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Abstract: We derive exact strong-contrast expansions for the effective dielectrictensor $\epeff$ of electromagnetic waves propagating in a two-phase compositerandom medium with isotropic components explicitly in terms of certainintegrals over the $n$-point correlation functions of the medium. Our focus isthe long-wavelength regime, i.e., when the wavelength is much larger than thescale of inhomogeneities in the medium. Lower-order truncations of theseexpansions lead to approximations for the effective dielectric constant thatdepend upon whether the medium is below or above the percolation threshold. Inparticular, we apply two- and three-point approximations for $\epeff$ to avariety of different three-dimensional model microstructures, includingdispersions of hard spheres, hard oriented spheroids and fully penetrablespheres as well as Debye random media, the random checkerboard, andpower-law-correlated materials. We demonstrate the importance of employing$n$-point correlation functions of order higher than two for highdielectric-phase-contrast ratio. We show that disorder in the microstructureresults in an imaginary component of the effective dielectric tensor that isdirectly related to the {\it coarseness} of the composite, i.e., localvolume-fraction fluctuations for infinitely large windows. The source of thisimaginary component is the attenuation of the coherent homogenized wave due toscattering. We also remark on whether there is such attenuation in the case ofa two-phase medium with a quasiperiodic structure.



Author: Mikael C. Rechtsman, Salvatore Torquato

Source: https://arxiv.org/







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