Wave transport in random media: The ballistic to diffusive transition

The character of wave transport through a strongly scattering medium, excit ed by a pulsed plane-wave source, is investigated as a function of sample t hickness over the range from about one to 13 mean free paths. To examine th e behavior theoretically, we perform a first-principles calculation of both the frequency correlation function of the transmitted field and the time-d omain profile of the transmitted intensity. These quantities are investigat ed experimentally using an ultrasonic technique, which allows us to separat e the ballistic and scattered components of the total transmitted field, an d hence to measure the scattered component unambiguously in thin samples. F or sample thicknesses greater than about four mean free paths, we find good agreement between our theory, the diffusion approximation, and our experim ental: data for both the frequency correlation function and the intensity t ime profile. In thinner samples, there are systematic differences between t heory and experiment. To characterize the transition from ballistic to diff usive behavior in thin samples, we focus on the arrival time of the peak in the scattered component of the transmitted intensity; unexpectedly we find that the scattered peak arrival time exhibits an abrupt crossover between ballistic and diffusive behavior when the ratio of sample thickness to mean free path, L/l, is approximately equal to 3. Excellent agreement is obtain ed between our theory and experiment for this crossover behavior over the e ntire range of sample thicknesses investigated. [S1063-651X(99)12009-9].