Abstract

Population pulsations are demonstrated as a basic mechanism for nonlinear optical interaction in a semiconductor laser by detecting the optical beat frequency in the noise spectrum of the injection current.

© 1989 Optical Society of America

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References

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  1. H. Haken, Laser Theory (Springer-Verlag, Berlin, 1984).
  2. W. E. Lamb, Phys. Rev. 134, A1429 (1964).
    [CrossRef]
  3. M. Sargent, M. O. Scully, W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974), Chap. 9.
  4. See, e.g., R. L. Fork, M. A. Pollack, Phys. Rev. 139, A1408 (1965);R. A. McFarlane, Phys.Rev. 135, 1543 (1964).
    [CrossRef]
  5. M. Yamada, Y. Suematsu, J. Appl. Phys. 52, 2653 (1981).
    [CrossRef]
  6. R. F. Kazarinov, C. H. Henry, R. A. Logan, J. Appl. Phys. 53, 4631 (1982).
    [CrossRef]
  7. W. Elsässer, E. O. Göbel, IEEE J. Quantum Electron. QE-21, 687 (1985).
    [CrossRef]
  8. G. P. Agrawal, Opt. Lett. 12, 260 (1987).
    [CrossRef] [PubMed]
  9. G. P. Agrawal, J. Opt. Soc. Am. B 5, 147 (1988).
    [CrossRef]
  10. K. Inoue, T. Mukai, T. Saitoh, Appl. Phys. Lett. 51, 1051 (1987).
    [CrossRef]
  11. R. Nietzke, P. Panknin, W. Elsässer, E. O. Göbel, Appl. Phys. Lett. 51, 1298 (1987).
    [CrossRef]
  12. H. Nakajima, R. Frey, Appl. Phys. Lett. 47, 769 (1985).
    [CrossRef]
  13. Y. H. Lee, A. Chavez-Pirson, S. W. Koch, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, Phys. Rev. Lett. 57, 19 (1986).
  14. C. H. Henry, IEEE J. Quantum Electron. QE-18, 259 (1982).
    [CrossRef]
  15. A description of modulated laser fields and power spectra for a current-modulated laser, taking into account both intensity and frequency modulation, is given in H. Olesen, G. Jacobsen, IEEE J. Quantum Electron. QE-18, 2069 (1982).
    [CrossRef]

1988 (1)

1987 (3)

G. P. Agrawal, Opt. Lett. 12, 260 (1987).
[CrossRef] [PubMed]

K. Inoue, T. Mukai, T. Saitoh, Appl. Phys. Lett. 51, 1051 (1987).
[CrossRef]

R. Nietzke, P. Panknin, W. Elsässer, E. O. Göbel, Appl. Phys. Lett. 51, 1298 (1987).
[CrossRef]

1986 (1)

Y. H. Lee, A. Chavez-Pirson, S. W. Koch, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, Phys. Rev. Lett. 57, 19 (1986).

1985 (2)

H. Nakajima, R. Frey, Appl. Phys. Lett. 47, 769 (1985).
[CrossRef]

W. Elsässer, E. O. Göbel, IEEE J. Quantum Electron. QE-21, 687 (1985).
[CrossRef]

1982 (3)

C. H. Henry, IEEE J. Quantum Electron. QE-18, 259 (1982).
[CrossRef]

A description of modulated laser fields and power spectra for a current-modulated laser, taking into account both intensity and frequency modulation, is given in H. Olesen, G. Jacobsen, IEEE J. Quantum Electron. QE-18, 2069 (1982).
[CrossRef]

R. F. Kazarinov, C. H. Henry, R. A. Logan, J. Appl. Phys. 53, 4631 (1982).
[CrossRef]

1981 (1)

M. Yamada, Y. Suematsu, J. Appl. Phys. 52, 2653 (1981).
[CrossRef]

1965 (1)

See, e.g., R. L. Fork, M. A. Pollack, Phys. Rev. 139, A1408 (1965);R. A. McFarlane, Phys.Rev. 135, 1543 (1964).
[CrossRef]

1964 (1)

W. E. Lamb, Phys. Rev. 134, A1429 (1964).
[CrossRef]

Agrawal, G. P.

Chavez-Pirson, A.

Y. H. Lee, A. Chavez-Pirson, S. W. Koch, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, Phys. Rev. Lett. 57, 19 (1986).

Elsässer, W.

R. Nietzke, P. Panknin, W. Elsässer, E. O. Göbel, Appl. Phys. Lett. 51, 1298 (1987).
[CrossRef]

W. Elsässer, E. O. Göbel, IEEE J. Quantum Electron. QE-21, 687 (1985).
[CrossRef]

Fork, R. L.

See, e.g., R. L. Fork, M. A. Pollack, Phys. Rev. 139, A1408 (1965);R. A. McFarlane, Phys.Rev. 135, 1543 (1964).
[CrossRef]

Frey, R.

H. Nakajima, R. Frey, Appl. Phys. Lett. 47, 769 (1985).
[CrossRef]

Gibbs, H. M.

Y. H. Lee, A. Chavez-Pirson, S. W. Koch, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, Phys. Rev. Lett. 57, 19 (1986).

Göbel, E. O.

R. Nietzke, P. Panknin, W. Elsässer, E. O. Göbel, Appl. Phys. Lett. 51, 1298 (1987).
[CrossRef]

W. Elsässer, E. O. Göbel, IEEE J. Quantum Electron. QE-21, 687 (1985).
[CrossRef]

Haken, H.

H. Haken, Laser Theory (Springer-Verlag, Berlin, 1984).

Henry, C. H.

C. H. Henry, IEEE J. Quantum Electron. QE-18, 259 (1982).
[CrossRef]

R. F. Kazarinov, C. H. Henry, R. A. Logan, J. Appl. Phys. 53, 4631 (1982).
[CrossRef]

Inoue, K.

K. Inoue, T. Mukai, T. Saitoh, Appl. Phys. Lett. 51, 1051 (1987).
[CrossRef]

Jacobsen, G.

A description of modulated laser fields and power spectra for a current-modulated laser, taking into account both intensity and frequency modulation, is given in H. Olesen, G. Jacobsen, IEEE J. Quantum Electron. QE-18, 2069 (1982).
[CrossRef]

Jeffery, A.

Y. H. Lee, A. Chavez-Pirson, S. W. Koch, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, Phys. Rev. Lett. 57, 19 (1986).

Kazarinov, R. F.

R. F. Kazarinov, C. H. Henry, R. A. Logan, J. Appl. Phys. 53, 4631 (1982).
[CrossRef]

Koch, S. W.

Y. H. Lee, A. Chavez-Pirson, S. W. Koch, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, Phys. Rev. Lett. 57, 19 (1986).

Lamb, W. E.

W. E. Lamb, Phys. Rev. 134, A1429 (1964).
[CrossRef]

M. Sargent, M. O. Scully, W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974), Chap. 9.

Lee, Y. H.

Y. H. Lee, A. Chavez-Pirson, S. W. Koch, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, Phys. Rev. Lett. 57, 19 (1986).

Logan, R. A.

R. F. Kazarinov, C. H. Henry, R. A. Logan, J. Appl. Phys. 53, 4631 (1982).
[CrossRef]

Morhange, J.

Y. H. Lee, A. Chavez-Pirson, S. W. Koch, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, Phys. Rev. Lett. 57, 19 (1986).

Mukai, T.

K. Inoue, T. Mukai, T. Saitoh, Appl. Phys. Lett. 51, 1051 (1987).
[CrossRef]

Nakajima, H.

H. Nakajima, R. Frey, Appl. Phys. Lett. 47, 769 (1985).
[CrossRef]

Nietzke, R.

R. Nietzke, P. Panknin, W. Elsässer, E. O. Göbel, Appl. Phys. Lett. 51, 1298 (1987).
[CrossRef]

Olesen, H.

A description of modulated laser fields and power spectra for a current-modulated laser, taking into account both intensity and frequency modulation, is given in H. Olesen, G. Jacobsen, IEEE J. Quantum Electron. QE-18, 2069 (1982).
[CrossRef]

Panknin, P.

R. Nietzke, P. Panknin, W. Elsässer, E. O. Göbel, Appl. Phys. Lett. 51, 1298 (1987).
[CrossRef]

Park, S. H.

Y. H. Lee, A. Chavez-Pirson, S. W. Koch, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, Phys. Rev. Lett. 57, 19 (1986).

Peyghambarian, N.

Y. H. Lee, A. Chavez-Pirson, S. W. Koch, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, Phys. Rev. Lett. 57, 19 (1986).

Pollack, M. A.

See, e.g., R. L. Fork, M. A. Pollack, Phys. Rev. 139, A1408 (1965);R. A. McFarlane, Phys.Rev. 135, 1543 (1964).
[CrossRef]

Saitoh, T.

K. Inoue, T. Mukai, T. Saitoh, Appl. Phys. Lett. 51, 1051 (1987).
[CrossRef]

Sargent, M.

M. Sargent, M. O. Scully, W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974), Chap. 9.

Scully, M. O.

M. Sargent, M. O. Scully, W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974), Chap. 9.

Suematsu, Y.

M. Yamada, Y. Suematsu, J. Appl. Phys. 52, 2653 (1981).
[CrossRef]

Yamada, M.

M. Yamada, Y. Suematsu, J. Appl. Phys. 52, 2653 (1981).
[CrossRef]

Appl. Phys. Lett. (3)

K. Inoue, T. Mukai, T. Saitoh, Appl. Phys. Lett. 51, 1051 (1987).
[CrossRef]

R. Nietzke, P. Panknin, W. Elsässer, E. O. Göbel, Appl. Phys. Lett. 51, 1298 (1987).
[CrossRef]

H. Nakajima, R. Frey, Appl. Phys. Lett. 47, 769 (1985).
[CrossRef]

IEEE J. Quantum Electron. (3)

C. H. Henry, IEEE J. Quantum Electron. QE-18, 259 (1982).
[CrossRef]

A description of modulated laser fields and power spectra for a current-modulated laser, taking into account both intensity and frequency modulation, is given in H. Olesen, G. Jacobsen, IEEE J. Quantum Electron. QE-18, 2069 (1982).
[CrossRef]

W. Elsässer, E. O. Göbel, IEEE J. Quantum Electron. QE-21, 687 (1985).
[CrossRef]

J. Appl. Phys. (2)

M. Yamada, Y. Suematsu, J. Appl. Phys. 52, 2653 (1981).
[CrossRef]

R. F. Kazarinov, C. H. Henry, R. A. Logan, J. Appl. Phys. 53, 4631 (1982).
[CrossRef]

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

Opt. Lett. (1)

Phys. Rev. (2)

W. E. Lamb, Phys. Rev. 134, A1429 (1964).
[CrossRef]

See, e.g., R. L. Fork, M. A. Pollack, Phys. Rev. 139, A1408 (1965);R. A. McFarlane, Phys.Rev. 135, 1543 (1964).
[CrossRef]

Phys. Rev. Lett. (1)

Y. H. Lee, A. Chavez-Pirson, S. W. Koch, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, Phys. Rev. Lett. 57, 19 (1986).

Other (2)

H. Haken, Laser Theory (Springer-Verlag, Berlin, 1984).

M. Sargent, M. O. Scully, W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974), Chap. 9.

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Figures (3)

Fig. 1
Fig. 1

Experimental setup for simultaneous detection of the optical spectrum and the HF noise of the injection current in a four-wave-mixing experiment performed with two semiconductor lasers (SL1 and SL2). In conventional four-wave-mixing terminology SL1 corresponds to the pump laser and SL2 corresponds to the probe laser.

Fig. 2
Fig. 2

Optical frequency spectra obtained with a plane Fabry–Perot interferometer (the spectral resolution) for a frequency separation of the emission of SL1 and SL2 of (top) Δω = 1.15 GHz and (bottom) Δω = 1.30 GHz. The generated frequency sidebands are labeled PCn (n = 1, 2, 3, 4).

Fig. 3
Fig. 3

HF noise spectrum of the dc injection current of SL1 in the four-wave-mixing experiment for (top) Δω = 1.15 GHz and (bottom) 1.31 GHz. The corresponding optical spectra are shown in Fig. 2. The beat frequency Δω appears as a pronounced peak in the noise spectrum.

Equations (2)

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n = n 0 + Δ n n 0 cos ( Δ ω t ) ,
E ( ω ) = A exp ( i ω t ) = A { j = I j ( Δ n ω 1 n 0 Δ ω ) × exp [ i ( ω 1 + j Δ ω ) t ] } ,

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