Nondiffractive propagation in sonic crystals

Abstract

Sonic crystals are media with a periodic modulation of the acoustic parameters, such as the density and the bulk modulus. They have recently attracted a great interest, because of their potential applications in the control of sound propagation, used as reflectors, focusers, or waveguides. All these properties are related with the dispersion introduced by the crystal anisotropy. We report on the nondiffractive propagation of sound in two‐dimensional sonic crystals. It is shown that, for given frequencies and directions of incidence, a narrow sonic beam can propagate without diffractive broadening. Such nondiffractive sonic beams exist in crystals with perfect symmetry and do not require the presence of defects, differently from other waveguiding phenomena reported previously. The cancellation of diffraction has been predicted using the plane‐wave expansion method to evaluate the dispersion surfaces of the crystal and the spatial dispersion (isofrequency) curves. It occurs for frequencies and wave vectors for which dispersion curves have zero curvature, denoting a transition between focusing and defocusing regimes. By means of perturbative techniques, a simple analytical expression for the nondiffractive conditions has been obtained. The phenomenon is also demonstrated by numerical integration of the acoustic equations using FDTD techniques. [Support from Spanish MEC, Project FIS2005‐07931‐C03‐01/03, is acknowledged.]