Abstract
The propagation of classical waves in one-dimensional random media is examined in presence of short-range correlation in disorder. A classical analogous of the Kronig-Penney model is proposed by means a chain of repeated sub-systems, each of them constituted by a mass connected to a rigid foundation by a spring. The masses are related to each other by a string submitted to uniform tension. The nature of the modes is investigated by using different transfer matrix formalisms. It is shown that in presence of short-range correlation in the medium which corresponds to the RD model- the localization-delocalization transition occurs at a resonance frequency . The divergence of near is studied, and the critical exponent that characterizes the power-law behavior of near is estimated. Moreover an exact analytical study is carried out for the delocalization properties of the waves in the RD media. In particular, we predict the resonance frequency at which the waves can propagate in the entire chain. The transmission properties of the system are numerically studied using a statistical procedure yielding various physical magnitudes such the transmission coefficient, the localization length and critical exponents. In particular, it is shown that the presence of correlation in disorder restores a large number of extended Bloch-like modes in contradiction with the general conclusion of the localization phenomenon in one-dimensional systems with correlated disorder.
Highlights
More than a half century ago, Anderson [1] introduced the concept of localization induced by disorder
The purpose of the present paper is to examine the interplay between the effects of topological disorder and short range order on the propagation of classical waves by means of an analytical model for the case of a quasi-one-dimensional string loaded by N massspring systems has introduced by Richoux et al [20]
We have to notice that the existence of the set of extended modes in a mini band around the resonance frequency c provides from the smooth transition since the recursive matrix elements are very close together, in other words aA c aB c. This typical feature is completely preserved in the corresponding uncorrelated disorder since there is no difference between the host and impurity unit cells as originally reported by Ishii [31] for the random KP model
Summary
More than a half century ago, Anderson [1] introduced the concept of localization induced by disorder. The main idea is the presence of the RDM within a short length correlation restores the tunnel effect which competes with disorder and is strong enough to create the condition of delocalization These conclusions hold only for the quantum case since the competition between destructive interference and tunnel effect is the major cause leading to the localization or delocalization of the electronic states. The opportunity to control this feature opens new and relevant perspectives for technological purposes In this context, the purpose of the present paper is to examine the interplay between the effects of topological disorder and short range order on the propagation of classical waves by means of an analytical model for the case of a quasi-one-dimensional string loaded by N massspring systems has introduced by Richoux et al [20]. The conditions to breakdown the localization phenomenon and to restore the propagations of wave are suggested
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