Abstract

The nearly degenerate four-wave mixing technique is used to investigate the physical origin of period doubling in the route toward chaos. This spectroscopic approach identifies resonantly enhanced nearly degenerate four-wave mixing processes as being responsible for the generation of subharmonic frequencies. The technique presented in the case of GaAlAs semiconductor lasers could be applied to the study of monomode instabilities occurring in any laser or bistable devices.

© 1989 Optical Society of America

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References

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  1. J. R. Tredicce, F. T. Arecchi, G. L. Lippi, G. P. Puccioni, J. Opt. Soc. Am. B 2, 173 (1985).
    [CrossRef]
  2. H. G. Winful, Y. C. Chen, J. M. Liu, Appl. Phys. Lett. 48, 616 (1986).
    [CrossRef]
  3. C. H. Lee, T. H. Yoon, S. Y. Shin, Appl. Phys. Lett. 46, 95 (1985).
    [CrossRef]
  4. Y. C. Chen, H. G. Winful, J. M. Liu, Appl. Phys. Lett. 47, 208 (1985).
    [CrossRef]
  5. M. Tang, S. Wang, Appl. Phys. Lett. 48, 900 (1986).
    [CrossRef]
  6. G. P. Agrawal, Appl. Phys. Lett. 49, 1013 (1986).
    [CrossRef]
  7. H. Kawaguchi, Appl. Phys. Lett. 45, 1264 (1984).
    [CrossRef]
  8. K. Otsuka, H. Iwamura, Phys. Rev. A 28, 3153 (1983).
    [CrossRef]
  9. T. Mukai, K. Otsuka, Phys. Rev. Lett. 55, 1711 (1985).
    [CrossRef] [PubMed]
  10. K. Otsuka, J. Opt. Soc. Am. B 2, 168 (1985).
    [CrossRef]
  11. F. Mogensen, G. Jacobsen, H. Holesen, Opt. Quantum Electron. 16, 183 (1984).
    [CrossRef]
  12. B. Thédrez, R. Frey, Opt. Lett. 13, 105 (1988).
    [CrossRef] [PubMed]
  13. R. Frey, B. Thédrez, J. Opt. Soc. Am. B 5, 1176 (1988).
    [CrossRef]
  14. R. Frey, B. Thédrez, J. Phys. (Paris) 49, C2-393 (1988).
    [CrossRef]
  15. C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynbert, Processus d’interactions entre photons et atomes (Interéditions, Paris, 1988), Chap. VI.
  16. M. D. Levenson, C. Flytzanis, N. Bloembergen, Phys. Rev. B 6, 3962 (1972).
    [CrossRef]

1988 (3)

1986 (3)

M. Tang, S. Wang, Appl. Phys. Lett. 48, 900 (1986).
[CrossRef]

G. P. Agrawal, Appl. Phys. Lett. 49, 1013 (1986).
[CrossRef]

H. G. Winful, Y. C. Chen, J. M. Liu, Appl. Phys. Lett. 48, 616 (1986).
[CrossRef]

1985 (5)

C. H. Lee, T. H. Yoon, S. Y. Shin, Appl. Phys. Lett. 46, 95 (1985).
[CrossRef]

Y. C. Chen, H. G. Winful, J. M. Liu, Appl. Phys. Lett. 47, 208 (1985).
[CrossRef]

T. Mukai, K. Otsuka, Phys. Rev. Lett. 55, 1711 (1985).
[CrossRef] [PubMed]

K. Otsuka, J. Opt. Soc. Am. B 2, 168 (1985).
[CrossRef]

J. R. Tredicce, F. T. Arecchi, G. L. Lippi, G. P. Puccioni, J. Opt. Soc. Am. B 2, 173 (1985).
[CrossRef]

1984 (2)

F. Mogensen, G. Jacobsen, H. Holesen, Opt. Quantum Electron. 16, 183 (1984).
[CrossRef]

H. Kawaguchi, Appl. Phys. Lett. 45, 1264 (1984).
[CrossRef]

1983 (1)

K. Otsuka, H. Iwamura, Phys. Rev. A 28, 3153 (1983).
[CrossRef]

1972 (1)

M. D. Levenson, C. Flytzanis, N. Bloembergen, Phys. Rev. B 6, 3962 (1972).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Appl. Phys. Lett. 49, 1013 (1986).
[CrossRef]

Arecchi, F. T.

Bloembergen, N.

M. D. Levenson, C. Flytzanis, N. Bloembergen, Phys. Rev. B 6, 3962 (1972).
[CrossRef]

Chen, Y. C.

H. G. Winful, Y. C. Chen, J. M. Liu, Appl. Phys. Lett. 48, 616 (1986).
[CrossRef]

Y. C. Chen, H. G. Winful, J. M. Liu, Appl. Phys. Lett. 47, 208 (1985).
[CrossRef]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynbert, Processus d’interactions entre photons et atomes (Interéditions, Paris, 1988), Chap. VI.

Dupont-Roc, J.

C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynbert, Processus d’interactions entre photons et atomes (Interéditions, Paris, 1988), Chap. VI.

Flytzanis, C.

M. D. Levenson, C. Flytzanis, N. Bloembergen, Phys. Rev. B 6, 3962 (1972).
[CrossRef]

Frey, R.

Grynbert, G.

C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynbert, Processus d’interactions entre photons et atomes (Interéditions, Paris, 1988), Chap. VI.

Holesen, H.

F. Mogensen, G. Jacobsen, H. Holesen, Opt. Quantum Electron. 16, 183 (1984).
[CrossRef]

Iwamura, H.

K. Otsuka, H. Iwamura, Phys. Rev. A 28, 3153 (1983).
[CrossRef]

Jacobsen, G.

F. Mogensen, G. Jacobsen, H. Holesen, Opt. Quantum Electron. 16, 183 (1984).
[CrossRef]

Kawaguchi, H.

H. Kawaguchi, Appl. Phys. Lett. 45, 1264 (1984).
[CrossRef]

Lee, C. H.

C. H. Lee, T. H. Yoon, S. Y. Shin, Appl. Phys. Lett. 46, 95 (1985).
[CrossRef]

Levenson, M. D.

M. D. Levenson, C. Flytzanis, N. Bloembergen, Phys. Rev. B 6, 3962 (1972).
[CrossRef]

Lippi, G. L.

Liu, J. M.

H. G. Winful, Y. C. Chen, J. M. Liu, Appl. Phys. Lett. 48, 616 (1986).
[CrossRef]

Y. C. Chen, H. G. Winful, J. M. Liu, Appl. Phys. Lett. 47, 208 (1985).
[CrossRef]

Mogensen, F.

F. Mogensen, G. Jacobsen, H. Holesen, Opt. Quantum Electron. 16, 183 (1984).
[CrossRef]

Mukai, T.

T. Mukai, K. Otsuka, Phys. Rev. Lett. 55, 1711 (1985).
[CrossRef] [PubMed]

Otsuka, K.

T. Mukai, K. Otsuka, Phys. Rev. Lett. 55, 1711 (1985).
[CrossRef] [PubMed]

K. Otsuka, J. Opt. Soc. Am. B 2, 168 (1985).
[CrossRef]

K. Otsuka, H. Iwamura, Phys. Rev. A 28, 3153 (1983).
[CrossRef]

Puccioni, G. P.

Shin, S. Y.

C. H. Lee, T. H. Yoon, S. Y. Shin, Appl. Phys. Lett. 46, 95 (1985).
[CrossRef]

Tang, M.

M. Tang, S. Wang, Appl. Phys. Lett. 48, 900 (1986).
[CrossRef]

Thédrez, B.

Tredicce, J. R.

Wang, S.

M. Tang, S. Wang, Appl. Phys. Lett. 48, 900 (1986).
[CrossRef]

Winful, H. G.

H. G. Winful, Y. C. Chen, J. M. Liu, Appl. Phys. Lett. 48, 616 (1986).
[CrossRef]

Y. C. Chen, H. G. Winful, J. M. Liu, Appl. Phys. Lett. 47, 208 (1985).
[CrossRef]

Yoon, T. H.

C. H. Lee, T. H. Yoon, S. Y. Shin, Appl. Phys. Lett. 46, 95 (1985).
[CrossRef]

Appl. Phys. Lett. (6)

H. G. Winful, Y. C. Chen, J. M. Liu, Appl. Phys. Lett. 48, 616 (1986).
[CrossRef]

C. H. Lee, T. H. Yoon, S. Y. Shin, Appl. Phys. Lett. 46, 95 (1985).
[CrossRef]

Y. C. Chen, H. G. Winful, J. M. Liu, Appl. Phys. Lett. 47, 208 (1985).
[CrossRef]

M. Tang, S. Wang, Appl. Phys. Lett. 48, 900 (1986).
[CrossRef]

G. P. Agrawal, Appl. Phys. Lett. 49, 1013 (1986).
[CrossRef]

H. Kawaguchi, Appl. Phys. Lett. 45, 1264 (1984).
[CrossRef]

J. Opt. Soc. Am. B (3)

J. Phys. (Paris) (1)

R. Frey, B. Thédrez, J. Phys. (Paris) 49, C2-393 (1988).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

F. Mogensen, G. Jacobsen, H. Holesen, Opt. Quantum Electron. 16, 183 (1984).
[CrossRef]

Phys. Rev. A (1)

K. Otsuka, H. Iwamura, Phys. Rev. A 28, 3153 (1983).
[CrossRef]

Phys. Rev. B (1)

M. D. Levenson, C. Flytzanis, N. Bloembergen, Phys. Rev. B 6, 3962 (1972).
[CrossRef]

Phys. Rev. Lett. (1)

T. Mukai, K. Otsuka, Phys. Rev. Lett. 55, 1711 (1985).
[CrossRef] [PubMed]

Other (1)

C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynbert, Processus d’interactions entre photons et atomes (Interéditions, Paris, 1988), Chap. VI.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Typical NDFWM spectrum. O1, O1*, O2, and O2* denote frequencies ω + δω, ωδω, ω − Ω + δω, and ω + Ω − δω, respectively.

Fig. 3
Fig. 3

Conjugate intensity at frequency ωδω for laser L0 operated in the unstable injected regime.

Fig. 4
Fig. 4

Different mixing processes involved in the generation of the conjugate wave of frequency ωδω. Processes (b) and (c) are resonant twice when δω = Ω/2.

Equations (4)

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P ( ω δω ) = χ ( 3 ) [ ω , ω , ( ω + δω ) ] A 2 ( ω ) A * ( ω + δω ) + χ ( 3 ) [ ω + δω , ω Ω + ( Ω 2 δω ) , ω ] A ( ω + δω ) × A [ ω Ω + ( Ω 2 δω ) ] A * ( ω ) + χ ( 3 ) { ω + δω , ω , [ ω + Ω ( Ω 2 δω ) ] } × A ( ω + δω ) A ( ω ) A * [ ω + Ω ( Ω 2 δω ) ] ,
χ ( 3 ) [ ω , ω , ( ω + δω ) ] K 1 δ ω 2 ,
χ ( 3 ) [ ω + δω , ω Ω + ( Ω 2 δω ) , ω ] K 2 δω ( Ω 2 δω + i Γ ) ,
χ ( 3 ) { ω + δω , ω , [ ω + Ω ( Ω 2 δω ) ] } K 3 δω ( Ω 2 δω + i Γ ) 2 ,

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