| We have studied the effects of weak localization (WL) on the dynamics of wave propagations in mesoscopic random media both in the diffusive regime and at the Anderson localization transition. The WL effects are treated in the framework of the self-consistent theory of localization. In the diffusion regime, we have investigated the crossover of the transport behavior between two key experimental geometries: quasi-1D waveguides and slabs. In the case of quasi-1D waveguides, we found a time-dependent diffusion constant from the time-resolved transmitted intensity. In the case of slabs, the diffusion constant is almost constant. These results are in agreements with both the microwave and optical experiments, respectively. At the localization transition, we have studied the scaling behaviors of classical wave transport in disordered slabs. Our results show that the transmission coefficient scale with sample thickness as <T(L)> ∝ ln L/L2, which is different from the <T( L)> ∝ 1/L2 behavior obtained previously for electrons. The physical origin of the logarithmic factor will be discussed. Finally, we have studied the effects of WL in thin disordered slabs with internal reflections. By considering both internal reflections and WL effects in the Bethe-Salpeter equation, we are able to observe the anomalous transport behavior found in previous experiments when the scattering strength is sufficiently strong. |
