Propagation in one-dimensional crystals with positional and compositional disorder

Propagation in perturbed one-dimensional phononic or photonic crystals, with both compositional and positional disorder, is considered. The coherent potential approximation is used to obtain the band structure and the Floquet normal form of the periodic-on-average perturbed crystal, which is modified differently with respect to the two kinds of disorder. For finite size crystals, the transmission amplitude is calculated and compared to direct numerical simulations and to an estimate based on localization length. The transmission spectrum is found to be better described using the full expression of the Floquet modes of the disordered, but periodic on average, medium.