Dynamic properties of photonic crystals and their effective refractive index

TLDR: In this paper, it was shown that although the kinematic properties of light at an interface between two media are consistent with this index definition, in some cases the dynamic properties are not.

Abstract: The reflection and refraction properties of light at an interface between two media are usually classified as kinematic and dynamic. Both are determined by the refractive indices of the media. The kinematic properties refer to the direction of light propagation, whereas the dynamic properties refer to the polarization, magnitude, and phase changes of the reflected and refracted waves. Metamaterials and photonic crystals are often assigned an effective refractive index defined by their dispersion curves. This work shows for the first time, to our knowledge, that although the kinematic properties are consistent with this index definition, in some cases the dynamic properties are not. This observation has important implications for photonic crystal understanding and design because it shows that their rich physical phenomena cannot always be simplified to a description in terms of an effective refractive index.