The spatially modulated materials, also known as sonic crystals (SC) in acoustics, are famous mostly due to their celebrated temporal dispersion properties, in particular due to the appearance of band gaps in the dispersion curves. In addition to the peculiarities of temporal dispersion, the spatially modulated materials are known also to modify the spatial dispersion, allowing to manipulate the diffraction of the waves. Many interesting effects on the beam propagation characteristics have been recently predicted, like self-collimation, super-refraction or focusing. We present a theoretical and experimental study of the propagation of sound beams in- and behind the two- and three-dimensional sonic crystals. We find that the beam profile is strongly influenced by the size (relative to the crystal period) and frequency of the radiating source. Narrow beams (those with broad spatial spectrum) are shown to propagate differently than broad beams. Novel effects as spatial filtering (the removal of selected spatial frequencies in the wave spectrum) are presented, and its application to the generation of high quality directive sources is discussed. The influence on the lens-like behavior (focusing) of the sonic crystal on an incident acoustic beam is also discussed.
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