Advertisement

Optical Bistability, Chaos in the Coherent Two-Photon Processes

  • G. S. Agarwal
  • Surendra Singh
Conference paper

Abstract

In this paper recent work1–4 on intracavity coherent two-photon processes is reviewed and some new results are presented. Various instabilities due to the cooperative interaction between the atoms as reflected in the outp field are described. This study is moti-vated by the recent work 5–7 on the instabilities in single-photon processes. We solve the coupled Maxwell-Bloch equations for coherent two-photon processes8 with boundary conditions appropriate to a ring cavity using Ikeda5 et al.’s method and obtain a two-dimensional map characterizing the output field. The mean field behavior and the resulting critical exponents are discussed. Several different routes to chaos are shown to be possible. We also comment on the oscillator models of two-photon instabilities.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    F. T. Arecchi and A. Politi, Lett. Nuovo Cimento 23, 65 (1978);CrossRefGoogle Scholar
  2. G. P. Agrawal and C. Flytzanis, Phys. Rev. Lett. 44, 1058 (1980);ADSCrossRefGoogle Scholar
  3. J. A. Herman and B. V. Thompson in Op i.ca2 BL6,tabit ty, edited by C. M. Bowden, M. Cif tan and H. R. Robl ( Plenum, New York, 1981 ), p. 199.Google Scholar
  4. 2.
    G. S. Agarwal, Opt. Commun. 35, 149 (1980).ADSCrossRefGoogle Scholar
  5. 3.
    J. A. Herman and B. V. Thompson, Opt. Lett. 7, 301 (1982).ADSCrossRefGoogle Scholar
  6. 4.
    Surendra Singh and G. S. Agarwal, Opt. Commun. (in press).Google Scholar
  7. 5.
    K. Ikeda and O. Akimoto, Phys. Rev. Lett. 48, 617 (1982).ADSCrossRefMathSciNetGoogle Scholar
  8. 6.
    H. J. Carmichael, R. R. Snapp and W. C. Schieve, Phys. Rev. A26, 3408 (1982);ADSCrossRefGoogle Scholar
  9. E. Abraham and W. J. Firth and J. Carr, Phys. Lett. 91A, 47 (1982).CrossRefGoogle Scholar
  10. 7.
    H. M. Gibbs, F. D. Hopf, D. L. Kaplan and R. L. Shoemaker, Phys. Rev. Lett. 46, 474 (1981).ADSCrossRefGoogle Scholar
  11. 8.
    M. Takatsuji, Phys. Rev. A19. Eidson in Cohekence in Spect’to4copy and Modetn Phydic.o, edited by F. T. Arecchi, R. Bonifacio and M. O. Scully ( Plenum, New York, 1979 ), p. 131.Google Scholar
  12. 9.
    R. Bonifacio and L. A. Lugiato, Lett. Nuovo Cimento 21, 505 (1978).CrossRefGoogle Scholar
  13. 10.
    E. Giacobino, M. Devaud, F. Biraben and G. Grynberg, Phys. Rev. Lett. 45, 434 (1980).ADSCrossRefGoogle Scholar
  14. 11.
    G. S. Agarwal and S. R. Shenoy, Phys. Rev. B25, 1879 (1982).ADSCrossRefGoogle Scholar
  15. 12.
    R. Bonifacio and L. A. Lugiato, Phys. Rev. A18, 1129 (1978).ADSCrossRefGoogle Scholar
  16. 13.
    D. E. Grant and H. J. Kimble, Opt. Commun. 44, 415 (1983).ADSCrossRefGoogle Scholar
  17. 14.
    M. J. Feigenbaum, J. Stat. Phys. 19, 25 (1978).Google Scholar
  18. 14.
    M. J. Feigenbaum, J. Stat. Phys. 19, 25 (1978); R. M. May, Nature 261, 459 (1976).ADSCrossRefGoogle Scholar
  19. 15.
    J. Crutchfield, M. Nauenberg and J. Rudnick, Phys. Rev. Lett. 46, 933 (1981);ADSCrossRefMathSciNetGoogle Scholar
  20. B. Shraiman, C. E. Wayne and P. C. Martin, Phys. Rev. Lett. 46, 935 (1981).ADSCrossRefMathSciNetGoogle Scholar
  21. 16.
    Cf. C. G. B. Garrett, IEEE J. Quantum Electron. QE-4, 70 (1968).Google Scholar
  22. 17.
    H. Haug, S. W. Koch, R. Neumann and H. E. Schmidt, Z. Phys. B49, 79 (1982).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • G. S. Agarwal
    • 1
  • Surendra Singh
    • 2
  1. 1.School of PhysicsUniversity of HyderabadHyderabadIndia
  2. 2.Dept. of PhysicsUniversity of ArkansasFayettevilleUSA

Personalised recommendations