Localization of surface acoustic waves in a one-dimensional quasicrystal

We present and interpret experimental results on the propagation of surface acoustic waves on a quasiperiodically corrugated solid. The surface is made of a thousand grooves engraved according to a Fibonacci sequence. This type of one-dimensional system has been much studied theoretically in the literature in the context of electronic or phonon propagation. It exhibits many interesting transport features that recall some properties of strongly disordered systems related to Anderson localization. We report precise results on the reflection and transmission frequency dependence as well as on the temporal impulse response of the system. The experimental results recover nicely the features that have been predicted. In particular, this type of system has been conjectured to correspond to a critical regime of the localization transition. By comparing two systems of different lengths, we indeed observe a characteristic signature of the criticality, related to the asymptotic approximation of the quasicrystal by periodic subsystems of increasing periods. This case is intermediate between a regime of extended proper modes associated with a continuous spectrum and a regime of localized modes corresponding to a pure-point spectrum.