Abstract

We report on the static and dynamic behavior of the intensity and polarization of the light transmitted by a Fabry–Perot cavity filled with sodium vapor without a buffer gas. The light beam is resonant with the D1 transition, and the behavior can be traced back to the simultaneous presence of Zeeman pumping and hyperfine pumping in the sodium ground state, combined with velocity-selective hole-burning effects. Together with optical bistability, tristability, and pitchfork bifurcation, the system displays intrinsic oscillations in the absence of a magnetic field. We discuss the features of these phenomena, particularly the appearance of Hopf bifurcations, and the ways they are affected by the experimental control parameters. We also report evidence of period doubling and of more-complex dynamics in the presence of a magnetic field.

© 1988 Optical Society of America

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  1. H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, Phys. Rev. Lett. 36, 1135 (1976).
    [Crossref]
  2. A recent review research on OB can be found in H. M. Gibbs, Optical Bistability (Academic, New York, 1985).A review of theory can be found in L. A. Lugiato, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1984), Vol. XXI.
  3. F. T. Arecchi, G. Giusfredi, E. Petriella, and P. Salieri, Appl. Phys. B 29, 79 (1982).
    [Crossref]
  4. M. Kitano, T. Yabuzaki, and T. Ogawa, Phys. Rev. Lett. 46, 926 (1981).
    [Crossref]
  5. S. Cecchi, G. Giusfredi, E. Petriella, and P. Salieri, Phys. Rev. Lett. 49, 1928 (1982).
    [Crossref]
  6. W. J. Sandle and A. Gallagher, Phys. Rev. A 24, 2017 (1981).
    [Crossref]
  7. K. G. Weyer, H. Wiedenmann, M. Rateike, W. R. MacGillivray, P. Meystre, and H. Walther, Opt. Commun. 37, 426 (1981).
    [Crossref]
  8. D. E. Grant and H. J. Kimble, Opt. Lett. 7, 353 (1982);A. T. Rosenberger, L. A. Orozco, and H. J. Kimble, Phys. Rev. A 28, 2569 (1983).
    [Crossref] [PubMed]
  9. M. W. Hamilton, W. J. Sandle, J. T. Chilwell, J. S. Satchell, and D. M. Warrington, Opt. Commun. 48, 190 (1983).
    [Crossref]
  10. E. Giacobino, Opt. Commun. 56, 249 (1985).
    [Crossref]
  11. W. E. Schultz, W. R. MacGillivray, and M. C. Standage, Opt. Commun. 45, 67 (1983).
    [Crossref]
  12. J. Mlynek, F. Mitschke, R. Deserno, and W. Lange, Phys. Rev. A 29, 1297 (1984).
    [Crossref]
  13. F. Mitschke, R. Deserno, J. Mlynek, and W. Lange, IEEE J. Quantum Electron. QE-21, 1435 (1985), and references therein.
    [Crossref]
  14. C. Parigger, P. Hannaford, W. J. Sandle, and R. J. Ballag, Phys. Rev. A 31, 4043 (1985).
    [Crossref] [PubMed]
  15. G. Giusfredi, P. Salieri, S. Cecchi, and F. T. Arecchi, Opt. Commun. 54, 39 (1985).
    [Crossref]
  16. L. A. Lugiato, L. M. Narducci, D. K. Bandy, and C. A. Pennise, Opt. Commun. 43, 281 (1982);Opt. Commun. 44, 207 (1983);L. A. Lugiato, R. J. Horowicz, G. Strini, and L. M. Narducci, Phys. Rev. A 30, 1366 (1984).
    [Crossref]
  17. L. A. Orozco, A. T. Rosenberger, and H. J. Kimble, Phys. Rev. Lett. 53, 2547 (1984).
    [Crossref]
  18. C. M. Savage, H. J. Carmichael, and D. F. Walls, Opt. Commun. 42, 211 (1982).
    [Crossref]
  19. F. T. Arecchi, J. Kurmann, and A. Politi, Opt. Commun. 44, 421 (1983).
    [Crossref]
  20. H. J. Carmichael, C. M. Savage, and D. F. Walls, Phys. Rev. Lett. 50, 163 (1983).
    [Crossref]
  21. M. Kitano, T. Yabuzaki, and T. Ogawa, Phys. Rev. A 24, 3156 (1981).
    [Crossref]
  22. F. Mitschke, J. Mlynek, and W. Lange, Phys. Rev. Lett. 50, 1660 (1983).
    [Crossref]
  23. N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965).
  24. W. Happer, Rev. Mod. Phys. 44, 169 (1972).
    [Crossref]
  25. Y. Silberberg and I. Bar-Joseph, J. Opt. Soc. Am. B 1, 662 (1984).
    [Crossref]
  26. A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, Phys. Rev. Lett. 58, 2432 (1987).
    [Crossref] [PubMed]
  27. I. P. Areshev, T. A. Murina, N. N. Rosanov, and V. K. Subashiev, Opt. Commun. 47, 414 (1983).
    [Crossref]
  28. F. Marquis, P. Dobiasch, P. Meystre, and M. E. Wright, J. Opt. Soc. Am. B 3, 50 (1986).
    [Crossref]
  29. J. E. Bjorkhholm, P. W. Smith, W. J. Tomlinson, and A. E. Kaplan, Opt. Lett. 6, 345 (1981);K. Tay, H. M. Gibbs, N. Peyghamberian, and A. Mysyrowicz, Opt. Lett. 10, 220 (1985).
    [Crossref]
  30. H. M. Gibbs, M. W. Derstine, F. A. Hopf, D. L. Kaplan, M. C. Rushford, R. L. Schoemaker, D. A. Weinberger, and W. H. Wing, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1982), paper FL2;see also H. M. Gibbs, Optical Bistability (Academic, New York, 1985), pp. 246–247.
  31. J. V. Moloney, F. A. Hopf, and H. M. Gibbs, Phys. Rev. A 25, 3442 (1982);J. V. Moloney, Phys. Rev. Lett. 53, 556 (1984).
    [Crossref]
  32. G. Giusfredi, S. Cecchi, E. Petriella, P. Salieri, and F. T. Arecchi, in Instabilities and Chaos in Quantum Optics, F. T. Arecchi and R. G. Harrison, eds. (Springer-Verlag, Berlin, 1987).
  33. A. Moretti and F. Strumia, Phys. Rev. A 3, 349 (1971).
    [Crossref]
  34. S. L. McCall, Appl. Phys. Lett. 32, 284 (1978).
    [Crossref]
  35. H. M. Gibbs, J. L. Jewell, S. S. Tarng, A. C. Gossard, and W. Wiegmann, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1981), p. 42.
  36. M. M. Cheung, S. D. Durbin, and Y. R. Shen, Opt. Lett. 8, 39 (1983).
    [Crossref] [PubMed]
  37. P. G. Pappas, R. A. Forber, W. W. Quivers, R. R. Dasari, M. S. Feld, and D. E. Murnick, Phys. Rev. Lett. 47236 (1981).
    [Crossref]

1987 (1)

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, Phys. Rev. Lett. 58, 2432 (1987).
[Crossref] [PubMed]

1986 (1)

1985 (4)

E. Giacobino, Opt. Commun. 56, 249 (1985).
[Crossref]

F. Mitschke, R. Deserno, J. Mlynek, and W. Lange, IEEE J. Quantum Electron. QE-21, 1435 (1985), and references therein.
[Crossref]

C. Parigger, P. Hannaford, W. J. Sandle, and R. J. Ballag, Phys. Rev. A 31, 4043 (1985).
[Crossref] [PubMed]

G. Giusfredi, P. Salieri, S. Cecchi, and F. T. Arecchi, Opt. Commun. 54, 39 (1985).
[Crossref]

1984 (3)

J. Mlynek, F. Mitschke, R. Deserno, and W. Lange, Phys. Rev. A 29, 1297 (1984).
[Crossref]

L. A. Orozco, A. T. Rosenberger, and H. J. Kimble, Phys. Rev. Lett. 53, 2547 (1984).
[Crossref]

Y. Silberberg and I. Bar-Joseph, J. Opt. Soc. Am. B 1, 662 (1984).
[Crossref]

1983 (7)

M. M. Cheung, S. D. Durbin, and Y. R. Shen, Opt. Lett. 8, 39 (1983).
[Crossref] [PubMed]

I. P. Areshev, T. A. Murina, N. N. Rosanov, and V. K. Subashiev, Opt. Commun. 47, 414 (1983).
[Crossref]

F. T. Arecchi, J. Kurmann, and A. Politi, Opt. Commun. 44, 421 (1983).
[Crossref]

H. J. Carmichael, C. M. Savage, and D. F. Walls, Phys. Rev. Lett. 50, 163 (1983).
[Crossref]

F. Mitschke, J. Mlynek, and W. Lange, Phys. Rev. Lett. 50, 1660 (1983).
[Crossref]

M. W. Hamilton, W. J. Sandle, J. T. Chilwell, J. S. Satchell, and D. M. Warrington, Opt. Commun. 48, 190 (1983).
[Crossref]

W. E. Schultz, W. R. MacGillivray, and M. C. Standage, Opt. Commun. 45, 67 (1983).
[Crossref]

1982 (6)

D. E. Grant and H. J. Kimble, Opt. Lett. 7, 353 (1982);A. T. Rosenberger, L. A. Orozco, and H. J. Kimble, Phys. Rev. A 28, 2569 (1983).
[Crossref] [PubMed]

F. T. Arecchi, G. Giusfredi, E. Petriella, and P. Salieri, Appl. Phys. B 29, 79 (1982).
[Crossref]

S. Cecchi, G. Giusfredi, E. Petriella, and P. Salieri, Phys. Rev. Lett. 49, 1928 (1982).
[Crossref]

C. M. Savage, H. J. Carmichael, and D. F. Walls, Opt. Commun. 42, 211 (1982).
[Crossref]

L. A. Lugiato, L. M. Narducci, D. K. Bandy, and C. A. Pennise, Opt. Commun. 43, 281 (1982);Opt. Commun. 44, 207 (1983);L. A. Lugiato, R. J. Horowicz, G. Strini, and L. M. Narducci, Phys. Rev. A 30, 1366 (1984).
[Crossref]

J. V. Moloney, F. A. Hopf, and H. M. Gibbs, Phys. Rev. A 25, 3442 (1982);J. V. Moloney, Phys. Rev. Lett. 53, 556 (1984).
[Crossref]

1981 (6)

P. G. Pappas, R. A. Forber, W. W. Quivers, R. R. Dasari, M. S. Feld, and D. E. Murnick, Phys. Rev. Lett. 47236 (1981).
[Crossref]

M. Kitano, T. Yabuzaki, and T. Ogawa, Phys. Rev. A 24, 3156 (1981).
[Crossref]

J. E. Bjorkhholm, P. W. Smith, W. J. Tomlinson, and A. E. Kaplan, Opt. Lett. 6, 345 (1981);K. Tay, H. M. Gibbs, N. Peyghamberian, and A. Mysyrowicz, Opt. Lett. 10, 220 (1985).
[Crossref]

W. J. Sandle and A. Gallagher, Phys. Rev. A 24, 2017 (1981).
[Crossref]

K. G. Weyer, H. Wiedenmann, M. Rateike, W. R. MacGillivray, P. Meystre, and H. Walther, Opt. Commun. 37, 426 (1981).
[Crossref]

M. Kitano, T. Yabuzaki, and T. Ogawa, Phys. Rev. Lett. 46, 926 (1981).
[Crossref]

1978 (1)

S. L. McCall, Appl. Phys. Lett. 32, 284 (1978).
[Crossref]

1976 (1)

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, Phys. Rev. Lett. 36, 1135 (1976).
[Crossref]

1972 (1)

W. Happer, Rev. Mod. Phys. 44, 169 (1972).
[Crossref]

1971 (1)

A. Moretti and F. Strumia, Phys. Rev. A 3, 349 (1971).
[Crossref]

Ackerhalt, J. R.

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, Phys. Rev. Lett. 58, 2432 (1987).
[Crossref] [PubMed]

Arecchi, F. T.

G. Giusfredi, P. Salieri, S. Cecchi, and F. T. Arecchi, Opt. Commun. 54, 39 (1985).
[Crossref]

F. T. Arecchi, J. Kurmann, and A. Politi, Opt. Commun. 44, 421 (1983).
[Crossref]

F. T. Arecchi, G. Giusfredi, E. Petriella, and P. Salieri, Appl. Phys. B 29, 79 (1982).
[Crossref]

G. Giusfredi, S. Cecchi, E. Petriella, P. Salieri, and F. T. Arecchi, in Instabilities and Chaos in Quantum Optics, F. T. Arecchi and R. G. Harrison, eds. (Springer-Verlag, Berlin, 1987).

Areshev, I. P.

I. P. Areshev, T. A. Murina, N. N. Rosanov, and V. K. Subashiev, Opt. Commun. 47, 414 (1983).
[Crossref]

Ballag, R. J.

C. Parigger, P. Hannaford, W. J. Sandle, and R. J. Ballag, Phys. Rev. A 31, 4043 (1985).
[Crossref] [PubMed]

Bandy, D. K.

L. A. Lugiato, L. M. Narducci, D. K. Bandy, and C. A. Pennise, Opt. Commun. 43, 281 (1982);Opt. Commun. 44, 207 (1983);L. A. Lugiato, R. J. Horowicz, G. Strini, and L. M. Narducci, Phys. Rev. A 30, 1366 (1984).
[Crossref]

Bar-Joseph, I.

Bjorkhholm, J. E.

Bloembergen, N.

N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965).

Boyd, R. W.

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, Phys. Rev. Lett. 58, 2432 (1987).
[Crossref] [PubMed]

Carmichael, H. J.

H. J. Carmichael, C. M. Savage, and D. F. Walls, Phys. Rev. Lett. 50, 163 (1983).
[Crossref]

C. M. Savage, H. J. Carmichael, and D. F. Walls, Opt. Commun. 42, 211 (1982).
[Crossref]

Cecchi, S.

G. Giusfredi, P. Salieri, S. Cecchi, and F. T. Arecchi, Opt. Commun. 54, 39 (1985).
[Crossref]

S. Cecchi, G. Giusfredi, E. Petriella, and P. Salieri, Phys. Rev. Lett. 49, 1928 (1982).
[Crossref]

G. Giusfredi, S. Cecchi, E. Petriella, P. Salieri, and F. T. Arecchi, in Instabilities and Chaos in Quantum Optics, F. T. Arecchi and R. G. Harrison, eds. (Springer-Verlag, Berlin, 1987).

Cheung, M. M.

Chilwell, J. T.

M. W. Hamilton, W. J. Sandle, J. T. Chilwell, J. S. Satchell, and D. M. Warrington, Opt. Commun. 48, 190 (1983).
[Crossref]

Dasari, R. R.

P. G. Pappas, R. A. Forber, W. W. Quivers, R. R. Dasari, M. S. Feld, and D. E. Murnick, Phys. Rev. Lett. 47236 (1981).
[Crossref]

Derstine, M. W.

H. M. Gibbs, M. W. Derstine, F. A. Hopf, D. L. Kaplan, M. C. Rushford, R. L. Schoemaker, D. A. Weinberger, and W. H. Wing, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1982), paper FL2;see also H. M. Gibbs, Optical Bistability (Academic, New York, 1985), pp. 246–247.

Deserno, R.

F. Mitschke, R. Deserno, J. Mlynek, and W. Lange, IEEE J. Quantum Electron. QE-21, 1435 (1985), and references therein.
[Crossref]

J. Mlynek, F. Mitschke, R. Deserno, and W. Lange, Phys. Rev. A 29, 1297 (1984).
[Crossref]

Dobiasch, P.

Durbin, S. D.

Feld, M. S.

P. G. Pappas, R. A. Forber, W. W. Quivers, R. R. Dasari, M. S. Feld, and D. E. Murnick, Phys. Rev. Lett. 47236 (1981).
[Crossref]

Forber, R. A.

P. G. Pappas, R. A. Forber, W. W. Quivers, R. R. Dasari, M. S. Feld, and D. E. Murnick, Phys. Rev. Lett. 47236 (1981).
[Crossref]

Gaeta, A. L.

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, Phys. Rev. Lett. 58, 2432 (1987).
[Crossref] [PubMed]

Gallagher, A.

W. J. Sandle and A. Gallagher, Phys. Rev. A 24, 2017 (1981).
[Crossref]

Giacobino, E.

E. Giacobino, Opt. Commun. 56, 249 (1985).
[Crossref]

Gibbs, H. M.

J. V. Moloney, F. A. Hopf, and H. M. Gibbs, Phys. Rev. A 25, 3442 (1982);J. V. Moloney, Phys. Rev. Lett. 53, 556 (1984).
[Crossref]

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, Phys. Rev. Lett. 36, 1135 (1976).
[Crossref]

A recent review research on OB can be found in H. M. Gibbs, Optical Bistability (Academic, New York, 1985).A review of theory can be found in L. A. Lugiato, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1984), Vol. XXI.

H. M. Gibbs, J. L. Jewell, S. S. Tarng, A. C. Gossard, and W. Wiegmann, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1981), p. 42.

H. M. Gibbs, M. W. Derstine, F. A. Hopf, D. L. Kaplan, M. C. Rushford, R. L. Schoemaker, D. A. Weinberger, and W. H. Wing, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1982), paper FL2;see also H. M. Gibbs, Optical Bistability (Academic, New York, 1985), pp. 246–247.

Giusfredi, G.

G. Giusfredi, P. Salieri, S. Cecchi, and F. T. Arecchi, Opt. Commun. 54, 39 (1985).
[Crossref]

S. Cecchi, G. Giusfredi, E. Petriella, and P. Salieri, Phys. Rev. Lett. 49, 1928 (1982).
[Crossref]

F. T. Arecchi, G. Giusfredi, E. Petriella, and P. Salieri, Appl. Phys. B 29, 79 (1982).
[Crossref]

G. Giusfredi, S. Cecchi, E. Petriella, P. Salieri, and F. T. Arecchi, in Instabilities and Chaos in Quantum Optics, F. T. Arecchi and R. G. Harrison, eds. (Springer-Verlag, Berlin, 1987).

Gossard, A. C.

H. M. Gibbs, J. L. Jewell, S. S. Tarng, A. C. Gossard, and W. Wiegmann, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1981), p. 42.

Grant, D. E.

Hamilton, M. W.

M. W. Hamilton, W. J. Sandle, J. T. Chilwell, J. S. Satchell, and D. M. Warrington, Opt. Commun. 48, 190 (1983).
[Crossref]

Hannaford, P.

C. Parigger, P. Hannaford, W. J. Sandle, and R. J. Ballag, Phys. Rev. A 31, 4043 (1985).
[Crossref] [PubMed]

Happer, W.

W. Happer, Rev. Mod. Phys. 44, 169 (1972).
[Crossref]

Hopf, F. A.

J. V. Moloney, F. A. Hopf, and H. M. Gibbs, Phys. Rev. A 25, 3442 (1982);J. V. Moloney, Phys. Rev. Lett. 53, 556 (1984).
[Crossref]

H. M. Gibbs, M. W. Derstine, F. A. Hopf, D. L. Kaplan, M. C. Rushford, R. L. Schoemaker, D. A. Weinberger, and W. H. Wing, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1982), paper FL2;see also H. M. Gibbs, Optical Bistability (Academic, New York, 1985), pp. 246–247.

Jewell, J. L.

H. M. Gibbs, J. L. Jewell, S. S. Tarng, A. C. Gossard, and W. Wiegmann, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1981), p. 42.

Kaplan, A. E.

Kaplan, D. L.

H. M. Gibbs, M. W. Derstine, F. A. Hopf, D. L. Kaplan, M. C. Rushford, R. L. Schoemaker, D. A. Weinberger, and W. H. Wing, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1982), paper FL2;see also H. M. Gibbs, Optical Bistability (Academic, New York, 1985), pp. 246–247.

Kimble, H. J.

Kitano, M.

M. Kitano, T. Yabuzaki, and T. Ogawa, Phys. Rev. Lett. 46, 926 (1981).
[Crossref]

M. Kitano, T. Yabuzaki, and T. Ogawa, Phys. Rev. A 24, 3156 (1981).
[Crossref]

Kurmann, J.

F. T. Arecchi, J. Kurmann, and A. Politi, Opt. Commun. 44, 421 (1983).
[Crossref]

Lange, W.

F. Mitschke, R. Deserno, J. Mlynek, and W. Lange, IEEE J. Quantum Electron. QE-21, 1435 (1985), and references therein.
[Crossref]

J. Mlynek, F. Mitschke, R. Deserno, and W. Lange, Phys. Rev. A 29, 1297 (1984).
[Crossref]

F. Mitschke, J. Mlynek, and W. Lange, Phys. Rev. Lett. 50, 1660 (1983).
[Crossref]

Lugiato, L. A.

L. A. Lugiato, L. M. Narducci, D. K. Bandy, and C. A. Pennise, Opt. Commun. 43, 281 (1982);Opt. Commun. 44, 207 (1983);L. A. Lugiato, R. J. Horowicz, G. Strini, and L. M. Narducci, Phys. Rev. A 30, 1366 (1984).
[Crossref]

MacGillivray, W. R.

W. E. Schultz, W. R. MacGillivray, and M. C. Standage, Opt. Commun. 45, 67 (1983).
[Crossref]

K. G. Weyer, H. Wiedenmann, M. Rateike, W. R. MacGillivray, P. Meystre, and H. Walther, Opt. Commun. 37, 426 (1981).
[Crossref]

Marquis, F.

McCall, S. L.

S. L. McCall, Appl. Phys. Lett. 32, 284 (1978).
[Crossref]

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, Phys. Rev. Lett. 36, 1135 (1976).
[Crossref]

Meystre, P.

F. Marquis, P. Dobiasch, P. Meystre, and M. E. Wright, J. Opt. Soc. Am. B 3, 50 (1986).
[Crossref]

K. G. Weyer, H. Wiedenmann, M. Rateike, W. R. MacGillivray, P. Meystre, and H. Walther, Opt. Commun. 37, 426 (1981).
[Crossref]

Milonni, P. W.

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, Phys. Rev. Lett. 58, 2432 (1987).
[Crossref] [PubMed]

Mitschke, F.

F. Mitschke, R. Deserno, J. Mlynek, and W. Lange, IEEE J. Quantum Electron. QE-21, 1435 (1985), and references therein.
[Crossref]

J. Mlynek, F. Mitschke, R. Deserno, and W. Lange, Phys. Rev. A 29, 1297 (1984).
[Crossref]

F. Mitschke, J. Mlynek, and W. Lange, Phys. Rev. Lett. 50, 1660 (1983).
[Crossref]

Mlynek, J.

F. Mitschke, R. Deserno, J. Mlynek, and W. Lange, IEEE J. Quantum Electron. QE-21, 1435 (1985), and references therein.
[Crossref]

J. Mlynek, F. Mitschke, R. Deserno, and W. Lange, Phys. Rev. A 29, 1297 (1984).
[Crossref]

F. Mitschke, J. Mlynek, and W. Lange, Phys. Rev. Lett. 50, 1660 (1983).
[Crossref]

Moloney, J. V.

J. V. Moloney, F. A. Hopf, and H. M. Gibbs, Phys. Rev. A 25, 3442 (1982);J. V. Moloney, Phys. Rev. Lett. 53, 556 (1984).
[Crossref]

Moretti, A.

A. Moretti and F. Strumia, Phys. Rev. A 3, 349 (1971).
[Crossref]

Murina, T. A.

I. P. Areshev, T. A. Murina, N. N. Rosanov, and V. K. Subashiev, Opt. Commun. 47, 414 (1983).
[Crossref]

Murnick, D. E.

P. G. Pappas, R. A. Forber, W. W. Quivers, R. R. Dasari, M. S. Feld, and D. E. Murnick, Phys. Rev. Lett. 47236 (1981).
[Crossref]

Narducci, L. M.

L. A. Lugiato, L. M. Narducci, D. K. Bandy, and C. A. Pennise, Opt. Commun. 43, 281 (1982);Opt. Commun. 44, 207 (1983);L. A. Lugiato, R. J. Horowicz, G. Strini, and L. M. Narducci, Phys. Rev. A 30, 1366 (1984).
[Crossref]

Ogawa, T.

M. Kitano, T. Yabuzaki, and T. Ogawa, Phys. Rev. A 24, 3156 (1981).
[Crossref]

M. Kitano, T. Yabuzaki, and T. Ogawa, Phys. Rev. Lett. 46, 926 (1981).
[Crossref]

Orozco, L. A.

L. A. Orozco, A. T. Rosenberger, and H. J. Kimble, Phys. Rev. Lett. 53, 2547 (1984).
[Crossref]

Pappas, P. G.

P. G. Pappas, R. A. Forber, W. W. Quivers, R. R. Dasari, M. S. Feld, and D. E. Murnick, Phys. Rev. Lett. 47236 (1981).
[Crossref]

Parigger, C.

C. Parigger, P. Hannaford, W. J. Sandle, and R. J. Ballag, Phys. Rev. A 31, 4043 (1985).
[Crossref] [PubMed]

Pennise, C. A.

L. A. Lugiato, L. M. Narducci, D. K. Bandy, and C. A. Pennise, Opt. Commun. 43, 281 (1982);Opt. Commun. 44, 207 (1983);L. A. Lugiato, R. J. Horowicz, G. Strini, and L. M. Narducci, Phys. Rev. A 30, 1366 (1984).
[Crossref]

Petriella, E.

S. Cecchi, G. Giusfredi, E. Petriella, and P. Salieri, Phys. Rev. Lett. 49, 1928 (1982).
[Crossref]

F. T. Arecchi, G. Giusfredi, E. Petriella, and P. Salieri, Appl. Phys. B 29, 79 (1982).
[Crossref]

G. Giusfredi, S. Cecchi, E. Petriella, P. Salieri, and F. T. Arecchi, in Instabilities and Chaos in Quantum Optics, F. T. Arecchi and R. G. Harrison, eds. (Springer-Verlag, Berlin, 1987).

Politi, A.

F. T. Arecchi, J. Kurmann, and A. Politi, Opt. Commun. 44, 421 (1983).
[Crossref]

Quivers, W. W.

P. G. Pappas, R. A. Forber, W. W. Quivers, R. R. Dasari, M. S. Feld, and D. E. Murnick, Phys. Rev. Lett. 47236 (1981).
[Crossref]

Rateike, M.

K. G. Weyer, H. Wiedenmann, M. Rateike, W. R. MacGillivray, P. Meystre, and H. Walther, Opt. Commun. 37, 426 (1981).
[Crossref]

Rosanov, N. N.

I. P. Areshev, T. A. Murina, N. N. Rosanov, and V. K. Subashiev, Opt. Commun. 47, 414 (1983).
[Crossref]

Rosenberger, A. T.

L. A. Orozco, A. T. Rosenberger, and H. J. Kimble, Phys. Rev. Lett. 53, 2547 (1984).
[Crossref]

Rushford, M. C.

H. M. Gibbs, M. W. Derstine, F. A. Hopf, D. L. Kaplan, M. C. Rushford, R. L. Schoemaker, D. A. Weinberger, and W. H. Wing, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1982), paper FL2;see also H. M. Gibbs, Optical Bistability (Academic, New York, 1985), pp. 246–247.

Salieri, P.

G. Giusfredi, P. Salieri, S. Cecchi, and F. T. Arecchi, Opt. Commun. 54, 39 (1985).
[Crossref]

F. T. Arecchi, G. Giusfredi, E. Petriella, and P. Salieri, Appl. Phys. B 29, 79 (1982).
[Crossref]

S. Cecchi, G. Giusfredi, E. Petriella, and P. Salieri, Phys. Rev. Lett. 49, 1928 (1982).
[Crossref]

G. Giusfredi, S. Cecchi, E. Petriella, P. Salieri, and F. T. Arecchi, in Instabilities and Chaos in Quantum Optics, F. T. Arecchi and R. G. Harrison, eds. (Springer-Verlag, Berlin, 1987).

Sandle, W. J.

C. Parigger, P. Hannaford, W. J. Sandle, and R. J. Ballag, Phys. Rev. A 31, 4043 (1985).
[Crossref] [PubMed]

M. W. Hamilton, W. J. Sandle, J. T. Chilwell, J. S. Satchell, and D. M. Warrington, Opt. Commun. 48, 190 (1983).
[Crossref]

W. J. Sandle and A. Gallagher, Phys. Rev. A 24, 2017 (1981).
[Crossref]

Satchell, J. S.

M. W. Hamilton, W. J. Sandle, J. T. Chilwell, J. S. Satchell, and D. M. Warrington, Opt. Commun. 48, 190 (1983).
[Crossref]

Savage, C. M.

H. J. Carmichael, C. M. Savage, and D. F. Walls, Phys. Rev. Lett. 50, 163 (1983).
[Crossref]

C. M. Savage, H. J. Carmichael, and D. F. Walls, Opt. Commun. 42, 211 (1982).
[Crossref]

Schoemaker, R. L.

H. M. Gibbs, M. W. Derstine, F. A. Hopf, D. L. Kaplan, M. C. Rushford, R. L. Schoemaker, D. A. Weinberger, and W. H. Wing, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1982), paper FL2;see also H. M. Gibbs, Optical Bistability (Academic, New York, 1985), pp. 246–247.

Schultz, W. E.

W. E. Schultz, W. R. MacGillivray, and M. C. Standage, Opt. Commun. 45, 67 (1983).
[Crossref]

Shen, Y. R.

Silberberg, Y.

Smith, P. W.

Standage, M. C.

W. E. Schultz, W. R. MacGillivray, and M. C. Standage, Opt. Commun. 45, 67 (1983).
[Crossref]

Strumia, F.

A. Moretti and F. Strumia, Phys. Rev. A 3, 349 (1971).
[Crossref]

Subashiev, V. K.

I. P. Areshev, T. A. Murina, N. N. Rosanov, and V. K. Subashiev, Opt. Commun. 47, 414 (1983).
[Crossref]

Tarng, S. S.

H. M. Gibbs, J. L. Jewell, S. S. Tarng, A. C. Gossard, and W. Wiegmann, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1981), p. 42.

Tomlinson, W. J.

Venkatesan, T. N. C.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, Phys. Rev. Lett. 36, 1135 (1976).
[Crossref]

Walls, D. F.

H. J. Carmichael, C. M. Savage, and D. F. Walls, Phys. Rev. Lett. 50, 163 (1983).
[Crossref]

C. M. Savage, H. J. Carmichael, and D. F. Walls, Opt. Commun. 42, 211 (1982).
[Crossref]

Walther, H.

K. G. Weyer, H. Wiedenmann, M. Rateike, W. R. MacGillivray, P. Meystre, and H. Walther, Opt. Commun. 37, 426 (1981).
[Crossref]

Warrington, D. M.

M. W. Hamilton, W. J. Sandle, J. T. Chilwell, J. S. Satchell, and D. M. Warrington, Opt. Commun. 48, 190 (1983).
[Crossref]

Weinberger, D. A.

H. M. Gibbs, M. W. Derstine, F. A. Hopf, D. L. Kaplan, M. C. Rushford, R. L. Schoemaker, D. A. Weinberger, and W. H. Wing, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1982), paper FL2;see also H. M. Gibbs, Optical Bistability (Academic, New York, 1985), pp. 246–247.

Weyer, K. G.

K. G. Weyer, H. Wiedenmann, M. Rateike, W. R. MacGillivray, P. Meystre, and H. Walther, Opt. Commun. 37, 426 (1981).
[Crossref]

Wiedenmann, H.

K. G. Weyer, H. Wiedenmann, M. Rateike, W. R. MacGillivray, P. Meystre, and H. Walther, Opt. Commun. 37, 426 (1981).
[Crossref]

Wiegmann, W.

H. M. Gibbs, J. L. Jewell, S. S. Tarng, A. C. Gossard, and W. Wiegmann, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1981), p. 42.

Wing, W. H.

H. M. Gibbs, M. W. Derstine, F. A. Hopf, D. L. Kaplan, M. C. Rushford, R. L. Schoemaker, D. A. Weinberger, and W. H. Wing, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1982), paper FL2;see also H. M. Gibbs, Optical Bistability (Academic, New York, 1985), pp. 246–247.

Wright, M. E.

Yabuzaki, T.

M. Kitano, T. Yabuzaki, and T. Ogawa, Phys. Rev. Lett. 46, 926 (1981).
[Crossref]

M. Kitano, T. Yabuzaki, and T. Ogawa, Phys. Rev. A 24, 3156 (1981).
[Crossref]

Appl. Phys. B (1)

F. T. Arecchi, G. Giusfredi, E. Petriella, and P. Salieri, Appl. Phys. B 29, 79 (1982).
[Crossref]

Appl. Phys. Lett. (1)

S. L. McCall, Appl. Phys. Lett. 32, 284 (1978).
[Crossref]

IEEE J. Quantum Electron. (1)

F. Mitschke, R. Deserno, J. Mlynek, and W. Lange, IEEE J. Quantum Electron. QE-21, 1435 (1985), and references therein.
[Crossref]

J. Opt. Soc. Am. B (2)

Opt. Commun. (9)

K. G. Weyer, H. Wiedenmann, M. Rateike, W. R. MacGillivray, P. Meystre, and H. Walther, Opt. Commun. 37, 426 (1981).
[Crossref]

I. P. Areshev, T. A. Murina, N. N. Rosanov, and V. K. Subashiev, Opt. Commun. 47, 414 (1983).
[Crossref]

G. Giusfredi, P. Salieri, S. Cecchi, and F. T. Arecchi, Opt. Commun. 54, 39 (1985).
[Crossref]

L. A. Lugiato, L. M. Narducci, D. K. Bandy, and C. A. Pennise, Opt. Commun. 43, 281 (1982);Opt. Commun. 44, 207 (1983);L. A. Lugiato, R. J. Horowicz, G. Strini, and L. M. Narducci, Phys. Rev. A 30, 1366 (1984).
[Crossref]

M. W. Hamilton, W. J. Sandle, J. T. Chilwell, J. S. Satchell, and D. M. Warrington, Opt. Commun. 48, 190 (1983).
[Crossref]

E. Giacobino, Opt. Commun. 56, 249 (1985).
[Crossref]

W. E. Schultz, W. R. MacGillivray, and M. C. Standage, Opt. Commun. 45, 67 (1983).
[Crossref]

C. M. Savage, H. J. Carmichael, and D. F. Walls, Opt. Commun. 42, 211 (1982).
[Crossref]

F. T. Arecchi, J. Kurmann, and A. Politi, Opt. Commun. 44, 421 (1983).
[Crossref]

Opt. Lett. (3)

Phys. Rev. A (6)

A. Moretti and F. Strumia, Phys. Rev. A 3, 349 (1971).
[Crossref]

J. V. Moloney, F. A. Hopf, and H. M. Gibbs, Phys. Rev. A 25, 3442 (1982);J. V. Moloney, Phys. Rev. Lett. 53, 556 (1984).
[Crossref]

W. J. Sandle and A. Gallagher, Phys. Rev. A 24, 2017 (1981).
[Crossref]

M. Kitano, T. Yabuzaki, and T. Ogawa, Phys. Rev. A 24, 3156 (1981).
[Crossref]

J. Mlynek, F. Mitschke, R. Deserno, and W. Lange, Phys. Rev. A 29, 1297 (1984).
[Crossref]

C. Parigger, P. Hannaford, W. J. Sandle, and R. J. Ballag, Phys. Rev. A 31, 4043 (1985).
[Crossref] [PubMed]

Phys. Rev. Lett. (8)

L. A. Orozco, A. T. Rosenberger, and H. J. Kimble, Phys. Rev. Lett. 53, 2547 (1984).
[Crossref]

F. Mitschke, J. Mlynek, and W. Lange, Phys. Rev. Lett. 50, 1660 (1983).
[Crossref]

H. J. Carmichael, C. M. Savage, and D. F. Walls, Phys. Rev. Lett. 50, 163 (1983).
[Crossref]

M. Kitano, T. Yabuzaki, and T. Ogawa, Phys. Rev. Lett. 46, 926 (1981).
[Crossref]

S. Cecchi, G. Giusfredi, E. Petriella, and P. Salieri, Phys. Rev. Lett. 49, 1928 (1982).
[Crossref]

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, Phys. Rev. Lett. 36, 1135 (1976).
[Crossref]

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, Phys. Rev. Lett. 58, 2432 (1987).
[Crossref] [PubMed]

P. G. Pappas, R. A. Forber, W. W. Quivers, R. R. Dasari, M. S. Feld, and D. E. Murnick, Phys. Rev. Lett. 47236 (1981).
[Crossref]

Rev. Mod. Phys. (1)

W. Happer, Rev. Mod. Phys. 44, 169 (1972).
[Crossref]

Other (5)

G. Giusfredi, S. Cecchi, E. Petriella, P. Salieri, and F. T. Arecchi, in Instabilities and Chaos in Quantum Optics, F. T. Arecchi and R. G. Harrison, eds. (Springer-Verlag, Berlin, 1987).

H. M. Gibbs, M. W. Derstine, F. A. Hopf, D. L. Kaplan, M. C. Rushford, R. L. Schoemaker, D. A. Weinberger, and W. H. Wing, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1982), paper FL2;see also H. M. Gibbs, Optical Bistability (Academic, New York, 1985), pp. 246–247.

H. M. Gibbs, J. L. Jewell, S. S. Tarng, A. C. Gossard, and W. Wiegmann, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1981), p. 42.

A recent review research on OB can be found in H. M. Gibbs, Optical Bistability (Academic, New York, 1985).A review of theory can be found in L. A. Lugiato, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1984), Vol. XXI.

N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965).

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Figures (15)

Fig. 1
Fig. 1

Experimental setup. B, T, and L are, respectively, the controller of the magnetic field, the oven temperature, and the piezoelectric alignment of the Na FP cell (surrounded by three Helmholtz coils). F.I., Faraday isolator; Te, beam coupling telescope; P.C., Pockels cell; W, Wollaston prism; Din, DL, DR, photodiodes. The laser frequency is monitored on a monochromator (M), a spectrum analyzer (S.A.), and a reference Na cell (Na R.). The beam power is locked to the signal of a waveform generator (W.G.) via a noise-eater loop: EOM, electro-optic modulator; D, differential amplifier (no auto-oscillation is present). The signals are recorded on a scope or a transient digitizer (T.D.). λ/4, quarter-wave plates; Tr, trigger.

Fig. 2
Fig. 2

Phase diagram, simplified from Fig. 2 of Ref. 5, summarizing the observed behavior with B = 0 and linearly polarized input light the (power up to ∼60 mW; N is the Na density; νLν0 is the laser detuning Δ). The width of each region depends on power and cavity tuning (always optimized); the Na density is known within ±20% of its value. The meaning of the terms OT, OB, and PB and their sums is displayed in Fig. 3. The oscillations are observed in the hatched region below ν2 and above ν0; the dashed line includes the region where OB cycles also appear.

Fig. 3
Fig. 3

Stationary transmitted signals versus input power (Pin) at constant cavity length (l) as they appear in the various regions of Fig. 2. LS and HS, low- and high-transmission branches, respectively, symmetrical in the two output circular powers PL and PR; LA and RA, left- and right-polarized transmission branches, respectively. (a) Regions ν2 < νL < ν0 and ν1 < νL: simple OB cycles are mainly present. (b) Region ν0 < νL < ν1 at low Na densities. In this figure PB, which is not a hysteresis cycle, appears with a precise linear polarization; however, a hysteresis appears when the input polarization instead of Pin is scanned. (c) OB + PB, region ν0 < νL < ν1 at high densities: an OB cycle is superimposed upon PB. The dynamics of the upward jump shows two steps: an unstable symmetrical state is reached at first, and then the system falls on the LA or RA state. (d) PB + OB, region νL < ν2: the LS branch still bifurcates into the LA and RA branches, but at higher Pin an inverse OT cycle brings the system to a HS state. At the available power this behavior is not present in region ν0 < νL < ν1. (e) OT + PB as in (d) but for a different l: an OT cycle replaces the PB.

Fig. 4
Fig. 4

Transmitted power of the two circular components versus time (t = 10 μsec/division,PL(R) = 0.22 mW/division). Pin = 55 mW, N = 3.8 × 1011 cm−3, Δ = 0.19 GHz.

Fig. 5
Fig. 5

Region νL < ν1, Pin scanning with a triangular waveform, at (a) 20 Hz and (b) 200 Hz. For proper laser frequency and cavity tunings, oscillations appear in place of the inverse OT cycle of Fig. 3(e). N = 2×1011cm−3, Δ = − 1.08GHz. (a) Transmitted power of the two circular components versus input power. (b) Digitized signal of a circular component, Pin = 0 to ∼50 mW, sample time 625 nsec; in this and in the following figures a vertical dashed line indicates the inversion point: Pin increases at the left and decreases at the right. (c) Magnification of a part of (b); each cross gives the Δt interval between the corresponding peak and the previous one. For the digitized signal the vertical scale is in arbitrary units; however, it may be evaluated by comparison with (a). This applies also for the figures that follow.

Fig. 6
Fig. 6

Pin scanning (at ∼20 Hz) in region ν0 < νL < ν1 at two different Na densities. For proper tunings, the oscillations are found to replace the bifurcation in both the low- and high-density cases of Figs. 3(b) and 3(c). (a) N = 1.2 × 1011 cm−3, Δ = 0.08 GHz. (b) N = 3.8 × 1011 cm−3, Δ = 0.19 GHz (same conditions as in Fig. 4).

Fig. 7
Fig. 7

Digitized signal in region ν0 < νL < ν1 at low densities. The crosses and the points give the periods Δt of the oscillations as in Fig. 5(c). (a) Pin scanning (0 to ∼50 mW at 200 Hz), sample time 1 μMsec, N = 1.2 × 1011 cm−3, Δ = 0.08 GHz. (b) Magnification of (a). (c) Pin scanning (0 to ∼45 mW at 200 Hz), sample time 0.5 μsec, N = 2.1 × 1011 cm−3, (d) Transmitted signal versus time as in (c) but at constant Pin = 38 mW; the oscillation frequency is ∼235 kHz. The steps in the digitized signal [particularly visible in (c)] come from a defect in our digitizer that causes a loss of 2 levels for every 16; one unit in the vertical scale corresponds to 50 levels.

Fig. 8
Fig. 8

Pin scanning (200 Hz) in region ν0 < νL < ν1 at high densities; N = 3.2 × 1011 cm−3, Δ = 0.18 GHz, sample time 625 nsec. (a) and (b) Differ in mistuning. (c) Magnification of (b). Lower points in (a) and (c) yield the period, as do the crosses in Fig. 5(c).

Fig. 9
Fig. 9

l scanning with a sinusoidal modulation. The doubling of the peak arises from mechanical hysteresis of the FP cavity. (a) Region νL < ν2, 20-Hz modulation, Pin = 25 mW, N = 2 × 1011 cm−3, Δ = −1.04 GHz. (b) Region ν0 < νL < ν1 30-Hz modulation, Pin = 40 mW, but for this photo the beam diameter was ∼1.8 mm, N = 1.2 × 1011 cm−3, Δ = 0.16 GHz.

Fig. 10
Fig. 10

l scanning in region νL < ν2. 80-Hz sinusoidal modulation, Pin = 25 mW, N = 2 × 1011 cm−3, (a), (c) Transmitted signal versus l. The horizontal scale is normalized to the modulation amplitude, one unit corresponding to about 30 nm; the zero is the center of the modulation. (b), (d) The same signals versus time. (a), (b) Δ = −1.08 GHz. (c), (d) Δ = −1.04 GHz. Crosses as in Fig. 5(c).

Fig. 11
Fig. 11

l scanning in region ν0 < νL < ν1. 200-Hz sinusoidal modulation, sample time 500 nsec, Pin = 45 mW, N = 2.1 × 1011 cm−3. (a) Transmitted signal versus l, horizontal scale as in Figs. 10(a) and 10(c). (b) The same signal versus time for decreasing l. Lower points same as crosses in Fig. 5(c).

Fig. 12
Fig. 12

Pin scanning at 15 Hz. N = 2.1 × 1011 cm−3, Δ = 0.22 GHz. Similar behavior is observed at higher densities with the addition of an OB cycle.

Fig. 13
Fig. 13

(a)–(d) Sequence of Pin scanning (up to 45 mW at 1 kHz) at increasing l. Sample time 160 nsec, N = 1.2 × 1011 cm−3, Δ = 0.05 GHz.

Fig. 14
Fig. 14

Experimental conditions similar to those in Fig. 7. Longitudinal magnetic field BL = 0.04 G. (a) Pin scanning, lower points same crosses as in Fig. 3(c). (b) Magnification of (a), (c): constant Pin = 38 mW.

Fig. 15
Fig. 15

BV = 0.67 G (Larmor frequency 460 kHz, oscillation frequency ∼220 kHz). Pin = 35 mW, N = 2.1 × 1011 cm−3, region ν0 < νL < ν1.

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