Open problems in the optics of crystals: the role of multiple scattering

The thickness b of the transition boundary layer, always present in crystals and giving still unsolved problems for the boundary conditions, is shown to be essentially determined by the multiple scattering of light, due to the inhomogeneity of any periodic structure. The parameter b depends on the orientation theta of the boundary plane with respect to the crystal lattice, and diverges for some critical orientations where strong macroscopic effects are found, which cannot be interpreted by any macroscopic model based on bulk and boundary equations. Our analysis exhaustively defines the limits of validity of macroscopic models for periodic nanoscale structures and solid crystals.