Acoustic and electromagnetic quasimodes in dispersed random media

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Abstract
A generalized coherent-potential-approximation (GCPA) approach is developed for the identification of quasimodes in dispersed random media and the calculation of their dispersion relations. Application of this approach to colloidal suspensions of solid spheres yields the prediction of two acoustic modes in excellent agreement with the observations of a recent Brillouin-scattering experiment [J. Liu, L. Ye, D. A. Weitz, and P. Sheng, Phys. Rev. Lett. 65, 2602 (1990)]. We show that whereas the high-frequency mode is associated with the solid-sphere antiresonances, the low-frequency mode arises from the coupling of the internal resonances between neighboring spheres. Our theory yields quantitative agreement with the measured dispersion relations with no adjustable parameters, and provides a theoretical explanation for the observed frequency gaps in the excitation spectra. Application of the GCPA to the electromagnetic wave in dispersed random media is also described.