Disappearance of allowed bands in light scattering from a binary photonic crystal beyond the second critical angle

We consider light scattering from a binary (two-layered) photonic crystal. When the index of refraction of the incident medium exceeds that of either layer, total internal reflection may occur, which is a type of phase transition. At band edges (similar to the case where the index of refraction of the incident medium is less than those of the layers), the two Bloch waves describing propagation become degenerate and a hybrid Floquet mode is required to understand the response. For angles of incidence exceeding the second critical angle (when total internal reflection occurs in both layers), the allowed bands disappear entirely.