Reflectionless Acoustic Waves in One-Dimensional Elastic Structure with Correlated Disorder

We study, via Dean's method and scattering transfer-matrix approach, the acoustic waves of one-dimensional structure with correlated disorder, which is realized by randomly inserting impurity segments into a pure host chain. There exist completely reflectionless acoustic modes, whose number is less than the number of atoms in a segment by 1. The frequencies of these modes are situated in the smooth parts of the phonon spectrum. We present the curves of transmission of incident waves versus frequencies, which show sharp resonant peaks at the reflectionless modes. The possible applications of this property are discussed.