J. Phys. I France
Volume 2, Numéro 10, October 1992
Page(s) 1861 - 1867
DOI: 10.1051/jp1:1992109
J. Phys. I France 2 (1992) 1861-1867

Can strong localization of waves be attained by internal resonances ?

Didier Sornette1, 2 and Jean-Philippe Bouchaud3

1  Laboratoire de Physique de la Matière Condensée CNRS URA 190, Université de Nice-Sophia Antipolis, Parc Valrose, 06034 Nice Cedex, France
2  X-RS, Parc-Club, 28 rue Jean Rostand, 91893 Orsay Cedex, France
3  Laboratoire de Physique Statistique, E.N.S., 24 rue Lhomond, 75231 Paris Cedex 05, France

(Received 3 April 1992, accepted in final form 21 July 1992)

An inhomogeneous medium with scatterers presenting internal resonances has been suggested to be an efficient system to localize classical waves. Within a mean-field approach describing the internal degrees of freedom of the scatterers and their strong interactions in the near field regime, we find the existence of two longitudinal modes associated with the scatterers and embedding medium degrees of freedom. Anderson localization is shown to be reached in a rather large frequency interval for the " slow " mode, above the single scatterer resonant frequency, whereas the " fast " mode is never localized. We discuss an experimental situation where the localization of the " slow " mode could be observed.

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