Nonlinear Behavior and Optical Bistability in Composite Media

  • David J. Bergman
  • Ohad Levy
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 101)


The nonlinear response of a composite medium to an external electric field can be greatly enhanced if the system is near a strong isolated quasistatic resonance. This situation, achievable in metal-dielectric composites, can result in bistability of the bulk effective dielectric response. Close enough to the resonance, the bistability can occur in field intensities so low that the local nonlinear behavior is weak everywhere inside the composite medium. This allows for the development of calculational methods for the nonlinear behavior based on a “zero virtual work” variational principal and a selection of trial fields of the form suggested by a corresponding linear system. In composites where the nonlinear component has a second harmonic generation capability, the enhancement can lead to induced third order nonlinearity, as well as bistability, at the fundamental frequency. The enhancement in this case can be achieved near a quasistatic resonance at either the fundamental or the harmonic frequencies.

Key words

Nonlinear Materials Optical Bistability Composites 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D. Ricard, in Nonlinear Optics: Materials and Devices, eds C. Flytzanis and J.L. Oudar, Springer-Verlag, Berlin, 1986.Google Scholar
  2. [2]
    D. Ricard, Physica A 157, 301 (1989).CrossRefGoogle Scholar
  3. [3]
    K.M. Leung, Phys. Rev. A 33, 2461 (1986).CrossRefGoogle Scholar
  4. [4]
    M. Milgrom, Astrophys. J. 302, 617 (1986).CrossRefGoogle Scholar
  5. [5]
    D.J. Bergman and D. Stroud, Solid State Physics 46, 147 (1992).CrossRefGoogle Scholar
  6. [6]
    J.W. Haus, N. Kalyaniwalla, R. Inguva, M. Bloemer and C.M. Bowden, J. Opt. Soc. Am. B6, 797 (1989).Google Scholar
  7. [7]
    J.W. Haus, N. Kalyaniwalla, R. Inguva and C.M. Bowden, J. Appl. Phys. 65, 1420 (1989).CrossRefGoogle Scholar
  8. [8]
    N. Kalyaniwalla, J.W. Haus, R. Inguva and M.H. Birnboim, Phys. Rev. A 42, 5613 (1990).CrossRefGoogle Scholar
  9. [9]
    D.J. Bergman, O. Levy and D. Stroud, Phys. Rev. B 49, 129 (1994).CrossRefGoogle Scholar
  10. [10]
    O. Levy and D.J. Bergman, Physica A 207, 157 (1994).CrossRefGoogle Scholar
  11. [11]
    R. Levy-Nathansohn and D.J. Bergman, J. Appl. Phys. 77, 4263 (1994).CrossRefGoogle Scholar
  12. [12]
    O. Levy, D.J. Bergman and D. Stroud, Phys. Rev. E 52, 3184 (1995).CrossRefGoogle Scholar
  13. [13]
    D.J. Bergman, J. Phys. C: solid state Phys. 12, 4947 (1979).CrossRefGoogle Scholar
  14. [14]
    D.J. Bergman, in Les Methodes de l’Homogénéisation: Théorie et Applications en Physique, École d’Été d’Analyse Numérique, pages 1–128, EditionEyrolles, Paris (1985).Google Scholar
  15. [15]
    F.A. Hopf, C.M. Bowden and W.H. Louisell, Phys. Rev. A 29, 2591 (1984).CrossRefGoogle Scholar
  16. [16]
    D.S. Chemla and D.A.B. Miller, Opt. Lett. 8, 522 (1986).CrossRefGoogle Scholar
  17. [17]
    S. Schmitt-Rink, D.A.B. Miller and D.S. Chemla, Phys. Rev. B 35, 8113 (1987).CrossRefGoogle Scholar
  18. [18]
    L.D. Landau, E.M. Lifshitz and L.P. Pitaevskii, Electrodynamics of Continuous Media, 2nd Edition, Pergamon Press (1984).Google Scholar
  19. [19]
    Y.R. Shen, The Principles of Nonlinear Optics, John Wiley & Sons (1984).Google Scholar
  20. [20]
    R.W. Boyd, Nonlinear Optics, Academic Press (1992).Google Scholar
  21. [21]
    D.J. Bergman, Phys. Rep. 43, 377–407 (1978). Also published in: Willis E. Lamb, a festschrift on the occasion of his 65-th birthday, eds. D. ter-Haar and M.O. Scully, pp. 377-407, North-Holland, Amsterdam (1978).MathSciNetCrossRefGoogle Scholar
  22. [22]
    P.B. Johnson and R.W. Christy, Phys. Rev. B 6, 4370 (1972).CrossRefGoogle Scholar
  23. [23]
    T.Y. Chang, Opt. Eng. 20, 220 (1981).Google Scholar
  24. [24]
    R. Landauer, in Electrical Transport and Optical Properties of Inhomogeneous Media, edited by J.C. Garland and D.B. Tanner, Aip Conference Proceedings No. 40 (1978).Google Scholar
  25. [25]
    R.K. Jain and R.C. Lind, J. Opt. Soc. Am. 73, 647 (1983).CrossRefGoogle Scholar
  26. [26]
    R. Neuendorf, M. Quinten and U. Kreibig, J. Chem. Phys. 104, 6348 (1996).CrossRefGoogle Scholar
  27. [27]
    D. Stroud and P.M. Hui, Phys. Rev. B 37, 8719 (1988).CrossRefGoogle Scholar
  28. [28]
    A. Yariv, Quantum Electronics, 3rd Edition, John Wiley & Sons (1989).Google Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • David J. Bergman
    • 1
  • Ohad Levy
    • 2
  1. 1.School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

Personalised recommendations