Effects of the Radial Variation of the Electric Field on Some Instabilities in Optical Bistability and Lasers

  • L. A. Lugiato
  • M. Milani


The overwhelming majority of theories for laser and optical bistability (OB) have been worked out within the plane wave approximation. However, recently, several authors have focussed their attention on giving a description of these systems which fully includes the transverse variation of the electromagnetic field. The reason for doing that is twofold. First of all, in OB the field injected into the cavity has typically a Gaussian radial profile, and therefore it is impossible to obtain a reasonable quantitative agreement between theory and experiment without including this feature in the theory. Second, in the case of instabilities it has been shown that the radial variation of the field induces not only quantitative but even qualitative changes in the behaviour of the system. E.g., in the case of dispersive OB in a ring cavity with plane mirrors, the route to chaos changes from period doubling to quasiperiodic1. Other striking examples will be given in this paper.


Transverse Mode Ring Cavity Radial Variation Incident Field Optical Bistability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1).
    J.V. Moloney, F.A. Hopf and H.M. Gibbs, Phys. Rev. A 25, 3442 (1982)ADSCrossRefGoogle Scholar
  2. 2).
    R.J. Ballagh, J. Cooper, M.W. Hamilton, W.J. Sandle and D.M. Warrington, Opt. Commun. 37, 143 (1981)ADSCrossRefGoogle Scholar
  3. 3).
    E. Arimondo, A. Gozzini, F. Lovitch and E. Pistelli in Optical Bistability, Proc. Int. Conf. Asheville, North Carolina 1980, edited by C.M. Bowden, M. Ciftan and H.R. Robl, Plenum Press, New York 1981Google Scholar
  4. 4).
    P.D. Drummond, IEEE J. Quant. Electron. QE-17, 301 (1981)ADSCrossRefGoogle Scholar
  5. 5).
    N.N. Rosanov and V.E. Semenov, Opt. Commun. 38, 435 (1981)ADSCrossRefGoogle Scholar
  6. 6).
    W.J. Firth and E.M. Wright, Opt. Commun. 40, 223 (1982)ADSCrossRefGoogle Scholar
  7. 7).
    J.V. Moloney, M.R. Belic and H.M. Gibbs, Opt. Commun. 41, 379 (1982)ADSCrossRefGoogle Scholar
  8. 8).
    J.V. Moloney and H.M. Gibbs, Phys. Rev. Lett. 48, 1607 (1982)ADSCrossRefGoogle Scholar
  9. 9).
    H. Haken, Z. Physik 190, 327 (1966)MathSciNetADSCrossRefGoogle Scholar
  10. 10).
    H. Risken, C. Schmid and M. Weidlich, Z. Physik 194, 337 (1966)ADSCrossRefGoogle Scholar
  11. 11).
    H. Haken, Phys. Lett. 53 A, 77 (1975)Google Scholar
  12. 12).
    E.N. Lorenz, J. Atmos. Sci. 20, 130 (1963)ADSCrossRefGoogle Scholar
  13. 13).
    H. Risken and Nummedal, J. Appl. Phys. 39, 4662 (1968)ADSCrossRefGoogle Scholar
  14. 14).
    R. Graham and H. Haken, Z. Physik 213, 420 (1968)ADSCrossRefGoogle Scholar
  15. 15).
    R. Bonifacio and L.A. Lugiato, Lett. Nuovo Cimento 21, 510 (1978)CrossRefGoogle Scholar
  16. 16).
    L.A. Lugiato, Opt. Commun. 33, 108 (1981)ADSCrossRefGoogle Scholar
  17. 17).
    K. Ikeda, Opt. Commun. 30, 257 (1979)ADSCrossRefGoogle Scholar
  18. 18).
    L.A. Lugiato, M.L. Asquini and L.M. Narducci, Opt. Commun. 41, 450 (1982)ADSCrossRefGoogle Scholar
  19. 19).
    W.J. Sandle and A. Gallagher, Phys. Rev. A 24, 2017 (1981)ADSCrossRefGoogle Scholar
  20. 20).
    D.E. Grant and J.H. Kimble, Opt. Lett. 7, 353 (1982)ADSCrossRefGoogle Scholar
  21. 21).
    L.A. Lugiato and M. Milani, Z. f. Physik B 50, 171 (1983)ADSCrossRefGoogle Scholar
  22. 22).
    R. Bonifacio and L.A. Lugiato, in Dissipative Systems in Quantum Optics; Resonance Fluorescence, Optical Bistability, Superfluorescence, edited by R. Bonifacio, Springer-Verlag, BerlinGoogle Scholar
  23. 23).
    L.A. Lugiato and M. Milani, Opt. Commun. 46, 57 (1983)ADSCrossRefGoogle Scholar
  24. 24).
    F.T. Arecchi, G. Giusfredi, E. Petriella and P. Salieri Appl. Phys. B 29, 79 (1982)ADSCrossRefGoogle Scholar
  25. 25).
    M.L. Minden and L.W. Casperson, IEEE Journ. of Quantum Electronics QE-18, 1952 (1982)ADSCrossRefGoogle Scholar
  26. 26).
    S.T. Hendow and M. Sargent III, Opt. Commun. 40, 385 (1982)ADSCrossRefGoogle Scholar
  27. 27).
    P. Mandel, Opt. Commun. 44, 400 (1983)MathSciNetADSCrossRefGoogle Scholar
  28. 28).
    L.A. Lugiato, L.M. Narducci, D. Bandy and N. Abraham, Opt. Commun., in pressGoogle Scholar
  29. 29).
    L.W. Casperson, IEEE Journal Quantum Electron. QE-14, 756 (1978)ADSCrossRefGoogle Scholar
  30. 30).
    J. Beatley and N.B. Abraham, Opt. Commun. 41, 52 (1982)ADSCrossRefGoogle Scholar
  31. 31).
    L.A. Lugiato, L.M. Narducci, D. Bandy and C. Pennise, Opt. Commun. 43, 281 (1982)ADSCrossRefGoogle Scholar
  32. 32).
    L.A. Lugiato, L.M. Narducci, D. Bandy and C.A. Pennise, submitted for publicationGoogle Scholar
  33. 33).
    H.J. Powell and G.J. Wolga, IEEE Journ. Quantum Electron. QE-7, 219 (1971)ADSGoogle Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • L. A. Lugiato
    • 1
  • M. Milani
    • 1
  1. 1.Dipartimento di Fisica dell’UniversitàMilanoItaly

Personalised recommendations