Self-consistent approach to electromagnetic wave propagation in composite media: Application to model granular metals

A self-consistent method is developed to treat the propagation of electromagnetic waves in composite media. The theory reduces to the effective-medium approximation in the static limit, but unlike the latter is not necessarily limited to composites in which only electron-dipole scattering contributes. The self-consistency condition on the effective complex propagation constant $k_{\mathrm{eff}}\left(\omega \right)\equiv \frac{{\left[{\epsilon }_{\mathrm{eff}}\right(\omega \left)\right]}^{\frac{1}{2}}\omega }{c}$ reduces to the requirement that ${\epsilon }_{\mathrm{eff}}$ be chosen so that the "forward-scattering amplitude" of particles embedded in this medium should vanish on the average. The approximation is applied to far-infrared absorption in a model granular metal. Absorption due to induced eddy currents, properly included in the new theory, but neglected in the existing quasistatic theories, is shown overwhelmingly to dominate the classical absorption coefficient of such composites below the insulator-metal transition even for very small particles.