Abstract

The semiconductor laser simulator MINILASE is being extended to simulate vertical cavity surface emitting lasers (VCSELs). The electronic system analysis for VCSELs is identical to that for edge emitting lasers. A brief discussion of the capabilities of MINILASE in this domain will be presented. In order to simulate VCSELs, the optical mode solver in MINILASE must be extended to handle the reduced index guiding and significant gain guiding typical of many VCSEL structures. A new approach to solving the optical problem which employs active cavity modes rather than the standard passive cavity modes is developed. This new approach results in an integral eigenvalue equation in required gain amplitudes and corresponding modal fields. Sample results from an early implementation of a gain eigenvalue solver are shown to clarify the possibilities of this approach.

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References

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  1. D. Burak and R. Binder, "Cold-Cavity Vectorial Eigenmodes of VCSEL's," IEEE J. Quantum Electron. 33, 1205-1215 (1997).
    [CrossRef]
  2. C.C. Lin and D.G. Deppe, "Self-Consistent Calculation of Lasing Modes in a Planar Microcavity," J. Lightwave Technol. 13, 575-580 (1995).
    [CrossRef]
  3. H. Bissessur and K. Iga, "FD-BPM Modeling of Vertical Cavity Surface Emitting Lasers," Proc. SPIE 2994, 150-158 (1997).
    [CrossRef]
  4. 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]
  5. M. Grupen, G. Kosinovsky, and K. Hess, "The eect of carrier capture on the modulation bandwidth of quantum well lasers," in Proceedings of the International Electron Devices Meeting, (IEEE Electron Devices Society, Washington, D.C., 1993) pp. 23.6.1-23.6.4.
  6. S. Selberherr, Analysis and Simulation of Semiconductor Devices (Springer-Verlag, Wien-New York, 1984).
    [CrossRef]
  7. M. Grupen, K. Hess, and G.H. Song, "Simulation of transport over heterojunctions," in Proc. 4th International Conf. Simul. Semicon. Dev. Process., Vol. 4 (IEEE Electron Devices Society, Zurich, 1991) p. 303-311.
  8. M. Grupen and K. Hess, "Severe gain suppression due to dynamic carrier heating in quantum well lasers," Appl. Phys. Lett. 70, 808-810 (1997).
    [CrossRef]
  9. M. Grupen and K. Hess, "Simulation of carrier transport and nonlinearities in quantum well laser diodes," IEEE J. Quantum Electron. 34, 120-140 (1998).
    [CrossRef]
  10. G.P. Agrawal and N.K. Dutta, Semiconductor Lasers, Second Edition (Van Nostrand Reinhold, New York, 1993) pp. 39-55.
  11. W.C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990) pp. 57-79, 375-418.

Other (11)

D. Burak and R. Binder, "Cold-Cavity Vectorial Eigenmodes of VCSEL's," IEEE J. Quantum Electron. 33, 1205-1215 (1997).
[CrossRef]

C.C. Lin and D.G. Deppe, "Self-Consistent Calculation of Lasing Modes in a Planar Microcavity," J. Lightwave Technol. 13, 575-580 (1995).
[CrossRef]

H. Bissessur and K. Iga, "FD-BPM Modeling of Vertical Cavity Surface Emitting Lasers," Proc. SPIE 2994, 150-158 (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]

M. Grupen, G. Kosinovsky, and K. Hess, "The eect of carrier capture on the modulation bandwidth of quantum well lasers," in Proceedings of the International Electron Devices Meeting, (IEEE Electron Devices Society, Washington, D.C., 1993) pp. 23.6.1-23.6.4.

S. Selberherr, Analysis and Simulation of Semiconductor Devices (Springer-Verlag, Wien-New York, 1984).
[CrossRef]

M. Grupen, K. Hess, and G.H. Song, "Simulation of transport over heterojunctions," in Proc. 4th International Conf. Simul. Semicon. Dev. Process., Vol. 4 (IEEE Electron Devices Society, Zurich, 1991) p. 303-311.

M. Grupen and K. Hess, "Severe gain suppression due to dynamic carrier heating in quantum well lasers," Appl. Phys. Lett. 70, 808-810 (1997).
[CrossRef]

M. Grupen and K. Hess, "Simulation of carrier transport and nonlinearities in quantum well laser diodes," IEEE J. Quantum Electron. 34, 120-140 (1998).
[CrossRef]

G.P. Agrawal and N.K. Dutta, Semiconductor Lasers, Second Edition (Van Nostrand Reinhold, New York, 1993) pp. 39-55.

W.C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990) pp. 57-79, 375-418.

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Figures (3)

Fig. 1.
Fig. 1.

Index guided VCSEL structure used to generate results described below. λo =1 μm

Fig. 2.
Fig. 2.

First six complex gain eigenvalues plotted at discrete intervals in frequecy; the first two are essentially degenerate. The gain eigenvalues corresponding to the first three modes are circled and labeled. A mode can lase only at the frequency at which its gain eigenvalue curve crosses the real axis. Therefore modes 1&2 lase at λ ≃ 1.0007λo and mode 3 lases at λ ≃ 0.9999λo . The magnitude of K at the crossing frequency determines the amount of gain required for the corresponding mode to lase. Thus we see that mode 3 requires more gain to lase than modes 1&2.

Fig. 3.
Fig. 3.

Transverse mode patterns of the (a) first and second, and (b) third optical modes. The first mode is primarily -polarized and the second is primarily ŷ polarized. The third mode is primarily ŷ-polarized. The next three modes shown in Fig. 2 are permutations of the third mode, with either field pattern or polarization rotated 90 degrees, or both.

Equations (10)

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dS dt = S ( G 1 τ phot ) + R spon
( r , ω ) = o [ cav ( r , ω ) + χ gain ( r , ω ) ]
× × E ( r , ω ) ω 2 μ o o cav ( r , ω ) E ( r , ω ) = ω 2 μ o o χ gain ( r , ω ) E ( r , ω )
= μ o J stim ( r , ω )
E ( r , ω ) = d 3 r G cav ( r , r ω ) · J stim ( r , ω )
= d 3 r G cav ( r , r ω ) · [ i ω o χ gain ( r , ω ) E ( r , ω ) ] ,
1 κ ( ω ) E ( r , ω ) = G ( ω ) · χ gain ( 0 ) E ( r , ω ) ,
G · χ gain ( 0 ) E ( r ) i ω o d r G cav ( r , r ) · [ χ gain ( 0 ) ( r ) E ( r ) ] .
( r , ω ) = o [ cav ( r , ω ) + χ cav ( r , ω ) + χ gain ( r , ω ) ]
1 κ ( ω ) ( 1 G ( ω ) χ cav ) · E ( r , ω ) = G ( ω ) χ gain ( 0 ) · E ( r , ω ) .

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