Abstract

An approximation to the Maxwell-Semiconductor Bloch equations is used to model transverse mode dynamics of vertical-cavity surface-emitting lasers (VCSELs). The time-evolution of the spatial profiles of the laser field and carrier density is solved by a finite-difference algorithm. The algorithm is fairly general; it can handle devices of any shape, which are either gain or index guided or both. Also there is no a priori assumption about the type or number of modes. The physical modeling includes the nonlinear carrier dependence of the optical gain and refractive index and dispersion effects on the gain and the refractive index are also included.

© 1999 Optical Society of America

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  1. W. W. Chow, S. W. Koch, and M. Sargent, Semiconductor Laser Physics, (Springer, Heidelberg, Berlin, 1994).
    [Crossref]
  2. J. Y. Law, G. H. M. van Tartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on the injection dynamics of vertical-cavity surface-emitting lasers,” Quantum Semiclass. Opt.,  9, 737 (1997).
    [Crossref]
  3. P. M. Goorjian and G. P. Agrawal, “Computational Modeling of Ultrashort Optical Pulse Propagation in Nonlinear Optical Materials,” Paper NME31, Nonlinear Optics: Materials, Fundamentals and Applications, 11, 1996 OSA Technical Digest Series, Washington, D.C., 1996, 132–133.
  4. P. M. Goorjian and G. P. Agrawal, “Computational Modeling of Ultrafast Optical Pulse Propagation in Semiconductor Materials,” Paper QThE9, Quantum Optoelectronics, Spring Topical Meeting, OSA, Washington, D. C, Nevada, March 17–21, 1997.
  5. P. M. Goorjian and G. P. Agrawal, “Maxwell-Bloch Equations Modeling of Ultrashort Optical Pulse Propagation in Semiconductor Materials,” Paper WB2, OSA 1997 Annual Meeting, Washington, D. C, October 12–17, 1997.
  6. C. Z. Ning, R. A. Indik, and J. V. Moloney, “Effective Bloch-equations for semiconductor lasers and ampliers,” IEEE J. Quantum Electron. 33, 1543 (1997).
    [Crossref]
  7. T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney, and C. Z. Ning, “Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers,” Phys. Rev. A 58, 3279 (1998).
    [Crossref]
  8. C. Z. Ning, J. V. Moloney, and R. A. Indik, “A first-principles fully space-time resolved model of a semiconductor laser,” Quantum Semiclass. Opt.,  9, 681(1997).
    [Crossref]
  9. A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. W. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic Instabilities in MFA-MOPA Semiconductor Lasers,” IEEE J. Quantum Electron. 34, 166, (1998).
    [Crossref]
  10. C. Z. Ning, S. Bischoff, S. W. Koch, G. K. Harkness, J. V. Moloney, and W. W. Chow “Micro-scopic Modeling of VCSELs: Many-body interaction, plasma heating, and transverse dynamics,” Optical Engineering, April, 1998.
  11. C. Z. Ning, R. A. Indik, and J. V. Moloney, “A self-consistent approach to thermal e ects in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 12, 1993–2004, 1995.
    [Crossref]
  12. P. M. Goorjian and C. Z. Ning, “Computational Modeling of Vertical-Cavity Surface-Emitting Lasers,” Paper Thc15, Nonlinear Optics Topical Meeting, Kauai, HI, August 9–14, 1998.
  13. P. M. Goorjian and C. Z. Ning, “Simulation of Transverse Modes in Vertical-Cavity Surface-Emitting Lasers,” 1998 Annual Meeting of the Optical Society of America, Washington, D. C, October 5–9, 1998.
  14. P. M. Goorjian and C. Z. Ning, “Transverse Mode Dynamics of VCSELs through Space-Time Simulation,” Paper 3625–45, Integrated Optoelectronic Devices, Photonics West, 1999, (SPIE), San Jose, CA, January 23–29, 1999.
  15. P. M. Goorjian and C. Z. Ning, “Transverse Mode Dynamics of VCSELs through Space-Time Simulation,” http://science.nas.nasa.gov/egoorjian/Pub/pub.html
  16. C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. 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]
  17. Y. Satuby and M. Orenstein, “Small-Signal Modulation of MultitransverseModes Vertical-Cavity Surface-Emitting Lasers,” IEEE Photonics Tech. Letters,  10, 757–759, (1998).
    [Crossref]

1998 (3)

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

A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. W. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic Instabilities in MFA-MOPA Semiconductor Lasers,” IEEE J. Quantum Electron. 34, 166, (1998).
[Crossref]

Y. Satuby and M. Orenstein, “Small-Signal Modulation of MultitransverseModes Vertical-Cavity Surface-Emitting Lasers,” IEEE Photonics Tech. Letters,  10, 757–759, (1998).
[Crossref]

1997 (3)

C. Z. Ning, J. V. Moloney, and R. A. Indik, “A first-principles fully space-time resolved model of a semiconductor laser,” Quantum Semiclass. Opt.,  9, 681(1997).
[Crossref]

J. Y. Law, G. H. M. van Tartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on the injection dynamics of vertical-cavity surface-emitting lasers,” Quantum Semiclass. Opt.,  9, 737 (1997).
[Crossref]

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

1995 (1)

1991 (1)

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. 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]

Agrawal, G. P.

J. Y. Law, G. H. M. van Tartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on the injection dynamics of vertical-cavity surface-emitting lasers,” Quantum Semiclass. Opt.,  9, 737 (1997).
[Crossref]

P. M. Goorjian and G. P. Agrawal, “Computational Modeling of Ultrashort Optical Pulse Propagation in Nonlinear Optical Materials,” Paper NME31, Nonlinear Optics: Materials, Fundamentals and Applications, 11, 1996 OSA Technical Digest Series, Washington, D.C., 1996, 132–133.

P. M. Goorjian and G. P. Agrawal, “Computational Modeling of Ultrafast Optical Pulse Propagation in Semiconductor Materials,” Paper QThE9, Quantum Optoelectronics, Spring Topical Meeting, OSA, Washington, D. C, Nevada, March 17–21, 1997.

P. M. Goorjian and G. P. Agrawal, “Maxwell-Bloch Equations Modeling of Ultrashort Optical Pulse Propagation in Semiconductor Materials,” Paper WB2, OSA 1997 Annual Meeting, Washington, D. C, October 12–17, 1997.

Bischoff, S.

C. Z. Ning, S. Bischoff, S. W. Koch, G. K. Harkness, J. V. Moloney, and W. W. Chow “Micro-scopic Modeling of VCSELs: Many-body interaction, plasma heating, and transverse dynamics,” Optical Engineering, April, 1998.

Bossert, D. J.

A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. W. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic Instabilities in MFA-MOPA Semiconductor Lasers,” IEEE J. Quantum Electron. 34, 166, (1998).
[Crossref]

Chang-Hasnain, C. J.

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

Chow, W. W.

C. Z. Ning, S. Bischoff, S. W. Koch, G. K. Harkness, J. V. Moloney, and W. W. Chow “Micro-scopic Modeling of VCSELs: Many-body interaction, plasma heating, and transverse dynamics,” Optical Engineering, April, 1998.

W. W. Chow, S. W. Koch, and M. Sargent, Semiconductor Laser Physics, (Springer, Heidelberg, Berlin, 1994).
[Crossref]

Egan, A.

A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. W. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic Instabilities in MFA-MOPA Semiconductor Lasers,” IEEE J. Quantum Electron. 34, 166, (1998).
[Crossref]

Florez, L. T.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. 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]

Goorjian, P. M.

P. M. Goorjian and C. Z. Ning, “Computational Modeling of Vertical-Cavity Surface-Emitting Lasers,” Paper Thc15, Nonlinear Optics Topical Meeting, Kauai, HI, August 9–14, 1998.

P. M. Goorjian and C. Z. Ning, “Simulation of Transverse Modes in Vertical-Cavity Surface-Emitting Lasers,” 1998 Annual Meeting of the Optical Society of America, Washington, D. C, October 5–9, 1998.

P. M. Goorjian and C. Z. Ning, “Transverse Mode Dynamics of VCSELs through Space-Time Simulation,” Paper 3625–45, Integrated Optoelectronic Devices, Photonics West, 1999, (SPIE), San Jose, CA, January 23–29, 1999.

P. M. Goorjian and C. Z. Ning, “Transverse Mode Dynamics of VCSELs through Space-Time Simulation,” http://science.nas.nasa.gov/egoorjian/Pub/pub.html

P. M. Goorjian and G. P. Agrawal, “Computational Modeling of Ultrafast Optical Pulse Propagation in Semiconductor Materials,” Paper QThE9, Quantum Optoelectronics, Spring Topical Meeting, OSA, Washington, D. C, Nevada, March 17–21, 1997.

P. M. Goorjian and G. P. Agrawal, “Computational Modeling of Ultrashort Optical Pulse Propagation in Nonlinear Optical Materials,” Paper NME31, Nonlinear Optics: Materials, Fundamentals and Applications, 11, 1996 OSA Technical Digest Series, Washington, D.C., 1996, 132–133.

P. M. Goorjian and G. P. Agrawal, “Maxwell-Bloch Equations Modeling of Ultrashort Optical Pulse Propagation in Semiconductor Materials,” Paper WB2, OSA 1997 Annual Meeting, Washington, D. C, October 12–17, 1997.

Harbison, J. P.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. 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.

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

C. Z. Ning, S. Bischoff, S. W. Koch, G. K. Harkness, J. V. Moloney, and W. W. Chow “Micro-scopic Modeling of VCSELs: Many-body interaction, plasma heating, and transverse dynamics,” Optical Engineering, April, 1998.

Hasnain, G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. 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]

Indik, R. A.

A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. W. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic Instabilities in MFA-MOPA Semiconductor Lasers,” IEEE J. Quantum Electron. 34, 166, (1998).
[Crossref]

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

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

C. Z. Ning, J. V. Moloney, and R. A. Indik, “A first-principles fully space-time resolved model of a semiconductor laser,” Quantum Semiclass. Opt.,  9, 681(1997).
[Crossref]

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

Koch, S. W.

C. Z. Ning, S. Bischoff, S. W. Koch, G. K. Harkness, J. V. Moloney, and W. W. Chow “Micro-scopic Modeling of VCSELs: Many-body interaction, plasma heating, and transverse dynamics,” Optical Engineering, April, 1998.

W. W. Chow, S. W. Koch, and M. Sargent, Semiconductor Laser Physics, (Springer, Heidelberg, Berlin, 1994).
[Crossref]

Law, J. Y.

J. Y. Law, G. H. M. van Tartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on the injection dynamics of vertical-cavity surface-emitting lasers,” Quantum Semiclass. Opt.,  9, 737 (1997).
[Crossref]

McInerney, J. G.

A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. W. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic Instabilities in MFA-MOPA Semiconductor Lasers,” IEEE J. Quantum Electron. 34, 166, (1998).
[Crossref]

Moloney, J. V.

A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. W. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic Instabilities in MFA-MOPA Semiconductor Lasers,” IEEE J. Quantum Electron. 34, 166, (1998).
[Crossref]

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

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

C. Z. Ning, J. V. Moloney, and R. A. Indik, “A first-principles fully space-time resolved model of a semiconductor laser,” Quantum Semiclass. Opt.,  9, 681(1997).
[Crossref]

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

C. Z. Ning, S. Bischoff, S. W. Koch, G. K. Harkness, J. V. Moloney, and W. W. Chow “Micro-scopic Modeling of VCSELs: Many-body interaction, plasma heating, and transverse dynamics,” Optical Engineering, April, 1998.

Ning, C. Z.

A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. W. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic Instabilities in MFA-MOPA Semiconductor Lasers,” IEEE J. Quantum Electron. 34, 166, (1998).
[Crossref]

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

C. Z. Ning, J. V. Moloney, and R. A. Indik, “A first-principles fully space-time resolved model of a semiconductor laser,” Quantum Semiclass. Opt.,  9, 681(1997).
[Crossref]

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

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

P. M. Goorjian and C. Z. Ning, “Simulation of Transverse Modes in Vertical-Cavity Surface-Emitting Lasers,” 1998 Annual Meeting of the Optical Society of America, Washington, D. C, October 5–9, 1998.

P. M. Goorjian and C. Z. Ning, “Computational Modeling of Vertical-Cavity Surface-Emitting Lasers,” Paper Thc15, Nonlinear Optics Topical Meeting, Kauai, HI, August 9–14, 1998.

P. M. Goorjian and C. Z. Ning, “Transverse Mode Dynamics of VCSELs through Space-Time Simulation,” http://science.nas.nasa.gov/egoorjian/Pub/pub.html

P. M. Goorjian and C. Z. Ning, “Transverse Mode Dynamics of VCSELs through Space-Time Simulation,” Paper 3625–45, Integrated Optoelectronic Devices, Photonics West, 1999, (SPIE), San Jose, CA, January 23–29, 1999.

C. Z. Ning, S. Bischoff, S. W. Koch, G. K. Harkness, J. V. Moloney, and W. W. Chow “Micro-scopic Modeling of VCSELs: Many-body interaction, plasma heating, and transverse dynamics,” Optical Engineering, April, 1998.

Orenstein, M.

Y. Satuby and M. Orenstein, “Small-Signal Modulation of MultitransverseModes Vertical-Cavity Surface-Emitting Lasers,” IEEE Photonics Tech. Letters,  10, 757–759, (1998).
[Crossref]

Rossler, T.

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

Sargent, M.

W. W. Chow, S. W. Koch, and M. Sargent, Semiconductor Laser Physics, (Springer, Heidelberg, Berlin, 1994).
[Crossref]

Satuby, Y.

Y. Satuby and M. Orenstein, “Small-Signal Modulation of MultitransverseModes Vertical-Cavity Surface-Emitting Lasers,” IEEE Photonics Tech. Letters,  10, 757–759, (1998).
[Crossref]

Stoffel, N. G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. 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]

van Tartwijk, G. H. M.

J. Y. Law, G. H. M. van Tartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on the injection dynamics of vertical-cavity surface-emitting lasers,” Quantum Semiclass. Opt.,  9, 737 (1997).
[Crossref]

Von Lehmen, A. C.

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

Wright, M. W.

A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. W. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic Instabilities in MFA-MOPA Semiconductor Lasers,” IEEE J. Quantum Electron. 34, 166, (1998).
[Crossref]

IEEE J. Quantum Electron. (3)

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

A. Egan, C. Z. Ning, J. V. Moloney, R. A. Indik, M. W. Wright, D. J. Bossert, and J. G. McInerney, “Dynamic Instabilities in MFA-MOPA Semiconductor Lasers,” IEEE J. Quantum Electron. 34, 166, (1998).
[Crossref]

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. 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]

IEEE Photonics Tech. Letters (1)

Y. Satuby and M. Orenstein, “Small-Signal Modulation of MultitransverseModes Vertical-Cavity Surface-Emitting Lasers,” IEEE Photonics Tech. Letters,  10, 757–759, (1998).
[Crossref]

J. Opt. Soc. Am. B (1)

Phys. Rev. A (1)

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

Quantum Semiclass. Opt. (2)

C. Z. Ning, J. V. Moloney, and R. A. Indik, “A first-principles fully space-time resolved model of a semiconductor laser,” Quantum Semiclass. Opt.,  9, 681(1997).
[Crossref]

J. Y. Law, G. H. M. van Tartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on the injection dynamics of vertical-cavity surface-emitting lasers,” Quantum Semiclass. Opt.,  9, 737 (1997).
[Crossref]

Other (9)

P. M. Goorjian and G. P. Agrawal, “Computational Modeling of Ultrashort Optical Pulse Propagation in Nonlinear Optical Materials,” Paper NME31, Nonlinear Optics: Materials, Fundamentals and Applications, 11, 1996 OSA Technical Digest Series, Washington, D.C., 1996, 132–133.

P. M. Goorjian and G. P. Agrawal, “Computational Modeling of Ultrafast Optical Pulse Propagation in Semiconductor Materials,” Paper QThE9, Quantum Optoelectronics, Spring Topical Meeting, OSA, Washington, D. C, Nevada, March 17–21, 1997.

P. M. Goorjian and G. P. Agrawal, “Maxwell-Bloch Equations Modeling of Ultrashort Optical Pulse Propagation in Semiconductor Materials,” Paper WB2, OSA 1997 Annual Meeting, Washington, D. C, October 12–17, 1997.

C. Z. Ning, S. Bischoff, S. W. Koch, G. K. Harkness, J. V. Moloney, and W. W. Chow “Micro-scopic Modeling of VCSELs: Many-body interaction, plasma heating, and transverse dynamics,” Optical Engineering, April, 1998.

P. M. Goorjian and C. Z. Ning, “Computational Modeling of Vertical-Cavity Surface-Emitting Lasers,” Paper Thc15, Nonlinear Optics Topical Meeting, Kauai, HI, August 9–14, 1998.

P. M. Goorjian and C. Z. Ning, “Simulation of Transverse Modes in Vertical-Cavity Surface-Emitting Lasers,” 1998 Annual Meeting of the Optical Society of America, Washington, D. C, October 5–9, 1998.

P. M. Goorjian and C. Z. Ning, “Transverse Mode Dynamics of VCSELs through Space-Time Simulation,” Paper 3625–45, Integrated Optoelectronic Devices, Photonics West, 1999, (SPIE), San Jose, CA, January 23–29, 1999.

P. M. Goorjian and C. Z. Ning, “Transverse Mode Dynamics of VCSELs through Space-Time Simulation,” http://science.nas.nasa.gov/egoorjian/Pub/pub.html

W. W. Chow, S. W. Koch, and M. Sargent, Semiconductor Laser Physics, (Springer, Heidelberg, Berlin, 1994).
[Crossref]

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Figures (10)

Figure 1.
Figure 1.

The Computed gain spectra (dashed lines) and parameter gain spectra (solid lines); here the gain equals G(ω,N)=-KIm(X(ω;N))

Figure 2.
Figure 2.

Steady Laser Intensity Field

Figure 3.
Figure 3.

Instantaneous Light Field

Figure 4.
Figure 4.

Average Light Field

Figure 5.
Figure 5.

Instantaneous Light Field

Figure 6.
Figure 6.

Average Light Field

Figure 7.
Figure 7.

Instantaneous Light Field

Figure 8.
Figure 8.

Average Light Field

Figure 9.
Figure 9.

Instantaneous Light Field

Figure 10.
Figure 10.

Average Light Field

Equations (8)

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

n g c E t = i 2 K 2 E κ E + i KT 2 0 b P + i δ n ( x , y ) n b KE
N t = D N N γ n N + η J ( x , y ) e + L Γ 2 i 4 ( P * E P E * )
P = P 0 + P 1
P 0 = 0 b χ 0 ( N ) E
d P 1 dt = Γ 1 ( N ) P 1 + i ( ω c ω 1 ( N ) ) P 1 i 0 b A 1 ( N ) E
P ( ω ) = 0 b χ ( ω , N ) E ( ω )
χ ( ω , N ) = 2 n b δ n ( ω , N ) i K G ( ω , N )
χ ( ω , N ) χ 0 ( N ) + χ 1 ( ω , N ) χ 0 ( N ) + A 1 ( N ) i Γ 1 ( N ) + ( ω c + ω ω 1 ( N ) )

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