Localization of Electromagnetic Waves in 2D Random Media

  • Arkadiusz Orłowski
  • Marian Rusek
Part of the NATO ASI Series book series (NSSB, volume 358)

Abstract

Recently random dielectric structures with typical length scale matching the wavelength of electromagnetic radiation in the microwave and optical part of the spectrum have attracted much attention. Propagation of electromagnetic waves in these structures resembles the properties of electrons in disordered semiconductors. Therefore many ideas concerning transport properties of light and microwaves in such media exploit the theoretical methods and concepts of solid-state physics that were developed over many decades. One of them is the concept of electron localization in noncrystalline systems such as amorphous semiconductors or disordered insulators. As shown by Anderson1, in a sufficiently disordered infinite material an entire band of electronic states can be spatially localized. Thus for any energy from this band the stationary solution of the Schrödinger equation is localized for almost any realization of the random potential. Prior to the work due to Anderson, it was believed that electronic states in infinite media are either extended, by analogy with the Bloch picture for crystalline solids, or are trapped around isolated spatial regions such as surfaces and impurities2.

Keywords

Microwave Lution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. W. Anderson, Absence of diffusion in certain random lattices, Phys. Rev. 109, 1492 (1958).CrossRefGoogle Scholar
  2. 2.
    T. V. Ramakrishnan, Electron localization, In: Ref.[32], pp. 213-304.Google Scholar
  3. 3.
    E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Scaling theory of localization: Absence of quantum diffusion in two dimensions, Phys. Rev. Lett. 42, 673 (1979).CrossRefGoogle Scholar
  4. 4.
    B. Souillard, Waves and electrons in inhomogeneous media, In: Ref.[32], pp. 305-382.Google Scholar
  5. 5.
    M. Kaveh, What to expect from similarities between the Schrödinger and Maxwell equations, In: Ref.[9], pp. 21-34.Google Scholar
  6. 6.
    S. John, Electromagnetic absorption in a disordered medium near a photon mobility edge, Phys. Rev. Lett. 53, 2169 (1984).CrossRefGoogle Scholar
  7. 7.
    P. W. Anderson, The question of classical localization. A theory of white paint? Phil. Mag. B 52, 505 (1985).CrossRefGoogle Scholar
  8. 8.
    S. John, Strong localization of photons in certain disordered dielectric superlattices, Phys. Rev. Lett. 58, 2486 (1987).CrossRefGoogle Scholar
  9. 9.
    W. van Haeringen and D. Lenstra, editors, Analogies in Optics and Micro Electronics (Kluwer, Dordrecht, 1990).Google Scholar
  10. 10.
    C. M. Soukoulis, editor, Photonic Band Gaps and Localization, New York, 1993. NATO ASI Series, Plenum.Google Scholar
  11. 11.
    E. Akkermans, P. E. Wolf, and R. Maynard, Coherent backscattering of light by disordered media: Analysis of the peak line shape, Phys. Rev. Lett. 56, 1471 (1986).CrossRefGoogle Scholar
  12. 12.
    M. J. Stephen and G. Cwillich, Rayleigh scattering and weak localization: Effects of polarization, Phys. Rev. B 34, 7564 (1986).CrossRefGoogle Scholar
  13. 13.
    F. C. MacKintosh and S. John, Coherent backscattering of light in the presence of time-reversal-noninvariant and parity-nonconserving media, Phys. Rev. B 37, 1884 (1988).CrossRefGoogle Scholar
  14. 14.
    Y. Kuga and A. Ishimaru, Retroreflectance from a dense distribution of spherical particles, J. Opt. Soc. Am. A 1, 831 (1984).CrossRefGoogle Scholar
  15. 15.
    M. P. van Albada and E. Lagendijk, Observation of weak localization of light in a random medium, Phys. Rev. Lett. 55, 2692 (1985).CrossRefGoogle Scholar
  16. 16.
    P.-E. Wolf and G. Maret, Weak localization and coherent backscattering of photons in disordered media, Phys. Rev. Lett. 55, 2696 (1985).CrossRefGoogle Scholar
  17. 17.
    M. P. van Albada, A. Lagendijk, and M. B. van der Mark, Towards observation of Anderson localization of light, In: Ref.[9], pp. 85-103.Google Scholar
  18. 18.
    G. H. Watson Jr., P. A. Fleury, and S. L. McCall, Search for photon localization in the time domain, Phys. Rev. Lett. 58, 945 (1987).CrossRefGoogle Scholar
  19. 19.
    A. Z. Genack, Optical transmition in disordered media, Phys. Rev. Lett. 58, 2043 (1987).CrossRefGoogle Scholar
  20. 20.
    J. M. Drake and A. Z. Genack, Observation of nonclassical optical diffusion, Phys. Rev. Lett. 63, 259 (1989).CrossRefGoogle Scholar
  21. 21.
    A. Z. Genack and N. Garcia, Observation of photon localization in a three-dimensional disordered system, Phys. Rev. Lett. 66, 2064 (1991).CrossRefGoogle Scholar
  22. 22.
    R. Dalichaouch, J. P. Armstrong, S. Schultz, P. M. Platzman, and S. L. McCall, Microwave localization by two-dimensional random scattering, Nature 354, 53 (1991).CrossRefGoogle Scholar
  23. 23.
    S. John, Localization of light, Physics Today 44, 32 (May 1991).CrossRefGoogle Scholar
  24. 24.
    Barbara Goss Levi, Light travels more slowly through strongly scattering materials, Physics Today 44, 17 (June 1991).Google Scholar
  25. 25.
    J. Kroha, C. M. Sokoulis, and P. Wölfle, Localization of classical waves in a random medium: A self-consistent theory, Phys. Rev. B 47, 11093 (1993).CrossRefGoogle Scholar
  26. 26.
    B. A. van Tiggelen and E. Kogan, Analogies between light and electrons: Density of states and Friedel’s identity, Phys. Rev. A 49, 708 (1994).CrossRefGoogle Scholar
  27. 27.
    M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, Speed of propagation of classical waves in strongly scattering media, Phys. Rev. Lett. 66, 3132 (1991).CrossRefGoogle Scholar
  28. 28.
    G. D. Mahan, Many-Particle Physics (Plenum, New York, 1981).Google Scholar
  29. 29.
    M. Born and E. Wolf, Principles of Optics (Pergamon Press, Oxford-London, 1965).Google Scholar
  30. 30.
    M. Rusek, A. Orlowski, and J. Mostowski, Localization of light in three-dimensional random dielectric media, Phys. Rev. E 53, 4122 (1996).CrossRefGoogle Scholar
  31. 31.
    M. Rusek and A. Orlowski, Analytical approach to localization of electromagnetic waves in two-dimensional random media, Phys. Rev. E 51, R2763 (1995).CrossRefGoogle Scholar
  32. 32.
    J. Souletie, J. Vannimenus, and R. Stora, editors, Chance and Matter (North-Holland, Amsterdam, 1987).Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Arkadiusz Orłowski
    • 1
    • 2
  • Marian Rusek
    • 2
  1. 1.Arbeitsgruppe “Nichtklassische Strahlung” der Max-Planck-GesellschaftHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Instytut FizykiPolska Akademia NaukWarszawaPoland

Personalised recommendations