Statistics of the cumulative phase of microwave radiation in random media

We determine the cumulative phase of microwave radiation transmitted through a sample of randomly positioned polystyrene spheres in measurements of the field versus frequency and investigate its statistics. Its probability distribution is Gaussian at all frequencies with a variance which is nearly equal to the ensemble average of the phase. These results are consistent with our observation that the correlation function of the phase derivative with the ensemble average value of the phase is nearly the same exponential function for diffusing waves over a wide frequency range. Finally, we indicate ways in which the study of the cumulative phase can elucidate wave transport in random systems.