Detecting quasiperiodic structures with double diffraction

Center for Complex Systems Research, Department of Physics, University of Illinois at Urbana-Champaign Urbana, IL 61801, USA

Received: 27 May 2007
Accepted: 2 November 2007

Abstract

We study interference patterns of double-diffraction systems with quasiperiodic structures. A quasiperiodic linear array of scatterers converts single delta pulses into a sequence of quasiperiodic pulses. This pulse train is diffracted from a second set of scatterers. We find that the interference pattern after the second diffraction has a pronounced peak if both sets of scatterers have similar quasiperiodic structures. We show that this method can be used for identifying the Fibonacci chain and related quasiperiodic sequences, if the number of scatterers in the first set is at least twice as large as the number of scatterers in the second set, and if the distances among the two sets of scatterers and the detector are all large compared to the size of the sets. This method may provide a methodology for identifying the structure of quasicrystals and quasiperiodic layered materials with a large signal-to-noise ratio.