Sensitivity of layered structures in critical conditions

We conduct two-scale homogenization of multilayered structures composed of nonmagnetic isotropic materials. The resulting effective model involves a relation between the electric field and electric displacement and non intuitive transmission conditions at the interfaces with the surrounding media. In transverse electric polarization, the model reduces to a fully local model and in transverse magnetic polarization, classical non local terms appear. Comparaison with direct numerics show that the model is accurate up to the critical conditions near total reflection.