Statistical properties of waves transmitted [1] and reflected [2] from random media are discussed in terms of Random Matrix Theory (RMT). Exact numerical calculations in surface randomly corrugated waveguides are presented. By increasing the length of the disordered region, we are able to analyze the transition from ballistic to diffusive regimes as well as from diffusion to localization in detail. Although the transport in these systems is strongly nonisotropic, the analysis of the probability distributions of both the transport coefficients and the spatial intensity [3] remarkably agrees with the analytical predictions of RMT. Our results predict unexpected strong finite size effects when the number of propagating channels is small [3].
[1] A. Garcia-Martin, J.A. Torres, J.J. Saenz and M. Nieto-Vesperinas, Phys. Rev. Lett. 80, 4165 (1998).
[2] A. Garcia-Martin, T. Lopez-Ciudad, J.J. Saenz and M. Nieto-Vesperinas, Phys. Rev. Lett. 81, 329 (1998)
[3] A. Garcia-Martin, R. Gomez-Medina, J.J. Saenz and M. Nieto-Vesperinas, submitted to Phys. Rev. Lett. (2000)