Monitoring dynamic matter using the mesoscopic phase statistics of random wave fields

Abstract

In strongly scattering materials, multiple scattering tends to randomize the phase of transmitted or reflected waves and, as a result, the phase has often been overlooked. In this talk, the use of phase information to monitor the dynamics of multiply scattering media will be described and illustrated through measurements of the temporal fluctuations of ultrasonic waves transmitted through a time-varying mesoscopic sample. The probability distribution of the wrapped phase difference as a function of evolution time, as well as its variance, is measured and compared with theoretical predictions based on circular Gaussian (C1) statistics. Excellent agreement is found. A fundamental relationship between the variance in the phase of the transmitted waves and the fluctuations in the phase of individual scattering paths is predicted theoretically and verified experimentally. This relationship not only gives deeper insight into the physics of the phase of multiply scattered waves, but also provides a new way of probing the motion of the scatterers in the medium. To investigate dynamics on longer time scales, we also investigate the variance and correlations of the cumulative phase. This combination of wrapped and cumulative phase measurements allows both the short and long time dynamics to be probed with excellent sensitivity.