On the homogenization of thin isotropic layers

Homogenization of extremely thin dielectric or composite layers is considered. 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 makes the effective permittivity inhomogeneous, and the slab becomes effectively anisotropic. The anisotropy effect cannot he neglected for slabs whose thickness is on the order of the depth of one molecular or inclusion layer. The analysis results in approximate second-order boundary conditions, which describe the electromagnetic properties of the layer. Numerical examples show that the effect in reflection coefficient cannot be neglected if the depth of the boundary layer is a quarter of the slab thickness. Also, the magnitude of the boundary effect increases for higher slab permittivities.