Propagation in one-dimensional crystals with positional and compositional disorder

Propagation in perturbed one-dimensional phononic or photonic crystals, with bothcompositional and positional disorder, is considered. The coherent potential approximationis used to obtain the band structure and the Floquet normal form of theperiodic-on-average perturbed crystal, which is modified differently with respect to thetwo kinds of disorder. For finite size crystals, the transmission amplitude is calculatedand compared to direct numerical simulations and to an estimate based on localizationlength. The transmission spectrum is found to be better described using the fullexpression of the Floquet modes of the disordered, but periodic on average, medium.