Breakdown of Diffusion in Dynamics of Extended Waves in Mesoscopic Media

We report the observation of nonexponential decay of pulsed microwave transmission through quasi-one-dimensional random dielectric media signaling the breakdown of the diffusion model. The decay rate of transmission falls nearly linearly in time corresponding to a nearly Gaussian distribution of the coupling strengths of quasinormal electromagnetic modes to free space at the sample surfaces. The peak and width of this distribution scale as $L^{-2.05}$ and $L^{-1.81}$, respectively.