).
    [Crossref]
  20. T. Heide, “Steady state and modal properties of vertical cavity surface emitting lasers,” M.S. thesis (Royal Institute of Technology, Stockholm, 1996).
  21. G. Liu, J.-F. Seurin, S. L. Chuang, D. I. Babic, S. W. Corzine, M. Tan, D. C. Barnes, and T. N. Tiouririne, “Mode selectivity study of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 726–729 (1998).
    [Crossref]
  22. COST 268 modeling exercise ( http://www.ele.kth.se/COST268/WG1/WGExcercise1.html ), based on R. Kuszelewicz, Centre National d’Etudes en Télécommunication, Paris (personal communication, 1998).

1999 (1)

B. Demeulenaere, P. Bienstman, B. Dhoedt, and R. Baets, “Detailed study of AlAs-oxidized apertures in VCSEL cavities for optimized modal performance,” IEEE J. Quantum Electron. 35, 358–367 (1999).
[Crossref]

1998 (6)

E. R. Hegblom, N. M. Margalit, A. Fiore, and L. A. Coldren, “Small efficient vertical cavity lasers with tapered oxide apertures,” Electron. Lett. 34, 895–897 (1998).
[Crossref]

G. R. Hadley, “Low-truncation-error finite difference equations for photonics simulation. II. Vertical-cavity surface-emitting lasers,” J. Lightwave Technol. 16, 142–151 (1998).
[Crossref]

M. J. Noble, J. P. Loehr, and J. A. Lott, “Analysis of microcavity lasing modes using a full-vector weighted index method,” IEEE J. Quantum Electron. 34, 1892–1903 (1998).
[Crossref]

M. J. Noble, J. P. Loehr, and J. A. Lott, “Quasi-exact optical analysis of oxide apertured microcavity VCSEL’s using vector finite elements,” IEEE J. Quantum Electron. 34, 2327–2339 (1998).
[Crossref]

B. Klein, L. F. Register, K. Hess, D. G. Deppe, and Q. Deng, “Self-consistent Green’s function approach to the analysis of dielectrically apertured vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 3324–3326 (1998).
[Crossref]

G. Liu, J.-F. Seurin, S. L. Chuang, D. I. Babic, S. W. Corzine, M. Tan, D. C. Barnes, and T. N. Tiouririne, “Mode selectivity study of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 726–729 (1998).
[Crossref]

1997 (4)

S. Rapp, J. Piprek, K. Streubel, J. André, and J. Wallin, “Temperature sensitivity of 1.54 µm vertical cavity lasers with an InP-based Bragg reflector,” IEEE J. Quantum Electron. 33, 1839–1845 (1997).
[Crossref]

D. Burak and R. Binder, “Cold-cavity vectorial eigenmodes of VCSEL’s,” IEEE J. Quantum Electron. 33, 1205–1215 (1997).
[Crossref]

R. Kuszelewicz and G. Aubert, “Modal matrix theory for light propagation in laterally restricted stratified media,” J. Opt. Soc. Am. A 14, 3262–3272 (1997).
[Crossref]

D. L. Huffaker and D. G. Deppe, “Improved performance of oxide-confined vertical-cavity surface-emitting lasers using a tunnel injection active region,” Appl. Phys. Lett. 71, 1449–1451 (1997).
[Crossref]

1996 (3)

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, “Comprehensive numerical modeling of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 607–616 (1996).
[Crossref]

L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996).
[Crossref]

K. Streubel, S. Rapp, J. André, and J. Wallin, “Room-temperature pulsed operation of 1.5 µm vertical cavity lasers with an InP-based Bragg reflector,” IEEE Photon. Technol. Lett. 8, 1121–1123 (1996).
[Crossref]

1995 (3)

K. D. Choquette, K. L. Lear, R. P. Schneider, K. M. Geib, J. J. Figiel, and R. Hull, “Fabrication and performance of selectively oxidized vertical cavity lasers,” IEEE Photon. Technol. Lett. 7, 1237–1239 (1995).
[Crossref]

G. R. Hadley, “Effective index model for vertical-cavity surface-emitting lasers,” Opt. Lett. 20, 1483–1485 (1995).
[Crossref] [PubMed]

K. L. Lear, K. D. Choquette, R. P. Schneider, S. P. Kilcoyne, and K. M. Geib, “Selectively oxidized vertical cavity surface emitting lasers with 50% power conversion efficiency,” Electron. Lett. 31, 208–209 (1995).
[Crossref]

1994 (1)

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

André, J.

S. Rapp, J. Piprek, K. Streubel, J. André, and J. Wallin, “Temperature sensitivity of 1.54 µm vertical cavity lasers with an InP-based Bragg reflector,” IEEE J. Quantum Electron. 33, 1839–1845 (1997).
[Crossref]

K. Streubel, S. Rapp, J. André, and J. Wallin, “Room-temperature pulsed operation of 1.5 µm vertical cavity lasers with an InP-based Bragg reflector,” IEEE Photon. Technol. Lett. 8, 1121–1123 (1996).
[Crossref]

Aubert, G.

Babic, D. I.

G. Liu, J.-F. Seurin, S. L. Chuang, D. I. Babic, S. W. Corzine, M. Tan, D. C. Barnes, and T. N. Tiouririne, “Mode selectivity study of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 726–729 (1998).
[Crossref]

Baets, R.

B. Demeulenaere, P. Bienstman, B. Dhoedt, and R. Baets, “Detailed study of AlAs-oxidized apertures in VCSEL cavities for optimized modal performance,” IEEE J. Quantum Electron. 35, 358–367 (1999).
[Crossref]

Barnes, D. C.

G. Liu, J.-F. Seurin, S. L. Chuang, D. I. Babic, S. W. Corzine, M. Tan, D. C. Barnes, and T. N. Tiouririne, “Mode selectivity study of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 726–729 (1998).
[Crossref]

Bienstman, P.

B. Demeulenaere, P. Bienstman, B. Dhoedt, and R. Baets, “Detailed study of AlAs-oxidized apertures in VCSEL cavities for optimized modal performance,” IEEE J. Quantum Electron. 35, 358–367 (1999).
[Crossref]

Binder, R.

D. Burak and R. Binder, “Cold-cavity vectorial eigenmodes of VCSEL’s,” IEEE J. Quantum Electron. 33, 1205–1215 (1997).
[Crossref]

Burak, D.

D. Burak and R. Binder, “Cold-cavity vectorial eigenmodes of VCSEL’s,” IEEE J. Quantum Electron. 33, 1205–1215 (1997).
[Crossref]

Chew, W. C.

W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990).

Choquette, K. D.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, “Comprehensive numerical modeling of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 607–616 (1996).
[Crossref]

K. L. Lear, K. D. Choquette, R. P. Schneider, S. P. Kilcoyne, and K. M. Geib, “Selectively oxidized vertical cavity surface emitting lasers with 50% power conversion efficiency,” Electron. Lett. 31, 208–209 (1995).
[Crossref]

K. D. Choquette, K. L. Lear, R. P. Schneider, K. M. Geib, J. J. Figiel, and R. Hull, “Fabrication and performance of selectively oxidized vertical cavity lasers,” IEEE Photon. Technol. Lett. 7, 1237–1239 (1995).
[Crossref]

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

Chuang, S. L.

G. Liu, J.-F. Seurin, S. L. Chuang, D. I. Babic, S. W. Corzine, M. Tan, D. C. Barnes, and T. N. Tiouririne, “Mode selectivity study of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 726–729 (1998).
[Crossref]

Coldren, L. A.

E. R. Hegblom, N. M. Margalit, A. Fiore, and L. A. Coldren, “Small efficient vertical cavity lasers with tapered oxide apertures,” Electron. Lett. 34, 895–897 (1998).
[Crossref]

Corzine, S. W.

G. Liu, J.-F. Seurin, S. L. Chuang, D. I. Babic, S. W. Corzine, M. Tan, D. C. Barnes, and T. N. Tiouririne, “Mode selectivity study of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 726–729 (1998).
[Crossref]

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, “Comprehensive numerical modeling of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 607–616 (1996).
[Crossref]

Demeulenaere, B.

B. Demeulenaere, P. Bienstman, B. Dhoedt, and R. Baets, “Detailed study of AlAs-oxidized apertures in VCSEL cavities for optimized modal performance,” IEEE J. Quantum Electron. 35, 358–367 (1999).
[Crossref]

Deng, Q.

B. Klein, L. F. Register, K. Hess, D. G. Deppe, and Q. Deng, “Self-consistent Green’s function approach to the analysis of dielectrically apertured vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 3324–3326 (1998).
[Crossref]

Deppe, D. G.

B. Klein, L. F. Register, K. Hess, D. G. Deppe, and Q. Deng, “Self-consistent Green’s function approach to the analysis of dielectrically apertured vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 3324–3326 (1998).
[Crossref]

D. L. Huffaker and D. G. Deppe, “Improved performance of oxide-confined vertical-cavity surface-emitting lasers using a tunnel injection active region,” Appl. Phys. Lett. 71, 1449–1451 (1997).
[Crossref]

Dhoedt, B.

B. Demeulenaere, P. Bienstman, B. Dhoedt, and R. Baets, “Detailed study of AlAs-oxidized apertures in VCSEL cavities for optimized modal performance,” IEEE J. Quantum Electron. 35, 358–367 (1999).
[Crossref]

Figiel, J. J.

K. D. Choquette, K. L. Lear, R. P. Schneider, K. M. Geib, J. J. Figiel, and R. Hull, “Fabrication and performance of selectively oxidized vertical cavity lasers,” IEEE Photon. Technol. Lett. 7, 1237–1239 (1995).
[Crossref]

Fiore, A.

E. R. Hegblom, N. M. Margalit, A. Fiore, and L. A. Coldren, “Small efficient vertical cavity lasers with tapered oxide apertures,” Electron. Lett. 34, 895–897 (1998).
[Crossref]

Geib, K. M.

K. L. Lear, K. D. Choquette, R. P. Schneider, S. P. Kilcoyne, and K. M. Geib, “Selectively oxidized vertical cavity surface emitting lasers with 50% power conversion efficiency,” Electron. Lett. 31, 208–209 (1995).
[Crossref]

K. D. Choquette, K. L. Lear, R. P. Schneider, K. M. Geib, J. J. Figiel, and R. Hull, “Fabrication and performance of selectively oxidized vertical cavity lasers,” IEEE Photon. Technol. Lett. 7, 1237–1239 (1995).
[Crossref]

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

Hadley, G. R.

Hegblom, E. R.

E. R. Hegblom, N. M. Margalit, A. Fiore, and L. A. Coldren, “Small efficient vertical cavity lasers with tapered oxide apertures,” Electron. Lett. 34, 895–897 (1998).
[Crossref]

Heide, T.

T. Heide, “Steady state and modal properties of vertical cavity surface emitting lasers,” M.S. thesis (Royal Institute of Technology, Stockholm, 1996).

Hess, K.

B. Klein, L. F. Register, K. Hess, D. G. Deppe, and Q. Deng, “Self-consistent Green’s function approach to the analysis of dielectrically apertured vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 3324–3326 (1998).
[Crossref]

Huffaker, D. L.

D. L. Huffaker and D. G. Deppe, “Improved performance of oxide-confined vertical-cavity surface-emitting lasers using a tunnel injection active region,” Appl. Phys. Lett. 71, 1449–1451 (1997).
[Crossref]

Hull, R.

K. D. Choquette, K. L. Lear, R. P. Schneider, K. M. Geib, J. J. Figiel, and R. Hull, “Fabrication and performance of selectively oxidized vertical cavity lasers,” IEEE Photon. Technol. Lett. 7, 1237–1239 (1995).
[Crossref]

Kilcoyne, S. P.

K. L. Lear, K. D. Choquette, R. P. Schneider, S. P. Kilcoyne, and K. M. Geib, “Selectively oxidized vertical cavity surface emitting lasers with 50% power conversion efficiency,” Electron. Lett. 31, 208–209 (1995).
[Crossref]

Klein, B.

B. Klein, L. F. Register, K. Hess, D. G. Deppe, and Q. Deng, “Self-consistent Green’s function approach to the analysis of dielectrically apertured vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 3324–3326 (1998).
[Crossref]

Kuszelewicz, R.

R. Kuszelewicz and G. Aubert, “Modal matrix theory for light propagation in laterally restricted stratified media,” J. Opt. Soc. Am. A 14, 3262–3272 (1997).
[Crossref]

COST 268 modeling exercise ( http://www.ele.kth.se/COST268/WG1/WGExcercise1.html ), based on R. Kuszelewicz, Centre National d’Etudes en Télécommunication, Paris (personal communication, 1998).

Lear, K. L.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, “Comprehensive numerical modeling of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 607–616 (1996).
[Crossref]

K. D. Choquette, K. L. Lear, R. P. Schneider, K. M. Geib, J. J. Figiel, and R. Hull, “Fabrication and performance of selectively oxidized vertical cavity lasers,” IEEE Photon. Technol. Lett. 7, 1237–1239 (1995).
[Crossref]

K. L. Lear, K. D. Choquette, R. P. Schneider, S. P. Kilcoyne, and K. M. Geib, “Selectively oxidized vertical cavity surface emitting lasers with 50% power conversion efficiency,” Electron. Lett. 31, 208–209 (1995).
[Crossref]

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

Li, L.

Liu, G.

G. Liu, J.-F. Seurin, S. L. Chuang, D. I. Babic, S. W. Corzine, M. Tan, D. C. Barnes, and T. N. Tiouririne, “Mode selectivity study of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 726–729 (1998).
[Crossref]

Loehr, J. P.

M. J. Noble, J. P. Loehr, and J. A. Lott, “Quasi-exact optical analysis of oxide apertured microcavity VCSEL’s using vector finite elements,” IEEE J. Quantum Electron. 34, 2327–2339 (1998).
[Crossref]

M. J. Noble, J. P. Loehr, and J. A. Lott, “Analysis of microcavity lasing modes using a full-vector weighted index method,” IEEE J. Quantum Electron. 34, 1892–1903 (1998).
[Crossref]

M. J. Noble, J. P. Loehr, and J. A. Lott, “Semi-analytic calculation of diffraction losses and threshold currents in microcavity VCSELs,” in IEEE LEOS Annual Meeting (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 212–213, paper WI3.

Lott, J. A.

M. J. Noble, J. P. Loehr, and J. A. Lott, “Analysis of microcavity lasing modes using a full-vector weighted index method,” IEEE J. Quantum Electron. 34, 1892–1903 (1998).
[Crossref]

M. J. Noble, J. P. Loehr, and J. A. Lott, “Quasi-exact optical analysis of oxide apertured microcavity VCSEL’s using vector finite elements,” IEEE J. Quantum Electron. 34, 2327–2339 (1998).
[Crossref]

M. J. Noble, J. P. Loehr, and J. A. Lott, “Semi-analytic calculation of diffraction losses and threshold currents in microcavity VCSELs,” in IEEE LEOS Annual Meeting (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 212–213, paper WI3.

Margalit, N. M.

E. R. Hegblom, N. M. Margalit, A. Fiore, and L. A. Coldren, “Small efficient vertical cavity lasers with tapered oxide apertures,” Electron. Lett. 34, 895–897 (1998).
[Crossref]

Noble, M. J.

M. J. Noble, J. P. Loehr, and J. A. Lott, “Quasi-exact optical analysis of oxide apertured microcavity VCSEL’s using vector finite elements,” IEEE J. Quantum Electron. 34, 2327–2339 (1998).
[Crossref]

M. J. Noble, J. P. Loehr, and J. A. Lott, “Analysis of microcavity lasing modes using a full-vector weighted index method,” IEEE J. Quantum Electron. 34, 1892–1903 (1998).
[Crossref]

M. J. Noble, J. P. Loehr, and J. A. Lott, “Semi-analytic calculation of diffraction losses and threshold currents in microcavity VCSELs,” in IEEE LEOS Annual Meeting (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 212–213, paper WI3.

Piprek, J.

S. Rapp, J. Piprek, K. Streubel, J. André, and J. Wallin, “Temperature sensitivity of 1.54 µm vertical cavity lasers with an InP-based Bragg reflector,” IEEE J. Quantum Electron. 33, 1839–1845 (1997).
[Crossref]

Rapp, S.

S. Rapp, J. Piprek, K. Streubel, J. André, and J. Wallin, “Temperature sensitivity of 1.54 µm vertical cavity lasers with an InP-based Bragg reflector,” IEEE J. Quantum Electron. 33, 1839–1845 (1997).
[Crossref]

K. Streubel, S. Rapp, J. André, and J. Wallin, “Room-temperature pulsed operation of 1.5 µm vertical cavity lasers with an InP-based Bragg reflector,” IEEE Photon. Technol. Lett. 8, 1121–1123 (1996).
[Crossref]

Register, L. F.

B. Klein, L. F. Register, K. Hess, D. G. Deppe, and Q. Deng, “Self-consistent Green’s function approach to the analysis of dielectrically apertured vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 3324–3326 (1998).
[Crossref]

Schneider, R. P.

K. L. Lear, K. D. Choquette, R. P. Schneider, S. P. Kilcoyne, and K. M. Geib, “Selectively oxidized vertical cavity surface emitting lasers with 50% power conversion efficiency,” Electron. Lett. 31, 208–209 (1995).
[Crossref]

K. D. Choquette, K. L. Lear, R. P. Schneider, K. M. Geib, J. J. Figiel, and R. Hull, “Fabrication and performance of selectively oxidized vertical cavity lasers,” IEEE Photon. Technol. Lett. 7, 1237–1239 (1995).
[Crossref]

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

Scott, J. W.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, “Comprehensive numerical modeling of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 607–616 (1996).
[Crossref]

Seurin, J.-F.

G. Liu, J.-F. Seurin, S. L. Chuang, D. I. Babic, S. W. Corzine, M. Tan, D. C. Barnes, and T. N. Tiouririne, “Mode selectivity study of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 726–729 (1998).
[Crossref]

Streubel, K.

S. Rapp, J. Piprek, K. Streubel, J. André, and J. Wallin, “Temperature sensitivity of 1.54 µm vertical cavity lasers with an InP-based Bragg reflector,” IEEE J. Quantum Electron. 33, 1839–1845 (1997).
[Crossref]

K. Streubel, S. Rapp, J. André, and J. Wallin, “Room-temperature pulsed operation of 1.5 µm vertical cavity lasers with an InP-based Bragg reflector,” IEEE Photon. Technol. Lett. 8, 1121–1123 (1996).
[Crossref]

Tan, M.

G. Liu, J.-F. Seurin, S. L. Chuang, D. I. Babic, S. W. Corzine, M. Tan, D. C. Barnes, and T. N. Tiouririne, “Mode selectivity study of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 726–729 (1998).
[Crossref]

Tiouririne, T. N.

G. Liu, J.-F. Seurin, S. L. Chuang, D. I. Babic, S. W. Corzine, M. Tan, D. C. Barnes, and T. N. Tiouririne, “Mode selectivity study of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 726–729 (1998).
[Crossref]

Wallin, J.

S. Rapp, J. Piprek, K. Streubel, J. André, and J. Wallin, “Temperature sensitivity of 1.54 µm vertical cavity lasers with an InP-based Bragg reflector,” IEEE J. Quantum Electron. 33, 1839–1845 (1997).
[Crossref]

K. Streubel, S. Rapp, J. André, and J. Wallin, “Room-temperature pulsed operation of 1.5 µm vertical cavity lasers with an InP-based Bragg reflector,” IEEE Photon. Technol. Lett. 8, 1121–1123 (1996).
[Crossref]

Warren, M. E.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, “Comprehensive numerical modeling of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 607–616 (1996).
[Crossref]

Appl. Phys. Lett. (3)

D. L. Huffaker and D. G. Deppe, “Improved performance of oxide-confined vertical-cavity surface-emitting lasers using a tunnel injection active region,” Appl. Phys. Lett. 71, 1449–1451 (1997).
[Crossref]

B. Klein, L. F. Register, K. Hess, D. G. Deppe, and Q. Deng, “Self-consistent Green’s function approach to the analysis of dielectrically apertured vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 3324–3326 (1998).
[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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M. J. Noble, J. P. Loehr, and J. A. Lott, “Quasi-exact optical analysis of oxide apertured microcavity VCSEL’s using vector finite elements,” IEEE J. Quantum Electron. 34, 2327–2339 (1998).
[Crossref]

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[Crossref]

M. J. Noble, J. P. Loehr, and J. A. Lott, “Analysis of microcavity lasing modes using a full-vector weighted index method,” IEEE J. Quantum Electron. 34, 1892–1903 (1998).
[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (2)

Opt. Lett. (1)

Other (4)

M. J. Noble, J. P. Loehr, and J. A. Lott, “Semi-analytic calculation of diffraction losses and threshold currents in microcavity VCSELs,” in IEEE LEOS Annual Meeting (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 212–213, paper WI3.

T. Heide, “Steady state and modal properties of vertical cavity surface emitting lasers,” M.S. thesis (Royal Institute of Technology, Stockholm, 1996).

COST 268 modeling exercise ( http://www.ele.kth.se/COST268/WG1/WGExcercise1.html ), based on R. Kuszelewicz, Centre National d’Etudes en Télécommunication, Paris (personal communication, 1998).

W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990).

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Figures (10)

Fig. 1
Fig. 1

VCSEL model geometry.

Fig. 2
Fig. 2

Typical observed (λ, σi) plot.

Fig. 3
Fig. 3

Typical observed (gain, σi) plot at phase resonance.

Fig. 4
Fig. 4

Airpost VCSEL structure.

Fig. 5
Fig. 5

Regrown VCSEL structure.

Fig. 6
Fig. 6

Threshold material gain (airpost VCSEL).

Fig. 7
Fig. 7

Threshold material gain (regrown VCSEL).

Fig. 8
Fig. 8

Al-oxidized VCSEL.

Fig. 9
Fig. 9

Threshold material gain (oxidized VCSEL): 1, node oxide; 5, antinode oxide; no, no oxide; all, λ/4 oxide.

Fig. 10
Fig. 10

Lasing wavelength (oxidized VCSEL): 1, node oxide; 5, antinode oxide; no, no oxide; all, λ/4 oxide.

Equations (3)

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

Eitot(r, φ, z)=k{Ai,k+Ei,k(r, φ)exp(-jβi,k z)+Ai,k-Ei,k(r, φ)exp(jβi,k  z)},
Hitot(r, φ, z)=k{Ai,k+Hi,k(r, φ)exp(-jβi,k z)-Ai,k- Hi,k(r, φ)exp(jβi,k z)}.
RtopRbota=a.

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