Disordered photonic crystals: a cluster coherent potential approach using photonic Wannier functions

Abstract

We present a cluster coherent potential approach for disordered photonic crystals (PhCs) that is based on maximally localized Wannier functions. In particular, the Wannier basis facilitates an efficient representation of the photonic band structure of a defect-free PhC and the Green’s function thereof, which we discuss first. Moreover, the Wannier basis allows for adapting elaborate approaches developed for the analysis of disorder in electronic and phononic systems to PhCs. Our detailed studies reveal that neither the virtual crystal approximation nor the single-site coherent potential approximation (CPA) provides a reliable description of the effects of disorder in PhCs. Rather, we demonstrate that a cluster based CPA yields qualitatively and quantitatively useful results even for strong disorder. In all these approaches, we include multiple bands, enforce the proper translational properties of the effective medium, and incorporate interaction beyond nearest neighbor coupling. We also discuss the efficient evaluation of the corresponding system of equations. Our results establish a firm basis for various extensions, such as to the theory of Anderson localization or random lasing in disordered PhCs.