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Propagation of light in discrete media

Abstract

Anderson localization of electromagnetic waves in three-dimensional disordered dielectric structures is studied using a simple yet realistic theoretical model. An effective approach based on analysis of probability distributions, not averages, is developed. The disordered dielectric medium is modeled by a system of randomly distributed coupled electric dipoles. Properties of the spectra of random matrices describing multiple elastic scattering in such a medium are investigated. A sound physical interpretation of obtained results is proposed and consequences for Anderson localization of electromagnetic waves in 3D disordered dielectric media are discussed. Appearance of localized electromagnetic waves, emerging in the limit of infinite system, is numerically observed. Applicability of the heuristic Ioffe-Regel criterion to localization of electromagnetic waves in 3D random dielectric media is studied. It is suggested that localization could be achieved without tuning the frequency of monochromatic electromagnetic waves to match the internal (Mie-type) resonances of individual scatterers. A possible explanation for the lack of experimental evidence for strong localization in 3D as well as suggestions how to make localization experimentally feasible are also given. Rather peculiar requirements for setting in localization in 3D as compared to 2D are indicated.

Contents

  1. Introduction
    • Anderson localization
    • Weak localization
    • Partial analogy
    • Resonances and localization
  2. General considerations
    • Non-radiating antennas
    • Elastic scattering
  3. Discrete medium
    • Localized states
    • Resonances
    • Model of a dielectric medium
  4. Localization of light
    • Probability distributions
    • Long-wavelength limit
  5. Summary
  6. Appendix
    • Localization in vacuum

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A PDF file containing the thesis (in Polish!):

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