Scattering matrix of the boundary of a nonlocal metamaterial providing insights into non-Maxwellian boundary conditions due to spatial dispersion

We present a simple model of the interface between a local homogeneous medium and a potentially nonlocal metamaterial/photonic crystal. This model allows us to calculate the scattering matrix elements of the interface for a plane wave of light normally incident upon the interface from either direction. The resulting scattering matrix provides insight into the non-Maxwellian boundary conditions present at the interface between a homogeneous medium and a metamaterial/photonic crystal with strong spatial dispersion. We present the model mathematically. As an example, the model is used to calculate the scattering matrix of the interface between vacuum and a simple photonic crystal. Several tests of the calculated scattering matrix elements are presented. Finally, we used the results of the scattering model to postulate possible forms for the non-Maxwellian boundary conditions.