Abstract

Microcavities with subwavelength features, such as oxide apertures and etched-mesa edges, suffer wide-angle scattering that cannot be captured by the paraxial propagation limit; hence the scattering cannot be fully accounted for by index guiding or by lenslike phase shifts. We present a systematic treatment by using the Born approximation in the vector Maxwell equations. We then introduce the scattering losses in the cavity round-trip matrix, by using a Gauss–Laguerre representation of the cavity modes. Optimization of the round-trip coefficient including confinement, diffraction, and scattering losses yields the mode waist in laterally open vertical cavity surface emitting laser (VCSEL) cavities. A simple equation relating the current aperture to mode spot size is obtained. The analytic results are applied to etched-mesa and oxide-confined VCSEL designs. Predictions for the mode waist and threshold current are comparable with experimental results in oxide-confined VCSELs.

© 2001 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 VCSELs,” Appl. Phys. Lett. 65, 97–99 (1994).
  2. K. D. Choquette, R. P. Schneider, K. L. Lear, and K. M. Geib, “Low threshold VCSELs fabricated by selective oxidization,” Electron. Lett. 30, 2043–2044 (1994).
  3. Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold index-guided InGaAs/GaAlAs VCSELs with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).
  4. G. M. Yang, M. H. MacDougal, and P. D. Dapkus, “Ultralow threshold current VCSELs obtained with selective oxidization,” Electron. Lett. 31, 886–887 (1995).
  5. B. J. Thibeault, K. Bertilsson, E. R. Hegblom, E. Strzelecka, P. D. Floyd, R. Naone, and L. A. Coldren, “High-speed characteristics of low optical loss oxide-apertured VCSELs,” IEEE Photon. Technol. Lett. 9, 11–13 (1997).
  6. H. J. Unold, S. W. Mahmoud, F. Eberhard, R. Jaeger, M. Kicherer, F. Mederer, M. C. Riedl, and K. J. Ebeling, “Large-area, single-mode selectively oxidized VCSELs: approaches and experimental,” in Vertical-Cavity Surface Emitting Lasers IV, K. D. Choquette and C. Lei, eds. Proc. SPIE 3946, 207–217 (2000).
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  13. B. Demeulenaere, P. Bienstman, B. Dhoedt, and R. G. Baets, “Detailed study of AlAs-oxidized apertures in VCSEL cavities for optimized modal performance,” IEEE J. Quantum Electron. 35, 358–367 (1999).
  14. P. Bienstman, R. G. Baets, J. Vukusic, A. Larsson, M. Noble, M. Brunner, K. Gulden, P. Debernardi, H. Wenzel, and B. Klein, “Comparison of optical VCSEL models of the simulation of position dependent effects of thin oxide apertures,” Rep. COST268 (1999).
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  21. S. P. Hegarty, G. Huyet, P. Porta, J. G. McInerney, K. D. Choquette, K. M. Geib, and H. Q. Hou, “Transverse mode structure and pattern formation in oxide-confined VCSELs,” J. Opt. Soc. Am. B 16, 2060–2071 (2000).
  22. J. D. Lambkin, T. Calvert, B. Corbett, J. Woodhead, S. M. Pinches, A. Onischenko, T. E. Sale, J. Hosea, P. Van Daele, K. Van de Putte, A. Van Hove, A. Valster, J. G. McInerney, and P. Porta, “Development of a red VCSEL-to-plastic fiber module for use in parallel optical links,” (in Vertical-Cavity Surface-Emitting Lasers IV, K. D. Choquette and C. Lei eds.) Proc. SPIE 3946, 95–105 (2000).

2001 (1)

2000 (3)

J. D. Lambkin, T. Calvert, B. Corbett, J. Woodhead, S. M. Pinches, A. Onischenko, T. E. Sale, J. Hosea, P. Van Daele, K. Van de Putte, A. Van Hove, A. Valster, J. G. McInerney, and P. Porta, “Development of a red VCSEL-to-plastic fiber module for use in parallel optical links,” (in Vertical-Cavity Surface-Emitting Lasers IV, K. D. Choquette and C. Lei eds.) Proc. SPIE 3946, 95–105 (2000).

S. P. Hegarty, G. Huyet, P. Porta, J. G. McInerney, K. D. Choquette, K. M. Geib, and H. Q. Hou, “Transverse mode structure and pattern formation in oxide-confined VCSELs,” J. Opt. Soc. Am. B 16, 2060–2071 (2000).

H. J. Unold, S. W. Mahmoud, F. Eberhard, R. Jaeger, M. Kicherer, F. Mederer, M. C. Riedl, and K. J. Ebeling, “Large-area, single-mode selectively oxidized VCSELs: approaches and experimental,” in Vertical-Cavity Surface Emitting Lasers IV, K. D. Choquette and C. Lei, eds. Proc. SPIE 3946, 207–217 (2000).

1999 (2)

A. E. Bond, P. D. Dapkus, and J. D. O’Brien, “Design of low-loss single-mode VCSELs,” IEEE J. Sel. Top. in Quantum Electron. 5, 574–581 (1999).

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

1998 (1)

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 VCSELs,” Appl. Phys. Lett. 73, 726–729 (1998).

1997 (4)

B. J. Thibeault, K. Bertilsson, E. R. Hegblom, E. Strzelecka, P. D. Floyd, R. Naone, and L. A. Coldren, “High-speed characteristics of low optical loss oxide-apertured VCSELs,” IEEE Photon. Technol. Lett. 9, 11–13 (1997).

E. R. Hegblom, D. I. Babic, B. J. Thibeault, and L. A. Coldren, “Scattering losses from dielectric apertures in VCSELs,” IEEE J. Sel. Top. Quantum Electron 3, 379–389 (1997).

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

K. D. Choquette, W. W. Chow, G. R. Hadley, H. Q. Chow, and K. M. Gab, “Scalability of small-aperture selectively oxidized VCSELs,” Appl. Phys. Lett. 70, 823–825 (1997).

1996 (1)

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. Corzine, “Comprehensive numerical modeling of VCSELs,” IEEE J. Quantum Electron. 32, 607–616 (1996).

1995 (2)

Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold index-guided InGaAs/GaAlAs VCSELs with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).

G. M. Yang, M. H. MacDougal, and P. D. Dapkus, “Ultralow threshold current VCSELs obtained with selective oxidization,” Electron. Lett. 31, 886–887 (1995).

1994 (2)

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

K. D. Choquette, R. P. Schneider, K. L. Lear, and K. M. Geib, “Low threshold VCSELs fabricated by selective oxidization,” Electron. Lett. 30, 2043–2044 (1994).

1992 (1)

D. I. Babic and S. W. Corzine, “Analytic expressions for reflection delay, penetration depth and absorptance of quarter-wave dielectric mirrors,” IEEE J. Quantum Electron. 28, 514–524 (1992).

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 VCSELs,” Appl. Phys. Lett. 73, 726–729 (1998).

E. R. Hegblom, D. I. Babic, B. J. Thibeault, and L. A. Coldren, “Scattering losses from dielectric apertures in VCSELs,” IEEE J. Sel. Top. Quantum Electron 3, 379–389 (1997).

D. I. Babic and S. W. Corzine, “Analytic expressions for reflection delay, penetration depth and absorptance of quarter-wave dielectric mirrors,” IEEE J. Quantum Electron. 28, 514–524 (1992).

Baets, R. G.

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

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 VCSELs,” Appl. Phys. Lett. 73, 726–729 (1998).

Bertilsson, K.

B. J. Thibeault, K. Bertilsson, E. R. Hegblom, E. Strzelecka, P. D. Floyd, R. Naone, and L. A. Coldren, “High-speed characteristics of low optical loss oxide-apertured VCSELs,” IEEE Photon. Technol. Lett. 9, 11–13 (1997).

Bienstman, P.

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

Binder, R.

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

Bond, A. E.

A. E. Bond, P. D. Dapkus, and J. D. O’Brien, “Design of low-loss single-mode VCSELs,” IEEE J. Sel. Top. in Quantum Electron. 5, 574–581 (1999).

Burak, D.

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

Calvert, T.

J. D. Lambkin, T. Calvert, B. Corbett, J. Woodhead, S. M. Pinches, A. Onischenko, T. E. Sale, J. Hosea, P. Van Daele, K. Van de Putte, A. Van Hove, A. Valster, J. G. McInerney, and P. Porta, “Development of a red VCSEL-to-plastic fiber module for use in parallel optical links,” (in Vertical-Cavity Surface-Emitting Lasers IV, K. D. Choquette and C. Lei eds.) Proc. SPIE 3946, 95–105 (2000).

Choquette, K. D.

S. P. Hegarty, G. Huyet, P. Porta, J. G. McInerney, K. D. Choquette, K. M. Geib, and H. Q. Hou, “Transverse mode structure and pattern formation in oxide-confined VCSELs,” J. Opt. Soc. Am. B 16, 2060–2071 (2000).

K. D. Choquette, W. W. Chow, G. R. Hadley, H. Q. Chow, and K. M. Gab, “Scalability of small-aperture selectively oxidized VCSELs,” Appl. Phys. Lett. 70, 823–825 (1997).

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. Corzine, “Comprehensive numerical modeling of VCSELs,” IEEE J. Quantum Electron. 32, 607–616 (1996).

K. D. Choquette, R. P. Schneider, K. L. Lear, and K. M. Geib, “Low threshold VCSELs fabricated by selective oxidization,” Electron. Lett. 30, 2043–2044 (1994).

Chow, H. Q.

K. D. Choquette, W. W. Chow, G. R. Hadley, H. Q. Chow, and K. M. Gab, “Scalability of small-aperture selectively oxidized VCSELs,” Appl. Phys. Lett. 70, 823–825 (1997).

Chow, W. W.

K. D. Choquette, W. W. Chow, G. R. Hadley, H. Q. Chow, and K. M. Gab, “Scalability of small-aperture selectively oxidized VCSELs,” Appl. Phys. Lett. 70, 823–825 (1997).

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 VCSELs,” Appl. Phys. Lett. 73, 726–729 (1998).

Coldren, L. A.

E. R. Hegblom, D. I. Babic, B. J. Thibeault, and L. A. Coldren, “Scattering losses from dielectric apertures in VCSELs,” IEEE J. Sel. Top. Quantum Electron 3, 379–389 (1997).

B. J. Thibeault, K. Bertilsson, E. R. Hegblom, E. Strzelecka, P. D. Floyd, R. Naone, and L. A. Coldren, “High-speed characteristics of low optical loss oxide-apertured VCSELs,” IEEE Photon. Technol. Lett. 9, 11–13 (1997).

Corbett, B.

J. D. Lambkin, T. Calvert, B. Corbett, J. Woodhead, S. M. Pinches, A. Onischenko, T. E. Sale, J. Hosea, P. Van Daele, K. Van de Putte, A. Van Hove, A. Valster, J. G. McInerney, and P. Porta, “Development of a red VCSEL-to-plastic fiber module for use in parallel optical links,” (in Vertical-Cavity Surface-Emitting Lasers IV, K. D. Choquette and C. Lei eds.) Proc. SPIE 3946, 95–105 (2000).

Corzine, S.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. Corzine, “Comprehensive numerical modeling of VCSELs,” IEEE J. Quantum Electron. 32, 607–616 (1996).

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 VCSELs,” Appl. Phys. Lett. 73, 726–729 (1998).

D. I. Babic and S. W. Corzine, “Analytic expressions for reflection delay, penetration depth and absorptance of quarter-wave dielectric mirrors,” IEEE J. Quantum Electron. 28, 514–524 (1992).

Dapkus, P. D.

A. E. Bond, P. D. Dapkus, and J. D. O’Brien, “Design of low-loss single-mode VCSELs,” IEEE J. Sel. Top. in Quantum Electron. 5, 574–581 (1999).

G. M. Yang, M. H. MacDougal, and P. D. Dapkus, “Ultralow threshold current VCSELs obtained with selective oxidization,” Electron. Lett. 31, 886–887 (1995).

Demeulenaere, B.

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

Deppe, D. G.

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

Dhoedt, B.

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

Dialetis, D.

Ebeling, K. J.

H. J. Unold, S. W. Mahmoud, F. Eberhard, R. Jaeger, M. Kicherer, F. Mederer, M. C. Riedl, and K. J. Ebeling, “Large-area, single-mode selectively oxidized VCSELs: approaches and experimental,” in Vertical-Cavity Surface Emitting Lasers IV, K. D. Choquette and C. Lei, eds. Proc. SPIE 3946, 207–217 (2000).

Eberhard, F.

H. J. Unold, S. W. Mahmoud, F. Eberhard, R. Jaeger, M. Kicherer, F. Mederer, M. C. Riedl, and K. J. Ebeling, “Large-area, single-mode selectively oxidized VCSELs: approaches and experimental,” in Vertical-Cavity Surface Emitting Lasers IV, K. D. Choquette and C. Lei, eds. Proc. SPIE 3946, 207–217 (2000).

Floyd, P. D.

B. J. Thibeault, K. Bertilsson, E. R. Hegblom, E. Strzelecka, P. D. Floyd, R. Naone, and L. A. Coldren, “High-speed characteristics of low optical loss oxide-apertured VCSELs,” IEEE Photon. Technol. Lett. 9, 11–13 (1997).

Gab, K. M.

K. D. Choquette, W. W. Chow, G. R. Hadley, H. Q. Chow, and K. M. Gab, “Scalability of small-aperture selectively oxidized VCSELs,” Appl. Phys. Lett. 70, 823–825 (1997).

Geib, K. M.

S. P. Hegarty, G. Huyet, P. Porta, J. G. McInerney, K. D. Choquette, K. M. Geib, and H. Q. Hou, “Transverse mode structure and pattern formation in oxide-confined VCSELs,” J. Opt. Soc. Am. B 16, 2060–2071 (2000).

K. D. Choquette, R. P. Schneider, K. L. Lear, and K. M. Geib, “Low threshold VCSELs fabricated by selective oxidization,” Electron. Lett. 30, 2043–2044 (1994).

Hadley, G. R.

K. D. Choquette, W. W. Chow, G. R. Hadley, H. Q. Chow, and K. M. Gab, “Scalability of small-aperture selectively oxidized VCSELs,” Appl. Phys. Lett. 70, 823–825 (1997).

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. Corzine, “Comprehensive numerical modeling of VCSELs,” IEEE J. Quantum Electron. 32, 607–616 (1996).

Hatori, N.

Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold index-guided InGaAs/GaAlAs VCSELs with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).

Hayashi, Y.

Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold index-guided InGaAs/GaAlAs VCSELs with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).

Hegarty, S. P.

Hegblom, E. R.

B. J. Thibeault, K. Bertilsson, E. R. Hegblom, E. Strzelecka, P. D. Floyd, R. Naone, and L. A. Coldren, “High-speed characteristics of low optical loss oxide-apertured VCSELs,” IEEE Photon. Technol. Lett. 9, 11–13 (1997).

E. R. Hegblom, D. I. Babic, B. J. Thibeault, and L. A. Coldren, “Scattering losses from dielectric apertures in VCSELs,” IEEE J. Sel. Top. Quantum Electron 3, 379–389 (1997).

Hosea, J.

J. D. Lambkin, T. Calvert, B. Corbett, J. Woodhead, S. M. Pinches, A. Onischenko, T. E. Sale, J. Hosea, P. Van Daele, K. Van de Putte, A. Van Hove, A. Valster, J. G. McInerney, and P. Porta, “Development of a red VCSEL-to-plastic fiber module for use in parallel optical links,” (in Vertical-Cavity Surface-Emitting Lasers IV, K. D. Choquette and C. Lei eds.) Proc. SPIE 3946, 95–105 (2000).

Hou, H. Q.

Huffaker, D. L.

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

Huyet, G.

Iga, K.

Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold index-guided InGaAs/GaAlAs VCSELs with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).

Inman, J-M.

Jaeger, R.

H. J. Unold, S. W. Mahmoud, F. Eberhard, R. Jaeger, M. Kicherer, F. Mederer, M. C. Riedl, and K. J. Ebeling, “Large-area, single-mode selectively oxidized VCSELs: approaches and experimental,” in Vertical-Cavity Surface Emitting Lasers IV, K. D. Choquette and C. Lei, eds. Proc. SPIE 3946, 207–217 (2000).

Kicherer, M.

H. J. Unold, S. W. Mahmoud, F. Eberhard, R. Jaeger, M. Kicherer, F. Mederer, M. C. Riedl, and K. J. Ebeling, “Large-area, single-mode selectively oxidized VCSELs: approaches and experimental,” in Vertical-Cavity Surface Emitting Lasers IV, K. D. Choquette and C. Lei, eds. Proc. SPIE 3946, 207–217 (2000).

Koyama, F.

Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold index-guided InGaAs/GaAlAs VCSELs with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).

Kumar, K.

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

Lambkin, J. D.

J. D. Lambkin, T. Calvert, B. Corbett, J. Woodhead, S. M. Pinches, A. Onischenko, T. E. Sale, J. Hosea, P. Van Daele, K. Van de Putte, A. Van Hove, A. Valster, J. G. McInerney, and P. Porta, “Development of a red VCSEL-to-plastic fiber module for use in parallel optical links,” (in Vertical-Cavity Surface-Emitting Lasers IV, K. D. Choquette and C. Lei eds.) Proc. SPIE 3946, 95–105 (2000).

Lear, K. L.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. Corzine, “Comprehensive numerical modeling of VCSELs,” IEEE J. Quantum Electron. 32, 607–616 (1996).

K. D. Choquette, R. P. Schneider, K. L. Lear, and K. M. Geib, “Low threshold VCSELs fabricated by selective oxidization,” Electron. Lett. 30, 2043–2044 (1994).

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 VCSELs,” Appl. Phys. Lett. 73, 726–729 (1998).

MacDougal, M. H.

G. M. Yang, M. H. MacDougal, and P. D. Dapkus, “Ultralow threshold current VCSELs obtained with selective oxidization,” Electron. Lett. 31, 886–887 (1995).

Mahmoud, S. W.

H. J. Unold, S. W. Mahmoud, F. Eberhard, R. Jaeger, M. Kicherer, F. Mederer, M. C. Riedl, and K. J. Ebeling, “Large-area, single-mode selectively oxidized VCSELs: approaches and experimental,” in Vertical-Cavity Surface Emitting Lasers IV, K. D. Choquette and C. Lei, eds. Proc. SPIE 3946, 207–217 (2000).

Matsutani, A.

Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold index-guided InGaAs/GaAlAs VCSELs with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).

McInerney, J. G.

S. P. Hegarty, G. Huyet, P. Porta, J. G. McInerney, K. D. Choquette, K. M. Geib, and H. Q. Hou, “Transverse mode structure and pattern formation in oxide-confined VCSELs,” J. Opt. Soc. Am. B 16, 2060–2071 (2000).

J. D. Lambkin, T. Calvert, B. Corbett, J. Woodhead, S. M. Pinches, A. Onischenko, T. E. Sale, J. Hosea, P. Van Daele, K. Van de Putte, A. Van Hove, A. Valster, J. G. McInerney, and P. Porta, “Development of a red VCSEL-to-plastic fiber module for use in parallel optical links,” (in Vertical-Cavity Surface-Emitting Lasers IV, K. D. Choquette and C. Lei eds.) Proc. SPIE 3946, 95–105 (2000).

Mederer, F.

H. J. Unold, S. W. Mahmoud, F. Eberhard, R. Jaeger, M. Kicherer, F. Mederer, M. C. Riedl, and K. J. Ebeling, “Large-area, single-mode selectively oxidized VCSELs: approaches and experimental,” in Vertical-Cavity Surface Emitting Lasers IV, K. D. Choquette and C. Lei, eds. Proc. SPIE 3946, 207–217 (2000).

Mukaihara, T.

Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold index-guided InGaAs/GaAlAs VCSELs with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).

Naone, R.

B. J. Thibeault, K. Bertilsson, E. R. Hegblom, E. Strzelecka, P. D. Floyd, R. Naone, and L. A. Coldren, “High-speed characteristics of low optical loss oxide-apertured VCSELs,” IEEE Photon. Technol. Lett. 9, 11–13 (1997).

O’Brien, J. D.

A. E. Bond, P. D. Dapkus, and J. D. O’Brien, “Design of low-loss single-mode VCSELs,” IEEE J. Sel. Top. in Quantum Electron. 5, 574–581 (1999).

Ohnoki, N.

Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold index-guided InGaAs/GaAlAs VCSELs with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).

Onischenko, A.

J. D. Lambkin, T. Calvert, B. Corbett, J. Woodhead, S. M. Pinches, A. Onischenko, T. E. Sale, J. Hosea, P. Van Daele, K. Van de Putte, A. Van Hove, A. Valster, J. G. McInerney, and P. Porta, “Development of a red VCSEL-to-plastic fiber module for use in parallel optical links,” (in Vertical-Cavity Surface-Emitting Lasers IV, K. D. Choquette and C. Lei eds.) Proc. SPIE 3946, 95–105 (2000).

Phillips, A.

Pinches, S. M.

J. D. Lambkin, T. Calvert, B. Corbett, J. Woodhead, S. M. Pinches, A. Onischenko, T. E. Sale, J. Hosea, P. Van Daele, K. Van de Putte, A. Van Hove, A. Valster, J. G. McInerney, and P. Porta, “Development of a red VCSEL-to-plastic fiber module for use in parallel optical links,” (in Vertical-Cavity Surface-Emitting Lasers IV, K. D. Choquette and C. Lei eds.) Proc. SPIE 3946, 95–105 (2000).

Porta, P.

J. D. Lambkin, T. Calvert, B. Corbett, J. Woodhead, S. M. Pinches, A. Onischenko, T. E. Sale, J. Hosea, P. Van Daele, K. Van de Putte, A. Van Hove, A. Valster, J. G. McInerney, and P. Porta, “Development of a red VCSEL-to-plastic fiber module for use in parallel optical links,” (in Vertical-Cavity Surface-Emitting Lasers IV, K. D. Choquette and C. Lei eds.) Proc. SPIE 3946, 95–105 (2000).

S. P. Hegarty, G. Huyet, P. Porta, J. G. McInerney, K. D. Choquette, K. M. Geib, and H. Q. Hou, “Transverse mode structure and pattern formation in oxide-confined VCSELs,” J. Opt. Soc. Am. B 16, 2060–2071 (2000).

Riedl, M. C.

H. J. Unold, S. W. Mahmoud, F. Eberhard, R. Jaeger, M. Kicherer, F. Mederer, M. C. Riedl, and K. J. Ebeling, “Large-area, single-mode selectively oxidized VCSELs: approaches and experimental,” in Vertical-Cavity Surface Emitting Lasers IV, K. D. Choquette and C. Lei, eds. Proc. SPIE 3946, 207–217 (2000).

Riyopoulos, S.

Rogers, T. J.

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

Sale, T. E.

J. D. Lambkin, T. Calvert, B. Corbett, J. Woodhead, S. M. Pinches, A. Onischenko, T. E. Sale, J. Hosea, P. Van Daele, K. Van de Putte, A. Van Hove, A. Valster, J. G. McInerney, and P. Porta, “Development of a red VCSEL-to-plastic fiber module for use in parallel optical links,” (in Vertical-Cavity Surface-Emitting Lasers IV, K. D. Choquette and C. Lei eds.) Proc. SPIE 3946, 95–105 (2000).

Schneider, R. P.

K. D. Choquette, R. P. Schneider, K. L. Lear, and K. M. Geib, “Low threshold VCSELs fabricated by selective oxidization,” Electron. Lett. 30, 2043–2044 (1994).

Scott, J. W.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. Corzine, “Comprehensive numerical modeling of VCSELs,” IEEE J. Quantum Electron. 32, 607–616 (1996).

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 VCSELs,” Appl. Phys. Lett. 73, 726–729 (1998).

Strzelecka, E.

B. J. Thibeault, K. Bertilsson, E. R. Hegblom, E. Strzelecka, P. D. Floyd, R. Naone, and L. A. Coldren, “High-speed characteristics of low optical loss oxide-apertured VCSELs,” IEEE Photon. Technol. Lett. 9, 11–13 (1997).

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 VCSELs,” Appl. Phys. Lett. 73, 726–729 (1998).

Thibeault, B. J.

E. R. Hegblom, D. I. Babic, B. J. Thibeault, and L. A. Coldren, “Scattering losses from dielectric apertures in VCSELs,” IEEE J. Sel. Top. Quantum Electron 3, 379–389 (1997).

B. J. Thibeault, K. Bertilsson, E. R. Hegblom, E. Strzelecka, P. D. Floyd, R. Naone, and L. A. Coldren, “High-speed characteristics of low optical loss oxide-apertured VCSELs,” IEEE Photon. Technol. Lett. 9, 11–13 (1997).

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 VCSELs,” Appl. Phys. Lett. 73, 726–729 (1998).

Unold, H. J.

H. J. Unold, S. W. Mahmoud, F. Eberhard, R. Jaeger, M. Kicherer, F. Mederer, M. C. Riedl, and K. J. Ebeling, “Large-area, single-mode selectively oxidized VCSELs: approaches and experimental,” in Vertical-Cavity Surface Emitting Lasers IV, K. D. Choquette and C. Lei, eds. Proc. SPIE 3946, 207–217 (2000).

Valster, A.

J. D. Lambkin, T. Calvert, B. Corbett, J. Woodhead, S. M. Pinches, A. Onischenko, T. E. Sale, J. Hosea, P. Van Daele, K. Van de Putte, A. Van Hove, A. Valster, J. G. McInerney, and P. Porta, “Development of a red VCSEL-to-plastic fiber module for use in parallel optical links,” (in Vertical-Cavity Surface-Emitting Lasers IV, K. D. Choquette and C. Lei eds.) Proc. SPIE 3946, 95–105 (2000).

Van Daele, P.

J. D. Lambkin, T. Calvert, B. Corbett, J. Woodhead, S. M. Pinches, A. Onischenko, T. E. Sale, J. Hosea, P. Van Daele, K. Van de Putte, A. Van Hove, A. Valster, J. G. McInerney, and P. Porta, “Development of a red VCSEL-to-plastic fiber module for use in parallel optical links,” (in Vertical-Cavity Surface-Emitting Lasers IV, K. D. Choquette and C. Lei eds.) Proc. SPIE 3946, 95–105 (2000).

Van de Putte, K.

J. D. Lambkin, T. Calvert, B. Corbett, J. Woodhead, S. M. Pinches, A. Onischenko, T. E. Sale, J. Hosea, P. Van Daele, K. Van de Putte, A. Van Hove, A. Valster, J. G. McInerney, and P. Porta, “Development of a red VCSEL-to-plastic fiber module for use in parallel optical links,” (in Vertical-Cavity Surface-Emitting Lasers IV, K. D. Choquette and C. Lei eds.) Proc. SPIE 3946, 95–105 (2000).

Van Hove, A.

J. D. Lambkin, T. Calvert, B. Corbett, J. Woodhead, S. M. Pinches, A. Onischenko, T. E. Sale, J. Hosea, P. Van Daele, K. Van de Putte, A. Van Hove, A. Valster, J. G. McInerney, and P. Porta, “Development of a red VCSEL-to-plastic fiber module for use in parallel optical links,” (in Vertical-Cavity Surface-Emitting Lasers IV, K. D. Choquette and C. Lei eds.) Proc. SPIE 3946, 95–105 (2000).

Warren, M. E.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. Corzine, “Comprehensive numerical modeling of VCSELs,” IEEE J. Quantum Electron. 32, 607–616 (1996).

Woodhead, J.

J. D. Lambkin, T. Calvert, B. Corbett, J. Woodhead, S. M. Pinches, A. Onischenko, T. E. Sale, J. Hosea, P. Van Daele, K. Van de Putte, A. Van Hove, A. Valster, J. G. McInerney, and P. Porta, “Development of a red VCSEL-to-plastic fiber module for use in parallel optical links,” (in Vertical-Cavity Surface-Emitting Lasers IV, K. D. Choquette and C. Lei eds.) Proc. SPIE 3946, 95–105 (2000).

Yang, G. M.

G. M. Yang, M. H. MacDougal, and P. D. Dapkus, “Ultralow threshold current VCSELs obtained with selective oxidization,” Electron. Lett. 31, 886–887 (1995).

Appl. Phys. Lett. (3)

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

K. D. Choquette, W. W. Chow, G. R. Hadley, H. Q. Chow, and K. M. Gab, “Scalability of small-aperture selectively oxidized VCSELs,” Appl. Phys. Lett. 70, 823–825 (1997).

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 VCSELs,” Appl. Phys. Lett. 73, 726–729 (1998).

Electron. Lett. (3)

K. D. Choquette, R. P. Schneider, K. L. Lear, and K. M. Geib, “Low threshold VCSELs fabricated by selective oxidization,” Electron. Lett. 30, 2043–2044 (1994).

Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold index-guided InGaAs/GaAlAs VCSELs with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).

G. M. Yang, M. H. MacDougal, and P. D. Dapkus, “Ultralow threshold current VCSELs obtained with selective oxidization,” Electron. Lett. 31, 886–887 (1995).

IEEE J. Quantum Electron. (4)

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. Corzine, “Comprehensive numerical modeling of VCSELs,” IEEE J. Quantum Electron. 32, 607–616 (1996).

D. I. Babic and S. W. Corzine, “Analytic expressions for reflection delay, penetration depth and absorptance of quarter-wave dielectric mirrors,” IEEE J. Quantum Electron. 28, 514–524 (1992).

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

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

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

A. E. Bond, P. D. Dapkus, and J. D. O’Brien, “Design of low-loss single-mode VCSELs,” IEEE J. Sel. Top. in Quantum Electron. 5, 574–581 (1999).

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

E. R. Hegblom, D. I. Babic, B. J. Thibeault, and L. A. Coldren, “Scattering losses from dielectric apertures in VCSELs,” IEEE J. Sel. Top. Quantum Electron 3, 379–389 (1997).

IEEE Photon. Technol. Lett. (1)

B. J. Thibeault, K. Bertilsson, E. R. Hegblom, E. Strzelecka, P. D. Floyd, R. Naone, and L. A. Coldren, “High-speed characteristics of low optical loss oxide-apertured VCSELs,” IEEE Photon. Technol. Lett. 9, 11–13 (1997).

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

Proc. SPIE (2)

H. J. Unold, S. W. Mahmoud, F. Eberhard, R. Jaeger, M. Kicherer, F. Mederer, M. C. Riedl, and K. J. Ebeling, “Large-area, single-mode selectively oxidized VCSELs: approaches and experimental,” in Vertical-Cavity Surface Emitting Lasers IV, K. D. Choquette and C. Lei, eds. Proc. SPIE 3946, 207–217 (2000).

J. D. Lambkin, T. Calvert, B. Corbett, J. Woodhead, S. M. Pinches, A. Onischenko, T. E. Sale, J. Hosea, P. Van Daele, K. Van de Putte, A. Van Hove, A. Valster, J. G. McInerney, and P. Porta, “Development of a red VCSEL-to-plastic fiber module for use in parallel optical links,” (in Vertical-Cavity Surface-Emitting Lasers IV, K. D. Choquette and C. Lei eds.) Proc. SPIE 3946, 95–105 (2000).

Other (5)

P. Bienstman, R. G. Baets, J. Vukusic, A. Larsson, M. Noble, M. Brunner, K. Gulden, P. Debernardi, H. Wenzel, and B. Klein, “Comparison of optical VCSEL models of the simulation of position dependent effects of thin oxide apertures,” Rep. COST268 (1999).

J. D. Jackson Classical Electrodynamics 2nd. ed. (Wiley, New York, 1975), pp. 391–397.

S. Riyopoulos, D. Dialetis, J. Liu, and B. Riely, “Generic representation of active cavity VCSEL eigenmodes by optimized waist gain guided Gauss–Laguerre modes,” IEEE J. Sel. Top. Quantum Electron. (to be published).

D. I. Babic, “Double-fused long wavelength VCSELs,” Ph.D. dissertation (University of California, Santa Barbara, Calif. 1995), pp. 67–212.

See, for example, C. C. Davis, Lasers and Electro-optics (Cambridge, U. Press, Cambridge, UK, 1996), pp. 416–423.

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