Journal of Experimental and Theoretical Physics

, Volume 93, Issue 5, pp 1004–1016 | Cite as

Optical bistability

  • Yu. N. Ovchinnikov
  • I. M. Sigal
Atoms, Spectra, Radiation


We consider the problem of the wave propagation through a nonlinear medium. We derive a dynamic system that governs the behavior of standing (or solitary) waves. The form of this system alone suffices to understand the qualitative dependence of solutions of the original equation on the intensity of the incident wave. We solve this dynamical system in the leading order in the nonlinearity strength. We find multiple solutions of the original problem for a given incoming wave and turning points of these solutions as a function of the wave intensity. We briefly investigate stability of different branches. Our results yield an analytic description of the optical bistability phenomenon.


Spectroscopy Dynamic System State Physics Field Theory Elementary Particle 
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.
    H. G. Winful, J. H. Marburger, and E. Germire, Appl. Phys. Lett. 35, 379 (1979).CrossRefADSGoogle Scholar
  2. 2.
    Wei Chen and D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).ADSGoogle Scholar
  3. 3.
    Wei Chen and D. L. Mills, Phys. Rev. B 36, 6269 (1987).ADSGoogle Scholar
  4. 4.
    Wei Chen and D. L. Mills, Phys. Rev. B 35, 524 (1987).ADSGoogle Scholar
  5. 5.
    D. L. Mills and S. E. Trullinger, Phys. Rev. B 36, 947 (1987).ADSGoogle Scholar
  6. 6.
    J. E. Sipe and H. G. Winful, Opt. Lett. 13, 132 (1988).ADSGoogle Scholar
  7. 7.
    C. M. de Sterke and J. E. Sipe, Phys. Rev. A 38, 5149 (1988).ADSGoogle Scholar
  8. 8.
    D. N. Christodoulides and R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).CrossRefADSGoogle Scholar
  9. 9.
    A. B. Aceves and S. Wabmitz, Phys. Lett. A 141, 37 (1989).CrossRefADSGoogle Scholar
  10. 10.
    N. O. Sankey, D. F. Prelewitz, and T. G. Brown, Appl. Phys. Lett. 60, 1427 (1992).CrossRefADSGoogle Scholar
  11. 11.
    C. M. de Sterke and J. E. Sipe, in Progress in Optics XXXIII, Ed. by E. Wolf (North-Holland, Amsterdam, 1994), p. 203.Google Scholar
  12. 12.
    S. Dutta Gupta, in Progress in Optics XXXIII, Ed. by E. Wolf (North-Holland, Amsterdam, 1998).Google Scholar
  13. 13.
    D. Henning and G. P. Tsironis, Phys. Rep. 307, 333 (1999).ADSMathSciNetGoogle Scholar
  14. 14.
    G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, 1989; Mir, Moscow, 1996).Google Scholar
  15. 15.
    N. Bloembergen, Nonlinear Optics: a Lecture Note and Reprint Volum (W. A. Benjamin, New York, 1965; Mir, Moscow, 1966).Google Scholar
  16. 16.
    H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, New York, 1985; Mir, Moscow, 1988).Google Scholar
  17. 17.
    D. L. Mills, Nonlinear Optics: Basic Concepts (Springer-Verlag, New York, 1991).Google Scholar
  18. 18.
    Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984; Nauka, Moscow, 1989).Google Scholar
  19. 19.
    W. A. Strauss, Nonlinear Wave Equations (American Mathematical Society, Providence, 1989), CBMS Regional Conference Series in Mathematics, No. 73, 1987.Google Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 2001

Authors and Affiliations

  • Yu. N. Ovchinnikov
    • 1
  • I. M. Sigal
    • 2
  1. 1.Laudau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow oblastRussia
  2. 2.Department of MathematicsUniversity of TorontoCanada

Personalised recommendations