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.

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References

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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 amplifiers," 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 "Microscopic 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 effects 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/~goorjian/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 Multitransverse Modes Vertical-Cavity Surface-Emitting Lasers," IEEE Photonics Tech. Letters, 10, 757-759, (1998).
    [CrossRef]

Other (17)

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

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, R. A. Indik and J. V. Moloney, "Effective Bloch-equations for semiconductor lasers and amplifiers," IEEE J. Quantum Electron. 33, 1543 (1997).
[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]

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

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

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/~goorjian/Pub/pub.html

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]

Y. Satuby and M. Orenstein, "Small-Signal Modulation of Multitransverse Modes Vertical-Cavity Surface-Emitting Lasers," IEEE Photonics Tech. Letters, 10, 757-759, (1998).
[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)

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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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