Abstract

A self-consistently coupled three-dimensional dynamical model is presented for the first time, to our knowledge, to simulate noncircular vertical-cavity surface-emitting lasers. The electric, thermal, and optical processes are formulated using finite-volume-method discretization adopted on a unified mesh consisting of prism elements. Steady-state and dynamical calculations are shown for specially designed structures. An efficient numerical treatment enables one to perform large-scale calculations on single computers.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. D. Choquette, K. M. Geib, H. C. Chui, B. E. Hammons, H. Q. Hou, and T. J. Drummond, "Selective oxidation of buried AlGaAs versus AlAs layers," Appl. Phys. Lett. 69, 1385-1387 (1996).
    [CrossRef]
  2. A. Furukawa, S. Sasaki, M. Hoshi, A. Matsuzono, K. Moritoh, and T. Baba, "High-power single-mode vertical-cavity surface-emitting lasers with triangular holey structure," Appl. Phys. Lett. 85, 5161-5163 (2004).
    [CrossRef]
  3. N. Yokouchi, A. Y. Danner, and K. D. Choquette, "Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers," IEEE J. Sel. Top. Quantum Electron. 9, 1439-1445 (2003).
    [CrossRef]
  4. P. S. Ivanov, H. J. Unold, R. Michalzik, J. Maehnss, K. J. Ebeling, and I. A. Sukhoivanov, "Theoretical study of cold-cavity single-mode conditions in vertical-cavity surface-emitting lasers with incorporated two-dimensional photonic crystals," J. Opt. Soc. Am. B 20, 2442-2447 (2003).
    [CrossRef]
  5. H. Liu, M. Yan, P. Shum, H. Ghafouri-Shiraz, and D. Liu, "Design and analysis of anti-resonant reflecting photonic crystal VCSEL lasers," Opt. Express 12, 4269-4274 (2004).
    [CrossRef] [PubMed]
  6. P. Debernardi, H. J. Unold, J. Maehnss, R. Michalzik, G. P. Bava, and K. J. Ebeling, "Single-mode, single-polarization VCSELs via elliptical surface etching: experiments and theory," IEEE J. Sel. Top. Quantum Electron. 9, 1394-1404 (2003).
    [CrossRef]
  7. P. Debernardi, J. M. Ostermann, M. Feneberg, C. Jalics, and R. Michalzik, "Reliable polarization control of VCSELs through monolithically integrated surface gratings: a comparative theoretical and experimental study," IEEE J. Sel. Top. Quantum Electron. 11, 107-116 (2005).
    [CrossRef]
  8. G. P. Bava, P. Debernardi, and L. Fratta, "Three-dimensional model for vectorial fields in vertical-cavity surface-emitting lasers," Phys. Rev. A 63, 023816 (2001).
    [CrossRef]
  9. P. Debernardi, G. P. Bava, C. Degen, I. Fischer, and W. Elsässer, "Influence of anisotropies on transverse modes in oxide-confined VCSELs," IEEE J. Quantum Electron. 38, 73-84 (2002).
    [CrossRef]
  10. P. Nyakas, Z. Puskás, T. Kárpáti, T. Veszprémi, G. Zsombok, G. Varga, and N. Hashizume, "Optical simulation of vertical-cavity surface-emitting lasers with non-cylindrical oxide confinement," Opt. Commun. 250, 389-397 (2005).
    [CrossRef]
  11. M. J. Noble, J. P. Loehr, and J. A. Lott, "Analysis of microcavity VCSEL lasing modes using a full-vector weighted index method," IEEE J. Quantum Electron. 34, 1890-1903 (1998).
    [CrossRef]
  12. A. Valle and L. Pesquera, "Analytical calculation of transverse-mode characteristics in vertical-cavity surface-emitting lasers," J. Opt. Soc. Am. B 19, 1549-1557 (2002).
    [CrossRef]
  13. M. X. Jungo, D. Erni, and W. Bächtold, "VISTAS: a comprehensive system-oriented spatiotemporal VCSEL model," IEEE J. Sel. Top. Quantum Electron. 9, 939-948 (2003).
    [CrossRef]
  14. 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]
  15. J. S. Gustavsson, J. A. Vukusic, J. Bengtsson, and A. Larsson, "A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 38, 203-212 (2002).
    [CrossRef]
  16. J. S. Gustavsson, Å. Haglund, J. J. Bengtsson, P. Modh, and A. Larsson, "Dynamic behavior of fundamental-mode stabilized VCSELs using a shallow surface relief," IEEE J. Quantum Electron. 40, 607-619 (2004).
    [CrossRef]
  17. J. S. Gustavsson, J. Bengtsson, and A. Larsson, "Spatially dependent noise model for vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 40, 1163-1176 (2004).
    [CrossRef]
  18. M. Streiff, A. Witzig, M. Pfeiffer, P. Royo, and W. Fichtner, "A comprehensive VCSEL device simulator," IEEE J. Sel. Top. Quantum Electron. 9, 879-891 (2003).
    [CrossRef]
  19. A. Christ, N. Kuster, M. Streiff, A. Witzig, and W. Fichtner, "Correction of the numerical reflection coefficient of the finite-difference time-domain method for efficient simulation of vertical-cavity surface-emitting lasers," J. Opt. Soc. Am. B 20, 1401-1408 (2003).
    [CrossRef]
  20. R. Michalzik and K. J. Ebeling, "Modeling and design of proton-implanted ultralow-threshold vertical-cavity laser diodes," IEEE J. Quantum Electron. 29, 1963-1974 (1993).
    [CrossRef]
  21. PICS3D, User's Manual, Version 4.6.1 (Crosslight Software Inc., 2001).
  22. W. Nakwaski and M. Osinski, "Thermal analysis of GaAs-AlGaAs etched-well surface-emitting double-heterostructure lasers with dielectric mirrors," IEEE J. Quantum Electron. 29, 1981-1995 (1993).
    [CrossRef]
  23. C. H. Henry, R. A. Logan, F. R. Merritt, and J. P. Luongo, "The effect of intervalence band absorption on the thermal behavior of InGaAsP lasers," IEEE J. Quantum Electron. QE-19, 947-952 (1983).
    [CrossRef]
  24. R. Mittra and Ü. Pekel, "A new look at the perfectly matched layer (PML) concept for the reflectionless absorption of electromagnetic waves," IEEE Microw. Guid. Wave Lett. 5, 84-86 (1995).
    [CrossRef]
  25. P. Debernardi and G. P. Bava, "Coupled mode theory: a powerful tool for analyzing complex VCSELs and designing advanced device features," IEEE J. Sel. Top. Quantum Electron. 9, 905-917 (2003).
    [CrossRef]
  26. P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
    [CrossRef]
  27. S. Shinada and F. Koyama, "Single high-order transverse mode surface-emitting laser with controlled far-field pattern," IEEE Photon. Technol. Lett. 14, 1641-1643 (2002).
    [CrossRef]

2005 (2)

P. Debernardi, J. M. Ostermann, M. Feneberg, C. Jalics, and R. Michalzik, "Reliable polarization control of VCSELs through monolithically integrated surface gratings: a comparative theoretical and experimental study," IEEE J. Sel. Top. Quantum Electron. 11, 107-116 (2005).
[CrossRef]

P. Nyakas, Z. Puskás, T. Kárpáti, T. Veszprémi, G. Zsombok, G. Varga, and N. Hashizume, "Optical simulation of vertical-cavity surface-emitting lasers with non-cylindrical oxide confinement," Opt. Commun. 250, 389-397 (2005).
[CrossRef]

2004 (4)

J. S. Gustavsson, Å. Haglund, J. J. Bengtsson, P. Modh, and A. Larsson, "Dynamic behavior of fundamental-mode stabilized VCSELs using a shallow surface relief," IEEE J. Quantum Electron. 40, 607-619 (2004).
[CrossRef]

J. S. Gustavsson, J. Bengtsson, and A. Larsson, "Spatially dependent noise model for vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 40, 1163-1176 (2004).
[CrossRef]

A. Furukawa, S. Sasaki, M. Hoshi, A. Matsuzono, K. Moritoh, and T. Baba, "High-power single-mode vertical-cavity surface-emitting lasers with triangular holey structure," Appl. Phys. Lett. 85, 5161-5163 (2004).
[CrossRef]

H. Liu, M. Yan, P. Shum, H. Ghafouri-Shiraz, and D. Liu, "Design and analysis of anti-resonant reflecting photonic crystal VCSEL lasers," Opt. Express 12, 4269-4274 (2004).
[CrossRef] [PubMed]

2003 (7)

P. Debernardi, H. J. Unold, J. Maehnss, R. Michalzik, G. P. Bava, and K. J. Ebeling, "Single-mode, single-polarization VCSELs via elliptical surface etching: experiments and theory," IEEE J. Sel. Top. Quantum Electron. 9, 1394-1404 (2003).
[CrossRef]

N. Yokouchi, A. Y. Danner, and K. D. Choquette, "Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers," IEEE J. Sel. Top. Quantum Electron. 9, 1439-1445 (2003).
[CrossRef]

P. S. Ivanov, H. J. Unold, R. Michalzik, J. Maehnss, K. J. Ebeling, and I. A. Sukhoivanov, "Theoretical study of cold-cavity single-mode conditions in vertical-cavity surface-emitting lasers with incorporated two-dimensional photonic crystals," J. Opt. Soc. Am. B 20, 2442-2447 (2003).
[CrossRef]

M. Streiff, A. Witzig, M. Pfeiffer, P. Royo, and W. Fichtner, "A comprehensive VCSEL device simulator," IEEE J. Sel. Top. Quantum Electron. 9, 879-891 (2003).
[CrossRef]

A. Christ, N. Kuster, M. Streiff, A. Witzig, and W. Fichtner, "Correction of the numerical reflection coefficient of the finite-difference time-domain method for efficient simulation of vertical-cavity surface-emitting lasers," J. Opt. Soc. Am. B 20, 1401-1408 (2003).
[CrossRef]

M. X. Jungo, D. Erni, and W. Bächtold, "VISTAS: a comprehensive system-oriented spatiotemporal VCSEL model," IEEE J. Sel. Top. Quantum Electron. 9, 939-948 (2003).
[CrossRef]

P. Debernardi and G. P. Bava, "Coupled mode theory: a powerful tool for analyzing complex VCSELs and designing advanced device features," IEEE J. Sel. Top. Quantum Electron. 9, 905-917 (2003).
[CrossRef]

2002 (4)

A. Valle and L. Pesquera, "Analytical calculation of transverse-mode characteristics in vertical-cavity surface-emitting lasers," J. Opt. Soc. Am. B 19, 1549-1557 (2002).
[CrossRef]

J. S. Gustavsson, J. A. Vukusic, J. Bengtsson, and A. Larsson, "A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 38, 203-212 (2002).
[CrossRef]

S. Shinada and F. Koyama, "Single high-order transverse mode surface-emitting laser with controlled far-field pattern," IEEE Photon. Technol. Lett. 14, 1641-1643 (2002).
[CrossRef]

P. Debernardi, G. P. Bava, C. Degen, I. Fischer, and W. Elsässer, "Influence of anisotropies on transverse modes in oxide-confined VCSELs," IEEE J. Quantum Electron. 38, 73-84 (2002).
[CrossRef]

2001 (2)

G. P. Bava, P. Debernardi, and L. Fratta, "Three-dimensional model for vectorial fields in vertical-cavity surface-emitting lasers," Phys. Rev. A 63, 023816 (2001).
[CrossRef]

P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
[CrossRef]

1998 (1)

M. J. Noble, J. P. Loehr, and J. A. Lott, "Analysis of microcavity VCSEL lasing modes using a full-vector weighted index method," IEEE J. Quantum Electron. 34, 1890-1903 (1998).
[CrossRef]

1996 (2)

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. M. Geib, H. C. Chui, B. E. Hammons, H. Q. Hou, and T. J. Drummond, "Selective oxidation of buried AlGaAs versus AlAs layers," Appl. Phys. Lett. 69, 1385-1387 (1996).
[CrossRef]

1995 (1)

R. Mittra and Ü. Pekel, "A new look at the perfectly matched layer (PML) concept for the reflectionless absorption of electromagnetic waves," IEEE Microw. Guid. Wave Lett. 5, 84-86 (1995).
[CrossRef]

1993 (2)

R. Michalzik and K. J. Ebeling, "Modeling and design of proton-implanted ultralow-threshold vertical-cavity laser diodes," IEEE J. Quantum Electron. 29, 1963-1974 (1993).
[CrossRef]

W. Nakwaski and M. Osinski, "Thermal analysis of GaAs-AlGaAs etched-well surface-emitting double-heterostructure lasers with dielectric mirrors," IEEE J. Quantum Electron. 29, 1981-1995 (1993).
[CrossRef]

1983 (1)

C. H. Henry, R. A. Logan, F. R. Merritt, and J. P. Luongo, "The effect of intervalence band absorption on the thermal behavior of InGaAsP lasers," IEEE J. Quantum Electron. QE-19, 947-952 (1983).
[CrossRef]

Baba, T.

A. Furukawa, S. Sasaki, M. Hoshi, A. Matsuzono, K. Moritoh, and T. Baba, "High-power single-mode vertical-cavity surface-emitting lasers with triangular holey structure," Appl. Phys. Lett. 85, 5161-5163 (2004).
[CrossRef]

Bächtold, W.

M. X. Jungo, D. Erni, and W. Bächtold, "VISTAS: a comprehensive system-oriented spatiotemporal VCSEL model," IEEE J. Sel. Top. Quantum Electron. 9, 939-948 (2003).
[CrossRef]

Baets, R.

P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
[CrossRef]

Bava, G. P.

P. Debernardi and G. P. Bava, "Coupled mode theory: a powerful tool for analyzing complex VCSELs and designing advanced device features," IEEE J. Sel. Top. Quantum Electron. 9, 905-917 (2003).
[CrossRef]

P. Debernardi, H. J. Unold, J. Maehnss, R. Michalzik, G. P. Bava, and K. J. Ebeling, "Single-mode, single-polarization VCSELs via elliptical surface etching: experiments and theory," IEEE J. Sel. Top. Quantum Electron. 9, 1394-1404 (2003).
[CrossRef]

P. Debernardi, G. P. Bava, C. Degen, I. Fischer, and W. Elsässer, "Influence of anisotropies on transverse modes in oxide-confined VCSELs," IEEE J. Quantum Electron. 38, 73-84 (2002).
[CrossRef]

G. P. Bava, P. Debernardi, and L. Fratta, "Three-dimensional model for vectorial fields in vertical-cavity surface-emitting lasers," Phys. Rev. A 63, 023816 (2001).
[CrossRef]

P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
[CrossRef]

Bengtsson, J.

J. S. Gustavsson, J. Bengtsson, and A. Larsson, "Spatially dependent noise model for vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 40, 1163-1176 (2004).
[CrossRef]

J. S. Gustavsson, J. A. Vukusic, J. Bengtsson, and A. Larsson, "A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 38, 203-212 (2002).
[CrossRef]

Bengtsson, J. J.

J. S. Gustavsson, Å. Haglund, J. J. Bengtsson, P. Modh, and A. Larsson, "Dynamic behavior of fundamental-mode stabilized VCSELs using a shallow surface relief," IEEE J. Quantum Electron. 40, 607-619 (2004).
[CrossRef]

Bienstman, P.

P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
[CrossRef]

Brunner, M.

P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
[CrossRef]

Choquette, K. D.

N. Yokouchi, A. Y. Danner, and K. D. Choquette, "Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers," IEEE J. Sel. Top. Quantum Electron. 9, 1439-1445 (2003).
[CrossRef]

K. D. Choquette, K. M. Geib, H. C. Chui, B. E. Hammons, H. Q. Hou, and T. J. Drummond, "Selective oxidation of buried AlGaAs versus AlAs layers," Appl. Phys. Lett. 69, 1385-1387 (1996).
[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]

Christ, A.

Chuang, S. L.

P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
[CrossRef]

Chui, H. C.

K. D. Choquette, K. M. Geib, H. C. Chui, B. E. Hammons, H. Q. Hou, and T. J. Drummond, "Selective oxidation of buried AlGaAs versus AlAs layers," Appl. Phys. Lett. 69, 1385-1387 (1996).
[CrossRef]

Conradi, O.

P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
[CrossRef]

Corzine, S. 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]

Danner, A. Y.

N. Yokouchi, A. Y. Danner, and K. D. Choquette, "Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers," IEEE J. Sel. Top. Quantum Electron. 9, 1439-1445 (2003).
[CrossRef]

Debernardi, P.

P. Debernardi, J. M. Ostermann, M. Feneberg, C. Jalics, and R. Michalzik, "Reliable polarization control of VCSELs through monolithically integrated surface gratings: a comparative theoretical and experimental study," IEEE J. Sel. Top. Quantum Electron. 11, 107-116 (2005).
[CrossRef]

P. Debernardi, H. J. Unold, J. Maehnss, R. Michalzik, G. P. Bava, and K. J. Ebeling, "Single-mode, single-polarization VCSELs via elliptical surface etching: experiments and theory," IEEE J. Sel. Top. Quantum Electron. 9, 1394-1404 (2003).
[CrossRef]

P. Debernardi and G. P. Bava, "Coupled mode theory: a powerful tool for analyzing complex VCSELs and designing advanced device features," IEEE J. Sel. Top. Quantum Electron. 9, 905-917 (2003).
[CrossRef]

P. Debernardi, G. P. Bava, C. Degen, I. Fischer, and W. Elsässer, "Influence of anisotropies on transverse modes in oxide-confined VCSELs," IEEE J. Quantum Electron. 38, 73-84 (2002).
[CrossRef]

G. P. Bava, P. Debernardi, and L. Fratta, "Three-dimensional model for vectorial fields in vertical-cavity surface-emitting lasers," Phys. Rev. A 63, 023816 (2001).
[CrossRef]

P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
[CrossRef]

Degen, C.

P. Debernardi, G. P. Bava, C. Degen, I. Fischer, and W. Elsässer, "Influence of anisotropies on transverse modes in oxide-confined VCSELs," IEEE J. Quantum Electron. 38, 73-84 (2002).
[CrossRef]

Drummond, T. J.

K. D. Choquette, K. M. Geib, H. C. Chui, B. E. Hammons, H. Q. Hou, and T. J. Drummond, "Selective oxidation of buried AlGaAs versus AlAs layers," Appl. Phys. Lett. 69, 1385-1387 (1996).
[CrossRef]

Ebeling, K. J.

P. S. Ivanov, H. J. Unold, R. Michalzik, J. Maehnss, K. J. Ebeling, and I. A. Sukhoivanov, "Theoretical study of cold-cavity single-mode conditions in vertical-cavity surface-emitting lasers with incorporated two-dimensional photonic crystals," J. Opt. Soc. Am. B 20, 2442-2447 (2003).
[CrossRef]

P. Debernardi, H. J. Unold, J. Maehnss, R. Michalzik, G. P. Bava, and K. J. Ebeling, "Single-mode, single-polarization VCSELs via elliptical surface etching: experiments and theory," IEEE J. Sel. Top. Quantum Electron. 9, 1394-1404 (2003).
[CrossRef]

R. Michalzik and K. J. Ebeling, "Modeling and design of proton-implanted ultralow-threshold vertical-cavity laser diodes," IEEE J. Quantum Electron. 29, 1963-1974 (1993).
[CrossRef]

Elsässer, W.

P. Debernardi, G. P. Bava, C. Degen, I. Fischer, and W. Elsässer, "Influence of anisotropies on transverse modes in oxide-confined VCSELs," IEEE J. Quantum Electron. 38, 73-84 (2002).
[CrossRef]

Erni, D.

M. X. Jungo, D. Erni, and W. Bächtold, "VISTAS: a comprehensive system-oriented spatiotemporal VCSEL model," IEEE J. Sel. Top. Quantum Electron. 9, 939-948 (2003).
[CrossRef]

Feneberg, M.

P. Debernardi, J. M. Ostermann, M. Feneberg, C. Jalics, and R. Michalzik, "Reliable polarization control of VCSELs through monolithically integrated surface gratings: a comparative theoretical and experimental study," IEEE J. Sel. Top. Quantum Electron. 11, 107-116 (2005).
[CrossRef]

Fichtner, W.

Fischer, I.

P. Debernardi, G. P. Bava, C. Degen, I. Fischer, and W. Elsässer, "Influence of anisotropies on transverse modes in oxide-confined VCSELs," IEEE J. Quantum Electron. 38, 73-84 (2002).
[CrossRef]

Fratta, L.

G. P. Bava, P. Debernardi, and L. Fratta, "Three-dimensional model for vectorial fields in vertical-cavity surface-emitting lasers," Phys. Rev. A 63, 023816 (2001).
[CrossRef]

P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
[CrossRef]

Furukawa, A.

A. Furukawa, S. Sasaki, M. Hoshi, A. Matsuzono, K. Moritoh, and T. Baba, "High-power single-mode vertical-cavity surface-emitting lasers with triangular holey structure," Appl. Phys. Lett. 85, 5161-5163 (2004).
[CrossRef]

Geib, K. M.

K. D. Choquette, K. M. Geib, H. C. Chui, B. E. Hammons, H. Q. Hou, and T. J. Drummond, "Selective oxidation of buried AlGaAs versus AlAs layers," Appl. Phys. Lett. 69, 1385-1387 (1996).
[CrossRef]

Ghafouri-Shiraz, H.

Gulden, K.

P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
[CrossRef]

Gustavsson, J. S.

J. S. Gustavsson, J. Bengtsson, and A. Larsson, "Spatially dependent noise model for vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 40, 1163-1176 (2004).
[CrossRef]

J. S. Gustavsson, Å. Haglund, J. J. Bengtsson, P. Modh, and A. Larsson, "Dynamic behavior of fundamental-mode stabilized VCSELs using a shallow surface relief," IEEE J. Quantum Electron. 40, 607-619 (2004).
[CrossRef]

J. S. Gustavsson, J. A. Vukusic, J. Bengtsson, and A. Larsson, "A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 38, 203-212 (2002).
[CrossRef]

Hadley, G. R.

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]

Haglund, Å.

J. S. Gustavsson, Å. Haglund, J. J. Bengtsson, P. Modh, and A. Larsson, "Dynamic behavior of fundamental-mode stabilized VCSELs using a shallow surface relief," IEEE J. Quantum Electron. 40, 607-619 (2004).
[CrossRef]

Hammons, B. E.

K. D. Choquette, K. M. Geib, H. C. Chui, B. E. Hammons, H. Q. Hou, and T. J. Drummond, "Selective oxidation of buried AlGaAs versus AlAs layers," Appl. Phys. Lett. 69, 1385-1387 (1996).
[CrossRef]

Hashizume, N.

P. Nyakas, Z. Puskás, T. Kárpáti, T. Veszprémi, G. Zsombok, G. Varga, and N. Hashizume, "Optical simulation of vertical-cavity surface-emitting lasers with non-cylindrical oxide confinement," Opt. Commun. 250, 389-397 (2005).
[CrossRef]

Henry, C. H.

C. H. Henry, R. A. Logan, F. R. Merritt, and J. P. Luongo, "The effect of intervalence band absorption on the thermal behavior of InGaAsP lasers," IEEE J. Quantum Electron. QE-19, 947-952 (1983).
[CrossRef]

Hoshi, M.

A. Furukawa, S. Sasaki, M. Hoshi, A. Matsuzono, K. Moritoh, and T. Baba, "High-power single-mode vertical-cavity surface-emitting lasers with triangular holey structure," Appl. Phys. Lett. 85, 5161-5163 (2004).
[CrossRef]

Hou, H. Q.

K. D. Choquette, K. M. Geib, H. C. Chui, B. E. Hammons, H. Q. Hou, and T. J. Drummond, "Selective oxidation of buried AlGaAs versus AlAs layers," Appl. Phys. Lett. 69, 1385-1387 (1996).
[CrossRef]

Ivanov, P. S.

Jalics, C.

P. Debernardi, J. M. Ostermann, M. Feneberg, C. Jalics, and R. Michalzik, "Reliable polarization control of VCSELs through monolithically integrated surface gratings: a comparative theoretical and experimental study," IEEE J. Sel. Top. Quantum Electron. 11, 107-116 (2005).
[CrossRef]

Jungo, M. X.

M. X. Jungo, D. Erni, and W. Bächtold, "VISTAS: a comprehensive system-oriented spatiotemporal VCSEL model," IEEE J. Sel. Top. Quantum Electron. 9, 939-948 (2003).
[CrossRef]

Kárpáti, T.

P. Nyakas, Z. Puskás, T. Kárpáti, T. Veszprémi, G. Zsombok, G. Varga, and N. Hashizume, "Optical simulation of vertical-cavity surface-emitting lasers with non-cylindrical oxide confinement," Opt. Commun. 250, 389-397 (2005).
[CrossRef]

Klein, B.

P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
[CrossRef]

Koyama, F.

S. Shinada and F. Koyama, "Single high-order transverse mode surface-emitting laser with controlled far-field pattern," IEEE Photon. Technol. Lett. 14, 1641-1643 (2002).
[CrossRef]

Kuster, N.

Larsson, A.

J. S. Gustavsson, J. Bengtsson, and A. Larsson, "Spatially dependent noise model for vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 40, 1163-1176 (2004).
[CrossRef]

J. S. Gustavsson, Å. Haglund, J. J. Bengtsson, P. Modh, and A. Larsson, "Dynamic behavior of fundamental-mode stabilized VCSELs using a shallow surface relief," IEEE J. Quantum Electron. 40, 607-619 (2004).
[CrossRef]

J. S. Gustavsson, J. A. Vukusic, J. Bengtsson, and A. Larsson, "A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 38, 203-212 (2002).
[CrossRef]

P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
[CrossRef]

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]

Liu, D.

Liu, H.

Loehr, J. P.

M. J. Noble, J. P. Loehr, and J. A. Lott, "Analysis of microcavity VCSEL lasing modes using a full-vector weighted index method," IEEE J. Quantum Electron. 34, 1890-1903 (1998).
[CrossRef]

Logan, R. A.

C. H. Henry, R. A. Logan, F. R. Merritt, and J. P. Luongo, "The effect of intervalence band absorption on the thermal behavior of InGaAsP lasers," IEEE J. Quantum Electron. QE-19, 947-952 (1983).
[CrossRef]

Lott, J. A.

M. J. Noble, J. P. Loehr, and J. A. Lott, "Analysis of microcavity VCSEL lasing modes using a full-vector weighted index method," IEEE J. Quantum Electron. 34, 1890-1903 (1998).
[CrossRef]

Luongo, J. P.

C. H. Henry, R. A. Logan, F. R. Merritt, and J. P. Luongo, "The effect of intervalence band absorption on the thermal behavior of InGaAsP lasers," IEEE J. Quantum Electron. QE-19, 947-952 (1983).
[CrossRef]

Maehnss, J.

P. S. Ivanov, H. J. Unold, R. Michalzik, J. Maehnss, K. J. Ebeling, and I. A. Sukhoivanov, "Theoretical study of cold-cavity single-mode conditions in vertical-cavity surface-emitting lasers with incorporated two-dimensional photonic crystals," J. Opt. Soc. Am. B 20, 2442-2447 (2003).
[CrossRef]

P. Debernardi, H. J. Unold, J. Maehnss, R. Michalzik, G. P. Bava, and K. J. Ebeling, "Single-mode, single-polarization VCSELs via elliptical surface etching: experiments and theory," IEEE J. Sel. Top. Quantum Electron. 9, 1394-1404 (2003).
[CrossRef]

Matsuzono, A.

A. Furukawa, S. Sasaki, M. Hoshi, A. Matsuzono, K. Moritoh, and T. Baba, "High-power single-mode vertical-cavity surface-emitting lasers with triangular holey structure," Appl. Phys. Lett. 85, 5161-5163 (2004).
[CrossRef]

Merritt, F. R.

C. H. Henry, R. A. Logan, F. R. Merritt, and J. P. Luongo, "The effect of intervalence band absorption on the thermal behavior of InGaAsP lasers," IEEE J. Quantum Electron. QE-19, 947-952 (1983).
[CrossRef]

Michalzik, R.

P. Debernardi, J. M. Ostermann, M. Feneberg, C. Jalics, and R. Michalzik, "Reliable polarization control of VCSELs through monolithically integrated surface gratings: a comparative theoretical and experimental study," IEEE J. Sel. Top. Quantum Electron. 11, 107-116 (2005).
[CrossRef]

P. Debernardi, H. J. Unold, J. Maehnss, R. Michalzik, G. P. Bava, and K. J. Ebeling, "Single-mode, single-polarization VCSELs via elliptical surface etching: experiments and theory," IEEE J. Sel. Top. Quantum Electron. 9, 1394-1404 (2003).
[CrossRef]

P. S. Ivanov, H. J. Unold, R. Michalzik, J. Maehnss, K. J. Ebeling, and I. A. Sukhoivanov, "Theoretical study of cold-cavity single-mode conditions in vertical-cavity surface-emitting lasers with incorporated two-dimensional photonic crystals," J. Opt. Soc. Am. B 20, 2442-2447 (2003).
[CrossRef]

R. Michalzik and K. J. Ebeling, "Modeling and design of proton-implanted ultralow-threshold vertical-cavity laser diodes," IEEE J. Quantum Electron. 29, 1963-1974 (1993).
[CrossRef]

Mittra, R.

R. Mittra and Ü. Pekel, "A new look at the perfectly matched layer (PML) concept for the reflectionless absorption of electromagnetic waves," IEEE Microw. Guid. Wave Lett. 5, 84-86 (1995).
[CrossRef]

Modh, P.

J. S. Gustavsson, Å. Haglund, J. J. Bengtsson, P. Modh, and A. Larsson, "Dynamic behavior of fundamental-mode stabilized VCSELs using a shallow surface relief," IEEE J. Quantum Electron. 40, 607-619 (2004).
[CrossRef]

Moritoh, K.

A. Furukawa, S. Sasaki, M. Hoshi, A. Matsuzono, K. Moritoh, and T. Baba, "High-power single-mode vertical-cavity surface-emitting lasers with triangular holey structure," Appl. Phys. Lett. 85, 5161-5163 (2004).
[CrossRef]

Nakwaski, W.

W. Nakwaski and M. Osinski, "Thermal analysis of GaAs-AlGaAs etched-well surface-emitting double-heterostructure lasers with dielectric mirrors," IEEE J. Quantum Electron. 29, 1981-1995 (1993).
[CrossRef]

Noble, M. J.

P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
[CrossRef]

M. J. Noble, J. P. Loehr, and J. A. Lott, "Analysis of microcavity VCSEL lasing modes using a full-vector weighted index method," IEEE J. Quantum Electron. 34, 1890-1903 (1998).
[CrossRef]

Nyakas, P.

P. Nyakas, Z. Puskás, T. Kárpáti, T. Veszprémi, G. Zsombok, G. Varga, and N. Hashizume, "Optical simulation of vertical-cavity surface-emitting lasers with non-cylindrical oxide confinement," Opt. Commun. 250, 389-397 (2005).
[CrossRef]

Osinski, M.

W. Nakwaski and M. Osinski, "Thermal analysis of GaAs-AlGaAs etched-well surface-emitting double-heterostructure lasers with dielectric mirrors," IEEE J. Quantum Electron. 29, 1981-1995 (1993).
[CrossRef]

Ostermann, J. M.

P. Debernardi, J. M. Ostermann, M. Feneberg, C. Jalics, and R. Michalzik, "Reliable polarization control of VCSELs through monolithically integrated surface gratings: a comparative theoretical and experimental study," IEEE J. Sel. Top. Quantum Electron. 11, 107-116 (2005).
[CrossRef]

Pekel, Ü.

R. Mittra and Ü. Pekel, "A new look at the perfectly matched layer (PML) concept for the reflectionless absorption of electromagnetic waves," IEEE Microw. Guid. Wave Lett. 5, 84-86 (1995).
[CrossRef]

Pesquera, L.

Pfeiffer, M.

M. Streiff, A. Witzig, M. Pfeiffer, P. Royo, and W. Fichtner, "A comprehensive VCSEL device simulator," IEEE J. Sel. Top. Quantum Electron. 9, 879-891 (2003).
[CrossRef]

Pregla, R.

P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
[CrossRef]

Puskás, Z.

P. Nyakas, Z. Puskás, T. Kárpáti, T. Veszprémi, G. Zsombok, G. Varga, and N. Hashizume, "Optical simulation of vertical-cavity surface-emitting lasers with non-cylindrical oxide confinement," Opt. Commun. 250, 389-397 (2005).
[CrossRef]

Riyopoulos, S. A.

P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
[CrossRef]

Royo, P.

M. Streiff, A. Witzig, M. Pfeiffer, P. Royo, and W. Fichtner, "A comprehensive VCSEL device simulator," IEEE J. Sel. Top. Quantum Electron. 9, 879-891 (2003).
[CrossRef]

Sasaki, S.

A. Furukawa, S. Sasaki, M. Hoshi, A. Matsuzono, K. Moritoh, and T. Baba, "High-power single-mode vertical-cavity surface-emitting lasers with triangular holey structure," Appl. Phys. Lett. 85, 5161-5163 (2004).
[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. P.

P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
[CrossRef]

Shinada, S.

S. Shinada and F. Koyama, "Single high-order transverse mode surface-emitting laser with controlled far-field pattern," IEEE Photon. Technol. Lett. 14, 1641-1643 (2002).
[CrossRef]

Shum, P.

Streiff, M.

Sukhoivanov, I. A.

Unold, H. J.

P. S. Ivanov, H. J. Unold, R. Michalzik, J. Maehnss, K. J. Ebeling, and I. A. Sukhoivanov, "Theoretical study of cold-cavity single-mode conditions in vertical-cavity surface-emitting lasers with incorporated two-dimensional photonic crystals," J. Opt. Soc. Am. B 20, 2442-2447 (2003).
[CrossRef]

P. Debernardi, H. J. Unold, J. Maehnss, R. Michalzik, G. P. Bava, and K. J. Ebeling, "Single-mode, single-polarization VCSELs via elliptical surface etching: experiments and theory," IEEE J. Sel. Top. Quantum Electron. 9, 1394-1404 (2003).
[CrossRef]

Valle, A.

Varga, G.

P. Nyakas, Z. Puskás, T. Kárpáti, T. Veszprémi, G. Zsombok, G. Varga, and N. Hashizume, "Optical simulation of vertical-cavity surface-emitting lasers with non-cylindrical oxide confinement," Opt. Commun. 250, 389-397 (2005).
[CrossRef]

Veszprémi, T.

P. Nyakas, Z. Puskás, T. Kárpáti, T. Veszprémi, G. Zsombok, G. Varga, and N. Hashizume, "Optical simulation of vertical-cavity surface-emitting lasers with non-cylindrical oxide confinement," Opt. Commun. 250, 389-397 (2005).
[CrossRef]

Vukusic, J.

P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
[CrossRef]

Vukusic, J. A.

J. S. Gustavsson, J. A. Vukusic, J. Bengtsson, and A. Larsson, "A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 38, 203-212 (2002).
[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]

Wenzel, H.

P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
[CrossRef]

Witzig, A.

Yan, M.

Yokouchi, N.

N. Yokouchi, A. Y. Danner, and K. D. Choquette, "Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers," IEEE J. Sel. Top. Quantum Electron. 9, 1439-1445 (2003).
[CrossRef]

Zsombok, G.

P. Nyakas, Z. Puskás, T. Kárpáti, T. Veszprémi, G. Zsombok, G. Varga, and N. Hashizume, "Optical simulation of vertical-cavity surface-emitting lasers with non-cylindrical oxide confinement," Opt. Commun. 250, 389-397 (2005).
[CrossRef]

Appl. Phys. Lett. (2)

K. D. Choquette, K. M. Geib, H. C. Chui, B. E. Hammons, H. Q. Hou, and T. J. Drummond, "Selective oxidation of buried AlGaAs versus AlAs layers," Appl. Phys. Lett. 69, 1385-1387 (1996).
[CrossRef]

A. Furukawa, S. Sasaki, M. Hoshi, A. Matsuzono, K. Moritoh, and T. Baba, "High-power single-mode vertical-cavity surface-emitting lasers with triangular holey structure," Appl. Phys. Lett. 85, 5161-5163 (2004).
[CrossRef]

IEEE J. Quantum Electron. (10)

P. Debernardi, G. P. Bava, C. Degen, I. Fischer, and W. Elsässer, "Influence of anisotropies on transverse modes in oxide-confined VCSELs," IEEE J. Quantum Electron. 38, 73-84 (2002).
[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]

J. S. Gustavsson, J. A. Vukusic, J. Bengtsson, and A. Larsson, "A comprehensive model for the modal dynamics of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 38, 203-212 (2002).
[CrossRef]

J. S. Gustavsson, Å. Haglund, J. J. Bengtsson, P. Modh, and A. Larsson, "Dynamic behavior of fundamental-mode stabilized VCSELs using a shallow surface relief," IEEE J. Quantum Electron. 40, 607-619 (2004).
[CrossRef]

J. S. Gustavsson, J. Bengtsson, and A. Larsson, "Spatially dependent noise model for vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 40, 1163-1176 (2004).
[CrossRef]

M. J. Noble, J. P. Loehr, and J. A. Lott, "Analysis of microcavity VCSEL lasing modes using a full-vector weighted index method," IEEE J. Quantum Electron. 34, 1890-1903 (1998).
[CrossRef]

R. Michalzik and K. J. Ebeling, "Modeling and design of proton-implanted ultralow-threshold vertical-cavity laser diodes," IEEE J. Quantum Electron. 29, 1963-1974 (1993).
[CrossRef]

W. Nakwaski and M. Osinski, "Thermal analysis of GaAs-AlGaAs etched-well surface-emitting double-heterostructure lasers with dielectric mirrors," IEEE J. Quantum Electron. 29, 1981-1995 (1993).
[CrossRef]

C. H. Henry, R. A. Logan, F. R. Merritt, and J. P. Luongo, "The effect of intervalence band absorption on the thermal behavior of InGaAsP lasers," IEEE J. Quantum Electron. QE-19, 947-952 (1983).
[CrossRef]

P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M. J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G. P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S. A. Riyopoulos, J.-F. P. Seurin, and S. L. Chuang, "Comparison of optical VCSEL models on the simulation of oxide-confined devices," IEEE J. Quantum Electron. 37, 1618-1631 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (6)

M. X. Jungo, D. Erni, and W. Bächtold, "VISTAS: a comprehensive system-oriented spatiotemporal VCSEL model," IEEE J. Sel. Top. Quantum Electron. 9, 939-948 (2003).
[CrossRef]

P. Debernardi and G. P. Bava, "Coupled mode theory: a powerful tool for analyzing complex VCSELs and designing advanced device features," IEEE J. Sel. Top. Quantum Electron. 9, 905-917 (2003).
[CrossRef]

M. Streiff, A. Witzig, M. Pfeiffer, P. Royo, and W. Fichtner, "A comprehensive VCSEL device simulator," IEEE J. Sel. Top. Quantum Electron. 9, 879-891 (2003).
[CrossRef]

P. Debernardi, H. J. Unold, J. Maehnss, R. Michalzik, G. P. Bava, and K. J. Ebeling, "Single-mode, single-polarization VCSELs via elliptical surface etching: experiments and theory," IEEE J. Sel. Top. Quantum Electron. 9, 1394-1404 (2003).
[CrossRef]

P. Debernardi, J. M. Ostermann, M. Feneberg, C. Jalics, and R. Michalzik, "Reliable polarization control of VCSELs through monolithically integrated surface gratings: a comparative theoretical and experimental study," IEEE J. Sel. Top. Quantum Electron. 11, 107-116 (2005).
[CrossRef]

N. Yokouchi, A. Y. Danner, and K. D. Choquette, "Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers," IEEE J. Sel. Top. Quantum Electron. 9, 1439-1445 (2003).
[CrossRef]

IEEE Microw. Guid. Wave Lett. (1)

R. Mittra and Ü. Pekel, "A new look at the perfectly matched layer (PML) concept for the reflectionless absorption of electromagnetic waves," IEEE Microw. Guid. Wave Lett. 5, 84-86 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. Shinada and F. Koyama, "Single high-order transverse mode surface-emitting laser with controlled far-field pattern," IEEE Photon. Technol. Lett. 14, 1641-1643 (2002).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

P. Nyakas, Z. Puskás, T. Kárpáti, T. Veszprémi, G. Zsombok, G. Varga, and N. Hashizume, "Optical simulation of vertical-cavity surface-emitting lasers with non-cylindrical oxide confinement," Opt. Commun. 250, 389-397 (2005).
[CrossRef]

Opt. Express (1)

Phys. Rev. A (1)

G. P. Bava, P. Debernardi, and L. Fratta, "Three-dimensional model for vectorial fields in vertical-cavity surface-emitting lasers," Phys. Rev. A 63, 023816 (2001).
[CrossRef]

Other (1)

PICS3D, User's Manual, Version 4.6.1 (Crosslight Software Inc., 2001).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Sample lateral mesh created with relaxed Delaunay triangularization. Thick contours represent symmetry surfaces, material interfaces, and PML boundaries. The innermost region bordered by a curvilinear tetragon is the core, and the second is the oxide. Both overlap with a triangular surface relief. The third region is the artificial absorbing media with complex spatial variables.

Fig. 2
Fig. 2

Dual element of a typical single prism having 12 side faces. Representative points of prisms are marked with filled circles. Since system equations are integrated over these columns, fluxes have to be formulated on the faces.

Fig. 3
Fig. 3

Near-field CCD image of the VCSEL summarized in Table 2 with a noncircular aperture of nearly 100 μ m 2 area. Driving current was 7 mA . Although clear multimode emission is observed, the intensity of the LP 21 mode oriented to the corners of the aperture dominates.

Fig. 4
Fig. 4

Computed light–current characteristics for five optical modes. The inset shows the intensity distribution in the quantum well at 15 mA .

Fig. 5
Fig. 5

Large-signal analysis for five competitive modes. The insets show near-field patterns at 0, 200, and 1000 ps .

Fig. 6
Fig. 6

Calculated small-signal modulation response function.

Fig. 7
Fig. 7

Schematics of the VCSEL with triangular surface reliefs.

Fig. 8
Fig. 8

Cold-cavity modal losses of the fundamental and few higher-order modes versus hole position. Dashed line represents total loss of 188 cm 1 if the topmost layer is fully removed; solid line at 28.4 cm 1 is for the unetched VCSEL.

Fig. 9
Fig. 9

Calculated light–current characteristics for five lowest-order optical modes. The intensity profile in the quantum well at 15 mA is displayed in the inset.

Fig. 10
Fig. 10

Cold-cavity modal losses of the fundamental and four higher-order modes versus elliptical relief size. Dashed line represents total loss of 188 cm 1 if the topmost layer is fully removed; solid line at 28.4 cm 1 is for the VCSEL without surface pattern.

Fig. 11
Fig. 11

Light–current characteristics with five modes included in the calculation. The intensity profile in the quantum well at 10 mA driving current is displayed in the inset.

Tables (2)

Tables Icon

Table 1 Model Parameters

Tables Icon

Table 2 Layer Structure of the Simulated VCSEL

Equations (16)

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

( σ Φ ) = 0 .
μ ( T ) = μ ( T 0 ) ( T 0 T ) 2.3 .
c ρ T t = ( κ T ) + R nr + R joule + R abs. .
κ ( T ) = κ ( T 0 ) ( T 0 T ) 1.25 .
2 Ψ = k 0 2 ϵ Ψ ,
n ( T ) = n ( T 0 ) [ 1 + n T ( T T 0 ) ] ,
n ( T ) = n ( T 0 ) exp ( T T 0 T abs ) .
n t = η j e d A n B n 2 C n 3 + D Δ n v g g ( n ) Ψ i 2 S i ,
S i t = β B n 2 d V + v g [ g ( n ) Ψ i 2 d V L i ] S i .
g ( n , λ , T ) = a 0 ln ( n n 0 ) { 1 [ λ 0 + λ T ( T T 0 ) λ Δ λ 0 ] 2 } ,
L = c J ( k 0 ) v g ,
V ( σ Φ ) d V = i ( σ T Φ ) i A i + ( σ Φ z ) t A t + ( σ Φ z ) b A b ,
( Φ x Φ y ) = [ x 1 x 2 y 1 y 2 x 1 x 3 y 1 y 3 ] 1 ( Φ 1 Φ 2 Φ 1 Φ 3 ) ,
Φ 1 Φ 2 = i σ 1 i Δ z 1 i + σ 2 i Δ z 2 i + 1 r i A Δ i 3 j i ,
s 2 Ψ = k 0 2 ϵ Ψ ,
s = [ s x 1 0 0 0 s y 1 0 0 0 s z 1 ] ,

Metrics