Equivalent Refractive Index of Multilayer-Type Photonic Crystals

Method of calculating the equivalent refractive index of multilayer-type photonic crystals is proposed. The equivalent index here refers to the Herpin's index which has been conventionally utilized for the design of antireflective (AR) coatings on flat multilayer filters. The index is directly connected to the Fresnel reflection coefficient between the ambient media and photonic crystals. The procedure of calculating the equivalent index of autocloning-type photonic crystals, which consists of multilayer of zigzag cross section, is described. Difference between the indices of photonic crystals and flat multilayer is also discussed.