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 that signals the breakdown of the diffusion model of transport for temporally coherent extended waves. The decay rate of transmission falls nearly linearly in time due to a nearly gaussian distribution of the coupling strengths of quasi-normal 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.