Phononic Quasicrystals
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Phononic Quasicrystals Daniel Sutter, Günter Krauss, Walter Steurer Laboratory of Crystallography, Swiss Federal Institute of Technology, 8092-Zürich, Switzerland ABSTRACT Phononic crystals are to sound what photonic crystals are to light and crystals are to electrons. If the wavelength is of the same order of magnitude as the typical distances between the objects in their ordered arrangement, then the interaction is dominated by diffraction besides refraction. Depending on the spectral properties of the material, band gaps appear for certain frequencies. In special cases, these gaps are omni-directional. A huge amount of applicationdriven research has been performed on photonic crystals, much less on phononic crystals, and almost nothing on phononic quasicrystals. We present here the first experimental studies on twodimensional, quasiperiodic, phononic crystals. Our experiments have been performed with ultrasound on phononic crystals and quasicrystals consisting of steel cylinders in water. The pros and cons of phononic quasicrystals are discussed. INTRODUCTION Phononic crystals are composites of at least two materials with different mechanical properties (elastic constants and density). The spatial arrangement of the two materials is either periodic or quasiperiodic. Sonic waves with wavelengths of the order of the period of the arrangements are diffracted within such structures. This causes their dispersion curves to split into bands, in analogy to gap formation in dispersion curves of electrons in crystals or photons in photonic crystals. Phononic crystals with simple structures have been studied intensively in the last ten years. Various periodic structures have been analyzed for several combinations of constituent materials (solid, liquid and gaseous). The means for making theoretical predictions of their bandstructures have become feasible and provide data of satisfactory reliability. Some of the parameters, which can be exploited to tailor these properties, have been identified and reviewed (e.g. [1]). Two of them are particularly potent. Given the geometrical structure of a phononic crystal, its bandstructure can be modified by changing the volume fraction of the two materials or by coating the scatterers with a third material. Changing the volume fractions alters the width of gaps while their positions are retained. Coating of the scattering objects with a soft material (e.g. rubber) allows the spectral properties on the relative frequency scale to be shifted [2]. Much less is known about phononic quasicrystals. Mostly one-dimensional quasiperiodic systems have been investigated. Bandstructures for layered composites following the Fibonacci, the Thue-Morse or the Rudin-Shapiro sequences, for instance, have been analyzed by Velasco et al. [3]. The bandstructures found for these systems are quite similar to those of periodic sequences and the transition from one to the other has been studied. Two-dimensional quasiperiodic phononic crystals have hardly been treated at all. It was only last year that
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