Second Order Homogenization of Subwavelength Stratified Media Including Finite Size Effect

We present a homogenization method to find the effective behavior of a periodically stratified slab which accounts for the finite size of the slab. The effective behavior is that of a homogeneous anisotropic slab associated with discontinuity conditions, or jump conditions, for the displacement and for the normal stress at the boundaries of the slab. The coefficients entering in the effective homogenized wave equation are related to the geometry and to the composition of the layers only, as in the classical homogenization. Those entering in the jump conditions are related to boundary layer effects, and thus they depend also on the properties of the media surrounding the slab. The validity of our homogenization method is inspected in the case of layers associated with Neumann boundary conditions.