Bulk effective dielectric constant of a composite with a periodic microgeometry

A method is presented for calculating the bulk effective dielectric constant of a two-component composite with a periodic microstructure. The method is based on a Fourier-space representation of an integral equation for the electric potential, which is used to produce a continued-fraction expansion for the dielectric constant. The method enabled us to include a much larger number of Fourier components in the calculation—up to 2×${10}^5$ different values of reciprocal-lattice vectors—than some previously proposed Fourier methods. Consequently our method provides the possibility of performing reliable calculations of the dielectric constant of periodic composites that are neither dilute nor low contrast, and are not restricted to arrays of nonoverlapping spheres. We present results for a cubic array of nonoverlapping spheres, intended to serve as a test of quality, as well as results for a cubic array of overlapping spheres and a two-dimensional square array of prismatic inclusions for comparison with previous work.