Abstract

The dynamics of transverse modes of vertical-cavity surface-emitting lasers were simulated by use of a model that incorporates microscopically computed gain and refractive index with many-body effects. The model equations were solved by finite-difference methods in two-dimensional space and time domains without any a priori assumptions of symmetry of solutions or types and number of modes. Simulation was carried out for devices with and without index guiding at various pumping levels. We show that index-guided vertical-cavity surface-emitting lasers involve more transverse modes than purely gain-guided devices at the same pumping level. Both time-resolved and time-averaged near-field patterns over several time scales are investigated. Complicated spatial and temporal dynamic behaviors occur at higher pumping levels that include azimuthal rotating waves and intensity oscillations owing to dynamic competition between modes of the same order and those of different orders.

© 1999 Optical Society of America

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  1. For a survey of recent progress in VCSEL’s, see C. Chang-Hasnain, ed., Advances in Vertical Cavity Surface Emitting Lasers, Vol. 15 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997).
  2. W. W. Chow, K. D. Choquette, M. H. Crawford, K. L. Lear, and G. R. Hadley, “Design, fabrication, and performance of infrared and visible vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 1810–1824 (1997).
    [CrossRef]
  3. C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
    [CrossRef]
  4. M. Orenstein, Y. Satuby, U. Ben-Ami, and J. P. Harbison, “Transverse modes and lasing characteristics of selectively grown vertical cavity semiconductor lasers,” Appl. Phys. Lett. 69, 1840–1842 (1996).
    [CrossRef]
  5. Y. Satuby and M. Orenstein, “Limits of the modulation response of a single-mode proton implanted VCSEL,” IEEE Photon. Technol. Lett. 10, 760–762 (1998).
    [CrossRef]
  6. Y. Satuby and M. Orenstein, “Small signal modulation of multitransverse modes vertical-cavity surface-emitting semiconductor lasers,” IEEE Photon. Technol. Lett. 10, 757–759 (1998).
    [CrossRef]
  7. R. A. Morgan, G. D. Guth, M. W. Focht, M. T. Asom, K. Kojima, L. E. Rogers, and S. E. Callis, “Transverse mode control of vertical-cavity top-surface-emitting lasers,” IEEE Photon. Technol. Lett. 4, 374–377 (1993).
    [CrossRef]
  8. K. Tai, Y. Lai, K. F. Huang, T. C. Huang, T. D. Lee, and C. C. Wu, “Transverse mode emission characteristics of gain-guided surface-emitting lasers,” Appl. Phys. Lett. 63, 2624–2626 (1993).
    [CrossRef]
  9. G. C. Wilson, D. M. Kuchta, J. D. Walker, and J. S. Smith, “Spatial hole burning and self-focusing in vertical-cavity surface-emitting laser diodes,” Appl. Phys. Lett. 64, 542–544 (1994).
    [CrossRef]
  10. K. H. Hahn, M. R. Tan, Y. M. Houng, and S. Y. Wang, “Large area multitransverse-mode VCSELs for modal noise-reduction in multimode fibre systems,” Electron. Lett. 29, 1482–1483 (1993).
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    [CrossRef]
  13. H. Li, T. Lucas, J. G. McInerney, and R. Morgan, “Transverse modes and patterns of electrically pumped vertical-cavity surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1619–1636 (1994).
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  14. F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos Solitons Fractals 4, 1575–1596 (1994).
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  15. J. Heinrich, E. Zeeb, and K. J. Ebeling, “Transverse mode under external feedback and fiber coupling efficiencies of VCSEL’s,” IEEE Photon. Technol. Lett. 10, 1365–1367 (1998).
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  16. I. Hoersch, R. Kusche, O. Marti, B. Weidl, and K. J. Ebeling, “Spectrally resolved near-field mode imaging of vertical-cavity semiconductor lasers,” J. Appl. Phys. 79, 3831–3834 (1996).
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  17. J. A. DeAro, K. D. Weston, R. W. Herrick, P. M. Petroff, and S. K. Buratto, “Near-field scanning optical microscopy of cleaved vertical-cavity surface-emitting lasers,” Semicond. Sci. Technol. 13, 1364–1367 (1998).
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  19. T. Milster, W. Jiang, E. Walker, D. Burak, P. Claisse, P. Kelly, and R. Binder, “A single-mode high-power vertical cavity surface emitting laser,” Appl. Phys. Lett. 72, 3425–3427 (1998).
    [CrossRef]
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    [CrossRef]
  25. A. Valle, “High-frequency beam steering induced by switching of high-order transverse modes in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 1607–1609 (1998).
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  26. W. Nakwaski and R. P. Sarzala, “Transverse modes in gain-guided vertical-cavity surface-emitting lasers,” Opt. Commun. 148, 63–69 (1998).
    [CrossRef]
  27. M. 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]
  28. M. Noble, J. Shin, K. D. Choquette, J. P. Loehr, J. A. Lott, and Y. Lee, “Calculation and measurements of resonant-mode blueshifts in oxide-apertured VCSELs,” IEEE Photon. Technol. Lett. 10, 475–477 (1998).
    [CrossRef]
  29. D. Burak and R. Binder, “Electromagnetic characterization of vertical-cavity surface-emitting lasers based on a vectorial eigenmode calculation,” Appl. Phys. Lett. 72, 891–893 (1998).
    [CrossRef]
  30. D. Burak and R. Binder, “Cold-cavity vectorial eigenmodes of VCSELs,” IEEE J. Quantum Electron. 33, 1205–1215 (1997).
    [CrossRef]
  31. X. M. Gong, A. K. Chan, and H. F. Taylor, “Lateral mode discrimination in surface emitting DBR lasers with cylindrical symmetry,” IEEE J. Quantum Electron. 30, 1212–1218 (1994).
    [CrossRef]
  32. B. Demeulenaere, P. Bienstman, B. Dhoedt, and R. G. Baets, “Detailed study of AlAs-oxidized apertures in VCSEL cavities for optimized model performance,” IEEE J. Quantum Electron. 35, 358–367 (1999).
    [CrossRef]
  33. 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]
  34. H. Wenzel and H.-J. Wünsche, “The effective frequency method in the analysis of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 1156–1162 (1997).
    [CrossRef]
  35. D. Burak, S. A. Kemme, R. K. Kostuk, and R. Binder, “Spectral identification of transverse lasing modes of multiple index-guided vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 3501–3503 (1998).
    [CrossRef]
  36. 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]
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    [CrossRef]
  38. P. M. Goorjian and C. Z. Ning, “Transverse mode dynamics of VCSELs through space–time domain simulation,” in Physics and Simulation of Optoelectronic Devices VII, P. Blood, A. Ishibashi, and M. Osinski, eds., Proc. SPIE 3625, 395–403 (1999).
    [CrossRef]
  39. C. Z. Ning, S. Bischoff, S. W. Koch, G. K. Harkness, J. V. Moloney, and W. W. Chow, “Microscopic modeling of vertical-cavity surface-emitting lasers: many-body interaction, plasma heating, and transverse dynamics,” Opt. Eng. 37, 1175–1181 (1998).
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    [CrossRef]
  43. C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, “A first-principles fully space–time resolved model for a semiconductor laser,” Quantum Semiclassic. Opt. 9, 681–691 (1997).
    [CrossRef]
  44. J. V. Moloney, R. A. Indik, and C. Z. Ning, “Full space–time simulation of the high-brightness semiconductor lasers,” IEEE Photon. Technol. Lett. 9, 731–733 (1997).
    [CrossRef]
  45. J. V. Moloney, A. Egan, C. Z. Ning, and R. A. Indik, “Spontaneous spatiotemporal instabilities in current modulated master oscillator power amplifier lasers,” IEEE Photon. Technol. Lett. 10, 1229–1231 (1998).
    [CrossRef]
  46. A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic instabilities in master oscillator power amplifier semiconductor lasers,” IEEE J. Quantum Electron. 34, 166–170 (1998).
    [CrossRef]
  47. P. M. W. Skovgaard, J. G. McInerney, J. V. Moloney, R. A. Indik, and C. Z. Ning, “Enhanced stability of MFA-MOPA semiconductor lasers using a nonlinear, trumpet-shaped flare,” IEEE Photon. Technol. Lett. 9, 1220–1222 (1997).
    [CrossRef]
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  50. C. Z. Ning, R. A. Indik, and J. V. Moloney, “Self-consistent approach to thermal effects in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 12, 1993–2004 (1995).
    [CrossRef]
  51. S. Hughes, A. Knorr, S. W. Koch, R. Binder, R. Indik, and J. V. Moloney, “The influence of electron–hole-scattering on the gain spectra of highly excited semiconductors,” Solid State Commun. 100, 555–559 (1996).
    [CrossRef]
  52. A. Girndt, F. Jahnke, A. Knorr, S. W. Koch, and W. W. Chow, “Multi-band Bloch equations and gain spectra of highly excited II–VI semiconductor quantum wells,” Phys. Status Solidi B 202, 725–739 (1997).
    [CrossRef]
  53. W. W. Chow, A. Knorr, S. Hughes, A. Girndt, and S. W. Koch, “Carrier correlation effects in a quantum well semiconductor laser medium,” IEEE J. Sel. Top. Quantum Electron. 3, 136–141 (1997).
    [CrossRef]
  54. J. Yao, G. P. Agrawal, P. Gallion, and C. Bowden, “Semiconductor laser dynamics beyond the rate-equation approximation,” Opt. Commun. 119, 246–255 (1995).
    [CrossRef]
  55. W. Yuen, G. S. Li, and C. J. Chang-Hasnain, “Multiple-wavelength vertical-cavity surface-emitting laser arrays with a record wavelength span,” IEEE Photon. Technol. Lett. 8, 4–6 (1996).
    [CrossRef]
  56. A. Fiore, Y. A. Akulova, J. Ko, E. R. Hegblom, and L. A. Coldren, “Low-threshold multiple-wavelength vertical-cavity laser arrays obtained by postgrowth wet oxidation,” Electron. Lett. 34, 1857–1858 (1998).
    [CrossRef]
  57. R. Michalzik and K. J. Ebeling, “Generalized BV diagrams for higher order transverse modes in planar vertical-cavity laser diodes,” IEEE J. Quantum Electron. 31, 1371–1379 (1995).
    [CrossRef]

1999 (2)

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

P. M. Goorjian and C. Z. Ning, “Transverse mode dynamics of VCSELs through space–time domain simulation,” in Physics and Simulation of Optoelectronic Devices VII, P. Blood, A. Ishibashi, and M. Osinski, eds., Proc. SPIE 3625, 395–403 (1999).
[CrossRef]

1998 (20)

C. Z. Ning, S. Bischoff, S. W. Koch, G. K. Harkness, J. V. Moloney, and W. W. Chow, “Microscopic modeling of vertical-cavity surface-emitting lasers: many-body interaction, plasma heating, and transverse dynamics,” Opt. Eng. 37, 1175–1181 (1998).
[CrossRef]

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

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. Burak, S. A. Kemme, R. K. Kostuk, and R. Binder, “Spectral identification of transverse lasing modes of multiple index-guided vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 3501–3503 (1998).
[CrossRef]

A. Valle, “Selection and modulation of high-order transverse modes in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 34, 1924–1932 (1998).
[CrossRef]

A. Valle, “High-frequency beam steering induced by switching of high-order transverse modes in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 1607–1609 (1998).
[CrossRef]

W. Nakwaski and R. P. Sarzala, “Transverse modes in gain-guided vertical-cavity surface-emitting lasers,” Opt. Commun. 148, 63–69 (1998).
[CrossRef]

M. 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]

M. Noble, J. Shin, K. D. Choquette, J. P. Loehr, J. A. Lott, and Y. Lee, “Calculation and measurements of resonant-mode blueshifts in oxide-apertured VCSELs,” IEEE Photon. Technol. Lett. 10, 475–477 (1998).
[CrossRef]

D. Burak and R. Binder, “Electromagnetic characterization of vertical-cavity surface-emitting lasers based on a vectorial eigenmode calculation,” Appl. Phys. Lett. 72, 891–893 (1998).
[CrossRef]

Y. Satuby and M. Orenstein, “Limits of the modulation response of a single-mode proton implanted VCSEL,” IEEE Photon. Technol. Lett. 10, 760–762 (1998).
[CrossRef]

Y. Satuby and M. Orenstein, “Small signal modulation of multitransverse modes vertical-cavity surface-emitting semiconductor lasers,” IEEE Photon. Technol. Lett. 10, 757–759 (1998).
[CrossRef]

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

J. Heinrich, E. Zeeb, and K. J. Ebeling, “Transverse mode under external feedback and fiber coupling efficiencies of VCSEL’s,” IEEE Photon. Technol. Lett. 10, 1365–1367 (1998).
[CrossRef]

J. A. DeAro, K. D. Weston, R. W. Herrick, P. M. Petroff, and S. K. Buratto, “Near-field scanning optical microscopy of cleaved vertical-cavity surface-emitting lasers,” Semicond. Sci. Technol. 13, 1364–1367 (1998).
[CrossRef]

T. Milster, W. Jiang, E. Walker, D. Burak, P. Claisse, P. Kelly, and R. Binder, “A single-mode high-power vertical cavity surface emitting laser,” Appl. Phys. Lett. 72, 3425–3427 (1998).
[CrossRef]

J. V. Moloney, A. Egan, C. Z. Ning, and R. A. Indik, “Spontaneous spatiotemporal instabilities in current modulated master oscillator power amplifier lasers,” IEEE Photon. Technol. Lett. 10, 1229–1231 (1998).
[CrossRef]

A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic instabilities in master oscillator power amplifier semiconductor lasers,” IEEE J. Quantum Electron. 34, 166–170 (1998).
[CrossRef]

A. Fiore, Y. A. Akulova, J. Ko, E. R. Hegblom, and L. A. Coldren, “Low-threshold multiple-wavelength vertical-cavity laser arrays obtained by postgrowth wet oxidation,” Electron. Lett. 34, 1857–1858 (1998).
[CrossRef]

J. Y. Law and G. P. Agrawal, “Feedback-induced chaos and intensity-noise enhancement in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 15, 562–569 (1998).
[CrossRef]

1997 (11)

P. M. W. Skovgaard, J. G. McInerney, J. V. Moloney, R. A. Indik, and C. Z. Ning, “Enhanced stability of MFA-MOPA semiconductor lasers using a nonlinear, trumpet-shaped flare,” IEEE Photon. Technol. Lett. 9, 1220–1222 (1997).
[CrossRef]

C. Z. Ning, R. A. Indik, J. V. Moloney, W. W. Chow, A. Girndt, S. W. Koch, and R. Binder, “Incorporating many-body effects into modeling of semiconductor lasers and amplifiers,” in Physics and Simulation of Optoelectronic Devices V, W. W. Chow and M. Osinski, eds., Proc. SPIE 2994, 666–677 (1997).

C. Z. Ning, R. A. Indik, and J. V. Moloney, “Effective Bloch equations for semiconductor lasers and amplifiers,” IEEE J. Quantum Electron. 33, 1543–1550 (1997).
[CrossRef]

C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, “A first-principles fully space–time resolved model for a semiconductor laser,” Quantum Semiclassic. Opt. 9, 681–691 (1997).
[CrossRef]

J. V. Moloney, R. A. Indik, and C. Z. Ning, “Full space–time simulation of the high-brightness semiconductor lasers,” IEEE Photon. Technol. Lett. 9, 731–733 (1997).
[CrossRef]

A. Girndt, F. Jahnke, A. Knorr, S. W. Koch, and W. W. Chow, “Multi-band Bloch equations and gain spectra of highly excited II–VI semiconductor quantum wells,” Phys. Status Solidi B 202, 725–739 (1997).
[CrossRef]

W. W. Chow, A. Knorr, S. Hughes, A. Girndt, and S. W. Koch, “Carrier correlation effects in a quantum well semiconductor laser medium,” IEEE J. Sel. Top. Quantum Electron. 3, 136–141 (1997).
[CrossRef]

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

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

J. Y. Law and G. P. Agrawal, “Effects of spatial hole burning on gain switching in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 462–468 (1997).
[CrossRef]

H. Wenzel and H.-J. Wünsche, “The effective frequency method in the analysis of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 1156–1162 (1997).
[CrossRef]

1996 (6)

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]

M. Orenstein, Y. Satuby, U. Ben-Ami, and J. P. Harbison, “Transverse modes and lasing characteristics of selectively grown vertical cavity semiconductor lasers,” Appl. Phys. Lett. 69, 1840–1842 (1996).
[CrossRef]

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

I. Hoersch, R. Kusche, O. Marti, B. Weidl, and K. J. Ebeling, “Spectrally resolved near-field mode imaging of vertical-cavity semiconductor lasers,” J. Appl. Phys. 79, 3831–3834 (1996).
[CrossRef]

S. Hughes, A. Knorr, S. W. Koch, R. Binder, R. Indik, and J. V. Moloney, “The influence of electron–hole-scattering on the gain spectra of highly excited semiconductors,” Solid State Commun. 100, 555–559 (1996).
[CrossRef]

W. Yuen, G. S. Li, and C. J. Chang-Hasnain, “Multiple-wavelength vertical-cavity surface-emitting laser arrays with a record wavelength span,” IEEE Photon. Technol. Lett. 8, 4–6 (1996).
[CrossRef]

1995 (4)

R. Michalzik and K. J. Ebeling, “Generalized BV diagrams for higher order transverse modes in planar vertical-cavity laser diodes,” IEEE J. Quantum Electron. 31, 1371–1379 (1995).
[CrossRef]

C. Z. Ning, R. A. Indik, and J. V. Moloney, “Self-consistent approach to thermal effects in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 12, 1993–2004 (1995).
[CrossRef]

J. Yao, G. P. Agrawal, P. Gallion, and C. Bowden, “Semiconductor laser dynamics beyond the rate-equation approximation,” Opt. Commun. 119, 246–255 (1995).
[CrossRef]

A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical-cavity surface-emitting laser diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
[CrossRef]

1994 (5)

X. M. Gong, A. K. Chan, and H. F. Taylor, “Lateral mode discrimination in surface emitting DBR lasers with cylindrical symmetry,” IEEE J. Quantum Electron. 30, 1212–1218 (1994).
[CrossRef]

H. Li, T. Lucas, J. G. McInerney, and R. Morgan, “Transverse modes and patterns of electrically pumped vertical-cavity surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1619–1636 (1994).
[CrossRef]

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos Solitons Fractals 4, 1575–1596 (1994).
[CrossRef]

F. Prati, A. Tesei, L. A. Lugiato, and R. J. Horowicz, “Stable states in surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1637–1654 (1994).
[CrossRef]

G. C. Wilson, D. M. Kuchta, J. D. Walker, and J. S. Smith, “Spatial hole burning and self-focusing in vertical-cavity surface-emitting laser diodes,” Appl. Phys. Lett. 64, 542–544 (1994).
[CrossRef]

1993 (3)

K. H. Hahn, M. R. Tan, Y. M. Houng, and S. Y. Wang, “Large area multitransverse-mode VCSELs for modal noise-reduction in multimode fibre systems,” Electron. Lett. 29, 1482–1483 (1993).
[CrossRef]

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

K. Tai, Y. Lai, K. F. Huang, T. C. Huang, T. D. Lee, and C. C. Wu, “Transverse mode emission characteristics of gain-guided surface-emitting lasers,” Appl. Phys. Lett. 63, 2624–2626 (1993).
[CrossRef]

1991 (1)

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

1982 (1)

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. QE-18, 259–264 (1982).
[CrossRef]

1967 (1)

H. Haug and H. Haken, “Theory of noise in semiconductor laser emission,” Z. Phys. 204, 262–275 (1967).
[CrossRef]

Agrawal, G. P.

J. Y. Law and G. P. Agrawal, “Feedback-induced chaos and intensity-noise enhancement in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 15, 562–569 (1998).
[CrossRef]

J. Y. Law and G. P. Agrawal, “Effects of spatial hole burning on gain switching in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 462–468 (1997).
[CrossRef]

J. Yao, G. P. Agrawal, P. Gallion, and C. Bowden, “Semiconductor laser dynamics beyond the rate-equation approximation,” Opt. Commun. 119, 246–255 (1995).
[CrossRef]

Akulova, Y. A.

A. Fiore, Y. A. Akulova, J. Ko, E. R. Hegblom, and L. A. Coldren, “Low-threshold multiple-wavelength vertical-cavity laser arrays obtained by postgrowth wet oxidation,” Electron. Lett. 34, 1857–1858 (1998).
[CrossRef]

Asom, M. T.

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

Baets, R. G.

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

Ben-Ami, U.

M. Orenstein, Y. Satuby, U. Ben-Ami, and J. P. Harbison, “Transverse modes and lasing characteristics of selectively grown vertical cavity semiconductor lasers,” Appl. Phys. Lett. 69, 1840–1842 (1996).
[CrossRef]

Bienstman, P.

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

Binder, R.

D. Burak, S. A. Kemme, R. K. Kostuk, and R. Binder, “Spectral identification of transverse lasing modes of multiple index-guided vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 3501–3503 (1998).
[CrossRef]

D. Burak and R. Binder, “Electromagnetic characterization of vertical-cavity surface-emitting lasers based on a vectorial eigenmode calculation,” Appl. Phys. Lett. 72, 891–893 (1998).
[CrossRef]

T. Milster, W. Jiang, E. Walker, D. Burak, P. Claisse, P. Kelly, and R. Binder, “A single-mode high-power vertical cavity surface emitting laser,” Appl. Phys. Lett. 72, 3425–3427 (1998).
[CrossRef]

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

C. Z. Ning, R. A. Indik, J. V. Moloney, W. W. Chow, A. Girndt, S. W. Koch, and R. Binder, “Incorporating many-body effects into modeling of semiconductor lasers and amplifiers,” in Physics and Simulation of Optoelectronic Devices V, W. W. Chow and M. Osinski, eds., Proc. SPIE 2994, 666–677 (1997).

S. Hughes, A. Knorr, S. W. Koch, R. Binder, R. Indik, and J. V. Moloney, “The influence of electron–hole-scattering on the gain spectra of highly excited semiconductors,” Solid State Commun. 100, 555–559 (1996).
[CrossRef]

Bischoff, S.

C. Z. Ning, S. Bischoff, S. W. Koch, G. K. Harkness, J. V. Moloney, and W. W. Chow, “Microscopic modeling of vertical-cavity surface-emitting lasers: many-body interaction, plasma heating, and transverse dynamics,” Opt. Eng. 37, 1175–1181 (1998).
[CrossRef]

Bossert, D. J.

A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic instabilities in master oscillator power amplifier semiconductor lasers,” IEEE J. Quantum Electron. 34, 166–170 (1998).
[CrossRef]

Bowden, C.

J. Yao, G. P. Agrawal, P. Gallion, and C. Bowden, “Semiconductor laser dynamics beyond the rate-equation approximation,” Opt. Commun. 119, 246–255 (1995).
[CrossRef]

Brennan, T. M.

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos Solitons Fractals 4, 1575–1596 (1994).
[CrossRef]

Burak, D.

D. Burak, S. A. Kemme, R. K. Kostuk, and R. Binder, “Spectral identification of transverse lasing modes of multiple index-guided vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 3501–3503 (1998).
[CrossRef]

D. Burak and R. Binder, “Electromagnetic characterization of vertical-cavity surface-emitting lasers based on a vectorial eigenmode calculation,” Appl. Phys. Lett. 72, 891–893 (1998).
[CrossRef]

T. Milster, W. Jiang, E. Walker, D. Burak, P. Claisse, P. Kelly, and R. Binder, “A single-mode high-power vertical cavity surface emitting laser,” Appl. Phys. Lett. 72, 3425–3427 (1998).
[CrossRef]

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

Buratto, S. K.

J. A. DeAro, K. D. Weston, R. W. Herrick, P. M. Petroff, and S. K. Buratto, “Near-field scanning optical microscopy of cleaved vertical-cavity surface-emitting lasers,” Semicond. Sci. Technol. 13, 1364–1367 (1998).
[CrossRef]

Callis, S. E.

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

Chan, A. K.

X. M. Gong, A. K. Chan, and H. F. Taylor, “Lateral mode discrimination in surface emitting DBR lasers with cylindrical symmetry,” IEEE J. Quantum Electron. 30, 1212–1218 (1994).
[CrossRef]

Chang-Hasnain, C. J.

W. Yuen, G. S. Li, and C. J. Chang-Hasnain, “Multiple-wavelength vertical-cavity surface-emitting laser arrays with a record wavelength span,” IEEE Photon. Technol. Lett. 8, 4–6 (1996).
[CrossRef]

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

Choquette, K. D.

M. Noble, J. Shin, K. D. Choquette, J. P. Loehr, J. A. Lott, and Y. Lee, “Calculation and measurements of resonant-mode blueshifts in oxide-apertured VCSELs,” IEEE Photon. Technol. Lett. 10, 475–477 (1998).
[CrossRef]

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

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

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]

Chow, W. W.

C. Z. Ning, S. Bischoff, S. W. Koch, G. K. Harkness, J. V. Moloney, and W. W. Chow, “Microscopic modeling of vertical-cavity surface-emitting lasers: many-body interaction, plasma heating, and transverse dynamics,” Opt. Eng. 37, 1175–1181 (1998).
[CrossRef]

A. Girndt, F. Jahnke, A. Knorr, S. W. Koch, and W. W. Chow, “Multi-band Bloch equations and gain spectra of highly excited II–VI semiconductor quantum wells,” Phys. Status Solidi B 202, 725–739 (1997).
[CrossRef]

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

W. W. Chow, A. Knorr, S. Hughes, A. Girndt, and S. W. Koch, “Carrier correlation effects in a quantum well semiconductor laser medium,” IEEE J. Sel. Top. Quantum Electron. 3, 136–141 (1997).
[CrossRef]

C. Z. Ning, R. A. Indik, J. V. Moloney, W. W. Chow, A. Girndt, S. W. Koch, and R. Binder, “Incorporating many-body effects into modeling of semiconductor lasers and amplifiers,” in Physics and Simulation of Optoelectronic Devices V, W. W. Chow and M. Osinski, eds., Proc. SPIE 2994, 666–677 (1997).

Claisse, P.

T. Milster, W. Jiang, E. Walker, D. Burak, P. Claisse, P. Kelly, and R. Binder, “A single-mode high-power vertical cavity surface emitting laser,” Appl. Phys. Lett. 72, 3425–3427 (1998).
[CrossRef]

Coldren, L. A.

A. Fiore, Y. A. Akulova, J. Ko, E. R. Hegblom, and L. A. Coldren, “Low-threshold multiple-wavelength vertical-cavity laser arrays obtained by postgrowth wet oxidation,” Electron. Lett. 34, 1857–1858 (1998).
[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]

Crawford, M. H.

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

de Colstoun, F. B.

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos Solitons Fractals 4, 1575–1596 (1994).
[CrossRef]

DeAro, J. A.

J. A. DeAro, K. D. Weston, R. W. Herrick, P. M. Petroff, and S. K. Buratto, “Near-field scanning optical microscopy of cleaved vertical-cavity surface-emitting lasers,” Semicond. Sci. Technol. 13, 1364–1367 (1998).
[CrossRef]

Demeulenaere, B.

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

Deng, H.

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

Deng, Q.

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

Deppe, D. G.

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

Dhoedt, B.

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

Ebeling, K. J.

J. Heinrich, E. Zeeb, and K. J. Ebeling, “Transverse mode under external feedback and fiber coupling efficiencies of VCSEL’s,” IEEE Photon. Technol. Lett. 10, 1365–1367 (1998).
[CrossRef]

I. Hoersch, R. Kusche, O. Marti, B. Weidl, and K. J. Ebeling, “Spectrally resolved near-field mode imaging of vertical-cavity semiconductor lasers,” J. Appl. Phys. 79, 3831–3834 (1996).
[CrossRef]

R. Michalzik and K. J. Ebeling, “Generalized BV diagrams for higher order transverse modes in planar vertical-cavity laser diodes,” IEEE J. Quantum Electron. 31, 1371–1379 (1995).
[CrossRef]

Egan, A.

A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic instabilities in master oscillator power amplifier semiconductor lasers,” IEEE J. Quantum Electron. 34, 166–170 (1998).
[CrossRef]

J. V. Moloney, A. Egan, C. Z. Ning, and R. A. Indik, “Spontaneous spatiotemporal instabilities in current modulated master oscillator power amplifier lasers,” IEEE Photon. Technol. Lett. 10, 1229–1231 (1998).
[CrossRef]

C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, “A first-principles fully space–time resolved model for a semiconductor laser,” Quantum Semiclassic. Opt. 9, 681–691 (1997).
[CrossRef]

Fedorov, A. V.

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos Solitons Fractals 4, 1575–1596 (1994).
[CrossRef]

Fiore, A.

A. Fiore, Y. A. Akulova, J. Ko, E. R. Hegblom, and L. A. Coldren, “Low-threshold multiple-wavelength vertical-cavity laser arrays obtained by postgrowth wet oxidation,” Electron. Lett. 34, 1857–1858 (1998).
[CrossRef]

Florez, L. T.

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

Focht, M. W.

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

Gallion, P.

J. Yao, G. P. Agrawal, P. Gallion, and C. Bowden, “Semiconductor laser dynamics beyond the rate-equation approximation,” Opt. Commun. 119, 246–255 (1995).
[CrossRef]

Geib, K. M.

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

Girndt, A.

A. Girndt, F. Jahnke, A. Knorr, S. W. Koch, and W. W. Chow, “Multi-band Bloch equations and gain spectra of highly excited II–VI semiconductor quantum wells,” Phys. Status Solidi B 202, 725–739 (1997).
[CrossRef]

W. W. Chow, A. Knorr, S. Hughes, A. Girndt, and S. W. Koch, “Carrier correlation effects in a quantum well semiconductor laser medium,” IEEE J. Sel. Top. Quantum Electron. 3, 136–141 (1997).
[CrossRef]

C. Z. Ning, R. A. Indik, J. V. Moloney, W. W. Chow, A. Girndt, S. W. Koch, and R. Binder, “Incorporating many-body effects into modeling of semiconductor lasers and amplifiers,” in Physics and Simulation of Optoelectronic Devices V, W. W. Chow and M. Osinski, eds., Proc. SPIE 2994, 666–677 (1997).

Gong, X. M.

X. M. Gong, A. K. Chan, and H. F. Taylor, “Lateral mode discrimination in surface emitting DBR lasers with cylindrical symmetry,” IEEE J. Quantum Electron. 30, 1212–1218 (1994).
[CrossRef]

Goorjian, P. M.

P. M. Goorjian and C. Z. Ning, “Transverse mode dynamics of VCSELs through space–time domain simulation,” in Physics and Simulation of Optoelectronic Devices VII, P. Blood, A. Ishibashi, and M. Osinski, eds., Proc. SPIE 3625, 395–403 (1999).
[CrossRef]

Guth, G. D.

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

Hadley, G. R.

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

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]

Hahn, K. H.

K. H. Hahn, M. R. Tan, Y. M. Houng, and S. Y. Wang, “Large area multitransverse-mode VCSELs for modal noise-reduction in multimode fibre systems,” Electron. Lett. 29, 1482–1483 (1993).
[CrossRef]

Haken, H.

H. Haug and H. Haken, “Theory of noise in semiconductor laser emission,” Z. Phys. 204, 262–275 (1967).
[CrossRef]

Hammons, B. G.

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos Solitons Fractals 4, 1575–1596 (1994).
[CrossRef]

Harbison, J. P.

M. Orenstein, Y. Satuby, U. Ben-Ami, and J. P. Harbison, “Transverse modes and lasing characteristics of selectively grown vertical cavity semiconductor lasers,” Appl. Phys. Lett. 69, 1840–1842 (1996).
[CrossRef]

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

Harkness, G. K.

C. Z. Ning, S. Bischoff, S. W. Koch, G. K. Harkness, J. V. Moloney, and W. W. Chow, “Microscopic modeling of vertical-cavity surface-emitting lasers: many-body interaction, plasma heating, and transverse dynamics,” Opt. Eng. 37, 1175–1181 (1998).
[CrossRef]

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

Hasnain, G.

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

Haug, H.

H. Haug and H. Haken, “Theory of noise in semiconductor laser emission,” Z. Phys. 204, 262–275 (1967).
[CrossRef]

Hegarty, S. P.

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

Hegblom, E. R.

A. Fiore, Y. A. Akulova, J. Ko, E. R. Hegblom, and L. A. Coldren, “Low-threshold multiple-wavelength vertical-cavity laser arrays obtained by postgrowth wet oxidation,” Electron. Lett. 34, 1857–1858 (1998).
[CrossRef]

Heinrich, J.

J. Heinrich, E. Zeeb, and K. J. Ebeling, “Transverse mode under external feedback and fiber coupling efficiencies of VCSEL’s,” IEEE Photon. Technol. Lett. 10, 1365–1367 (1998).
[CrossRef]

Henry, C. H.

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. QE-18, 259–264 (1982).
[CrossRef]

Herrick, R. W.

J. A. DeAro, K. D. Weston, R. W. Herrick, P. M. Petroff, and S. K. Buratto, “Near-field scanning optical microscopy of cleaved vertical-cavity surface-emitting lasers,” Semicond. Sci. Technol. 13, 1364–1367 (1998).
[CrossRef]

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]

Hoersch, I.

I. Hoersch, R. Kusche, O. Marti, B. Weidl, and K. J. Ebeling, “Spectrally resolved near-field mode imaging of vertical-cavity semiconductor lasers,” J. Appl. Phys. 79, 3831–3834 (1996).
[CrossRef]

Horowicz, R. J.

F. Prati, A. Tesei, L. A. Lugiato, and R. J. Horowicz, “Stable states in surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1637–1654 (1994).
[CrossRef]

Hou, H. Q.

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

Houng, Y. M.

K. H. Hahn, M. R. Tan, Y. M. Houng, and S. Y. Wang, “Large area multitransverse-mode VCSELs for modal noise-reduction in multimode fibre systems,” Electron. Lett. 29, 1482–1483 (1993).
[CrossRef]

Huang, K. F.

K. Tai, Y. Lai, K. F. Huang, T. C. Huang, T. D. Lee, and C. C. Wu, “Transverse mode emission characteristics of gain-guided surface-emitting lasers,” Appl. Phys. Lett. 63, 2624–2626 (1993).
[CrossRef]

Huang, T. C.

K. Tai, Y. Lai, K. F. Huang, T. C. Huang, T. D. Lee, and C. C. Wu, “Transverse mode emission characteristics of gain-guided surface-emitting lasers,” Appl. Phys. Lett. 63, 2624–2626 (1993).
[CrossRef]

Huffaker, D. L.

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

Hughes, S.

W. W. Chow, A. Knorr, S. Hughes, A. Girndt, and S. W. Koch, “Carrier correlation effects in a quantum well semiconductor laser medium,” IEEE J. Sel. Top. Quantum Electron. 3, 136–141 (1997).
[CrossRef]

S. Hughes, A. Knorr, S. W. Koch, R. Binder, R. Indik, and J. V. Moloney, “The influence of electron–hole-scattering on the gain spectra of highly excited semiconductors,” Solid State Commun. 100, 555–559 (1996).
[CrossRef]

Huyet, G.

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

Indik, R.

S. Hughes, A. Knorr, S. W. Koch, R. Binder, R. Indik, and J. V. Moloney, “The influence of electron–hole-scattering on the gain spectra of highly excited semiconductors,” Solid State Commun. 100, 555–559 (1996).
[CrossRef]

Indik, R. A.

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

J. V. Moloney, A. Egan, C. Z. Ning, and R. A. Indik, “Spontaneous spatiotemporal instabilities in current modulated master oscillator power amplifier lasers,” IEEE Photon. Technol. Lett. 10, 1229–1231 (1998).
[CrossRef]

A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic instabilities in master oscillator power amplifier semiconductor lasers,” IEEE J. Quantum Electron. 34, 166–170 (1998).
[CrossRef]

C. Z. Ning, R. A. Indik, J. V. Moloney, W. W. Chow, A. Girndt, S. W. Koch, and R. Binder, “Incorporating many-body effects into modeling of semiconductor lasers and amplifiers,” in Physics and Simulation of Optoelectronic Devices V, W. W. Chow and M. Osinski, eds., Proc. SPIE 2994, 666–677 (1997).

C. Z. Ning, R. A. Indik, and J. V. Moloney, “Effective Bloch equations for semiconductor lasers and amplifiers,” IEEE J. Quantum Electron. 33, 1543–1550 (1997).
[CrossRef]

P. M. W. Skovgaard, J. G. McInerney, J. V. Moloney, R. A. Indik, and C. Z. Ning, “Enhanced stability of MFA-MOPA semiconductor lasers using a nonlinear, trumpet-shaped flare,” IEEE Photon. Technol. Lett. 9, 1220–1222 (1997).
[CrossRef]

C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, “A first-principles fully space–time resolved model for a semiconductor laser,” Quantum Semiclassic. Opt. 9, 681–691 (1997).
[CrossRef]

J. V. Moloney, R. A. Indik, and C. Z. Ning, “Full space–time simulation of the high-brightness semiconductor lasers,” IEEE Photon. Technol. Lett. 9, 731–733 (1997).
[CrossRef]

C. Z. Ning, R. A. Indik, and J. V. Moloney, “Self-consistent approach to thermal effects in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 12, 1993–2004 (1995).
[CrossRef]

Jahnke, F.

A. Girndt, F. Jahnke, A. Knorr, S. W. Koch, and W. W. Chow, “Multi-band Bloch equations and gain spectra of highly excited II–VI semiconductor quantum wells,” Phys. Status Solidi B 202, 725–739 (1997).
[CrossRef]

Jiang, W.

T. Milster, W. Jiang, E. Walker, D. Burak, P. Claisse, P. Kelly, and R. Binder, “A single-mode high-power vertical cavity surface emitting laser,” Appl. Phys. Lett. 72, 3425–3427 (1998).
[CrossRef]

Kelly, P.

T. Milster, W. Jiang, E. Walker, D. Burak, P. Claisse, P. Kelly, and R. Binder, “A single-mode high-power vertical cavity surface emitting laser,” Appl. Phys. Lett. 72, 3425–3427 (1998).
[CrossRef]

Kemme, S. A.

D. Burak, S. A. Kemme, R. K. Kostuk, and R. Binder, “Spectral identification of transverse lasing modes of multiple index-guided vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 3501–3503 (1998).
[CrossRef]

Khitrova, G.

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos Solitons Fractals 4, 1575–1596 (1994).
[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]

Knorr, A.

A. Girndt, F. Jahnke, A. Knorr, S. W. Koch, and W. W. Chow, “Multi-band Bloch equations and gain spectra of highly excited II–VI semiconductor quantum wells,” Phys. Status Solidi B 202, 725–739 (1997).
[CrossRef]

W. W. Chow, A. Knorr, S. Hughes, A. Girndt, and S. W. Koch, “Carrier correlation effects in a quantum well semiconductor laser medium,” IEEE J. Sel. Top. Quantum Electron. 3, 136–141 (1997).
[CrossRef]

S. Hughes, A. Knorr, S. W. Koch, R. Binder, R. Indik, and J. V. Moloney, “The influence of electron–hole-scattering on the gain spectra of highly excited semiconductors,” Solid State Commun. 100, 555–559 (1996).
[CrossRef]

Ko, J.

A. Fiore, Y. A. Akulova, J. Ko, E. R. Hegblom, and L. A. Coldren, “Low-threshold multiple-wavelength vertical-cavity laser arrays obtained by postgrowth wet oxidation,” Electron. Lett. 34, 1857–1858 (1998).
[CrossRef]

Koch, S. W.

C. Z. Ning, S. Bischoff, S. W. Koch, G. K. Harkness, J. V. Moloney, and W. W. Chow, “Microscopic modeling of vertical-cavity surface-emitting lasers: many-body interaction, plasma heating, and transverse dynamics,” Opt. Eng. 37, 1175–1181 (1998).
[CrossRef]

A. Girndt, F. Jahnke, A. Knorr, S. W. Koch, and W. W. Chow, “Multi-band Bloch equations and gain spectra of highly excited II–VI semiconductor quantum wells,” Phys. Status Solidi B 202, 725–739 (1997).
[CrossRef]

W. W. Chow, A. Knorr, S. Hughes, A. Girndt, and S. W. Koch, “Carrier correlation effects in a quantum well semiconductor laser medium,” IEEE J. Sel. Top. Quantum Electron. 3, 136–141 (1997).
[CrossRef]

C. Z. Ning, R. A. Indik, J. V. Moloney, W. W. Chow, A. Girndt, S. W. Koch, and R. Binder, “Incorporating many-body effects into modeling of semiconductor lasers and amplifiers,” in Physics and Simulation of Optoelectronic Devices V, W. W. Chow and M. Osinski, eds., Proc. SPIE 2994, 666–677 (1997).

S. Hughes, A. Knorr, S. W. Koch, R. Binder, R. Indik, and J. V. Moloney, “The influence of electron–hole-scattering on the gain spectra of highly excited semiconductors,” Solid State Commun. 100, 555–559 (1996).
[CrossRef]

Kojima, K.

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

Kostuk, R. K.

D. Burak, S. A. Kemme, R. K. Kostuk, and R. Binder, “Spectral identification of transverse lasing modes of multiple index-guided vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 3501–3503 (1998).
[CrossRef]

Kuchta, D. M.

G. C. Wilson, D. M. Kuchta, J. D. Walker, and J. S. Smith, “Spatial hole burning and self-focusing in vertical-cavity surface-emitting laser diodes,” Appl. Phys. Lett. 64, 542–544 (1994).
[CrossRef]

Kusche, R.

I. Hoersch, R. Kusche, O. Marti, B. Weidl, and K. J. Ebeling, “Spectrally resolved near-field mode imaging of vertical-cavity semiconductor lasers,” J. Appl. Phys. 79, 3831–3834 (1996).
[CrossRef]

Lai, Y.

K. Tai, Y. Lai, K. F. Huang, T. C. Huang, T. D. Lee, and C. C. Wu, “Transverse mode emission characteristics of gain-guided surface-emitting lasers,” Appl. Phys. Lett. 63, 2624–2626 (1993).
[CrossRef]

Law, J. Y.

J. Y. Law and G. P. Agrawal, “Feedback-induced chaos and intensity-noise enhancement in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 15, 562–569 (1998).
[CrossRef]

J. Y. Law and G. P. Agrawal, “Effects of spatial hole burning on gain switching in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33, 462–468 (1997).
[CrossRef]

Lear, K. L.

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

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]

Lee, T. D.

K. Tai, Y. Lai, K. F. Huang, T. C. Huang, T. D. Lee, and C. C. Wu, “Transverse mode emission characteristics of gain-guided surface-emitting lasers,” Appl. Phys. Lett. 63, 2624–2626 (1993).
[CrossRef]

Lee, Y.

M. Noble, J. Shin, K. D. Choquette, J. P. Loehr, J. A. Lott, and Y. Lee, “Calculation and measurements of resonant-mode blueshifts in oxide-apertured VCSELs,” IEEE Photon. Technol. Lett. 10, 475–477 (1998).
[CrossRef]

Li, G. S.

W. Yuen, G. S. Li, and C. J. Chang-Hasnain, “Multiple-wavelength vertical-cavity surface-emitting laser arrays with a record wavelength span,” IEEE Photon. Technol. Lett. 8, 4–6 (1996).
[CrossRef]

Li, H.

H. Li, T. Lucas, J. G. McInerney, and R. Morgan, “Transverse modes and patterns of electrically pumped vertical-cavity surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1619–1636 (1994).
[CrossRef]

Loehr, J. P.

M. Noble, J. Shin, K. D. Choquette, J. P. Loehr, J. A. Lott, and Y. Lee, “Calculation and measurements of resonant-mode blueshifts in oxide-apertured VCSELs,” IEEE Photon. Technol. Lett. 10, 475–477 (1998).
[CrossRef]

M. 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]

Lott, J. A.

M. 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]

M. Noble, J. Shin, K. D. Choquette, J. P. Loehr, J. A. Lott, and Y. Lee, “Calculation and measurements of resonant-mode blueshifts in oxide-apertured VCSELs,” IEEE Photon. Technol. Lett. 10, 475–477 (1998).
[CrossRef]

Lowry, C.

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos Solitons Fractals 4, 1575–1596 (1994).
[CrossRef]

Lucas, T.

H. Li, T. Lucas, J. G. McInerney, and R. Morgan, “Transverse modes and patterns of electrically pumped vertical-cavity surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1619–1636 (1994).
[CrossRef]

Lugiato, L. A.

F. Prati, A. Tesei, L. A. Lugiato, and R. J. Horowicz, “Stable states in surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1637–1654 (1994).
[CrossRef]

Maker, P. D.

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos Solitons Fractals 4, 1575–1596 (1994).
[CrossRef]

Marti, O.

I. Hoersch, R. Kusche, O. Marti, B. Weidl, and K. J. Ebeling, “Spectrally resolved near-field mode imaging of vertical-cavity semiconductor lasers,” J. Appl. Phys. 79, 3831–3834 (1996).
[CrossRef]

McInerney, J. G.

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

A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic instabilities in master oscillator power amplifier semiconductor lasers,” IEEE J. Quantum Electron. 34, 166–170 (1998).
[CrossRef]

P. M. W. Skovgaard, J. G. McInerney, J. V. Moloney, R. A. Indik, and C. Z. Ning, “Enhanced stability of MFA-MOPA semiconductor lasers using a nonlinear, trumpet-shaped flare,” IEEE Photon. Technol. Lett. 9, 1220–1222 (1997).
[CrossRef]

H. Li, T. Lucas, J. G. McInerney, and R. Morgan, “Transverse modes and patterns of electrically pumped vertical-cavity surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1619–1636 (1994).
[CrossRef]

Michalzik, R.

R. Michalzik and K. J. Ebeling, “Generalized BV diagrams for higher order transverse modes in planar vertical-cavity laser diodes,” IEEE J. Quantum Electron. 31, 1371–1379 (1995).
[CrossRef]

Milster, T.

T. Milster, W. Jiang, E. Walker, D. Burak, P. Claisse, P. Kelly, and R. Binder, “A single-mode high-power vertical cavity surface emitting laser,” Appl. Phys. Lett. 72, 3425–3427 (1998).
[CrossRef]

Moloney, J. V.

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

J. V. Moloney, A. Egan, C. Z. Ning, and R. A. Indik, “Spontaneous spatiotemporal instabilities in current modulated master oscillator power amplifier lasers,” IEEE Photon. Technol. Lett. 10, 1229–1231 (1998).
[CrossRef]

C. Z. Ning, S. Bischoff, S. W. Koch, G. K. Harkness, J. V. Moloney, and W. W. Chow, “Microscopic modeling of vertical-cavity surface-emitting lasers: many-body interaction, plasma heating, and transverse dynamics,” Opt. Eng. 37, 1175–1181 (1998).
[CrossRef]

A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic instabilities in master oscillator power amplifier semiconductor lasers,” IEEE J. Quantum Electron. 34, 166–170 (1998).
[CrossRef]

C. Z. Ning, R. A. Indik, J. V. Moloney, W. W. Chow, A. Girndt, S. W. Koch, and R. Binder, “Incorporating many-body effects into modeling of semiconductor lasers and amplifiers,” in Physics and Simulation of Optoelectronic Devices V, W. W. Chow and M. Osinski, eds., Proc. SPIE 2994, 666–677 (1997).

C. Z. Ning, R. A. Indik, and J. V. Moloney, “Effective Bloch equations for semiconductor lasers and amplifiers,” IEEE J. Quantum Electron. 33, 1543–1550 (1997).
[CrossRef]

C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, “A first-principles fully space–time resolved model for a semiconductor laser,” Quantum Semiclassic. Opt. 9, 681–691 (1997).
[CrossRef]

P. M. W. Skovgaard, J. G. McInerney, J. V. Moloney, R. A. Indik, and C. Z. Ning, “Enhanced stability of MFA-MOPA semiconductor lasers using a nonlinear, trumpet-shaped flare,” IEEE Photon. Technol. Lett. 9, 1220–1222 (1997).
[CrossRef]

J. V. Moloney, R. A. Indik, and C. Z. Ning, “Full space–time simulation of the high-brightness semiconductor lasers,” IEEE Photon. Technol. Lett. 9, 731–733 (1997).
[CrossRef]

S. Hughes, A. Knorr, S. W. Koch, R. Binder, R. Indik, and J. V. Moloney, “The influence of electron–hole-scattering on the gain spectra of highly excited semiconductors,” Solid State Commun. 100, 555–559 (1996).
[CrossRef]

C. Z. Ning, R. A. Indik, and J. V. Moloney, “Self-consistent approach to thermal effects in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 12, 1993–2004 (1995).
[CrossRef]

Morgan, R.

H. Li, T. Lucas, J. G. McInerney, and R. Morgan, “Transverse modes and patterns of electrically pumped vertical-cavity surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1619–1636 (1994).
[CrossRef]

Morgan, R. A.

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

Nakwaski, W.

W. Nakwaski and R. P. Sarzala, “Transverse modes in gain-guided vertical-cavity surface-emitting lasers,” Opt. Commun. 148, 63–69 (1998).
[CrossRef]

Nelson, T. R.

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos Solitons Fractals 4, 1575–1596 (1994).
[CrossRef]

Ning, C. Z.

P. M. Goorjian and C. Z. Ning, “Transverse mode dynamics of VCSELs through space–time domain simulation,” in Physics and Simulation of Optoelectronic Devices VII, P. Blood, A. Ishibashi, and M. Osinski, eds., Proc. SPIE 3625, 395–403 (1999).
[CrossRef]

A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic instabilities in master oscillator power amplifier semiconductor lasers,” IEEE J. Quantum Electron. 34, 166–170 (1998).
[CrossRef]

C. Z. Ning, S. Bischoff, S. W. Koch, G. K. Harkness, J. V. Moloney, and W. W. Chow, “Microscopic modeling of vertical-cavity surface-emitting lasers: many-body interaction, plasma heating, and transverse dynamics,” Opt. Eng. 37, 1175–1181 (1998).
[CrossRef]

J. V. Moloney, A. Egan, C. Z. Ning, and R. A. Indik, “Spontaneous spatiotemporal instabilities in current modulated master oscillator power amplifier lasers,” IEEE Photon. Technol. Lett. 10, 1229–1231 (1998).
[CrossRef]

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

J. V. Moloney, R. A. Indik, and C. Z. Ning, “Full space–time simulation of the high-brightness semiconductor lasers,” IEEE Photon. Technol. Lett. 9, 731–733 (1997).
[CrossRef]

P. M. W. Skovgaard, J. G. McInerney, J. V. Moloney, R. A. Indik, and C. Z. Ning, “Enhanced stability of MFA-MOPA semiconductor lasers using a nonlinear, trumpet-shaped flare,” IEEE Photon. Technol. Lett. 9, 1220–1222 (1997).
[CrossRef]

C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, “A first-principles fully space–time resolved model for a semiconductor laser,” Quantum Semiclassic. Opt. 9, 681–691 (1997).
[CrossRef]

C. Z. Ning, R. A. Indik, J. V. Moloney, W. W. Chow, A. Girndt, S. W. Koch, and R. Binder, “Incorporating many-body effects into modeling of semiconductor lasers and amplifiers,” in Physics and Simulation of Optoelectronic Devices V, W. W. Chow and M. Osinski, eds., Proc. SPIE 2994, 666–677 (1997).

C. Z. Ning, R. A. Indik, and J. V. Moloney, “Effective Bloch equations for semiconductor lasers and amplifiers,” IEEE J. Quantum Electron. 33, 1543–1550 (1997).
[CrossRef]

C. Z. Ning, R. A. Indik, and J. V. Moloney, “Self-consistent approach to thermal effects in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 12, 1993–2004 (1995).
[CrossRef]

Noble, M.

M. Noble, J. Shin, K. D. Choquette, J. P. Loehr, J. A. Lott, and Y. Lee, “Calculation and measurements of resonant-mode blueshifts in oxide-apertured VCSELs,” IEEE Photon. Technol. Lett. 10, 475–477 (1998).
[CrossRef]

M. 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]

Orenstein, M.

Y. Satuby and M. Orenstein, “Small signal modulation of multitransverse modes vertical-cavity surface-emitting semiconductor lasers,” IEEE Photon. Technol. Lett. 10, 757–759 (1998).
[CrossRef]

Y. Satuby and M. Orenstein, “Limits of the modulation response of a single-mode proton implanted VCSEL,” IEEE Photon. Technol. Lett. 10, 760–762 (1998).
[CrossRef]

M. Orenstein, Y. Satuby, U. Ben-Ami, and J. P. Harbison, “Transverse modes and lasing characteristics of selectively grown vertical cavity semiconductor lasers,” Appl. Phys. Lett. 69, 1840–1842 (1996).
[CrossRef]

Petroff, P. M.

J. A. DeAro, K. D. Weston, R. W. Herrick, P. M. Petroff, and S. K. Buratto, “Near-field scanning optical microscopy of cleaved vertical-cavity surface-emitting lasers,” Semicond. Sci. Technol. 13, 1364–1367 (1998).
[CrossRef]

Prati, F.

F. Prati, A. Tesei, L. A. Lugiato, and R. J. Horowicz, “Stable states in surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1637–1654 (1994).
[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]

Rogers, L. E.

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

Rössler, T.

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

Sarma, J.

A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical-cavity surface-emitting laser diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
[CrossRef]

Sarzala, R. P.

W. Nakwaski and R. P. Sarzala, “Transverse modes in gain-guided vertical-cavity surface-emitting lasers,” Opt. Commun. 148, 63–69 (1998).
[CrossRef]

Satuby, Y.

Y. Satuby and M. Orenstein, “Limits of the modulation response of a single-mode proton implanted VCSEL,” IEEE Photon. Technol. Lett. 10, 760–762 (1998).
[CrossRef]

Y. Satuby and M. Orenstein, “Small signal modulation of multitransverse modes vertical-cavity surface-emitting semiconductor lasers,” IEEE Photon. Technol. Lett. 10, 757–759 (1998).
[CrossRef]

M. Orenstein, Y. Satuby, U. Ben-Ami, and J. P. Harbison, “Transverse modes and lasing characteristics of selectively grown vertical cavity semiconductor lasers,” Appl. Phys. Lett. 69, 1840–1842 (1996).
[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]

Shin, J.

M. Noble, J. Shin, K. D. Choquette, J. P. Loehr, J. A. Lott, and Y. Lee, “Calculation and measurements of resonant-mode blueshifts in oxide-apertured VCSELs,” IEEE Photon. Technol. Lett. 10, 475–477 (1998).
[CrossRef]

Shore, K. A.

A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical-cavity surface-emitting laser diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
[CrossRef]

Skovgaard, P. M. W.

P. M. W. Skovgaard, J. G. McInerney, J. V. Moloney, R. A. Indik, and C. Z. Ning, “Enhanced stability of MFA-MOPA semiconductor lasers using a nonlinear, trumpet-shaped flare,” IEEE Photon. Technol. Lett. 9, 1220–1222 (1997).
[CrossRef]

Smith, J. S.

G. C. Wilson, D. M. Kuchta, J. D. Walker, and J. S. Smith, “Spatial hole burning and self-focusing in vertical-cavity surface-emitting laser diodes,” Appl. Phys. Lett. 64, 542–544 (1994).
[CrossRef]

Stoffel, N. G.

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

Tai, K.

K. Tai, Y. Lai, K. F. Huang, T. C. Huang, T. D. Lee, and C. C. Wu, “Transverse mode emission characteristics of gain-guided surface-emitting lasers,” Appl. Phys. Lett. 63, 2624–2626 (1993).
[CrossRef]

Tan, M. R.

K. H. Hahn, M. R. Tan, Y. M. Houng, and S. Y. Wang, “Large area multitransverse-mode VCSELs for modal noise-reduction in multimode fibre systems,” Electron. Lett. 29, 1482–1483 (1993).
[CrossRef]

Taylor, H. F.

X. M. Gong, A. K. Chan, and H. F. Taylor, “Lateral mode discrimination in surface emitting DBR lasers with cylindrical symmetry,” IEEE J. Quantum Electron. 30, 1212–1218 (1994).
[CrossRef]

Tesei, A.

F. Prati, A. Tesei, L. A. Lugiato, and R. J. Horowicz, “Stable states in surface-emitting semiconductor lasers,” Chaos Solitons Fractals 4, 1637–1654 (1994).
[CrossRef]

Valle, A.

A. Valle, “Selection and modulation of high-order transverse modes in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 34, 1924–1932 (1998).
[CrossRef]

A. Valle, “High-frequency beam steering induced by switching of high-order transverse modes in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 1607–1609 (1998).
[CrossRef]

A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical-cavity surface-emitting laser diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
[CrossRef]

Von Lehmen, A.

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

Walker, E.

T. Milster, W. Jiang, E. Walker, D. Burak, P. Claisse, P. Kelly, and R. Binder, “A single-mode high-power vertical cavity surface emitting laser,” Appl. Phys. Lett. 72, 3425–3427 (1998).
[CrossRef]

Walker, J. D.

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I. Hoersch, R. Kusche, O. Marti, B. Weidl, and K. J. Ebeling, “Spectrally resolved near-field mode imaging of vertical-cavity semiconductor lasers,” J. Appl. Phys. 79, 3831–3834 (1996).
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J. A. DeAro, K. D. Weston, R. W. Herrick, P. M. Petroff, and S. K. Buratto, “Near-field scanning optical microscopy of cleaved vertical-cavity surface-emitting lasers,” Semicond. Sci. Technol. 13, 1364–1367 (1998).
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G. C. Wilson, D. M. Kuchta, J. D. Walker, and J. S. Smith, “Spatial hole burning and self-focusing in vertical-cavity surface-emitting laser diodes,” Appl. Phys. Lett. 64, 542–544 (1994).
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A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic instabilities in master oscillator power amplifier semiconductor lasers,” IEEE J. Quantum Electron. 34, 166–170 (1998).
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J. Yao, G. P. Agrawal, P. Gallion, and C. Bowden, “Semiconductor laser dynamics beyond the rate-equation approximation,” Opt. Commun. 119, 246–255 (1995).
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W. Yuen, G. S. Li, and C. J. Chang-Hasnain, “Multiple-wavelength vertical-cavity surface-emitting laser arrays with a record wavelength span,” IEEE Photon. Technol. Lett. 8, 4–6 (1996).
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S. P. Hegarty, G. Huyet, J. G. McInerney, K. D. Choquette, K. M. Geib, and H. Q. Hou, “Size dependence of transverse mode structure in oxide-confined vertical-cavity laser diodes,” Appl. Phys. Lett. 73, 596–598 (1998).
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A. Valle, “High-frequency beam steering induced by switching of high-order transverse modes in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 1607–1609 (1998).
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D. Burak and R. Binder, “Electromagnetic characterization of vertical-cavity surface-emitting lasers based on a vectorial eigenmode calculation,” Appl. Phys. Lett. 72, 891–893 (1998).
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Electron. Lett. (2)

K. H. Hahn, M. R. Tan, Y. M. Houng, and S. Y. Wang, “Large area multitransverse-mode VCSELs for modal noise-reduction in multimode fibre systems,” Electron. Lett. 29, 1482–1483 (1993).
[CrossRef]

A. Fiore, Y. A. Akulova, J. Ko, E. R. Hegblom, and L. A. Coldren, “Low-threshold multiple-wavelength vertical-cavity laser arrays obtained by postgrowth wet oxidation,” Electron. Lett. 34, 1857–1858 (1998).
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A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic instabilities in master oscillator power amplifier semiconductor lasers,” IEEE J. Quantum Electron. 34, 166–170 (1998).
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IEEE J. Sel. Top. Quantum Electron. (1)

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[CrossRef]

IEEE Photon. Technol. Lett. (9)

W. Yuen, G. S. Li, and C. J. Chang-Hasnain, “Multiple-wavelength vertical-cavity surface-emitting laser arrays with a record wavelength span,” IEEE Photon. Technol. Lett. 8, 4–6 (1996).
[CrossRef]

P. M. W. Skovgaard, J. G. McInerney, J. V. Moloney, R. A. Indik, and C. Z. Ning, “Enhanced stability of MFA-MOPA semiconductor lasers using a nonlinear, trumpet-shaped flare,” IEEE Photon. Technol. Lett. 9, 1220–1222 (1997).
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J. V. Moloney, R. A. Indik, and C. Z. Ning, “Full space–time simulation of the high-brightness semiconductor lasers,” IEEE Photon. Technol. Lett. 9, 731–733 (1997).
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J. V. Moloney, A. Egan, C. Z. Ning, and R. A. Indik, “Spontaneous spatiotemporal instabilities in current modulated master oscillator power amplifier lasers,” IEEE Photon. Technol. Lett. 10, 1229–1231 (1998).
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M. Noble, J. Shin, K. D. Choquette, J. P. Loehr, J. A. Lott, and Y. Lee, “Calculation and measurements of resonant-mode blueshifts in oxide-apertured VCSELs,” IEEE Photon. Technol. Lett. 10, 475–477 (1998).
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J. Heinrich, E. Zeeb, and K. J. Ebeling, “Transverse mode under external feedback and fiber coupling efficiencies of VCSEL’s,” IEEE Photon. Technol. Lett. 10, 1365–1367 (1998).
[CrossRef]

Y. Satuby and M. Orenstein, “Limits of the modulation response of a single-mode proton implanted VCSEL,” IEEE Photon. Technol. Lett. 10, 760–762 (1998).
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Y. Satuby and M. Orenstein, “Small signal modulation of multitransverse modes vertical-cavity surface-emitting semiconductor lasers,” IEEE Photon. Technol. Lett. 10, 757–759 (1998).
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J. Appl. Phys. (1)

I. Hoersch, R. Kusche, O. Marti, B. Weidl, and K. J. Ebeling, “Spectrally resolved near-field mode imaging of vertical-cavity semiconductor lasers,” J. Appl. Phys. 79, 3831–3834 (1996).
[CrossRef]

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

Opt. Commun. (2)

J. Yao, G. P. Agrawal, P. Gallion, and C. Bowden, “Semiconductor laser dynamics beyond the rate-equation approximation,” Opt. Commun. 119, 246–255 (1995).
[CrossRef]

W. Nakwaski and R. P. Sarzala, “Transverse modes in gain-guided vertical-cavity surface-emitting lasers,” Opt. Commun. 148, 63–69 (1998).
[CrossRef]

Opt. Eng. (1)

C. Z. Ning, S. Bischoff, S. W. Koch, G. K. Harkness, J. V. Moloney, and W. W. Chow, “Microscopic modeling of vertical-cavity surface-emitting lasers: many-body interaction, plasma heating, and transverse dynamics,” Opt. Eng. 37, 1175–1181 (1998).
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Phys. Rev. A (1)

T. Rössler, R. A. Indik, G. K. Harkness, J. V. Moloney, and C. Z. Ning, “Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers,” Phys. Rev. A 58, 3279–3292 (1998).
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Phys. Status Solidi B (1)

A. Girndt, F. Jahnke, A. Knorr, S. W. Koch, and W. W. Chow, “Multi-band Bloch equations and gain spectra of highly excited II–VI semiconductor quantum wells,” Phys. Status Solidi B 202, 725–739 (1997).
[CrossRef]

Proc. SPIE (2)

C. Z. Ning, R. A. Indik, J. V. Moloney, W. W. Chow, A. Girndt, S. W. Koch, and R. Binder, “Incorporating many-body effects into modeling of semiconductor lasers and amplifiers,” in Physics and Simulation of Optoelectronic Devices V, W. W. Chow and M. Osinski, eds., Proc. SPIE 2994, 666–677 (1997).

P. M. Goorjian and C. Z. Ning, “Transverse mode dynamics of VCSELs through space–time domain simulation,” in Physics and Simulation of Optoelectronic Devices VII, P. Blood, A. Ishibashi, and M. Osinski, eds., Proc. SPIE 3625, 395–403 (1999).
[CrossRef]

Quantum Semiclassic. Opt. (1)

C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, “A first-principles fully space–time resolved model for a semiconductor laser,” Quantum Semiclassic. Opt. 9, 681–691 (1997).
[CrossRef]

Semicond. Sci. Technol. (1)

J. A. DeAro, K. D. Weston, R. W. Herrick, P. M. Petroff, and S. K. Buratto, “Near-field scanning optical microscopy of cleaved vertical-cavity surface-emitting lasers,” Semicond. Sci. Technol. 13, 1364–1367 (1998).
[CrossRef]

Solid State Commun. (1)

S. Hughes, A. Knorr, S. W. Koch, R. Binder, R. Indik, and J. V. Moloney, “The influence of electron–hole-scattering on the gain spectra of highly excited semiconductors,” Solid State Commun. 100, 555–559 (1996).
[CrossRef]

Z. Phys. (1)

H. Haug and H. Haken, “Theory of noise in semiconductor laser emission,” Z. Phys. 204, 262–275 (1967).
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Other (3)

W. W. Chow, S. W. Koch, and M. Sargent, Semiconductor Laser Physics (Springer-Verlag, Berlin, 1994), Chap. 4, pp. 119–156.

For a survey of recent progress in VCSEL’s, see C. Chang-Hasnain, ed., Advances in Vertical Cavity Surface Emitting Lasers, Vol. 15 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997).

C. Mignosi, P. Dowd, L. Raddatz, I. H. White, M. C. Nowell, D. G. Cunningham, M. R. Tan, and S. Y. Wang, “Dynamics of mode partitioning in gain guided GaAs vertical cavity surface emitting lasers,” in Advances in Vertical Cavity Surface Emitting Lasers, C. Chang-Hasnain, ed., Vol. 15 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997), pp. 77–82.

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Figures (16)

Fig. 1
Fig. 1

Real and imaginary parts of optical susceptibility (χ) for three carrier densities computed from the microscopic theory (dashed curves) and fitted with the effective Lorentzian parameters (solid curves). QW, quantum well.

Fig. 2
Fig. 2

Index confinement and pumping current profiles (gain guidings) for disk- and ring-shaped contacts.

Fig. 3
Fig. 3

Snapshots of the near-field patterns at eight different moments for a gain-guided VCSEL 7.5 µm in diameter at J=0.7J0.

Fig. 4
Fig. 4

Time evolution of the local field for the gain-guided 7.5-µm VCSEL at J=0.7J0. The five locations are indicated in the inset.

Fig. 5
Fig. 5

Power spectra for the local fields and the average field presented in Fig. 4.

Fig. 6
Fig. 6

Snapshots of the near-field patterns at nine moments for a gain-guided VCSEL 7.5 µm in diameter at J=1.5J0.

Fig. 7
Fig. 7

(a) Time evolution and (b) power spectra for the local fields and the average field presented in Fig. 6.

Fig. 8
Fig. 8

Snapshots of the near-field patterns at 12 different moments for a gain- and index-guided VCSEL 7.5 µm in diameter at J=0.7J0.

Fig. 9
Fig. 9

Time evolution of the local fields and of the average field for the VCSEL of Fig. 8a. Letters a, c, t, b, r, and l have the same meanings as in Fig. 4.

Fig. 10
Fig. 10

Power spectra for the local fields and the average field presented in Fig. 9. Note that top and bottom (or left and right) signals have the same spectra.

Fig. 11
Fig. 11

Snapshots of the near-field patterns at different moments for the gain- and index-guided VCSEL 7.5 µm in diameter at J=1.5J0.

Fig. 12
Fig. 12

Time-averaged near-field patterns with (a–d) and without (e and f ) index guiding at J=0.7J0. c, d, f, 3D profiles. b, d, Averaged over 0.138 ns; a, c, averaged over 1.38 ns.

Fig. 13
Fig. 13

Time-averaged near field at J=1.5J0 without index guiding. a–c, Averaged over 0.138 ns; d, averaged over 1.38 ns.

Fig. 14
Fig. 14

3D profiles of the time-averaged near field at J=1.5J0 with index guiding; a and b are averaged over 0.138 and 1.38 ns; respectively.

Fig. 15
Fig. 15

3D profiles of the near field for a 15-µm device with index guiding averaged over 1.38 ns. The pumping currents are (from a to h) 0.3, 0.4, 0.5, 0.6, 0.7, 1.0, 1.25, and 1.5 times J0.

Fig. 16
Fig. 16

Contour images of the near field (a–e, snapshots; f, time averaged over 1.38 ns) of a ring VCSEL. Consult text for parameters.

Equations (3)

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

ngcEt=i2K2E-κE+i δn(x, y)KnbE+iKΓ20b(P0+P1),
P1t={-Γ1(N)+i[δ0-δ1(N)]}P1-i0bA1(N)E,
Nt=DNN-γnN+ηJ(x, y)e+i LΓ8[(P0+P1)*E-(P0+P1)E*],

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