On Electrodynamics of One-Dimensional Heterogeneous System Beyond Homogenization Approximation

  • A. P. Vinogradov
  • A. M. Merzlikin
Part of the NATO Science Series book series (NAII, volume 89)


This chapter discusses electromagnetic modelling of one-dimensionally inhomogeneous materials. Different spatial scales are taken into account and the analysis is extended beyond the basic homogenization approximation. The wave localization is related to the total increase of band gaps with the infinite growth of the size and structural complexity of the cell.


Optical Path Triple System Bragg Reflection Constitutive Parameter Localization Length 
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.
    Born M. and Huang Kun (1954), Dynamical theory of crystal lattices, The Clarendon Press, OxfordGoogle Scholar
  2. 2.
    Brekhovskikh V.L.. (1985) The effective permittivity of a random medium by accounting the second moments of fields, JEW, 89, 2013–2020. (in Russian)Google Scholar
  3. 3.
    Sobel’man I.I. (2002) On the theory of light scattering in gases, Physics Uspekhi 245, 75–80Google Scholar
  4. 4.
    Sheng P. (1995) Introduction to wave scattering, localization, and mesoscopic phenomena, Academic Press, London.Google Scholar
  5. 5.
    Sanchez-Palensia E. (1980) Non-homogeneous media and vibration theory, Springer-Verlag, New York.Google Scholar
  6. 6.
    Rytov S. M., (1956) Acoustic properties of a finely layered medium, Akust. Zh. 11, 71–83Google Scholar
  7. 7.
    Brekhovskikh L. M. (1960) Waves in Layered Media, Academic, New YorkGoogle Scholar
  8. 8.
    Djafari Rouhani B. and Sapriel J. (1986) Effective dielectric and photoelastic tensors of superlattices in the long wave regime, Phys. Rev. B 34, 7114–7117.CrossRefGoogle Scholar
  9. 9.
    Akcakaya E. and Farnell G. W. (1988) Effective elastic and piezoelectric constant of superlattices, J. Appl. Phys. 64, 4469–4473.CrossRefGoogle Scholar
  10. 10.
    Slepyan G. Ya., Gurevich A. V., and Maximenko S. A. (1995) Floquet-Bloch waves in periodic chiral media, Phys. Rev. E, 51, 2543–2549.CrossRefGoogle Scholar
  11. 11.
    Semchenko I. V. (1990) Gyrotropic properties of superlattices in the long wavelength approximation, Kristallografiya, 35, 1047–1050 (in Russian).Google Scholar
  12. 12.
    Francsechetti G. (1967) A complete analysis of the reflection and transmission methods for measuring the complex permeability and permittivity of materials at microwaves, Acta frequenza, 36, 757–764.Google Scholar
  13. 13.
    Born M. and Wolf E. (1980) Principles of optics, sixth ed. Pergamon Press, OxfordGoogle Scholar
  14. 14.
    Thouless D. J. (1972) A relation between the density of state and range of localization for one dimensional random systems, J. Phys. C., 5, 77–81CrossRefGoogle Scholar
  15. 15.
    Herbert D. C, Jones R. (1971) Localized states in disordered systems, J. Phys. C, 4, 1145–1161CrossRefGoogle Scholar
  16. 16.
    Pi-Gang Luan and Zhen Ye (2001) Acoustic wave propagation in a one-dimensional layered system, Phys Rev E, 63, 066611-1-066611-8Google Scholar
  17. 17.
    Klyatskin V. and Saichev A. (1992) Static and dynamic localization of plane waves in disordered laminar media, UspehkiFiz. Nauk, 162, 16–193 (in Russian)Google Scholar
  18. 18.
    Freilikher V., Pustilnik M. and Yurkevich I. (1994) Wave transmission through lossy media in the strong-localization regime, Phys. Rev. B, 50, 6017–6022CrossRefGoogle Scholar
  19. 19.
    Kim K. (1998) Reflection coefficient and localization length of waves in one-dimensional random media, Phys. Rev. B, 58, 6153–6160CrossRefGoogle Scholar
  20. 20.
    Vinogradov A. and Merzlikin A. (2002) On the problem of homogenization of one-dimensional systems, JETP 121, 1–8 (in Russian)Google Scholar
  21. 21.
    McGurn A. R., Maradudin A. A. (1993) Anderson localization in one-dimensional randomly disordered optical systems that are periodic on average, Phys. Rev. B, 47, 13120–13125CrossRefGoogle Scholar
  22. 22.
    Bulgakov S. A., Nieto-Vasperinas M. (1997) Frequency properties of random photonic lattices, Waves in Random Media, 7, 183–192CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • A. P. Vinogradov
    • 1
  • A. M. Merzlikin
    • 1
  1. 1.Institute of Theoretical and Applied Electromagnetism (ITAE)JIHT Russian Academy of SciencesMoscowRussia

Personalised recommendations