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

Ameneh Sheikhan, M. Reza Rahimi Tabar, Muhammad Sahimi
2009 Physical Review B  
Localization of electromagnetic waves in two-dimensional ͑2D͒ and three-dimensional ͑3D͒ media with random permittivities is studied by numerical simulations of the Maxwell's equations. Using the transfermatrix method, the minimum positive Lyapunov exponent ␥ m of the model is computed, the inverse of which is the localization length. Finite-size scaling analysis of ␥ m is carried out in order to check the localizationdelocalization transition in 2D and 3D. We show that in 3D disordered media ␥
more » ... m exhibits two distinct types of frequency dependence over two frequency ranges, hence indicating the existence of a localizationdelocalization transition at a critical frequency c . The critical exponent of the localization length in 3D is estimated to be, Ӎ 1.57Ϯ 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.
doi:10.1103/physrevb.80.035130 fatcat:h2wxhecdyvdbxhggy4a6fokpum