First-principles Fourier approach for the calculation of the effective dielectric constant of periodic composites

We present a simple first-principles Fourier approach to the calculation of the effective dielectric constant of periodic composites. The method involves the solution of the inhomogeneous Maxwell equations, in which the spatially dependent dielectric constant {ε}(r) is represented by its Fourier components and the resulting field equations are solved in the wave-vector domain. This approach avoids the matching of boundary conditions along the material interfaces inherent in the traditional boundary-value approach, thus offering generality and simplicity for handling periodic systems with arbitrary unit-cell geometries. Application of the approach is illustrated by two examples, and the results are compared with known solutions.