Abstract

Experiments using intracavity nearly degenerate four-wave mixing in GaAlAs semiconductor laser oscillators and resonant-type amplifiers suggest that the resonance-relaxation process can be simply interpreted in terms of the dynamic Stark effect for a two-level system. This new interpretation is confirmed by a theoretical development demonstrating that lasers and resonant-type amplifiers can actually be represented well by an equivalent two-level system that takes into account both the semiconductor medium and cavity constants. Such an analysis can be useful for the study of higher-order instabilities.

© 1988 Optical Society of America

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References

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  1. T. L. Paoli, J. E. Ripper, Proc. IEEE 58, 1457 (1970).
    [CrossRef]
  2. S. Kobayashi, T. Kimura, IEEE J. Quantum Electron. QE-18, 575 (1982).
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    [CrossRef]
  4. A. S. Sudbo, L. Bjerkan, IEEE J. Quantum Electron. QE-19, 1542 (1983).
    [CrossRef]
  5. P. Spano, S. Piazzola, M. Tamburrini, IEEE J. Quantum Electron. QE-22, 427 (1986).
    [CrossRef]
  6. K. Vahala, Ch. Harder, A. Yariv, Appl. Phys. Lett. 42, 211 (1983).
    [CrossRef]
  7. H. Nakajima, R. Frey, Appl. Phys. Lett. 47, 769 (1985).
    [CrossRef]
  8. S. H. Autler, C. H. Townes, Phys. Rev. 100, 703 (1955).
    [CrossRef]
  9. B. R. Mollow, Phys. Rev. 188, 1969 (1969).
    [CrossRef]
  10. T. Y. Fu, M. Sargent, Opt. Lett. 4, 366 (1979).
    [CrossRef] [PubMed]
  11. D. J. Harter, R. W. Boyd, IEEE J. Quantum Electron. QE-16, 1126 (1980).
    [CrossRef]
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    [CrossRef]
  13. D. G. Steel, R. C. Lind, Opt. Lett. 6, 587 (1981).
    [CrossRef] [PubMed]
  14. D. J. Harter, P. Narum, M. G. Raymer, R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981).
    [CrossRef]
  15. F. de Rougemont, R. Frey, “Two-level approach of saturation properties in semiconductor materials,” Phys. Rev. B (to be published).
  16. B. Thédrez, A. Jones, R. Frey, “Two-level description of gain and mixing susceptibilities in amplifying semiconductor materials,” submitted to IEEE J. Quantum Electron.
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    [CrossRef]
  18. R. Frey, Opt. Lett. 11, 91 (1986).
    [CrossRef] [PubMed]

1986 (2)

P. Spano, S. Piazzola, M. Tamburrini, IEEE J. Quantum Electron. QE-22, 427 (1986).
[CrossRef]

R. Frey, Opt. Lett. 11, 91 (1986).
[CrossRef] [PubMed]

1985 (1)

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

1983 (3)

K. Vahala, Ch. Harder, A. Yariv, Appl. Phys. Lett. 42, 211 (1983).
[CrossRef]

K. Vahala, A. Yariv, IEEE J. Quantum Electron. QE-19, 1096 (1983).K. Vahala, A. Yariv, IEEE J. Quantum Electron. QE-19, 1102 (1983).
[CrossRef]

A. S. Sudbo, L. Bjerkan, IEEE J. Quantum Electron. QE-19, 1542 (1983).
[CrossRef]

1982 (2)

S. Kobayashi, T. Kimura, IEEE J. Quantum Electron. QE-18, 575 (1982).
[CrossRef]

J. Nilsen, A. Yariv, IEEE J. Quantum Electron. QE-18, 1947 (1982).
[CrossRef]

1981 (3)

D. G. Steel, R. C. Lind, Opt. Lett. 6, 587 (1981).
[CrossRef] [PubMed]

D. J. Harter, P. Narum, M. G. Raymer, R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981).
[CrossRef]

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

1980 (1)

D. J. Harter, R. W. Boyd, IEEE J. Quantum Electron. QE-16, 1126 (1980).
[CrossRef]

1979 (1)

1970 (1)

T. L. Paoli, J. E. Ripper, Proc. IEEE 58, 1457 (1970).
[CrossRef]

1969 (1)

B. R. Mollow, Phys. Rev. 188, 1969 (1969).
[CrossRef]

1955 (1)

S. H. Autler, C. H. Townes, Phys. Rev. 100, 703 (1955).
[CrossRef]

Autler, S. H.

S. H. Autler, C. H. Townes, Phys. Rev. 100, 703 (1955).
[CrossRef]

Bjerkan, L.

A. S. Sudbo, L. Bjerkan, IEEE J. Quantum Electron. QE-19, 1542 (1983).
[CrossRef]

Boyd, R. W.

D. J. Harter, P. Narum, M. G. Raymer, R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981).
[CrossRef]

D. J. Harter, R. W. Boyd, IEEE J. Quantum Electron. QE-16, 1126 (1980).
[CrossRef]

de Rougemont, F.

F. de Rougemont, R. Frey, “Two-level approach of saturation properties in semiconductor materials,” Phys. Rev. B (to be published).

Frey, R.

R. Frey, Opt. Lett. 11, 91 (1986).
[CrossRef] [PubMed]

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

F. de Rougemont, R. Frey, “Two-level approach of saturation properties in semiconductor materials,” Phys. Rev. B (to be published).

B. Thédrez, A. Jones, R. Frey, “Two-level description of gain and mixing susceptibilities in amplifying semiconductor materials,” submitted to IEEE J. Quantum Electron.

Fu, T. Y.

Harder, Ch.

K. Vahala, Ch. Harder, A. Yariv, Appl. Phys. Lett. 42, 211 (1983).
[CrossRef]

Harter, D. J.

D. J. Harter, P. Narum, M. G. Raymer, R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981).
[CrossRef]

D. J. Harter, R. W. Boyd, IEEE J. Quantum Electron. QE-16, 1126 (1980).
[CrossRef]

Jones, A.

B. Thédrez, A. Jones, R. Frey, “Two-level description of gain and mixing susceptibilities in amplifying semiconductor materials,” submitted to IEEE J. Quantum Electron.

Kimura, T.

S. Kobayashi, T. Kimura, IEEE J. Quantum Electron. QE-18, 575 (1982).
[CrossRef]

Kobayashi, S.

S. Kobayashi, T. Kimura, IEEE J. Quantum Electron. QE-18, 575 (1982).
[CrossRef]

Lind, R. C.

Mollow, B. R.

B. R. Mollow, Phys. Rev. 188, 1969 (1969).
[CrossRef]

Nakajima, H.

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

Narum, P.

D. J. Harter, P. Narum, M. G. Raymer, R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981).
[CrossRef]

Nilsen, J.

J. Nilsen, A. Yariv, IEEE J. Quantum Electron. QE-18, 1947 (1982).
[CrossRef]

Paoli, T. L.

T. L. Paoli, J. E. Ripper, Proc. IEEE 58, 1457 (1970).
[CrossRef]

Piazzola, S.

P. Spano, S. Piazzola, M. Tamburrini, IEEE J. Quantum Electron. QE-22, 427 (1986).
[CrossRef]

Raymer, M. G.

D. J. Harter, P. Narum, M. G. Raymer, R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981).
[CrossRef]

Ripper, J. E.

T. L. Paoli, J. E. Ripper, Proc. IEEE 58, 1457 (1970).
[CrossRef]

Sargent, M.

Spano, P.

P. Spano, S. Piazzola, M. Tamburrini, IEEE J. Quantum Electron. QE-22, 427 (1986).
[CrossRef]

Steel, D. G.

Sudbo, A. S.

A. S. Sudbo, L. Bjerkan, IEEE J. Quantum Electron. QE-19, 1542 (1983).
[CrossRef]

Suematsu, Y.

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

Tamburrini, M.

P. Spano, S. Piazzola, M. Tamburrini, IEEE J. Quantum Electron. QE-22, 427 (1986).
[CrossRef]

Thédrez, B.

B. Thédrez, A. Jones, R. Frey, “Two-level description of gain and mixing susceptibilities in amplifying semiconductor materials,” submitted to IEEE J. Quantum Electron.

Townes, C. H.

S. H. Autler, C. H. Townes, Phys. Rev. 100, 703 (1955).
[CrossRef]

Vahala, K.

K. Vahala, Ch. Harder, A. Yariv, Appl. Phys. Lett. 42, 211 (1983).
[CrossRef]

K. Vahala, A. Yariv, IEEE J. Quantum Electron. QE-19, 1096 (1983).K. Vahala, A. Yariv, IEEE J. Quantum Electron. QE-19, 1102 (1983).
[CrossRef]

Yamada, M.

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

Yariv, A.

K. Vahala, A. Yariv, IEEE J. Quantum Electron. QE-19, 1096 (1983).K. Vahala, A. Yariv, IEEE J. Quantum Electron. QE-19, 1102 (1983).
[CrossRef]

K. Vahala, Ch. Harder, A. Yariv, Appl. Phys. Lett. 42, 211 (1983).
[CrossRef]

J. Nilsen, A. Yariv, IEEE J. Quantum Electron. QE-18, 1947 (1982).
[CrossRef]

Appl. Phys. Lett. (2)

K. Vahala, Ch. Harder, A. Yariv, Appl. Phys. Lett. 42, 211 (1983).
[CrossRef]

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

IEEE J. Quantum Electron. (6)

S. Kobayashi, T. Kimura, IEEE J. Quantum Electron. QE-18, 575 (1982).
[CrossRef]

K. Vahala, A. Yariv, IEEE J. Quantum Electron. QE-19, 1096 (1983).K. Vahala, A. Yariv, IEEE J. Quantum Electron. QE-19, 1102 (1983).
[CrossRef]

A. S. Sudbo, L. Bjerkan, IEEE J. Quantum Electron. QE-19, 1542 (1983).
[CrossRef]

P. Spano, S. Piazzola, M. Tamburrini, IEEE J. Quantum Electron. QE-22, 427 (1986).
[CrossRef]

D. J. Harter, R. W. Boyd, IEEE J. Quantum Electron. QE-16, 1126 (1980).
[CrossRef]

J. Nilsen, A. Yariv, IEEE J. Quantum Electron. QE-18, 1947 (1982).
[CrossRef]

J. Appl. Phys. (1)

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

Opt. Lett. (3)

Phys. Rev. (2)

S. H. Autler, C. H. Townes, Phys. Rev. 100, 703 (1955).
[CrossRef]

B. R. Mollow, Phys. Rev. 188, 1969 (1969).
[CrossRef]

Phys. Rev. Lett. (1)

D. J. Harter, P. Narum, M. G. Raymer, R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981).
[CrossRef]

Proc. IEEE (1)

T. L. Paoli, J. E. Ripper, Proc. IEEE 58, 1457 (1970).
[CrossRef]

Other (2)

F. de Rougemont, R. Frey, “Two-level approach of saturation properties in semiconductor materials,” Phys. Rev. B (to be published).

B. Thédrez, A. Jones, R. Frey, “Two-level description of gain and mixing susceptibilities in amplifying semiconductor materials,” submitted to IEEE J. Quantum Electron.

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Figures (2)

Fig. 1
Fig. 1

Experimental setup. L0–L2, GaAlAs semiconductor laser diodes; M0, M1, monochromators; A1, A2, attenuators; O.I1, O.I2, optical isolators; B.S.’s beam splitters; F.P., Fabry–Perot interferometer; P.M., photomultiplier; V’s voltmeters.

Fig. 2
Fig. 2

Generalized Rabi frequency squared versus the cavity detuning squared: (a) and (b) correspond to an output power from L0 of 80 and 210 μW, respectively. Dots are experimental values, and dashed lines are theoretical plots.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

Ω 2 = Δ ω c 2 + Ω 0 2 ,
P ( ω ) = α 0 c n 4 π ω ( Δ + i ) E ( ω ) 1 + Δ 2 + | E ( ω ) E s | 2 ,
A ± ( z ) = A ± ( 0 ) exp { ± 1 2 [ α 0 ( 1 i Δ ) 1 + Δ 2 + I p z ] } .
A + ( 0 ) [ 1 R exp ( β 0 L + i Ө ) ] = t E 0 ,
A ( 0 ) { 1 R 1 exp [ ( β 0 L + i Ө ) ] } = t E 0 / R 1 / 2 ,
I p = | A + | 2 + | A | 2 / E s = | F + | 2 + | F | 2 / | E s | 2 = 2 | A + ( 0 ) | 2 [ ( 1 R ) / ( | E s | 2 R ln ( 1 / R ) ] .
β = α 0 ( 1 i δ ) 1 + Δ 2 + I p ,

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