Abstract

We use an effective-index self-consistent dynamical model for vertical-cavity surface-emitting lasers (VCSELs) with cylindrical symmetry to show that self-sustained pulsations can appear in VCSELs with a small radius of the current aperture and a small built-in effective-index step. The appearance of these self-sustained pulsations is due to carrier-induced antiguiding: The waveguiding is improved during the front slope of the optical pulse as a result of the carrier depletion and is worsened on the back slope of the optical pulse because of the restoration of the carrier density.

© 2004 Optical Society of America

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    [CrossRef]
  2. L. A. D’Asaro, J. M. Cherlow, and T. L. Paoli, “Continuous microwave oscillations in GaAs junction laser,” IEEE J. Quantum Electron. 4, 164–167 (1968).
    [CrossRef]
  3. T. L. Paoli, “Changes in the optical properties of CW (AlGa)As junction lasers during accelerated aging,” IEEE J. Quantum Electron. 5, 351–359 (1977).
    [CrossRef]
  4. E. S. Yang, P. G. McMullin, A. W. Smith, J. Blum, and K. K. Shih, “Degradation-induced microwave oscillations in double-heterostructure injection lasers,” Appl. Phys. Lett. 24, 324–326 (1974).
    [CrossRef]
  5. R. W. Dixon and W. B. Joyce, “A possible model for sustained oscillations (pulsations) in (AlGa)As double-heterostructure lasers,” IEEE J. Quantum Electron. 15, 470–474 (1979).
    [CrossRef]
  6. T.-P. Lee and R. H. R. Roldax, “Repetitive Q-switched light pulses from GaAs injection lasers with tandem double-section stripe geometry,” IEEE J. Quantum Electron. 6, 339–352 (1970).
    [CrossRef]
  7. C. Harder, K. Y. Lau, and A. Yariv, “Bistability and pulsations in semiconductor lasers with inhomegeneous current injection,” IEEE J. Quantum Electron. 18, 1351–1361 (1982).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2004

2002

2001

T. W. Carr and T. Erneux, “Dimensionless rate equations and simple conditions,” IEEE J. Quantum Electron. 37, 1171–1177 (2001).
[CrossRef]

2000

M. B. Willemsen, A. S. van de Nes, M. P. van Exter, J. P. Woerdman, M. Brunner, and R. H. Hövel, “Self-pulsations in vertical-cavity semiconductor lasers,” Appl. Phys. Lett. 77, 3514–3516 (2000).
[CrossRef]

1999

C. R. Mirasso, G. H. M. van Tartwijk, E. Hernández-Garcia, D. Lenstra, S. Lynch, P. Landais, P. Phelan, J. O’Gorman, M. San Miguel, and W. Elsässer, “Self-pulsating semiconductor lasers: theory and experiment,” IEEE J. Quantum Electron. 35, 764–770 (1999).
[CrossRef]

1998

K. Panajotov, B. Ryvkin, J. Dackaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

1995

M. San Miguel, Q. Feng, and J. V. Moloney, “Light polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52, 1728–1739 (1995).
[CrossRef] [PubMed]

R. Hadley, “Effective index model for vertical-cavity surface-emitting lasers,” Opt. Lett. 20, 1483–1485 (1995).
[CrossRef] [PubMed]

D. G. H. Nugent, R. G. S. Plumb, M. A. Fisher, and D. A. O. Davies, “Self-pulsations in vertical-cavity surface-emitting lasers,” Electron. Lett. 31, 43–44 (1995).
[CrossRef]

A. Valle, J. Sarma, and K. A. Shore, “Secondary pulsations driven by spatial hole burning in modulated vertical-cavity surface-emitting laser diodes,” J. Opt. Soc. Am. B 12, 1741–1746 (1995).
[CrossRef]

1994

J. Buus, “Unstable waveguiding in VCSELs,” IEEE Photon. Technol. Lett. 6, 1179–1181 (1994).
[CrossRef]

1993

M. Yamada, “A theoretical analysis of self-sustained pulsation phenomena in narrow-stripe semiconductor lasers,” IEEE J. Quantum Electron. 29, 1330–1336 (1993).
[CrossRef]

1991

N. K. Dutta, L. W. Tu, G. Hasnain, G. Zydzik, Y. H. Wang, and A. Y. Cho, “Anomalous temporal response of gain guided surface emitting lasers,” Electron. Lett. 27, 208–210 (1991).
[CrossRef]

1990

N. K. Dutta, “Analysis of current spreading, carrier diffusion, and transverse mode guiding in surface emitting lasers,” J. Appl. Phys. 68, 1961–1963 (1990).
[CrossRef]

1982

C. Harder, K. Y. Lau, and A. Yariv, “Bistability and pulsations in semiconductor lasers with inhomegeneous current injection,” IEEE J. Quantum Electron. 18, 1351–1361 (1982).
[CrossRef]

1980

R. Lang, “Intensity pulsation enhancement by self-focusing in semiconductor injection lasers,” Jpn. J. Appl. Phys. 19, L93–L96 (1980).
[CrossRef]

1979

R. W. Dixon and W. B. Joyce, “A possible model for sustained oscillations (pulsations) in (AlGa)As double-heterostructure lasers,” IEEE J. Quantum Electron. 15, 470–474 (1979).
[CrossRef]

1977

T. L. Paoli, “Changes in the optical properties of CW (AlGa)As junction lasers during accelerated aging,” IEEE J. Quantum Electron. 5, 351–359 (1977).
[CrossRef]

1974

E. S. Yang, P. G. McMullin, A. W. Smith, J. Blum, and K. K. Shih, “Degradation-induced microwave oscillations in double-heterostructure injection lasers,” Appl. Phys. Lett. 24, 324–326 (1974).
[CrossRef]

1970

T.-P. Lee and R. H. R. Roldax, “Repetitive Q-switched light pulses from GaAs injection lasers with tandem double-section stripe geometry,” IEEE J. Quantum Electron. 6, 339–352 (1970).
[CrossRef]

1968

N. G. Basov, “Dynamics of injection lasers,” IEEE J. Quantum Electron. 4, 855–864 (1968).
[CrossRef]

L. A. D’Asaro, J. M. Cherlow, and T. L. Paoli, “Continuous microwave oscillations in GaAs junction laser,” IEEE J. Quantum Electron. 4, 164–167 (1968).
[CrossRef]

Basov, N. G.

N. G. Basov, “Dynamics of injection lasers,” IEEE J. Quantum Electron. 4, 855–864 (1968).
[CrossRef]

Blum, J.

E. S. Yang, P. G. McMullin, A. W. Smith, J. Blum, and K. K. Shih, “Degradation-induced microwave oscillations in double-heterostructure injection lasers,” Appl. Phys. Lett. 24, 324–326 (1974).
[CrossRef]

Brunner, M.

M. B. Willemsen, A. S. van de Nes, M. P. van Exter, J. P. Woerdman, M. Brunner, and R. H. Hövel, “Self-pulsations in vertical-cavity semiconductor lasers,” Appl. Phys. Lett. 77, 3514–3516 (2000).
[CrossRef]

Buus, J.

J. Buus, “Unstable waveguiding in VCSELs,” IEEE Photon. Technol. Lett. 6, 1179–1181 (1994).
[CrossRef]

Carr, T. W.

T. W. Carr and T. Erneux, “Dimensionless rate equations and simple conditions,” IEEE J. Quantum Electron. 37, 1171–1177 (2001).
[CrossRef]

Cherlow, J. M.

L. A. D’Asaro, J. M. Cherlow, and T. L. Paoli, “Continuous microwave oscillations in GaAs junction laser,” IEEE J. Quantum Electron. 4, 164–167 (1968).
[CrossRef]

Cho, A. Y.

N. K. Dutta, L. W. Tu, G. Hasnain, G. Zydzik, Y. H. Wang, and A. Y. Cho, “Anomalous temporal response of gain guided surface emitting lasers,” Electron. Lett. 27, 208–210 (1991).
[CrossRef]

D’Asaro, L. A.

L. A. D’Asaro, J. M. Cherlow, and T. L. Paoli, “Continuous microwave oscillations in GaAs junction laser,” IEEE J. Quantum Electron. 4, 164–167 (1968).
[CrossRef]

Dackaert, J.

K. Panajotov, B. Ryvkin, J. Dackaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

Danckaert, J.

Davies, D. A. O.

D. G. H. Nugent, R. G. S. Plumb, M. A. Fisher, and D. A. O. Davies, “Self-pulsations in vertical-cavity surface-emitting lasers,” Electron. Lett. 31, 43–44 (1995).
[CrossRef]

Dixon, R. W.

R. W. Dixon and W. B. Joyce, “A possible model for sustained oscillations (pulsations) in (AlGa)As double-heterostructure lasers,” IEEE J. Quantum Electron. 15, 470–474 (1979).
[CrossRef]

Dutta, N. K.

N. K. Dutta, L. W. Tu, G. Hasnain, G. Zydzik, Y. H. Wang, and A. Y. Cho, “Anomalous temporal response of gain guided surface emitting lasers,” Electron. Lett. 27, 208–210 (1991).
[CrossRef]

N. K. Dutta, “Analysis of current spreading, carrier diffusion, and transverse mode guiding in surface emitting lasers,” J. Appl. Phys. 68, 1961–1963 (1990).
[CrossRef]

Elsässer, W.

C. R. Mirasso, G. H. M. van Tartwijk, E. Hernández-Garcia, D. Lenstra, S. Lynch, P. Landais, P. Phelan, J. O’Gorman, M. San Miguel, and W. Elsässer, “Self-pulsating semiconductor lasers: theory and experiment,” IEEE J. Quantum Electron. 35, 764–770 (1999).
[CrossRef]

Erneux, T.

Feng, Q.

M. San Miguel, Q. Feng, and J. V. Moloney, “Light polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52, 1728–1739 (1995).
[CrossRef] [PubMed]

Fisher, M. A.

D. G. H. Nugent, R. G. S. Plumb, M. A. Fisher, and D. A. O. Davies, “Self-pulsations in vertical-cavity surface-emitting lasers,” Electron. Lett. 31, 43–44 (1995).
[CrossRef]

Hadley, R.

Harder, C.

C. Harder, K. Y. Lau, and A. Yariv, “Bistability and pulsations in semiconductor lasers with inhomegeneous current injection,” IEEE J. Quantum Electron. 18, 1351–1361 (1982).
[CrossRef]

Hasnain, G.

N. K. Dutta, L. W. Tu, G. Hasnain, G. Zydzik, Y. H. Wang, and A. Y. Cho, “Anomalous temporal response of gain guided surface emitting lasers,” Electron. Lett. 27, 208–210 (1991).
[CrossRef]

Hernández-Garcia, E.

C. R. Mirasso, G. H. M. van Tartwijk, E. Hernández-Garcia, D. Lenstra, S. Lynch, P. Landais, P. Phelan, J. O’Gorman, M. San Miguel, and W. Elsässer, “Self-pulsating semiconductor lasers: theory and experiment,” IEEE J. Quantum Electron. 35, 764–770 (1999).
[CrossRef]

Hövel, R. H.

M. B. Willemsen, A. S. van de Nes, M. P. van Exter, J. P. Woerdman, M. Brunner, and R. H. Hövel, “Self-pulsations in vertical-cavity semiconductor lasers,” Appl. Phys. Lett. 77, 3514–3516 (2000).
[CrossRef]

Joyce, W. B.

R. W. Dixon and W. B. Joyce, “A possible model for sustained oscillations (pulsations) in (AlGa)As double-heterostructure lasers,” IEEE J. Quantum Electron. 15, 470–474 (1979).
[CrossRef]

Landais, P.

C. R. Mirasso, G. H. M. van Tartwijk, E. Hernández-Garcia, D. Lenstra, S. Lynch, P. Landais, P. Phelan, J. O’Gorman, M. San Miguel, and W. Elsässer, “Self-pulsating semiconductor lasers: theory and experiment,” IEEE J. Quantum Electron. 35, 764–770 (1999).
[CrossRef]

Lang, R.

R. Lang, “Intensity pulsation enhancement by self-focusing in semiconductor injection lasers,” Jpn. J. Appl. Phys. 19, L93–L96 (1980).
[CrossRef]

Lau, K. Y.

C. Harder, K. Y. Lau, and A. Yariv, “Bistability and pulsations in semiconductor lasers with inhomegeneous current injection,” IEEE J. Quantum Electron. 18, 1351–1361 (1982).
[CrossRef]

Lee, T.-P.

T.-P. Lee and R. H. R. Roldax, “Repetitive Q-switched light pulses from GaAs injection lasers with tandem double-section stripe geometry,” IEEE J. Quantum Electron. 6, 339–352 (1970).
[CrossRef]

Lenstra, D.

C. R. Mirasso, G. H. M. van Tartwijk, E. Hernández-Garcia, D. Lenstra, S. Lynch, P. Landais, P. Phelan, J. O’Gorman, M. San Miguel, and W. Elsässer, “Self-pulsating semiconductor lasers: theory and experiment,” IEEE J. Quantum Electron. 35, 764–770 (1999).
[CrossRef]

Lynch, S.

C. R. Mirasso, G. H. M. van Tartwijk, E. Hernández-Garcia, D. Lenstra, S. Lynch, P. Landais, P. Phelan, J. O’Gorman, M. San Miguel, and W. Elsässer, “Self-pulsating semiconductor lasers: theory and experiment,” IEEE J. Quantum Electron. 35, 764–770 (1999).
[CrossRef]

McMullin, P. G.

E. S. Yang, P. G. McMullin, A. W. Smith, J. Blum, and K. K. Shih, “Degradation-induced microwave oscillations in double-heterostructure injection lasers,” Appl. Phys. Lett. 24, 324–326 (1974).
[CrossRef]

Mirasso, C. R.

A. Scirè, J. Mulet, C. R. Mirasso, and M. San Miguel, “Intensity and polarization self-pulsations in vertical-cavity surface-emitting lasers,” Opt. Lett. 27, 391–393 (2002).
[CrossRef]

C. R. Mirasso, G. H. M. van Tartwijk, E. Hernández-Garcia, D. Lenstra, S. Lynch, P. Landais, P. Phelan, J. O’Gorman, M. San Miguel, and W. Elsässer, “Self-pulsating semiconductor lasers: theory and experiment,” IEEE J. Quantum Electron. 35, 764–770 (1999).
[CrossRef]

Moloney, J. V.

M. San Miguel, Q. Feng, and J. V. Moloney, “Light polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52, 1728–1739 (1995).
[CrossRef] [PubMed]

Mulet, J.

Nugent, D. G. H.

D. G. H. Nugent, R. G. S. Plumb, M. A. Fisher, and D. A. O. Davies, “Self-pulsations in vertical-cavity surface-emitting lasers,” Electron. Lett. 31, 43–44 (1995).
[CrossRef]

O’Gorman, J.

C. R. Mirasso, G. H. M. van Tartwijk, E. Hernández-Garcia, D. Lenstra, S. Lynch, P. Landais, P. Phelan, J. O’Gorman, M. San Miguel, and W. Elsässer, “Self-pulsating semiconductor lasers: theory and experiment,” IEEE J. Quantum Electron. 35, 764–770 (1999).
[CrossRef]

Panajotov, K.

G. Van Der Sande, K. Panajotov, J. Danckaert, M. Peeters, I. Veretennicof, and T. Erneux, “Waveguiding effects in self-pulsing vertical-cavity surface-emitting lasers,” Opt. Lett. 29, 53–55 (2004).
[CrossRef] [PubMed]

K. Panajotov, B. Ryvkin, J. Dackaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

Paoli, T. L.

T. L. Paoli, “Changes in the optical properties of CW (AlGa)As junction lasers during accelerated aging,” IEEE J. Quantum Electron. 5, 351–359 (1977).
[CrossRef]

L. A. D’Asaro, J. M. Cherlow, and T. L. Paoli, “Continuous microwave oscillations in GaAs junction laser,” IEEE J. Quantum Electron. 4, 164–167 (1968).
[CrossRef]

Peeters, M.

G. Van Der Sande, K. Panajotov, J. Danckaert, M. Peeters, I. Veretennicof, and T. Erneux, “Waveguiding effects in self-pulsing vertical-cavity surface-emitting lasers,” Opt. Lett. 29, 53–55 (2004).
[CrossRef] [PubMed]

K. Panajotov, B. Ryvkin, J. Dackaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

Phelan, P.

C. R. Mirasso, G. H. M. van Tartwijk, E. Hernández-Garcia, D. Lenstra, S. Lynch, P. Landais, P. Phelan, J. O’Gorman, M. San Miguel, and W. Elsässer, “Self-pulsating semiconductor lasers: theory and experiment,” IEEE J. Quantum Electron. 35, 764–770 (1999).
[CrossRef]

Plumb, R. G. S.

D. G. H. Nugent, R. G. S. Plumb, M. A. Fisher, and D. A. O. Davies, “Self-pulsations in vertical-cavity surface-emitting lasers,” Electron. Lett. 31, 43–44 (1995).
[CrossRef]

Roldax, R. H. R.

T.-P. Lee and R. H. R. Roldax, “Repetitive Q-switched light pulses from GaAs injection lasers with tandem double-section stripe geometry,” IEEE J. Quantum Electron. 6, 339–352 (1970).
[CrossRef]

Ryvkin, B.

K. Panajotov, B. Ryvkin, J. Dackaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

San Miguel, M.

A. Scirè, J. Mulet, C. R. Mirasso, and M. San Miguel, “Intensity and polarization self-pulsations in vertical-cavity surface-emitting lasers,” Opt. Lett. 27, 391–393 (2002).
[CrossRef]

C. R. Mirasso, G. H. M. van Tartwijk, E. Hernández-Garcia, D. Lenstra, S. Lynch, P. Landais, P. Phelan, J. O’Gorman, M. San Miguel, and W. Elsässer, “Self-pulsating semiconductor lasers: theory and experiment,” IEEE J. Quantum Electron. 35, 764–770 (1999).
[CrossRef]

M. San Miguel, Q. Feng, and J. V. Moloney, “Light polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52, 1728–1739 (1995).
[CrossRef] [PubMed]

Sarma, J.

Scirè, A.

Shih, K. K.

E. S. Yang, P. G. McMullin, A. W. Smith, J. Blum, and K. K. Shih, “Degradation-induced microwave oscillations in double-heterostructure injection lasers,” Appl. Phys. Lett. 24, 324–326 (1974).
[CrossRef]

Shore, K. A.

Smith, A. W.

E. S. Yang, P. G. McMullin, A. W. Smith, J. Blum, and K. K. Shih, “Degradation-induced microwave oscillations in double-heterostructure injection lasers,” Appl. Phys. Lett. 24, 324–326 (1974).
[CrossRef]

Thienpont, H.

K. Panajotov, B. Ryvkin, J. Dackaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

Tu, L. W.

N. K. Dutta, L. W. Tu, G. Hasnain, G. Zydzik, Y. H. Wang, and A. Y. Cho, “Anomalous temporal response of gain guided surface emitting lasers,” Electron. Lett. 27, 208–210 (1991).
[CrossRef]

Valle, A.

van de Nes, A. S.

M. B. Willemsen, A. S. van de Nes, M. P. van Exter, J. P. Woerdman, M. Brunner, and R. H. Hövel, “Self-pulsations in vertical-cavity semiconductor lasers,” Appl. Phys. Lett. 77, 3514–3516 (2000).
[CrossRef]

Van Der Sande, G.

van Exter, M. P.

M. B. Willemsen, A. S. van de Nes, M. P. van Exter, J. P. Woerdman, M. Brunner, and R. H. Hövel, “Self-pulsations in vertical-cavity semiconductor lasers,” Appl. Phys. Lett. 77, 3514–3516 (2000).
[CrossRef]

van Tartwijk, G. H. M.

C. R. Mirasso, G. H. M. van Tartwijk, E. Hernández-Garcia, D. Lenstra, S. Lynch, P. Landais, P. Phelan, J. O’Gorman, M. San Miguel, and W. Elsässer, “Self-pulsating semiconductor lasers: theory and experiment,” IEEE J. Quantum Electron. 35, 764–770 (1999).
[CrossRef]

Veretennicof, I.

Veretennicoff, I.

K. Panajotov, B. Ryvkin, J. Dackaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photon. Technol. Lett. 10, 6–8 (1998).
[CrossRef]

Wang, Y. H.

N. K. Dutta, L. W. Tu, G. Hasnain, G. Zydzik, Y. H. Wang, and A. Y. Cho, “Anomalous temporal response of gain guided surface emitting lasers,” Electron. Lett. 27, 208–210 (1991).
[CrossRef]

Willemsen, M. B.

M. B. Willemsen, A. S. van de Nes, M. P. van Exter, J. P. Woerdman, M. Brunner, and R. H. Hövel, “Self-pulsations in vertical-cavity semiconductor lasers,” Appl. Phys. Lett. 77, 3514–3516 (2000).
[CrossRef]

Woerdman, J. P.

M. B. Willemsen, A. S. van de Nes, M. P. van Exter, J. P. Woerdman, M. Brunner, and R. H. Hövel, “Self-pulsations in vertical-cavity semiconductor lasers,” Appl. Phys. Lett. 77, 3514–3516 (2000).
[CrossRef]

Yamada, M.

M. Yamada, “A theoretical analysis of self-sustained pulsation phenomena in narrow-stripe semiconductor lasers,” IEEE J. Quantum Electron. 29, 1330–1336 (1993).
[CrossRef]

Yang, E. S.

E. S. Yang, P. G. McMullin, A. W. Smith, J. Blum, and K. K. Shih, “Degradation-induced microwave oscillations in double-heterostructure injection lasers,” Appl. Phys. Lett. 24, 324–326 (1974).
[CrossRef]

Yariv, A.

C. Harder, K. Y. Lau, and A. Yariv, “Bistability and pulsations in semiconductor lasers with inhomegeneous current injection,” IEEE J. Quantum Electron. 18, 1351–1361 (1982).
[CrossRef]

Zydzik, G.

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Figures (11)

Fig. 1
Fig. 1

VCSEL output power versus time for a stepwise injection current with duration of 20 ns of each step of 0.2 mA. The onset of self-pulsation happens at approximately 3 mA. At approximately 5.5 mA, the laser action ceases.

Fig. 2
Fig. 2

Detailed time traces from Fig. 1 at a fixed dc: (a) J=2.6 mA, (b) J=2.7 mA, (c) J=2.8 mA, (d) J=3.0 mA, (e) J=3.4 mA, (f) J=4.0 mA, (g) J=4.6 mA, (h) J=5.0 mA, and (i) J=5.4 mA.

Fig. 3
Fig. 3

Optical spectra calculated as Fourier transforms of the complex electric field time traces taken at the center of the oxide aperture (r=0) for the typical SSP regimes from Fig. 2.

Fig. 4
Fig. 4

Power spectra calculated as Fourier transforms of the output-power time traces for the typical SSP regimes from Fig. 2.

Fig. 5
Fig. 5

Development of the carrier density N (gray curve) and the output power P (black curve) during the buildup of the optical pulse. The arrows point to four characteristic moments in the pulse formation, which are considered further in Fig. 6.

Fig. 6
Fig. 6

(a) Radial distribution of the carrier density, (b) the refractive index, and (c) the optical power at the different characteristic moments during the pulse development shown in Fig. 5: black (gray) curve for the maximum (minimum) of the optical power (solid curve) and carrier density (dashed curve).

Fig. 7
Fig. 7

Development of the carrier density N (gray curve) and the intracavity optical power P (black curve) during the buildup of the optical pulse for different injection currents: (a) J=3 mA and (b) J=4 mA.

Fig. 8
Fig. 8

Development of the carrier density N (gray curves) and the intracavity optical power P (black curves) during the buildup of the optical pulse for different radial positions: at the center of the oxide aperture, r=0 (continuous curves), and at the aperture rim, r=2 µm (dashed curves).

Fig. 9
Fig. 9

VCSEL output power versus time for a stepwise injection current with duration of 20 ns of each step of 0.04 mA for the case of TL. The lasers start operating in a SSP regime that undergoes a transition to steady state at J4.3 mA.

Fig. 10
Fig. 10

Frequency of SSP fSSP as a function of the injection current J for the case of built-in index guiding (VCSEL parameters as in Fig. 1) and for the case of TL (VCSEL parameters as in Fig. 9).

Fig. 11
Fig. 11

Time traces of polarization-resolved output power during SSP in VCSEL; cavity birefringence and dichroism, are taken into account.

Tables (1)

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Table 1 VCSEL Parameters Used in the Calculations

Equations (8)

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E(r, z, t)=E(r, t)Ψ(z)exp(-jωt).
Ei 2Ψiz2+Ψi 1r r r Eir+ωi2c2(i+Δi)ΨiEi
+j2ωic2iΨi Eit=0.
2Ψiz2+ωi2c2iΨi=ωi2c2neff,i2Ψi.
Ei(r, t)t=jc22ωii(r, t) ωi2c2[Δi(r, t)+neff,i2(r, t)]+1r r r rEi(r, t),
A=Ψ*(z;r)A(z;r)Ψ(z;r)dzΨ*(z;r)Ψ(z;r)dz.
Δi(r, t)=2dnidTniT(r, t)-j αtot,ik0-j aik0 lnNNtri-2ni dnidNN(r, t),
N(r, t)t=Dn 1r r r N(r, t)r+j(r, t)ed-N(r, t)τe-Rstim(r, t),

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