On the homogenization of thin isotropic layers

Homogenization of extremely thin dielectric or composite layers is consider ed. Special attention is focused on the fact that the permittivity near the surface of the slab is affected by the presence of the boundary. This make s the effective permittivity inhomogeneous, and the slab becomes effectivel y anisotropic. The anisotropy effect cannot be neglected for slabs whose th ickness is on the order of the depth of one molecular or inclusion layer. T he analysis results in approximate second-order boundary conditions, which describe electromagnetic properties of the layer, Numerical examples show t hat the effect in reflection coefficient cannot be neglected if the depth o f the boundary layer is a quarter of the slab thickness. Also, the magnitud e of the boundary effect increases for higher slab permittivities.