Phase statistics of multiply scattered ultrasonic waves in dynamic mesoscopic systems

Abstract

In weakly scattering materials, detecting motion by measuring the change in phase of reflected ultrasonic waves forms the basis of the well-known technique of Doppler ultrasound. In strongly scattering media, these methods break down and the technique of diffusing acoustic wave spectroscopy (DAWS) was developed [Cowan et al., Phys. Rev. Lett. 85, 453 (2000)]. To explore the use of phase information to investigate the dynamics of multiply scattering media, the temporal fluctuations in the phase of ultrasonic waves transmitted through a time-varying mesoscopic sample have been measured. We have compared phase statistics and correlations to detailed theoretical predictions based on circular Gaussian (C1) statistics [Genack et al., Phys. Rev. Lett. 82, 412 (1999)]. So far, excellent agreement is found. The cumulative phase is found to undergo a Brownian type process, described by a phase diffusion coefficient. 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, mesoscopic way of probing the motion of the scatterers in the sample. a)Currently at Department of Physics, University of Toronto, Toronto, ON, Canada M5S 3E3