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

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 gamma(m) of the model is computed, the inverse of which is the localization length. Finite-size scaling analysis of gamma(m) is carried out in order to check the localization-delocalization transition in 2D and 3D. We show that in 3D disordered media gamma(m) exhibits two distinct types of frequency dependence over two frequency ranges, hence indicating the existence of a localization-delocalization transition at a critical frequency omega(c). The critical exponent nu of the localization length in 3D is estimated to be, nu similar or equal to 1.57 +/- 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.