Abstract

We investigate the threshold behavior of vertical-cavity surface-emitting lasers (VCSEL’s) by solving the set of coupled equations for carrier density, field amplitude, and plasma and lattice temperatures. We show that, because of plasma heating and lattice heating, the threshold of VCSEL’s can be continuous or discontinuous with bistability between lasing and nonlasing states (correspondingly second-or first-order phase transition), depending on the relative position of the cavity frequency to the gain bandwidth and on the ambient (substrate) temperature of the device.

© 1995 Optical Society of America

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  1. P. L. Gourley, S. K. Lyo, T. M. Brennan, B. E. Hammons, C. F. Schaus, S. Sun, Appl. Phys. Lett. 55, 2698 (1989).
    [CrossRef]
  2. J. W. Scott, S. W. Corzine, D. B. Young, L. A. Coldren, Appl. Phys. Lett. 62, 1050 (1993); IEEE J. Quantum Electron. 29, 1295 (1993).
    [CrossRef]
  3. B. Lu. P. Zhou, J. Cheng, K. J. Malloy, Appl. Phys. Lett. 65, 1337 (1994); Proc. Soc. Photo-Opt. Instrum. Eng. 2147, 12 (1994).
    [CrossRef]
  4. W. Nakwaski, M. Osinski, IEEE J. Quantum Electron. 27, 1391 (1991); Proc. Soc. Photo-Opt. Instrum. Eng. 2146, 365 (1994).
    [CrossRef]
  5. F. Jahnke, S. W. Koch, Opt. Lett. 18, 1438 (1993); F. Jahnke, K. Henneberger, W. Schäfer, S. W. Koch, J. Opt. Soc. Am. B 10, 2396 (1993).
    [CrossRef] [PubMed]
  6. C. Z. Ning, R. A. Indik, J. V. Moloney, “Selfconsistent approach to thermal effects in vertical-cavity surface-emitting lasers,” submitted toJ. Opt. Soc. Am. B.
  7. C. Z. Ning, J. V. Moloney, Appl. Phys. Lett. 66, 559 (1995).
    [CrossRef]
  8. H. Haken, Synergetics, An Introduction, 3rd ed. (Springer-Verlag, Berlin, 1983), Chap 8, p. 225.
  9. L. Lugiato, in Progress in Optics, E. Wolf, ed. (North- Holland, Amsterdam, 1984), Vol. XXI, p. 69.
  10. B. Lu, Center for High Technological Materials, University of New Mexico, Albuquerque, N.M. 87131 (personal communication, 1994).

1995

C. Z. Ning, J. V. Moloney, Appl. Phys. Lett. 66, 559 (1995).
[CrossRef]

1994

B. Lu. P. Zhou, J. Cheng, K. J. Malloy, Appl. Phys. Lett. 65, 1337 (1994); Proc. Soc. Photo-Opt. Instrum. Eng. 2147, 12 (1994).
[CrossRef]

1993

J. W. Scott, S. W. Corzine, D. B. Young, L. A. Coldren, Appl. Phys. Lett. 62, 1050 (1993); IEEE J. Quantum Electron. 29, 1295 (1993).
[CrossRef]

F. Jahnke, S. W. Koch, Opt. Lett. 18, 1438 (1993); F. Jahnke, K. Henneberger, W. Schäfer, S. W. Koch, J. Opt. Soc. Am. B 10, 2396 (1993).
[CrossRef] [PubMed]

1991

W. Nakwaski, M. Osinski, IEEE J. Quantum Electron. 27, 1391 (1991); Proc. Soc. Photo-Opt. Instrum. Eng. 2146, 365 (1994).
[CrossRef]

1989

P. L. Gourley, S. K. Lyo, T. M. Brennan, B. E. Hammons, C. F. Schaus, S. Sun, Appl. Phys. Lett. 55, 2698 (1989).
[CrossRef]

Brennan, T. M.

P. L. Gourley, S. K. Lyo, T. M. Brennan, B. E. Hammons, C. F. Schaus, S. Sun, Appl. Phys. Lett. 55, 2698 (1989).
[CrossRef]

Cheng, J.

B. Lu. P. Zhou, J. Cheng, K. J. Malloy, Appl. Phys. Lett. 65, 1337 (1994); Proc. Soc. Photo-Opt. Instrum. Eng. 2147, 12 (1994).
[CrossRef]

Coldren, L. A.

J. W. Scott, S. W. Corzine, D. B. Young, L. A. Coldren, Appl. Phys. Lett. 62, 1050 (1993); IEEE J. Quantum Electron. 29, 1295 (1993).
[CrossRef]

Corzine, S. W.

J. W. Scott, S. W. Corzine, D. B. Young, L. A. Coldren, Appl. Phys. Lett. 62, 1050 (1993); IEEE J. Quantum Electron. 29, 1295 (1993).
[CrossRef]

Gourley, P. L.

P. L. Gourley, S. K. Lyo, T. M. Brennan, B. E. Hammons, C. F. Schaus, S. Sun, Appl. Phys. Lett. 55, 2698 (1989).
[CrossRef]

Haken, H.

H. Haken, Synergetics, An Introduction, 3rd ed. (Springer-Verlag, Berlin, 1983), Chap 8, p. 225.

Hammons, B. E.

P. L. Gourley, S. K. Lyo, T. M. Brennan, B. E. Hammons, C. F. Schaus, S. Sun, Appl. Phys. Lett. 55, 2698 (1989).
[CrossRef]

Indik, R. A.

C. Z. Ning, R. A. Indik, J. V. Moloney, “Selfconsistent approach to thermal effects in vertical-cavity surface-emitting lasers,” submitted toJ. Opt. Soc. Am. B.

Jahnke, F.

Koch, S. W.

Lu, B.

B. Lu, Center for High Technological Materials, University of New Mexico, Albuquerque, N.M. 87131 (personal communication, 1994).

Lugiato, L.

L. Lugiato, in Progress in Optics, E. Wolf, ed. (North- Holland, Amsterdam, 1984), Vol. XXI, p. 69.

Lyo, S. K.

P. L. Gourley, S. K. Lyo, T. M. Brennan, B. E. Hammons, C. F. Schaus, S. Sun, Appl. Phys. Lett. 55, 2698 (1989).
[CrossRef]

Malloy, K. J.

B. Lu. P. Zhou, J. Cheng, K. J. Malloy, Appl. Phys. Lett. 65, 1337 (1994); Proc. Soc. Photo-Opt. Instrum. Eng. 2147, 12 (1994).
[CrossRef]

Moloney, J. V.

C. Z. Ning, J. V. Moloney, Appl. Phys. Lett. 66, 559 (1995).
[CrossRef]

C. Z. Ning, R. A. Indik, J. V. Moloney, “Selfconsistent approach to thermal effects in vertical-cavity surface-emitting lasers,” submitted toJ. Opt. Soc. Am. B.

Nakwaski, W.

W. Nakwaski, M. Osinski, IEEE J. Quantum Electron. 27, 1391 (1991); Proc. Soc. Photo-Opt. Instrum. Eng. 2146, 365 (1994).
[CrossRef]

Ning, C. Z.

C. Z. Ning, J. V. Moloney, Appl. Phys. Lett. 66, 559 (1995).
[CrossRef]

C. Z. Ning, R. A. Indik, J. V. Moloney, “Selfconsistent approach to thermal effects in vertical-cavity surface-emitting lasers,” submitted toJ. Opt. Soc. Am. B.

Osinski, M.

W. Nakwaski, M. Osinski, IEEE J. Quantum Electron. 27, 1391 (1991); Proc. Soc. Photo-Opt. Instrum. Eng. 2146, 365 (1994).
[CrossRef]

Schaus, C. F.

P. L. Gourley, S. K. Lyo, T. M. Brennan, B. E. Hammons, C. F. Schaus, S. Sun, Appl. Phys. Lett. 55, 2698 (1989).
[CrossRef]

Scott, J. W.

J. W. Scott, S. W. Corzine, D. B. Young, L. A. Coldren, Appl. Phys. Lett. 62, 1050 (1993); IEEE J. Quantum Electron. 29, 1295 (1993).
[CrossRef]

Sun, S.

P. L. Gourley, S. K. Lyo, T. M. Brennan, B. E. Hammons, C. F. Schaus, S. Sun, Appl. Phys. Lett. 55, 2698 (1989).
[CrossRef]

Young, D. B.

J. W. Scott, S. W. Corzine, D. B. Young, L. A. Coldren, Appl. Phys. Lett. 62, 1050 (1993); IEEE J. Quantum Electron. 29, 1295 (1993).
[CrossRef]

Zhou, B. Lu. P.

B. Lu. P. Zhou, J. Cheng, K. J. Malloy, Appl. Phys. Lett. 65, 1337 (1994); Proc. Soc. Photo-Opt. Instrum. Eng. 2147, 12 (1994).
[CrossRef]

Appl. Phys. Lett.

P. L. Gourley, S. K. Lyo, T. M. Brennan, B. E. Hammons, C. F. Schaus, S. Sun, Appl. Phys. Lett. 55, 2698 (1989).
[CrossRef]

J. W. Scott, S. W. Corzine, D. B. Young, L. A. Coldren, Appl. Phys. Lett. 62, 1050 (1993); IEEE J. Quantum Electron. 29, 1295 (1993).
[CrossRef]

B. Lu. P. Zhou, J. Cheng, K. J. Malloy, Appl. Phys. Lett. 65, 1337 (1994); Proc. Soc. Photo-Opt. Instrum. Eng. 2147, 12 (1994).
[CrossRef]

C. Z. Ning, J. V. Moloney, Appl. Phys. Lett. 66, 559 (1995).
[CrossRef]

IEEE J. Quantum Electron.

W. Nakwaski, M. Osinski, IEEE J. Quantum Electron. 27, 1391 (1991); Proc. Soc. Photo-Opt. Instrum. Eng. 2146, 365 (1994).
[CrossRef]

Opt. Lett.

Other

C. Z. Ning, R. A. Indik, J. V. Moloney, “Selfconsistent approach to thermal effects in vertical-cavity surface-emitting lasers,” submitted toJ. Opt. Soc. Am. B.

H. Haken, Synergetics, An Introduction, 3rd ed. (Springer-Verlag, Berlin, 1983), Chap 8, p. 225.

L. Lugiato, in Progress in Optics, E. Wolf, ed. (North- Holland, Amsterdam, 1984), Vol. XXI, p. 69.

B. Lu, Center for High Technological Materials, University of New Mexico, Albuquerque, N.M. 87131 (personal communication, 1994).

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