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Numerical simulations of localization of electromagnetic waves in two- and three-dimensional disordered media

Sheikhan, A ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1103/PhysRevB.80.035130
  3. Publisher: 2009
  4. Abstract:
  5. Localization of electromagnetic waves in two-dimensional (2D) and three-dimensional (3D) media with random permittivities is studied by numerical simulations of the Maxwell's equations. Using the transfer-matrix method, the minimum positive Lyapunov exponent γm of the model is computed, the inverse of which is the localization length. Finite-size scaling analysis of γm is carried out in order to check the localization-delocalization transition in 2D and 3D. We show that in 3D disordered media γm exhibits two distinct types of frequency dependence over two frequency ranges, hence indicating the existence of a localization-delocalization transition at a critical frequency ωc. The critical exponent ν of the localization length in 3D is estimated to be, ν1.57±0.07. At the transition point in the 3D media, the distribution function of the level spacings is independent of the system size, and is represented well by the semi-Poisson distribution. The 2D model can be mapped onto the 2D Anderson model and, hence, there is no localization-delocalization transition. © 2009 The American Physical Society
  6. Keywords:
  7. Theories and models ; Localized states ; Disordered structures ; Amorphous and glassy solids ; Localized modes
  8. Source: Physical Review B - Condensed Matter and Materials Physics ; Volume 80, Issue 3 , 2009 ; 10980121 (ISSN)
  9. URL: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.035130