Abstract

A theoretical analysis has been undertaken of steady-state transverse-mode selection in vertical-cavity surface-emitting lasers (VCSEL’s) that are subject to optical feedback in an external-cavity configuration. Multiple reflections in the external cavity are taken into account. The influence of thermal effects on mode selection is also treated, and noise properties of the configuration are discussed. In the analysis specific attention is paid to the competition between the two lowest-order modes (LP01 and LP11 degenerate modes) that are appropriate to the chosen circularly symmetric vertical-cavity surface-emitting laser structure. It is shown that preferential excitation of either mode can be effected by the appropriate choice of optical feedback delay. It is also shown that multiple reflections in the external cavity can affect the mode selection, depending on the optical feedback delay. Thermal effects are shown to be detrimental for transverse-mode selection. Strategies for the minimization of thermal effects on mode selection are also discussed. Finally, the relative intensity noise spectrum for each transverse mode is shown to maintain its double-peaked structure and low mode-partition noise in the presence of optical feedback. A change from a twin-peaked to a single-peaked structure of this spectrum is also observed when the optical feedback delay is changed.

© 1999 Optical Society of America

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  1. C. J. Chang-Hasnain, M. Orenstein, A. C. von Lehmen, L. T. Florez, J. P. Harbison, and N. G. Stoffel, “Transverse mode characteristics of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 57, 218–220 (1990).
    [CrossRef]
  2. M. Ogura, S. Fujii, T. Okada, M. Mori, T. Asaka, and H. Iwanu, “Transverse mode characteristics of DBR-surface emitting laser with buried heterostructure,” Jpn. J. Appl. Phys. 30, 3879–3882 (1991).
    [CrossRef]
  3. 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]
  4. 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. 5, 374–377 (1993).
    [CrossRef]
  5. C. H. Chong and J. Sarma, “Lasing mode selection in vertical cavity surface emitting laser diodes,” IEEE Photon. Technol. Lett. 5, 761–763 (1993).
    [CrossRef]
  6. C. H. Chong and J. Sarma, “Self-consistent calculation of two-dimensional diffusion equation for a modal gain analysis of lasing modes in cylindrical VCSELs,” in Physics and Simulation of Optoelectronic Devices II, W. W. Chow and M. Osinski, eds., Proc. SPIE 2146, 397–408 (1994).
    [CrossRef]
  7. D. Vakhshoori, J. D. Wynn, G. J. Zydik, R. E. Leibenguth, M. T. Asom, K. Kojima, and R. A. Morgan, “Top-surface emitting lasers with 1.9-V threshold voltage and the effect of spatial hole burning on their transverse mode operation and efficiencies,” Appl. Phys. Lett. 62, 1448–1450 (1993).
    [CrossRef]
  8. J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modelling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295–1307 (1993).
    [CrossRef]
  9. R. Michalzik and K. J. Ebeling, “Modelling and design of proton implanted ultra-low threshold vertical cavity laser diodes,” IEEE J. Quantum Electron. 29, 1963–1974 (1993).
    [CrossRef]
  10. D. Tauber, G. Wang, R. S. Geels, J. E. Bowers, and L. A. Coldren, “Large and small signal dynamics of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 62, 325–327 (1993).
    [CrossRef]
  11. A. Valle, J. Sarma, and K. A. Shore, “Dynamics of transverse mode competition in vertical cavity surface emitting semiconductor lasers,” Opt. Commun. 115, 297–302 (1995).
    [CrossRef]
  12. A. Valle, J. Sarma, and K. A. Shore, “Spatial hole-burning effects on the dynamics of vertical cavity surface emitting semiconductor lasers,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
    [CrossRef]
  13. See, e.g., K. Petermann, Laser Diode Modulation and Noise (Kluwer Academic, Dordrecht, The Netherlands, 1988).
  14. J. Dellunde, A. Valle, and K. A. Shore, “Transverse-mode selection in external-cavity vertical-cavity surface-emitting laser diodes,” J. Opt. Soc. Am. B 13, 2477–2483 (1996).
    [CrossRef]
  15. J. Y. Law and G. P. Agrawal, “Effects of optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 353–358 (1997).
    [CrossRef]
  16. J. Heinrich, E. Zeeb, and K. J. Ebeling, “Transverse modes under external feedback and fiber coupling efficiencies of VCSELs,” IEEE Photon. Technol. Lett. 10, 1365–1367 (1999).
    [CrossRef]
  17. L. N. Langley and K. A. Shore, “The effect of optical feedback on noise properties of vertical cavity surface emitting lasers,” IEE Proc. Optoelectron. 144, 34–38 (1997).
    [CrossRef]
  18. J. Y. Law and G. P. Agrawal, “Mode partition noise in vertical cavity surface emitting lasers,” IEEE Photon. Technol. Lett. 9, 437–439 (1997).
    [CrossRef]
  19. 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]
  20. E. Hernandez-Garcia, C. Mirasso, K. A. Shore, and M. San Miguel, “Turn-on jitter of external cavity semiconductor lasers,” IEEE J. Quantum Electron. 30, 241–248 (1994).
    [CrossRef]
  21. L. N. Langley and K. A. Shore, “The effect of external optical feedback on timing jitter in modulated laser dodes,” J. Lightwave Technol. 11, 434–441 (1993).
    [CrossRef]
  22. A. Valle, L. Pesquera, and K. A. Shore, “Polarization selection and sensitivity of external cavity vertical-cavity surface-emitting laser diodes,” IEEE Photon. Technol. Lett. 10, 639–641 (1998).
    [CrossRef]
  23. D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, “Modal reflection of quarter-wave mirrors in vertical cavity lasers,” IEEE J. Quantum Electron. 29, 1950–1962 (1993).
    [CrossRef]
  24. A. Valle and L. Pesquera, “Mode partition noise in multi-transverse mode vertical-cavity surface-emitting lasers,” in Physics and Simulation of Optoelectronic Devices VII, P. Blood, A. Ishibashi, and M. Osinski, eds., Proc. SPIE 3625, 414–425 (1999).
    [CrossRef]

1999 (2)

J. Heinrich, E. Zeeb, and K. J. Ebeling, “Transverse modes under external feedback and fiber coupling efficiencies of VCSELs,” IEEE Photon. Technol. Lett. 10, 1365–1367 (1999).
[CrossRef]

A. Valle and L. Pesquera, “Mode partition noise in multi-transverse mode vertical-cavity surface-emitting lasers,” in Physics and Simulation of Optoelectronic Devices VII, P. Blood, A. Ishibashi, and M. Osinski, eds., Proc. SPIE 3625, 414–425 (1999).
[CrossRef]

1998 (2)

A. Valle, L. Pesquera, and K. A. Shore, “Polarization selection and sensitivity of external cavity vertical-cavity surface-emitting laser diodes,” IEEE Photon. Technol. Lett. 10, 639–641 (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 (3)

L. N. Langley and K. A. Shore, “The effect of optical feedback on noise properties of vertical cavity surface emitting lasers,” IEE Proc. Optoelectron. 144, 34–38 (1997).
[CrossRef]

J. Y. Law and G. P. Agrawal, “Mode partition noise in vertical cavity surface emitting lasers,” IEEE Photon. Technol. Lett. 9, 437–439 (1997).
[CrossRef]

J. Y. Law and G. P. Agrawal, “Effects of optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 353–358 (1997).
[CrossRef]

1996 (1)

1995 (2)

A. Valle, J. Sarma, and K. A. Shore, “Dynamics of transverse mode competition in vertical cavity surface emitting semiconductor lasers,” Opt. Commun. 115, 297–302 (1995).
[CrossRef]

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

1994 (2)

E. Hernandez-Garcia, C. Mirasso, K. A. Shore, and M. San Miguel, “Turn-on jitter of external cavity semiconductor lasers,” IEEE J. Quantum Electron. 30, 241–248 (1994).
[CrossRef]

C. H. Chong and J. Sarma, “Self-consistent calculation of two-dimensional diffusion equation for a modal gain analysis of lasing modes in cylindrical VCSELs,” in Physics and Simulation of Optoelectronic Devices II, W. W. Chow and M. Osinski, eds., Proc. SPIE 2146, 397–408 (1994).
[CrossRef]

1993 (8)

D. Vakhshoori, J. D. Wynn, G. J. Zydik, R. E. Leibenguth, M. T. Asom, K. Kojima, and R. A. Morgan, “Top-surface emitting lasers with 1.9-V threshold voltage and the effect of spatial hole burning on their transverse mode operation and efficiencies,” Appl. Phys. Lett. 62, 1448–1450 (1993).
[CrossRef]

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modelling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295–1307 (1993).
[CrossRef]

R. Michalzik and K. J. Ebeling, “Modelling and design of proton implanted ultra-low threshold vertical cavity laser diodes,” IEEE J. Quantum Electron. 29, 1963–1974 (1993).
[CrossRef]

D. Tauber, G. Wang, R. S. Geels, J. E. Bowers, and L. A. Coldren, “Large and small signal dynamics of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 62, 325–327 (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. 5, 374–377 (1993).
[CrossRef]

C. H. Chong and J. Sarma, “Lasing mode selection in vertical cavity surface emitting laser diodes,” IEEE Photon. Technol. Lett. 5, 761–763 (1993).
[CrossRef]

L. N. Langley and K. A. Shore, “The effect of external optical feedback on timing jitter in modulated laser dodes,” J. Lightwave Technol. 11, 434–441 (1993).
[CrossRef]

D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, “Modal reflection of quarter-wave mirrors in vertical cavity lasers,” IEEE J. Quantum Electron. 29, 1950–1962 (1993).
[CrossRef]

1991 (2)

M. Ogura, S. Fujii, T. Okada, M. Mori, T. Asaka, and H. Iwanu, “Transverse mode characteristics of DBR-surface emitting laser with buried heterostructure,” Jpn. J. Appl. Phys. 30, 3879–3882 (1991).
[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]

1990 (1)

C. J. Chang-Hasnain, M. Orenstein, A. C. von Lehmen, L. T. Florez, J. P. Harbison, and N. G. Stoffel, “Transverse mode characteristics of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 57, 218–220 (1990).
[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 optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 353–358 (1997).
[CrossRef]

J. Y. Law and G. P. Agrawal, “Mode partition noise in vertical cavity surface emitting lasers,” IEEE Photon. Technol. Lett. 9, 437–439 (1997).
[CrossRef]

Asaka, T.

M. Ogura, S. Fujii, T. Okada, M. Mori, T. Asaka, and H. Iwanu, “Transverse mode characteristics of DBR-surface emitting laser with buried heterostructure,” Jpn. J. Appl. Phys. 30, 3879–3882 (1991).
[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. 5, 374–377 (1993).
[CrossRef]

D. Vakhshoori, J. D. Wynn, G. J. Zydik, R. E. Leibenguth, M. T. Asom, K. Kojima, and R. A. Morgan, “Top-surface emitting lasers with 1.9-V threshold voltage and the effect of spatial hole burning on their transverse mode operation and efficiencies,” Appl. Phys. Lett. 62, 1448–1450 (1993).
[CrossRef]

Babic, D. I.

D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, “Modal reflection of quarter-wave mirrors in vertical cavity lasers,” IEEE J. Quantum Electron. 29, 1950–1962 (1993).
[CrossRef]

Bowers, J. E.

D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, “Modal reflection of quarter-wave mirrors in vertical cavity lasers,” IEEE J. Quantum Electron. 29, 1950–1962 (1993).
[CrossRef]

D. Tauber, G. Wang, R. S. Geels, J. E. Bowers, and L. A. Coldren, “Large and small signal dynamics of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 62, 325–327 (1993).
[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. 5, 374–377 (1993).
[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]

C. J. Chang-Hasnain, M. Orenstein, A. C. von Lehmen, L. T. Florez, J. P. Harbison, and N. G. Stoffel, “Transverse mode characteristics of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 57, 218–220 (1990).
[CrossRef]

Chong, C. H.

C. H. Chong and J. Sarma, “Self-consistent calculation of two-dimensional diffusion equation for a modal gain analysis of lasing modes in cylindrical VCSELs,” in Physics and Simulation of Optoelectronic Devices II, W. W. Chow and M. Osinski, eds., Proc. SPIE 2146, 397–408 (1994).
[CrossRef]

C. H. Chong and J. Sarma, “Lasing mode selection in vertical cavity surface emitting laser diodes,” IEEE Photon. Technol. Lett. 5, 761–763 (1993).
[CrossRef]

Chung, Y.

D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, “Modal reflection of quarter-wave mirrors in vertical cavity lasers,” IEEE J. Quantum Electron. 29, 1950–1962 (1993).
[CrossRef]

Coldren, L. A.

D. Tauber, G. Wang, R. S. Geels, J. E. Bowers, and L. A. Coldren, “Large and small signal dynamics of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 62, 325–327 (1993).
[CrossRef]

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modelling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295–1307 (1993).
[CrossRef]

Corzine, S. W.

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modelling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295–1307 (1993).
[CrossRef]

Dagli, N.

D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, “Modal reflection of quarter-wave mirrors in vertical cavity lasers,” IEEE J. Quantum Electron. 29, 1950–1962 (1993).
[CrossRef]

Dellunde, J.

Ebeling, K. J.

J. Heinrich, E. Zeeb, and K. J. Ebeling, “Transverse modes under external feedback and fiber coupling efficiencies of VCSELs,” IEEE Photon. Technol. Lett. 10, 1365–1367 (1999).
[CrossRef]

R. Michalzik and K. J. Ebeling, “Modelling and design of proton implanted ultra-low threshold vertical cavity laser diodes,” IEEE J. Quantum Electron. 29, 1963–1974 (1993).
[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]

C. J. Chang-Hasnain, M. Orenstein, A. C. von Lehmen, L. T. Florez, J. P. Harbison, and N. G. Stoffel, “Transverse mode characteristics of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 57, 218–220 (1990).
[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. 5, 374–377 (1993).
[CrossRef]

Fujii, S.

M. Ogura, S. Fujii, T. Okada, M. Mori, T. Asaka, and H. Iwanu, “Transverse mode characteristics of DBR-surface emitting laser with buried heterostructure,” Jpn. J. Appl. Phys. 30, 3879–3882 (1991).
[CrossRef]

Geels, R. S.

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modelling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295–1307 (1993).
[CrossRef]

D. Tauber, G. Wang, R. S. Geels, J. E. Bowers, and L. A. Coldren, “Large and small signal dynamics of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 62, 325–327 (1993).
[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. 5, 374–377 (1993).
[CrossRef]

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]

C. J. Chang-Hasnain, M. Orenstein, A. C. von Lehmen, L. T. Florez, J. P. Harbison, and N. G. Stoffel, “Transverse mode characteristics of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 57, 218–220 (1990).
[CrossRef]

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]

Heinrich, J.

J. Heinrich, E. Zeeb, and K. J. Ebeling, “Transverse modes under external feedback and fiber coupling efficiencies of VCSELs,” IEEE Photon. Technol. Lett. 10, 1365–1367 (1999).
[CrossRef]

Hernandez-Garcia, E.

E. Hernandez-Garcia, C. Mirasso, K. A. Shore, and M. San Miguel, “Turn-on jitter of external cavity semiconductor lasers,” IEEE J. Quantum Electron. 30, 241–248 (1994).
[CrossRef]

Iwanu, H.

M. Ogura, S. Fujii, T. Okada, M. Mori, T. Asaka, and H. Iwanu, “Transverse mode characteristics of DBR-surface emitting laser with buried heterostructure,” Jpn. J. Appl. Phys. 30, 3879–3882 (1991).
[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. 5, 374–377 (1993).
[CrossRef]

D. Vakhshoori, J. D. Wynn, G. J. Zydik, R. E. Leibenguth, M. T. Asom, K. Kojima, and R. A. Morgan, “Top-surface emitting lasers with 1.9-V threshold voltage and the effect of spatial hole burning on their transverse mode operation and efficiencies,” Appl. Phys. Lett. 62, 1448–1450 (1993).
[CrossRef]

Langley, L. N.

L. N. Langley and K. A. Shore, “The effect of optical feedback on noise properties of vertical cavity surface emitting lasers,” IEE Proc. Optoelectron. 144, 34–38 (1997).
[CrossRef]

L. N. Langley and K. A. Shore, “The effect of external optical feedback on timing jitter in modulated laser dodes,” J. Lightwave Technol. 11, 434–441 (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 optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 353–358 (1997).
[CrossRef]

J. Y. Law and G. P. Agrawal, “Mode partition noise in vertical cavity surface emitting lasers,” IEEE Photon. Technol. Lett. 9, 437–439 (1997).
[CrossRef]

Leibenguth, R. E.

D. Vakhshoori, J. D. Wynn, G. J. Zydik, R. E. Leibenguth, M. T. Asom, K. Kojima, and R. A. Morgan, “Top-surface emitting lasers with 1.9-V threshold voltage and the effect of spatial hole burning on their transverse mode operation and efficiencies,” Appl. Phys. Lett. 62, 1448–1450 (1993).
[CrossRef]

Michalzik, R.

R. Michalzik and K. J. Ebeling, “Modelling and design of proton implanted ultra-low threshold vertical cavity laser diodes,” IEEE J. Quantum Electron. 29, 1963–1974 (1993).
[CrossRef]

Mirasso, C.

E. Hernandez-Garcia, C. Mirasso, K. A. Shore, and M. San Miguel, “Turn-on jitter of external cavity semiconductor lasers,” IEEE J. Quantum Electron. 30, 241–248 (1994).
[CrossRef]

Morgan, R. A.

D. Vakhshoori, J. D. Wynn, G. J. Zydik, R. E. Leibenguth, M. T. Asom, K. Kojima, and R. A. Morgan, “Top-surface emitting lasers with 1.9-V threshold voltage and the effect of spatial hole burning on their transverse mode operation and efficiencies,” Appl. Phys. Lett. 62, 1448–1450 (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. 5, 374–377 (1993).
[CrossRef]

Mori, M.

M. Ogura, S. Fujii, T. Okada, M. Mori, T. Asaka, and H. Iwanu, “Transverse mode characteristics of DBR-surface emitting laser with buried heterostructure,” Jpn. J. Appl. Phys. 30, 3879–3882 (1991).
[CrossRef]

Ogura, M.

M. Ogura, S. Fujii, T. Okada, M. Mori, T. Asaka, and H. Iwanu, “Transverse mode characteristics of DBR-surface emitting laser with buried heterostructure,” Jpn. J. Appl. Phys. 30, 3879–3882 (1991).
[CrossRef]

Okada, T.

M. Ogura, S. Fujii, T. Okada, M. Mori, T. Asaka, and H. Iwanu, “Transverse mode characteristics of DBR-surface emitting laser with buried heterostructure,” Jpn. J. Appl. Phys. 30, 3879–3882 (1991).
[CrossRef]

Orenstein, M.

C. J. Chang-Hasnain, M. Orenstein, A. C. von Lehmen, L. T. Florez, J. P. Harbison, and N. G. Stoffel, “Transverse mode characteristics of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 57, 218–220 (1990).
[CrossRef]

Pesquera, L.

A. Valle and L. Pesquera, “Mode partition noise in multi-transverse mode vertical-cavity surface-emitting lasers,” in Physics and Simulation of Optoelectronic Devices VII, P. Blood, A. Ishibashi, and M. Osinski, eds., Proc. SPIE 3625, 414–425 (1999).
[CrossRef]

A. Valle, L. Pesquera, and K. A. Shore, “Polarization selection and sensitivity of external cavity vertical-cavity surface-emitting laser diodes,” IEEE Photon. Technol. Lett. 10, 639–641 (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. 5, 374–377 (1993).
[CrossRef]

San Miguel, M.

E. Hernandez-Garcia, C. Mirasso, K. A. Shore, and M. San Miguel, “Turn-on jitter of external cavity semiconductor lasers,” IEEE J. Quantum Electron. 30, 241–248 (1994).
[CrossRef]

Sarma, J.

A. Valle, J. Sarma, and K. A. Shore, “Dynamics of transverse mode competition in vertical cavity surface emitting semiconductor lasers,” Opt. Commun. 115, 297–302 (1995).
[CrossRef]

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

C. H. Chong and J. Sarma, “Self-consistent calculation of two-dimensional diffusion equation for a modal gain analysis of lasing modes in cylindrical VCSELs,” in Physics and Simulation of Optoelectronic Devices II, W. W. Chow and M. Osinski, eds., Proc. SPIE 2146, 397–408 (1994).
[CrossRef]

C. H. Chong and J. Sarma, “Lasing mode selection in vertical cavity surface emitting laser diodes,” IEEE Photon. Technol. Lett. 5, 761–763 (1993).
[CrossRef]

Scott, J. W.

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modelling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295–1307 (1993).
[CrossRef]

Shore, K. A.

A. Valle, L. Pesquera, and K. A. Shore, “Polarization selection and sensitivity of external cavity vertical-cavity surface-emitting laser diodes,” IEEE Photon. Technol. Lett. 10, 639–641 (1998).
[CrossRef]

L. N. Langley and K. A. Shore, “The effect of optical feedback on noise properties of vertical cavity surface emitting lasers,” IEE Proc. Optoelectron. 144, 34–38 (1997).
[CrossRef]

J. Dellunde, A. Valle, and K. A. Shore, “Transverse-mode selection in external-cavity vertical-cavity surface-emitting laser diodes,” J. Opt. Soc. Am. B 13, 2477–2483 (1996).
[CrossRef]

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

A. Valle, J. Sarma, and K. A. Shore, “Dynamics of transverse mode competition in vertical cavity surface emitting semiconductor lasers,” Opt. Commun. 115, 297–302 (1995).
[CrossRef]

E. Hernandez-Garcia, C. Mirasso, K. A. Shore, and M. San Miguel, “Turn-on jitter of external cavity semiconductor lasers,” IEEE J. Quantum Electron. 30, 241–248 (1994).
[CrossRef]

L. N. Langley and K. A. Shore, “The effect of external optical feedback on timing jitter in modulated laser dodes,” J. Lightwave Technol. 11, 434–441 (1993).
[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]

C. J. Chang-Hasnain, M. Orenstein, A. C. von Lehmen, L. T. Florez, J. P. Harbison, and N. G. Stoffel, “Transverse mode characteristics of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 57, 218–220 (1990).
[CrossRef]

Tauber, D.

D. Tauber, G. Wang, R. S. Geels, J. E. Bowers, and L. A. Coldren, “Large and small signal dynamics of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 62, 325–327 (1993).
[CrossRef]

Vakhshoori, D.

D. Vakhshoori, J. D. Wynn, G. J. Zydik, R. E. Leibenguth, M. T. Asom, K. Kojima, and R. A. Morgan, “Top-surface emitting lasers with 1.9-V threshold voltage and the effect of spatial hole burning on their transverse mode operation and efficiencies,” Appl. Phys. Lett. 62, 1448–1450 (1993).
[CrossRef]

Valle, A.

A. Valle and L. Pesquera, “Mode partition noise in multi-transverse mode vertical-cavity surface-emitting lasers,” in Physics and Simulation of Optoelectronic Devices VII, P. Blood, A. Ishibashi, and M. Osinski, eds., Proc. SPIE 3625, 414–425 (1999).
[CrossRef]

A. Valle, L. Pesquera, and K. A. Shore, “Polarization selection and sensitivity of external cavity vertical-cavity surface-emitting laser diodes,” IEEE Photon. Technol. Lett. 10, 639–641 (1998).
[CrossRef]

J. Dellunde, A. Valle, and K. A. Shore, “Transverse-mode selection in external-cavity vertical-cavity surface-emitting laser diodes,” J. Opt. Soc. Am. B 13, 2477–2483 (1996).
[CrossRef]

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

A. Valle, J. Sarma, and K. A. Shore, “Dynamics of transverse mode competition in vertical cavity surface emitting semiconductor lasers,” Opt. Commun. 115, 297–302 (1995).
[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]

C. J. Chang-Hasnain, M. Orenstein, A. C. von Lehmen, L. T. Florez, J. P. Harbison, and N. G. Stoffel, “Transverse mode characteristics of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 57, 218–220 (1990).
[CrossRef]

Wang, G.

D. Tauber, G. Wang, R. S. Geels, J. E. Bowers, and L. A. Coldren, “Large and small signal dynamics of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 62, 325–327 (1993).
[CrossRef]

Wynn, J. D.

D. Vakhshoori, J. D. Wynn, G. J. Zydik, R. E. Leibenguth, M. T. Asom, K. Kojima, and R. A. Morgan, “Top-surface emitting lasers with 1.9-V threshold voltage and the effect of spatial hole burning on their transverse mode operation and efficiencies,” Appl. Phys. Lett. 62, 1448–1450 (1993).
[CrossRef]

Zeeb, E.

J. Heinrich, E. Zeeb, and K. J. Ebeling, “Transverse modes under external feedback and fiber coupling efficiencies of VCSELs,” IEEE Photon. Technol. Lett. 10, 1365–1367 (1999).
[CrossRef]

Zydik, G. J.

D. Vakhshoori, J. D. Wynn, G. J. Zydik, R. E. Leibenguth, M. T. Asom, K. Kojima, and R. A. Morgan, “Top-surface emitting lasers with 1.9-V threshold voltage and the effect of spatial hole burning on their transverse mode operation and efficiencies,” Appl. Phys. Lett. 62, 1448–1450 (1993).
[CrossRef]

Appl. Phys. Lett. (3)

C. J. Chang-Hasnain, M. Orenstein, A. C. von Lehmen, L. T. Florez, J. P. Harbison, and N. G. Stoffel, “Transverse mode characteristics of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 57, 218–220 (1990).
[CrossRef]

D. Vakhshoori, J. D. Wynn, G. J. Zydik, R. E. Leibenguth, M. T. Asom, K. Kojima, and R. A. Morgan, “Top-surface emitting lasers with 1.9-V threshold voltage and the effect of spatial hole burning on their transverse mode operation and efficiencies,” Appl. Phys. Lett. 62, 1448–1450 (1993).
[CrossRef]

D. Tauber, G. Wang, R. S. Geels, J. E. Bowers, and L. A. Coldren, “Large and small signal dynamics of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 62, 325–327 (1993).
[CrossRef]

IEE Proc. Optoelectron. (1)

L. N. Langley and K. A. Shore, “The effect of optical feedback on noise properties of vertical cavity surface emitting lasers,” IEE Proc. Optoelectron. 144, 34–38 (1997).
[CrossRef]

IEEE J. Quantum Electron. (6)

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

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modelling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295–1307 (1993).
[CrossRef]

R. Michalzik and K. J. Ebeling, “Modelling and design of proton implanted ultra-low threshold vertical cavity laser diodes,” IEEE J. Quantum Electron. 29, 1963–1974 (1993).
[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]

E. Hernandez-Garcia, C. Mirasso, K. A. Shore, and M. San Miguel, “Turn-on jitter of external cavity semiconductor lasers,” IEEE J. Quantum Electron. 30, 241–248 (1994).
[CrossRef]

D. I. Babic, Y. Chung, N. Dagli, and J. E. Bowers, “Modal reflection of quarter-wave mirrors in vertical cavity lasers,” IEEE J. Quantum Electron. 29, 1950–1962 (1993).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. Y. Law and G. P. Agrawal, “Effects of optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 353–358 (1997).
[CrossRef]

IEEE Photon. Technol. Lett. (5)

J. Heinrich, E. Zeeb, and K. J. Ebeling, “Transverse modes under external feedback and fiber coupling efficiencies of VCSELs,” IEEE Photon. Technol. Lett. 10, 1365–1367 (1999).
[CrossRef]

J. Y. Law and G. P. Agrawal, “Mode partition noise in vertical cavity surface emitting lasers,” IEEE Photon. Technol. Lett. 9, 437–439 (1997).
[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. 5, 374–377 (1993).
[CrossRef]

C. H. Chong and J. Sarma, “Lasing mode selection in vertical cavity surface emitting laser diodes,” IEEE Photon. Technol. Lett. 5, 761–763 (1993).
[CrossRef]

A. Valle, L. Pesquera, and K. A. Shore, “Polarization selection and sensitivity of external cavity vertical-cavity surface-emitting laser diodes,” IEEE Photon. Technol. Lett. 10, 639–641 (1998).
[CrossRef]

J. Lightwave Technol. (1)

L. N. Langley and K. A. Shore, “The effect of external optical feedback on timing jitter in modulated laser dodes,” J. Lightwave Technol. 11, 434–441 (1993).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

M. Ogura, S. Fujii, T. Okada, M. Mori, T. Asaka, and H. Iwanu, “Transverse mode characteristics of DBR-surface emitting laser with buried heterostructure,” Jpn. J. Appl. Phys. 30, 3879–3882 (1991).
[CrossRef]

Opt. Commun. (1)

A. Valle, J. Sarma, and K. A. Shore, “Dynamics of transverse mode competition in vertical cavity surface emitting semiconductor lasers,” Opt. Commun. 115, 297–302 (1995).
[CrossRef]

Proc. SPIE (2)

C. H. Chong and J. Sarma, “Self-consistent calculation of two-dimensional diffusion equation for a modal gain analysis of lasing modes in cylindrical VCSELs,” in Physics and Simulation of Optoelectronic Devices II, W. W. Chow and M. Osinski, eds., Proc. SPIE 2146, 397–408 (1994).
[CrossRef]

A. Valle and L. Pesquera, “Mode partition noise in multi-transverse mode vertical-cavity surface-emitting lasers,” in Physics and Simulation of Optoelectronic Devices VII, P. Blood, A. Ishibashi, and M. Osinski, eds., Proc. SPIE 3625, 414–425 (1999).
[CrossRef]

Other (1)

See, e.g., K. Petermann, Laser Diode Modulation and Noise (Kluwer Academic, Dordrecht, The Netherlands, 1988).

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of the external-cavity VCSEL structure.

Fig. 2
Fig. 2

Normalized radial intensity profiles of the LP01 and the degenerate LP11 modes of the structure shown in Fig. 1.

Fig. 3
Fig. 3

(a) Threshold gain and (b) threshold current as functions of external-cavity round-trip time. Solid and dashed curves correspond to LP01 and LP11, respectively. Thin and thick curves correspond to one and multiple reflections, respectively. We have labeled the mode that dominates in each zone. The external reflectivity is 8.3%. Calculations are performed for (ω2-ω1)τπ/2.

Fig. 4
Fig. 4

(a) Steady-state carrier-density profile when the LP01 mode is favored (τ1.0007 ps) for two different injection currents: 4 kA/cm2 (squares), and 15 kA/cm2 (plus signs). (b) Steady-state carrier-density profile when the LP11 mode is favored (τ1.0014 ps) for two injection currents: 4 kA/cm2 (squares), and 15 kA/cm2 (plus signs). Power profiles for LP01 and LP11 modes are plotted at the bottom of each figure by dashed and dotted curves, respectively.

Fig. 5
Fig. 5

Effect of thermal effects on light-current curves [mW(kA/cm2)] for the LP01 (asterisks) and the LP11 (circles) modes of a VCSEL subject to optical feedback when the LP11 mode is favored: (a) without thermal effects for (ω2-ω1)τπ (τ=2.0771 ps), (b) with thermal effects (Δλ/ΔI=0.3 nm/mA) for (ω2-ω1)τπ (τ=2.0771 ps), (c) with thermal effects (Δλ/ΔI=0.3 nm/mA) for (ω2-ω1)τ3π (τ=6.2372 ps).

Fig. 6
Fig. 6

Current density versus external-cavity round-trip time mode-selection band diagram with thermal effects (Δλ/ΔI=0.3 nm/mA) taken into account for (ω2-ω1)τ3π. We have labeled the mode that dominates in each band.

Fig. 7
Fig. 7

Light-current characteristics for (ω2-ω1)τπ/2 (τ=1.0398 ps) when the LP11 mode is favored: without thermal effects (without temperature) for the LP01 and the LP11 modes and with thermal effects for the LP01 mode (solid curve) and the LP11 mode (dashed curve). δλ/ΔI=0.15 nm/mA, and τ=1.0398 ps. For the solitary VCSEL the threshold currents for the LP01 and the LP11 modes are near 2.9 and 4.2 kA/cm2, respectively.

Fig. 8
Fig. 8

Light-current characteristics for (ω2-ω1)τπ/2 (τ=1.0382 ps) when the LP01 mode is favored: without thermal effects (without temperature) for the LP01 and the LP11 modes and with thermal effects for the LP01 mode (solid curve) and the LP11 mode (dashed curve). Δλ/ΔI=0.15 nm/mA, and τ=1.0382 ps.

Fig. 9
Fig. 9

RIN spectrum for (a) a solitary VCSEL and for (b) a VCSEL with optical feedback. The injected current is 9 kA/cm2, and the external reflectivity is 8.3%. LP01, LP11, and total power are plotted by thin solid curves [top curve in (a), middle in (b)]; dashed curves [middle curve in (a), top in (b)]; and thick solid curves, respectively.

Tables (1)

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Table 1 Device and Material Parameters

Equations (13)

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Ψmn(r)=Jm(umnr/a)Jm(umn),
Ψmn(r)=Km(wmnr/a)Km(wmn)
umn=a[(ncoreκmn)2-β¯2]1/2,
wmn=a[β¯2-(ncladdκmn)2]1/2,
Nt=Dn2N-BN2-i aigi(t)|Ei|2Ψi2(r)+j0(r, t)ed,
Ψi=0Ψi2(r)rdr,
gi=1Ψi0 Ψi2(r)A0[N(r, t)-Nt]rdr.
dEidt=1-iα2vgΓgi(t)-1τpEi(t)+m=1 κm,i exp(imωiτ)Ei(t-mτ)+βπd0aN(r, t)rdrτn1/2ξi(t),
κm,i=(1-R)τLR(-1)m-1[Rextηi(RRext)(m-1)]1/2.
ξi(t)ξj*(t)=2δijδ(t-t).
gth,i=1vgΓ1τp-2 m=1 κm cos(mωiτ).
gth,1-gth,2=-2κ1vgΓ[cos(ω1τ)+sin(ω1τ)-2(RRext) cos(2ω1τ)].
gth,i=1vgΓ1τpi-2κ1 cos2πcτλi×1-πa2λiΔλΔI(j0-jth).

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