Abstract

A model of microcavity semiconductor lasers in which both the cavity field and the gain medium are quantized is presented. The equation of motion for the elements of the reduced density matrix for the field in the photon number representation is developed and numerically solved to find the steady-state photon number distribution and the laser linewidth for a variety of operating conditions. For typical semiconductor microcavity operating conditions, the intensity noise is smaller and the laser linewidth is larger for lasers with a larger fraction of spontaneous emission into the cavity mode. However, for very-low-loss microcavity lasers, if the rate of spontaneous emission into the cavity mode exceeds the loss rate, the laser can appear to turn on at pump rates for which the gain medium is not inverted. In this anamolous regime, the laser intensity noise increases with an increased fraction of spontaneous emission into the cavity mode.

© 2007 Optical Society of America

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  1. M. O. Scully and W. E. Lamb, Jr., "Quantum theory of an optical maser. I. General theory," Phys. Rev. 159, 208-226 (1967).
    [CrossRef]
  2. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).
  3. P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer-Verlag, 1991).
  4. W. W. Chow, S. W. Koch, and M. Sargent III, Semiconductor Laser Physics (Springer, 1993).
  5. G. P. Agrawal and N. K. Dutta, Long-Wavelength Semiconductors (Van Nostrand Reinhold, 1986).
  6. H. Haug and H. Haken, "Theory of noise in semiconductor laser emission," Z. Phys. 204, 262-275 (1967).
  7. H. Haug, "Quantum-mechanical rate equations for semiconductor lasers," Phys. Rev. 184, 338-248 (1969).
    [CrossRef]
  8. H. Haug and S. W. Koch, "Semiconductor laser theory with many-body effects," Phys. Rev. A 39, 1887-1898 (1989).
    [CrossRef]
  9. P. R. Rice and H. J. Carmichael, "Photon statistics of a cavity-QED laser: a comment on the laser-phase-transition analogy," Phys. Rev. A 50, 4318-4329 (1994).
    [CrossRef]
  10. C. W. Gardiner and A. Eschmann, "Master-equation theory of semiconductor lasers," Phys. Rev. A 51, 4982-4995 (1995).
    [CrossRef]
  11. Y. Yamamoto, "AM and FM quantum noise in semiconductor lasers--Part I: Theoretical analysis," IEEE J. Quantum Electron. QE-19, 34-36 (1983).
    [CrossRef]
  12. A. Imamoglu and Y. Yamamoto, "Turnstile device for heralded single photons: Coulomb blockade of electron and hole tunneling in quantum confined p-i-n heterojunctions," Phys. Rev. Lett. 72, 210-213 (1994).
    [CrossRef]
  13. R. Jin, D. Boggavarapu, M. Sargent III, P. Meystre, H. A. Gibbs, and G. Khitrova, "Photon-number correlations near the threshold of microcavity lasers in the weak-coupling regime," Phys. Rev. A 49, 4038-4042 (1994).
    [CrossRef]
  14. L. M. Pedrotti, M. Sokol, and P. R. Rice, "Linewidth of four-level microcavity lasers," Phys. Rev. A 59, 2295-2301 (1999).
    [CrossRef]
  15. U. Mohideen, R. E. Slusher, F. Jahnke, and S. W. Koch, "Semiconductor microcavity linewidths," Phys. Rev. Lett. 73, 1785-1788 (1994).
    [CrossRef]
  16. R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, "Threshold characteristics of semiconductor microdisk lasers," Appl. Phys. Lett. 63, 1310-1312 (1993).
    [CrossRef]
  17. R. E. Slusher (Lucent Technologies, Bell Laboratories, Murray Hill, N.J. 07974, USA) and U. Mohideen (Department of Physics, University of California Riverside, Riverside, Calif. 92521, USA) (personal communication, 1995).

1999 (1)

L. M. Pedrotti, M. Sokol, and P. R. Rice, "Linewidth of four-level microcavity lasers," Phys. Rev. A 59, 2295-2301 (1999).
[CrossRef]

1995 (1)

C. W. Gardiner and A. Eschmann, "Master-equation theory of semiconductor lasers," Phys. Rev. A 51, 4982-4995 (1995).
[CrossRef]

1994 (4)

A. Imamoglu and Y. Yamamoto, "Turnstile device for heralded single photons: Coulomb blockade of electron and hole tunneling in quantum confined p-i-n heterojunctions," Phys. Rev. Lett. 72, 210-213 (1994).
[CrossRef]

R. Jin, D. Boggavarapu, M. Sargent III, P. Meystre, H. A. Gibbs, and G. Khitrova, "Photon-number correlations near the threshold of microcavity lasers in the weak-coupling regime," Phys. Rev. A 49, 4038-4042 (1994).
[CrossRef]

U. Mohideen, R. E. Slusher, F. Jahnke, and S. W. Koch, "Semiconductor microcavity linewidths," Phys. Rev. Lett. 73, 1785-1788 (1994).
[CrossRef]

P. R. Rice and H. J. Carmichael, "Photon statistics of a cavity-QED laser: a comment on the laser-phase-transition analogy," Phys. Rev. A 50, 4318-4329 (1994).
[CrossRef]

1993 (1)

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, "Threshold characteristics of semiconductor microdisk lasers," Appl. Phys. Lett. 63, 1310-1312 (1993).
[CrossRef]

1989 (1)

H. Haug and S. W. Koch, "Semiconductor laser theory with many-body effects," Phys. Rev. A 39, 1887-1898 (1989).
[CrossRef]

1983 (1)

Y. Yamamoto, "AM and FM quantum noise in semiconductor lasers--Part I: Theoretical analysis," IEEE J. Quantum Electron. QE-19, 34-36 (1983).
[CrossRef]

1969 (1)

H. Haug, "Quantum-mechanical rate equations for semiconductor lasers," Phys. Rev. 184, 338-248 (1969).
[CrossRef]

1967 (2)

M. O. Scully and W. E. Lamb, Jr., "Quantum theory of an optical maser. I. General theory," Phys. Rev. 159, 208-226 (1967).
[CrossRef]

H. Haug and H. Haken, "Theory of noise in semiconductor laser emission," Z. Phys. 204, 262-275 (1967).

Agrawal, G. P.

G. P. Agrawal and N. K. Dutta, Long-Wavelength Semiconductors (Van Nostrand Reinhold, 1986).

Boggavarapu, D.

R. Jin, D. Boggavarapu, M. Sargent III, P. Meystre, H. A. Gibbs, and G. Khitrova, "Photon-number correlations near the threshold of microcavity lasers in the weak-coupling regime," Phys. Rev. A 49, 4038-4042 (1994).
[CrossRef]

Carmichael, H. J.

P. R. Rice and H. J. Carmichael, "Photon statistics of a cavity-QED laser: a comment on the laser-phase-transition analogy," Phys. Rev. A 50, 4318-4329 (1994).
[CrossRef]

Chow, W. W.

W. W. Chow, S. W. Koch, and M. Sargent III, Semiconductor Laser Physics (Springer, 1993).

Dutta, N. K.

G. P. Agrawal and N. K. Dutta, Long-Wavelength Semiconductors (Van Nostrand Reinhold, 1986).

Eschmann, A.

C. W. Gardiner and A. Eschmann, "Master-equation theory of semiconductor lasers," Phys. Rev. A 51, 4982-4995 (1995).
[CrossRef]

Gardiner, C. W.

C. W. Gardiner and A. Eschmann, "Master-equation theory of semiconductor lasers," Phys. Rev. A 51, 4982-4995 (1995).
[CrossRef]

Gibbs, H. A.

R. Jin, D. Boggavarapu, M. Sargent III, P. Meystre, H. A. Gibbs, and G. Khitrova, "Photon-number correlations near the threshold of microcavity lasers in the weak-coupling regime," Phys. Rev. A 49, 4038-4042 (1994).
[CrossRef]

Haken, H.

H. Haug and H. Haken, "Theory of noise in semiconductor laser emission," Z. Phys. 204, 262-275 (1967).

Haug, H.

H. Haug and S. W. Koch, "Semiconductor laser theory with many-body effects," Phys. Rev. A 39, 1887-1898 (1989).
[CrossRef]

H. Haug, "Quantum-mechanical rate equations for semiconductor lasers," Phys. Rev. 184, 338-248 (1969).
[CrossRef]

H. Haug and H. Haken, "Theory of noise in semiconductor laser emission," Z. Phys. 204, 262-275 (1967).

Imamoglu, A.

A. Imamoglu and Y. Yamamoto, "Turnstile device for heralded single photons: Coulomb blockade of electron and hole tunneling in quantum confined p-i-n heterojunctions," Phys. Rev. Lett. 72, 210-213 (1994).
[CrossRef]

Jahnke, F.

U. Mohideen, R. E. Slusher, F. Jahnke, and S. W. Koch, "Semiconductor microcavity linewidths," Phys. Rev. Lett. 73, 1785-1788 (1994).
[CrossRef]

Jin, R.

R. Jin, D. Boggavarapu, M. Sargent III, P. Meystre, H. A. Gibbs, and G. Khitrova, "Photon-number correlations near the threshold of microcavity lasers in the weak-coupling regime," Phys. Rev. A 49, 4038-4042 (1994).
[CrossRef]

Khitrova, G.

R. Jin, D. Boggavarapu, M. Sargent III, P. Meystre, H. A. Gibbs, and G. Khitrova, "Photon-number correlations near the threshold of microcavity lasers in the weak-coupling regime," Phys. Rev. A 49, 4038-4042 (1994).
[CrossRef]

Koch, S. W.

U. Mohideen, R. E. Slusher, F. Jahnke, and S. W. Koch, "Semiconductor microcavity linewidths," Phys. Rev. Lett. 73, 1785-1788 (1994).
[CrossRef]

H. Haug and S. W. Koch, "Semiconductor laser theory with many-body effects," Phys. Rev. A 39, 1887-1898 (1989).
[CrossRef]

W. W. Chow, S. W. Koch, and M. Sargent III, Semiconductor Laser Physics (Springer, 1993).

Lamb, W. E.

M. O. Scully and W. E. Lamb, Jr., "Quantum theory of an optical maser. I. General theory," Phys. Rev. 159, 208-226 (1967).
[CrossRef]

Levi, A. F. J.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, "Threshold characteristics of semiconductor microdisk lasers," Appl. Phys. Lett. 63, 1310-1312 (1993).
[CrossRef]

Logan, R. A.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, "Threshold characteristics of semiconductor microdisk lasers," Appl. Phys. Lett. 63, 1310-1312 (1993).
[CrossRef]

McCall, S. L.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, "Threshold characteristics of semiconductor microdisk lasers," Appl. Phys. Lett. 63, 1310-1312 (1993).
[CrossRef]

Meystre, P.

R. Jin, D. Boggavarapu, M. Sargent III, P. Meystre, H. A. Gibbs, and G. Khitrova, "Photon-number correlations near the threshold of microcavity lasers in the weak-coupling regime," Phys. Rev. A 49, 4038-4042 (1994).
[CrossRef]

P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer-Verlag, 1991).

Mohideen, U.

U. Mohideen, R. E. Slusher, F. Jahnke, and S. W. Koch, "Semiconductor microcavity linewidths," Phys. Rev. Lett. 73, 1785-1788 (1994).
[CrossRef]

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, "Threshold characteristics of semiconductor microdisk lasers," Appl. Phys. Lett. 63, 1310-1312 (1993).
[CrossRef]

R. E. Slusher (Lucent Technologies, Bell Laboratories, Murray Hill, N.J. 07974, USA) and U. Mohideen (Department of Physics, University of California Riverside, Riverside, Calif. 92521, USA) (personal communication, 1995).

Pearton, S. J.

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, "Threshold characteristics of semiconductor microdisk lasers," Appl. Phys. Lett. 63, 1310-1312 (1993).
[CrossRef]

Pedrotti, L. M.

L. M. Pedrotti, M. Sokol, and P. R. Rice, "Linewidth of four-level microcavity lasers," Phys. Rev. A 59, 2295-2301 (1999).
[CrossRef]

Rice, P. R.

L. M. Pedrotti, M. Sokol, and P. R. Rice, "Linewidth of four-level microcavity lasers," Phys. Rev. A 59, 2295-2301 (1999).
[CrossRef]

P. R. Rice and H. J. Carmichael, "Photon statistics of a cavity-QED laser: a comment on the laser-phase-transition analogy," Phys. Rev. A 50, 4318-4329 (1994).
[CrossRef]

Sargent, M.

R. Jin, D. Boggavarapu, M. Sargent III, P. Meystre, H. A. Gibbs, and G. Khitrova, "Photon-number correlations near the threshold of microcavity lasers in the weak-coupling regime," Phys. Rev. A 49, 4038-4042 (1994).
[CrossRef]

P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer-Verlag, 1991).

W. W. Chow, S. W. Koch, and M. Sargent III, Semiconductor Laser Physics (Springer, 1993).

Scully, M. O.

M. O. Scully and W. E. Lamb, Jr., "Quantum theory of an optical maser. I. General theory," Phys. Rev. 159, 208-226 (1967).
[CrossRef]

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).

Slusher, R. E.

U. Mohideen, R. E. Slusher, F. Jahnke, and S. W. Koch, "Semiconductor microcavity linewidths," Phys. Rev. Lett. 73, 1785-1788 (1994).
[CrossRef]

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, "Threshold characteristics of semiconductor microdisk lasers," Appl. Phys. Lett. 63, 1310-1312 (1993).
[CrossRef]

R. E. Slusher (Lucent Technologies, Bell Laboratories, Murray Hill, N.J. 07974, USA) and U. Mohideen (Department of Physics, University of California Riverside, Riverside, Calif. 92521, USA) (personal communication, 1995).

Sokol, M.

L. M. Pedrotti, M. Sokol, and P. R. Rice, "Linewidth of four-level microcavity lasers," Phys. Rev. A 59, 2295-2301 (1999).
[CrossRef]

Yamamoto, Y.

A. Imamoglu and Y. Yamamoto, "Turnstile device for heralded single photons: Coulomb blockade of electron and hole tunneling in quantum confined p-i-n heterojunctions," Phys. Rev. Lett. 72, 210-213 (1994).
[CrossRef]

Y. Yamamoto, "AM and FM quantum noise in semiconductor lasers--Part I: Theoretical analysis," IEEE J. Quantum Electron. QE-19, 34-36 (1983).
[CrossRef]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).

Appl. Phys. Lett. (1)

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, "Threshold characteristics of semiconductor microdisk lasers," Appl. Phys. Lett. 63, 1310-1312 (1993).
[CrossRef]

IEEE J. Quantum Electron. (1)

Y. Yamamoto, "AM and FM quantum noise in semiconductor lasers--Part I: Theoretical analysis," IEEE J. Quantum Electron. QE-19, 34-36 (1983).
[CrossRef]

Phys. Rev. (2)

M. O. Scully and W. E. Lamb, Jr., "Quantum theory of an optical maser. I. General theory," Phys. Rev. 159, 208-226 (1967).
[CrossRef]

H. Haug, "Quantum-mechanical rate equations for semiconductor lasers," Phys. Rev. 184, 338-248 (1969).
[CrossRef]

Phys. Rev. A (5)

H. Haug and S. W. Koch, "Semiconductor laser theory with many-body effects," Phys. Rev. A 39, 1887-1898 (1989).
[CrossRef]

P. R. Rice and H. J. Carmichael, "Photon statistics of a cavity-QED laser: a comment on the laser-phase-transition analogy," Phys. Rev. A 50, 4318-4329 (1994).
[CrossRef]

C. W. Gardiner and A. Eschmann, "Master-equation theory of semiconductor lasers," Phys. Rev. A 51, 4982-4995 (1995).
[CrossRef]

R. Jin, D. Boggavarapu, M. Sargent III, P. Meystre, H. A. Gibbs, and G. Khitrova, "Photon-number correlations near the threshold of microcavity lasers in the weak-coupling regime," Phys. Rev. A 49, 4038-4042 (1994).
[CrossRef]

L. M. Pedrotti, M. Sokol, and P. R. Rice, "Linewidth of four-level microcavity lasers," Phys. Rev. A 59, 2295-2301 (1999).
[CrossRef]

Phys. Rev. Lett. (2)

U. Mohideen, R. E. Slusher, F. Jahnke, and S. W. Koch, "Semiconductor microcavity linewidths," Phys. Rev. Lett. 73, 1785-1788 (1994).
[CrossRef]

A. Imamoglu and Y. Yamamoto, "Turnstile device for heralded single photons: Coulomb blockade of electron and hole tunneling in quantum confined p-i-n heterojunctions," Phys. Rev. Lett. 72, 210-213 (1994).
[CrossRef]

Z. Phys. (1)

H. Haug and H. Haken, "Theory of noise in semiconductor laser emission," Z. Phys. 204, 262-275 (1967).

Other (5)

R. E. Slusher (Lucent Technologies, Bell Laboratories, Murray Hill, N.J. 07974, USA) and U. Mohideen (Department of Physics, University of California Riverside, Riverside, Calif. 92521, USA) (personal communication, 1995).

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).

P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer-Verlag, 1991).

W. W. Chow, S. W. Koch, and M. Sargent III, Semiconductor Laser Physics (Springer, 1993).

G. P. Agrawal and N. K. Dutta, Long-Wavelength Semiconductors (Van Nostrand Reinhold, 1986).

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