Analytical theory of light localization in one-dimensional disordered photonic crystals

Abstract

Influence of the various types of disorder on propagation of light in one-dimensional periodic structures is studied analytically using statistical approach based on a Fokker–Planck type equation. It is shown that light localization length behaves non-monotonically as a function of disorder amplitude in all the examined models except for purely geometric disorder. This feature is explained by crossover between weak disorder regime corresponding to gradual destruction of the reflecting properties of a photonic crystal and strong disorder regime, when periodic component of the refractive index can be treated as a perturbation. The region of small disorder is shown to be universal provided that a disorder parameter is properly introduced.