Interferometric method of determining the refraction index of two-dimensional sonic crystals

Abstract

Sonic crystals are defined as materials consisting of periodic distributions of acoustic scatterers in another medium with different elastic properties. These materials present two main acoustical features: they present ranges of frequencies where the acoustic wave propagation is forbidden and, moreover, they can be used to construct acoustical refractive devices. We present here an interferometric method of characterizing directly the refraction index of these materials. We focused our research on sonic crystals constructed with a periodic distribution of rigid cylinders in air. The interferometric method used is based on the acoustical analog of an optical device called Fresnel's biprism. Our numerical predictions are in good agreement with the experimental results obtained and allow us to estimate the refraction index for very low frequencies. Moreover, in this range we show the nonlinear behavior in the dispersion relation refraction index versus frequency. Finally, we analyze the relationship between the refraction index and some typical sonic crystal parameters. In view of the results we can conclude that this method offers certain advantages with respect to the classical method used to obtain the refraction index in sonic crystals with airborne propagation: the phase delay method.