Finite size effect for the effective propagation in a periodic structure with disorder
Résumé
Propagation in periodic media are known to display specific properties such as forbidden bad gap for instance. When disorder is introduced in the periodic medium, these properties are modified and it is instructive to obtain the effective medium that characterize how is the medium response in average. In this work, we are interested by finite size effects and we consider the effective medium theory of a finite slab of periodic medium perturbed by weak disorder. By applying the Dyson formalism for the Green function, it is shown that the effective potential is inhomogeneous in space and depends on the size of the slab. It is an instance of the importance of size effect for finite slab concerning the averaged response or the averaged scattering. A comparison of the results obtained with this inhomogeneous effective potential and the results obtained by CPA method will be presented.
Domaines
Acoustique [physics.class-ph]
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