Eur. Phys. J. B (2013) 86: 486
https://doi.org/10.1140/epjb/e2013-40893-4

Regular Article

Propagation in one-dimensional crystals with positional and compositional disorder

¹ Institut Langevin, 1 rue Jussieu, 75005 Paris, France
² Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO 80401, USA

^a e-mail: agnes.maurel@espci.fr

Received: 29 July 2013
Received in final form: 5 October 2013
Published online: 28 November 2013

Abstract

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.