Energy-density CPA: a new e!ective medium theory for classical waves

We present the framework of an e!ective medium theory to calculate the transport properties of classical waves in disorderedmedia, Busch and Soukoulis (Phys. Rev. Lett. 75 (1995) 3442). It is based on the principle that the wave energy density should be uniform when averaged over length scales larger than the size of the basic scattering unit and can, therefore, be applied to electromagnetic, Busch and Soukoulis (Phys. Rev. B 54 (1996) 893); Kirchner et al. (Phys. Rev. B 57 (1998) 277) as well as elastic waves, Kafesaki and Economou (Europhys. Lett. 37 (1997) 7); Soukoulis et al. (Phys. Rev. Lett. 82 (1999) 2000). Within this energy-density CPA (ECPA) resonant scattering of the individual scatterer is treated exactly, and by using a coated sphere as the basic scattering unit, multiple scattering contributions are incorporated in a mean-"eld sense. In the long-wavelength limit we are able to calculate e!ective material properties exactly. Results for the mean-free path, transport velocity, and the di!usion coe$cient for "nite frequencies agree qualitatively and quantitatively with experiment for all densities of scatterers, Busch and Soukoulis (Phys. Rev. B 54 (1996) 893); Gomez et al. (Europhys. Lett. 48 (1999) 22). A study of the localization parameter kM l within this e!ective-medium approach allows to identify the optimal parameters for localization, Kirchner et al. (Phys. Rev. B 57 (1998) 277). 2001 Elsevier Science B.V. All rights reserved.