Abstract

A theoretical study is performed of the multimode dynamics and steady-state transverse-mode selection in vertical-cavity surface-emitting lasers subject to weak optical feedback in an external-cavity configuration. Attention is focused on the competition between the two lowest-order modes (LP01 and LP11 degenerate modes) 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 appropriate choice of optical feedback delay. Opportunities for enhancing modal discrimination by adjusting the strength of optical feedback are also presented.

© 1996 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. Techn. 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. Techn. Lett. 5, 761–763 (1993).
    [CrossRef]
  6. C. H. Chong and J. Sarma, “Self-consistent calculations of two-dimensional carrier distribution and modal gain of lasing modes in cylindrical VCSEL’s,” in Physics and Simulation of Optoelectronic Devices II, Proc. SPIE2146 (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 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. A. Valle, J. Sarma, and K. A. Shore, “Secondary pulsations driven by spatial hole burning in vertical cavity surface emitting laser diodes,” J. Opt. Soc. Am. B 12, 1741–1746 (1995).
    [CrossRef]
  14. See, e.g., K. Petermann, Laser Diode Modulation and Noise (Kluwer Academic, Dordrecht, 1988).
    [CrossRef]
  15. L. N. Langley, “Optical feedback in semiconductor lasers,” Ph.D. dissertion (University of Bath, Bath, UK, 1995).
  16. 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]
  17. A. Sapia and J. Dellunde, “Jitter measurements in gain switched semiconductor laser coupled to optical fibers,” in Semiconductor Lasers: Advanced Devices and Applications, Vol. 20 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper TuE12.
  18. L. N. Langley, K. A. Shore, and J. Mork, “Dynamical and noise properties of semiconductor lasers subject to strong optical feedback,” Opt. Lett. 19, 2137–2139 (1994).
    [CrossRef] [PubMed]
  19. K. H. Hahn, M. R. Tan, and S. Y. Wang, “Intensity noise of large area vertical cavity surface emitting lasers in multimode optical fiber links,” Electron. Lett. 30, 139–140 (1994).
    [CrossRef]
  20. L. N. Langley and K. A. Shore, “The effect of external optical feedback on timing jitter in modulated laser diodes,” J. Lightwave Technol. 11, 434–441 (1993).
    [CrossRef]
  21. F. Koyama, K. Morito, and K. Iga, “Intensity noise and polarization stability of GaAlAs-GaAs surface emitting lasers,” IEEE J. Quantum Electron. 27, 1410–1416 (1991).
    [CrossRef]
  22. M. S. Sodha and A. K. Ghatak, Inhomogeneous Optical Waveguides, (Plenum, New York, 1977), pp. 61–71.
  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. T. Ryan, G. P. Agrawal, G. R. Gray, and E. C. Gage, “Optical-feedback-induced chaos and its control in multimode semiconductor lasers,” IEEE J. Quantum Electron. 30, 668–679 (1994).
    [CrossRef]

1995 (3)

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]

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

1994 (4)

A. T. Ryan, G. P. Agrawal, G. R. Gray, and E. C. Gage, “Optical-feedback-induced chaos and its control in multimode semiconductor lasers,” IEEE J. Quantum Electron. 30, 668–679 (1994).
[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, K. A. Shore, and J. Mork, “Dynamical and noise properties of semiconductor lasers subject to strong optical feedback,” Opt. Lett. 19, 2137–2139 (1994).
[CrossRef] [PubMed]

K. H. Hahn, M. R. Tan, and S. Y. Wang, “Intensity noise of large area vertical cavity surface emitting lasers in multimode optical fiber links,” Electron. Lett. 30, 139–140 (1994).
[CrossRef]

1993 (8)

L. N. Langley and K. A. Shore, “The effect of external optical feedback on timing jitter in modulated laser diodes,” J. Lightwave Technol. 11, 434–441 (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. Techn. Lett. 5, 374–377 (1993).
[CrossRef]

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

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modelling temperature 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]

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 (3)

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]

F. Koyama, K. Morito, and K. Iga, “Intensity noise and polarization stability of GaAlAs-GaAs surface emitting lasers,” IEEE J. Quantum Electron. 27, 1410–1416 (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.

A. T. Ryan, G. P. Agrawal, G. R. Gray, and E. C. Gage, “Optical-feedback-induced chaos and its control in multimode semiconductor lasers,” IEEE J. Quantum Electron. 30, 668–679 (1994).
[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. Techn. 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. Techn. 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, “Lasing mode selection in vertical cavity surface emitting laser diodes,” IEEE Photon. Techn. Lett. 5, 761–763 (1993).
[CrossRef]

C. H. Chong and J. Sarma, “Self-consistent calculations of two-dimensional carrier distribution and modal gain of lasing modes in cylindrical VCSEL’s,” in Physics and Simulation of Optoelectronic Devices II, Proc. SPIE2146 (1994).
[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.

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modelling temperature 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]

Corzine, S. W.

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modelling temperature 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.

A. Sapia and J. Dellunde, “Jitter measurements in gain switched semiconductor laser coupled to optical fibers,” in Semiconductor Lasers: Advanced Devices and Applications, Vol. 20 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper TuE12.

Ebeling, K. J.

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. Techn. 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]

Gage, E. C.

A. T. Ryan, G. P. Agrawal, G. R. Gray, and E. C. Gage, “Optical-feedback-induced chaos and its control in multimode semiconductor lasers,” IEEE J. Quantum Electron. 30, 668–679 (1994).
[CrossRef]

Geels, R. S.

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 and spatial hole burning to optimize vertical cavity surface emitting laser performance,” IEEE J. Quantum Electron. 29, 1295–1307 (1993).
[CrossRef]

Ghatak, A. K.

M. S. Sodha and A. K. Ghatak, Inhomogeneous Optical Waveguides, (Plenum, New York, 1977), pp. 61–71.

Gray, G. R.

A. T. Ryan, G. P. Agrawal, G. R. Gray, and E. C. Gage, “Optical-feedback-induced chaos and its control in multimode semiconductor lasers,” IEEE J. Quantum Electron. 30, 668–679 (1994).
[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. Techn. Lett. 5, 374–377 (1993).
[CrossRef]

Hahn, K. H.

K. H. Hahn, M. R. Tan, and S. Y. Wang, “Intensity noise of large area vertical cavity surface emitting lasers in multimode optical fiber links,” Electron. Lett. 30, 139–140 (1994).
[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]

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]

Iga, K.

F. Koyama, K. Morito, and K. Iga, “Intensity noise and polarization stability of GaAlAs-GaAs surface emitting lasers,” IEEE J. Quantum Electron. 27, 1410–1416 (1991).
[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. Techn. 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]

Koyama, F.

F. Koyama, K. Morito, and K. Iga, “Intensity noise and polarization stability of GaAlAs-GaAs surface emitting lasers,” IEEE J. Quantum Electron. 27, 1410–1416 (1991).
[CrossRef]

Langley, L. N.

L. N. Langley, K. A. Shore, and J. Mork, “Dynamical and noise properties of semiconductor lasers subject to strong optical feedback,” Opt. Lett. 19, 2137–2139 (1994).
[CrossRef] [PubMed]

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

L. N. Langley, “Optical feedback in semiconductor lasers,” Ph.D. dissertion (University of Bath, Bath, UK, 1995).

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. Techn. 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]

Morito, K.

F. Koyama, K. Morito, and K. Iga, “Intensity noise and polarization stability of GaAlAs-GaAs surface emitting lasers,” IEEE J. Quantum Electron. 27, 1410–1416 (1991).
[CrossRef]

Mork, J.

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]

Petermann, K.

See, e.g., K. Petermann, Laser Diode Modulation and Noise (Kluwer Academic, Dordrecht, 1988).
[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. Techn. Lett. 5, 374–377 (1993).
[CrossRef]

Ryan, A. T.

A. T. Ryan, G. P. Agrawal, G. R. Gray, and E. C. Gage, “Optical-feedback-induced chaos and its control in multimode semiconductor lasers,” IEEE J. Quantum Electron. 30, 668–679 (1994).
[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]

Sapia, A.

A. Sapia and J. Dellunde, “Jitter measurements in gain switched semiconductor laser coupled to optical fibers,” in Semiconductor Lasers: Advanced Devices and Applications, Vol. 20 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper TuE12.

Sarma, J.

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]

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

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

C. H. Chong and J. Sarma, “Self-consistent calculations of two-dimensional carrier distribution and modal gain of lasing modes in cylindrical VCSEL’s,” in Physics and Simulation of Optoelectronic Devices II, Proc. SPIE2146 (1994).
[CrossRef]

Scott, J. W.

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modelling temperature 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, J. Sarma, and K. A. Shore, “Secondary pulsations driven by spatial hole burning in vertical cavity surface emitting laser diodes,” J. Opt. Soc. Am. B 12, 1741–1746 (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]

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]

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, K. A. Shore, and J. Mork, “Dynamical and noise properties of semiconductor lasers subject to strong optical feedback,” Opt. Lett. 19, 2137–2139 (1994).
[CrossRef] [PubMed]

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

Sodha, M. S.

M. S. Sodha and A. K. Ghatak, Inhomogeneous Optical Waveguides, (Plenum, New York, 1977), pp. 61–71.

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]

Tan, M. R.

K. H. Hahn, M. R. Tan, and S. Y. Wang, “Intensity noise of large area vertical cavity surface emitting lasers in multimode optical fiber links,” Electron. Lett. 30, 139–140 (1994).
[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, 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]

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

Wang, S. Y.

K. H. Hahn, M. R. Tan, and S. Y. Wang, “Intensity noise of large area vertical cavity surface emitting lasers in multimode optical fiber links,” Electron. Lett. 30, 139–140 (1994).
[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]

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]

Electron. Lett. (1)

K. H. Hahn, M. R. Tan, and S. Y. Wang, “Intensity noise of large area vertical cavity surface emitting lasers in multimode optical fiber links,” Electron. Lett. 30, 139–140 (1994).
[CrossRef]

IEEE J. Quantum Electron. (7)

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]

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 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]

F. Koyama, K. Morito, and K. Iga, “Intensity noise and polarization stability of GaAlAs-GaAs surface emitting lasers,” IEEE J. Quantum Electron. 27, 1410–1416 (1991).
[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]

A. T. Ryan, G. P. Agrawal, G. R. Gray, and E. C. Gage, “Optical-feedback-induced chaos and its control in multimode semiconductor lasers,” IEEE J. Quantum Electron. 30, 668–679 (1994).
[CrossRef]

IEEE J. Quantum. Electron. (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]

IEEE Photon. Techn. Lett. (2)

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. Techn. Lett. 5, 374–377 (1993).
[CrossRef]

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

J. Lightwave Technol. (1)

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

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

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]

Opt. Lett. (1)

Other (5)

M. S. Sodha and A. K. Ghatak, Inhomogeneous Optical Waveguides, (Plenum, New York, 1977), pp. 61–71.

See, e.g., K. Petermann, Laser Diode Modulation and Noise (Kluwer Academic, Dordrecht, 1988).
[CrossRef]

L. N. Langley, “Optical feedback in semiconductor lasers,” Ph.D. dissertion (University of Bath, Bath, UK, 1995).

A. Sapia and J. Dellunde, “Jitter measurements in gain switched semiconductor laser coupled to optical fibers,” in Semiconductor Lasers: Advanced Devices and Applications, Vol. 20 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper TuE12.

C. H. Chong and J. Sarma, “Self-consistent calculations of two-dimensional carrier distribution and modal gain of lasing modes in cylindrical VCSEL’s,” in Physics and Simulation of Optoelectronic Devices II, Proc. SPIE2146 (1994).
[CrossRef]

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Figures (8)

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 of Fig. 1.

Fig. 3
Fig. 3

(a) Threshold currents of the LP01 (*) and the LP11 (◯) modes as a function of external-cavity round-trip time. The solitary laser threshold currents for the LP01 (dotted line) and the LP11 (solid line) modes are included. (b) Threshold gain of the LP01 (*) and the LP11 (◯) modes as a function of external-cavity round-trip time. The solid line is the threshold gain of the solitary laser.

Fig. 4
Fig. 4

LI curves for a VCSEL subject to feedback at κi=0.025 ps-1 and τ = 2.0028 ps. Modal power for the LP01 (*) and the LP11 (◯) modes are plotted. The LI curve of the solitary VCSEL is included as a reference for the LP01 (solid curve) and the LP11 (dashed curve) modes.

Fig. 5
Fig. 5

Effect of optical feedback strength on threshold currents of the LP01 (*) and the LP11 (◯) modes. The external-cavity configuration favors LP01.

Fig. 6
Fig. 6

Maximum threshold current (◯) and minimum threshold current (*) for the LP01 mode as a function of optical feedback strength.

Fig. 7
Fig. 7

Maximum threshold current (◯) and minimum threshold current (*) for the LP11 mode as a function of optical feedback strength.

Fig. 8
Fig. 8

Tolerance of device to optical feedback as a function of the external-cavity round-trip time. The laser drive current is set at 4 × 107 A/m2, where the free-running laser is monomode (MSR is 25 dB). In zone I the transverse-mode suppression ratio (MSR) is greater than 10 dB. In zone II the MSR is less than 10 dB.

Tables (1)

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Table 1 Device and Material Parameters

Equations (13)

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Ψmn(r,ϕ)=Jm(ur/a)cos(mϕ)/Jm(u)Ψi(r)cos(mϕ),
Ψmn(r,ϕ)=Km(wr/a)cos(mϕ)/Km(w)Ψi(r)cos(mϕ),
u=a(1k02-βmn2)1/2,
w=a(βmn2-2k02)1/2,
Nt=Dn2N-BN2-iaigi(t)|Ei|2Ψi2(r)+j0(r,ϕ,t)/ed,
Ψi=0Ψi2(r)rdr,
gi(t)=12πΨi02π0Ψi2(r)A0[N(r,ϕ,t)-Nt]rdrdϕ.
2N=1/r/r(rN/r)+1/r22N/2ϕ.
dEidt=1-iα2νgΓgi(t)-1τpiEi(t)+κi exp(iωiτ)Ei(t-τ)+βN¯(t)2τnξi(t),
gith=1VgΓ1τpi-2κi cos(ωiτ).
N¯(t)=d02π0aN(r,ϕ,t)rdrdϕ.
κi=1τLi(1-R)RRextηi.
ξi(t)ξj*(t)=2δijδ(t-t).

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