One-dimensional photonic crystal design

In this article we present a method to determine the band spectrum, band gaps, and discrete energy levels, of a one-dimensional photonic crystal with localized impurities. For one-dimensional crystals with piece wise constant refractive indices we develop an algorithm  to recover the refractive index distribution from the period map. Finally, we derive the relationship between the period map and the scattering matrix containing the information on the localized modes.