The propagation of acoustic waves in a phononic crystal slab consisting of piezoelectric inclusions placed periodically in an isotropic host material is analyzed. Numerical examples are obtained for a square lattice of quartz cylinders embedded in an epoxy matrix. It is found that several complete band gaps with a variable bandwidth exist for elastic waves of any polarization and incidence. In addition to the filling fraction, it is found that a key parameter for the existence and the width of these complete band gaps is the ratio of the slab thickness, d, to the lattice period, a. Especially, we have explored how these absolute band gaps close up as the parameter d/a increases. Significantly, it is observed that the band gaps of a phononic crystal slab are distinct from those of bulk acoustic waves propagating in the plane of an infinite two-dimensional phononic crystal with the same composition. The band gaps of the slab are strongly affected by the presence of cutoff frequency modes that cannot be excited in infinite media.

We demonstrate experimentally the guiding and the bending of acoustic waves in highly confined waveguides formed by removing rods from a periodic two-dimensional lattice of steel cylinders immersed in water. Full transmission is observed for a one-period-wide straight waveguide within the full band gap of the perfect phononic crystal. However, when the waveguide width is doubled, destructive interference causes the transmission to vanish in the center of the passband. Waveguiding over a wide frequency range is obtained for a one-period-wide waveguide with two sharp 90° bends. Finite-difference time-domain computations are found to be in good agreement with the measurements

Wavelength-scale periodic microstructuring dramatically alters the optical properties of materials. An example is glass photonic crystal fibre(1) ( PCF), which guides light by means of a lattice of hollow micro/nanochannels running axially along its length. In this letter, we explore stimulated Brillouin scattering in PCFs with subwavelength-scale solid silica glass cores. The large refractive-index difference between air and glass allows much tighter confinement of light than is possible in all-solid single-mode glass optical fibres made using conventional techniques. When the silica-air PCF has a core diameter of around 70% of the vacuum wavelength of the launched laser light, we find that the spontaneous Brillouin signal develops a highly unusual multi-peaked spectrum with Stokes frequency shifts in the 10-GHz range. We attribute these peaks to several families of guided acoustic modes each with different proportions of longitudinal and shear strain, strongly localized to the core(2,3). At the same time, the threshold power for stimulated Brillouin scattering(4) increases fivefold. The results show that Brillouin scattering is strongly affected by nanoscale microstructuring, opening new opportunities for controlling light-sound interactions in optical fibres