Analysis of the reflection properties of sonic crystal devices.

The phenomenon of band-gaps typical of wave propagation in periodic materials has been a subject of extensive investigations. In acoustics, the interest is mainly related with the ability of such structures, the so-called sonic crystals, of blocking the propagation of sound at certain frequencies, acting as filters. Recently, there is an increasing interest in the use of sonic crystals to control the beam propagation, and a number of interesting features as focusing and collimation have been predicted and observed. At the root of these phenomena is the angle-dependent dispersion introduced by the crystal. In propagating regimes, for frequencies outside the gap, the particular form of the dispersion relations in the wavenumber (reciprocal) space allows us to determine the spatial characteristics of the transmitted field. In this work, we merge the two ideas above, and investigate the spatial characteristics of the reflected acoustic field when its frequency belongs to a band-gap. In a band-gap, the propagating modes are substituted by evanescent ones, defined by complex wavenumbers. We evaluate the complex dispersion relation, and relate the particular form of the isofrequency contours in k-space with the numerically evaluated spatial distribution of the reflected field. Different reflection regimes are presented and discussed.