Dispersive Optical Bistability with Fluctuations

  • R. Graham
  • A. Schenzle


We consider the phenomenon of dispersive optical bistability as an example of a non-equilibrium steady state lacking detailed balance. The Fokker Planck equation for the transmitted electromagnetic field is derived. For a special case of parameters we present an exact solution of the stationary distribution. In the limit of small fluctuations the Folkker Planck equation is reduced to the form of a Hamilton Jacobi equation for a, “non-equilibrium thermodynamic potential”. This equation is solved approximately by analytical methods. The “non-equilibrium thermodynamic potential” acts like a free energy for the first order type phase transitions far from thermodynamic equilibrium lacking the property of detailed balance.


External Field Fokker Planck Equation Detailed Balance Hamilton Jacobi Equation Deterministic Equation 
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  1. 1.
    R. Graham and H. Haken, Z. Phys. 31, 237 (1970).MathSciNetGoogle Scholar
  2. 2.
    De Giorgio and M. O. Scully, Phys. Rev. A2, 1170 (1970).ADSGoogle Scholar
  3. 3.
    J. F. Scott, M. Sargent, III and C. D. Contrell, Optics Comm. 15, 13 (1975), S. T. Dembinsky and A. Kossakowski, Z. Phys. B25, 20 (1976).ADSCrossRefGoogle Scholar
  4. 4.
    R. B. Schaefer and C. R. Willis, Phys. Lett. 58A, 53 (1976).ADSGoogle Scholar
  5. 5.
    A. Szöke, V. Danen, S. Goldhar, and N. A. Kurnit, Appl. Phys. Lett. 15, 376 (1969).ADSCrossRefGoogle Scholar
  6. 6.
    S. L. McCall, Phys. Rev. A9, 1515 (1974).ADSGoogle Scholar
  7. 7.
    H. M. Gibbs, S. L. McCall and T. N. C. Venkatesan, Phys. Rev. Lett. 36, 1135 (1976).ADSCrossRefGoogle Scholar
  8. 8.
    R. Bonifacio and L. Lugiato, Optics Comm. 19, 172 (1976).ADSCrossRefGoogle Scholar
  9. 9.
    S. R. DeGroot and P. Mazur, Nonequilibrium Thermodynamics, North-Holland, Amsterdam (1962).Google Scholar
  10. 10.
    H. Haken, Handbuch der Physik, Springer, Berlin, Vol. XXV/2c.Google Scholar
  11. 11.
    A. Schenzle and H. Brand, Optics Comm. 27, 485 (1978), Optics Comm. 31, 401 (1979).ADSCrossRefGoogle Scholar
  12. 12.
    R. Bonifacio, M. Gronchi and L. A. Lugiato, Phys. Rev. A18, 2266 (1978).ADSGoogle Scholar
  13. 13.
    L. Onsager, Phys. Rev. 37, 405 (1931); 38, 2265 (1931).ADSMATHCrossRefGoogle Scholar
  14. 14.
    J. L. Lebowitz and P. G. Bergman, Ann. Phys. 1, 1 (1957).ADSMATHCrossRefGoogle Scholar
  15. 15.
    W. H. Fleming, J. Diff. Equ. 5, 515 (1969).MathSciNetADSMATHCrossRefGoogle Scholar
  16. 16.
    R. Bonifacio, L. A. Lugiato and M. Gronchi, in Laser Spectroscopy IV, ed. H. Walther and K. W. Rothe, Springer (1979).Google Scholar
  17. 17.
    G. P. Agarwal and H. J. Carmichael, Phys. Rev. A19, 2074 (1979).ADSGoogle Scholar
  18. 18.
    S. S. Hassan, P. D. Drumond and D. F. Walls, Opt. Comm. 27, 480 (1978).ADSCrossRefGoogle Scholar
  19. 19.
    R. Bonifacio and L. A. Lugiato, Lett. Nuovo Cimento 21, 517 (1978).CrossRefGoogle Scholar
  20. 20.
    G. S. Agarwal, L. M. Narducci, R. Gilmore and D. Hsua Feng, Phys. Rev. A18, 620 (1978).ADSGoogle Scholar
  21. 21.
    A. Schenzle and H. Brand Phys. Rev. A20, 1628 (1979).ADSGoogle Scholar
  22. 22.
    R. Graham and A. Schenzle, Phys. Rev. A, to be published.Google Scholar
  23. 23.
    I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals Series and Products, Academic Press (1965).Google Scholar
  24. 24.
    M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover Publ., New York (1965).Google Scholar

Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • R. Graham
    • 1
  • A. Schenzle
    • 1
  1. 1.University of EssenEssenW-Germany

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